THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING A COMPREHENSIVE CYCLE ANALYSIS AND DIGITAL COMPUTER SIMULATION FOR SPARK-IGNITED ENGINES Donald J. Patterson A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the University of Michigan Department of Mechanical Engineering 1962 June, 1962 IP-567

ACKNOWLEDGMENTS The author wishes to express his thanks to all those who helped in the development and execution of this study. In particular he wishes to thank Professor Gordon J. Van Wylen, Chairman of the Doctoral Committee, for his constant encouragement and counsel. He also wishes to thank Professor's Jay Bolt, William Mirsky, Herman Merte, Bernard Galler, and Dr. Craig Marks for their many valuable suggestions. The assistance of the computing Center Staff of the University of Michigan who generously made available their facilities and who provided many helpful suggestions for the programming involved in the thesis is gratefully acknowledged. ii

TABLE OF CONTENTS Page ACKNOWLEDGMENTS.................................*..... * i LIST OF TABLES.................................................. v LIST OF FIGURES................................................9 vi LIST OF APPENDICES............................................... viii NOMENCLATURE.................................................. x I INTRODUCTION............................................ 1 A. Purpose...........****....******* B. Previous Work....................... C. Scope of This Paper......... 10 II THE THERMODYNAMIC PROPERTIES AND COMPOSITION OF THE 11 WORKING FLUID IN A SPARK-IGNITED ENGINE................. e A. General.................. B, Calculation of Ideal Gas Thermodynamic Properties..... 13 1. Empirical Heat Capacity Equations............. 1.... 2. Computation of Thermodynamic Functions and Equilibrium Constants from Empirical Heat Capacity Equations.................................... 15 C. The Composition of the Products of Combustion...... 24 1. Assumption of Chemical Equilibirum............... 24 2. The Chemical Composition at Equilibrium........ 3.1 a. General....................................... 31 b. Computation of Homogeneous Gas Equilibrium.... 33 c. Computation of Frozen Equilibrium 43 3. Computer Solution of the Equations of Chemical Equilibrium........................................ 46 III SIMULATION OF THE FUEL-AIR ENGINE CYCLE ON A DIGITAL COMPUTER.................................................. 47 A. General........................................... * 47 B. Results and Discussion................................ 50 IV COMBUSTION IN A SPARK-IGNITED ENGINE...................... 55 A. General............................................. 55 B. Flame Propagation.................. 54 C. Thermal Theory of Flame Propagation for A Bimolecular Second-Order Reaction...e...........** —..***.*e... 59 iii

TABLE OF CONTENTS (CONT'D) Page Do Use of the Thermal Theory Equations to Predict Turbulent Flame Propagation Velocity................. 66 V HEAT TRANSFER IN A SPARK-IGNITED ENGINE................o 69 A o General oo.oooooooooo................................... o o o o o o o o o o o 69 Bo Convective Heat Transfer o................oooooooo4ooo 72 1< Temperature Distribution and Heat Flow in a Finite Plate in Contact with a Uniform Medium whose Temperature Varies Periodically............ 72 2. The Convective Heat Transfer Coefficiento........ 80 Co Radiant Heat Transfer 0,0........,000.0.00,000000000 82 VI THE ANALYTICAL MODEL FOR SPARK-IGNITED ENGINE CYCLE CALCULATIONSo............................................ 85 Ao General.o.ooo.ooo.ooooooooooooooooooooooooooooooooo 85 B. The Cycle Processes.................... 86 Co The Cycle Characteristics o o............o.... oo...., 102 Do Computational Method.....000000,00.0 00.000 0000000.000 103 VII CALCULATED RESULTS FROM THE ANALYTICAL MODEL...........o 104 Ao General o..........000.................................... 104 B, The "Normal Cycle"oooo0oo0,oooooo0ooooooooo oo 105 Co Comparison of the Analytical and Experimental "Normal Cycles" o 106 "Normal Cycles.o o o 4 o o o o Co o o o o o o o o 0o o o o o o o o o o 0 o o o o o oo 106 Do Effect of Exhaust Temperature........................ 111 Eo Influence of Heat Transfer and Flame Propagation Rates 0. 0,.0 0 0 0 0 0 0 0 0 0 0 0 0 0 112 Fo Availability and Irreversibilityo......,,,,,,,,,,,,.. 115 Go The Analytical Model and the Fuel-Air Cycleo.0,,,,00, 117 H. Concluding Remarks 0.....,0000000.*00000000.00000000 0 118 APPENDI CESORP.......0000......... a..............000.0.000 0,00,00 156 BIBLIOGRAPHYo..00000..0000.000,.00000,00000.000000000 00000, 0000 283 iv

LIST OF TABLES Table Page I Ideal Gas Empirical Heat Capacity Equations........... 16 II Fundamental Thermodynamic Properties.................. 17 III Calculated and Tabular Values of Ideal Gas Heat Capacity, C~.................... 18 p IV Calculated and Tabular Values of Ideal Gas Enthalpy, H~ - H............................. 20 V Calculated and Tabular Values of Ideal Gas Entropy, S~ 21 VI Calculated Values of Log1o of the Equilibrium Constant, VII Pertinent Dimensions for Engine of Figure 11.......... 121 VIII Volume-Area-Length Relationships for the Combustion Chamber of Figure 11........................... o.122 IX Normal Engine Cycle Operating Conditions............... 123 X Amount of Heat Transferred.................... 124 XI Digit Changed in the Partial Pressure of Each Constituent for Selected Values of Relative Error..... 158 v

LIST OF FIGURES Figure Page 1 The Otto Cycle....................................... 5 2a Mole Fraction Vs Temperature, 02................... 38 2b Mole Fraction Vs Temperature, N2..................... 38 2c Mole Fraction Vs Temperature, CO2.........,..... 39 2d Mole Fraction Vs Temperature, H20............... 39 2e Mole Fraction Vs Temperature, CO.................... 40 2f Mole Fraction Vs Temperature, H..................... 40 2g Mole Fraction Vs Temperature, OH..................... 41 2h Mole Fraction Vs Temperature, NO..................... 41 2i Mole Fraction Vs Temperature, 0................e.Xe 42 2j Mole Fraction Vs Temperature, H..................... 42 5 Indicator Diagram for the Fuel-Air Cycle Engine at Part Throttle................ 48 4 Efficiency and Mean Effective Pressure Vs Compression Ratio for Lean Mixtures............................... 51 5 Efficiency and Mean Effective Pressure Vs Compression for a Mixture of Octene and 110 Percent Theoretical Air.................................................. 52 6 Wrinkled Flame Front Model of Scurlock and Grover.... 57 7 Schematic Diagram and Temperature Profile in the Region of the Reaction Zone.......................... 60 8 Heat Transfer Model for the Internal Combustion Engine. o * e........ o..................... 74 9 Indicator Diagram for the Engine of the "Analytical Model" at Part Throttle.............................. 87 10 Mathematical Model for Combustion and Heat Transfer.. 96-97 vi

LIST OF FIGURES (CONT'D) Figure Page 11 View of Engine Combustion Chamber Showing Spherical Flame Propagation Pattern......... 0................000 120 12 Cylinder Pressure Vs Crank Angle for a 1.0:1 Compression Ratio Engine With Normal Rate of Flame Propagation...oo00o 00 ooooa0 ooooooooo.oooooo 125 13 Pressure-Volume Diagram for a 10:1 Compression Ratio Engine With Normal Rate of Flame Propagation. 126 14 Pressure-Volume Diagram for a 10:1 Compression Ratio Engine With Rapid Rate of Flame Propagation.o 127 15 Pressure-Volume Diagram for a 10:1 Compression Ratio Engine With Reduced Rate of Flame Propagation 128 16 Cylinder Pressure Vs Crank Angle for a 10:1 Compression Ratio Engine With Normal Heat Transfer 129 17 Calculated Thermal Efficiency and Mean Effective Pressure Vs Flame Propagation Rate for a 10:1 Compression Ratio Engine.00 0 o............... 00000 130 18 Entropy-Volume Diagram for a 10:1 Compression Ratio Engine with Normal Rate of Flame Propagation........ 131 19 Availability Vs Crank Angle for a 10:1 Compression Ratio Engine With Normal Rate of Flame Propagation and Heat Transfer.....ooooooooooooooooo4ocoooo.o.ooo 132 20 Availability Vs Crank Angle for a 10:1 Compression Ratio Engine With No Heat Transfer and Normal Flame Propagation Rate 00.0..00000000000000000000000000000 133 21 Flame Speed and Effective Flame Temperature Vs Crank Angle for a 10:1 Compression Ratio Engine With Normal Flame Propagation and Heat Transfer Rates...........................00000000000000000000000000000 134 22 Relationship Between Mass and Volume of Burned Charge for a 10:1 Compression Ratio Engine With Normal Rate of Flame Propagation..............0000000 135 23 Flow Diagram for the Subroutine Computing the Composition of the Products of Combustiono 00000o0.o 159 vii

LIST OF APPENDICES Appendix Page A. POLYNOMIAL APPROXIMATION BY THE METHOD OF LEAST SQUARES........................................... 136 B. EQUILIBRIUM CONSTANT AS A FUNCTION OF TEMPERATURE. 140 C. CALCULATION OF THERMODYNAMIC PROPERTIES FROM EMPIRICAL HEAT CAPACITY EQUATIONS................ 144 A. General.......................... e o lb. *eo 144 B. Method of Calculation........................ 146 1. Computation of the Enthalpy............... 146 2. Computation of the Entropy................ 147 5. Computation of (1H/T)................... 149 4. Computation of (.S/,T)... 149 5. Computation of the Equilibrium Constant... 150 C. Computer Programs........................ o o 151 D. THE TIME RATE OF TEMPERATURE CHANGE DURING EXPANSION....................................... 152 E. METHOD OF SOLUTION OF THE EQUATIONS OF SIMULTANEOUS GAS EQUILIBRIUM........... 154 F. MATHEMATICAL ANALYSIS, FLOW DIAGRAM, AND COMPUTER PROGRAM FOR THE FUEL-AIR CYCLE..................... 160 A. General...................... e e' o.... 160 B. Mathematical Analysis....................... 161 1. Exhaust Residual - Initial Approximation... 161 2. Mixing of the Fresh Charge and Exhaust Residual..,................................ 162 35. Isentropic Compression..................... 163 4. Constant Volume Adiabatic Combustion....... 164 5. Isentropic Expansion...1. 65 6. Expansion to Exhaust Pressure.............. 165 7. Exhaust Residual........................ 166 8. Net Work... 0........... 166 9. Thermal Efficiency........................ 166 10. Mean Effective Pressure.................... 167 C. Flow Diagram................................ 168 D. Computer Program............................. 172 viii

LIST OF APPENDICES (CONT'D) Appendix Page Go ITERATIVE METHODS FOR SOLUTION OF IMPLICIT FUNCTIONS OF A SINGLE VARIABLE o o o o o o o o o o o o o o o o o o 178 A. General..,o o oo...........ooooo ooooooooo. 178 B, Methods of Solution.......... o......0000000,0000 178 14 Newton's Method o o o, o o, o o o.......o. o 178 2, Half-Interval Method,,,o........o,,,o,,.o,, 179 H, CALCULATION OF THE RATE OF RADIANT HEAT TRANSFER o.. 180 I. FLOW DIAGRAM AND PROGRAM LISTING FOR THE ANALYTICAL MODELO 0 0' 000 O a0 0.o 0 0 a 0 0 0 000. a 0 0 0 0 a 0 0 00000 0 0 0 0 184 A, Flow Diagram-.... o o o o o o o 184 Bo Explanation of Symbols Used in Flow Diagram and Computer Programo..o...0 o....... oooooo.oooo 198 Jo SPECIAL THERMODYNAMIC CONSIDERATION ASSOCIATED WITH INTER-RELATED STATE CHANGES OF TWO DISTINCT GASEOUS REGIONS, o....0o o4 o o0o 00.....o...a... 0.a00000 231 Ao Isentropic Change of Volume of Each Regiono..o.. 231 Bo Change of Volume With Known Values of Internal Energy and Entropy,, o.o...00...O....,00,00000000 232 Ko CALCULATED DATAo, O........... oo......,,, a0.0..0 235 ix

NOMENCLATURE A Area ATC After top center a Atoms of carbon per molecule of fuel a Activity BDC Bottom center piston position BTC Before top center Bore Engine bore b Atoms of hydrogen per molecule of fuel C Constant pressure heat capacity per mole p C Constant volume heat capacity per mole v c Mole ratio of nitrogen to oxygen in atmospheric air c Constant pressure heat capacity per unit mass E Activation energy F Exhaust residual mass fraction F A constant, F = RT/V F0 Moles of fuel inducted per engine power cycle f Fugacity G Gibbs free energy G Mass rate of flow per unit area H Enthalpy h Convective heat transfer coefficient J Conversion factor from heat to work units K Equilibrium constant based on concentrations Kp Equilibrium constant based on partial pressures x

NOMENCIATURE (CONT'D) K1 Flame speed factor (Equation (4-24) ) k Heat capacity ratio k Thermal conductivity L Hydraulic radius M Molecular weight mep Indicated mean effective pressure n Polytropic exponent n. Number of moles of component'i' P Pressure P.i Partial pressure of component'i' Q Amount of heat transferred q Rate of heat transfer R Universal gas constant Rod Engine connecting rod length r Compression ratio rpm Engine speed S Entropy S, aminar flame speed St Turbulent flame speed Stroke Piston stroke T Temperature TDC Top center piston position t Time U Internal energy xi

NOMENCLATURE (CONT'D) V Volume Vbot Clearance volume plus swept volume Vtop Clearance volume v Specific volume W Work w Average piston velocity x Square root of partial pressure of 02 x Air-fuel ratio, fraction chemically correct air Y Square root of partial pressure of H2 7 Square root of partial pressure of N2 a ~Thermal diffusivity. a = p cp/k tHe Enthalpy of combustion AHf Enthalpy of formation P lThermal efficiency Tv Volumetric efficiency 0 Crank angle degrees, 0~ = BDC piston position 0 =e T/To |j Viscosity p Density p ^Fuel-air ratio, fraction chemically correct fuel, 0 = 1/x SUPERSCRIPTS f Designates a trial value o Ideal gas state xii

,NOMENCLATURE (CONT'D) SUBSCRIPTS b Burned e Exhaust manifold f Flame element f Fuel i Inlet manifold P Constant pressure p Piston t Total u Unburned w Wall 0 Reference state 298 298.16 xiii

I. INTRODUCTION A. Purpose The purpose of this investigation was to study the four stroke spark ignited internal combustion engine cycle from a fundamental point of view. The effects of mixture composition, combustion chamber geometry, flame propagation, and heat transfer were incorporated into an analytical model, suitable for programming on a digital computer, which approximates more closely than heretofore possible the actual performance of an engine. This work is primarily concerned with the development of such a model and the subsequent evaluation of the individual effects of the heat transfer and flame propagation phenomena on the thermal efficiency and indicated mean effective pressure of the hyphothetical engine. Experimentally determined performance data are compared with values calculated using the analytical model. B. Previous Work In 1876 Nicolas Otto constructed the first successful gas engine which employed compression prior to the combustion of the charge. This innovation, although suggested earlier by Beau de Rochas in 1862, produced an engine which was more efficient than any heretofore and marked the beginning of the modern four stroke cycle spark-ignited engine (l 2). Although it was the introduction of the compression process which accounted for the improved efficiency, Otto himself did not seem to realize this and attributed the improvement in efficiency to a stratification of the charge. Only when thermodynamic analyses of the various gas engine cycles of the day were made were the relative merits of Ottos engine understood. -1

-2The earliest.attempts to analytically study engines largely followed the fundamental work of Sadi Carnot. As in any mathematical simulation of a real physical process, an analytical model was developed which incorporated the salient features of the physical process which it approximated. In the case of Otto's engine, the processes which the working fluid underwent could be closely approximated by the constant volume cycle, now commonly called the Otto cycle. The Otto cycle is composed of four highly idealized processes (see Figure 1), Process 1-2. Compression of the working fluid from volume V1 to V2. This occurs reversibly and adiabatically, therfore, isentropically, Process 2-3. Constant volume heat addition. An amount,of heat Q is added to the working fluid thereby raising its temperature to T3 and its pressure to P * This occurs when the piston is at the top center position. Process 3-4. Expansion of the working fluid from V2 to V1. This expansion occurs isentropically. Process 4-1. Constant volume heat rejection. An amount of heat Q2 is transferred from the working fluid, lowering its temperature to T1 and its pressure to Pl, thus completing the cycle. The isentropic compression and expansion follow the path PVk = a constant, where'k is the ratio of heat capacity of the working fluid at constant pressure to that at constant volume. The work of the cycle is Q1' Q2 and its thermal efficiency is Q1 - Q.Q - 2

-53 w U) 0. 2 4 VOLUME co~ ~ ~~~~Fgr \..TeOt y3e

-4For an Otto cycle engine of compression ratio'rT this can be expressed as =1 - ()k (1-2) The mean effective pressure, defined as the quotient of the cycle work and the displacement is mep= -. i (1-3) V1- V2 Thus, as a consequence of such an analysis, convenient mathematical expressions were developed for the efficiency and mean effective pressure of an engine operating on this idealized Otto cycle. Because at this time knowledge about the properties of the working fluid was meager, it was decided to adopt. as an analytical model for the Otto cycle, the constant volume cycle operating on an idealized fluid having the properties of air at standard conditions. In 1905 a committee of the Institution of Civil Engineers(3) recommended that the air cycle efficiency be officially adopted as the standard of comparison against which measured values from internal combustion engines might be compared. This decision was based on the result of tests which consistantly showed that at a given compression ratio measured efficiencies were from 50% to 70% of air cycle efficiencies. This report left little doubt concerning the value of compression in the internal combustion engine. Shortly thereafter, Clerk 4), using heat capacities deduced by experimental methods^, showed that in considering the actual heat capacity of the working fluid, the attainable thermal efficiencies were considerably lower than those predicted by the air cycle analysis. In 1908, Hopkinson^ (6 analyzed the Otto cycle engine using the heat capacity

-5of the mixture calculated from the known values for the individual constituents. By this, he was able to quantitatively predict the influence of the fuel-air ratio on the thermal efficiency and mean effective pressure and thus confirm experimental evidence that leaner mixtures tended to give higher thermal efficiencies. His analysis took account of the exhaust residual. Not until 1921, was an analysis of the constant volume cycle carried out which considered the actual composition of the working fluid including the effects of dissociation. At this time this became possible because accurate heat capacity data and sufficient information on the extent of dissociation of carbon, hydrogen, oxygen, and nitrogen systems at elevated temperatures were available. This analysis, by Tizard and Pye(7) assumed that during compression the working fluid was primarily composed of air, but that after combustion and during expansion, the working fluid consisted of 02, N2, CO2, H20, CO, and H2 in a state of chemical equilibrium. Because of the complexity of the analysis, no analytical expressions for thermal efficiency or mean effective pressure could be derived. Whereas the effect of compression ratio on the performance of the Otto cycle engine was shown by the air cycle analysis, that of mixture composition was shown by Clerk's analysis, and that of fuel-air ratio was shown by Hopkinson's analysis, the effects of dissociation were introduced by Tizard and Pyeo In doing so they answered three pressing problems of the day. First, because of dissociation effects, the highest combustion temperatures and mean effective pressures occur with mixtures 10 to,15 percent richer than stoiciometric. Second, for increasingly rich mixtures the mean effective pressure, which is a measure of the power output, is rela

-6tively constant and only decreases slowly as the fuel-air ratio is increased. Third, the thermal efficiency of the engine increases as the mixture is leaned out. This last effect is due to the fact that both heat capacity and dissociation increase with an increase in temperature. Whereas the best measured thermal efficiencies are as low as 50 to 70 percent of the air cycle efficiency, they are 80 to 85 percent of those calculated by Tizard and Pye's method. Many people had been openly critical of the validity of the air cycle analysis, but now it was realized that at a given compression ratio, the efficiency calculated from the air cycle represented an optimum value which could be approached in practice only with very lean mixtures. This study was the first of many which analyzed the Otto cycle engine in this manner. In 1924, Goodenough and Felbeck(8) presented a comprehensive discussion of the theory of chemical equilibrium and the effects of dissociation on the maximum temperatures and pressures attainable in combustion processes, Using the results of this analysis Goodenough and Baker(9), in 1927, presented a complete thermodynamic analysis of the Otto cycle together with the results of numerous calculations. Their analysis followed along the same lines as Tizard and Pye's, but in addition included the effects of the mixing of the exhaust residual with the fresh charge. In 1935, Hershey, Eberhardt, and Hottel(10) presented thermodynamic charts from which the properties of the working fluid in the Otto cycle engine could be read. These eliminated the tedious calculations of Goodenough and Baker. The charts, based on spectroscopic heat capacity data, allowed for complex dissociation at high temperatures. The species included 02, N2, CO2, H20, CO, H2, OH, NO, 0, and H in the products of combustion.

-7The charts have been widely used from the time of their introduction for the analysis of the Otto cycle engine and have been revised a number of times to allow for improvements in fundamental data (see bibliography of Reference 11). While the charts allow a considerable reduction in the mathematical difficulties of the Otto cycle analysis, they are not general, having been developed for a particular fuel and a selected number of fuelair ratios. The analysis of the Otto cycle proposed by Hershey, Eberhardt, and Hottel was very similar to that proposed by Goodenough and Baker but considered the induction and exhaust processes in detail. The Otto cycle is termed the fuel-air cycle when the actual properties of the working fluid are considered just as it was termed the air cycle when air was considered to be the working fluid. The fuel-air cycle is described in more detail in Chapter III. In spite of the refinements of the fuel-air cycle analysis, measured thermal efficiencies were still between 80 and 90 percent of those calculated. This is because many important phenomena present in actual engines are disregarded in the simplicity of the Otto cycle engine. Two significant items neglected are the flame propagation and the heat transfer. However incorporating these effects into an analytical model poses extremely complex mathematical problems. Nevertheless some investigators have attempted to include one or another of these phenomena in their analysis. Attempts to consider the effects of flame propagation (progressive burning of the charge), were first made in connection with thermodynamic studies of combustion in constant volume bombs. Among the earliest was an analysis by Nagel(12) in 1907. A similar analysis was made by

-8Rosecrans(13) in 1926 which made use of the equilibrium studies of Goodenough and Felbeck. Endres(14) was among the first to consider the effects of piston motion. Hershey, Eberhardt and Hottel(10) suggested a method by which the temperature gradients in a constant volume bomb could be calculated considering mixture composition, variable specific heats, and dissociation, In 1937, Hottel and Eberhardt(15) extended the work of Reference 10 and proposed a method for calculating the temperature gradients in an engine considering both piston motion and spark advance. Pressure volume diagrams were calculated for the combustion portion of the cycle assuming no heat was transfered to the cylinder walls. Rassweiler and Withrow(16) and Rassweiler, Withrow, and Cornelius (17) suggested a method for treating the combined effects of flame propagation and piston motion in internal combustion engines in order to analyze combustion photographs. In 1940 Withrow and Cornelius (18) proposed a method for calculating the pressure rise in an internal combustion engine. They combined the analysis of the previous two references with the thermodynamic charts of Reference 10. Rabezanna, Kalmar, and Candelise(l9) in 1939, proposed a method for the analysis of flame propagation and expansion during combustion which took into acount combustion chamber geometry, spark advance, and piston motion. Although this analysis considered the thermodynamics of the working fluid in an uncomplicated manner, pressure-time diagrams could be calculated from measured flame propagation rates by their method. These analyses of flame propagation in internal combustion engines were hindered in two respects. First, fundamental information about the nature of the flame propagation in an internal combustion engine

-9was not available. Second, the sheer magnitude of the calculations involved, assuming that flame propagation information were available, would have precluded any extensive analysis. All of these studies assumed that the engine operated under adiabatic conditions, In 1940, David and Leah(20) presented charts of "attainable thermal efficiency" and fuel consumption for Otto cycle engines. These charts were computed from an analysis similar to that of Hershey, Eberhardt, and Hottel, but included a prescribed amount of heat transfer during the constant volume combustion and subsequent expansion. A concise presentation of References 10 and 15 was published in 1948(11), the thermodynamic charts having been revised in light of more accurate thermodynamic data. However no new technique for internal combustion engine analysis was introduced. In 1950, Leah (21) illustrated a technique for approximating the thermal efficiencies the Otto cycle engine for any hydrocarbon fuel from charts. Edson(22) in 1961 presented the results of calculations on the fuel-air cycle model made on a digital computer. These convered a wide range of variables. A portion of the work done in the investigation being reported involves an analysis similar to that made by Edson and is reported in Chapter III. The problem of considering the combined effects of mixture composition, variable specific heats, dissociation, flame propagation, and heat transfer simultaneously presented such a formidable mathematical obstacle that not until the widespread use of automatic computing machines was such an analysis contemplated. In 1960, Edson(23)proposed an analytical model for combustion in the internal combustion engine which was suitable for programming on a digital computer. His analysis included the effects of

-10flame propagation and piston motion but did not include heat transfero To date no computed results have been reported. C. Scope of This Paper The remainder of this paper describes the development and evaluation of a comprehensive cycle analysis and digital computer simulation for spark-ignited internal combustion engines. Chapter II describes a method which is used for the determination of the thermodynamic properties and composition of the working fluid. Chapter III presents the results of computations using a well known internal combustion engine cycle analysis but employing the methods of Chapter II to describe the working fluid. Chapters IV and V discuss the nature of the flame propagation and heat transfer in the spark-ignited engine. Chapter VI describes an analytical model for engine cycle calculation which includes both heat transfer and flame propagation effectsO Chapter VII presents results of computer calculation made using this analytical model. These are compared with experimental engine data,

II. THE THERMODYNAMIC PROPERTIES AND COMPOSITION OF THE WORKING FLUID IN A SPARK-IGNITED ENGINE A. General This chapter describes a method by which the thermodynamic properties and composition of the working fluid of an internal combustion engine can be calculated. The method presented is ultimately employed to describe the working fluid of the "analytical model" engine proposed in Chapter VI. It is also employed in the fuel-air engine cycle analysis discussed in Chapter III. For the reaction between a hydrocarbon fuel and oxygen and nitrogen, the following equation can be written when stoiciometric proportions of oxygen and nitrogen, subsequently referred to as air, are present. CaHb + (a+b/4)02 + c(a+b/4)N2 = aCO2 + b/2H20 + c(a+b/4)N2 (2-1) where'c1 is the mole ratio of nitrogen to oxygen in air and'a' and'b' are the number of carbon and hydrogen atoms in a molecule of fuel. When an excess of air is present, the following equation can be written~ CaHb + x(a+b/4)02 + cx(a+b/4)N2 = aC02 + b/2H20 + (x-l)(a+b/4)02 + cx(a+b/4)N2 (2-2) where'x' is the fraction of chemically correct air entering the reaction. When'x' is less than one, that is for rich mixtures, no oxygen is present in the products but some CO and H2 will be. These equations tend to over simplify the combustion process and many more chemical species will be present in the products due to dissociation. -11

-12While it is true that atmospheric air contains substances other than oxygen and nitrogen, only water vapor exists to any appreciable extent. In order to establish a reference base for all the calculations, dry air is assumed. Dry air at sea level has the following composition(24): Basis: 100 moles dry air 02 20.99 N2 78.03 A 0.94 CO2 0.03 H2 0.01 79-01 100.00 For the purposes of this work, the argon, carbon dioxide, and hydrogen normally found in air are lumped together with the nitrogen and are assumed to have the same thermodynamic properties as nitrogen. Thus air is assumed to be composed of 79.01 parts of nitrogen by volume to 20.99 of oxygen, their ratio'c' being 3.764 to 1. The error in the value of the thermo/ dynamic properties calculated on this basis is about 0.4% or less. Furthermore, all substances including the fuel are treated as ideal gases and mixtures are assumed to follow Daltonts law of partial pressures. The error in the thermodynamic properties introduced by this assumption varies as it depends on the temperature and pressure. Because of the nature of the Otto cycle, the highest pressures always coincide with the highest temperatures and thus the deviation from ideal gas behavior tends to be small. Such deviations as may exist are greatest during the induction and compression processes. Reference 11 presents charts for

-13corrections to ideal gas thermal functions calculated by the BeattieBridgman equation of state for octene-air mixtures. For such a hydrocarbon-air mixture which is compressed isentropically from room temperature and pressure, the ideal gas thermodynamic properties will be no more than about 0.5percent greater than those of the real gas for the states encountered along this path. B. Calculation of Ideal Gas Thermodynamic Properties 1. Empirical Heat Capacity Equations In a carbon, hydrogen, oxygen, nitrogen system at high temperatures, dissociation produces many chemical species whose individual thermodynamic properties must be known in order to compute the gross properties of the working fluid which they comprise. These thermodynamic properties are normally presented in tabular form or may be calculated from equations approximating the tabular data. Since the analytical model for the internal combustion engine presented in this study is designed to be simulated mathematically on a digital computer, it was decided to calculate the thermodynamic properties from ideal gas empirical heat capacity equations, This obviates the use of a large amount of computer storage capacity for the tables, Hougen, Watson, and Ragatz have tabulated a number of heat capacity equations in the appendix of their recent text(25) which includes most of the equations developed by Kobe and his associates(26). Either a single equation was used for a rather narrow temperature range (such as 273-1500~K) giving fairly accurate results, but not covering the higher temperatures, or a single equation for a larger temperature range (such as 273-3800~K) with a significant decrease in accuracy. Spencer(27) presents

-14heat capacity equations calculated by the method of least squares for a number of hydrocarbons. Williams(28) presents heat capacity equations for a large number of substances. Two sets of constants are given for each substance, one set for the temperature range 500-3000~K, the other for the range 3000-6000~K. In these references the constants for the empirical heat capacity equations are presented as five or six digit numbers. In order to achieve greater accuracy than the above equations afford in the desired temperature range, it was decided to develope highly accurate empirical heat capacity equations for the required substanceso Two equations were developed for each compound, the first covering the range 298.16-1500~K and the second the range 1500-3500~Ko Moreover, since a high speed computing machine capable of handling eight digit numbers was to be employed, the constants were calculated and used as eight digit numbers. The basic data used to develope the equations came from tables of ideal gas heat capacity at one atmosphere as a function of temperature. For the substances employed here, two sources were used, the American Petroleum Institute Report 44 (29) and the National Bureau of Standards Circular 564(30), Using these data, empirical equations for the heat capacity as a function of temperature were developed by the method of least squares, the details of which are given in Appendix A, The equations for each substance are of the form: Cp = a0 + alT + a2T2 + a3T3 (2-3) 298.16-1500~K Cp = b0 + blT + b2T2 + b3T3 (2-4) 1500-3500~K

-15Table I gives the data source, the a's and b's, the maximum percent deviation, and the root mean square deviation for those substances which comprise the working fluid of an internal combustion engine. For these substances Table II lists the enthalpies of formation and absolute entropies at 298.16~K, the enthalpies and entropies at 1500~K, and the enthalpy and free energy of reaction at 1500~K, for selected reactions ('all quantities at 1 atmosphere pressure). Table III gives selected values of heat capacity as a function of temperature, listing both the tabular and calculated value at each point. The heat capacity representation in the range 1500-3500~K proved to be very accurate. The maximum deviation for any of the substances considered was less than 0.1 percent of the tabular value. In this range, the use of such approximating equations will represent the tabular function within the stated uncertainty of the table. In the range from 298.16-15000~K where the heat capacity function changes rapidly with temperature, the accuracy is less. The maximum percentage deviation is about 0.6 percent of the tabular value for some substances, less than 0.3 percent for most. 2. Computation of Thermodynamic Functions and Equilibrium Constants From Empirical Heat Capacity Equations The computation of the ideal gas thermodynamic functions and equilibirum constants from the empirical heat capacity equations developed in the previous section is most conveniently made by arranging the constants for each substance (the a's and b's) and the necessary fundamental data in matrix form. The thermodynamic functions then can be calculated, as required, by a series of matrix multiplications. This procedure is outlined in Appendix C.

-16ooooooooooooo oo~o oo888888888.-to 000000000000000 01 0 00000 0000000000000 *0000000000 0* 0 0^ C0 0coo H 0 0 r0 1 0^. 0^ 0 0COrcOJ-tL~o ^Oooo- ~ oooJ 0000000000 H0000000000000 HHOOHOOOOO ~,H C CO'. - 0 0 0 0 ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~c \, nAIA'~ Cm a 499 cc) -~ c j Lr\. Q - Co C C \ t\ oo\oo Q ooo o oo CYC') Cj — H Lr n\0( 0 (XiY) oc) b' o b o o o o 0X Lt\ C;C;0OJ; "C;;C CO CJ H; co CO LAO C; 0;C Cl) 000000000000~^cnoo t~ oo's m ~0~~~ 0 0~0 ~o H I Ioir~i-rN~rs~r~t^-LrN~rNLTNO-^'-t-^' l t^DLOAOir\...O cOC o0 H )?0000000000000 ^ U)0000000000'.'r- I I I I Ioo I o 110c I Ioo o = s I H'&i I\ I. 10 H O~i-jHcl\m H-O H 0 0CCO \o H CJ I-H 0-HCO-t'c O0C 0 H LCLCL f~l\^("-=t-3 -CO-=^ —Q O\CO ~ocp'1 (Xoi-io on p0O<^HOHO8Lr.00 Cr1 o r -i00tc - CnC0 H~5 EO<1>-OO\OC\ JC'1HcOOO \ EH Lr\ HLr\ Lr\ 0 P-I CO f* * * * *C) * * * * * * (Y cr^ 0000000000000 O 0000000000 H 4 C..) I I I I I I 1 I I I I I I I I I +~~~. + H H8 CM M McO \ C J 0 8nO 0 C'J 01 CM O ) C O -i C\ - O 0 "^ c8?CI'~ C?^ 8 H. 000000000^8 pq H HOJOConOC.1001Q COL OJQ tH Ht-c1OHHC7QL-3'Luo H oH0 " L r\C',\ 0 C) O1\'-t —- H,r H o-0OC' 0 d -dL \-OO O 0 4 co Orl\ rli CON lOa- oO O\OO l_0 COOnHH L\ -O-I, L?\ 3 -zt O \ \ cLu\ (\ HO 0 CY' CO H 0 H O CY) C- -C'J CY)ON H 0\ +, 0 L 1 H - 9 C Co 0\ 0 0 0 0 0 0 0 0 0 0 0 0 l 00 00 00 00 Cl +~ I I I I I I I1I + 0 11 HII1 0 0 oi yyyyyHHHHHyyHHHo0~ HHCdJHHHHHHH H-' I U" I- ~ OLA ~ 0L8 I L(Q H L 0L 0 00 0 0 O0 ~-HrCJO- ~ DOl * 0 0 0 00o0oo000000000 0000000000o I ^^^^.^^^^ggaa^^@H^^^^O^~~~~~I I CO 1 1 rl II\ Ir I; I:d \ I \ I I 1 C \) I NI co LI- I n I r I C? ~~8o la. 0, +.~ -p 0 ~.3 c~ 3 03 0 q C)\ 0U)U) C 0 * C\Jco QOH OP\UC\IJ j po J o ) 03 \ ClO(N 0 J (X c 0o } C OU)COt -L~l'-^o~ot^-^-Ln-^Hm rt> 0OC\ -C i - 41 0\ co 4-' %0 0 0 Lr.\\,Ho P, ^ Lr\ c C'N — 0 C) -t -. - L^ tRN i -tL\=-^ ^~ -? ~ ~ C I 1 I I I I i I I I I IC 1 1 I I I 1 1 I 1 I CO - C c) * ~~~m ~~Jo o;U (uu c~ c o c o'~~~~~~~~~~~~~~~~~~~~~~~~~~L P, PD oL - +CI -1 L 11, -:4 44 +-4-4-4-: -'P -: o! co ~~dr 9i o M ai a) C) i C) ~~~~~0 0~~~~~~~~~~~~~~~~~~ ~~

-17TABLE II *FUNDAMENTAL THERMODYNAMIC PROPERTIES Substance Hf2g98 S982 (H1500-H298) Sl500 Zc298 cal/mole cal/mole-~K +A HO298 cal/mole-~K kcal/mole cal/mole 02 0 49.014b 9705.3b 61.6639b -- N2 0 45.767a 9181.3a 57.786a C2 -94051.8a 51.070b -79303.6b 69.812b H20 -57797.9a 45.106b -46303.6b 59.8567b CO -26415.7a 47.301a -17130.3a 59.436a -- H2 0 31.208b 8673.6b 42.7206b -- OH 10060.Oa 43.888a 18863.3a 55.568a -- NO 21600.Oa 50.339a 31099.8a 62.760a 0 59159.Oa 38.469a 65204.9a 46.64la H 52089.0a 27.327a 58059. 7a 35.419a -- n-Heptane 44890.0a 102.24a -- 1075.85a n-Octane 49820.a 111.55a - 1222.77a 1-Octene 19820.0a 110.55a -- 1194.97a Reaction A HO (AG~/RT) cal mole C02 = CO + 102 67026.0 12.192 H20 = H2 + |02 59830.0 13.180 NO = 1N2 + O2 -21656.0 -5.7379 OH = H2 + j2 -9673.8 -1.5465 0 = 02 -60352.0 -12.292 H = JH2 -53723.0 -10.948 * All quantities at 1 atmosphere pressure. a Reference 29. b Reference 30.

-18ccO coco co 0 co co 0co 00 00 o co coco co co coco co co cOJc coco co co 0 0ON 0101 00 00\ NO O| ONO g ONO m,\ C(N \ Om ONON 0 0 ON( I. 1 I-0:Lr- u-\|L - Lr\If LC l( -U -~I — I - -:d i- -_ _ftl_ -r co \D cs I1 O O on co UN LT\ Ir -=td1 -=!t \101 _t cm Cs O 0 cm j tl- l-( _:t roj_: -4- Ot| O~J m cm ro 0m CD OJ J 0 C 0\\ O c c- co c0 OH- L- co 00 0 0 _ N' 0 R Oc 00 0R0 ON0 \ o17\(C\ 0ON \ m m ON a\ 0 00 0 co HH HH cv1\1 t * I ~ N1N M1 t-CC c co * g * ~ *I ~1 ONO 0 o \ a.OH - -oN Cvit-(c ON oLr'vo 01CN o C0Q — O (O 0 c- coqo. u OQ|~~~~~~~C' o rl n CY) t o c~l ro S =lsl CY')J CY) cn's o\- r Cy o\ \ c oi H\ cf~~~~-~~~j- CviC~~~~~~~~j cO CviCY ~ ~ ~ 8 c)CC ) 9 cy 00~ \'O \ CC -u^q r-H HH 0 0 0 0 C\J0 -oj Io -occi coc in i' co c \ 0 0' * * a I a * * * * a, I * I aI oo-, ~ -- -- L- i- - ci- t —M o - t. — t-o - co o co co co ONO\'s r3~~~~~~~~~~~~~~r co 0> c^M l- l^-t t- CM -t-^t Lrl \0 R-^l - oo \oo Roo _0t T\o\\\r4 - y! \ o! \t 0 0 i ON \1:\ Ul\!CM CM C0m \'I I \ o0 O 0 0 0 r-HH CY')_i -cv r- VA j! -I ( \ HH I l C C) cc HH| I- 0 I\0 \0 \D 0 t- M t- i t- t-i t- M t- [i tI- CI cI 00 00 Cd 00 O 0 0 P4~~~~~', ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~t~ —,!g ~ oc oo cciONN 1'0 (co*~Lc co A CC)L I M rL C) rIp(Y Oj -4Ht-l o CY') L \o 0 CY') (Y')Lrl\o CM 8 CY) <O I rl I CM CM r-q _:t Lrl\ U-\ Lrl\ CY') CM CY') CY') cn 0 cm I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~L N ~cc ~ ~ c'~ O H \I~ ~.0 HH H t3-^D -^\p u^OJ -= -^ ^ 000[ *OL( 010^1 cvi 01H - O-'OO- coco H - 0 o'oo i -t -- c oco o co oo coco coco oco ooo c~ocI UN~~~ cY0 1~ viiH K in 0 0 * *! * *) *cviL y *- * ci H Hcv * ~ cvi'.cci 01cvi LC\ cvi *ic 0 I 00 — J ONOQN Lcv L0\ HH t- 0101M CM 0CMOc (ii (Y) \ I 1 0 I^ CC) co o CC) ON-ON0C CY) CY') I S J rO co 0c\ Qcc coor\ ON O O\ CC) 00 O 0 10 0 iC cvi I^ CM CM ~>r4 HH H H rl ~ -H H HH H H HIH(1) Q ~ 0\olC)(\0 H|Lr\0| tl-\ VN-^ T 0 \0| lr,\0| 0 H 0l- OI co CM t CM Lr Hi Nc| \ cO LCo\ C O O N-\i p01 0 co O ci \0 co - cc \ - - \\- cvioo\ o o o lo coo\l\ ooo oC ol ~~~~~c'\ 010 ~O~ ONO -~-~ 0co* v~~~~~~~~~c ~ ~ ~ C; 0101 C; y *: -;. _;_t U f cot coco HHCO HH. HH H H 9 r-q LC I o-o o-i 1- ( o\ D n I o' i cvic i 00 \OLNI \O \Q-I c- I joi| A OMNON ONON1 0 0 cvicvi (Y) oO\ ON ON H-IH m coi CY,) (Yi') \O1O \ -t co ON ON \.D o'0 \ t t — CC*) --- ~ — cco co co Co)co coc c co ~ C (~C coo c EaI H i r- CO cmoo c. oo Lr\H OH\ 4101 CM m I 0t CO" CI rN \ 1 0101.00 ( r\ \-O'- P L-J 0 * 1 0 t..! 0. 0. *~t — t —- 0 i i u*' * a) \ b-h — t- M tI — c co o co COCO cocol co cci O N0 \ON CT\ON |ONOOIO \| o~~~~~~~~~~~~~~~ ~ o~~~ (i0'.c U) U) -H~~~~~~~~~~~~~~~~~~~~~~~~~~~O Hr- -_I- U\ LC\ H IC Hr-'sO tI I I — H Cc Hr-HI cvnic OJCM \O \ 00 o H01j U-' I I I* I I I - 4I- l i i i.** I II II I I ) o Lrl\r Lrf\Lr\ oooo ICrLrCN\ oo o ~oCoo t CLt-I o 0 u 1 1 I H H H. r-I H I I II I II 0 00 0 0 0 0 0 0 0 ~~o 8 8o o o o o o o 00 0 0 0 0 0 0 0 0 0 0N0 0 0 0 0 0 0 0 0 0 CM CH)LA\ O — OSC' tr 0 r\ Lr\ Q t\ 0 tHr dE4- r-IH rq r-4 8 CM cn (Y

-19% Tables IV and V list the calculated values of enthalpy and entropy alongside their corresponding tabular values as a function of temperature, The values of enthalpy are calculated from the following expression: Ho_ T0 Ho Ho +(Ho H0) HT - H T T- HT + where H~ - Ho~ = T COdT T TO TO P The entropy is calculated from S~ = S~ - S~ + (S~ ) T T TO To where T o T -ST =f | T o TOT 0 The quantities (HT - H0) and (S~ ) are the tabular values at the reference 0 0 temperature'T1'. For the substances reported here they are from the data sources indicated in Table I and are doubly underlined in Tables IV and V. The low temperature range reference temperature is 298.16~K for the substances from API 44 and 300~K for those from NBS 564. The high temperature range reference temperature is 1500~K in every case. In general, the calculated values of enthalpy and entropy deviate less, percentagewise, from their tabulated values than do the calculated values of the heat capacity from tabular values. Such calculations for mixtures are always more accurate than the least accurate component.

-20oMj Co m -C'4. o\ oN L\CO H o t — mm) ON ON ON ON ON' O ONO a\ NO \ o H HI 0~ 0~. m r=* -t - H H.4.4-. COcO H H H H |L(N'. ON 0 mp.4 t^ CO * o O *O 0" C OC 0 t-c I- ^-'.O'. C Lr'\ LC \ \ LNLr I m m1 H OJ 0 0 - co' 1 -n i- - --.44.4.1 ^d _..d-O -t -t.4.4. 4 ON:N.4 CAC HH N HH ^ r-(lCMC'1 ro41 m m - t|LN.o' ^- >- -t>- O N ON C\JCJ - t- _ ~ t -- -t.-t| 0o0 \0-t Coj\ c- - co - CN.\ - (1Ct ojm M mc[ CoCo oo' \ CO't- m mC t-i t-i t.- t - Ltr co ON\ Co ol CotC c- ^oi \1i o m CM JC oCMj cOCo (7ONON 00 o HH.4.t LV\Lt \ LfNLr\lLt\Lr\ Lr ^ L\ L(N L(jNU -:4.4 -- ) m 1Co mm \0\D ^O^O~~~~~~~\ \0^ 0 \D0\0 \O^Q O^O ^O\ O \ 0 rsO O q.1 \D O Hr-I'A \ \, HHilri i HH oj 01C m rY -t.4. |Lr\LC|\'. t-t- r -t- qO o oCM LCNL\ t-^rHH n rli rHH H HH C'J CJm cncO CMO 0OC\. U LC C'tl- t-co O 00 00 00 00 00 ell ~ ~ ~ ~ 1 0.c; 00 u'. -^1I -'j t OO.40.Q.0'.001 0. 0 H Hco..O ( M' O HO H4 -tO NC O 00^ o\B o ONON^- CIJCMo oJ OJ~ON~ 0O 7 o ( mm cV LrCi\ CJcm CMjC 0 \0 H r-q to-I to. ( rn Y) OCJ m.O.0 00..44 - ONO.4.4 0 10c1M mm L\ Lr\ \Do \ coo CO N H l\^'.0'.4 ONO 0C'JC CvQ M O (O 0ON L-. n coH coC C M\ Lo L 0 o\ O. 0 0 0 0m 0 00 p~~~i o~~~r-j~~~m m -si —^' t>-^- -t-^- Lr\L^ Q Q Q Q SQ^ C^C^ ^OL^ ojoj~~~~~~~~~~~O,\m 10 rl\ C~jC~'.0'.0 ONON.4IHH I \ L 01.4 01.4o c m o \o m O S H crC( (MONLr \ OLr\0 II ooNL~~ LON C\ COCO\[ moo) H LCNLC[ m NN CY) m co m N ~ ~ ~~.4.4'.~~~~~~~'.0 t~~~~~~***t~~~~~ ONON9 9 H H rHH CMjCMj C~ o m -\o r-( Lr ryC H. r4 o L\ Mo LN(\ 1 t-.4.4.4 co 0i c m Ht COO No IM \oj \m m ojo \ oj -i- O^ ^ O ^ T O o\(cjc t i\ m md ojo U-NH CM 0-t- LfN OJOJ1 HH1 CJO C coc) (MCMII LfNIC\ tf~~~~~~~~~~.P-~3 ~jC~ N CO g " oi oj ojll m ml S 3 ^ ^ ~~-t c CCi- \ M \t \10 \Q \D 3 1~ Q - co SE C^ Oj o? -? t Q 1 \(U ^OO — t \0 co0 -N^\OO(0 =t' OJOJ 0 0 0 01 0 0 0 0 0 0 0 0 CO IM LfNL\NUN ~- O M'.0. ON HH COM H HM 0 E{ LQ'. I H C?^ CO'.0o'.0'.0'.~-s*= O'. L4 CmH HH COO ONON oo -t-=- Hoo n H ojojoj o o mmt-'.0^^oo oo o~o Hr- HH'.'. 01 oo CH 01\ 0 1'N H HH HHE: t co-c 0N 0 HO E01 0 Lr\ CO \O -^. LOL H C. 0Y 0 4 0 4 M 1 ON CMCOIM.4.411 m f OM C (M(M QQ.4 H>-t-.Ot6L0\L0 0000 oo0 Ho {HH Hii n - oj~H oj H m O~~~~~~~ _Smn c H H ( M H c r o LrNoit o a -- H 0 O C 0 0 0 0t -0 -. 0 to j o r-q r- co o \o ~ o \o oo o -4,. oj ~0 ^o r) H m ( \ o o o 1 43 - \,o Cy) cn rq q \oo \o, o o\j oI juo oj u-\ r- t -- t~~^ o oj cr<7 CY) om | m t^-o ojj c6\ OI O 0N0.4.O6r4 O N'. a -r'r*. C OC O CO 4 C~ C)MI - Ct.4c4 CY) O t- - t ON H8 U-U- ONON 0 H r- r- I jjH HH CYM CM CM- CM <~~~~~~~~~~( m n my r-H o~jo| r-im(.moY) trl\ irl\ rn t- r-\1' o l- co t>0 0- oo 03 o4j IJ Lrt t- L L\ o LrOC \ co O) Q — t \O o mn Q CYmC'\0O 00\ c m tCM t — I ooCoC Y? C.r'.o CMt-.oj o.4O. LC U.' Lr\ Lr Cr\MCM 0 0m -t-t ON O 01 00 U-\L(N 00\'.O'(\ \)C^1 00 t-t — O t-t- C MCMjd _ coCO c o Lp O CM I i-cji cocfN LCNLCN'.0'.D COCO 0 0 Hl. H r-1'II \.0\ 0 0 i - 0-JO o 01t100 0 0 0 00 0 0 0 0 0 0. 0I 4 1 II II II I a S -^ i^ t^ LT^ oo o^ oj \o m. -I'o o^ LT^ LT^ o o o oj' m <6 <o p p o o ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~o 1\C~ \ c mLr rl 0C~ c \0 1 CM tCOO Ho o tO j \ H tc- H O -:t- M-CM cococ0co0 I jI j 00 oi Lr \ r Hp 0P 0011 ONoll.4Ci HCo ONCO ON'. o.4'II VDIMOJJ coI Ir\Lr\ mm C OJ I COj3 mm Lr\L.\0.\0 co0c100 t-t — r-( 0 I0 I I r-\ iI\ o oII 0 — HH t- | r —1 iI OJ J OO mY n U (D 00 00 0 O0 0 0 O0 0 0 0 c cooH r- -0 Cjr4 ( - 1 t- CM CM \1 0 1 1 8 8 1 CO0 0oco c 0r 0r\ 0r\L,\ 0,\ 0 0 0 0d I o ~~ol= c r) -CY) L-~~o- ^vo!r t'jON C ~ N0 0 0 0 0 0 0 0 0 0 0 0 CMj cY Lf \ t~- H Yn U-N\ tIN 0 tIN\ 0 LCN\ i, ~ ~ ~ ~ ojojmcni-r\L~t> —o~ ~oj C a)H H H- CM CM cN' H~?^8888888 88888 ^-^~~ * * * * ** ** (o - m.f0 ~0^ [j o 0oojoom o o

-21c0 co C) n rX ( rHH oo o H H co co ca ODCO\O \ coC t- t — oj c| co oN C\\ON CJO 0 c co c 0 t — 0 0 HlH U L \ Q ojC\Jc oooo _t'-s- 0ON \10 \0 coco co co t —- -=- - -. — co c a \ C0\ co \O'O\ t-tj - t-i- CONON H H COJ*C c oo -) -t L\ ut'\L-\ L\ \^ \o 0 1-r- co co ON ON ~j cvij ojl o Cj oj oom ooi rn o oo oo n o o o c oo oo ooo ooo oo oo|l ooir cn c a,\ HH ^ \1H 1>-'- 0 \0 H r-IH -t-s- r\ Lr\ (N ON ON'0'<)H 0 0 n 000 000 On\O OC ON Cr\ C'j -- —, t —- coco0 0 \ 0\N |\0 \l VI V\ H r-H 00 co 00 0o 0 ooON \D'.O \0O\0 0o0 HH 00 cooa E510 0 0 H C J U ( C 00 0Mf co ca 1 -L\ 1 l Lr,': \ \0 U-\ Q \ O'~j'.0-\ -: Cx) 0 C fl 00 L 0 0 L. Lr\ Lr\ Hr L(\LC\ t.-t- O O — JC\J J C 0C'j coc o cmc( o OO -C-t'0 C00 00o cc 00 HH OJC'JOJO c LjL\ct' - t — coc > 0 00 H ~~~~~~~L-Ni\ ( L-\ Lf\| Lr\ U'\VN r\ Lr\I Lr\ Lr\ \D O \D \0 \0 \10\ \- \0 \D 10 \0o \O \10'^'o t>- l Q co OJ cm (C ooi coacn O o \ Ci t O to - Cijco co.\0- UNLf\H \ -41 OJH co Hnc L,'r.D O O oc It- u E-i cocaI ooool^F~p~loJONON OJ o c Ur\uU\\osO \0r \ 7\ 0c \ ONC co - r-l \co 0 \ 00 UI \ 0H\ O| t — r-IH cot _ - LP0 UN Lr\LPNco co tc- t -- O O cO J 0 a ~| * *I *0 *| *1 * | * * * * -t -t||-^ -t| -st'-^j-^ —^' Lr\Lr UN LrN ujr\ Lr\Lr U\ Lr\ j U\ ir \Lr U\ Ur\Lr\ LP^\ U \ \o \Ol\'o \^ o HC OOO 0^0 ON |ON CY)ln \J \llOOOO 00H0|o co O'.J' Hi HH1_1 -t - -t*- OcO HH -J.C\l C C' C L-\Q ON ON Io ^ H HH -t_-_ OOO-co -l-co oc\ i-t -Lro.oio C')o _N:.0 -rl- Lr\ LON \ CYo) I 0 o C\ ONN C oY)' C0j cJO -c —C — 4 0 co cocO -- coc M M *^ t^~~~~ ~~~~~~-1 t- 1^ 0; Cy CAO oo LT^ \Lr \'o o * CO 00 0^ 0,11 0^ 0^' i-I * A CY* oo i\' Lf^ \40 \;1 -S r-| ~~~~~~-^ -t -I t -tl Lr\LrTS Lr,\Lr\( Lr\ Lr,\ L,\ Lr\l LI'\ Lr Lf\Lr'\| LI'\ Lr'\( I \'O \' OO \1 ^ \D'O "o 1O^O t~~~-t — t-t- 00 ~~~~~~_: LLco c0~ c Ca' ONON - jC ONON HH o c oO u -:dc. I.~. c 0 H LrC\r\ c0)a Lf\-t - - _ — \ l L\ U\ Lr\ oooo oooo r-I1HH ON 0, Lc~lr I LrLP oNooN cJC'i -[r\'.a'. coca\ O O NCONONONO OJOJv- 00o'.a coca 0 -,; - -- -- CY') U\ Lr\ Lr\L Lr\LC\ Lt\LC clcLr\ oL| \Lt\ o'oI'o'o t0m Cj ~ C O t t I ) o -'o oc r~l 0 1 i r,\ ir,\ r\ ri Q~ -=t' \^\ r^- f- CM t - O OJ il v i t O r-I Lr\ -.4- U OJ P- ~~~~~~1 O~J O~j OHq ONQ1-0 00 Jro 0H HH 0 \ — -t-.f -=-J -4 0 I HH co'H ONON C\IC\J 0 0 ONON ONOO goO2 r- C\oC\J rS H i( 0 ^ o Lr\ 1- co 0 0 0^ 00 co o tco ~ 0- co o ol c L- I T\ U-\ L \Lr\O\ C'J-t \ O s0l0 O D \.00\10 l a - t?- t -c t1- H —| ONCO 4' t-I ONL OO-L CY \O 00 \O\ 0C'OO' tO'.O'\ 0'ICl.L o H _zt OON G\0 co ONI ONONH 0100 HO\c C \ ONC \ o 0- 0 HH HHCO OO \.0 \ \10J- ON 4) E-\ LN LrC ca cQ 0 c0rC Ho Cy Lr ON \O tt tca II 0 0 C o I r I II *I -4 _- (I-^-t -:t -:t-:t- LrU\ Lr, \ Lr\ L4\ Lr\ LrU-\LrN UNLrf\ VNL r,% P^1 \0 \' \10 \'^D \' O \0 \ L= - l- b — Lrf\ 01\ \j O -It.l coj 0 k^0o |00T - =t -^-st -11 0 c c OCJ C)ro g WHH 07\0| H I Lr-\ Lr _ HHj OjHH cc HHCY cm j \. - I \ IO \IH Io \ 0 2S 0' 0 0 0- t- l 0n r 0 0 0 0 \ 0 0 \ \0\ ON 0o 0 o H 0 0 0 0 0 0 0 0 0 0 0 00 ~ ~-P Cc0 11 88 0 -c — 0 j j \ZO\9 co* C) 0 0 -o — t I I o08 8 88 8 0 H H H 0o o OO OH (n Lr\ Ot- co Lr\ Lr\ Lr\ 0 ~ ~ LD I~ CY')t~1; ~l;I~~:'I LE r1!

-22Table VI lists values of the equilibrium constants, calculated from Equation (C-5) (see Appendix C) for the principle dissociation reactions in the high temperature products of a hydrocarbon-air reaction. A derivation of the expression for the equilibrium constant as a function of temperature is presented in Appendix B. The calculated values of the equilibirum constants usuallly deviate less, percentagewise, from their tabulated values than does the maximum percentage deviation exhibited by the heat capacity function of any of the reaction constituents. However, since the calculation for the equilibrium constant involves differences of thermodynamic functions, the percent deviation tends to get larger as.the absolute magnitude of the equilibrium constant diminishes. Because the heat capacity data were taken from several references no strickly comparable tabular values are available. In Tables III, IV, and V, a double entry is made at 1500~K. This is the break point between the two temperature ranges, The first entry is calculated from the heat capacity equations for the lower range whereas the second is calculated from those for the higher range. Any discontinuity at 1500'K could be removed by adding appropriate constants to the fundamental data at the beginning of each temperature range. However, as no particular advantage could be seen in doing.this, it was not done, Appendix C also indicates the proceedure used to calculate (H) and s

-23 -...'l cO Lr COO L\ CM o U) Co 0 L\ * oo 00 Q CM0 0t H i H 0 C0 0 CM L 0 r-H CM 0 CM + H t n 0 0 CO CM CM ON 0 c) H OYN L' O, — C 0 0 PI o I M o 04 C' CM H 1 H 0 0' OH q + H M O Y) L\ 4-P' r-H H LO\ 0 - O CM CM r- O r-I <0 \O CM ) H 0 H,_-~) CM -' 4 *' - o M I0 H 1 r~_ 0 0 p04 \ ~CM H O M O CCM CM CM CO)CM -:i ~ CM o; aL' 0 0 0 0 - O 0L\ C H 0 I1 CM 0 0 0 0 0 0 - O 4 O O O EH C M CM Hd.,

C. The Composition of the Products of Combustion 1. Assumption of Chemical Equilibrium Having developed a scheme by which the thermodynamic properties of a system can be calculated when the chemical composition of that system is known, it is now necessary to investigate the nature of high temperature combustion in order to establish not only what chemical species exist, but also the amount of each. The conditions under which combustion occurs are always idealized for the purpose of calculation and assumptions of homogeneity, steady state, and absence of wall effects are made which then allow the subject to be treated by the methods of steady state thermodynamics. Throughout this work such assumptions were made in determining the composition of the products of combustion. Combustion in an internal combustion engine occurs under conditions which are often far from ideal, Consequently results based on such calculations generally tend to over estimate the performance of the engineo Thus it is necessary to investigate the above mentioned assumptions in order to predict, at least qualitatively, in so far as possible, what effects deviations from these idealizations might have upon the chemical composition of the working fluid and ultimately upon the performance of the engine. Homogeneity It is a long established fact that the mixture in an internal combustion engine is not entirely homogeneous(34). Aside from wall effects, which will be discussed later, the the inhomogeneity arises during the induction of the fresh charge. During this process a mixture of air and both gaseous and liquid fuel in the form of droplets is inducted and mixed ~24

-25with residual exhaust gas. Whether or not efficient mixing occurs depends largely on the design of the carburator, manifold, and inlet valve as well as the engine speed. In any event the charge during compression is composed more or less of pockets rich in exhaust gas interspersed within regions of charge, some of which are richer and other leaner than the measured fuelair ratio. When combustion occurs, the products are hetrogeneous, reflecting the fact that the initial mixture was not homogeneous. Thus, for example, if a stoiciometric mixture of fuel and air were burned, one might expect to find evidence of products resulting from both rich and lean combustion. That is, carbon dioxide and hydrogen as well as oxygen would be present in concentrations in excess of expected equilibrium amounts. David and Leah have an interesting discussion of inhomogeneities caused by improper mixing. The effect of these inhomogeneities, assuming the difficulties of ignition and flame propagation can be overcome, is to cause incomplete combustion of the charge unless the mixture is quite lean. Pockets of unburned or partially burned gas may exist in the combustion chamber. Thus one would expect to find somewhat lower thermal efficiencies and mean effective pressures whenever mixing is not complete. Additional inhomogeneity resulting from the flame propagation process is manifest as a continuousstratification of the burned products. For a discussion of this phenomenon see Brown(35) or Hershey, Eberhardt, and Hottel(10) This subject will be treated more extensively in the discussion of the theoretical model for the internal combustion engine in Chapter VI.

-26Steady State The assumption of steady state is tantamount to the assumption of chemical equilibrium. The implication is that the system, comprising the products of combustion has been allowed to remain in a given state of temperature and volume long enough to reach a homogeneous condition. That is all chemical reactions have proceeded to such an extent that the rate of the forward reaction is just equalled by the rate of the reverse reaction. At this point, the free energy of the system is at its minimum value and no spontaneous change can occur within an isolated system. Thus, because this in an equilibrium state, the composition can be completely determined by the methods of classical thermodynamics, However, if the time available for combustion is short, true equilibrium may not be attained. The time during which the system is maintained at constant conditions is termed the residence time. In an internal combustion engine the residence time, strictly speaking, is zero. The system volume and temperature are constantly changing. Fortunately this change is usually relatively slow compared to the time required to achieve equilibrium. This is especially true during combustion as compared to expansion. To estimate the order of magnitude of the residence time in an internal combustion engine during combustion, one might consider the time required for one degree of crank revolution. During this period, changes in temperature and pressure are not large. For an engine operating at 2000 rpm this time is about 10-4 secondso While it is difficult, if not impossible at this time to quantatively predict the time interval necessary to. reach near equilibrium conditions in a system as complex as the

-27. working fluid of an internal combustion engine, it is known that,at the temperatures and pressures existant during combustion the relaxation times for many of the chemical species present are from 10-6 to 10-8 seconds or less(36 37) Thus one might expect that during combustion the chemical composition of the products could be calculated from equilibrium thermodynamics with very little error. However during expansion, when temperatures and pressures are lower and many recombination reactions are taking place, equilibrium is not always maintained, This condition is termed equilibirum lag. The reactions lag and give rise to compositions which would be considered in equilibrium if the temperature were higher. Not all reactions lag the same amount and for a complex system as in the internal combustion engine, an exact analysis on this basis would be difficult to make and apply. Nevertheless a simple analysis is illustrative of the more complex system behavior. Reference 37 describes a method whereby a pseudo temperature can be found for simple reactions which is suitable for the calculation of nonequilibrium compositions. In the case of recombination reactions requiring a three body collision between molecules A, B, and a third body M the following reaction can be written, Kf A + B + M Kf AB+M Kb where K and Kb denote the forward and reverse reaction rates respectively. f

-28The equilibrium constant Kc for this reaction is, (AB) Kf Kc =. = (A)(B) Kb where the parentheses denote concentrations in moles per unit volume. The resultant expression for the pseudo temperature is (37), [1 + (CvT/AU )] [-TT/ t] T'= T + - Kf(M) [(A) + (B) + l/K ] where T' = the pseudo temperature Cv= the heat capacity at constant volume for the system -AU = the heat of reaction at constant volume aT = the reciprocal of the residence time per degree Kc = the equilibrium constant at T' During the expansion stroke of an internal combustion engine, -6T/6t is of the order of 105 to 106 ~K per second (see Appendix D). Reference 37 suggests the following values for common recombination reactions: -AU from 50 to 150 kcal/mole and Kf about 1011 (moles/liter)2/seco The quantity (1 + CvT/AU) will be between 0 and 1 and consequently T' will be nearly equal to T unless the concentrations of A and B are very small in which case further recombinations will have only small effectso It must be remembered that the above numerical values will change as the state of the system changes and in particular the rate of recombination will become lower as the pressure and temperature of the system are reduced. Moreover other types of reactions occur which under certain circumstances may be quite slow. The decomposition of NO into N2

-29and 02 is an example of such a reaction. Concentration of NO considerably in excess of equilibrium amounts have been observed in the exhaust of both rocket and internal combustion engines. In the analysis of the expansion process in rocket engines where -3T/6t is 107 or 108 (46) chemical equilibrium is normally assumed. Thus the assumption of chemical equilibrium during expansion for internal combustion engine calculations is at least as good as it is for rocket engine calculations. The effect of assuming chemical equilibrium during expansion is to increase the thermal efficiency and indicated mean effective pressure of the engine cycle. This is because the recombination of the radicals releases energy which can be used to do work. There is a temperature, however, below which the rate of reaction is so slow that for all practical purposes no further reaction occurs and the equilibrium is effectively frozen. This temperature varies with the particular reaction. Gaydon(3 ) recommends 1500~K for the reaction CO = 1/2C02 + 1/2Csolid and Hottel(ll) suggests 1600~K for the water gas reaction. Some early studies of Lovell and Boyd(38) suggest 1600-1700~K as the temperature at which the equilibrium freezes in the exhaust of an internal combustion engine. However, 1500~K is used throughout this work as the temperature below which no further changes occur in composition. Wall Effects The presence of a wall can effectively quench a combustion reaction. This phenomenona occurs because the walls absorbe heat or chain carriers, one or both of which must be transferred ahead of the flame to

-530the unburned gas in sufficient quantity to continue the propagation of the flame. Thus in the region near a wall, unreacted or partially reacted quantities of mixture may be found. In an engine this region appears as a layer a few thousands of an inch thick around the inside of the combustion chamber, Daniel(39) presents photographs which illustrate the presents of this layer. It is commonly thought that quenching is a major cause of partially reacted products, such as CH4, in the exhaust. Because this dead space is a region of partially reacted or unreacted mixture, its effect is to reduce the thermal efficiency and mean effective pressure of an internal combustion engine. Summary In summary, inhomogeneities in the original mixture and quenching at the wall result in incomplete combustion of the charge. Even if the charge were completely homogeneous and were all burned, the rate of reaction may be so slow for some reactions that a state of chemical equilibrium is not attained in the products, especially during the expansion part of the cycle. Nevertheless to circumvent the inherent difficulties of treating these deviations from ideality, complete homogeneity and chemical equilibrium will be assumed to exist for the purposes of calculating the composition of the working fluid above 1500~K in the analytical model of the internal combustion engine. Below 1500~K, the composition will be assumed frozen at that composition which existed at 1500~K. These assumptions will always produce calculated thermal efficiencies and mean effective pressures which are higher than those found if the exact composition of the working fluid were used~

-512. The Chemical Composition at Equilibrium a. General The products of a hydrocarbon-air reaction consist of a number of atoms and molecules whose individual amounts vary with changes in pressure and temperature according to the laws of chemical kinetics, subject to the condition that the mass of each basic atomic specie remains constant. When the condition of chemical equilibrium is imposed on the system, the amount of each constituent can be found by purely thermodynamic consideration. For the range of pressures and temperatures encountered in the internal combustion engine, 10 gaseous species must be considered in the products: Reactants Products Specie No. Fuel-CaHb - 1 Air-02 02 2 I-N N2 3 CO2 4 H20 5 CO 6 H2 7 OH 8 NO 9 0 10 H 11 Additional species may be considered such as N, NO2, C, or CH4. However their amounts, calculated from equilibrium considerations, will be extremely small and their contribution to the overall thermodynamic properties of the system will be negligible. In order to establish the amount of each of the 10 constituents 10 equations are required. Since some of these equations are non-linear,

-32an explicit solution can not be obtained and resort must be made to a trial and error solution. Many solution techniques have been developed for such equations. Some are specifically directed at the solution of equations for the combustion of a hydrocarbon fuel with air and some are quite general in scope and are capable of treating systems of arbitrary reactants with solid, liquid or gaseous products. Hershey, Eberhardt, and Hottel (10) as well as Goodenough and Felbeck(8) employed the former, or specific type of solution, to their combustion equations. Vickland(40) analyzed a number of methods, both general and specific, finally adopting a combination of them which was suitable for a computer solution. Huff and Co-workers(41) proposed a method for treating arbitrary reactants and solid, liquid, or gaseous products which has been widely used for combustion calculations. Brinkly(37) proposed still a different method for treating a general system. This method was used by Edson(22), A summary and comparison of the most widely used general methods is presented in Zeleznik(42)o In comparing the rate of convergence for the general methods considered, it was found in Reference 42 that no significant advantage was obtained using any one general method in preference to another. In spite of the availability of numerous methods for computing equilibirum compositions, many of which provide for the simultaneous computation of the adiabatic flame temperature, it was felt that a much more efficient solution might be obtained if a computational method were used which was not general but was explicitly developed to solve only those equations which arise in the combustion of a hydrocarbon fuel with air. Such a system would contain carbon, hydrogen, oxygen, and nitrogen, and be comprised of the 10 listed species.

-33The computation scheme which is illustrated in the following section is based on the work of Ritter von Stein(43). An adaptation of this method for the combustion of a hydrocarbon fuel and air is presented by Schmidt(44). b. Computation of Homogeneous Gas Equilibrium A number of assumptions have been made or implied so far concerning the nature of the products of combustion. The following assumptions are essential to the computation of the gas composition1) The products are in a state of chemical equilibrium. 2) All the products are gaseous and can be treated as perfect gases. 3) The system comprising the products of combustion is homogeneous and is maintained at constant temperature and volume. 4) The fuel is a pure hydrocarbon of the form CaHbo 5) Air is a mixture of 02 and N2. 6) Only 10 species exist in the products. 7) The mass of each basic atomic specie is known and remains constant, The 10 equations necessary to determine the amount of each of the 10 constituents are determined from a consideration of the following: 1) The conservation of mass. 2) The law of mass action, governing chemical equilibrium. 3) The temperature and volume of the system, The Conservation of Mass The reactants are supposed to consist entirely of fuel, C H, and air, 02 and N2, and contain Nc mole atoms of carbon, Nh mole atoms of

-34hydrogen, No mole atoms of oxygen, and Nn mole atoms of nitrogen. Four mass balance equations can then be written between the number of mole atoms of each basic specie in the products and that in the reactants. To determine the number of mole atoms of carbon in the products the following equation can be written: mole atoms of carbon in products = ncO + ncO where n is the number of moles of a particular specie. Re-arranging this equation in terms of partial pressures yields: mole atoms of carbon in products = V/RT(pco + PCO) where T and V are the temperature and volume of the system. Since the mole atoms of carbon in the products must be equal those in the reactants -N = V/RT(PCo + PC Derived in a similar manner the four mass balance equations are~ F * Nc = C02 + CO (2-5) F - Nh = 2H20 + 2H2 + OH + H (2-6) F * N = 2CO02 + H20 + 202 + OH + NO + CO + 0 (2-7) F o N = 2N + NO (2-8) n 2 where F = RT/V and the formula names have been substituted for the partial pressures. The quantities on the right side of the equations are the "atom pressures" referred to by Ritter von Stein.

-535The Law of Mass Action The following reactions are considered to occur among the products. CO2 CO + 1/202 H 20= 1/2H2 + 1/202 OH = l/2H2 + 1/2~2 NO = 1/2N2 + 1/202 0 = 1/2 02 H = 1/2H2 By assuming the products to be perfect gases, the expressions for the equilibrium constants of these reactions can be written in terms of the partial pressures of the constituents. Letting 02 = X2 H2 y2 and N2 = Z2, they are Kj = CO X (2-9) K2 =- (2-10) H2 Y.X K 3 OH (2-11) K 3 X (2-12) K - - (2-13) 5 0 K6 = - (2-14) These six equations together with the 4 mass balance equations must then be solved together for the 10 unknown partial pressures. The equilibrium constants can be calculated by the method of Appendix C, Section 5.

-36Solution By re-arranging and substituting equations 2-9 through 2-14 into equations 2-5 through 2-8, the number of equations to be solved is reduced to four. F * NC = co(1 + -) (2-15) K1 F. Nh = 2(Y2 + Y X) + + (2-16) h K2 K3 K6 F NO = 2(K-9X) + X + 2X2 +- YX+ Z CO (2-17) K K 2 K3 K4 K5 F O Nn = 2Z2 + zx (2-18) K4 Solving Equation (2-18) for the positive value of Z, Z - + ( + FNn (2-19) and Equation (2-16) for the positive value of Y. - K) + K6 + V( + K)+ F 8 [1 + K ]F *Nh (2-20) 4(l + x K2 If Equation (2-15) is then substituted into Equation (2-17), X F-Nc 3 _ S +KY2X 2 + ZX X (2-21) FX 2X+ - + - + F NC + 2-21 0 1 + K 2 K3 K2 4 K1

-37" In light of Equations (2-19) and (2-20), Y and Z are functions of X only. Then Equation (2-21) is only a function of X, since the equilibrium constants are only a function of temperature. It then remains to obtain the positive value of X which satisfies Equation (2-21). A method for doing this is presented in Appendix Ealong with an estimate of the rate of convergence of the method. The quantity X having been determined, Y and Z can be calculated from Equations (2-19) and (2-20). The partial pressures can be calculated from Equations (2-9) through (2-15) re-arranged as follows: 02 = X- (2-22) N2 = Y2 (2-23) co =- FNc (2-24) H^O - XY2 (2-25) K2 co = C02K1 (2-26) X H2 = y2 (2-27) OH = K (2-28) NO = XZ (2-29) K4 0 =j- g(2-30) H Y H = E(2-31) The number of moles of each constituent is the partial pressure divided by the factor'F1. Figures 2a through 2j show calculated mole fractions of the various constituents in the products as a function of the temperature and pressure of the system for a stoiciometric mixture of octane and air. These curves are in good agreement with those of Reference 40.

-38z, ) 0 0 m s x CY e 80 0 0 *C 0 0 -.J _ _ a ).4-, 0\. D 0 o< ~ o\~ o~ 3~ o-xIL IJ?'1\ ~ -_8 -— S^- - r -"- o *sfl^^ o TO go. o To

-390 / t Sf f til 1 X X4 f t It 0 oo t 0 L E 440H so t 80 N011OV8L 310W 0 o 0 0 0 o, 4H 0 0 0 7o _ "0~ o To oNOI1OV.I 310f0

-4o0 I0 \ \ S z 4 its \ C0 PIN ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~4-, o CL \~~~~~~~~~~~~~~~a \ C TO Ot NOLLO'&IA TIOW..-. — _ _ _..- - - - - 1 "4-3 C.)~~~~~~~0 C o Ea ox Irl 0"~~~~~~~~~~. -~~~~~~~~~~~~~~~~~~~~~\ a m - cm \ \ \ ~7 y ^~~~~~~~~ TO~~ ~ *. sO sO'0 NOIl~3yd 310W

-410 -P 0.. - - _ ). - * E _... - - s- 0 0 w(' ~.C CH NO\\\ oz10 w I-\. Sx U ~. NN TO _"o,-o To,o - NOI3VM- 311OW 0 S~X t~ 10 <. NOI13U Y 101 CH 1\ a.^ \v\ ^ t~~~~~.. —_ _ _..-_- _ ^:;:;^_... - _ _ _ ~,~~~~~~~~~~~~~~~~~~~~~~w s'4^ ^, s^^^.50'-^^s^ ^~~C

-42Cd co ~I. V, I II.~ i ll-^.~~~~ _ _... H_.. - _ _C m I hi~ -r-'l

-43In order to calculate the composition at a given temperature and. pressure, rather than volume, a second trial and error solution must be made. If an initial estimate is made of what the volume might be at the given temperature and pressure and the calculations made as above, the total number of moles can be computed. From the number of moles, the pressure and the temperature, a new estimate of the volume can be made and the calculations repeated once more, leading to yet a third estimate of the volume. The entire process can then be repeated a third time and so on until the volumes calculated for any two sucessive iterations are within a specified amount of each other. For a reasonable good estimate of the volume initially, only about two additional iterations are required to achieve agreement in the fifth or sixth digit between two sucessive values of the volume. c. Computation of Frozen Equilibrium The products of combustion below 1500~K are assumed frozen. In addition to the assumptions made in connection with homogeneous gas equilibrium in Part 2 of this section the following additional assumptions are made for frozen equilibrium; 1) The composition of the products is frozen at the equilibrium composition which would exist at 15000K. 2) For lean and chemically correct mixtures, only 02, N2, CC2, and H20 are present. 3) For rich mixtures, only N2 Co2, H20, CO, and H2 are present,

-44Lean and Stoiciometric Mixtures For the calculation of the composition of lean and stoiciometric mixtures under the assumption of frozen equilibrium the mass balance equations are: F - N = CO2 c 2 F * Nh = 2H20 F - NO = 2C02 + H20 + 202 F o Nn = 2N2 Finally, the partial pressures of the constituents areCO = F - Nc (2-32) lH2 = F * Nh/2 (2-33) 02 = F. No/2 - F' Nh/4 - F N (2-34) N2 = F ~ Nn/2 (2-35) where the absolute value of the partial pressure of the oxygen is taken to avoid the possibility of an extremely small negative value of this quantity occurring near the stoiciometric point due to round-off errorso This consideration applies to computer solutions onlyo The number of moles of each constituent is its partial pressure divided by'F'. Rich Mixtures For the calculation of the composition of rich mixtures under the assumption of frozen equilibrium the mass balance equationsare: F c Nc = C02 + CO F ~ Nh = 22{2 + 2H2

-45F * NO = 2C02 + CO + H20 F Nn = 2 * N2 The following reaction is assumed to occur among the products of rich mixtures at 1500~K H20 + CO = CO2 + H2 The expression for the equilibrium constant of this reaction is CO2 ~ H2 K = H0 - C (2.36) As this reaction involves no change in the total number of moles, the computation at a given temperature and pressure is equivalent to that at a given temperature and volume. And in fact, the reaction is independent of the pressure of the system. Therefore the composition of the products depends only on the temperature. As a result, fixing the value of the equilibrium constant fixes the composition. Whenever the composition of the products is to be calculated when the temperature is below 1500~K, K is given its value at 1500~Ko This freezes the reaction at the temperature level. Letting Z = CFc and substituting the mass balance equations in the equation for the equilibrium constant, 1/2 Nh No + 1 + 1/Z Nc Nc K = --- ( 1 - 1/Z) (Z - 1) -C

-46At 1500 ~K K is 03747(29). Solving the above equation and substituting the value of K, 2 6.6752 (2-37) where (1+ Nh (1 + o.7494 4 No) 6 c =........ -- - -1.6688 UNO 1 The partial pressures are: CO= Fe Nc (2-38) 02 z H20 = F(No - Nc) - Co2 (2-39) co = |F N N- Co02 (2-40) H2 = |F I' H20l (2-41) N2 =F * (2-42) 2 Again absolute values are taken to assure that near the stoiciometric point no small negative partial pressures can be calculated due to round-off errors. The number of moles of each constituent is its partial pressure divided by'F'o 3. Computer Solution of the Equations of Chemical Equilibrium The solution technique developed in Part 2 and Appendix E has been programmed on a digital computer. A flow diagram for this program, is shown on Figure 23. Appendix E includes a discussion of many important features of the solution. A listing of the program written in the MAD language as an external function called AMOUNTO is included in Appendix I,

III. SIMULATION OF THE FUEL-AIR ENGINE CYCLE ON A DIGITAL COMPUTER A. General As the initial step toward the development of an improved model for the analysis of the internal combustion engine which could ultimately be programmed on a digital computer, the constant volume fuel-air engine cycle was programmed. The details of the mathematical analysis and computer program are included in Appendix F. The techniques developed in Chapter II have been used to calculate the composition and thermodynamic properties of the working fluid. The fuel-air cycle is composed of the following idealized processes (see Figure 3). Process 1-2. An isentropic compression of the working fluid from volume V to V2o Process 2-3. An adiabatic constant volume combustion, Process 3-4. An isentropic expansion of the working fluid from volume V2 to Vio Process 4-4. A further expansion to the exhaust pressure. That portion remaining in the cylinder undergoes an isentropic expansion, Process 4-5. A constant pressure adiabatic expulsion of the burned gas leaving some redual exhaust gas in the clearance volume. Process 5-1. An adiabatic induction and mixing of the fresh charge with the residual exhaust at the intake pressure, thus completing the cycle. -47

-483 U. a- 5.. I, 4'I VTOP VBOT. VOLUME Figure 3. Indicator diagram for the fuel-air cycle engine at part throttle.

-49The following assumption were made: 1. There is no chemical change in either the fuel or air prior to combustion. 2. After combustion and during expansion, the products are in a state of chemical equilibrium. 3. Equilibrium is frozen below 1500~K. 4. All processes are adiabatic. 5. There are no irreversible fluid flow effects. 6. All valve events occur at top or bottom centero A complete description of this cycle may be found in References 10 and 45. Calculations made using similar analytical models can be found in References 7, 9, 10, 11, 22, and 45. Reference 22 is of particular interest as the calculations were made on a digital computer. In as much as a great body of calculations already has been reported using the fuel-air cycle engine model, only selected values of the computer computations will be presented here. These deal with the effects of lean mixtures and high compression ratios on thermal efficiency and mean effective pressure. They are of special interest in light of the increasing effort to raise compression rations and utilize leaner mixtures in internal combustion engines. Thermodynamic charts available for the calculation of the fuel-air cycle are constructed for mixtures no leaner than 120 percent theoretical air and allow computations for compression ratios up to about 20 to 1(!) Both Tizard and Pye( and Goodenough and Baker(9) presented results of calculations for the effect of very lean mixtures on thermal efficiency. However these results are based upon now outdated heat capacity and dissociation data and their analytical models differ somewhat from that employed here.

-50B. Results and Discussion Figures 4 and 5 are plots of the results calculated by the aforementioned computer program for the fuel-air cycle engine. Figure 4 shows the effects of both compression ratio and air-fuel ratio on the thermal efficiency and mean effective pressure of lean octane-air mixtures. As the mixture becomes leaner, the efficiency approaches that of the aircycle, Equation (1-2), where'k' is 1.4 for air. It has been proposed by both Tizard and Pye and Goodenough and Baker that the thermal efficiency of the fuel air cycle can be expressed as e = - (l)n where'n' is a quantity derived from fuel-air cycle calculations. Goodenough and Baker proposed, for lean octance-air mixtures, that n = 0.3867 - ~ —-- 0.043 lOOx- 35 r where'x' is the fraction of theoretical air and'r' is the compression ratio. In order to better fit the curves of Figure 4, this expression was modified slightly. The modified expression, n = 0.374 0.1 o.o3 (3-1) x r will approximate the thermal efficiencies of Figure 4 within 005 percent. Figure 5 shows the influence of compression ratio on the thermal efficiency and mean effective pressure of a lean octene-air mixture for compression ratios up to 30'1. Edson(22) reports similar calculation for ratios up to 300:1 for a number of fuels and fuel-air ratios, Thermal efficiency and mean effective pressure continually increase as compression ratio is increased. Equation (3-1) is a good approximation for the thermal efficiencies of Figure 5o

-5170, 280 E THERMAL EFFICIENCY - - MEAN EFFECTIVE PRESSURE _ 60 -- — Al RCYCLE^^ C ~ x 3 d240 ~ 50 -— __ 1:1"^^^fM^^^-^^j^^ =1.4 200 m 30 1 -- - 120 Fuel - octane, T16 = 520~F, P a P 1 atm. Fuel - octane, Ti = 520~F, Pi = Pe = i atm.

-5280.-o -300 70 ------ 280 S50 - - -- - - -- -240 z U, 30 --- 200 20 18 6 10 14 18 22 26 30 COMPRESSION RATIO Figure 5. Efficiency and mean effective pressure vs compression fatio for a mixture of octene and 110 percent theoretical air. Fuel-air cycle analysis. Ti = 520, Pi = Pe = 1 atm.

IV. COMBUSTION IN A SPARK-IGNITED ENGINE Whereas the fuel-air cycle incorporates many important features of the internal combustion engine, it totally disregards two phenomena which are of primary importance. These are the progressive burning of the charge and the heat transfer. Prior to a discussion of their inclusion into the analytical model for the internal combustion engine described in Chapter VI, some discussion of the nature of each is warranted. This chapter deals with the nature of the combustion process and the following chapter deals with that of the heat transfer. A. General The combustion process in an internal combustion engine has been investigated photographically and by other methods. The studies of Rassweiler, Withrow, and Cornelius(16, 17 and 18) reveal that in normal combustion the spark induces a kernel of flame which subsequently propagates regularly in all directions. Their photographs show that during combustion two distinct gaseous regions exist in the chamber, a region of burned gas surrounded by a region of unburned gas. The two regions are separated by a definite reaction zone. This reaction zone or flamefront, as it is often called, is generally a spherical shell during the early stages of combustion but becomes distorted as it approaches the wall and tends to assume the shape of the combustion chamber. The apparent rate of flame propagation in an engine is very high. This is due to both the reaction rate and the expansion of the gases during the combustion process. At the beginning of combustion, the expansion rate is high compared to the reaction rate whereas at the end of combustion.53.

-54r it is lowo The fundamental quantity to be investigated is the flame front motion due to the reaction only. This is the flame propagation relative to the unburned gas. The remainder of this chapter is devoted to obtaining a general expression for the rate of flame propagation in an internal combustion engine. By necessity a number of assumptions have been made in order to simplify the equations involved. Perhaps the most serious of these are those of steady state and one dimensionality. Thus it must be recognized from the outset that the equation presented for the rate of flame propagation is only approximate. Its validity can be determined only by a direct comparison of calculated with experimental burning rates which can be done indirectly through a comparison of calculated and experimental pressure time diagrams for a particular engine. B. Flame Propagation Two regimes of flame propagation are recognized. the laminar and the turbulent. Laminar combustion is characterized by a well defined narrow flame front and a relatively low rate of reaction. Turbulent combustion is characterized by a less well defined thicker flame front and a much higher rate of reaction. Three somewhat separable modes of turbulent flame propagation have been observed (47 48) They are~ 1, Weak turbulence which wrinkles the continuous laminar flame front, thereby causing a higher effective rate of reaction due to the greater surface area through which the basic transport phenomena can occur;

~55~ 2. Stronger turbulence which disrupts the laminar flame front and creates a distribution of centers of deflagration which can be treated statistically; 3. Still stronger turbulence which shows its effects by locally diluting and preheating the initial centers of deflagration, such that a homogeneous reaction results in the limito Observed and calculated rates of flame propagation in internal combustion engines indicate that the combustion is in the turbulent regime (see Rabezanna, Kalmar, and Candelise(l9)). However little quantative information concerning the nature..-of the turbulence in internal combustion engines exists. Semenov(49) presents the results of some experimental studies which show that the turbulent fluctuations vary from point to point in the cycle, but sheds no light on the nature of the turbulence. A number of theories have been advanced to explain turbulent flame propagation (see Reference 50). Only the first mode of turbulent flame propagation has been studied analytically. Such studies generally assume that the turbulent buring velocity is related to the laminar velocity by a factor which is proportional to the level of turbulence in the reaction zone. The theory of Scurlock and Grover(51) one of the most recent, assumes a one dimensional steady state situation in which premixed fuel and air are fed.'. into the reaction zone at a rate such that the zone itself remains fixed relative to the source of the gas. As the level of turbulence is increased, the flow rate must be increased in order to prevent the reaction zone from moving upstream toward the source. The velocity at which

~56the premixed gases approach the reaction zone is equal in magnitude and opposite in direction to the flame propagation velocity. Scurlock and Grovers' analytical model assumes that the laminar flame front is wrinkled by large scale turbulence like that of the first mode. Figure 6 illustrates this wrinkling. The theory assumes that in this type of turbulent combustion the fundamental transport phenomena remain unchanged and hence the laminar flame speed normal to the flame front is unchangedo The increased rate of flame propagation due to turbulence is presumed to be caused only by the larger surface area over which the reaction can proceed. The wrinkles in Figure 6 are assumed to be cones with an average height proportional to, the root mean square displacement of a flame element from its mean flame front position, and an average base width proportional to Lu,the Eulerian scale of turbulence. The ratio of turbulent to laminar flame speed, derived from purely geometric considerations, is St At [ 11/2 ( ) -t =At = l 1 + k3 ( (4-1) S A L1 where k3 4kk/k2. Scurlock and Grover consider three effects which are -2 believed important to a determination of Y o These are eddy diffusion, flame propagation, and flame generated turbulence. Bolz and Burlage(48) have successfully used the theory of Scurlock und Grover to predict the growth of flame kernels in turbulent flow issuing from a jet. Mickelsen and Ernstein(52) in a similar experiment found good agreement between flame speeds obtained experimentally and those predicted by the theory of Scurlock and Grover over a range of fuel-air ratios and levels of

-57Mean flame position kI l rkld tuul Smooth laminar Wrinkled turbulent flame front flame front Figure 6. Wrinkled flame front model of Scurlock and Grover 5)1 turbulence. However the theoretical values were always higher than the experimental ones. They found that turbulent flame speed is a statistical quantity. Moreover their results indicated that the rate of laminar to turbulent flame speed (at least for propane) is not strongly dependent on fuel-air ratio, Because quantitative information about the nature of the turbulence in the working fluid of an engine is not available, none of these theories of turbulent flame propagation can be applied directly. However a relationship between the laminar and turbulent flame velocity

-58can be made. Namely, = K (4-2) Se where K is a quantity dependent only on the level of turbulence in the reaction zone. K must be determined from experimental data and is only valid for a given mean level of turbulence. Now it remains to find an expression for the laminar flame propagation velocity, The principle mechanisms of flame propagation are the transport of heat and active radicals from the reaction zone to the unburned gas ahead of the flame. A number of theories which take into account one or both of these mechanisms have been advanced to predict laminar propagation velocity (see Reference 50 and 53). Comprehensive theories which take into account both phenomena are difficult to apply and require information about reaction kinetics which is not known for many reactions. Hirshfelder et al. (54, 55) ( 55) have proposed such a theory and have applied it to a few elementary reactions. In a number of investigations of the burning velocity of hydrocarbon-air mixtures, less complex theories predict burning velocities which often agreed closely with experimental ones. In particular two theories have been widely employed for several investigations (for example Reference 58, 59, 60, and 61). One is the theory of Tanford and Pease(57) which predicts the velocity from a consideration of the concentration in the reaction zone of certain chemical species, such as H, O, and OHo These are supposed to act as agents to initiate and propagate the reaction. The other is the theory of Semenov(56) which predicts the burning velocity from purely

-59thermal consideration. Reference 60 reports particularly good agreement between experimental values and values calculated from the two theories for the maximum burning velocity of iso-octane-air mixtures at one atmosphere pressure over a range of widely different initial mixture temperatures. Whereas the two theories are based on seemingly unrelated phenomena, the consensus of opinion appears to be that no particular advantage is gained using one of these two simplified theories in preference to the other unless it is definitely known that the basic mechanism of the reaction in question favors one model. In general, equally good agreement has been obtained with either theory. In light of the above discussion a decision was made to use the thermal theory of Semenov to predict the laminar burning velocity of the hydrocarbon-air mixtures considered in this current study. Reference 59, 60, 62, and 63 treat the reaction between a hydrocarbon such as iso-octane and air as second-order bimolecular. Clarke(62) reports experimental work which shows this reaction to be bimolecular up to 23 atmospheres. C. Thermal Theory of Flame Propagation for A Bimolecular Second-Order Reaction Because the thermal theory of laminar flame propagation is so important to the results calculated from the analytical model of Chapter VI, a general development of this theory is made here for a bimolecular secondorder reaction. The original full derivation of this theory is in Reference 56. References 50 and 53 review the derivation. The thermal theory of flame propagation assumes a one dimensional steady state combustion model (see Figure 7). The reaction is propagated solely by the heating of the unburned gas in Zone I, initially at tempera

-60-FLAME p,, —-—'\ u, poU- z - pi u, REACTANTS PRODUCTS PREHEAT -REACTION ZONE - ZONE I I w I I XIr)~~~ l I-T -- ---- 0 To OD_ O 0 d + CO — DISTANCE, x Figure 7. Schematic diagram and temperature profile in the region of the reaction zone.

-61ture T, to a temperatureTi at which point the reaction begins. The reaction occurs completely in Zone II, wherein the temperature is raised to TL 1 The width of the reaction zone is'd'o Beyond Zone II no further reaction occurs. The notation below is used for the derivation which follows. Q' heat of reaction, cal/molecule of reactant c constant pressure heat capacity, cal/gm-OK p w rate of reaction, molecules of reactant/cm3-sec a concentration of fuel, molecules/cm3 b concentration of oxygen, molecules/cm3 P steric factor Z impact coefficient, number of collisions/cm3-sec d depth of reaction zone, cm M mass rate of flow. gr/cm2-sec; molecular weight p density, gr/cm3 D diffusion coefficient, cm2/sec X thermal conductivity, cal/cm-sec-~K The general equation for a bimolecular second-order reaction is c = ab a P ~ Z ~ exp (E/RT) (4-3) The following assumptions are made in connection with this theory; 1. Pressure is constant. 2. c and X are constant, 3. X/c = Dp (which is exact for the diffusion between two ideal gases whose molecules have the same size and weight).

-624, The total number of molecules is constant, 5. Below some temperature, Ti, which is near T the reaction rate is essentially zero. 6. In Zone II, the convection term in the energy balance equation is small with respect to the conduction and heat generation terms. The basic equations in Zone II are as follows Continuity equation for the fuel d a da Dp — - M- + a = O dx2 dx (44) ao= a PO P Energy equation X d2 cp dx2 dx (4-5) 3 = cp(T - T)/Q Equation of state p/p0 = T/T (4-6) Conservation of mass M = p pU = US = pS (4-7)

-63The boundary conditions for these equations are~ For x = - a = O, 0 = 0 (4-8) For x = +,o a = e = c (T- T0)/Q' (4-9) 0 p PO In consideration of assumption 3 Equations (4-4) and (4-5) are identical in form and have identical solutions if a and e coincide over the entire reaction zone. That is cpT + aQ'/p = cpTo + aoQ'/po = CpT1 (4-10) This means that the sum of the thermal and chemical energies per unit mass of mixture is constant in the reaction zone. Since this is approximately true, the differential Equation (4-4) can be replaced with the algebraic Equation, (4-10). Only the differential Equation (4-5) must now be solved. In light of assumption 6 Equation (4-5) can be rewritten d2T + =0 (4-11) dx2 X where at x = 0, T = Ti and at x = d, T = T. In region I, c = 0 according to assumption 5 and the energy equation is X dT d 0= (4-12) cp dx2 dx where at x =- oo, T = TO and at x = O, T = T. The condition which determines the value of'M' is that the heat transferred from Zone II to Zone I is equal to that received by Zone I.

-64That is, at x = 0 (dT) (dT) (4-13) dx 0,1 dx 0,II Solving Equations (4-11) and (4-12) and equating their derivatives according to (4-13.), the following equation is obtained - M 1 (4-14) Po cppO(T1-TO) where 1 Tj 1 T I = dT - dT (4-15) a0 To ~ 0 Since T. is assumed to be near T1, the reaction rate, Equation (4-3), can be approximated in order to facilitate the integration of Equation (4-15). The approximate equation is elld 2 = ab P Z exp(-E/RT1). exp(-aE/RT) (4-16) where a = T - T. From Equation (4-10) a _ Ta (4-17) ao T(T1-TO) Semenov suggests that for a lean mixture the concentration of 02 in the reaction zone can be approximated by its value in the combustion products. This quantity is b= T0 aT ) (4-18) T

-65Dugger and Simon(58) have performed the integration in an approximate manner. Their results are as follows2 m1 T RT1 1 (D dT - aefb * Z ~ - -1 exp(-E/RT1) (4-19) elfbeff E where 0, the equivalence ratio, is the ratio of the actual fuel-air ratio to the stoiciometric fuel-air ratio. For lean mixtures, X < 1, 2 aeff = T0 RT1/E beff = bo 1 ( 1 For rich mixtures, the roles of the a's and b's are reversed aeff = aoO 1 -- ( 1 RT/E) 2 TO RT1/E eff 0 T1 T1-TO The quantity'Z' is proportional to the square root of temperature and is (Reference 50, p. 151) z (dcolf + dcol,02) 8 T (Mf + M2 2 MfM 2 where dcol is the effective collision diameter and M is the molecular weight.

-66Semenov later relaxes some of the restrictions in assumptions 2, 3, and 4; -/Dp is allowed to assume any constant value not necessairly P unity; X is allowed to have the value 1/cp in Zone II; and the number of moles of products to the number of reactants can be the ratio no/n1. With the above considered, the final equation for ithe laminar flame propagation velocity'f a second-order bimolecular reaction is \/2 x1 dT n 2 x 2 s - -() (4-21) a 010 C7(T~rTO) 1 Because of the assumptions involved in the integration, Semenov concludes that for a bimolecular reaction, Equation (4-21) is valid for values of RT /E < 0.1o However recent investigations have demonstrated the reliability of the equation.for values of RT1/E up to 0.15 (5 59' 0) D. Use of the Thermal Theory Equations to Predict Turbulent Flame Propagation Velocity According to Equation (4-2) St = K * Sy (4-22) where Sl can be calculated from Equation (4-21). Because of the unknown constant in Equation (4-22), Equation (4-21) can be considerably simplified by factoring out those quantities which are themselves constants and by expressing other quantities as being proportional to the reaction temperature. In using Equation (4-21), Dugger and Simon(58) suggest that the thermal conductivity be expressed as the following function X = (:C + 5/4R)~/M k:p

-67and the diffusion coefficient as D = 1.336 4/p where t is the viscosity and M is the molecular weight. Dugger(61) proposes that the viscosity can be approximated by the following function of temperature: OC T0o67 Then,/Dp = (1 + 5/4 R/Cp) p p and X OC (C + 5/4R)/M 9 T0~67 p If Cp is approximated by its value at the flame temperature, c, then 7 0 67 T( / S V ap(T-TO) (1) (1 + 5/ 3 (423) The remaining quantities in Equation (4-23) can be calculated by the methods of Chapter II or are known from the initial state of the mixture. The final expression for the turbulent flame speed is 3.17 aeffbeffTl exp(-E/RT ) n3 2 R =S K1.iT. - ---- o (-). (1+5/4 - )3 (4-24) aoP (T1-To) n C

-68where K1 is determined from experimental data as explained in Chapter VI. K1 is proportional to the level of turbulence in the reaction zone. For a given value of K1, Equation (4-24) is valid for predicting the turbulent flame propagation velocity for a situation or variety of situations in which the level of turbulence remains substancially unchanged.

V. HEAT TRANSFER IN A SPARK-IGNITED ENGINE A, General There is no question that the heat transferred from the working fluid of an internal combustion engine measurably lowers the thermal efficiency and power output of the engine. Thus it is an important quantity to consider when analytically studying internal combustion engines. Various investigators have attempted to estimate the magnitude of this heat loss, However since the amount of heat transferred depends a great deal on the engine speed, size, combustion chamber geometry, compression ratio, and operating conditions; as well as the coolant type, temperature, and flow rate; there are often large differences between these various estimates. Lanchester(64) estimates the heat loss from the hot gases during combustion and expansion to be about 10 percent of the heat combustion of which 40 percent of this is lost during combustion. Janeway(65) estimates this heat loss to be 16 to 25 percent of the heat of combustion, depending on the speed, of which a fourth or a fifth is lost during combustion. David and Leah(20) suggest that the heat loss, expressed as a percentage of the heat of combustion, is 1500/N and 7500/N during combustion and expansion respectively where N is the engine speed in revolutions per minute. Pye(66) estimates that during expansion the heat loss is 10 percent and during combustion is 5 percent of the heat of combustiono Ricardo (6) suggests that 6 percent is transferred during combustion and 7 percent during expansion. How much reduction of the thermal efficiency and mean effective pressure of an engine this heat loss effects depends on the crank angle at ~69"

-70which it is transferred. Energy lost near the top center piston position is completely lost in so far.- as any useful work production in concerned. If an engine without any heat losses has a thermal efficiency of 30 percent and then 5 percent of the heat of combustion is lost at top center, the. thermal efficiency will be only 25 percent, a drop of 16 percent. The power output will be reduced by a like amount. However the same heat loss occurring later in the cycle, during expansion, effects a lesser reduction in the thermal efficiency and power output since some work has already been done prior to the decrease of internal energy due.to the heat transfer. Taylor(45) estimates that the reduction in power and efficiency due to heat loss during combustion.and expansion is about 10 percent of the equivalent fuel-air cycle power and efficiency. It is generally agreed that the magnitude of the heat transfer during compression prior to combustion is much smaller than that during combustion and expansion. To a first approximation the compression process can be treated as adiabatic. In addition to the heat transferred directly from the working fluid during compression, combustion, and expansion, additional heat is transferred to the coolant primarily during the exhaust stroke and as a result of piston friction. Because this study is mostly concerned with the analysis of the compression, combustion, and expansion processes, these additional heat quantities are not considered, The heat transferred from the working fluid to the cylinder surfaces is primarily convective in nature, although some (estimated to be 5 to 10 percent of the total) is lost by radiation. The radiation losses will be discussed later in this chapter. A number of investigators have found the principal heat transfer mechanism to be turbulent forced

-71l convection, an observation which correlates well with the nature of the flame propagation described in Chapter IV. These investigators correlated the average gas side Nusselt number with the Reynolds and Prandtl numbers as is commonly done with forced convection through tubes or over flat plates etc (68) This relationship is hL = (GL)a (Ckp)b k ( k where hL L = Nusselt number k GL GL = Reynolds number C. pc = Prandtl number k and C, a, and b are experimentally determined constants. Pinkel(69) developed a method for determining the average heat transfer coefficient in an internal combustion engine which is based upon this forced convection theory. This method with some modification has been used successfully to predict average heat transfer coefficients in many investigations (69, 70, 71, 72, 73, 74, and 75). Taylor(45), Chapter 8, describes this theory completelyo After examining experimental results from 16 different engines, Taylor and Toong(75) proposed the following expression U- = 10.(Re )~075 (5l1) g

-72Ue is the overall average heat transfer coefficient and Reg, the gas side Reynolds number, is equal to Gb/i, where b is the bore and G is the time averaged mass flow into the cylinder divided by the piston area. While these investigations shed light on the overall heat transfer process, showing that forced convection is the predominate heat transfer mechanism, they yield no information about the instantaneous heat transfer rates or how the convective heat transfer coefficient depends upon the state of working fluid. Analytical solutions which consider the multi-dimensional nature of the problem as well as the variation of the heat transfer coefficient can not be obtained. However an analytical solution based on a simplified one dimensional model with a constant heat transfer coefficient can be obtained and does yield a great deal of information about the nature of the forced convection. B. Convective Heat Transfer in Engines 1. Temperature Distribution and Heat Flow in a Finite Plate in Contact With a Uniform Medium Whose Temperature Varies Periodically To a first approximation, the working fluid in an internal combustion engine can be assumed to be contained in a hollow cylinder capped at both ends by flat plates. Dahl(78) has shown that in considering the temperature distribution in a hollow cylinder, the curvature may be neglected for many practical applications. If the ratio of the outside to the inside cylinder radius, ro/ri, is less than 1,49 the error in neglecting the curvature is approximately 25(rO/ri-l) percent. For the internal combustion engine, where the radius ratio is only slightly greater than one, the error in neglecting the curvature will probably notexceed 3 percent~

-73Thus the one dimensional flat plate analysis is equally valid for any combustion chamber surface which is either thin walled or has little curvature Figure 8 shows the model upon which the heat transfer analysis is based. It has the following characteristics. The wall temperature on the coolant side, T, is constant. This approximation has been born out by experimental studies. The gas temperature varies about its mean value, T, cosinusoidally. For this one dimensional situation, the equation for heat conduction in the solid wall is(78) d2T 1 dT (5 (5-2) dx2 a dt where a = cpp/k. This quantity is approximately constant over the rage of temperatures experienced by the wall and is assumed to be constant for the solution. The gas temperature is presumed to vary as Tg = To + ecos (t) (5-3) The solution of this problem for large values of time is composed of the sum of two solutions, the steady state and the steady periodic. That is, T(x,t) = TS(x) + Tp(x,t) (5-4) The boundary conditions are T(d,t) = T -k dT(o = h [To + ecos(ct) - Ts(O) T(Ot) (5-5) ax L'

-74GAS COOLANT SIDE SIDE 0 217 Tg To + 8Co~s(wt) \ / MEAN TEMPERATURE' PROFILE d WALL Figure 8, Heat transfer model for the internal combustion engine.

_75By considering the solution at large values of time, the transient starting solution is eliminated as well as one boundary condition, leaving the two boundary conditions (5-5). To obtain the solution (5-4); the boundary conditions(5-5) can be broken up into two pairs, one for each solution. For the steady state solution, the differential equation is d2T dx2 (56) and the boundary conditions are T,(d) = T, alT (0} r l (,5~7) -k dT = h To - Ts(0) dx. The solution of (5-6) with these boundary conditions is easily obtained as h(d-x)/k Ts(x) = Tc + LTo - Tc hd/k + 1 (5-8) For the periodic part, the differential equation is d2T 1 dT =_ - p (5-9) dx a dt and the boundary conditions are Tp(,t) = 0 kdT (Ot) [ d-k -'i = h 9cos(ct) - T(0,t) (5-10) dx i P

-76The first boundary condition is approximate only. However it will be seen later that the temperature fluctuations in the wall are damped out so quickly that the wall need not be very thick to approximately satisfy this boundary condition. The solution of this equation, according to Jakob(79) is T (x,t) = e ~emxcos(wtt - mx ) where 1 =1 2 (3-11) 1 + 2m/b+ 2m/b o = tan b/m and m - 2V 2a b = h/k The complete solution is T(xt) =+ Tc b + 1 + TOTe cos(wt - mx - ) (5-12) Jakob(79) presents a table of rq and E for various values of b/m. By substituting some typical numerical values for iron in Equation(5-12), the temperature distribution in an engine wall can be approximated. For iron, a = 0.5 ft2/hr and k = 36 Btu/hr-ft2-OF(80), A typical engine wall thickness is 0.25 in and speed is 2000 rpm or 4000.,, radians per min. The gas side heat transfer coefficient varies a good deal, but during the early portion of the expansion stroke, a value of 360 Btu/hr-ft2-~F is

-77representative(77). Thus b = 10/ft, m = 700/ft, E - t/4, and rT = 0.01o The average coolant side surface temperature is constant at a given point on the wall and 220~F is a reasonable value when the coolant is water(77) If e is 2000~F and TO is 2060~F, Equation (5-12), with the above numerical substitutions, is T(x,t) = 220 + 1840 (0.208 - ox) 1.208 + 20e-700Xcos(4000 t - 700x- r/4)~F A number of conclusions can be drawn immediately: 1. At the wall (x = d = 0.25/12 ft) the boundary condition is satisfied. The temperature fluctuations are reduced by a -factor of e+14~5 which is approximately 10+8. Thus treating the wall as a very thick plate for the purposes of obtaining the periodic part of the solution is a good assumption. 2. At the wall (x = 0) the. fluctuations are reduced to 1 percent of those in the gas or to 200F for the present exampleo This magnitude is in excellent agreement with experimentally measured temperature fluctuations reported in References 77 and 81. 3. At the wall (x=0) the fluctuations lag those in the gas by 45~. Because of the great simplification in the gas temperature fluctuation made for the derivation of (5-12), the 45~ figure is too large. Although this lag is always a positive quantity it is considerably less than 45~. The data of (82) Oguri(82) indicates that half this value may be a better estimate,

-784, The average surface temperature (x = 0) is about 540~F. This is much too high and reflects the fact that the temperature fluctuations are not cosinusiodal in nature. The relatively low temperatures during the exhaust and induction processes greatly reduce the average surface temperature appreciably. For a water side wall temperature of 220~F, Reference 77 reports a gas side wall temperature of 300~F. This value varies somewhat from point to point on the wall. Thus while Equation.. (5-12) must be recognized as being very approximate, it yields wall temperature distributions which at least reflect the more complex processes occuring within the cylinder. It shows that the average wall temperatures are much lower than the average gas temperatures and that the temperature fluctuations in the wall are a miniature replica of those in the gas. The heat transferred to the wall per unit area is q/A = -k ~ ( t) = kT Tcj bd — + 2mecos(ct —/4) (5-13) dX This equation.shows that the heat transfer is composed of a steady part plus a periodically varying part which is positive as often as it is negative. Substituting numerical values q/A = 36- 15250 + 19750cos(wt) = 350Btu/ft2-sec (maximum)

-79A number of conclusions can be drawn immediately: 1. The periodic term is of the same magnitude as the steady state term and during periods of low temperature some heat is transferred from the wall back to the working fluid (for example during the compression process). Thus the wall acts as a sort of flywheel in this respect, 2. For the cosinusoidal gas temperature variation assumed, the heat transfer fluctuations are in phase with the temperature fluctuations of the gas. However because of the many simplifications introduced into the solution this phase relationship is not exactly correct and in fact the gas temperature fluctuations will lead the heat transfer fluctuations by a few degrees. 3. The heat transfer rate calculated in the numerical example, 350 Btu/ft2-sec, compares favorably with the magnitude of the rates measures experimentally in Reference 77 for comparable engine operating conditionso A more complete solution of (5-2) can be made if it is assumed that the gas temperature varies as a Fourier sine and cosine series as follows 00 r Tg = T0 + n Ancos(mt) + Bnsin(rwt) (5-14) where TO is still the time averaged gas temperature. The complete solution

-8ois T [T 1 b(d-x) T(x,t) = T + To -T b -+ C bd + 1 (5-15) + Z e m x Ancos(.ots: - m'x)+Bnsin(not - - -m'x)] where m' = The other quantities remain the same as they were in Equation (5-10) except that m is replaced by m' in every case. If, in an actual engine, the heat transfer fluctuations and the gas temperature fluctuations are not out of phasetoo much, which appears to be the case (see Oguri(82)), then to a first approximation the heat transfer rate can be expressed as q/A = h(Tg - Tw) (5-16) where Tw is the average wall temperature and Tg is the instantaneous gas temperature of that gas in contact with the surface A, Since it has been shown that Tw is approximately constant at a point on the wall even for widely fluctuating gas temperatures, Equation (5-16) should predict the rate of heat transfer reasonably well when the appropriate value of'h' is employed in the computation. 2. The Convection Heat Transfer Coefficient The applicability of the exact solution of the preceeding section is limited, in part, due to the wide fluctuation in the value of the heat

-81transfer coefficient in the working fluid of an internal combustion engine. It may vary by as much as a factor of ten during the cycle. A number of investigators have attempted to express this variation in terms of the temperature, pressure, and density of the working fluid. Of the several expressions in the literature, two are of special interest. Nusselt(83) was among the first to formulate an expression for the heat transfer coefficient in an internal combustion engineo His expression, based on experimental observation, included radiation as well as convection effects. It is 4 4 5- = 0.99) (T/100)- (TW/100m2) o2 h =0. 99 P2 (1+1.24w) + 0.3562 w kcal/m2hr-OK coneco T - Tw convection radiation ~5-17) where'w' is the average piston speed in meters per sec. Eichelberg(8l) also deduced a formula from experimental data for the heat transfer coefficient. It is h = 2.1 N/ HP kcal/m2-hr-~K (5-18) Although these two equations are somewhat different in form, they have certain features in common. For example, both depend on the temperature and pressure of the working fluid and the engine speed. Moreover since the cycle temperature and pressure vary in a similar manner the square root of PT and the cube root of P2T tend to predict similar variations in the.eat transfer coefficient. (82) heat transfer coefficient. Oguri(82) reports that for'w' in the range of 4-6 meters per sec,, both expressions give comparable values of h over the compression, combustion, and expansion processes. Some recent investiga

_82tions have employed the expression of Eichelberg to predict heat transfer coefficients. Vincent and Henein(85)used Eichelberg's equation to predict thermal loadings of diesel engine cylinder walls. Overbye and Co-workers(^) determined'h' for a wide range of engine operating conditions. However not particularly good agreement between experimental and calculated values of'h' was found. On the other hand Oguri( reported reasonably good agreement between experimental and calculated (by Eichelberg.s equation) values of'h' at least for the combustion and expansion portions of the cycle. Oguri also presents a dimensionless correlation for the gas side Nusselt number but the expression contains constants which must be determined for each particular engine. Consequently, at this time it appears as if the formula of Eichelberg is about the best expressionc available for the convective heat transfer coefficient. In light of this, the equation, for the convection heat transfer rate per unit area is presumed to be q/A = 2.1w-PT T - Tw] kcal/m2-hr-~K (5-19) This equation will be used to calculate the rate of heat transfer during the combustion and expansion processes. The compression process, prior to combustion, will be treated as reversible and adiabatic. C. Radiant Heat Transfer in Engines The radiant component of heat transfer is small compared to the convective component in internal combustion engines exhibiting normal combustion. Nusselt(83) found that the radiant heat transfer was about 5 percent or less of the total heat transfer (see Equation (5-17) ).

-83Overbye and Co-workers deduced from their experimental observations that the radiant heat transfer was negligible. Baker and Laserson(86) found experimentally that the radiant heat transfer was quite low. In a 406 to 1 compression ratio engine the radiant heat transfer amounted to only 22 Btu/ft2sec. at its peak. This would be less than 10 percent of the total heat transfer. However for higher compression ratios it is expected that this percentage would increase. Thus a simple calculation is made below to see if this is the case. Of the principal constituents present in the products of an internal combustion engine, only CO2 and H20 emit any appreciable amount of radiation during normal combustion. McAdams(68) and Hottel(87) indicate a procedure by which the amount of radiation from these two constituents may be approximated. Unfortunately the curves from which the estimation is made do not extend into the range of temperatures and pressures found in a modern high compression ratio engine. Thus extensive and often questionable extrapolation is necessary. In Appendix H, a calculation is made of the maximum rate of heat transfer due to radiation by the method of these men. An engine operating on the fuel-air cycle at a compression ratio of 10 to 1 was selected for the calculations. The heat transfer was calculated immediately after the adiabatic combustion at top center in order to obtain the conditions where the radiation would be most severe. It was found that under these conditions the radiant heat transfer was still only 12 percent of the total at most. Because of the idealizations of the fuel-air cycle engine, the percentage is higher than it would be in an actual engine.

-84Thus it appears that in the operating range of the present day spark-ignited internal combustion engine, the amount of heat transferred by radiation during normal combustion is a small proportion of the total. Because of this, radiation will be neglected in the analytical model for the internal combustion engine being proposed in this study and Equation (5-19) will be employed for all heat transfer calculations.

VI, THE ANALYTICAL MODEL FOR SPARK IGNITED ENGINE CYCLE CALCULATIONS A. General The discussion of Chapter I indicates that the fuel-air cycle greatly oversimplifies many internal combustion engine processes in that it neglects fundamental phenomenona which significantly affect engine.performance. Of these phenomena, two are of particular importance, namely the heat transfer and the flame propagation. The purpose of this chapter is to describe an analytical model for internal combustion engine cycle calculations which includes these phenomena. Their inclusion into the cycle analysis, especially during the compression, combustion, and expansion processes, makes possible the calculation of a stepwise continuous pressure time diagram which shows many important features of the experimental by determined diagram. Moreover, this allows an explicit evaluation of the effects of these two phenomena on the efficiency and power output of the engine. A consideration of such variables as engine speed, spark advance, and combustion chamber geometry further enhances the similarity between the analytical model and the actual engine. The analytical model employs many features of the fuel-air cycle, especially in its treatment of the working fluid. The charge is presumed to be composed of a mixture of fuel and air which is burned during the cycle. The following assumptions, made in connection with the fuel-air cycle analysis in Chapter III, are also made for the analytical model: -85

-861o There is no chemical change in either fuel or air prior to combustion. 2, All products of combustion are in a state of chemical equilibrium at temperatures in excess of 1500~K and are in a state of frozen equilibrium below that temperature. 3. Induction, compression, and exhaust processes are adiabatic. 4. There are no irreversible fluid flow effects, 5. All valve events occur at top and bottom center, The thermodynamic properties of the working fluid as well as the composition of the products of combustion are computed by the methods illustrated in Chapter II, just as they were for the fuel-air cycle engine analysis of Chapter III. It is the combustion and expansion processes wherein the analytical model differs greatly from the fuel-air cycle, Both processes are assumed to occur in a stepwise manner and allowance for heat transfer is made during each. Figure 9 illustrates the pressure volume diagram for the assumed processes of this analytical model. B. The Cycle Processes 1. Process 1-2: Compression The working fluid is compressed from Point 1 (bottom center) to Point 2, Point 2 is an arbitrary crank angle where combustion begins, The compression is treated as a reversible and adiabatic process.

-873 wL\ cr! 4 L> \ a\ Pi 0 4 I I TOP VBOT. VOLUME Figure 9. Indicator diagram for the engine on the "analytical model" at part throttle.

-88Experimental studies have confirmed the general validity of this assumption. They show that during a normal engine cycle little heat is transferred during compression. The state of the system during this process is calculated at regular crank angle intervals in order to construct a pressure time diagram for this part of the cycle, The expression for the volume of the cylinder (including the clearance volume) as a function of crank angle and engine geometry is as follows: Bore2 Stroke /Stroke 2 V = Vtop + t 4 T 2 (1 + cos @) + Rod' 01 - 1 r (2 sin ) ) From this expression, the successive volume changes for the isentropic compression processes can be calculated, The total work done during the compression process is W!-2 = U1 - U2 The total heat transferred is zero, 2. Process 2-3: Combustion The combustion process begins at some crank angle or spark advance corresponding to Point 2, Strictly speaking, this may not be the true spark advance as no provision is made for any ignition delay. Combustion is assumed to progress in a stepwise manner with an arbitrary fraction of the total mass burning during each increment, A single increment is composed of seven steps. During each increment some heat is transferred and some piston motion occurs, The working fluid during combustion is assumed to be composed of two distinct gaseous regions, one of burned and one of unburned gaso

-89These are physically separated by a flame front, The unburned gas is compressed continuously during combustion due to the greater volume occupied by the hot products of combustiono Thus each increment that burns does so from slightly different initial conditions. Because of this, a temperature stratification is formed in the burned portion of the gas. At this stage in the analysis of the combustion process, a number of assumptions must be made, for it is impossible to consider in detail the mixing and heat transfer which may occur within the burned region and between the burned and unburned regions, Within the burned region it must be assumed that either complete uniformity exists because of rapid mixing and heat transfer or that no mixing or heat transfer occur whatsoever, and each burned increment follows an isentropic path subsequent to its combustion. This later assumption was made in an analysis by Hershey. (10) He cites experimental temperature measurements which confirm the stratification although these show it to be less than that calculated, It is not felt that an individual treatment of each burned increment in this manner will lead to significantly different or more meaningful results. Therefore in this analysis complete uniformity will be assumed in the burned region as well as in the unburned region. It will be assumed however that there is no mixing between the burned and unburned portions. Photographs of normal combustion processes show regular continuous flame fronts and do not indicate that appreciable mixing occurs,

-90The unburned portion of the gas will be assumed to follow an isentropic path. Pressure and temperature measurements taken in this region by Livengood et al. 88 show this to be a reasonably good assumption. This does not mean that there is no heat transfer to or from the unburned gas, but only that the net amount is very small. Thus one final assumption is made for the combustion process, namely, that heat is transferred from the burned to the unburned gas in an amount exactly equal to that transferred from the unburned gas to the combustion chamber surfaces, In effect this means that the burned gas will be charged with the entire internal energy decrease due to heat transfer and the unburned gas will always follow an isentropic path. Figures 10 a-h illustrates the seven steps comprising the combustion of the i'th mass increment. To the right of each figure, the total system (burned + unburned) thermodynamic properties are designated by appropriate symbols whenever a single property pertains to both regions. The two homogeneous regions are designated B (burned) and U (unburned). The bross-hatched area represents the currently inflamed mass element and is labeled F (flame element). Let the system pressure, volume, and internal energy at the completion of the (i-l)'st increment be PO, Vo, and Uo. Figure lOa illustrates the state of the system in this condition. Step 1 - Figure 10b - Constant pressure combustion of the i'th mass increment, A thin shell of gas whose thickness is (Ro - Ro) is burned. The system volume increases during this constant pressure

- 91combustion to V1. The state of the previously burned and still unburned portions remains unchanged. The flame element undergoes an isenthalpic process, burning to its equilibrium adiabatic flame temperature, Step 2.- Figure lOc - Constant pressure mixing of the flame element with the previously burned gases. The current flame element is mixed adiabatically with the previously burned portion. The end of this isenthalpic process finds a single homogeneous region of burned gas. The state of the unburned gas remains unchanged. Step 3 - Figure 10 d - Recompression to volume Vo. The volume of the system is changed back to Vo in such a way that the unburned gas follows an isentropic path and the total internal energy of the system after recompression is U0, During this step the pressure rises to P3' At this point in the process it is as if the system had experienced the combustion of a small increment of mass adiabatically and at constant volume. Step 4 - Figure lOe - Isentropic change of state due to piston motion. The combustion of the i'th mass increment has taken a finite amount of time. Call this At. During this interval the piston moves causing a change in the volume of the system. Each gaseous region is presumed to undergo an isentropic change of state. The system volume is changed to V4 and the pressure to P4. At is figured in Step 7 from a knowledge of the flame speed. An initial assumption is made for At. The work done in this step, which is the total work done during the combustion of the i'th mass increment, is i = Ui- Ui4

-92Step 5 - Figure 10f - Constant volume heat transfer, Heat is transferred from both regions to the combustion chamber surfaces and from the burned to the unburned gas, The volume of each region remains the same. Because the amount of heat transferred to the unburned gas is just off-set by that from the unburned gas to the walls, the unburned gas undergoes no change of state whatsoever during this step. The burned gas undergoes a constant volume process in which heat is transferred to the walls and to the unburned gas. Thus the internal energy of the gas is reduced by the amount of this heat transfer. Since heat is transferred from both burned and unburned regions, it is necessary to know, along with At, the amount of wall and piston area exposed to both burned and unburned gases, These areas differ with the flame front position and the crank angle and depend on the combustion chamber geometry. During a given combustion increment, subsequent to Step 4, the burned volume occupies a certain fraction of the entire combustion space. Corresponding to this volume fraction there.is a certain mean flame front position as well as a definite wall and piston surface area exposed to both burned and unburned regions. By initially assuming that combustion occurs at top center and that the flame front progresses spherically from the center of ignition, these area-lengthvolume relationships can be found by graphical constructiono Such quantities reduced to fractional form are presented in Table VII for the combustion chamber of Figure.,l The proper values can then be found by interpolation in the table (a three point interpolation is used in this work between the length-volume entries and a linear interpolation between the length-area entries).

-93It is often assumed that a small amount of piston motion does not change these area-length-volume relationships. Taub(89) reports that the result of detailed calculations of the possible effects of piston motion on these relationships indicates that no appreciable changes occurred for moderate amounts of piston motion, at least for the particular geometry investigated. However, for larger piston displacements their validity is questionable and a more detailed analysis of the combustion chamber may be necessary. This. is the case for the combustion chamber of Figure 11, To account for the effect of piston displacement on the position of the burned gas region in this chamber, the following assumptions were made. Prior to top center piston position the relations of Table VIII are presumed valid. After top center some burned gas is found in a right cylinder whose height is just equal to the piston displacement from top center and whose radius is equal to the radius of the flame front. The remaining burned gas occupies the combustion, chamber according to the volume-length relationships of Table VIIIo Refering to Figure 11, for a small amount of piston displacement the burned gas region would look like a short right cylinder which is shaped like the combustion chamber head on one end and has a hemispherical cap on the other, at least prior to the time when the hemispherical dish is filled with burned gas. Having determined the position of the flame front by the above assumptions, the wall, head, and piston areas exposed to the burned gas can then be calculated. The latter two are calculated from

-94a table such as Table VIII and the wall area is calculated from the crank angle as follows: Pt r Stroke / sin2 ~ Stroke2,] Awt i= Bore S 2 (1 + cosQ) + Rod (1 - 1 - sin2 St e2 (6-2) where the proportion of this exposed to the burned gas can be calculated geometrically. In a similar manner the areas exposed to the unburned gas can be found. For heat transfer calculations the heat and cylinder wall areas are added together. In Chapter V a decision was made to use the formula of Eichelberg(81), Equation (5-19), to compute the heat transfer. Considering heat transfer from both regions to the walls and piston, the expression for the total heat transfer during the i'th combustion increment is: i = 2.1 [ 4b (Awb(T4b - T) + Ab(T4b - T )) (6-3) + T4u- (Awu +(T T ((Tu Tp))] At Equation (6-3) assumes that all the combustion chamber surfaces with the exception of the piston surface are at some constant average temperature and that the piston surface temperature is at some other constant average temperature. In Chapter V, a discussion of the magnitude of the temperature fluxuations at the wall surface indicated that any point on the wall has a relatively constant temperature, However, no two points necessarily have the same temperature. Nevertheless an average overall wall temperature, while a great simplification, would still appear to be a reasonable assumption,

-95At the end of this step, the burned gas is in a state of chemical equilibrium at volume V4, Its internal energy has been decreased during this process by Qi. The pressure in each of the two regions is different, Step 6 - Figure lOg - Adiabatic constant energy readjustment to a uniform pressure. During this step the two regions are allowed to attain pressure equilibrium adiabatically, without a change in the total system volume, and therefore at constant internal energy, The unburned gas undergoes an isentropic change of state. The final pressure is P6, This step completes the combustion of the i'th increment. However, the time interval At is still not known, Step 7 - Figure lOh - Determination of the time interval required for combustion, The flame element of Figure lOb is isentropically compressed to the final pressure P6. It is assumed that this equilibrium state represents the average burned state for the i'th increment. The values of T7, Cp, and n7 are substituted into Equation (4-24) as T1, Cpl, and n1. The quantities needed in this equation for the state prior to combustion are those in the unburned gas just prior to Step 1. The flame speed, St, is now computed from Equation (4-24) with the following consideration. For air-fuel ratios in the region of five percent lean to five percent rich concentrations aeff and beff are taken as the average of the concentration at these two extremes, This is because in the derivation of these quantities, it was assumed that the concentration of the fuel was much greater than that of the oxygen or vice-versa, This refinement is suggested by Dugger and Simon,(5 8)

-96P =P (a) B F U = U0 LI^~ ~H H0 S L So RO 0 Initial State V = V1 H SH U = Ul Step 1 - Constant Pressure Burning (c) B U = U2 H = H0 H=H0 S =S Step 2 - Constant Pressure Mixing Figue 1. Ml M l fr P Tr r V VO (d) B U U = U H = H3 s = S3 Step 3 - Recompression to Original Volume Figure 10. Mathematical Model for Combustion and Heat Transfer.

-97P = P4 V = V4 U = U4 (e) B u H H4 H = H4 S = S3 Step 4 - Change of Volume Due to Piston Motion P - V = V4 (f) B U U = U5 H = H5 S = S5 Step 5 - Constant Volume Heat Transfer ________~___ P = P6 V = V4 U = U5 (g) B u H H =H6 S = S6 d- R6 Step 6 - Adiabatic Readjustment to Uniform Pressure (h) | B F U -,, P = ________P6 S = - Step 7 - Recompression of Flame Element to Final Pressure Figure 10. (Continued)

-98Corresponding to the volume fraction inflamed at the end of the (i-l)'st increment, there was some characteristic distance Ro, the radius of the spherical flame front. For the combustion chamber of Figure 11, Table VIII includes values of the flame front radius divided by the longest distance the flame travels if the combustion occurs at top center. The effects of small piston displacements on this volume fraction-distance fraction relationship are neglected. At the end of the combustion of the i'th increment, the flame front is at a distance R6 from the center of ignition (see Figure lOg). The difference, R6 - Ro is the total extension of the flame front during the combustion of the i'th increment. Part of this is due to expansion and part to flame propagation. That due to flame propagation is A= (R- R0) (6-4) For the first increment this quantity is A = (3/4 n V )1/3 (6-5) wherein it is assumed that after the combustion of the first increment the burned gas is spherical in shape. Vfo is the volume of the first mass increment prior to combustion. The time required for the increment to burn is At = /St (6-6) u

-99If the At assumed in Step 4 is not suitably close to that just calculated, Steps 4, 5, 6, and 7 are repeated until the change in successive At's is within a specified limit. When this is the case the i'th increment is completed and the (i+l)'st begun. The combustion process is continued until all the mass is consumed. This occurs at Point 3 on Figure 9. For this process the total heat transferred is Q2-3 = X Qi combustion The total work is ^-3= wi combustion If the flame speed constant, K1, Equation (4-24), is not known; some experimental data must be used to establish its value, The necessary information may be obtained from the experimental pressure-time diagram for the particular engine under consideration, It is necessary to know only the spark advance and the crank angle where the maximum pressure is obtained. The constant, K1, is determined as follows. The incremental combustion process is presumed to begin at the known spark advance. After the combustion of several increments the cylinder pressure will be observed to have reached a peak and then begin to decline. If the crank angle at. which this peak occurs is not sufficiently close to the crank angle where the peak occurs experimentally, then the constant can be corrected by a factor which is the ratio of the experimentally determined number of degrees from the beginning of combustion to the

-100point where the maximum pressure occurs to this same quantity just determined analytically. The combustion process is then repeated and the constant recorrected until the two peaks are suitably close together. When this is the case, the combustion process is then continued. Varying K1 primarily affects only the crank angle where the peak pressure occurs but indirectly affects the magnitude of the peak pressure in that the cylinder volume is a function of the crank angle. 3. Process 3-4: Expansion Some expansion has already occurred during the latter stages of the combustion process. However, Process 3-4 can be distinguished in that combustion is already completed and a single homogeneous region of burned gas is present, The expansion process is presumed to occur also in a stepwise manner, A single expansion increment consists of two steps. It corresponds to an incremental change in crank angle A9eO It is assumed that prior to the i'th expansion increment the pressure, temperature, an internal energy are PO, To, and U0O Step 1 - Constant volume heat transfer. At volume V0 heat is transferred from the hot gases, causing a reduction in the internal energy of the gases. The amount of this heat transfer is Qi = 2.lw -fPoTo [Awt(T ) A(T - T+ Ap(T - Tp)] At (6-7) where the total exposed wall area, Awt, is computed from Equation (6-2) for the current crank angle and At = AGe/6/rpm. The entropy at the end of Step 1 is S1 and the internal energy is U1 = U0 - Qio

-101Step 2 - Isentropic change of state due to piston motiono During the time interval At the system undergoes a change of state due to piston motion, The working fluid is presumed to expand isentropically to this new volume, At the end of Step 2, S2 = S1 and the internal energy is U2, The work done during this expansion increment is Wi =U - U1 The expansion process is continued until the piston reaches bottom center, Point 4 on Figure 9. The total heat transferred during this process is Qj34 =Qj i expansion The total work is o =-4 Wi expansion 4. Process 4-4: Expansion to the Exhaust Pressure At bottom center the exhaust valve opens and the gases expand to the exhaust pressure, Those which remain in the cylinder are presumed to have undergone an isentropic change of state, This process is identical to that of the fuel-air cycle and is more fully described in Appendix F, Part B, Section 7, 5. Process 4'-5: Exhaust The piston returns to top center, expelling all the gas except that remaining in the clearance volume, This process is presumed

-102to be adiabatic, The gases remaining in the clearance volume undergo no change of state. The fraction of gas remaining in the clearance volume is F = V5/V4,,. This process is identical to that of the fuel-air cycle and is discussed in Appendix F, Part B, Section 8. 6. Process 5-1: Induction and Mixing This adiabatic process is the same as that for the fuelair cycle and is described in Appendix F, Part B, Section 2o C. The Cycle Characteristics 1. Net Work The net cycle work is the sum of the work performed during compression, combustion, and expansion plus any pumping.work. This quantity is Wt =W1-2 + W3-4 + (Vbot - Vtop)(Pi - P)J (6-8) 2. Net Heat Transferred The net heat transferred is the sum of the heat transferred during combustion and expansion. This quantity is Qt= 2-3 + -4(69) 3, Thermal Efficiency The indicated thermal efficiency is the net work divided by the enthalpy of combustion of the fuel consumed. This is Wt ~ 100 0 - 1 (6-10) cH e F0

103where AH is the enthalpy of combustion per mole of fuel at 298160K c and 1 atmosphere pressure and F0 is the moles of fuel inducted per cycle. 4, Mean Effective Pressure The mean effective pressure is mep =Wt (6-11) (Vbot - Vtop)J 5. Volumetric Efficiency The volumetric efficiency is defined as the quotient of the actual mass of fresh charge inducted to that which would just fill the displaced volume at the inlet density, This quantity is = F0 Z (cx + x) RTi 100 (6-12) Pi(Vbot - Vtop) D. Computational Method The analytical model has been programmed on an IBM 709 digital computer. The MAD compiler language was used throughout, Appendix I contains a description of the program, a flow diagram, and a listing of the MAD statements, The following chapter reports the results of the computer calculations,

VII. CALCULATED RESULTS FROM THE ANALYTICAL MODEL A. General The scope of the calculations presented herein employing the analytical model is designed to accomplish three purposes. The first is to compare the characteristics of a calculated and an experimental cycle for a particular engine. The second is to predict performance characteristics for the engine operating under conditions for which no experimental data are available, assuming the flame speed and heat transfer representation is correct. Finally, the third is to study the availability and irreversibility associated with an engine cycle, For this work, a single engine was employed. This engine was selected because its combustion chamber geometry was relatively easy to describe mathematically and because its high compression ratio and advanced design were characteristic of current practice. Moreover the high compression ratio would diminish the influence of the exhaust residual whose composition and temperature were not known and could not be calculated accurately by the analytical model, Figure 11 is a sketch of the combustion chamber of this engine, It has a relatively flat head with an off-set hemispherical dish in the piston. Pertinent characteristics of the chamber are listed in Table VII, Table VIII lists its volume-area-length relationships. The compression ratio is 10 to 1. Experimental data for this engine were obtained through Professor Jay A. Bolt of the University of Michigan Department of Mechanical Engineering. -104

-105It is known that there will be differences between the calculated and experimental cycle characteristics, These are due to both over-simplifications in the analytical model and differences in operating conditions between the analytical model and the actual engine. Those due to over-simplifications in the model will be discussed later, Differences in operating conditions are due to either a difference in fuel type or to the fact that no experimental value is available for the parameter in question, The experimental data were taken using a blended hydrocarbon of approximate composition C7 35H14.7 whereas all calculations were made assuming iso-Octane, C8H18 as a fuel. The thermodynamic properties of the fuel were approximated by those of n-Octane (Tables II and III) and the activation energy was assumed to be 39000 cal/mole as reported in NACA Report 1300. (5) While it is felt the discrepancies between the analytical and experimental results introduced by this fuel difference are small, no investigation of the effects of fuel type has been conducted, Certain parameters which are necessary in the calculations were given assumed values because no experimental data were available, These are the wall, piston, and exhaust temperatures, They were given the values 420~K, 500~K, and,1000~K respectively and all calculations reported are made with these values unless otherwise noted. B. The "Normal Cycle" A single cycle was selected as a normal cycle against which the resulting analytical model calculations could be compared. Table

-lo6IX lists the operating conditions under which the actual engine was run and those for which calculations have been made, For the calculated cycle, the heat transfer was determined directly from Equation (5-19) and the flame speed from Equation (4-24) with K1 equal to 135,000. This is equivalent to a ratio of turbulent to laminar flame speed of slightly under 4 to 1. The numerical value was arrived at by comparing the experimental with the calculated pressure-time diagram and attempting to achieve good agreement over the early portion of the combustion process, This procedure is explained in Chapter VI. The heat transfer and flame speed calculated in this manner are termed "normal" and the resulting cycle is termed the "normal cycle," The curve designated as that for normal heat transfer in Figure 12 is the pressure-time curve resulting from the calculations, Figure 13 shows the corresponding pressure-volume diagram, The experimental curves are shown in each caseo It must be remembered that these experimental curves represent average values for a large number of cycles and do not necessarily conform to any one single cycleo The complete calculated data for these operating conditions are presented in the first set of data in Data Set A, Appendix Ko C. Comparison of the Analytical and Experimental "Normal Cycles" 1, The Pressure-Time and Pressure-Volume Diagrams a, The compression process On both Figures 12 and 13 it is seen that the assumption of a reversible and adiabatic compression process is a close approximation to the real process,

-107b. The combustion process 1) The ignition delay. No ignition delay was provided for in the calculations. The agreement between the calculated and experimental curves over the early portion of the combustion process indicates that the ignition delay is very small. This observation is in good agreement with the recent findings of Curry(90) who experimentally found the ignition delay to be very smallo 2) First portion of the combustion process. Up to about 8 degrees after top center the calculated pressure-time diagram corresponds closely to the experimental one, At this point about one half of the mass of mixture has been consumed. During this early portion of the combustion process the flame front is passing through the hemispherical dish in the piston but has not yet reached the surface of the piston. Thus, Very little heat is transferred as the hot gases are in contact with relatively little wall area. Figure 21 shows the magnitude of the flame speed as a function of crank angle, During this portion of the combustion process the flame speed nearly doubles. The close agreement between the experimental and calculated pressure-time diagrams in this region tends to validate Equation (4-24) for the flame speeds 3) Last portion of the combustion process, At about 8 degrees after top center, the hemispherical dish in the piston becomes completely filled with burned gas. In Figure 12 it is seen that at this point in the cycle the calculated curve abruptly departs from the experimental curve. The analytical model predicts that once the

-108piston cavity is filled with burned gas, the burning of successive mass increments requires a longer period of time, This is because the flame front must move further in the narrow quench region to burn equal mass increments than it did when the flame was propagating into the hemispherical dish. The experimental curve does not show this, Because of the many assumptions and simplifications inherent in the analytical model it is difficult to attribute the above deviation to a single factor. Nevertheless some comments are in order. First it must be recognized that the actual flame propagation does not occur spherically as shown in Figure 12 but occurs in such a way that the shape of the flame front tends to reflect the shape of the enclosing combustion chamber. Thus the surface area over which the reaction can occur becomes somewhat larger than that assumed by the analytical model. Moreover, the burned gas tends to move in mass toward a more central position in the chamber (experimentally shown by ionization gap studies) and this causes more surface area over which reactions can proceed than the analytical model assumes. Both these effects would tend to increase the effective burning rate slightly and in particular would cause the hemispherical dish to be completely filled by burned gas slightly later in the cycle. Thus, the inability to describe accurately the shape and position of the burned gas region leads to discrepancies between the calculated and experimental pressure-time diagrams. This is due to a necessary simplification in the analytical model. Second, as the hemispherical dish is filled, the flame front arrives at a sudden change in combustion chamber contour, Rabezanna et al, (19) have experimentally

-109studied chambers with sudden changes in contour and have found that in every case there is a sudden appreciable increase in the flame propagation rate whenever such a section change is encountered, This increase which is normally attributed to an increase in turbulence may be as much as 25 or 30 percent of the original flame speed. It is suspected that this latter over-simplification of the combustion process is the major cause of the differences observed between the experimental and calculated pressure-time curves during the last portion of the combustion process. In consequence of these factors the analytical model predicts a lower peak pressure and longer combustion time than is experimentally observed. The observed peak pressure is 875 psia whereas the calculated is 795 psia. The observed duration of combustion is 45 crank degrees whereas the calculated is 54 degrees. c. The Expansion Process During the expansion portion of the cycle, the calculated curve lies above that of the experimental curveo This indicates that its internal energy is greater. The difference between the two curves is due primarily to three factors. First, the analytical model gives less work done by the engine near the top center piston position and consequently more internal energy is present in the gas during the expansion stroke than would be the case if the experimental peak pressure were attained, This is clear from Figure 13 in which the area under the curve is proportional to the work. Second, complete combustion is assumed in the analytical model, In this respect the model represents an optimum condition which is approached but never

-110attained in practice, This assumption of complete combustion would tend to raise the calculated pressure-time curve higher than the measured one during the expansion stroke. Third, the volumetric efficiency of the engine represented by the calculated curve is slightly greater than that actually measured (97,6 percent verses a measured 94 percent). Thus there is slightly more mass present in the cylinder. Again this would tend to raise the calculated expansion curve higher than the measured curve, 2. Relationship Between Mass Burned and Volume of the Burned Charge Figure 22 shows the relationship between the mass burned and the volume of the burned chargeo Good agreement is seen between the calculated data and the curve presented by Rabezanna et al.(19) 3, Heat Transfer The total heat transferred during the cycle is 17o5 percent of the heat of combustion of which about one third of this is transferred during the combustion process, Although no experimental data are available concerning the actual heat transfer in this engine, these figures agree well with the estimates of Pye(66), Ricardo(67), and Janeway(65) From this and the shape of the pressure-time diagram it appears as if Equation (5-18), the expression proposed by Eichelberg(81), provides a reasonably good estimate of the convective heat transfer coefficient. 4, Rate of Pressure Rise The calculated pressure-time curve shows good agreement with the experimental curve especially in so far as the rate of pressure rise is concerned. Additional analysis with different combustion chamber

-l11geometries is needed before the analytical model can be used in combustion chamber design. 5. Power and Efficiency The calculated thermal efficiency of the cycle is 36,5 percent and the measured is 3558 percent (see Table IX)o Most of this difference can be attributed to incomplete combustion of the charge in the actual engine. The differences present in fuel type and volumetric efficiency are believed to affect the thermal efficiency only slightlyo If slightly incomplete combustion had been considered and the shape of the pressure volume diagram had remained essentially the same, the calculated thermal efficiency would have been slightly less instead of slightly greater than that measured. The calculated mean effective pressure is 182 psia whereas that measured was 166 psia. Most of this difference can be attributed to three factors, incomplete combustion, difference in volumetric efficiency, and fuel type. D. Effect of Exhaust Temperature Because the analytical model does not treat the exhaust process in detail, the temperature of the exhaust becomes a variable of the problem, For the high compression ratio engine considered in this study the effects of the exhaust residual on the temperatures and pressures of the cycle is slight and thus the temperature and composition of the exhaust residual do not have to be known with great accuracy. However the effect of a 200~K variation in the exhaust temperature was studied.

-112A single cycle was calculated with all operating conditions identical to those of the normal cycle except for the exhaust temperature, Instead of 1000~K, the exhaust temperature was assumed to be 1200~Ko The calculated results for this cycle are presented as Data Set E, Appendix Ko This change in exhaust temperature produced no significant changes in any of the cycle calculations. Eo Influence of Heat Transfer and Flame Propagation Rates This section describes the results of calculations which show the influence of changes in heat transfer and flame propagation rates on the engine cycle characteristics, The "normal" cycle was presumed to be the standard against which the other cycles could be compared. The operating conditions were exactly the same as those for the "normal cycle" with the exception that both the heat transfer coefficient and the flame speed were changed, In particular three different heat transfer rates were considered, no heat transfer, normal heat transfer as defined above, and twice normal heat transfer, Three different flame propagation rates were considered in combination with the three heat transfer rates, a normal rate of flame propagation as defined above, 115 percent of normal, and 85 percent of normal. The results of these calculations are presented in Data Sets A, B, and C of Appendix K, Figures 12 and 13 are the resulting pressure-time and pressure-volume diagrams for the normal rate of flame propagation, Figures 14 and 15 are the pressure-volume diagrams for the rapid and reduced rates of flame propagation respectively.

-113Looking at Figure 12, it is seen that the pressure-time curves for the three heat transfer rates become distinguishable near the peak pressure shortly after the hemispherical dish is filled with burned gas. This is the first point in the cycle where burned gas comes into contact with an appreciable wall area. The effects of the three different rates of heat transfer on the pressure-volume diagrams are similar for each of the three flame speeds considered. Increasing the amount of heat transfer causes the expansion curve to fall below that for a lesser amount of heat transfer, In each case the peak pressure changes only slightly. Figure 16 shows the effect of changing the rate of flame propagation while maintaining a normal rate of heat transfer. It is seen that the pressure-time diagrams and peak pressures are quite different for each different rate of flame propagation. Figure 17 shows the thermal efficiency and mean effective pressure for these nine sets of operating conditions, The most significant changes in thermal efficiency and mean effective pressure are caused by the changes in heat transfer rate, The changes effected by the differences in flame propagation rate are not large, It must be noted however, that the magnitude of the changes in heat transfer rate is much larger than that of the changes in flame propagation rate, From these results it appears that cycle to cycle variations in the flame propagation rate effect thermal efficiency and power output less than the pressure time diagram appears to indicate. This is because moderate variations in the pressure-volume diagram do not cause large

-114variations in either thermal efficiency or mean effective pressure, However, it is apparent that appreciable increases in these quantities can be effected by reducing the heat transfer. On Figure 17 are indicated the mean effective pressure and thermal efficiency calculated by a fuel-air cycle analysis, the results of which are included in Appendix K, Data Set D and are summarized in Table IX. These idealized values are approached by the analytical model engine with no heat transfer and rapid combustion, In fact the analytical model engine would attain these values of thermal efficiency and mean effective pressure if the combustion rate were greatly increased and the spark advance decreased toward zero degrees. The calculated peak pressure for the cycle with no heat transfer and rapid flame propagation was only about 835 psia whereas that of the fuel air cycle was 1326 psia. Thus a finite combustion time is very beneficial in that it keeps the peak pressures at reasonable levels and yet only slightly lowers thermal efficiency and mean effective pressure. Table X presents the amount of heat transferred as a percent of the heat of combustion for the two non-zero heat transfer rates and the three flame propagation rateso It is seen that the more rapid the rate of flame propagation, the higher the heat transfer. This is because the highest flame speed cycles were associated with the highest pressures and since the heat transfer coefficient is proportional to the square root of the cylinder pressure the amount of heat transfer increased as the flame speed increased. From this it can be inferred that the highest heat transfer during normal combustion is associated with the most efficient cycles,

-115Figure 18 is the entropy-volume diagram for the normal rate of flame propagation. Since the compression process is presumed to be reversible and adiabatic no entropy increase occurs, However the combustion process is highly irreversible as it occurs at a finite rate. Thus a large increase of entropy occurs during combustion. For the adiabatic cycle no further entropy change occurs during expansion, However, when heat transfer is taken into account the entropy is seen to decrease during the expansion stroke. This is because heat is transferred from the hot gases and thus the entropy change is negative. F. Availability and Irreversibility The availability is the maximum work which can be done by a system when it changes from a given state to a standard state. This maximum work can be realized only through reversible processes including reversible heat transfer to the surroundings. When irreversibilities occur the work realized is less than the maximum. The difference between the maximum and the actual work is termed the irreversibility of the process. The system in question is the closed system comprising the contents of the engine cylinder. For such a system the availability is: Availability =(U S) (U - ToS) (U - where the subscript refers to the standard state, Because the composition of the system changes due to combustion and dissociation, some difficulty arises in the definition of the standard state. For this work the standard state is taken as the

"116products of combustion at 1 atmosphere pressure and 298,16~K, The products are presumed to consist only of N2,C02, H20, and CO for the rich mixture considered here. The lower curve of Figure 19 shows the availability versus the crank angle for the operating conditions reported in the first set of data of Data Set A, Appendix K, These were conditions of normal heat transfer and normal flame propagation, Under these conditions the mole fractions constituting the products are as follows~ N2 0.718 CO2 0,105 CO 0.028 H20 0,150 and the total number of moles is 0,02059. The molal properties of these constituents in the standard state are given in Table IIo The value of U0 - ToSO is then. -702,7 cal, During the compression portion of the cycle, prior to combustion, the state changes are presumed to be reversible and adiabatic and thus the avaiability is increased by the amount of work done on the system. During combustion and expansion the availability decreases, If these processes were reversible the expansion work would be equal to the change in availability. However, this is not the case, The combustion process is highly irreversible as the entropy-volume diagram of Figure 18 shows. Both during combustion and expansion additional irreversibility is introduced due to heat transfer. This. is shown in Figure 19o Note that subsequent to the completion of the combustion process no additional irreversibility is introduced from this source and further increases are due to heat transfer only.

-117Figure 20 shows the availability as a function of crank angle for the normal rate of flame propagation with no heat transfer. For this cycle the only irreversibility is due to combustion, It is interesting to note the large amount of availability existent at the end of the expansion stroke in both Figures 19 and 20. It is a substantial fraction of the original availability. The thermal efficiency of the engine could be greatly increased if some method were found for taking advantage of all or a part of this potential energy, G. The Analytical Model and the Fuel-Air Cycle It has already been shown that the fuel-air cycle is the limiting case of the analytical model for rapid rates of flame propagation. In turn it was shown that the air cycle is the limiting case of the fuel-air cycle for extremely lean mixtures, The number of additional parameters included in the analytical model, not the least of which are the heat transfer and flame propagation, allow a mathematical analysis whose reasults show close similarity to the experimental data in many respects. Thus the analytical model provides a distinct improvement over the fuel-air cycle for internal combustion engine analysis. It must be pointed out however, that the analytical model calculations must be made on a digital computer whereas those of the fuel-air cycle require no such aid. Table IX lists the operating conditions and experimental results for the normal cycle, the calculated results from the analytical model, and those from the fuel-air cycle for similar engine operating

-118conditions. A comparison of the quantities presented indicates the improvement in the cycle analysis made possible by the analtyical model. Ho Concluding Remarks The correlation between the calculated and experimental data was largely satisfactory for the normal cycle considered. The major discrepancies appear to be caused by two factors. The first is the inability to describe accurately the shape and location of the burned gas region. The second and most influencial factor is the inability to predict the effect of section changes on turbulent flame propagation rate. In those portions of the cycle where the effects of these two factors are small the heat transfer and flame propagation appear to be described satisfactorily. Before the analytical model can be employed to evaluate new engine designs or to even aid in the design of combustion chambers, much more work will be needed to verify the calculated results, In particular the influence of combustion chamber geometry, different fuel type, and different engine operating conditions must be studied, More information is needed to describe the combustion process accurately, The expression employed in this study for the flame propagation rate needs improvement. In particular more information is needed about the turbulence in an engine so that the flame speed can be predicted directly from engine operating conditions without relying on an experimentally determined constant whose value under new operating conditions is highly questionableo

-119% In summary the analytical study of the internal combustion engine must proceed along two paths. First the analytical model must be studied by employing it to calculate engine cycles under widely varying operating conditions, Second, a research program must be undertaken to obtain the following information: 1. The nature of the turbulence in the cylinder of a spark ignited engine, 2. The influence of section change on the turbulent flame propagation rate, 3. The introduction of the preceding information into the analytical model for the prediction of the turbulent flame speed,

-120A A CENTER OF IGNITION SECTION AA I BORE Figure 11. View of engine combustion chamber showing spherical flame propagation pattern.

-121TABLE VII PERTINENT DIMENSIONS FOR ENGINE OF FIGURE 11 Dimension Symbol Numerical Value Bore Bore 3594 in 10 cm Stroke Stroke 2.46 in 6,25 cm Connecting Rod Rod 70065 in 17 9 cm Radius of Hemispherical Dish 1,06 in 2.79 cm Quench Height 0,05 in 1,27 cm Compression Ratio r 10 to 1 10 to 1 Clearance Volume Vp 333 in3 54.6 cm3 top Swept Volume Vbot 30,00 in3 492 cm3 Head Area Ah 12,13 in2 78 4 cm2 Piston Surface Area A 15535 in2 99o0 cm2 p Maximum Flame Travel Length If Combustion Occurs at Top Lt 2,4 in 601 cm Center

-122TABLE VIII VOLUME-AREA-LENGTH RELATIONSHIPS FOR THE COMBUSTION CHAMBER OF FIGURE. 11 L/Lt Ahb/Aht Ab/Apt V/Vt V/Vt L/Lt 0,0 0.0 0.0 0.0 0 0,0 0,0 0,05 oo o00 0,o00285 1 0,05 0. 150 o o oo 0.0 o 001875 2 o0,1 o196 0 15 005335 0,0 0,05353 3 0o15 0,230 0,2 0,0596 o.o 0.10629 4 0,2 0.260 0.25 0.0934 0.0 0.18093 5 0.25 0,282 0.3 0.1341 o.o 0,29034 6 0.3 0.304 0.35 0.1840 0.0 o.43688 7 0,35 0.322 o.4 0.2385 o.o 0.63774 8 o.4 0 340 0.45 0.299 0,449 0.77300 9 0,45 0,354 0.5 0.369 0.504 o.80343 10 0.5 0,368 0.55 o 446 0.566 0.83313 11 0,55 0 380 0o6 0,533 o.634 0.85971 12 o.6 0,392 0o65 0o625 0,706 0.88276 13 0.65 o.403 0.7 0.709 0.770 0,90933 14 0.7 0o414 0.75 0.777 0o825 09o3317 15 0O75 0o430 0.8 0.837 0.874 0,94724 16 0,8 0.490 0.85 0.894 0,917 0.96561 17 o.85 o0 580 0 9 0.938 0,954 0,98163 18 0. 9 o 686 0.95 0.979 0o985 o099101 19 0.95 o0804 1,0 1.0 1o0 1,0 20 1,0 1,0

-123TABLE IX NORMAL ENGINE CYCLE OPERATING CONDITIONS (wide open throttle) Compression Ratio: 10 to 1 Operating Condition Experimental Analytical Model Fuel-Air Cycle Fuel Blended Iso-Octane Iso-Octane Air-Fuel Ratio (fraction Theoretical air) 92,92 92 Piston Temperature Unknown 500~K -- Wall Temperature Unknown 4200K --- Manifold Temperature 320~K 320~K 320~K Manifold Pressure o99 atm o99 atm.99 atm Exhaust Temperature Unknown 1000~K 1240~K Exhaust Pressure 1003 atm 1.03 atm 1<,03 atm Spark Advance 16~ BTC 16~BTC Speed 2800 rpm 2800 rpm -- Peak Pressure 875 psia 795 psia 1326 psia Max. Rate of Pressure 85 psi/deg 85 psi/deg oo Rise Duration of Combustion 46 degrees 54 degrees -- Thermal Efficiency 3558 percent 36,5 percent 42,7 percent Mean Effective Pressure 166 psia 182 psia 213 psia Volumetric Efficiency 94 percent 97 percent 97 5 percent

-124TABLE X AMOUNT OF HEAT TRANSFERRED (Percent of heat of combustion) Compression Ratio: 10 to 1 Fuel: Iso-Octane Speed: 2800 rpm Ignition: 16~ BTC Rate of Normal Heat Transfer..Twice Normal Heat Transfer Flame During During Total: During During Total Propagation Combustion Expansion Combustion Expansion Normal 6.06 11.4 17.5 11,8 17.4 29,2 Rapid 5.71 12,3 18,0 11 2 18,8 30.0 Reduced 6.90 9.5 16,4 13,2 14,4 27 6

-1250 0 z z f 2 4 o- 840 - 0 wP? ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ^ 4 o 0 o 0 0Id xO_ 4 ____ * 0h w a VlSd' 3EInSS3Ed 3GNI-AO z co 0 0 8 8 8 8 0 0~~~~r 0 ~ ~ u

-12670 EXPERIMENTAL - EXPERIMENTAL 60.......X NO HEAT TRANSFER. 0 TWICE NORMAL HEAT TRANSFER A NORMAL HEAT TRANSFER 50 W 40 cr cr 30 X,_j x IC 0 0.1 0.2 0.3 0.4 05 0.6 CYLINDER VOLUME -LITERS Figure 13. Pressure-volume diagram for a 10:1 compression ratio engine with normal rate of flame propagation (Data Set A). Operating conditions listed in Table IX.

-12770 EXPERIMENTAL 60 l- X NO HEAT TRANSFER /Qq O( 0I~o NORMAL HEAT TRANSFER A TWICE NORMAL HEAT TRANSFER 50 4 40 w X U) O. 301 "O't l 0 Q I 0 20\ xJ \~ X\ -I I l 0 0.1 0.2 0.3 0.4 0.5 0.6 CYLINDER VOLUME -LITERS Figure 14. Pressure-volume diagram for a 10:1 compression ratio engine with rapid rate of flame propagation (Data Set B). Operating conditions listed in Table IX.

-12870 -- EXPERIMENTAL EXPERIMENTAL X NO HEAT TRANSFER 60 ___ 0 O NORMAL HEAT TRANSFER A TWICE NORMAL HEAT TRANSFER 50 I- 40,'. 30 crx 20 X__X x 0 0.1 0.2 0.3 0.4 0.5 0.6 CYLINDER VOLUME-LITERS Figure 15. Volume diagram for 10:1 compression ratio engine with reduced rate of flame propagation (Data Set C). Operating conditions listed in Table IX.

-129Z0.p i0 N. o VISd' 3dnSS~od y3GNIlAD "~ Y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~,~~~~~~~~~~~~~ - 4 4VI~d' 3NI5:I)I:0I - Io 4 0 0 (0

-13044 a -.....r 16 FUEL-AIR CYCLE rEFFICIENCY I FUEL-AIR CYCLE 42 -4 — MEAN EFFECTIVE 15 PRESSURE 40,,4 ) 38 --' ----- ------------- 13 g' 36. — - - - - 12 -- 1 —--— 9 3 34 I -'........ II 32 -- X - NO HEAT TRANSFER - -I-10 0 - NORMAL HEAT TRANSFER A TWICE NORMAL HEAT TRANSFER 30 - -- - - I — -- - 9 85 90 95 100 105 110 115 FLAME PROPAGATION RATE - % NORMAL RATE Figure 17. Calculated thermal efficiency and mean effective pressure vs flame propagation rate for a 10:1 compression ratio engine. Operating conditions listed in Table IX.

-1311.24 X 1.24 ____EXPANSION 1.20 1.16 1.12 1.08 I x 0 0 W 1.04 3 X NO HEAT TRANSFER 0 NORMAL HEAT TRANSFER ~ TWICE NORMAL HEAT TRANSFER X.96 -—.. X COMPRESSION.92.... 0.1.3.4.5.6.7 CYLINDER VOLUME - LITERS Figure 18. Entropy-volume diagram for a 10:1 compression ratio engine with normal rate of flame propagation (Data Set A).

-15280 I I I z F Z 43 o1 o Go / o 4_ ) CD 0 cd 9 a.^ %H co CIDZ~~~~~ ~ CO Uo co r-r U, 0 o Cd 0o s-I ( _$z~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~x 8 o 0O0 Q') Q Q QQ (~s~~- - s ~- n )' IV0- A11-11V-1VAV

-1335ivo- >4 OM 0 Q S 0 ~n —mr — 8 0 CUO. 8 <S /e I ^ o ~ U. 0 M NOISNVcX3 aW a- o:D.) z I. 0-c' 0 0 co NI:OM NOISN dXl 3 z I kz [ (^ w~~Ci P 4 1 \C W o$ SZ 0;c 0 ^ ------!_. ---- ^ ----- ^ ------ ^ —--- - o('-C)4 O _ _ _ _ _ _ U 0Id 0OO~~~~~~ 8 0 0 0 (~S~L- 0f)- (S - fn)'1qf - AlI118V-1VAV

-1341400 - 2700 o w I w 1800 710 7 w 1200F 2 Fla 2600 ss U. 10:1 compresn ro e heat transfer rates (Data Set A).)~U w 600 I' —BEGINNING OF CALCULATED -j COMBUSTION END OF COMBUSTION 400 ESTIMATED —---- 200 - -END OFCOMBUSTION FROM EXPERIMENTAL PRESSURE TIME DATA 700 710 720 10 20 30 40 BTC -— CRANK ANGLE DEGREES-ATC Figure 21. Flame speed and effective flame temperature vs crank angle for a 10:1 compression ratio engine with normal flame propagation and heat transfer rates (Data Set A).

-135100... / CURVE REDRAWN FROM RABEZANNA / -ETAL.(19) X 80 - X AVERAGE OF THREE HEAT TRANSFER RATES x, _ 3 260 - 60 80 100 no rate e pro Dat Set A).0 04 x 2 0 0 20 40 60 80 100 VOLUME PERCENT Figure 22. Relationship between mass and volume of the burned charge for a 10:1 compression ratio engine with normal rate of flame propagrtion (Data Set A).

APPETNDIX A POLYNOMIAL APPROXIMATION BY THE METHOD OF LEAST SQUARES In the discussion below the most important features of polynomial approximation by the method of least squares are presented along with an adaptation of this general method to the specific problem of obtaining empirical heat capacity equations from tabular data. For a complete treatment of the least squares method see a standard work on numerical analysis such as Reference 31. If a function f(x) is specified at a set of m + 1 equally reliable discrete points, xo, xl,... xm, an n'th degree polynomial of the form n f (x) Oa + alx + a2x2 + ) axk = y(x) k=O may be used to approximate f(x) over the set of points. Defining the error'v' by the equation n v = f(x) - y(x) = f(x) - akx k=O the principle of least squares defines the value of the a ks in such k a way that the sum of the v2's is a minimum. Relating vi to xi, this principle may be formally stated as follows: m m n 2 V i =f f(xi) - X akxi] = A Minimum i=O i=O k=O For a given set, xo, xl,... x, the above expression is a function of the ak's only, -136

"1375 To determine this minimum value, this function is differenciated with respect to each of the ak's and the resulting expressions equated to zero, Thus: m 2 vi =0o (k = 1) i=O m 2 v.x. = (k =2) i=0 0 m i n 2 ViXi 0 (k = n) i=O Noting that n vi = f(x) - y(xi) =Yi - akxi k=O where yi = f(xi), the above equations can be rewritten as follows. aO(m + 1)X + al xi an xi Yi aO Xi + a1 Xi + an xn = xYi 0 1i -0 n n+l n+n a xi + al Lx + ~ an Xi = iYi The summations are over all m + 1 pointso The above set of n + 1 equations can then be solved for the n + 1 unknowns (the ak's).

-138Note the coefficient matrix. m+ 1 x. 7 x. 2 n+l ~ i tz i 1 ~~0 i oo e V n Y Xn+1 n+n is symmetric. For the special case when f(x) = Cp, x = T, and n = 3, so that 2 5 Cp = a0 + alT + a2T + a3T the above set of equations reduces to: a (m + 1) + al T + a2 T2 + a T = Cp V2 3 a T+a1 T + a1 T + a2 T a = CpT 7T2 2 3 75 aO T2 + al jT3 + a2 T4 + a T5 = CT2 ao T + T4 + aT 2 T5 + a3 T6 = CpT3 Hildebrand(31), Chapter 10, describes a number of methods for solving such a system of non-homogeneous linear equations for ao, al, a2, and a3.

-139The root mean square error involved in such a polynomial approximation is defined as: m 1/2 RMS Error = [ E vi/(m+l)] i=O

APPENDIX B EQUILIBRIUM CONSTANT AS A FUNCTION OF TEMPERATURE Introduction The reader is referred to a text on chemical engineering thermodynamics for a more complete treatment of this subject. See, for example, Weber and Meissner(32), Chapter 21, Lewis and Randall(33) Chapter 20, or Hougen, Watson, and Ragatz(25), Chapter 25. If G is defined as the partial molal free-energy of a substance in any given state of pressure and temperature and G~ that in the standard state, then G_ - G~ = RT in f/f~ (B-l) where f is the fugacity in the given state and f~ is the fugacity in the standard state, For a chemical reaction of the form iL + mM +.o. = qQ + rR + oo0 (B-2) where., m, oo. q,r,,oo are the moles of component L,M,, Q,R,.oo respectively, the change in free-energy for this reaction in any state is AG = (qGQ + nGR + o. ) - (L + mGM + ) (B-3) By definition, a = f/f~ (B-5) where'a' is the activity in the nonstandard state. Combining Equations (B-l) through (B-5), the following equation is obtained: 140o

-141q r AG = AG~ + RTIn a aR I (B-6) When the reaction has reached a point such that there is no net change in the number of moles of any constituent, it is said that chemical equilibrium has been attained. The criterion for this equilibrium is that at constant temperature and pressure, there can be no change in the free-energy of the system. Consequently, when these limitations are imposed on Equation (B-6), AG must be zero for equilibrium and the following familiar expression for the equilibrium constant is obtained: AG~ = - RT an Ka K aQ aR.'o aa i m aL aM ~~ For a system in which the behavior of each component can be described by the equation of state P v = RT (B-7) the fugacity of each component becomes identically equal to its partial pressure in the system at all temperatures and pressures for which (B-7) is valid, When this is the case, the equilibrium constant is denoted by Kp, Choosing the standard state as the pure component at one atmosphere pressure, the equations become, AG~ = - RT in Kp Pq Pr I, (B-8) Kp - p m L M ~~~

A142where Pi is the partial pressure of the i'th component Kp is then referred to as the equilibrium constant at one atmosphere. The freeenergy change is termed the standard free-energy change of the reaction, This quantity depends upon temperature, the definition of the standard state of each component, and the number of moles entering into the stoichiometric Equation (B-2). Once the standard state pressure is fixed, the equilibrium constant becomes independent of the system pressure. Analogically to expression (B-4), expressions for AH~ and AS0, the standard state change in enthalpy and entropy for the reaction can be found. It immediately follows that AG~ = AH~ - TASo Effect of Temperature on i To determine the effect of temperature on the equilibrium constant, Equation (B-8) can be differentiated as follows: La[a (a, i] T[ aiG L T' RT )]p R LT aT T2 aT _P where = H~ AS0. T T However since ( )p = T( )p the above simplifies to: L T (p )] L [s'

-143AHO Since the quantity -2 is independent of pressure, this restriction can RT be removed. Then: d 0 d- (I K) dT (nKp RT2 Integrating this equation between T and To, where To is some reference temperature, and recalling that: TL O + TniCpidT + niCpi dT To P T T0 Products T Reactants the following equation for equilibrium constant as a function of temperature is obtained: ^p, -.ic = o fH 1 1 K TK TO R [1 n PT nPT R L OT T ] (B- 9) T -T + 7R niCpi - niCpi)dT dT To To Products Reactants

APPENDIX C CALCULATION OF THERMODYNAMIC PROPERTIES FROM EMPIRICAL HEAT CAPACITY EQUATIONS A. General For a system of's' chemical species, it is assumed that the ideal gas molal heat capacity at one atmosphere of the i-th component can be expressed as follows: C~ = ai+ aiT + 2iT2 + a3iT 298.16 - 1500~K b + b 11T bliT + T T b3 T 1500- 5500~K and that the molal enthalpy of formation and entropy at 298.16 and 1 atm pressure are (f298)i and (So298)i The standard state is the ideal gas at one atmosphere pressure. The calculation of the thermodynamic functions is made most conveniently by matrix algebra. The following matrix is defined for the temperature range 298.16- 1500~K: a1 a02 o..... all a12.. als a21 A = 31...... (f298)1 (144

-145and for the range 1500 - 35500~K: b01 b02..... bOs b b...... b b11 b12 i a 4 e ~ bls b21 a. b31.. (HO 1500)1 (S0 )... (5001 * * * where (Ho ) =(AH ) + (Ho H 1500 i f298) i 1500 298 i F'or a selected number of substances the appropriate constants for matrix A and B are presented in Tables I and II. It is assumed that the composition of the system of's' species whose properties are desired is known and that there are n moles of i component'i'. The following matrix will then be defined to represent the composition of the system: n= N

-146B. Method of Calculation 1. Computation of the Ideal Gas Enthalpy H = ni(LH~298)i + Z ni( - H29 Consider the second summation. For the temperature range 298.16 to 1500~K T ni(H - H98)i = ni C dT T0=298.16 2 TTa-i -; o T~aa, fo"1^ h- 1 = E ni [Toaoi(A-l) + 2 (0 -1) + (i-1)+ 3T (a1) [ 0 Oi(5A-1 2 A 3 A4 AFor the temperature range 1500 to 3500~K T Z n(HT - Hg8)i = ZE ni CodT + (H100 - H298)i n ni(HT - H298)i = CpidT + (H 0'T =1500 I r T62bli T'a5bri K'KB_ 4a + (H0 - H0 ) where 1500 298 0A = T/298.16 0B = T/1500 If the matrices KA and KB are defined as follows: 298.16 (eA-l) 298.16 (GA-1) (298.16)2 i298.1) l- I)3 44,449069 ( |1) |')3 ( 3 (3-|1) 8,835,413.6 (i3-l) KA = (98).16)4 e1)| 19,757,752102(0A4-1) 1 1 0 0

-1471500 (eB-1) 1500 (eB-l) (1500)| (-1) 1125.16(eB3-1) K 3 B B KB = |(1500)( 1) | | 1,265,625106(04 1) 1 1 0 0 the enthalpy of the mixture then can be calculated as the product of matrices. K' A * N r298.16 < T < 1500 H = { { ~ ~(C-1) t 4 B. N l 1500 < T < 35500 B (in cal) 2. Computation of the Ideal Gas Entropy = Z niS298i + Z ni(S-S 98)i R niln(xiP) where x. = mole fraction of the i-th component P = total system pressure Consider the second summation. For the temperature range 298.16 to 1500~K T Z ni(S-S~2n8)i i= Z n dT To=298.16 F= T, naoilnA+ Toali( ) + 2 ( ) = ni ailneA + Toali(OA-l) + -21 (O-l) + i (e5-1) 2 3 3 A

-148For the temperature range 1500 to 35500~K T Z ni(ST-S298) = n PiT (Soo - 98)i T ni(ST e9)i = S nji - (S1500 - S298)i ] T' =1500 0 2 T3b n ZG + T I bl(OB )+ 0 21 (02 i)+ 0 31 (e ) Z ni[bOilnOB + T (bl(B-1) + (eB-1) + (S1500 s298)i where JA = T/298.16' = T/1500 If the matrices KA and KB are defined now as follows: ln(eA) ln(OB) 298.16(OA-1) 1500(0B-1) 44449.693 ( -1) 1125o 103 (21) = BK= 6 8835413.6(03-1) 1125~10 (03-1) 0 0 1 1 the entropy of the mixture then can be calculated as follows: r KA * A * N 298.16 < T < 1500~K S = { }- R niln (xiP) ( (C-2) K B - N 1500 < T < 3500~K (in cal per ~K)

-1496H 3. Computation of (T)p The procedure here is the same as in Parts 1 and 2. If a matrix K is defined as follows: 1 T T2 K - T3 0 0 ( —H) then can be computed as the following product: 6T P 3-.H)s.P= rA r 298.16 < T < 15000K....dT P 1/T I 1 T K = T2 0 (TT)p = Cp =' N -C(-) then can be computed as the following product: a(in cl pr K) 298.16 < T < 1500~K ( P^ B} { ~ ~(CB4) 1500 < T _< 5500~K (in cal per OK2)

-1505. Computation of the.Equilibrium Constant K A general expression for Kp as a function of T with reference state at T0 is as follows: (see Equation (B-9) ) 0 T ARToQ 1 T in K ln K T T +J (En-CO-n-CO i ln P - l O - R " -T [(TR2- nIC i I Pi 0 Products Reactants +~[C1(lne+ -- i) 2 3 C2To 1 C5T0 (e2 2 CL3T1 + O(s+,,' " 2) CT + 2 + 3)+ C4- (93 +.3 4) 2 +) 6 kj- 12 )j where e = T/To C. nibji - nibji (j = 0, 1, 2, 3) Products Reactants For the temperature range 1500 < T < 3500~K, letT = 1500~K, then 0 = = T/1500 and note that -AG1500 ln K = R 15 Then substituting,Gioo ^iloo 1 r F in PT = 2980.785 + 2980.785 1 - R L 1 B ) (C-5) 750 C(&,+L - l) +1750 - C (2B 2 + 750 * C2B + 0- 1) + 375 10 + - 3) + 28125 4 104 O c4(eB +- - 4)

-151where AG~ and AH~ are the standard free-energy and enthalpy of reac1500 1o00 tion at 15000K in cal per mole and are listed in Table II for selected reactions. C. Computer Programs The computation of the thermodynamic properties and equilibrium constants by a computer is most conveniently made if the computational schemes are incorporated into a number of computer sub-programs or external functions. Such programs have been written in the MAD language for an IBM 704 or 709 computer and are listed in Appendix I. The functions dHarEE for computing enthalpy, entropy, dT- and (T)p, are called ENTHAL.O ENTROP., IPRIME., and SPRIME., respectively. That for computing the equilibrium constants is called EQUIL.

APPENDIX D THE TIME RATE OF TEMPERATURE CHANGE DURING EXPANSION In order to calculate the time rate of temperature change, aT/at during the expansion process of an internal combustion engine, the overall expansion can be approximated by a polytropic process. The maximum rate of change of volume with time is dV = (2TrN 60)(rb2/4) dt where r = the crank radius b = the bore N = the engine speed, rpm The temperature in the polytropic process is T T (V V1 and __ -n d V =T T (1-n) (V n (- ) Substituting aT T (n-) (. 2rb2N/120 (D-1) at V1 where T1 =th the temperature at TC V1 = the volume at TC n = the polytropic exponent -152

-7 53Some typical values of the constants are as follows: b = 4 in r = 1.25 in V1 = 3 33 cu in T = 2500 ~K N = 3000 rpm n = 1.5 Substituting these values in (D-l), L 1T 0 6 V1 1.3 * b - 10 ~ ( -) ~K/sec V, 1.3 (V-) will be between 0.1 and 1 so that, 0 to 1 05 to 6 ~K/sec at

APPENDIX E METHOD OF SOLUTION OF THE EQUATIONS OF SIMULTANEOUS GAS EQUILIBRIUM Equations (2-19) through (2-21) are repeated here for convenience Z + (4) + N- (2-19) 4K4 4K4 2 -(X/K + 1/K6) + (X/K3 + 1/K6)2 + 8 (1 + X/K2) ~ F.Nh 4(1 + X/K2) (22) (2-20) X/K1l F Nc Y2X X ZX X F F ~- = +-+ 2X + - + + F N + (2-21) O 1 + X/K1 K2 K K4 KC The problem is to find the value of X wich satisfies Equation (2-21), This equation can be restated as follows: f(X) = 0 (E-l) For any estimated value X1 the right hand side in general is not zero, f(X1) f and some correction to f(X1), Af(X1) must be made in order to equate it to zero. f(X1) + Af(Xl) = 0 (E-2) From (E-2), it is hoped that a correction AX1 to X1 can be found giving a value X2 which is closer to the correct answer. This correction is (df(X) f() (d(ln X))1' ln X (E-3) -154

-155Equating Equations (E-2) and (E-3), ff(x) f= (x1) f(X1) = - ( d(ln )1 ~ lin X = -- ln X Re-arranging, 21 f(X) f(x~) or -f(Xl) X2= X1 exp x (x) In general, for the i-th trial, -f (Xi) i+ = Xi. exp Xif(X) (E-4) The reason for generating Xi+l in this particular manner is to assure that it will always be positive if X1 initially is assumed positive. Thus the possibility of obtaining a solution with some negative partial pressures is eliminated. The calculation of f'(X) presents some problem. In the following equations the argument X will be dropped for convenience. df af df dZ af ff - f E) + ( f ( \ + If(^ dx y YdX aZ dX ax From Equation (2-21) f 2XY X ff x Y K2 K3 6Z K4 (E-6) O ff - Nc Kl y2 Y Z 1 -a-x (x= K + K4X + -- + ax (X.+Kz)2 K2 K3 Kj K5

-156From Equation (2-20) dY = (5 + 4F ) Nh) / - 4/K2 (-) / (E-7) dX K3 K3 K2 where a = 4 (1 + X/K2) = X/K3 + 1/K6 7 = + 2cF * Nh From Equation (2-19) dZ X/K4 - 1 ax - -- 44(E-8) dX 4K4 where P= V (K )+ 8 F n N If f(x) and f'(X) are evaluated at X. by Equations (2-21) and (E-5), a new values of X, Xi..l, can be calculated from Equation (E-4)o The Xi,.+ - Xi process can be repeated until - is less than some prescribed Xi value E2. The number of iterations required for convergence is about four, plus an additional four for each power of ten from which the estimate differs from the correct answer. Table XI gives the accuracy with which the partial pressures are calculated for various values of C2o It is assumed that the partial pressures are of the form OXXXX0X L 10XX. The number entered in the table is the digit which changes when the value of ~ was decreased by successive powers of 10. 2

-157In connection with the actual mechanics of the computer subroutine (see the flow diagram, Figure 23) which solves these equations for the partial pressures and moles of each component, it should be pointed out that f(xi) when Equation (E-4) is being computed and the quantity Xif'(X) exceeds 16, X1 is multiplied or divided by the quantity'e', the base of the natural logarithms. This precludes any wild fluctuation of the successive estimates for X. In the many thousands of times which this subroutine has.been called upon to compute the equilibrium composition, it has never failed to converge on the correct answers regardless of the value of the initial estimate.

-158TABLE XI DIGIT CHANGED IN THE PARTIAL PRESSURE OF EACH CONSTITUENT FOR SELECTED VALUES OF RELATIVE ERROR Stoiciometric Octene-Air Mixture Temperature, 2500~K Pressure, 19 Atm Relative Error xE1ror x 02 N2 CO2 H20 CO H2 OH NO 0 H X+1 _ —— x 2 Xi 0.01 4 7 5 6 4 4 4 4 4 4 0.001 5 8 6 7 5 5 5 5 5 5 0.0001 7 8 NC 7 7 7 7 7 7 7 Oo00001 NC NC NC NC NC 8 NC 8 8 8 NC - No Change

-1590X~~~~~~~ cLa.~~ Ej C\J i q N 0l IV I'I 0 10 o 0 - --- l o 4-~~~c ~~~~~~~ 4 ~II~~, O4 ~~x -o oo ] o ___^___ ______-I I X 0), o Af/^ ^^0 u "~~ oI 4CH 0 -t V o(0A I' 0 0 IQ)H C. CO ('3 VI. O I 0 a / \ ^So-p~co pcodojo i-i-~-^l^^ C ^ ^ ^. IH z IICO z co co 1E-f H, ~ -r EI co ET IId

APPENDIX F MATHEMATICAL ANALYSIS, FLOW DIAGRAM, AND COMPUTER PROGRAM LISTING FOR THE FUEL-AIR CYCLE A, General The mathematical analysis of the fuel-air cycle treats a number of quantities as variables. These are the fuel, the air-fuel ratio, the manifold temperature and pressure, the exhaust pressure, and the compression ratio. The fuel is described by specifying the number of carbon and hydrogen atoms per molecule of fuel; its enthalpy of combustion at the reference state; the constants for its empirical heat capacity equation, Table I; and its enthalpy of formation and entropy at the reference state, Table II. Two additional variables arise because of the iterative nature of some of the calculations. These are El, the allowable relative error in those thermodynamic properties calculated by trial and error methods, and e2, the allowable error in the equilibrium composition (see Appendix E). Among the quantities calculated from the cycle analysis are the pressure, temperature, enthalpy, entropy, and internal energy at each point of Figure 3. The indicated thermal efficiency, mean effective pressure, and exhaust gas residual fraction are also calculated. The analysis assumes that all enthalpies and entropies and their derivatives are computed by the methods of Chapter II, Section B, and the equilibrium composition of the products of combustion is computed by those of Chapter II, Section D. Internal energies and their derivatives are computed from the corresponding quantities for the enthalpy. -160

-161For a perfect gas, these are U = H - nRT and dU = dH nR dT dT Subscripts on thermodynamic properties refer to points on Figure 35 The metric system is used throughout. B. Mathematical Analysis 1o Exhaust Residual - Initial Approximation Computation begins with an assumption of the residual exhaust gas temperature T5. If the clearance volume is one liter and the pressure is Pe, the total number of moles remaining in the clearance volume is n = Pe/RT (F-l) An approximate exhaust gas composition can be calculated if it is assumed that the total number of moles of products per mole of fuel burned is the sum of the coefficients of the products in Equation 2-2. This quantity is ntt = a + b/2 + (a + b/4)(cx + x - l) (F2) The number of moles of each constituent present in the exhaust then will n5 be its coefficient from Equation (2-2)multiplie by n In the case of oxygen, the absolute value is taken to avoid a negative value for rich mixtures. Calculated in this manner, the exhaust composition is only approximate. This initial approximation is not repeated for subsequent cycles. At the end of the complete cycle, a new exhaust temperature and composition is computed from equilibrium considerations. The cycle is then repeated until there is an insignificant change in these quanitties from cycle to cycle. To facilitate the computation of the first cycle, the allowable

-162relative error El, discussed later, is increased by a factor of 100, 2. Mixing of the Fresh Charge and Exhaust Residual The inlet conditions, Point 0, being known, the thermodynamic properties of the fresh charge can be calculated per mole. After induction, the mixture will be contained in a volume of l1r liters, where'r' is the compression ratio. The number of moles of fresh charge and the final temperature of the mixture are to be found. If an initial guess T1 is made for the mixture temperature, the number of moles of fresh charge is Pir Pi RT - n5 (F-3) The prime denotes a temporary or approximate value. In a manner similar to that of Part 1, the individual number of moles of fuel, oxygen, and nitrogen can be calculated. If this entering mass is lumped with the residual exhaust gas and the enthalpy of the mixture is calculated, at TP 1 a value H1 is found. For the ideal adiabatic inlet process envisioned here and described in detail in Reference 45, Chapter 4, the enthalpy of the mixture is Hi = H + U + P.rJ (F-4) Whenever H' - H H -1 - > 1 (F-5) HI 1 where 1 is defined as the relative error, a corrected value for T{, T" must be found. This corrected value can be found by Newton's method, a

163derivation for which is found in Appendix G. The new Value is Hi - H 1 1. T" T- 1 f (F-6) \dT/ where, in light of Equations F-3 and F-4, dHl/1 HI n dHI - ^ (1 - 5 ) + T (F-7) This process is repeated until Equation(F-5) is not satisfied. The conditions at Point 1 are now known. 3. Isentropic Compression At Roint 2, the volume is one liter and S2 = S1. The composition remains unchanged during the compression. The temperature can be found by the following trial and error method. Assume a temperature T'. Then PI = n2RT2 (F-8) where n2 = n1. The entropy SI then can be calculated. Whenever SI - s 252 > E1 (F-9) I S a new value T2 must be found. S - S 2 2 T " =, I (F-10) where ~ wheeas2 as2 n2R [*r J kVrl-l T- (F-ll) V P 2 The process is repeated until Equation(F-9)is not satisfied. The conditions at Point 2 are now known.

-1644. Constant Volume Adiabatic Combustion This process occurs at constant internal energy and constant volume, that is U3 = U2 and V3 - 1. Moreover the products are in a state of chemical equilibrium. The problem is to find the adiabatic flame temperature and pressure at Point 3. If a temperature TV is assumed, the composition can be calculated according to the methods of Chapter II. The internal energy U1 can then be calculated. Whenever I u - U1 3- 3 >^ El(F-12) a new value T" must be found. One method for finding this is to use Newton's method, U- - u T T'' (F-13) dT wherein it is assumed that the difference between T'' and T! is so small that the effects of composition change are negligible. Because this is not always true, convergence may be slow or may not be obtained at all. However a second method can be employed, the Half-Interval convergence method. This method, which will always converge on the correct answer, is described in Appendix G. In this analysis both methods are employed. If a satisfactory solution is not found after using Newton's convergence method to generate five successive approximations to T, the Half-Interval method is used. If at the end of this fifth trial, the difference between T" and T' is AT, the next trial for T will be 3 3 3 U1 - U T1 T' - AT 33 (F-14) 3 3 IU - U I

-165Then whenever the quantity (U? - U3) changes sign, AT is halved. This half-interval method is continued until Equation F-12 is not satisfied. The conditions at Point 3 are then knowno 5. Isentropic Expansion At Point 4, the volume is'r' liters and S4 = S3. The products are still in a state of chemical equilibrium. The temperature T4 can be found by a method similar to that described in Section 3 for the compression. A temperature T' is assumed, the composition calculated, and the entropy SI determined. Whenever I- S S4 _ 4 (F-15) a new value T" must be found. Newton's method can be successfully used to generate T1. Whenever Equation F-15 is not satisfied, the conditions at Point 4 can be considered to be known. 6. Expansion to Exhaust Pressure When the exhaust valve opens the contents of the cylinder expand to the exhaust pressure, the overall process being irreversibleo Nevertheless, those gases remaining in the cylinder have undergone an isentropic expansion. At Point 4' V4 = r, S4 = S4 and the pressure is P For the purposes of calculating T4, let S4 = S4, that is, assume all the gas has expanded isentropically. The temperature TI can be found by a method identical to that of Section 5. The equilibrium composition is calculated for the case where the pressure and temperature, rather than the volume and temperature are known.

-1667. Exhaust Residual At Point 5, the piston has.exhausted all the products except those remaining in the clearance volume. The molar thermodynamic properties are identical to those at Point 4'. The fraction of total mass retained in the cylinder is 1/VT. Thus the temperature and composition of the exhaust residual are completely determined. Whenever T4- T55 (F-16) T where T5 is the exhaust gas temperature at the beginning of the cycle and T4, is that at the end, the entire cycle is repeated starting with Section 2. Prior to the second time the cycle is executed the relative error, Cl, is reduced to its initial value by dividing it by a factor of 100o The cycle is always repeated at least once. When e1 =.00001, about four complete cycles must be exhausted before Equation (F-16) is not satisfied. 8. Net Work The net work is the difference between the expansion and compression work plus any pumping work. This quantity is Wt = (U-U4) - (U2-U) + (r-)(Pie) J (17) 9. Thermal Efficiency The indicated thermal efficiency, defined as the net cycle work divided by the heat of combustion of the fuel consumed, is Wt -* 100 A -~.5 F (F-18) aHc~

-167where Fo are the moles of fuel consumed, calculated in Section 2, and LH~ is the higher heating value of the fuel per mole at 298.16~K and one atmosphere pressure. 10. Mean Effective Pressure The mean effective pressure is defined as the net work divided by the displacement of the engine. This quantity is wt tmep = mep (r - )J (F-19)

-168C. Flow Diagram r READ a, b, AH~o ~o READ CONSTANTS FOR HEAT C, VALUES FOR / - A CAPACITY EQUATIONS.- _ FUEL FROM TABLES I t START J-r TABLE I, AND FUNDAMENTAL _ AND II, DATA TABLE II FOR ALL AND xl... xnf SUBSTANCES EXCEPT FUEL T5 = 1200~K THROUGH \2 = e10 FOR i=l,1, FOR ii1 R = r, PiPe, T R2 = 1.9872 i > nf i ii > C = 3.764 4 x^xf XX k.> n5= P, /RT; COMPUTE n5 L5 5 l | ntOt FROM nr2= n — (a+/4(x-1) EQUATION (F-2) tot nr6 = 0 ns; b/2 n 5 na cx(a+b/4) nr - ~ nn r4 = 0 nr3 r77 = 4-nr5 tot ntot tot rzn10 I1 = ~' 100. _; T * ~ l j-oo.n5 TL- Ti'K k:l ext T = T

-169( 7 }>J=j+1,i Ti=NextT n'= - n5 F = 0no cl 0O\^ ___ RT' 5 0 +(a+b/4)(c+l) nmi = nfi+nri m 1 2 ri fl 2 _ fl 2=F x(a+b/4) f i =1,2,.. 7 COMPUTE H, Hi> i= T H1, lTO u *L OMPUTE Next HC-OM U USING EQUATIO FROM EQ.~F-6)...+ AAND (.S2/6T)V COMPUTE Next iI FROM T, T" FROM AND CF-8) AND (F-l) i) Nc=Foa+nm4+nm6 Nh Fob+2(nm+nm7) k^.1 NO = x(2Nc+ 112Nh) COMPUTE <N- Next=T C- g~lH2 AND H< 3 T5=4T (SEE EQUATIONS (2-5 TO (2-8) ) — NextT=T5 U Ul2 j ) =0

-170COMPUTE EQUILIBRIUM f {5 V-^ J j^^-^ TimNextT CONSTANTS, COMPOSITION'T\ —NextT OF PRODUCTS (THE npi ), AND n1 COMPUTE <EL I NST'-NextTS q=U-U NextT=T " COMPUTE O ___ ______FROM EQ.(-l -- - - aT= — T/ 2 qq. COMPUTE P =nRT -ANS --- S4 = S' 3 3 3 nHA~s3 4 COMPUTE -EQUILIBRIUM CONSTANTS, COMPOSITION OF PRODUCTS, (THE npi)) 4-T' - Next1T(T AND n, 4 COMBUTE S4 AND m _ _ n/RT4 (6S4,, S4 -S'-" P4 r --- NextT-'T PSOT')': Ej (SEE EQ. (F-ll) -' - V4I — 44 ^-^e NextT=T4 41 COMPUTE (P ) j=O.- S'S4 NextV=V4, --- k:l H AND U4

-171COMPUTE [ ~~TP )^ =J 4Next1 EQUILIBRIUM V=NextV CONSTANTS COMPUTE S1< tV41 - NextV n4fRT4j, COMPUTE AND 4 1 P -; NextV- EQUILIBRIUM AN DT )V4 / e COMPOSITION (Gasql. ^ —--------- " ~~(THE npi) AND NextT = T" > S;,-S | S, -S|COMPUTE I | nP2np2+i/2(np8+npnpl 4.-^ -^)1~/ r 4. H AND U4,18 nP3= np3+l/2np9 4,-s p7 nt/6T p7+4/2(n p8+npll) PRINT Pi, Pe, x, Ti, r, AH~, Tl=el/100 P iJ Pei O ~ | / T4 6=ep O) T0, Pi H, i,-lO, Tg, P, Hg' -'..- =T41 E2=E2/10O 2. T1, Pij Hj, SI, Ull I 2, T2, P2, H2, S2, U2, _ T T k 5, T35 P3, H3, S3 U3j 5' 4, T4, P4, H4, S4, U4, T 4', T4', P4', H4', S41' U4, 5, T5, P5, HS, S5, U5, PRINT U2 - U2 - U COMPUTE U4 - U NET WORK 4 - U3_ (EQN. (F-17)() (r-l)(Pi-Pe)J, 1 -NET WORK,, (EQN.(F-18) )ET WORK MEP P, (EQN.(F-1) ) 1/V4,

-172D. Computer Program for the Fuel-Air Cycle The following pages contain a listing of the computer program for the fuel-air cycle engine written in the MAD language for an IBM 704 computer. The external functions ENTHAL., ENTROP., HPRIME., and SPRIME. which compute the enthalpy and entropy as well as their temperature derivatives at constant pressure; EQUIL., the function which calculates the six equilibrium constants; and AMOUNT., the function which calculates the equilibrium composition, are listed in Appendix I and are not repeated here. The program contains a number of variable names most of which are explained in Appendix I. *Those names pertaining to this program only are: CARDS number of combinations of compression ratio, manifold pressure and temperature, and exhaust pressure for which computations are to be made: C NAME whenever NAME is not blank, additional intermediate output is provided. PHi an initial estimate of the value of X = at Point 0i (This is used in the computation of the equilibrium composition. In Appendix E it corresponds to X1 and in the external function AMOUNT. it corresponds to PH.) R2 gas constant in heat units VB clearance plus swept volumes, equal to r VT clearance volume, equal to 1 *Symbol after colon is an alternate designation. Symbol after colon is an alternate designation.

-173 $COMPILE MADePRINT OBJECTsPUNCH OBJECTEXECUTEDUMP HOTELOO1 DIMENSION AL(87 ALD-IM)',AH(-'87ALDIM)-N(-11) RE(12)7,K(11) — P("11)- -.:1__ 1,X(50,SPACE(4.1) INTEGER I IlJ1,J2',RE-CARDS'NFA"NAME VECTOR VALUES ALDIM 2,0,8,_` —-- - ROGR-_-C_.-O-.'6'R jM.Mr'1'ONS ALA-'HiW P,-K,'R 2 NC H N O-NN H -- NO N' RJITSPACE.ERR-O1Z- READ FORMAT SPHT1,NAME,AL(2l)..AL ( 118 ),AH(2,1)...AH( 118)._~-~~ —_~ —^.`~-_~-,___.__ ^_^ ^_^^ E C T R V A ~-'-`T —? —---—'-(-'E' —-— 8"* START READ FORMAT FUELRE(1)...,RE(12),ABHCOMBERROR1,CARDSAL(1,1 )........ AL( 1.8).AH(1)1 *....AH( 1,88) VECTOR VALUES FUEL = $12C6/4F10.5,I5/(4E15.8)*$ PRINT FORMAT-DUMP1 TAL-1;-.eAL —T8VECTOR VALUES DUMP1 = $1H1,4HAL =/(8E15.8)*$ PH3 = 1e -— H —-----— 1 — P —------- - ------------------------- ------ T5 = 1200. ERROR2 = ERRORi/10. R =.08205 R2 = 1.9872 C = 3.764 _. PRINT.....T FORMAT DUMP2.AH(1,1)...AH( 11,8) VECTOR VALUES DUMP2 s=$1HO,4HAH =/(8E15" 8)-*$ READ FORMAT' FULAAIRNFAX( 1).,X(NFA) VECTOR VALUES FULAIR = $I10/(14F5.4)*$ THROUGH LOOP1,FOR II = 1.lt11.G.CARDS READ FORMAT E'NG —NECR Nt-OA-i-PEXFHTMANVECTOR VALUES ENGINE = $ 6F10.5*$ PMAN....T7T~MA-6TI'-.':9 "-......... PEXH = PEXH/14.696 TMAN = TMAN/1.8 —'.............. —-------------- VT = 1./61.03 VB = CR*VT- -— _- -. —-__.THROUGH LOOP.,FOR I =1#1I. G*N FA T R U HL O P,F R 1....N.........*...................................... WHENEVER NAME.NE.$ $.... - - --- - PE[ 1i.., —-(F-ik — ME-;-Ai E(. RE 1.T-. —s-^ —-;.qADR_,.PT4A.NT46 P..X. HT. 1MAN*1.8,CR,HCOMB,VT*61.03,(VB-VT)*61 03 --- __. —O CO-N ONA ------.- - --. —-—. —------—. —.-.. —— ^ —-- -. —--.-.-.^.-,^ —.___ __ VECTOR VALUES HEAD1 = $1H1 /1HO#S28.64HIDEALIZED THERMODYN 1AMIC CYCLE FOR THE INTERNAL COMBU'"ST-IO'N" E'NG-INE/T —1-HOIO'1WIN'HTS- I"S T... 2A C6,15H RUN EMPLOYING 2C6,37H AS A FUEL* A'DDITIONAL COMMENT 3S ARE./lH0,9C6/ 1 HO ------!+-4FOLD PRESSURE = F10.5:,4H PSIS7 18MHEXHAUS'T PRESSURE = F10..5; 54H PS S8,16-HAI R-FUEL RAT'IO = F-'1-6'5'/1HO, 22HMANI FOLD T'EMPEMRATUR 6_____ _ 6E = F10.5,2H K56,19HCOMPRESSION RATIO = F10.5,S ll 17HH 7 OF COMBUSTION = F10.2,9'H CAL/MOLE/1:HO,18HCLEARANCE VOLUME:: = 8F10.5,7H CU.IN.,S5,14HSWEPT VOLUME = F10.5,7H CU.IN.*$ - -: —".-..-.................................................................................____ -.-____ —_-__________.___.J2 = 1 N5 = PEXH*VT/R/T5..... F5 = N5/(A+B/2-.+(A+B/4.)*(C*X+X-l. )) N(2)-... ABS'(F5*(A+B/4* —-X-'1)Y.. -—. ---- N2 = N(2) N(3) = F5*(A+B/4.)*C*X N3'= N(3)....""".......'.' I':4" —=N...4 F5*A"' - -A —.... --—.............-... —.... —... —------ --—.....J_1..,.-F5 *B/. =. ____F.,_........_ N(6) = 0. N(7) = 0....................._.........................................................................................

-174ERROR1 = ERROR1*100. ERROR2 = ERROR2*O100 TRANSFER TO LOCI L_-0.._O._____- J2 = J2 + 1 _ —-- T5 = T4P N5' PEXH*VT/R/T -.. NLL.F _2,,1.'~J.{.2J_1..,L 3N.{_:_+~NA.l ~N I II-(5) N I (_~N 6N:.). l......... N(2').= F5*N(2). -----— 2 L —-------------------------------------- N(3) = F5 N(3') ------- ---------- — N3 N —-3) —-------------------------- N.('4) = F5*N'(4) ___~_ -N5_ = F5*N(5) __-F_-_*__.______ -.... N(6) = F5*N(6) N(7) = F5*N(7) LOCI EXECUTE ENTROP.(2,7,S5,TN5,PEXH,N) EXEC UTEE ENTHAL r (2,7H5,T N)U5 = H5 - N5*.R2*T _W H EN E VE R.... NAM E.................................. $...................... PRINT. FORMAT HEAD2 PRINT FORMAT OUT,5,T5,PEXHH5oSSU5,N5,F5,N(2)..N(7) END OF'CONDITIONAL VECTOR VALUES HEAD2 =$1HO/8HOSTAT'IONS5,6HT - K,S58HP - ATM 1i.S558HH - CAL.$S7,11HS - CAL'./*KS8,8HU - CAL.S7,llHTOTAL MOL 2E5,S7,1HF*$.......... ^.. _. ^.,............................, ^...._............... TO = TMAN j'= 0. WHENEVER J2.E."1~,T=TO NEXTT = T1 ------— ^ —------------------------------ ----------- ---------------'LOOP4 T.= NEXTT __________~.~~~~~~L. =~j. + i,, NO = PMAN*VB/R/T-N5 FO NO/(1. +X*(A+B/4.)+C*X*(A+B/4.)) N(i') = FO N(2) = FO*X*(A+B-/4e,) N'(3) = N(2)*C EXECUTE ENTHAL.(1,3,HOTMANN). EXE'CUTE HPR"IM E'l'-"',3,-HPR"I M"',T,N-)'. HPRIM a HP.RIM - HO/T*(i. + N5/NO) H = HO + U5' + PMAN*VT*246.2179 - - - -N(2) = N(2) -+ N2 N(3) = N(3) + N3 ____ ^EXECUTE.ENTHA L,(.-7,HMIX.I N __'__ NEXTT = T.- (HMIX-H1)/HPRIM" WHENEVER.ABS.((HMIX-H.1)/HI)*.G.ERRORiTRANSFER TO LOOP4 T1 = T NT i NO T N5 EXECUTE ENTROPs(it7.$SlsTNIPMANN) U 1 L1R 2 V ____ ____* ___T__________ __T WHENEVER NAME*NE.s $ PRINT FORMAT-OUT, O,TOPMANHO,O,ONOFOFOFO*X*(A+B/4 ),FO* i'X*C*(A+B/4.),J PRINT FORMAT. OUT~1,iTlPMANH1,SlS,U1,NiON(1)**.N(7),J END OF CONDITIONAL.WHENEV1 E.R ERJ2 E i..L T. T'l*CR.P,*3 ~.......... _ N2 = N1 J = 0.

-175NEXTT = T2 LOOP5 T = NEXTT J = J + 1. P2 = T*CR*PMAN/Tl.. —---. EX,-EC UT E ENTRP —-—. 2,P-N.....N. —--... EX.ECUTE SPRIME ( 1,7SPR'IM,T..N) SPRIM = SPRIM - N2*R2/T NEXTT = T - (S2 - 51)/SPRIM W'"ffHENEVER —-A S (5 2-S51)/ —51- ).G'ER'ROR- 1rRAN SFE'R TO'OOP 5 - EXECUTE ENTHAL. (1,7H2,TN) ---— T - - -. --------------------.-.-. — -. —-.- -- ------------ T2 = T U2 = H2 - N2*R2*T ---- --------------— U2 — = -j2 -.-N2 R- - - ------- --------------------— ~_~ - -------—. —-- ---- WHENEVER NAME.NE.$ $ PRINT FORMAT OUT, 2,T2,P2,H2,S2,U2,N2,O.,N(1)...N(7),J END OF CONDITIONAL NC = FO*A + N(4) + N(6) NO =(2.*NC+.5*NH)*X NN = NO*C WHENEVER J2*.E.1T3 = 4.*T2 NEXTT = T3. = 0. LOOP6 T = NEXTT J = J + 1. --------—.. —--------— ^XE ^iT-F-(3U I —-- - -- --------- ------------------------------ ----— c —-- - EXECUTE AMOUNT.e(TVTN3,PH3,N) U3 = H3 - N3*R2*T -WHENEVER~J J.G 5'TRANSFE-R TO i"HAL.-IN"'"''-'...'.'.'".. EXECUTE HPRIME. (2 11 HPRIM#T'N) ^ —- - -- -- - --- -- ----- --- -- --- -- - - - - -- UPRIM = HPRIM - N3*R2 Q = (U2-U3)/T/UPRIM WHENEVER *ABS.(Q).L'. NEXTT = T*EXP.(Q) OTHERWISE.'NEXTT = T + 100o.*Q/.ABS.(Q) END OF CONDITIONAL DIF = *.ABS(T - NEXTT).SAVE DI F WHENEVER *ABS.((U3-U2)/U2)*.G.ERRORlITRANSFER TO LOOP6 TRANSFER TO END -HA_.F.IN QQ = U2 - U'3 WHENEVER Q/QQ *L4O'sDIIF = DIF/2NEXTT._...T + D I.F*.QQ/.ABS.( QQ')......... Q = QQ WHENEVER ~ABS ((U3-U2)/U2/U ).G.ERRORTRANSFER TO LOOP6 END P3- = N3*R*T/VT. T3 = T. _....-...EXECU-TE E.N —— ROP (-2 11-T —P-..5.... WHENEVER NAME.NE.$ $ PRINT FORMAT OUT33,T3,P3,H3 S3,U3'N3;o-N")-;N i)N( 1) jP ) 1P(11) SAVE END OF CONDITIONAL WHENEVER. J2.E#.1T4 = T3* ( 1/CR).P..3 NEXTT = T4.-.. _ -........ 0................. LOOP7 T = NEXTT J = J_~ 1.

-176-.......-..... —.................... E -'C —' - Q - L','( ).......... EXECUTE AMOUNTo(TVB9N4,PH4,N) P4 =N4*R*T/VB EXECUTE ENTROP.(2,11,S4,TpN4,P4,N) EXECUTE SPRIME'"(2'11 SPRIM, TN) SPRIM = SPRIM - N4*R2/T NEXTT = T - (S4-S3)/SPRIM WHENEVER.ABS.((S4-S3)/S3)*G.ERROR1,TRANSFER TO LOOP7 T4 = T EXECUTE ENTHAL#(2,_llH4,TN) U4 = H4 - N4*R2*T WHENEVER NAMENE.$ $ PRINT FORMAT OUT,4,"Tt4,P4'H4 S4-U4,N4,0., N( 1)...N( 11), JP(l ).... _.._11).......................:.._ 1. END OF CONDITIONAL WHENEVER J2 *E.1 T4P = T4 PH4 P = PH4................. V4P = N4*R*T4P/PEXH END.OF.CONDITIONAL NEXTT = T4P J = O0 NEXTV = V4P LOOP8 T = NEXTT —--------------- J = J + 1. EXECUTE EQUIL.(T) _ J3 = 0. BACK V = NEXTV J3 =J3 + 1. EXECUTE AMOUNT,(TVN4PPH4PN) NEXTV = N4P*R*T/PEXH __....._.. _ WHENEVER_ A'B... (NEXTV-V )/V ).G.ERROR 1,AN__FER TRO BACK. EXECUTE ENTROP( i2,11,S4P',TN4PPEXHN') EXECUTE SPRIME(2,tll1SPRIMTN)_ NEXTT = T - (S4P-S4)/SPRIM WHENEVER.ABS.((S4P-S4)/S4E).*G.ERROR!TRANSFER TO LOOP8 T4P = T P4P V N4P*R*T/V..............__...___. —_ ——.EC.ENTHA.L..2. 2...1H4:PT.N... U4.P = H4P - N4P*R2*T "-WHENEVER NAME NE$ $ $ PRINT FORMAT OUT'45# T4PP4P, H4P,S4PU4PtN4PO.,NV(l)...N(11) 1,JP(1):..P(11) J3 PRINT FORMAT NOTICE,J2,.ABS.(T5-T4P),NCtNHNONNVTVB END OF CONDITIONAL VECTOR VALUES NOTICE = $1HOQ23HAFTER ITERATION: NUMBER I2*51H ~1 THE ABSOLUTE DIFFERENCE BETWEEN T5 AND T4PRIME IS F10.5/1HO, —' —'246HtHE MOLE A-TOMiS OF THE FOLLOWIN' SBSTANC-S'' ARE-9H C-RBON 3E15.811.H HYDROGEN: E15.8#9H OXYGEN = E15l8,11H NITROGEN = E 415.8/5H VT = E158,912H Le AND VB = E15.8,3H L,*$ N(2) = N(2)+.5*(N(8)+N(9)+N(10)) N(3) = N(3) + "5*N(9) N(7) = N(7) + *5*(N(8)+N('11)) W WHENEVER J2 sEe 1 ___ ERROR1 = ERROR1/100. ERROR2 = ERROR2/100. TRANSFER TO LOOP

-177END OF CONDITIONAL WHENEVER.ABS.((T5-T4P)/T5),G*ERRORlTRANSFER TO LOOP PRINT FORMAT HEAD1ARE( )* -.RE( 2)PMA N*i14- 69- 6-"P'EXH 4r U *'-46gX-T 1MAN*1,8,CR HCOMB VT*61.03 (VB-VT )61.03 PR FNT- O —-R-M AT- H' —— AD-' 5-.- _-...- ---- --- -- - -- VECTOR VALUES HEAD3 = $1HOS18,36HSUMMARY OF RESULTS IN ENGLI ~...1""" -— SH SYSTEMt7HO 7HSTAT-ON',56'H T *R- R.,-S58H — 8 PSL-0,S"S —52 8HH - BTU..S511HS - BTU,/*R,56,8HU - CAL*$'' —'' PRINT FORMAT SUMMRYiO,TO*1*8,PMAN*14.696,HO/252*161,0,.-O'.,'-;"1",T'-' 11*1.8,PMAN*14.696,H1/252.161,51/252.161/1.8,U1/252.161,2,T2*1 2.8tP2*4.4696H2 /252.161S 2/252.161 /1.89U2/252 161,3,T T3* 1 8 P 3*14.696,H3/252.161,S3/252.161/1..8,U3/252.161,4,T4*1.8,P4*14.6 496,H4/252.16i-,S4/252. 161/ i8,U4i2 2161 45,T4P*1.8 P4P* 14696 5,_H4P/25161S4PS.4/252. 161/1.8 U4P/252.161_ __ __ _ 65,T5*1*.8,PEXH*14.696,H5/252. 61.55/252. 161/1.8,U5/252.161 VECTOR VALUES SUMMRY = $1H 4I4,S6,2F10O.33F15,8*$ VECT'OR- VALUES OUT. $iHO I4'S6,2F16 —i5'5E'-i-78-/7(6EQ*20.*$ - - WORK12 = (U2-U1)/252.161 WORK43 U3-U4)/252.161 - - - - - - --. WPUMP = ((VB-VT)*( PMAN-PEXH) )*24 2179/252. 161 WNET = WORK43-WORK12+WPUMP...RINT FORMAT RESULT,WORK12,WORK43 WPUMP WNEWNETWN/HCOMB/FO*25 1216.1,WNET*14.696/ (VB-VT)/24.2179*252.61 VECTOR VALUES RESULT = $1H.O/1HC,S10,7HRESULTS/lH+,S10,7HRESUL iTS/lHO 3i1HUNDER THE FOLLOWING ASSUMPTIONS/40H 1) ISENTROPIC C 20MPRESSION AND EXPANSION/30H 2) CONSTANT VOLUME COMBUSTION/20 3H 3) NO HEAT TRANSFER/1H0/1HO/ 4 _S6#30HCOMPRESSION WORK = E15#84H BTU/ 5 S6,3OHEXPANSION WORK --—.... E15:-8 —-4H~ BTU/ —---- 6 S6#30HPUMPING WORK - E15I8+4H BTU/ 7 S6#30HNET CYCLE WORK -------- — " EYY7TF —------ 8 S6t30HINDICATED THERMAL EFFICIENCY= E15.8o8H PERCENT/ 9 S6,30HMEAN EFFECTIVE PRESSURE - E15.8.4H PSI*$ ---- LOOP1 PRINT FORMAT RESULLVT/V4P FO* ( A+B/4 )* ( C*X+X) /(VB-VT ) 24 464 1028 VECTOR VALUES RESULL = $ 1 S6,3OHRESIDUAL WEIGHT FRACTION - — 5= --- Fl ------- ------- 2 S6330HVOLUMETRIC EFFICIENCY = E15.8#25H BASED ON 1 ATM 3. AND 25*K *$ TRANSFER TO.START END OF PROGRAM' —------ ---

APPENDIX G ITERATIVE METHODS FOR SOLUTION OF IMPLICIT FUNCTIONS OF A SINGLE VARIABLE A. General Consider a function of one variable, f(x) = 0 (G-l) It is desired to find the value of x which will satisfy(G-l). Assuming an initial value, xl, in general the function f(xl) will not be equal to zero and must be corrected by some amount, Af(xl), in order to equate it to zero. That is f(x1) + Af(xl) = 0 (G-2) It remains to find a correction to xl, Ax1, giving a new value x2 which is closer to the correct answer. B. Methods of Solution 1. Newton's Method Newton's method proposes the following relation for determining X2: df(x) Af(xl) e ( dx )'Ax1 ='(xl) Axl (G-5) Substituting(G-3) in (G-2), f(xl) X2 = X + Ax = x - ( (G-4) -178-178

-179In general, for the i-th trial, f(xi) Xi+l xi f'(xi) The interation is repeated until Axi is less than some prescibed value. 2. Half-Interval Method The Half-Interval method proposes that an arbitrary initial step size, Axl, be used between successive trials for x. This step size is then reduced as the correct answer is approached. The following relation is used to find x2: -f(x ) x2 = X1 + Ax1 (G-5) If(x1) I Ax1 If f(x2) is different in sign than f(xl), Ax2.=~ The negative sign is used in (G-5) since f(x2) >f(xl) whenever x2 > x, for all the functions considered, In general, for the i-th trial, Xi+l = xi - Ai ( (G-6) f(xi) I A=)x f(xi-1) where Ax. = -l whenever the ratio (-l.) is negative T2 iteration f(x.) The iteration is repeated until Ax. is less than some prescribed value.

APPENDIX H CALCULATION OF THE RATE OF RADIANT HEAT TRANSFER The rate of radiant heat transfer in an internal combustion engine will be calculated by the method of Hottel(87) and McAdams 68) Chapter IV. A sample calculation will be made to estimate the magnitude of the radiant heat transfer in a 10 to 1 compression ratio engine which will be taken to be representative of a present day high compression engine. This engine is assumed to run on the fuel-air-cycle (see Chapter III) which postulates an adiabatic combustion process at top center. If the radiation is calculated based on the state of the working fluid after this adiabatic combustion, the amount of radiant heat transfer found is expected to be considerably higher than that found in an actual engine where the maximum temperatures and pressures are appreciably lower. A normal combustion process is assumed for which the principal emitters are C02 and H20. The following notation is used in connection with the calculations; the figure numbers refer to figures in McAdams: Egc emissivity of CO2 from Figure 4-13 Egw emissivity of H20 from Figure 4-15 Ae correction for overlapping emission spectra from Figure 4-17 Cc pressure correction factor for CO2 from Figure 4-16 Cw pressure correction factor for H20 from Figure 4-14 eg emissivity of gas mixture a absorbtivity of wall e' factor to account for the non-black body character of the enclosure -180

-181For the transfer of heat by radiation from hot gases whose principal emitters are C02 and H20, the following formula applies: q/A = 1725' [ eg ( ) - ( ) ]Btu/ft2sec (H-l) where g = EgcCc + gwCw - Eg a = escCc + egwCw - s SC C gww 5 For the 10 to 1 compression ratio engine running on a stoiciometric mixture of iso-octane and air the following values were obtained from a fuel-air cycle analysis: maximum cycle gas temperature 5000~R maximum cycle gas pressure 100 atm mole fraction of CO2 0.1 mole fraction of H 0 0.13 It is recognized that in an actual engine during normal combustion the pressures are never as high as those predicted by the fuel-air cycle analysis. A figure of 67 atm or 1000 psia seemed to be a more reasonable value for the pressure than 100 atm and thus was used in the calculations. An average hydraulic radius is required for the calculations for which Hottel suggests volume of gas L = 3f4 -- ft area of boundary surface For an engine with a compact combustion chamber such as that used for the calculations reported in Chapter VII, 0.075 ft is an appropriate value.

-182Following the method of McAdams, pcL = 0.5 atm-ft pWL = 0.65atm-ft where pc and pw are the partial pressures of C02 and H20 respectively. From the appropriate figures in Reference 68, eg = 0.05 gw = 0.037 AE = 0.046 a = 1.0 Cc =1.75 = by extrapolation w =575 Then ~E = 0.21 for Esurface 09, = E 0.94 (from Reference 87) Substitution these values in (H-l) q/A = 70 Btu/ft2-sec The convective component of heat transfer can be calculated from Equation (5-18). If the speed is 3000 rpm and the stroke is 4 in., the average piston speed, w, is approximately 10 m/sec. For a wall temperature of 300~F, q/A = 490 Btu/ft2-sec

-183The total heat transfer is 560 Btu/ft -sec of which that due to radiation is about 12 percent. Because the assumptions and extrapolations used for this calculation always tended to overestimate the amount of radiant heat transfer it is felt that the percentage found is probably too high.

-184APPENDIX I FLOW DIAGRAM AND PROGRAM LISTING FOR THE ANALYTICAL MODEL A. Flow Diagram /READ CONSTANTS FOR HEAT READ RE, 1, 2,, 3 Aec Te, \ I CAPACIT'Y EQUATIONS4. TABLE STOP, nfa, nk, qky Inc, a, b, (_ START — I, AND FUNDAMENTAL DATA E x kk kk TABLE II FOR ALL nf- 1 nk SUBSTANCES qfact..., qfactqk R =.08205 Rl= 1.98719 < BRE AD Ah, A,t Lt, AND TABLE c = 3.764 READ F1....Finc 1' Inc OF VOLUME-AREA-LENGTH RELATION-, ---------- I -— SHIPS,.....,,,,,_HP READ Bore, Stroke, Rod, z P= Tab P Bore2 3 z = a+b/ 4 Rpm, Vtop, Pi, Ti, Pje V. — Stroke Tp_ Tp w w esa)' max THROUGH a \I x=X FOR i1 = 1,1! J< = 179-esa Vbot 1 i >n comdg VAe /THROUGH a (FOR i3 1 kk =.1 _ k=kki FORT qfact _ i\n ~:__ - i PA -23 >fact ( \ ___ i [- - 1 \ ^ / i __ i \^y

-185Nc = a ( - n RT= N = NO - x (2N c+2 h) Nn = c No - COMPUTE n, RT COMPOSITION V=NextV EQUILIBRIUM NextV=: COMPOSITION CONSTANTS CONSTANTS (THE nri AND | CO MPUTE e nr2= f5[ nr2nr2n9+nrl -V 1_ - V nr= fs(nr+nr9)/2 ncR NextV-V Vtop' \ NextV= PeTe IV f (n, +nrg/2) nr7= f5[nr7+(nr8+nrll)/2] nri f5 nri 2) = T1 1 j=O,5,6,yi = 4, 5, 6 n5 ~~T1=~Ti ~~ 1 NextT nttmi =i, n p V^T^^l <-<^=1><^- i =4,5,6,7 U5^i^ >~~~~~~~~~~~~~~~~~~~~~~~~~ii

PiVbot 0 J~jTi=ext n6 RTj Fo l+zx(c+l) nf3 =n f'oc'af2-FOzx nf I = F0 i = 1)2,3 22 COMPUTE NextT = T' Hd' H' $~ AND Hi - H I ~ (dH,/dT)l H1-HI EQUATIONS (F-4) f HI El. nl-H n:n5 AMD (F - 7 SAVE DATAA e 2= jCOMPUTE S2 = Si 9=O Sltl =8+ae, 2 ~V2 =Vb ot HiS1p U1.9 n U2 =I Ul 53 Ne xtT NextV=V~) v2 R k~k~l )-Y Lastlf=U2 E~.(-) COMPUTE C -T r3 ~-~ jt~o~ V2=NextV

-187CCMPUTE (J~ 73 r^3^1 T NextT Pt- 2 s' M 2>V EQN'S(F-8) AND (F-l) SAVE DATA e,-T2,P2,V2, ----- ______ ^ HJ,S2,U2,V2, NextT T 2 0,0, LastU - COMPUTE S; - S21 S Q U2, Ul - U2, 0 I<-H2 AND U2 - I: S Y. ____ y (~S2): CARBON Foa+nm4+nm6 < H-YnBOGEN = Fob+2(n%5+n%7) C k: Ncomdg 3~f ^: 1 ) OXYGEN = x(2NC+ 1/2Nh) NITROGEN = OXYGEN * c Q ~180 - Qsa j1j3 - (SEE EQN'S (2-5) WQ (2-8); Nc = CARBON, ETC.) Tu = T2S ( &3 P = P2 j - _ ( 4 Vu = V2 - Ft = 0 HU = H2 "ui nmi Qt = ~ e S" u -- i 2 - 180 - W = — Ec = U2?~x?2 *.7 H* s a nu = nI j4 ^ —-|5 ( s = " ^^^ v^,^ F - Fi $DONTNO, ~~~~LastP PP *-RE: $DONTNO$ tF<1 ~ 0" --- — ^ g^ i s' -~ i3iE E.E At = Ati | 4 = 6 — ___ nu / —"\ b( u 2. nff =n,.F VU Vt V(Q)l' 74 Vt = V(Q)^ —--- Ft=Ft +F po Mf m f " ml _ F Vff Vff = nff- R — TO = Tu COMPUTE __ COMPUTE R6 RO

-188Hf Hu Z Vu V - Vff nff Ncf = CARBON ~ F q Z V>z -ff. -O. - nu = nu - nff K nu Nof =, OXYGEN * F Hu = Hu - Hf Nnf NITROGEN. - Su = Su(1 - Z) Nhf m HYDROGEN F Afl, i4Tu Af2,i'nff - C: 1 ) ~ j~~l: -nuin(l z) nui' ii = i - 1 Afl Af, Fi Af2, i= Af2, ii' l) Tc =Afl,i ncc^Af2,i L Tt sHf Ncb x Ncb + Ncf Nhb x Nhb + Nhf 1/r \ ^1f,1,- -.- COMPUTE Af,,, -c Nob = Nob + Nof' =n Nnb = Nnb + Nn T Tc = Abli nc Ab, Tt Tt+H i 1 k=2 Aib =Ab2,ii + nc Abli Abl,ii 8

-189extT 1c = cT -- NextT PUElCOMPUTE 1 — NextV = CPOSITION 4EPOSITION * < vc 3, -- EQUILIBRI -- ce RTC ANDBER OF NextV CONSTANTS MOLES, ncc k2 = k2 + 3( 6 Ne;t /xtV -'V|., Dif = Tc - NextT -— ^ I -— V^ —-I * ~: "^ I — ~c RTc l ~ Q =Q'/Tt:C COMPUTE ( - >'CCA' tcc - l NextT k p ), tcprim c*- Iv COMPUTE ENTROPY,'cc' COMPUTE ENTHALPY, cc ( )p,'cprim. COMPUTE INTERNAL ENERG COMPUTE X3 ccl AmD NTROPY,'cc' T (|j),cprim— ifaDif/2 i > -— 1.-. QQ' _ COMPUTE Q>l*0 m - 0INTERNAL X v - - — I QQ^ * u cc - Tt _ENERGY,'cc' NextTTc - Dif. IQ'-1

-190^-^ "7 ~~yb ~ Vc COMPUTE Ab~i~ c nb =: ncc v^^^ ________Th Tb Ub AND 1-i —P2 Ab2,i = rlccl IbT bNU Hb = Tt < UC j2= 2+ 2t-2-3-o- KE + Ub: P = R/Vt(nbTb+nuTu) COMPUTE - S0 Uc = E Cvb AND CPU Tb =Ab~Ai nb = Ab4,i _____;* ~~~~~~~~~~Vb Ab~ii COMPUTE NextP I = "Uii En. (I-2) Au NextP ^ P a NextP NextT = Tu Ne-tT Tu ~ Tu( J = NextT NextT C= COMPUTE u SI - S_ AND VU SuTU Uat P _ —- v P (T U p I ----- - ---- I Tc = Th ^ ^^ /^"^ Tb = Tc COMPUTE Vc = bUu AM) Ub Tt = Ub al ^ ) b " C EC - Uu n"c = nb nb = ncc 77 COMPUTE - U= Ub + Uu bI AND 1S <t f =~ Vb + Vu 1. Hb AM) Sb Vt'*1^ V b+V

-191Ab3,~i Tb Ab-ji ~ nb COMPUTE R6 Ab5ti = VbTt = VE= a3 Tt r Aull, T J1 " \^y ^1,1^'Tt2 = Sb AU2i VU Tb = Ab3,i COMPUTE "b = Abqpi [ Q!^ ) —-<CTY = 2^>- <k -^ —— 1 Vt = 0 — Vbb = Ab5,1 V(~+6Bpm- At) T, ~ Au, Vuu = Aug 2 COMPUTE Vc = = Ttl <^j2 " 0^,^ COMPOSITION OF u BURNED PORTION Vbb + Vuu Sb = Tt2 COMPUTE < j - COMPUT - Vb FROM V, Y"b'Yu Vt Vb EQN. (1-1) TuvuY-1 I --------- I | -------- I | —--------— IT, = T (V^ 7U~1 VU Tu = NextT 4-r- NextT = Tu --- P R B(nbTb+nuTu) V —-YV 1 ________ ________. vt'^ T ^ COMPUTE NextT < s | - SU Su, r- ST nRTu Tu 1:4 a~~~~~~~~~~~~~~~~~~~~~~~~S S,I:E VU St AND %J Liu I ap, S U aTT- P ") 1400'^\ FTt = Sb (, I1 I<- T, = Tb \^_^/ ~ncc = nb

-192Tb = T (^ y- Vbb = V, -Vb Vt b c Vc =Vuut VbVbb Ec E COMPUTE k=3 J jl:0 =-Ub hhi=O Huf Uu =/ v ----- " ______ HL Ub Tb = Ab6i1 Vb = Ab, V- AA - u =,i p = R(nbTb+nuTu) Vt COMPUTE - U =E,kl=4- Qi AND hi jc -j (EQN'S (.6-3) -EC' Q iY AMD (5-l) ncc =A4, ncc=nff — ^ (4 AI )4- T, Tt=Sf EY

-193),i T f glame T - Af = nc LastAt = At COMPUTE Al FROM EQN. (6-4) COMPUTE ^S COMPUTE (a^ t, —----- -—, | s (EQN. (4-24)) Al FROM EQN. (6-5) I ^<^ve=JT>^ ^^V \, |^A-At L\aste = e wi = E - Ec - Qi LastAt - At: ~ x A t 1 He 6 i Wt = Wt + Wi Lt! At - + i SAVE DATA SAVE DATA ^ 9,,TUP,VVt 9,TbP,Vbl + H, v Uu + b RFt nu nbQil V^ Qt,Wi, Wthi ~^^^ ~< _Last~ - (180 - sa) --- \ P - LlastP: 0 -- NextKK=KK' - ( 7 max 1 0 sa'

-194r KK=NextKK1 > -' 0 (^75:~max-Last e= 6 Pmax=LastP j3..592 * - AT =i: inc P: LastP ( Nexpdg- 2 ~ec A0^560-0-N ^g.A9,/2 — ^At =' p2+1m aee=360_eNexpdg. ~c/2 2=J 2+1 T =T -AT c b COMPUTE Qj Ub - EAD iE U b T, Tj, (EQN'S (6-7) AND (5-l8)) k=6 -KEY Tt = Ub -

-195NextT=T - =KEY = 0+1c j+ - T =NextT COMPUTE COMPOSITION AND TOTAL e...NUMBER'OF COMPUTE ( ^ F- MQLES hn -- EQUILIBRIUM \.2 CONSTANTS % nbRTc k k Vb Dif= T - NextT. ~~~~.v J -, l. --. ~ COMPUTE ENTROPY, Next cc' AND -" Q'""' T),' cprim' - ccc-Tt COMPUTE 10 INTERNAL ENERGY. - cc' - AND/T:' cprim'' nbRT Vb COMPUTE ENTROPY,'cc'. NextT -=. 1 —-------—' ^ W. ^ QL:0 I QQ. oo — u-, =cc-Tt' 1 - Dif~COMPUTE E N ERt " fX'~ - INTERNAL ENERGY-'cc' Dif Dif/D

-196-. "nbRTb P6 T Tc AT T= Tc - T = Tb-T P Tb=c %b T Vb R1Cv | COMPUTE c,-cTb(V V = V(e) = S+Ae S Vb=V k=7 Y=2 Tt=S' --- ~SAVE DATA - Wi = E-Ub-Qi 6 Tb, P, Vb) Hb, I (^ COMPUTE Wt - Wt + Wi Sb, Ub, nb, Qi, 7( Hb AND Ub Tb Qc- t' Wi' Wt' hi Q~t = Qt + Qi AT 6T/ 2 > < Aee < At -' Rm: 6-6~ ~~eRpm =e, Ab e) 2: j~9 P RM exh Tc = Texh - - "1 a!~ r-<k —8>- T= sb ^-(, j?: tSb 3 ncc= nb R Texh= Tb( ex )1 COMPUTE Cp P~~~~

-197TOxh = P T SAVE DATA Vb = V, __ COMPUTE e) Tht PC C8 Onb I cc-CAb AOND Ub TVbEHbESbCUb. (STOP: 1 n- b = 5e W- = Wtnp -n +(nb8+"n1ll)/2 rnep - (VA - ^ ^ vt~)J0 ---- " i=Tb COMPUT VOLUMETRIC P TCOMPUTE /^T -T-."\ < ^ —-- ------- \ > PUMPING WORK, EF CITb E: STOP N OPRT RN E c —-Pump (Vbot-V topV ( Pi - Pe )J COMPUTE INDICATED MEAN COMPUTE ENDICATED EFFECTIVE PRESSURE/ THERMAL EFFICIENCY - 100 wt + Wt AH~ - F mep = c 0 (Vbot - Vtop)5 COMPUTE VOLUMETRIC PRINT EFFICIENCY SELECTED INPUT OPERAT- PRINT Fg.Z(cx+x)RT 100 — ^ ING CONDITIONS AND - ALL DATA rv" ----— Wt — Qt.,'qmepF, SAVED (V - }Pi PUMP" ('bot'top) i T)O o

-198B. Explanation of Symbols Used in Flow Diagram and Computer Program Symbol used in Meaning Symbol used in Flow Diagram Computer Program AL matrix of constants for empirical heat AL capacity equations in temperature range 298.16 - 1500~K and fundamental data at 298.16~K (see Tables I and II) AH matrix of constants for empirical heat AH capacity equations in temperature range 1500 - 3500~K and fundamental data at 1500~K (see Tables I and II).lAh surface area of combustion chamber head ATOT (1 or 2) - cm2 Apb piston head surface exposed to burned ANS (3) gas - cm2 Apu piston head surface exposed to unburned ANS (4) gas - cm2 A wall surface exposed to burned gas - cm2 ANS (1) wb Awu wall surface exposed to unburned gas - cm2 ANS (2) A t total piston head surface area - cm2 ATOT (3 or 4) Awt total exposed wall area - cm2 ARAA Af,Ab. Au three matrices in which are stored values AF(ji) J,1 Ji JY1 of temperature, volume, and number of AB(ji) moles at selected points in each of the AU(j,i)'i' combustion increments a number of carbon atoms per molecule of A fuel Bore engine bore - in BORE b number of hydrogen atoms per molecule of B fuel b 0 density of oxygen molecules in flame BO element prior to combustion

-199C constant pressure heat capacity- CP cal/mole-~K C constant volume heat capacity - cal mole-~K CV v c ratio of nitrogen to oxygen atoms in atmospheric air = 3.764 C cc trial value of a thermodynamic property CC cprime trial value of the derivative of a thermo- CPRIM dynamic property Dif an incremental change in temperature - ~K DIF E internal energy - cal E Ea activation energy - cal/mole of fuel EA.F mass fraction of gas remaining in clearance F volume - residual mass fraction F' moles of fuel inducted FO F't total fraction of mass burned FTOT Fl-FInc the Inc fractions into which the combustion FR(l)...FR(INC) process is divided I enthalpy - cal H dH dH T I 1Cp_ n HPRIM dT dT P h convective heat transfer coefficient in COEF portion - cal/cm2-OK Inc number of increments into which the combus- INC tion process is divided number of times complete cycle has been J5 executed KEY type of process undergone during a given KEY step by the burned portion or flame element Whenever KEY = 1, process is isenthalpic KEY = 2, process is isentropic and KEY = 3, process occurs at constant internal energy

-200kkl-kknk the nk flame speed constants KK(1)...KK(NK) Lt maximum extent of flame travel if combustion ATOT(5) occurs at top center - cm ml mass of charge in cylinder - gm Ml mf mass of fresh charge inflamed- gm MF mep indicated mean effective pressure - atm IMEP Nc,Nh,NONn or mole atoms of carbon, hydrogen, oxygen, NC,NH,NO,NN or Carbon, Hydrogen, and nitrogen (see Equations (2-5) to (2-8) ) CARBON, HYDRGN Oxygen, Nitrogen OXYGEN, NITRGN Ncomdg number of compression increments NCOMDG N number of expansion increments NEXPDG expdg n number of moles N nb total moles of burned gas NB n total moles of unburned gas NU nk number of flame speed constants NK (K1 Equation (4-24) ) for which computations are to be made nbi moles of i-th component of burned mixture N(i) nfi moles of i-th component of flame element NUN(i) n. moles of i-th component of unburned NUN(i) ml ~ ~ mixture prior to combustion npi moles of i-th component of burned products N(i) during exhaust process nri moles of i-th component of exhaust residual N(i) nui moles of i-th component of unburned gas NU(i) ncc temporary designation of number of moles NCC nff moles of fresh charge inflamed NFF nfa number of air-fuel ratios for which NFA computations are to be made P pressure - atm P

-201P exhaust pressure - atm PEXH e P intake manifold pressure - atm PMAN i PH an initial estimate of the value of PH X = P02 (This is used in the computation of the equilibrium composition) Q heat transferred - cal QB Q total heat transferred - cal QTOT t qk number of heat transfer constants QK (by which the heat transfer coefficient, Equation (5-18), and subsequently the computed amount of heat transferred, Equation (5-19) are multiplied) for which computations are to be made qfactl- qfactqk the qk heat transfer constants QFACT(l) QFACT(QK) R gas constant in work units = R 0,08205 1-atm/mole- K R1 gas constant in heat units = R1 1.98719 cal/mole-~K Ro flame front radius at end of (i-l)-st LASTL combustion increment R: outer radius of reaction zone prior to NEWL combustion of i-th combustion increment R6 flame front radius at end of i-th ANS(5) combustion increment Rod connecting rod length - in ROD RE remark - If RE is DONTNO it is assumed RE that the flame speed constant K1, Equation (4-24), is not known r compression ratio CR rpm engine speed-rev/min RPM S entropy - cal/~K S St turbulent flame speed - cm/sec ST -"cmse

-202STOP the maximum allowable number of times STOP the complete cycle can be executed Stroke piston stroke - cm STROKE (aT)V (aT) SPRIM (TTV 7T)V T temperature - ~K T Te exhaust temperature - ~K T5 T computed exhaust temperature - ~K TEXH exh Ti intake manifold temperature - ~K TMAN T. temperature of the gas after the heat T(J1) 02 ~ transfer step of the j2-th expansion increment - ~K T piston head surface temperature - ~K TPISTN P T wall temperature - ~K TW Tt alternate designation of a thermodynamic TT property U internal energy - cal U dU dU T dT CV n HPRIM dT dT V V volume - liters V Vt total system volume - liters VTOT Vff volume of fresh charge inflamed - liters VFF Vtop clearance volume - liters VTOP Vbot clearance plus swept volumes - liters VBOT W work - cal WORK Wump pumping work - cal WPUMP Wt total work performed - cal WTOT 1- Xn the nfoa air-fuel ratios (fraction X(l) ooX(NFA) a chemically correct air) Z Z = a + b/4 Z

-203y ratio of heat capacity at constant pressure G to that at constant volume AHO enthalpy of combustion - cal/mole of fuel HCOMB c AL extension of flame front due to chemical DS reaction At. time required for the combustion of the DT(i) i-th increment AG crank angle increments during the compression COMDG ~c ~ process nAe crank angle increments during the expansion EXPDG process ~al, ~ allowable relative error in the thermodynamic ERRORl properties e allowable relative error in the composition ERROR2 of the products e- allowable absolute error between the ERROR3 3' ~ calculated and experimental crank angles where maximum pressure occurs rP ~ indicated thermal efficiency - percent EFF T) ~ volumetric efficiency - percent VOLEFF v 0 crank angle where maximum pressure occurs PIMAX max (a = 0~ at bottom center and 180~ at top center) sa spark advance - degrees PI p density of flame element prior to RHf combustion - gr/liter SUPERSCRIPTS'T ~ designates a trial value of a property c SUBSCRIPTS b burned B u unburned U

-204f flame element F i intake manifold MAN e exhaust manifold EXH STATEMENT LABELS ~a ~ end of computation for one data set END Ca, entry to section which finds ENTRY1 T = T(H or S or U and P) ea section which finds the pressure of the ENTRY2 system with known volume and internal energy and known entropy in the burned portion 04 entry point for change of volume due to ENTRY4 piston motion a' entry to section which finds ENTCY1 1 T = T (H or S or U and V) PB ~ entry point for consideration of a second BEGIN data set,,, end of constant pressure combustion of LOC(1) i-th flame element - Step 1 P, ~ end of constant pressure mixing LOC(2) P:3 ~ end of recompression to original volume LOC(3) bP end of change of volume due to piston LOC(4) motion P5 end of recompression of flame element to LOC(5) final pressure - Step 7 P6 end of constant volume heat transfer of LCC(6) j2-th expansion increment p7 end of isentropic change of volume due to LCC(7) piston motion Y2 beginning of induction and mixing process LOOOP3 Z 2 ~ ~ ~ -~ r- - - - 1- i -NV1.,A VW Tn n0

-20580 entry point for recomputation of cycle dLOOP1 using a newly computed exhaust temperature &2 end of induction and beginning of step- LOOOP5 wise compression process 64 end of compression process and entry to RETURN combustion process &5 beginning of combustion ANOTHR 59 beginning of j2-th expansion increment LCC1 X_-3 finds T using Newton's method ENTRY(l-3) XI_3 finds T using Newton's method ENTCY(2-3) X5 6 finds T using half interval convergence ENTRY(4-6) method XI' finds T using half interval convergence ENTCY(5-6) 5-6`4 end of heat transfer and constant volume SPT(4) readjustment of the i-th combustion increment - Step 5 and 6 5ah, entry to section which computes the flame SPT(5) speed constant 56 completion of the i-th combustion increment SPT(6)

-206-.....$.COMPILE....MADRINT OBECT.N.. OBJECT EXECUTE.DUMP_..._._... 3- I CE 0 01 PROGRAM COMMON ALAHP,KR1,NC,NHNONNR.J2,REKKXTW, 1QFACT EARAT IOBORHO, SPEEDERROR2 CPF, TPISTNtATOT XX~ XNUM............... BORE....TROKEROD,VfOPVBO,PMANPEXH, TMA"N,RPM NtTHETAERRORli 3J3,STOP,T5,H5S5,U5NU5,QTOTWTOTFONEXTVHCOMB INC',ZCt 4 TZTX,COMDG "PMAX, NA'ME',CRPI -- INTEGER REI'.I1, I2,I13J,.J1,.J2.,J3,J4,LL1,L2,JCNKNFAINC, QK9 1NAMEXNUMNCOMDG, I A' VEKEYSOP SVEE9R DIMENSION, AL(87, ALDIM),AH ( 87',ALDIM),RE(12)o X-(10),KK( 5) QFACT 1(. i,NUN( 7),P(11 )N ( 11) K ( 11),XX( 105 XDI M) NAME.( 2) 2FR( 60),ANS(5),NU(7),ATO'T(5),TZ('1980). TX( 780),...3 -"..'''. IAB(420 DIM),AU ( 24uDIM ),AF (' 240 dDIM)",PHF(1 20DIM), 4PHB(120,DIM),DT( 60),TT(2) EQ- UIVALENCE'i(CPR IM';SPRIM) " (HPRIM,-CV-), (HM I X TTf), (TZ TZZERO') 1 ( TXTXZERO)... VECTOR VALUES DIM = 2.,0~60 VECTOR VALUES ALDIM = 2,:0,8 VECTOR VALUES XDIM = 2,0,21 READ FORMAT SPHT,AL( 1,:1)..AL(11,8),AH(1,1)...AH(11,8) VECTOR VALUES SPHT = $4E158'*$ READ FORMAT REMARK,RE...RE(12),ERROR1,ERROR2,ERROR3,COMDGT5,.......... TOP,NFANKQK, INC,Ai B, EA HCOMB., SPEED,NAME, ~ NAME ( 2 ) X (1 ).(..x 2(NFA),KK( 1).*KK(NK),QFACT ( 1) *,QFACT (QK) ---- -- -PRINTf FORMAT DUMP1,l$AL $9AL(1v). AL( 7,8) —-- Z = A+B/4'................ —— PR-INT FO —-, —MiA —--.... MP1$......A..E..l VEC.TO'R VALUES DUMP1 = $C6/(8E15,8)*$..VEC....-...........ETO'V VALES R-EM'ARK =$13 C6/5 Fl O1.0 5R 5I2/5"F01,"3"C67/(7F 10;'2-) 6'*$... READ FORMAT FRACTNXDIM('2),ATOT(1)T..ATOT(5),FR(1),.FR(INC ). —.......-.............. —-.-..-VECTOR - -VALUES FRACTN$10 —— i-F5 —— " —''" -—'-" —' -R = - 08205 R1 = 1,98'719 C 3.764 READ FORMAT'FRATXX(.l) *,. XX( 5,XDM() 2)..... VECTOR VALUES FRAT = $14F5e5*$' "._' XNUM = XD'M'(2')..................... DIM'(2) = INC -- PR-INT-FORMAT REARKi-'E R 2 ROR ERR-OR'2ER-ROR3,-iOM1GTT' 1tSTOP, NFA, NKQK, INC, AB,EAHCOMB,SPEED, NAME*.,* NAME(2) X(1)-.. 2X(NFA),KK(1) **.KK(NK) QFACT (1)",',QFACT(QK) PRINT FORMATFRACTBXDIM(2)ATOT1ATOT( 1) ATOT(5),FR(1) **.FR(INC), 1'X(lx i.1)";,,XX(59,XDIM(2)) VECTOR VAL.UES FRACTB = $ I'10'5F10.5/(14F8_5)_*$_ PH'51 = 1, BEGIN READ FORMAT ENGINE BORE,STROKE,RODRPMVTOPPMANPEXH,TMANTP 1ISTNTWPI,PIMAXD1'D2 VECTOR VALUES ENGINE.= $7F105*$.... BORE = BORE *2.54 STROKE=STROKE*2654 ROD ROD*2.54 - -- VTOP = VTOP/61.03 VBOT VTOP+3.1416*BORE/4000 *BORE*STROKE CR = VBOT/VTOP NCOMDG = (179.-PI)/COMDG J3 = 0..... THROUGH END, FOR Ii 1,1,I1.G'NFA........................................ X............... THROUGH END, FOR 12 = 1,1,I2.G.NK KK = KK(I2)

-207THROUGH END, FOR 13 KlI3GQ QFACT = QFACT(I3) PRINT FORMAT INTRO" NAME,.,NAME ( 2 ),XBORE/254,EATP'ISTNSTRO 1KE/2.54,TW,ROD/2.54,HCOMBTMAN,,VTOP61.03P,MAN 61.03*(VBOT-_VT 20P)tPEXHCRPI N5 = PEXH/R*VTOP/T5 NC = A NH = B NO = X*(2.*NC+.5*NH) NN = C*NO NCC = A+B/2_+Z*(C*X+X-lH).....-. —.......... -.- -.-.-....-....-.-.. NEXTV = NCC*R/PEXH*T5 EXECUTE EQUIL,(T5) PRINTFORMATINTOR1,RPM,INC,ERROR1*100.,KKQFACTRE(4),.:RE(12) BACK. VC = NEXTV EXECUTE AMOUNT.(T59VCNCCoPH51,N) NEXTV = NCC*R/PEXH*T5 ~.....I. - ~-.. - - I-.. -, — _u l l -- N-. — E I;-.......=-.-.N' C:-C' -Ex,-5...................................-....-............ WHENEVER.*ABS._((NEXTV-VC)/VC)..G.ERROR1,TRANSFER TO BACK F5 = VTOP/VC ~~.~,~.,~~,,.,~,;_.........N'(.2..)... = F5*(_N(2.+(N (9))+N(10)+N(8) )/2) N(3) = F5*(N(3)+N(9)/2*) N(4) = F5*N(4) _ N(5) = F5*N(5) N(6) = F5*N(6) N (7) =' F*(N(7 )+(N(8)+N('11))/2.) TRANSFER TO LOOC1 LOOOP1 N5 = PEXH/R*VTOP/T5 F5 N5/(N(2)+N.(3)+N(4)+N (5)+N(6)+N(7)) THROUGH LOOOP2,FORL'= 2,1-L1 G' L LOOqOP2 N(L1) = F5*N(L1)LOOC1 EXECUTE ENTHAL'(2,7,H5,T5TN) 3 J3 + 1.............. U5 = H5 - N5*Rl*TS. PRINT FORMAT HEAD3 VECTOR VALUES HEAD3 S $4HOL:O-"S2' -"'.'NCS+5HTI-ETAS4..... 1. - -*KtS4,8H:P - ATM.S7,6HV - L*S4,8HH - CALeS6'11HS - CAL,/*KS " 268HU - CALS511HTOTAL MOLS""'""$'...... EXECUTE ENTROP.(2,7?.S5.T5.N5.PEXHN) -* PRINTEORMAT OUT,5,O,540.,T5,PEXHVTOPoH5tS5#U5sN (24 N 17) NUN(4) ~N('4.) NUN(5) = N.(5) PRINT FORMAT HEAD3~ —------- - - - - -------- - NUN(6) = N(6).........................~...........:....N'N (..._.....).^..._...........-.-...,........ —.. WHENEVER J3~.E*1,T1= TMAN. NEXTT = T1 LOOO'P3 T ='NEXTT NO PMAN/R*VBOT/T- N5 FO = NO/{(1. + Z*x*(c+1.))r NUN(l) a FO NUN(2) = FO*Z*X NUN(3) = NUN(2)*C...-... ~~ EXECUTE ENTHAL.N1 -...3H.T._ E.XE.LLT.EHPRIM. T.HPRIM,.NUN) HPRIM = HPRIM - HO/T*(1. + NS/NO) H = HO + U5 + PMAN*VTOP*24.2179

-208--------------------------------------- ----------------------------------------- -- NUN(2) = NUN(2) + N(2) NUN(3) =.NUN(3) + N(3) EXECUTE.ENTHAL,( 1 7HMIX NT- )-' NEXTT - T - (HMIX-H )/HPRIM. — EY —'-; —-- B TT- -F1TEER —^AB-C -- -rT - - RR'RTiTR S'-7E'D —----------- N1 = NO + N5 __^ —-------- ----— iir —iN-QT — p-^)U = H -.N1"*R *T Ml = NUN( 1>*(12*01*A+00OO8*B)+NUN(2')*32.+NUN(3)*286O2+NUN(4)* 144.0 i+NUN ( -T.i 6+ —. — 6+N6*2- I+N —-N7 2OT T1 = T PRINT FORMATOUTOJfifo,TMAN,PMAN oVBOf.HO.OO #N0O 0o*X*ZFO 1*C*X*Z THETA = 0O JC = 0O..._^,-?-Z —------------------------------------------------------------------------ - TZ(TZZERO 0 2) = PM TZ (TZZERO + 4 -- —' TZ(TZZERO + 2 ) = PMAN _________ —--- TZ(;,TZZERO + 3 ) = VBOT TZ(TZZERO + 4 ) = H —' ——. — ---— ^ —-Ti (TZZERO+"='TZ.(:TZZERO + 6 ) = U -z- -..ZERO + T- I -.' TZZERO = TZZERO + 13 PRIN'T FORMAT OU:ToJi, i,0.,.T.PMANVBOT HS,UNi NUN( i)... iNUN(7 -.Mi V " VBOT LOOOP 5 THETA a THETA + COMDG-'LOOC2 JC."~ JC + - LASTU = U NEX:TV' VOLUME (THETA) EXEC.UTE HPRIMEi ( 17_CVV.TNUN) -^ —--—, —------ -. —----------------------- ----------- CV ='CV/Ni - RI NEXTT. T*(V/NEXTV).P.(R1/CV) ~ —^.. — - -------— S —- -I ^ a J _ —-------------------------- ------------------ ------ V = NEXTV j -0 LOOOP4 J J + 1 T = NEXTT P T*R/V*N1 EXECUTE ENTRO'P (1, 7,ST9 Nl.,P,NUN.) EX-ECUTE- SPRIME- ( i 7-SPRIM -TPNUN SPRIM = SPRIM - Nl/T*Rl NEXTT. T.-(S-S) /SPRIM —........ WHENEVER *ABS((NEXTT-T)/T).G.*iERRORilTRANSFER TO LOOOP4 E —----------—. —------------------------ -------------------- U = H - N.1Rl*T TZERO- ---------- ET —----------------------------------------------.TZ(TZZERO + 1 ).= T TZ(TZZERO + 2 ) = P TZ(TZZERO + 3 ) = V TZ('TZZERO +. 1 H TZ.(TZZERO + 5 ) S TZ ZZE —------------------ ----------- = U —-------------- TZ TZZERO + 7 ) = N 1 TZ('TZZERO + 8 ) = O0 TZIt(TZZERO + 9 ) _ O0

-209------ _____ _____-_-_ __ __ ___ __ _ _____.____ ___ —---------------------- _______ TZ(TZZERO + 10) = LASTU - U TZ (TZZ.ERO + 11) = Ul - U TZ(TZZERO + 12) = 0. TZZERO = TZZERO + 13 PRINT FORMAT.OUT~,2'JJC~THETfAT~PVH.SU WHENEVER JC_.L.NCOMDG, TRANSFER TO LOOOP5 WHENEVER JC.Eo NCOMDG THETA = 180.-PI. TRANSFER TO LOOC2 END OF CONDITIONAL_________ ___________ V2 V ______~_i_-_ — ^ - — t__;__T --- -- --- -- -- --- -- -- --- -- -- --- -_____ —- - H2 = H U2 " U P2 = P THROUGH END1 l FOR Llu1lt1 Ll.'G,7_ END1 NUC(L1:) = NUN(L1) ----- - W-HENEVER J3.E.l -. — 1 J1 = 0 OTHERWI SE Ji = J3 END OF CONDt ITIONAL CARBON. FO*A +NU( 4) +NU( 6) HYDRGN " FO*B +.2 *.(NU)('5 ) +NU( 7 )) OXYGEN X* ( 2 *CARBON+, 5'*HYDRGN - NITRGN = C*OXYGEN TZSAVE - TZZERQ RE-TUR.N THETA = 18.0*-PI ---- ------------------------------------ FTOT =. 0 ---- _ __.________ ___________________ _________ _______________________________ SEC = 0. THROUGH HEREt FOR LI = 1~1~Ll.G.*7HERE NUN(L1) = NU(L1) TU = T2 SU = Sl EC "U2NU = N1 ---------- --- -------- ____ -------------------- ------------------- -— ____________ --- VB' 0, VB =O0 WHENEVER RE(0) OE*$DONTNO$ -------------------- ---------------------------- J4 = 5 OTHERW SE J4 = 6 END OF CONDITIONAL ANOTHR LASTP = P I = I + 1 DT = DT( I) FR = FR(I )

-210FTOT = FTOT + FR VTOT = VOLUME (THETA) NFF - N1*FR MF = M1*FR VFF = NFF *R/P*TU EXECUTE AREA (VBVTOT. A.NS,Di.D2) LASTL = ANSi 5) EXECUTE AREA (VB+VFFVTOT,ANS D1iD2)' NEWL.= ANS(5) -— D —-— S - NEWL - LASTL _ ________ BO NUN(2)/VU RHO - MF/VFF TO = TU Zl NFF/NU HF a HU*Z1 VU VtU-VFF NU = NU-NFF HU = HU-,HF _________________________C___________________________ SU = SU *( 1 -Z1) NFC " CARBO'N*FR NFH = HYDRGN*FR _ _ —---- NFO - _ OXYGEN*_-FR_____________ FN a NITRGN*FR ____________KEY _ — - --— __ —--- ---------- _ _KE, 1' THROUGH LQOGC FOR L1 a 1,LLl*G.*7 LOC N- UN( LI) N MUN(L1 )*(1 -;ZI-' — -. WHENEVER J,*G.i61 TRANSFER TO SKIP - - ------------- -_ ------ ------ ----- --------— _____. DT(I) Ot WHENEVER I*G.6 1 --------------------------------------— T; MQ a FR(I) /FR(fII} -— T -------— F i -------- -- ------- ------------ OTHERWLSE —. -----— ~ — P-H-1-.iF -t1- — __ __ —----------------------------- AF(1II) a 4e*TU AF(2Il) = NFF END OF CONDITIONAL_ _____ ___ ---------------------------------------- SKIP TC AF( 1. I) _____AF2.I)_____ PH a PHF (II) TT i HF __ NC a NFC NH a NFH NN = NFN ENTRY1 J a 0 L2 _ KEY __ NEXTT a TC LOCI TC = NEXTT j 5 J+1 NEXTV t NCC*R/P*tC EX ECUTE E QU Lt -TC).L0t2 VC * NEXTV_____ _ EXECUTE AMOUNT* tTC.V'C tNCC.PH~N N) NEXTV' NCC *R/lP*TC

-211WHENEVER.ABSo((NEXTV-VC /VC). G.ERROR1,l TRANSFER TO -OCTRANSFER TO ENTRY(L2) ENTRY(l) EXECUTE ENTHAL (2 11 CCTC~N) EXECUTE HPRIME.(2,i1.CPRIMtTCN) ------------— _ —-— EXECUTE _HPRME_(2_llCP__R I___ __ _______________________________ ___ TRANSFER TO LESS....ENTRYJ_2. ----- EXECUTZEE EN TROP,2_11,_llC tCTC.tNCC P,N —--- EXECU'TE SPRIME. (2, 11.C PRIM TCN) TRANSFER TO LESS ENTRY('3) EXECUTE ENTHAL (2112,CC,TC,}N) --------- CC = CC-NCC*Rl*TC ____ —----------------- EXECUTE HPRIM E (2 11,CCPRI M TCN) CPRIM = CPRIM-NCC*R1 LESS Q m CC-TT NEXTT I TC-'Q/CPRIM WHENEVER J.E. 5 - L2= L2+3 _____ __ ________ — - -- -_-___- -__________________________________ - DIF =.ABS. (TC - NEXTT ) -----— ____________E___D OF COND ITIi _________O____NAL __ WHENEVER *.ABS( ('Q/'TT).G*ERRORl tTRANSFER TO LOC1' TRANSFER TO LOC(L). ENTRY(4) EXECUTE ENTHAL (2, 1,CC KtTCtN ) * --— ___-____-__TRANaFE___IP_ MOR E ENTRY'5) EXECUTE ENTROP (2,.1.CC.TCtNCC~,PN)-'TRANSFER TO MORE ENTRY1 6) EXECUTE ENTHAL., 2,11 CCTC~.N) CC. C:C-NCC*R1*TC MORE 0QQ CC-TT;_______________ —-E_____NEVER Q/QQiL _O*_DIlF_ =-,DIF/2 2 NEXTT' = TC - DIF QQ/.ABS (QQ) Q.= QQ _________a __________ ___ _ __ _ _ __ _ __ _ _ __ _ __________ _ __ _ ________ — -____ —--- WHENEVER -.A;BS'f(Q/TT').:,.G..ERROR1, TRANSFER TO LOC1 T.. TRANSFER TO LOC('L) LOC'() AF(1lI) TC AF(I2I) _NCC ________ PHF(o1I) a PH EXECUTE ENTROP. (2 t11SF. TC NCCP,N) WHENEVER I*.E*.1 TRANSFER TO LOC(2) END OF CONDITIONAL _________ TT = HB_ + TT______ NC = NBC + NC ----------- - NO_.' NBO + NO _ NH a NBH + NH NN' NBN + NN WHENEVER Jl *Le2 AB(1-I'_) AB (1*I'I) AB( 2I:) AB(2.II.)+NCC PHB(1tI) = 14 END OF CONDITIONAL _____ TTC = AB (t 1 I ) NCC = AB ( 2 I) _ ____ PH _ _PHB( 1tI)' = 2 ------- TRANSFER TO ENTRY1 LOC(2) AB(1,tI)=- TC —----- -__ -AB 2.I) = NCC _ PHB(1~I) a PH VB' VC

-212NB = NCC TB = TC HB = TT NBC = NC NBH = N'H NBO = NO NBN = NN L=3 L1 = 3 UB HB - NB*Rl*TB UU = HU -NU*Ri*TU UC = UB + UU WHENEVER JlGol TB AB3,3I) NB AB(4.IY VB = AB(5#I) ~-`I.-.. —---- — ~-'... — -. —'~`..-^..-.-.. -T^- -— O-. —------ ------—'' - ------------—' —-----—... VU =AU(2#I) PH = PHB(29I) UC E P = R/VTOT*(NB*TB+NU*TU) END OF CONDITIONAL KEY = 3 ENTRY2 JC = 0 -LOC J-iC =-JC +.-.-. —.-.-. —--—.... —-.- -... —.. ——. —-- EXECUTE HPRIMEC(2#11tCPtTB#N) NEXTP = R/VTOT*((EC-.UC)/CP + NB*TB + NU*TU) EXECUTE HPRIME*( 1,7.CP.TU.NUN TU = TU*(NEXTP/P),P.(R1/CP*NU) P NEXTP NEXTT = TU LOC4 TU - NEXTT EXECUTE'ENTROP (1t7?TTTU~NU,PPNUN) " EXECUTE"SPR I ME ('197 CPR I MvTUoNUN NEXTT = TU-((TT-SU)/CPRIM)' WHENEVER' sABS. TNEXTT)TU /TU) ER R7AN'Tl"c VU = NU*R/P*TU EXECUTE ENTHAL. (1 7,HUTU,NUN )..... UU = HU - NU*Rl*TU UB = EC- UU TC T NB TT = UB NCC = NB TRANSFER TO E.NTRY'. LOC(3) TB= TC VB = VC NB = NCC.UC..B + UL' - —.. —---. ——. VC = VU + VB......... WHENEVER *ABS.(VC-VTOT)/VTOT).G.ERROR1',TRANS'FER..TO LOC3' EXECUTE ENTH-ALe(2i11,HB#TBtN) PRINT FORMAT OUT,LJ, I TH.ETATU#,PiVU,:HU,'SU,'L NUNUNUN(1)i.NU 1N(7) — E — — EN-'-P-;-P2I —T —S —B —'iN' B P-P —N V'......... PRINT FORMAT OQUT,L1,JCI.,THETAA TB, P,VB,.HBSB UBNBN(2)...~N(1 11) TRANSFER TO SPT(L1)

-213______________________ _____________ _______________________ SPT(3) AB(3,'I) =TB AB(4,I) = NB -AB(5, I = VB AU(LIl) = T'U AU(2oI) = VU PHB(2.I) = PH _ —----------—.__-. —--------- --- ---------------------------------- TT(1) -SU PRINT FORMAT HEAD3 ---- SAVE- =- J -- -- __ -1- ____ __-_- -- EXECUTE AR EA (VB,~VTO TANS D1, D2 ) -ENTI RY 4 K___ EY - =2 —. —------ ----- - -----— _ ____ PHETA = 6.*RPM*DT+THETA VTOT = VOLUM E(PHETA) L 4 -TB = AB(3 —— I) —NB = AB(4tI)................ yB_____A,_B_ 5 I) —------ ---- ----------------- TU: AU (1 I.) __________V'UU AU(2,)_______ PH'.= PHB(2~I) SU " TTf(1) SB = TT(2) VC = VBB.,+ VUU -__ __ —-— _____________ ______ —---- ---- -------------------— ____ EXECU'TE EQUIL.(TB) EXECUTE AMOUNT (TBVBB,NB,PH,N) - JC * 0 3 ++ GB CPCP/(CP-R1*NB) _W —- -— __HENEVER_ I._E__INC_____________________ VB = -VTOT TB = TB*(VBB/VB).P.8( GB.-1. ) P = P*(VBB/V.B)..P.GB J4 = 6 TRANSFER TO'.PT1 ---- END OF_ CONDITIONAL EXECUTE HPRIMEl.(, 7,CP,TUNUN) GU =CP CP/(CP-R _NU) VB = VTO T /( 1*+VUU/VB8*(VC/VTOT)* P (GU-GB')/GB)) *VU ". VTOT - VB TU = TU* ( VUUI/VU).P ( GU-. ) TB = TB*-(VBB/'VB)_,(P_( GB-.1) P = R/VTOT* (NB*TB+NU*TU) _-_ NEXTT = TU, __ _ __ ___ LOC6 TU = NEXTT E-XECUTE ENTROP, ( 1 7,.SC, _TU_,N.''.P,NUN ) EXECUTE SPRIME*(1~7,SPRIMTUNUN-) NEXTT = TU-((SC-SU)/SPRIM) __.....VU NUR/PTU__ _____________________._ __ SPT1 TT a SB TC - TB _ _____ _ __ _ _ NCC = NB TRANSER TO ENTRYl LOC(-4.) TB = TC _ ____ __ _ VBB'VC NB = NCC VUU' VU

C..............B_ + V.UU....._ __ ___.___.___._____ _ __.__ WHENEVER.ABS.((VC-VTOT)/VTOT).G ERRORlTRANSFER TO LOC5 VB = VBB EXECUTE ENTHAL.(1,7,HUTUNUN) EXECUTE ENTHAL.(2,11HB,TB N)' ~... ~......3.-.-. ^, ^_ _ _ _ _ _ _ _ _ -— _ —-_-,._ ——._ — _ —------— _. -___-._U = HU-NU-*-R i*-TU PRINT FORMAT OUTL,JC,.I,P'HETATUP VUtHU SU UU NU NUN(1) *.NU 1N(7) UB = HB-NB*Ri*TB_ COEF = O0 EC = UU + UB PRINT FORMAT OUTL tJ I vPHET'ATTBP,'VB HB.SB UB NBN 2 N WHENEVER J1'E.0,TRANSFER TO SPT(.4) WHENEVER FTOT *LE. *02 TRANSFER TO SPT(4) ------ L 3__ L1 = 4 QB = QTRAN2( TB#TUtPDTA.NSCOEF) EC = EC-QB UC = EC WHENEVER J1iNE.1 VB = AB'(7,I) TU = AU(3ti) "VU =' AU(4' I') P = R/VTCT*(NB*TB+NU*TU) END OF CONDITIONAL ----- KEYY.. 3. _______________E___3 _____________________________________________ TRANSFER - TO EN'TRY2'- - SPT(4) A-AB (6.I ) = TB AB(7tI ) = VB AU.(3t I) = TU AU.(4.TI.) = VU.____..WHENEVER ITEeleTRANSFER TO LOC(5) L = 5 WHENEVER J__ G _1 PH = PHF(2, I) TC a AF(3,I) NCC= AF(4II) O^_THERWISE _ PH 1. NCC= NFF END OF CONDITIONAL TT = SF NC = NFC NH = NFH. NO = NFO NN = NFN - --- ---------------------------------------------------------- KEY 2 TRANSFER TO ENTRY1 "LO C 5 -— TFL'AME ----- ---- - ----- ----- ------------ PHF(2,I) = PH.... r....................... _.A-FTT...T —.. —.. —-----—.......-'-:-.... — AF(4.I) = NCC RATIO - N F ----— F/NC —----- EXECUTE HPRIME.(2,tllCPF. TC-N) " —----- ~CP —-- F CPF/1F C ---------------------- R2 = R1*NCC/MF EXECUTE STURB ( TO,: TFLAMES, ST R2 ) DT = DS/ST ~~~~~~A 1.........r.r...

-215NC NBC ______________NH NBH NO = NBO NN = NBN J1 = SAVE -____ - - — W. HENEVER *ABS( (PHETA_-THETA-6.*RPM*DT)/PHETA)e.G.EERROR1 SAVE = Jl TRANSFER TO ENTRY4 _ — DQ_-_q_ —-E J- 1I___ —---- F_-_C__NDT NAL_-_ —----------- PRINT FORMAT VOLUSTTFLAMECOEFFTOT ECTOR___VALUES VOU __$__14HOVOLUMES AGREES5 13HFLAME SPEED F10.5,tS5.8HTFLAME = F105,S5,20HH.EAT TRANSFER COEF = E158/ 219H FRACTQNI_ BURNED =, F1O.8*$ WORK = E-EC-QB L_T.IQ._.+___W_.T + WORK-__ QTOT = QTOT+QB LSTTH = THETA.. ETA.A-.HA__,_____A...... DT(I) = DT PRINT FORMAT INTRITHETA,TUPVTOTHU+HBSU+SBUU+UBNU+NBQB 1 QTOT.fWO'RK WTOT. SEC TB P tVB HB tSB UB N.B,ANS ANS5AN ),NEWL 2LASTL VECTOR VALUES INTRI =$56,4HTIMES5, 1HTS9,1HPS9 HVS9,HHS9t1HS _ S991HUS9,1HNS9, 2HQBS8 4 HQTOT 6,4HWORKS6 4HWTOT/(12F10,5 )*$ TX(TXZERO ) = THETA TX(TXZERO + 1 ) =TB TX(TXZERO + 2 ) = P TX(TXZERO + 3 ) = VB T.X(TXZERO + 4 = HB TX(TXZERO + 5 ) = SB TX(TXZERO + 6 ) = UB TX(TXZERO + 7 ) = NB T'X(.TXZERO+.8 ) STTX(TXZERO + 9 ) = TFLAME T'X(TXZERO + 10) = ANS(5) -TX(TXZERO + 11) = FTOT TX(TXZERO + 12) = VB/VTOT TXZERO_ = T.XZERO + 13.. TZ(TZZERO ) = THETA TZ(TZZERO + 1 ) = TU TZ(TZZERO + 2 ) = P.Z(._TZZERO + 3 ) VTOT ______ TZ{TZZERO + 4 = HU+HB TZ(TZZER.O + 5 ) SU+SB TZ(TZZERO + 6 = UU+UB TZ(TZZERO + 7 )'NU+NB TZ(TZZERO + 8 ) =QB.-......,..T...... 9.T ) TT...Z.i B..9....,T............. TZtTZZERO + 10) = WORK TZ(TZ-ZERO + 11) = WTOT TZ(TZZERO + 12) ='COEF TZZERO = TZZERO + 13 PRINT FORMAT HEAD3 ^. T__._IAJASF~R_E.O &PTU4..___._ ~, ~.,_~________T...LJ__ SPT(5) WHENEVER (P-LASTP)3GE.0,TRANSFER TO ANOTHR NEXTK = KK (LSTTH-(180. -PI).)/(PIMAX- (18 o0.-P I) )

-216WHENEVER eABS. (PIMAX-LSTTH) G.EERROR 3 J1 a J1 + 1 KK a NEXTK PRINT FORMAT OUTPOTtKK V-CT VAL us TP- - -------- -- -- --- — E1iT — --- - - -- --- ----- TRANSFER TO RETURN --------— N TN —----------------- -- ------ - J4 m 6 PMAX a LASTP WHENEVER J3.E.1 J1 a J3 OTHERWISE END OF CONDITIONAL SPT(6') WHENEVER P.G'LASTPP.MAX P WHENEVER I.L INC.TRANSFER TO ANOTHR EXECUTE OUTPUT*(F) ----— E^ —' —----— CUO FTp^-S —-1 ——. —----— c —--------- ------------------------------------------------------------------------ -- ----------- END CONTINUE TRANSFER TO BEGIN' VECTOR VALUES INTRO * $1H1,S35o49HA MODEL SIMULATINQ THE 1NTE iRNAL-COMBLST ION- EtGINE/7HOENGINES33 4HFUELS36~20HOPERATING CO -------------------- f7-NS- r F -— ^ —------------------------------------- 3EL RATIO F9.2/SH 8ORES8,F102,4H INS13,17HACTIVATION ENERGY.-i —---- --- ---— W^l^i^-4 r 7 - EF —-— PESN-n~!WzH —-.^^F^^-r —--------------------------------- --- 52.4H IN#.513, llHENTHALPY OFS29,9HWALL TEMPF14.2,2H K/4H RODS9t ~- --- 6F10*294H IN*.51'3.,O1HCOOMBUST1ONF1iZZZH CAL/MOLE MAN. TtMPa 7Ft14*22H K/12H CLEAR* VOL.F1.27H CU.INeS50,8HMAN. PReF15.2, ----— 8 —-------—' VWX _I 7 E PR —P FIB 4- — Ar —----- 9M/zSH COMPRESSION RATIQF5.2,7H TO ONES5010HSPARK ADVeF13#2*$ -------—' —-- -V-[. —--- TROI —B --------------------------—' ------- ------— 7 — --- 1STION OCCURS IN I3,34H INCREMENTS,. ERRORS ARE LESS THAN F10 25t33H PERCENT. FLAME SPEED FACTOR IS tl.6S/Z4H HtAT TKANSt"tR 3 FACTOR IS. F0le5,S3.10C6$* -----------------— _ —---— C —-— VIE —-. _ —— _ —-_ —— _-_ —---- -- ------------ INTERNAL FUNCTION VOLUME ZETA). 0007854*BORE*BORE* —STROKE/. —----------------— T2-; ^^Q 1 ^^COS + z ErK4-,-,^^T). I-S —----------------------------------------------------- * —------------— T-iW I Z+COS T- -ZET-CI-OT'/4-5'-T:RODI —I~;S'RT;TI-~TSTRO',E7~ga/Wi — 2ZETA*01745)/ROD) P2)))+ VTOP END OF PROGRAM _____ - _ ___ —_ —--— __-__-_-_-_-_-_-_ —_-_-___ _ __ ___ _ __ ___ — - - - - -- - --------- - _ - _ —------------ _ —--- __ —-- _ _ ___ —- - _ _ _- — C-C - 0156 - - - - - -- -- - - - - - - -- - - - -- - - -- --- -- - -- -- - -- -- - --- ---- -- - -- - -- - -- - -- - - - - - - - - - -- -- --- - -- --- - - - - -- -C.C — -. -- - - - - 1.5 —- 6 - --

-217$COMPILE MAD, PRINT OBJECT,PUNCH OBJECT 4FNSH001 EXTERNAL FUNCTION(ENERGY,TEMPT,VOL,PHPBACKLOOOP1,FD1)......_PROGRAM'COMMON AL..AH P K NC 9NH,NO NNR J2 R E K-KK X, TW. 1QFACT~EA,-RATIO,BO,RHOSPEED,ERROR2,CPFTPISTN,ATOT,XXXNUM, 2BORE,STROKE t ROD,VTOP,VBOT PMAN, PEXH TMAN, RPM _N ITHETA ERROR 1 3J3,STOPT5H5,55U5,N5-QTOTWTOTFONEXTVHCOMBINCZC 4 TZJTXPCOMDG, PMAXNAME CR. PI STATEMENT LABEL BACKTLOOOP1 INTEGER RE, I II I2 I3,JJJ1 J2,J3.rL2,'N1 N2 INCNAMEXNUM 2NEXPDG#,. KEY,STOP, TZZERO DIMENSION AL_87, ALDIM), AH(_87,ALDIM).RE(12.).X(10)_,KK(5), QFACT 1(5)' P(L1).N(1 1). K( 11)t XX(l 05.XDI-M),NAME(2)o RT(40),ATOT(5)}B(7 2),TZ.(1980) TX(780) EQUIVALENCE (TZ*TZZERO) VECTOR VALUES_ XDIM = 2,0.21 _ VECTOR VALUES ALDIM = 29,08 ENTRY TO FINISH. U'B = ENERGY TB = TEMPT'VB = VOL PH = P'HP DELTA'T a O0 NEXPDG a ( 359,-TH'ETA)/COMDG*2* - DTHETA = 360.-THETA-NEXPD'G*COMDG-/2-. D'T' DTHETA/6./RPM J1 =J'O1 + 1 LCC1 Jl a Jl + 1 TC =RT(Ji) -----------—... — -- - -,:. -,:................................................ —-.....-............................ E "UB WHENEVER J3.E*lTC=TB-DELTAT -ARAA = ARREA:e(THETA) QB QTRANS. (P.ARAACOEF) Q............l..,..-......._ _=.. 0 T_O _ +_ ___QB..... _..._ _ _............... UB - E-QB G - 6 KEY 3 3 TT UB ENTCY1. J = 0 L2 = KEY NEXTT = TC C..L C..2_1 _.. TC..E....T_..C.....NEXTT'..~......._......__. ___............................._.______~.........._... J.= J + 1 EXECUTE EQUIL.(TC) EXECUTE AMOUNT* (TCVB.NBPH.N)...' TR..,TANSER._RTO ENTCYL2).._._._ ___.. EN.TCY(2) P. NB*R/VB*TC EXECUTE ENTROP.(2,11,CCTCNB,P9N) EXECUTE SPRIME (2 11CPRIM, TC'N) CPRIM = CPRIM- NB*R1/TC TRANSFER TO LESSC ENTCY.(3) EXECUTE ENTHA L_.(2,11._CCTC. C N) CC = CC- NB*Rl*TC EXECUTE HPRI[ME (2,11,CPRIMTCN) CPRIM = CPRIM- NB*R1 LESSC Q = CC-TT NEXTT = TC-Q/CPRIM........... WHEN EVER —.J.-E..5.........._. L2 = L2+3 DIF =.ABS.(TC - NEXTT)

-218END OF CONDITIONAL WHENEVER 6ABS (Q/TT) *GERROR1 TRANSFER TO LCC(2)__ TRANSFER TO COMMOC ENTCY(5) P = NB*R/VB*TC EXECUTE ENTROP, (2,iiCC-TCNB NPN) TRANSFER TO MOREC ENTCY(6) EXECUTE EN THAL *-(2 1 CCTC C N CC = CC- NB*Rl*TC. MOREC QQ CC-TT WHENEVER Q/QQ.L....DIF = DIF/2. NEXTT = TC - DIF*QQ/,ABSe(QQ) Q = QQ WHENEVER — ABS-(Q/TfT)-GERROR-TRANSFER TO LCC(2) COMMOC PRINTFORMATOUTGJI, THETATC,PVB TTteOCC NB _ TRANSFER TO LCC(G) LCC(6) RT(J1)= TC - -*- -B- " TC —:^ ^ ^ -^ ---- ---------------------- ------ -------------------------------- TB = TC P = NB*R/VB*TB EXECUTE EN.TR-OP (2, 1 SBTB NBPN) THETA = THETA+D-THETA -. V = VOLUMEs.(THETA) -.-. — - TC TB*'VB,/V)*P(NB*Rl1/CPRIM) VB V G = 7 KEY ___ 2 ________________ TT SB TRANSFER TO ENTCY1 LC(7.. EXECUTE T ENTHALe( 2 11 HB T C.N)-. —.. — TB = TC UB = HB-NB*R B —--------------------------...... - ORK = _EUB-QB __ ___ ____ WTOT = WTOT+WORK PRINT FORMAT OU.TGJJl',THETATB, P'VBHB~SBUBNBN(2).-.N(ll 1) 0 Q QBQ TOT,WORKWTOT, COEF0 ARAA."""".-.... TZ(TZZERO ) = THETA -TZ(TZZERO B- 1..... —...... -. TZ(TZZERO + 2 ) = P TZ(TZZERO + 3 ) = VB TZ(TZZERO + 4 ) = HB TZ(TZZERO + 5 ) = SB TZ(.TZZERO + 6 ) = UB TZ(TZZERO +'7 ) = NB TZ(...............zTZZERO + 8 ) QB TZ(TZZERO + 9 ) = QTOT TZ(TZZERO + 10) = WORK TZ(TZZERO + 11) = WTOT-'TZ(TZZERO + 12) = COEF T"ZERO - T'ZZ'ERO.. +G... I'3 -R.S O. L WHENEVER THETA.G.359,TRANSSF ER TO LCC3 DELTAT = DELTAT/2s DTHETA C.CO"t4DG/2. -- DT = DTHETA/6e/RPM -------------— _ —-— __ — ^ ^.- ^ ^ ^ ^_- - - --—._ —-— F — - TRANSFER TOLCCLCC3 WHENEVER J3'.E.1 EXECUTE HPRIME.(211,CPRIM, TCN).................. TEXH = TB* (PEXH/P)_P_ ( R1*NB/CPR IM )

-219-.................EN-DO —DNAt ------—' —N. —-........... NEXTT = TEXH P = PEXH NEXTV = NB*R/PEXH*TEXH J= 0 LCC(3) TC = NEXTT J = J+. 1 EXECUTE EQUIL.(TC) LCC5 VB =.NEXT'V EXECUTE AMOUNT.(TCoVBoNBvPH9N) NEXTV = NB*R/PEXH*TC WHENEVER *AB'S ((NEXTV-VB)/VB),JG.ERRORilTRANSFER TO LCC5 EXECUTE ENTROP, (2,1.lCCTC-,NBP,N), Q = CC - TT EXECUTE SPRIME.(211#CPRIMtTCN) NEXTT = TC-Q/CPRIM WHENEVER *ABS.(Q/TT)#G.ERROR1,TRANSFER TO LCC(3). -..... — - I-....... _- T_-. —--.- —. - -.. -- —.. —-—.......- -- TEXH TC EXECUTE ENTHAL A(2 11,!HB TB,N)...... UB HB-NB*Rl*TB T.E..Z-ERT.......H-....._T.._.._.........._Z_. _._......_=T___HETA..__ TZ(TZZERO + 1.) TB TZ(TZZERO + 2 ) PEXH T'Z(TZZERO + 3 = VB TZiT-ZZERO + 4 ) HB T:Z(TZZERO'+ 5 ) = SB TZ(TZZERO + 6 ) UB. TZ(TZZERO + 7 ) = NB TZ(TZZERO + 8 ) = 0 TZ'(TZZERO + 9 QTOT —------------------------------------------- T.Z(TZZERO + 10) = 0. TZ(TZZERO + 11): WTOT TZ(TZZER.O + 12) = 0, TZZERO = TZZERO- + 13 PRINT FORMAT OUT,9,J1,J,360.,TBP. VBHBSB.UBNBN(2)_..N( 11) N(2) = N(2) +(N(9)+N(10)+N(8))/2. N(3) = N(3) + N(9)/2.'N(7) N(7)+(N(8)+N(11))/2, TC = T5 F = N5/NB TJZ(TZZERO )= 540O TZ(TZZERO + 1 ) = T5 TZ(TZZERO + 2 ) = PEXH TZ(TZZERO'+ 3 ) = VTOP TZ(TZZERO + 4 ) H5 TZ(TZZERO + 5 ) = S5 TZ(TZZERO' + 6 = U5 TZ(TZZERO + 7 ) N5 TZ(TZZERO + 8'= 0. TZ(TZZERO + 9 )= QTOT TZ(TZZERO + 10) = 0. TZ(TZZERO + 11) = WTOT TZ(TZZERO + 12) = O. -TZZERO = TZZERO.":..12... -.-.. —-...-. —.........WHENEVER STOPG.1T, 5=TB WHENEVER,ABS.((TC-TB)/TC).G.ERROR1,AND.J3-L-STOP~TRANSFER TO 1 LOOOP1

-220FUNCTION RETURN INTERNAL FUNCTION ARREA.(ZETA) = 3 1416*iBORE*(STROKE/2 *( 1+ 1COS. ( ZETA*:"'1745) )"+-ROD*('-SQRT. ( 1-'(Si'"N- (ZET-A —O-'1?745)*'S TR-O KE-. 2/-2./ROD) P.2))+D1)+ATOT( 1)...... —-." ——.. —-.- -'......TERJTNAL —'F UN'C TO' ON-VO0L-UMEZETA Z "ET ='-O 0'00785'4OT3F4B-ORE'BORE*-TSTR OKE/. 12*( 1 +COS.('ZETA*0.Q1745 ))+ROD*( 1- SQRT ( 1-( STROKE/2ES I N ( VECTOR'VALUES: OUT =$1HOQ313 S2.,3F103 F15 8 t4E158/ ( 6E20Q8 )*$ INTERNAL FUNCTION(PR AREA................ ENTRY TO OTRANS, $S = RPM/3000'.*STROKE S = 2.I*SQRT,('PR*TB)*SP.,33/36000# FUNCTION RETURN DT*S*(AREA*('TB-TW)+ATOT (3)*(TB-TPISTN *)- QFACT END OF_FUNCTION__ _...... _' INTERNAL FUNCTION(TEMP) ENTRY TO EQUIL............W....... E....R. ] E-E —-EMP'.LE. 150'.-;FUNCT6ION RETURN rR = TEMP/1500. RT = 1./TR B(1).= (ELOG. (TR)+RT-1.. )/.19872 8(2) = 750.00*(TR+RT-2.)/1,9872 B(3)' = 375000,00*(TR*TR+2,*RT-.-3*)/1*99872 8(4).............. =281250 0000 (.TRf*TR*TR+3 *RT- 4~ ) / 19872 B(7) = ( 1-'RT)/298Q0.78.5 K(4) = 0. THROUGH LOOP7,FOR VALUES OF I = 1,'23',47 L:O P 7 K(4 ) = K(4)+(AH(6I)+5AH( 2,I )-AH( 4I).)'B() K(4). EXP.(AH(4,8) +K(4)) K(5) = 0. THROUGH LOOP8,FOR VALUES OF I = 1,2,3*407 O-:bOP 8 "KT 5) K( (-' —-—' —y)- l"?;-Tfr'r7~T R;Tr5-~'iA-RI-2-FI-IA-R-(-SFI-FX'- - K(5) = EX.P,(AH(5,8).+K(5)) K ('8 ) = 0,.................................. THROUGH. LOOP9FOR VALUES OF I = 1,2,3,4,7 LOOP9 K(8) K(8)+( *( AH( 2tI)+AH(7'I))-AH(8"I' )"*'B)...... K(8) = EXP.(AH(8,8) +K(8))......K(7)...................................................................................................... THROUGH LOOP10,FOR VALUES OF I. = 1,2t3,447 LOOP10 Ki7) = K(7)+(.5'AH(7?I)-AH(11.tI))*B(I) K(7) = EXP(.AH(798) + K(7)) K(9) = O0 THROUGH LOOP'11oFOR VALUES OF I = 1,2,3,4,07 LOOP 11" "K(9) = K (9 )'+(".5*(AH(.2tI.)+AH (3I)-'AH(9-I..). K(9) = EXP,(AH(988). +K(.9)) K(2j''0. THROUGH LOOP12#FOR VALUES OF I = 192#3. 47 LOOP 1_2 K' (2.) K'- (2)+(.5*AH(2,I')'AH( 1"0I),) ----— " —-............ K(2) = EXP.(AH(2,'8) +K(2)) FUNCTION RETURN..... —. —-—.. END OF FUNCTION INTERNAL FUNCTION(N.lN 2 PROPTYTEMP BLANK) -.. ENTRY TO SPRIME, B(1) = I./TEMP B(2) = 1. *' " "' - -BT E M P - -... -.'- -' -' ""- " """"" --. — * -— **** —------ -* —--. --— *-*-*- -...... B(4).=. EMP* T-EMP. TRANSFER TO MATRIX ENTRY TO HPRIME.

-2218(1) 1o...........(.2. T E M P..................................................................... 8(3) = TE'MP*TEMP B(4) =_TEMP*TEMP*TEMP.......... TRANSFER TO MATRIX..................... EN.RTH_.NO.......T_.........................._.. _............... _..............:'.._..___.-__...... I 5 PROPTY =............... WHENEVER TEMP.G..1500*,t TRANSFER TO HIGHT.T R T E M P........................................................ 8(1) = 298.16*(TR - 1.). 1.L.2. = 44449.693 T(_R*TR - 1.) B.(3) = 8835413o6*(TR*TR*TR - 1.) 8(4) = 1975775200s*(TR*TR*TR*TR - 1.)_. B(5) = 1, TRANSFER TO LOW HIGHT T'R = TEMP/-500 —. B(1) = 1500.*(TR - 1.).(2) = 11.25000*(TR*TR -1.) B(3) 1125000000#*(_TR*TR*TR_ 1.) B(4) = 1265625E13*(TR*TR*TR*TR -1.) B(5) l= 1 TRANSFER TO HIGH MATRIX I = 4 PROPTY = 0. WHEN.EVER TEMP t*G 1500., TRANSFER _TO HIGH LOW THROUGH SUMB, FOR I2 = N1,1'I2*.GN2 TA 0- - THROUGH SUMA, FOR 13 11tI3"G..I SUMA TA TA + B(I3)*AL(12,3) " SUMB PROPTY = PROPTY + I N(12)*TA FUNCTION RET'URN_ HIGH THROUGH ADDAP FOR 12 = N11,I2'G.N2 TA = O. THROUGH ADDB, FOR I3 = lt,1I3G'.I A&DB TA TA + 8(13)*AH(I2,13) ADDA PROPTY = PROPTY + N(I2)*TA FUNCTION RETURN END OF FUNCTION INTERNAL FUNCTION (N1,N2,PROPTY,TEMPMOLESPTOTALBLANK) ENTRY TO ENTROP. PROPTY = 0. WHENEVER TEMP.G#1500,' TRANSFER TO BIGHT TR T..EMP/298. 16.______ ___ B(1) = ELOG*(TR) B(2)..= 298.16(TR 1-.) B(3) = 44449e693*(TR*TR - 1.) 8(4) = 88354 13.6*CTR*TR*TR 1.) 8(6) = 1..T.-.HR.OUGH BUMB._.FOR 1 2 N=..12.G.N2. _...IG. WHENEVER N(I2).E. OoTRANSFER TO BUMB TA = O. THROUGH BUMA, FOR VALUES OF 13 = 1'2,3,496 BUMA TA = TA + B(I3)*AL(I2,I3). -PROPTY = "PROPTY +.N( 12)'(TA -1. 9872* ELOG.(N'2) OTAL/M'-OL..J_.E._.._.__ _..............______- __ BUMB CONTINUE FUNCTION RETURN

-222BIGHT TR = TEMP/1500* B(1): ELOGs(TR) B(2) =-i50O.*(TR - i.) B(3) = 1125000.*(TR*TR -1.).B(4).'.. 1125000000.*(TR*TR*TR' - 1'). )... — - B(6) = 1.......... —--.. THRO~UGH""' - BD ODA~..'FOR 12'-'-" -' N-Tl, I 2 -.'G —.N'' -------------— 2 —-- WHENEVER N(I2).Es O,TRANSFER TO BDDA TA = 0O THROUGH BDDB, FOR VALUES OF 13 = 192,3,4',6.....BDDB - TA = TA + B(I3)"-AH(I2," —I3 PROPTY = PROPTY + N(I2)*(TA -1.9872*ELOG.(N(I2)*PTOTAL/MOL IES)) BDDA CONTINUE __ FUNCTION RETURN END OF FUNCTION --------------— N —------ - — P'V"-T'OL MOLES H A -------------------------- ENTRY TO AMOUNT. P(l) = O0 FA = TEMP*R/VOL.................WHENEVER "TEMP i*LE'.i'500,'TRANSFER TO- H2OASA'' WHENEVER PHH#LEeOPHH a 1, -------------' —- -^^ — -------—. —----------------------------------------------------- - NEX'TL E PH' —— i —LOOP1 L = NEXTL -------------------- -- ---------------------------------------------------------— T —~ —-- - S2 4'*(1. + L/K(5)) S3 "~' — SQR''' TL L''1171KTTf 7 —9'I'-'B~FFA*1NNTF -....... S4 - SQRT(S1*$S1 + 2*$S2'*FA*NH) ------------------------------------------------- S = S3/4. - L/4./K(9) ~ —D'',K(9N- Vl~~s3r —~IiT74 —— 7K-. —------ DMWRL = -(S2*(1./K(8)-.(S1/K(8)+4.*FA*NH/K(5) )/S4)+(S4-S1 )*4./ P(2) = L*L............................-.-.- - ---- - - — s — ------- ------- P(4) " NC*FA/(K(4)/L + 1.).............................L*M*M/K(5 ---—.. —---—. —'K P(6) ='P(4i*K(4)/L P(8) = L*M/K(8)...........P(9) --—.-.. —- ---------------------------------- P(10) a L/K(2) P(11) = M/K(7) FL = 2.*(P(2) +'P(4)+P(5) + P(6)+P(9)+P(8)+P( 10) - FA*NO "F"PR^ii CM-"= — -*K4)K(4l)'/-(L+K (4) )? T(-'T4)) +4+., *EL+M*M/K ( M ) +/K(")+ 1S/K(.9)+1./K(2.)+DMWRL*(L/K(8)+2e*L*M/K(5)) +DNWRL/K('9)*L ~I ~M-*-~ -- - aU — _-`- R —FL/L/7TML -- --------------------------------------- ---- WHENEVER *ABS.(M) *Le16e. —---------—. --- --- ------------------------------------------------------------- OTHERWISE EXTfL = L*'E'X"P-_1M-ABS. END OF CONDITIONAL WHENEVER'ABS. ( (:NEXT-L T/L G.ERROR2T.R~N-SFER —TO-L-OO PHH = L..-............... - -N — -- —. —---- --------------------- ----------------------......... H.2,0A&. ENEY.......N..EEi.. (..NC+NH/.4.) /NO * L.E, 51.~TRANSFER TO S I MPLE SI = NO/NC."1. S3 = (l1+NH/NC/.7494)/Sl-11668b';- -- L = ('53+5.QRT. (S3-S'' —------------------ ---------- - P(2) = O* P(4) = FA*NC/L P(5) = FA*(NO-NC)-P(4) P(6) - e-ABS-. —----- — N —- A -C —------------- P(7) =.ABS.(FA*NH/2- -P,(.5) - TRANSFER TO HERR....I.P..L...E. P.(2) =.ABS (FA*(NO/2.-NC-NH/4.)) P(4) = FA*NC P(5) = FA*NH/2. P(6) = 0. P(?) = O. HERR P(8) = 0O P(9) = O0 P(10) - 0. P(3) = FA*NN/2~ LOC2 MOLES = O0 _____ _ THROUGH LOOP2, FOR I = 1l1I.:G.11 ________________ N(I) = P(I)/FA....L_-QP2_ _ MOLES = MOLES + NMI) FUNCTION RETURN END OF FUNCTION END OF FUNCTION

-223$COMPILE MADtPkINiT O.bJECT.PUNCH OBJECT 30UTP201 EXTERNAL FUNCTION (F).....____ _ PROGRA;R COi,4MON ALAt ALH,P,K t R 1,NC,NHiOQ _ tNN t, J2 fRE, KK X, T' v, 1QFACTEA, RAT OBbQRHO, SPEED L ERROR2 CPF TP ISTN ATOT XX XNUM, 2BORESTROKERODVTOPVBOTPMIANPEXHTMANtRPM N THETAtERROR1, 3J 3STOP T5 H5,55 U5,N5 QTOT'WTOT F-0oN'EXTVtHCOMBINC-Z-C-,-.......... _ __TZ_.TX. t O__MDG PMAX NAME tCR tPI_ _ _ _ _ _ _ _ _______ INTEGER NUM2 INCRE NAME TZZERO DIMENS ION AL 8 ALIM)_ AH(87,ALDI M)E ( 12) XX( 1 ) KK(5) QFACT 1(5),P(11)N(11),K(11),XX(105,XDIM)tNAME(2) ATOT(5)J 2 TZ(1980,TDIM),TX( 780,TDIM) EQUIVALANCE (TZZEROTZ) VECTOR VALUES TDIM = 2,1913 VECTOR.VALUES ALDIM a 2,0,~8 VECTOR VALUES XDIM = 2,0t21 ENTRY. TO OUTPUT. PRINT FORMAT INTRO, NAMEe..NAME(2)_XIBORE/2.54,EATTPISTNSTRO 1KE/2. 54,TW tROD/2 54 HCOMB, TMAN VTOP*61.03, PMAN, 61,o03* (.VBOT-V.Tf....OP..EXti.......... P20P___-PEXH_ _ CCR_ PI_.__ I WPUMP: (VBOT-VTOP)*(PMAN-PEXH)*24.2179 WTOT = WTOT + WPUMP EFF = WTOT/HCOMB*100 /FO PRINT FORMAT INTORltRPMINCtERROR1*100,_KKQFACT_ RE(4).._RE( 112) IMEP = WTOT/(VBOT-VTOP)/24.2179 VOLEFF = FO*Z*(C*X+X)/(VBOT-VTOP)*RiPMAN*TMAN PRINT FORMAT RESULT,WPUMP,WTOT,QTOTEFF,IMEP,F,VOLEFF VECTOR VALUES RESULT = $1H2tS20,18HSUMMARY OF RESULTS/1HO/S6# 112HPUMPING WORKS18,E15_8_4H CAL/S6,14HNET CYCLE WORKS16,E15_8 2,4H CAL/56,19HNET HEAT TRANSFEREDSllE15.8t4H CAL/S6,28HINDIC -— SATED THERMAL EFFICIENCYS2,E15.8,8H PERCENT/S6,23HMEAN EFFECTI 4.VE PRESSURES7,E158,+4H ATM/56,24HRESIDUAL WEIGHT FRACTI-ON,-'t 5E15.8/S6,21HVOLUMETRIC EFFICIENCYS9E15 *8 8H PERCENT*$ NUM2 - TZZERO/13 -PRINT FORMAT HEADER VECTOR VALUES HEADER a $1H1/6H'OTHETAS5,1HTS6,1HPS5,1HVS9,1HH, 1 S9,lHSS9lHUS9,lHNS9,lHQS8'4HQTOTS7,1HWS8t4HWTOTS7t2HHB*$ PRINT FORMAT TABLE1lTZ( lt,)**TZ(NUM2,13).'Y VECTOR VALUES TABLE1 = $1H F6.2,F8'2,F7.2,F8.5,9F10.5*S PRINT FORMAT HEADR1 _._.. VECT.QR _AYLUES HEADR l _$lH1/6HOTHETAS5 1HTS6 1HPS551HVS9_ 1HH_ 1 S9,1HSS9,1HUS91lHNS5o50HFLAME SPEED, TEMP., AND EXTENT MASS-. —— _____ Z-...? 2FRo BUR'N.-VOL *$ PRINT FORMAT TABLElTX( 1,ltl) TX(INCo13) FUNCTION RETURN VECTOR VALUES INTRO = $1H1S3549HA MODEL SIMULATING THE INT 1 RNAL-COMBUSTION ENGINE/7HOENGINES33,4HFUELS36,20HOPERATING CO 2ND'ITIONS/28HOFOUR STROKE AUTOMOTIVE TYPES 123C6,S22,l14HAtR- FU 3EL RATIO F9.2/5H BORES8,F1O2,/4H INeS13,17HACTIVATION ENERGY 4F10;2,-24HC.- CAL./MOLE PISTON TEM-P-F-2 —2.2 —H-K —HS'R-OKES6 —F1 —O 52.4H INS3,rllHENTHALPY OFS29,9HWALL TEMPF14,2,2H K/4H RODS9s 6'F102,4H INeS13O10HCOMBUSTIONF17i2,22H CAL/MOLE. MAN. TEMP.7F14.2t2H K/12H CLEAR* VOL.F11.2'97H CU.IN.S50o8HMANo PR.F15i.2 84H. ATM/1-1H SWEPT VOL'F12- 2;7H' CUI -NS-5-O —ERXR-H -P-R-F5." - — 4R — AT'-r 9M/18H COMPRESSION RATIOFS52,7H TO ONES50,10HSPARK ADVF13.2*$ VECTOR VAi ES -— I N'T-OR-R i -$-8Oi5-H$'EE-S-[ 0~F-4;-.-RP-r - —' —------.........1STION OCCURS IN I3,34H INCREMENTS* ERRORS ARE LESS THAN F10, 25933H PERCENT. FLAME SPEED FACTOR IS E15.8/24H HEAT TRANSFER _^_ - - 3 -FACTOR IS FlO.5tS3,10C6*$.........................._FACT R.s...! O_. F ___O. } 3___C__*__......... —----------------—....... $COMPILE MADPRINT OBJECTPUNCH OBJECT 40TRAN01. —---—'-~'~' EWK -FU^^^^^^TI^^^^^^Tt^TUTU-0ASt — --------------------------- EXTEX N A —-FUNCTI'OlrTT-iTOTPR-FDTiA-Ns-REI DIMENSION AL(87.ALDIM'),AH(87,ALDIM),RE(12),X(10 )KK(5),QFACT 1(5) P(11).K(11 XX(105 XDIM)A(5) PROGRAM COMMON AL. AHPKR1,NCoNHNONNRJ2,RE KKXTWQFAC 1T. EA RAT! 0O BORHO, SPE- R -2-F'T-IS-T-X-X -O- BR TO 2KE,ROD,VTOP,VBOT,PMANPEXHTMANRPM.........______VECTOR VALUES XDIM = 2,0,21. ENTRY TO QTRAN2. S a RPM/3000.*STROK E HB = 2.1*SQRT.(PR*TB)*S.P..33/36000. HU a 2.1*SQRT.(PR*TU)*SP..33/36000_ FUNCTION RETURN DT*(HB*(ANS(1)*(TB-TW)+ANS( 3 r-V* (TB-T — SI-T + 1HU* (ANS(2)(TU-TW)+ANS(4) (TU-TPISTN))*QFACT END OF FUNCTION

-224sCOMPILE MADePRINT OBJECTsPUNCH OBJECT 6ANS0001 EXTERNAL FUNCTION (VB#VTOT9ANS,D1D2) PROGRAM COMMON AL, AHP,K,R1,NC,Nrl~NONNRJ2,RE~KKXTWQFAC 1T,EA,RATIOBO,RHO,SPEED;,ER'ROR2,CPFTP'ISTNA,tXX,XNUM,BORE 2STROKE,RODVTOPVBOTPMANPEXHTMANtRPMNTHETAERROR1 ERASABLE LOPL1PL2PDERDVWRFNEXTF','IO,'XMUMtF,'DL L I' iI2',I3', 1LO,L1,L2, AWAWAWB'AWU S.QgQQD IF INTEGER I IOI,'2.,XNUM-'3'J2 DIMENSION. AL.(87,ALDIM),AH(.87,ALDIM),RE.(12).X.(10),KK('5),QFACT 1(5) P(1l1), K(11),XX(105, XDIM) A(5),N(11) VECTOR VALUES ALDIM - 2,0,8 VECTOR VALUES XDIM = 2,0"21 ENTRY TO AREA. XDIM(2) = XNUM XMUM = XNUM - 1 DL = STROKE/2.*(1.+COS.(THETA'*01745)) + ROD*(1.-SQRTo(li (STROKE/j2 *S'INo-(THETA*ao 0'1745 )'/ROD ) P,2 )-) WHENEVER THETA.G. 180.,TRANSFER TO DOWN F " VB/VTOT*XMUM WHENEVER VB/VTOT *L..r03 ANS(5)' (VB/.0041888),P..33 OTHERWISE 11 = F +.5 WHENEVER 11.LE1,I11. = 2.RWHENEVER- I1. GE'XNUM'= -—''1..I"....- —.-.-.-. 12 = II + 1 13 = 12 + 1 10 (II - 1 L1 i (IO-F)*(F-'I2) L 2' F-IO)*(F-I1)72... - ANS(5) A'(5)*(L0*XX(5I1),+ Ll*XX(5tI2) + L2*XX(5,I3)) END OF CONDITIONAL ANS = VB F = ANS(5')-./A(5).*XMUM TRANSFER TO FINI'SH DOWN NEXTF' = ANS(5)/A(5)*XMUM BACK F'= NEXTF J2 = J2 + 1 ANS(5) - F*A(5)/XMUM I1 = F +.5 WHENEVER I1lLEOIl = 1 WH.ENEVER I' -GE. XNUM-".I. = XNUM-2........-.......-.I2 I + 1 13 = I2 + 1 10 = II - 1 LO (F-I1)*(F-I2)/2..-. LI = (IO-F)*(F —2) L2 -('F-IO)*(F-I1)/2. -.-.. WHENEVER J2.LE.5 LOP = F-(I1+I2)/2. LlP = IO+I2-2o*F L2P = F-(IO+I1)/2. ANS = VTOP*(LO*XX(4,I1) + L1*XX(4+I2) + L2*XX(4,I3)) WHENEVER ANS('5)'LE"'D 2........ ANS = ANS +.0031416*ANS(5)*ANS(5)*DL DER = 0062832*F*DL*(A(5)/XMUM).P.2 OTHERWISE

-225-------------------------------— _ —_ —--— _ —--— _-_-_ —_ —. —ANS = ANS + DL**ABSe (A( 1)* (tL0*XX( 1'I1)+L 1*XX( 1, I2 —L.-*XXt I -— 3 1 1/1000, DER DL*A(1)*(LOP*XX( 1,I )+L1P*XX(1, 12)+L2P*XX( 1 13) )/1000. END OF CONDITIONAL DVWRF = VTOP*(LOP*XX(4 I1)+LlP*XX(4,I2)+L2P*XX(4-I3 )).___________ ___- _ _______Q ------— _ ___- ___ _ ___ __-__ _ _ _ _ _ __.._. NEXTF = F + Q/tDVWRF+DER) DIF 2.AB RS*(NEXtF - F) OTHERWISE. —-_ —_ —_ —— ___A ___ —_- ___ _P__LQ*X_4_XIll_+_-__Ll+_*XA_(4-I_2)__+_ +. 2X-_- _! WHENEVER ANS(5)LE#D2 _-. _______ __ _ A_ _, 5 _.. —------------------— Q1A ^ A5 Ai_ _J _ —----- OTHERWISE AN.S Q ANS + DL*.ABS.tA(1)*(LQ*XX(1.I1)+L 1*XX(1_12)+ L2*XX(lI3_ 1)M)/1000. ----------------------- emN L~Q- N21.iIQO L —-------------------------------------------------------------—. ---- -- Q00 VB-ANS R —--------------------- EHE- _ER.^A6 Dj-I.__]_._..Q..._ F D I F / 2 _._______- _____NEXTF * F+DIF*QQ/eABS (QQ) END OF CONDITIONAL VWHENEVER *ABS. (NEXTF-F)/F)JG. 00O1,TRANSFER TO BACK ----------------— ~ AS —-E TOBCK —----------------------—. —------ --------------- FINISH It * F + 1. 12' I1 + 1 -------------- -------------------------------------------------------------------------------------------------------- 10 a 11 -1 LO 11' F Li F- I0 AW * 3.1416*BORE*(D.L + Dl) WHE-NEVER ANS(5) e6e 9*A G —-' —.-Ai 5 )- - AWB a AW _-_ — ---— ____ WBAWL_._._____.__ ______ __ ______._______________ _______._____ ___.__________________________________ __, ____, _ ____ AWU * O0 TRANSFER TO END END OF CONDITIONAL WHENEVER ANS(5) *G.D2 S (BORE- D2 ------— NS()/2 —-------------------------------------- AWB * AW*2e/3.1416*ATAN (SQRT,( (S-BORE/2)1*(S-BORE/2.+D2 1)/S/ S-ANS() ) --------- ------------------------ ------ ------ AWAU * AW - AWB OTHERWISE... — - - - - --- MU-A -AW- - —...._..___._....___._.___. -..______ -._..______._______ _.-__.__ _..._____.___________.____ - AW8 * O. END OF COND ITIONAL END ANS-(1) A(1)*(LO*XX(ZI1') + Ll*XX(oif2) - ANS(2) * Al1) -'ANS(1) ANSZ11) ANS(1 ) + AWB -___AN2__~_L ANJ2-NS( 2 ) + AWU ANS(3) * A(3)*(LO*XX(3,I1) + L1*XX(3,12)) -- ----- — _-_ _ __ — - + AWU_. _ _ _. _ _ _ _ _ _ _ __ _ ~ _ ~ _ _ ~ _ ANS(4) a A(3J -ANS(3) FUNCTION RETURN END OF FUNCTION ------------------------------------------------ --— _-_________.-.-_..________._ —-_. —_. —--------------------------------—'....... - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -------------------— 7 —----------------------------------------------------------- -------------

-226SCOMPILE MADtPRINT OBJECTtPUNCH OBJECT 4ENTHLO1 -— R-T- - ------------------------------------------------------- --------------------------------------- DIMENSION AL(87,ALDIM)tAH(87tALDIM)>X(1O),K(11)>P(11)B(5)} 1RE(12), KK(5) QFACT(5) ERASABLE BII2,I3STR*TAtPROPTY ---------- PROGRAM COMMON ALAH PKt-NC, NHNONN,,J2 KKTW- ---- ------------------------ VECTOR VALUES ALDIM * 2*0,8 ENTRY TO SPRIMEB(1) 1.'/TEMP ----------------------- - - - -------------------------------------------------------—, —----- B(3) ~ TEMP ----- - ---- - — M....... _ _.-_ _ _ — Tg.-P*TEMP- - - ___________________EO__ _ ____P_-E_-____________________-__-___ _______ ____ -____________ —_______-_ TRANSFER TO MATRIX ENTRY TO HPRIME. B(1) " 1. 8(3) ~ TEMP* TE'IP —-- ------------ B { 3 ~'- f:'.R V —. —. —---------------------------------- -----—. —-.... ____________ _ _B____ __ 44__49693TR__TR ~ 1 ____________________ _______ _______________________________________________________ _.WHENEVER TEMPt.GA.,OOep TRANSFER TO HIGHT:T.&,-,,,,,,,,,,, —,_I 29.- 1 1__L-E, - - - - - - -- - - - - -d- __ - - - -- - - - - - - - -- -. - -6 — 4), __1975775200..#(TR*TR*TTR 1_________________________________ _ 841) *2996*(ITR -- 1 — ) - B(2) -' 125000.*(TR*TR -1.-) iBO) * 1.4. ----- T_ --------------------------------------------------------------------------------- --—.-. — — AHT T SR T~ TRTEg/ 1I0.. -- 1OOO..(MATRIX I -.4 PT - TY -* O-'_................ TR.ANSFER TO HIGH LOW THROUGH 5UMBi FOR- 2- Ni.,I2.G.N2 THROUGH SUMA FOR 1.GT S^UA TA * TA + B( 13)*AL( 12 13) SUMS PROPTY * PROPTY + MN12)*TA -POPTT- PROI.TY FUNCTION RETURN 14H THROUGH. ADDA, FOR: I12 = N1.'1. I2.GN2 -------- ^^^^- -— ^^.^- - -__ —-—._ -_ __-_-~~_ —— _ —— _- - -__- - -- - --- - - - - -- - -~- - ~_~ -- - - TA O 0. -'THROUGH ADB". FOR 13.l,* 1*1.13*6. ASMS -,TSA -* TA + B(13)*AtH(12913) AMOA PROPTY. PROPTY + N(I 2)TA PROPTT PROPTY, - FUNCTION RETURN i —---— N —''TEGER I'TIi-~;h —2t-' ------- END OF FUNCTION - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -.C C C C.*....F 7 --

-227SCOMPILE MADPRINT OBJECT# PUNCH OBJECT 4ENTRP01 ------------ -— X- --— TBR — - -^-^^f T6-'INI -~mT^ TyT E- r Ar. ----------------- DIMENSION AL(87,ALDIM) AH(87,ALDIM ) X(10) B(6),K('11)P(11) _ 1RE(12) KK( 5),QFACT(5) SPACE(5) PROGRAM COMMON ALAHP,KRlNCNHNONNRoJ2'REKK~,X.TWQFACT 1 EARATIOBORHO,SPEEDERROR1 ERA__S__ABLE SPACEtBI2 I3,TR',TAPRO PTY VECTOR VALUES ALDIM a 2,0,8 ENTRY TO ENTROP PROPTY a 0O -------------------— _ __ WjEEyE -EOMPG. Sp00..TRANSFERTBIGHT TR * TEMP/298.16 ----------------— t ---------------------------------------------------------------- -------- - ---- -------- B(2) a 298X16*(TR - l.) ____ _3) __,__B_ a 44449.693*(TR*TR - 1>) B(4) * 8835413#6*(TR*TR*TR - 1.) THROUGH BUMB, FOR 12 a NlJlI2.GN2 ------------------------------------------------------- TA * 0O THROUGH BUMA. FOR VALUES OF 13 S 1.2*3.t4,6 BUMA TA a TA + B(.3)*AL(J2,13) lES —-------------------— _ (PN__-P__ -Y —?____ —PRO__PT.Y.+.NI2.)(TA —9 72*ELQOG (NI -2)*PTOTAL/_MOL 1ES') B__ B.-_ ____CON TINE_ __..__ _.., PROPTT * PROPTY FUNCTION RETURN BIGHT TR TEMP/1500e 8(1) * ELOG.(TR) B(2) a OO1500*TR - - B(3) 125000.*T'(TR*TR -1.) 8(6) * 1 THROUGH 8DDA~ FOR 12 * N'lltI2GesN2 WHENEVER N(12) *E. O'iTRANSFER TO BDDA TA a 0O THROUGH BDDOB FOR VALUES OF 13 * 1,2,3~4.6' —----- T —------ ---------- A + Bt3* —--- ---------------------------- --------- BDDB TA ~ TA. +B3)A-I2-3PROPTY a PROPTY + N(I2)*(TA -1.9872*EL06.eN(12)*PTOTAL/MOL lESt) PROPTT * PROPTY FUNCTION RETURN - INTEGER 12.I39N1-.-N2 END OF FUNCTION -----------------------------— ~-~ —-----------------------------------— c-~.c. —-:.

-228$CQM.-PILE... MAD~PRI.NT OBJECT~PUNCH OBJECT 4EQUILO1 EXTERNAL FUNCTION(TEMP) DIMENSION AL(87,ALDIM),AH(87, ALDIM),X ('10) _K( 11) tP(11) MB(7)'l 1RE( 12 )KK(5),QFACT(5),SPACEt5) PROGRAM COMMON ALAHP,KR1,NC,NH,NONN~RJ2,RE~KK~XTWtQFACT 1,EAR~.-.....-..-.-.-.. ^...AT-yo,8BO.RHOtSPEED,.RROR1"-".. VECTOR VALUES ALDIM = 2,0~8 ER.-.-'-RAASABLE-'S-PA"CE';TR";'RTYT' A..... "' ENTRY TO EQUIL* WHE'NEVER TEMP"'ELE: 1500".,FUNCTION RETURN. TR = TEMP./15'00................................._.....'R" -—'T.-..-.-..-.^..-.-..-.-...-.-...^............^.........................................................................................'....................................... B(1) = (ELOG.(TR)+RT-1.)/1~98728(2) = 750.000*( TR+RT'2-.*Ri" -3/19 87 2 B(3) = 375000,o00(TR*.R*tTR+2..*RT-34)/1l 9872 B(7) = (1.-RT)/2980.785 THROUGH LO'OP7~FOR VALUES OF I = 12347'_______ LOOP7' K(4) = K(4)+(AH(69I)+.5*AH(2II)-AH(4,I) )*B(I) __ _ K(4) = EXP.(AH(4 8) (4)) +K..............-.. K (5) = O0 THROUGH LOOP8,FOR VALUES OF I = 12,3,4,7 _____________________ L'OOP'' K.(5) = K(5)+(AH(7?.)+.5*AH(2I)-AH(5oI) )*B(I) K(5) = EXP.(AH(5,8) +K(5)) K'(8) 0.THROUGH LOOP9,FOR VALUES OF I = 1,2,347 __ "LOOP9 Ky8 I)ART.3*T rT iT+AfT r - K(8) = EXP,(AH(8~8) +K(8)) ----------------------------------- ---------------- K(7) = O0 THROUGH LOOP10OFOR VALUES OF I = 1,2,3~4~7 0 —--- L~rUIU —( —Kc-C- 7T- — I-Tl-B —--------- - K(7) EXP.(AH(78) +K(7)) __ _____ K(9) = O. THROUGH LOOP11FOR VALUES OF I = 1,2~3~4~7 LOOP 11 - K(9) K9(9 —--— R-2-"-' —-3' —"-A-a-i1"- IT K(9) = EXP.(AH(9,8) +K(9)) K(2) Os-. —THROUGH LOOP12.,FOR VALUES OF I = 1,2'3,4,7 LOOP12 K(2) = K( 2)+(,*5*AH(2,i-) O" )" B(i" K(2) EXP.(AH(2#8) +K(2)) -- FUNCTION RETURN INTEGER I.. —-------- END OF FUNCTION

-229$COMPILE MAD,PUNCH OBJECTPRINT OBJECT 3AMONTO1 EXTERNAL FUNCTION (TEMP-,VOL,-MOLES,'PHH,N) DIMENSION AL(87,ALDIM),AH(87,ALDIM),X(10),K(11),P(11) 1RE(12)#KK(5) QFACT(5),SPACE(5) PROGRAM COMMON AL,AH,PKRlNC NH,NO,NN,R,JL REKK,X,TWQFACT 1, EA,RAT I O, BO RHO,SPEEDg ERRORi ERASABLE SPA CEI,M,S,DNWRLDMWRLFLQ,F PRI'MLS4,S3,52,Slt L, 1NEXTL FA... ECOR__VALUET__AALD_IM_ = 2,098 ENTRY TO AMOUNT. P(- P!1-).... = 0. - FA = TEMP*R/VOL WHENEVER TEMP.LE.1500q,*TRANSFER TO H20GAS WHENEVER PHHeLEO.*iPHH = 1. NEXTL = PHH J1 = 0 LOOP1 L = NEXTL J1 = J +1 Sl L/K(8) + 1,/K(7) S2 a 4.(1. + L/K(5)) _....S..........3 S. L*L QR LL/K 9)/ K(+8 *FA*NN) __,_8 ____N.. S4 = SQRT.o(S*S1 + 2.*S2*FA*NH)........................................_..:. A __.? i.. __S.iL Sg.,,.,.~!.... S = S3/4. - L/4+/K(9) DNWRL = (L/K(9)/S3 —1,)/4./K(9) DMWRL = -(S2*(1./K(8)-(S1/K(8)+4.*FA*NH/K(5) )/S4)+(S4-S1)*4./ P(2) = L*L P(4) NC*FA/K(4 /L l_. P(6) = P(4)*K(4)/L _~~_._....... —... _,.M_____________ ____ P(8) - L*M/K(8) _P 9) S* SL/K(9) P(10) = L/K(2) P(Z1) = M/K(7) FL = 2.*(P(2) + P(4))+P(5) + P(6)+P(9)+Pf8)+P( 10) - FANO FPRIML = FA*NC*- K(/ 4)/ (L ) +K(4))/(L+K4 ) )+4*L+M*M/K(5)+ M/K(8)+ 1S/K( 9 )+1 L/K(2)+D MWRL*(L/K(82*L*M/K( 5)+DNWRL/K( 9 *L Q = -FL/L/FPRIML WHENEVER.ABS"(Q) *L-.16. NEXTL L*EXP#(Q) OTHERWISE NEXTL = L*EXP.(Q/.ABS.(Q)) ___-__ __ END OF CONDITIONAL WHENEVER *ABS{((NEXTL-L)./L).GERROR1TRANSFER _T LOOP1_ PHH = L' TRANSFER TO LOC2 H20GAS. - -WHENEVER (NC+NH/4')'/N0*LE*5 tTRANsFERfO M-fPUE ——'......... = NO/NC-le. ________ 53 = ( 1 +NH/NC/.7494)/S1-l6 1,s6688 L.. (S3+SQRT.(S3*53+6e6752/S1))/2., P(2) = 0. P(4) = FA*NC/L P(5) = FA — (NO(NC)P+) - ------....-.-....:..P(6.).. =ABS ( FA*NC —P (4+) )__ _____ _ __ P(.?) =,ABS.(FA*NH/2. -P(5)) TRANSFER TO HERR

-230-'SIMPLE P-(2.) -ABS( FA*(N-/2-NC-NH4-)) P(4) = FA*NC _ _ P(5) = FA*NH/2T P(6) = 0O ] — ---- ------- -—` — ~ —-- ------------------ HERR P(8) = 0o _HERR^ —~ - _ —--- - P-C9T j = -0-6 ----- ----- P(10) =0 O P(3) = FA*NN/2. PHH = 1l LOC2 MOLES = 0. THROUGH LOOP2* FOR.-I = 11-I.6,11 —-- N(I) =' P ('I)/ FA _ LOOP2 MOLES = MOLES + N(I) FUNCTION RETURN ---------------------------------------------------- ---- END OF-~FUNCTION sCOMPILE MAD,PUNCH OBJECTsPRINT OBJECT 4FLAME01 -_ —----— ~ —-— X —TU' —— F T TO- T I- -- -TF -T DIMENSION AL(87, ALDIM),AH(87,ALDIM), X(J10),K(11) P('11), 1RE(12),KK('5).,QFACT(5)9LOC(3) VECTOR VALUES' ALDIM; 2*0,8. —------ ----— ^^^^^^^^ ^^^^^^^^^^^^^^ PROGRAM COMMON AL;AH.PPK,R1,-N-tC-,TNhH, NO,NN', R,~ J2,~RE, KKX, ftW-T-FA'CT1 EA,.RATIO BO,RHOSPEEDERROR1lCPF ENTRY TO STU.RBe.........RHE.NEy.V,,AB6S. (X-1 )..GE. -05- __ J 1 --— HERWlSE J = 2' —. —_ —-- ----- -------- X ------------------------------------------ S2 X 9 ~; ___~~~_.N.. D _.... OE_.QF CON DIT I. ONAL: __A. LOCi WHENEVER X,.GE., 105 OTHERWI SE END OF'CONDITIO'NAL. - = F.'f.?...._/E A*iRi. TF_./.E.A. TZ,,,tF._.0.),.-_......T....... ___ ____ AE. Sl*TO/TF BE i BO.T_O/T F_*(1._ -PH! 1* 1~ -S1 ) )' _ —--------- _ _ TQLT J PHLI* lJ l - -------------- ---- ----- ---- ----- ---- ---- LAMDA = (TF.P..67)*(CPF+1.25*R2) WDT = AE*BE*SQRT.(TF)*S1* EXP.(-EA/R1/TF) --- --- -------------— I —---- ----------------- BRAKT = 1+1.25*R2/CPF:,_,,,__,___S~,a =KK*R.AK TRARATIIO*_QRT ( LAMDA*WDT/RHO/ CPF)____ ____ TRANSFER TO LOC(J) LOC 1) WHENEVER RE(I7.),t.E$HELP $ KK(1)'= SPEED/ST KK =' KK(1) ------- ----- — U —-- -- ---------------------- ST. = SPEED!...._______ R R 0_...._ _ END OF CONDITIONAL -F.UNCTION.R-ETURN_ --.~._~_ -._ ---- ------ LOC(2) J = 3 ___....... X = 1.05 Z = ST TRANSFER TO LOCI __________________ LOC(3) X = S2 ST = Z+10.*(X-.95)*(ST-Z) TRANSFER.TO LOC(1) INTEGER' JRE END OF.FUNCTION

APPENDIX J SPECIAL THERMODYNAMIC CONSIDERATIONS ASSOCIATED WITH INTER-RELATED STATE CHANGES OF TWO DISTINCT GASEOUS REGIONS A. Isentropic Change of Volume of Each Region Step 4 of the combustion process involves an isentropic change of volume of each of two gaseous regions. The two regions (burned and unburned) initially occupy a volume V and finally a volume V'. Pressure equilibrium is maintained between the regions. The fraction of the total volume occupied initially by each portion is known. It is desired to find what part of the total volume is occupied by the burned portion after the volume change. The burned gas is presumed to be initially at P, Tb, Vb, and Sb whereas the unburned gas is at P, Tu, Vu, and Su. After the volume change the burned gas is at P', T' V' and S' and the unburned gas at Pi, T', V' b b b u u and S'. Let the ratio of the heat capacity at constant pressure to that at constant volume be k and kb for the two regions at the initial volume and the difference between them ku - kb - In the unburned gas, for this isentropic volume change, V' ku P U) p, and in the burned, V kb P Vb' Equation these ( u = (Vb ub _ (.) VUu (Vb VbV -231

-232or v' V vp &/ku Vt u _ (b) = K Vu Vb Vb Vb where K can.be thought of as a correction factor to account for the differences in the heat capacity ratios. Solving the above expression for Vb and substitution V' = VI + V' b b u V' vb 1 + Vu/Vb * K VI VI The correction factor K can be approximated by assuming that = Vb V Thus the final expression for the volume of the burned portion after the isentropic change of volume is V' Vb- Vu' V,...I (Jl) 1~ + q u), (_)/kU B. Change of Volume with Known Values of Internal Energy and Entropy Step 3 of the combustion process involves the recompression of the system to a specified final volume and internal energy while maintaining the entropy of the unburned portion constant. Pressure equilibrium is maintained between both portions. It is desired to estimate the pressure of the system after this compression. The nb moles of burned gas are presumed to be initially at P, Tb, Vb, and U and have heat capacity C. The n moles of unburned b' b' b Pb u gas are presumed to be initially at P, T, V, and U and have heat capacity. After the change in volume the burned gas has properties P T V' C After the change in volume the burned gas has properties P, Tb V'

-233and U, and the unburned gas properties P, T', VT, and U'. The initial total internal energy is U = Uu + Ub and volume V = Vu + Vb. The final internal energy is U' = U' + Ub and volume is V' = V' + Vb. These four u b u b quantities are known. The change in internal energy of the unburned portion for this isentropic process is U - U = nC T [(-R/Cp - 1 u u u vUu LPt i The change of internal energy in the burned portion is r P IV I U I.- nbn- vb tV T U b nb vb [ b b] = Vb LnbR b Cv P' Ib pt (VI VI) nbCV R Cvb Tb The total change of internal energy for the system is the sum of the changes in each portion and is U - = U - Ub + U Uu P R/C P'V' = nuCv T(p) u - u(C+C) nbTbC + Cv u u Cb b vbR Rearranging r U'-U Cvu r R/P R/Cu Pt = v-U + nbTb + nuTu + - nuTu 1-(?T) ] } Cb Vb Neglecting the bracketted term as being small compared to the other terms the expression for the final pressure becomes:

-234-'' = { nbT + Tnuu } (J-2) V' I CCvbb Neglecting this term amounts to assuming that the entire internal energy decrease occurs in the burned portion.

APPENDIX K CALCULATED DATA The data sets presented are separated into three groups according to whether the flame propagation rate is normal, rapid, or reduced. These are referred to as Data Set A, B, and C respectively. Each set of data presented consists of four pages. The first page describes the current operating conditions of the engine and presents the results of the calculations. The second and third pages present the total system thermodynamic properties and other information as a function of crank angle. The fourth page presents the thermodynamic properties of the burned gas region and other information during the course of the combustion process only as a function of crank angle. The data following are given in the following notation and units: THETA crank angle degrees, 00 BDC T gas temperature, OK P cylinder pressure, atm V volume, liters H enthalpy, cal S entropy, cal/~K U internal energy, cal N moles Q incremental heat transfer, cal QTOT total heat transfer, cal W incremental work, cal WTOT total work, cal "2355

-236HB heat transfer coefficient in burned gas region, cal/cm2-~K (from Equation (5-18) ) FLAME SPEED flame propagation rate, cm/sec (from Equation (4-24) ) FLAME effective flame temperature, ~K TEMPERATURE (calculated in Step 7 of the combustion process) EXTENT OF radius of spherical flame front, cm FLAME (corresponds to R' in Figure 10-a) PROPAGATION ~ MASS-FR. mass fraction burned BURNED VOL.-FR. volume fraction occupied by burned gas BURNED For all the data calculated using the analytical model in Data Sets A, B, and C, the exhaust temperature is 1000~K. During each cycle 0000033 moles of fuel are inducted together with 0.0038 moles of 02 and 0,0143 moles of N2. For the number of increments considered in the calculations about 25 minutes of computer time are required on the IBM 709 for each set of operating conditions.

DATA SET A NORMAL FLAME PROPAGATION RATES -237

-238ii I L'." ("..I,_ —., O ~ ~ ~~E r'-,?,r,. Z -..I IE ".I (" *,..' OI.4.4~~~~~~~~~~~~*: U' *ij- r 1,.-., ".'. 4 J.'.;~ O:,,: D 0 0 Ct ^ D: CAi T 1j)*; C)! C.J *'.: t.'.0 0'IT Z',"'"''..-.1... I mW - _,: *-. WL W, Z:L 0l~ u **4 ~N Z ~;' q: Im!'u' i cL a, a:.1m 6 ai a i a IJ. -'W v:'t. 21I — _iW!L:LLJ W i cr LL.' I*;.CT i C). i L! IH- l L:. W;L I IIJ,.J S: D -J I'' " -. -,,U,.%:.:.::u'i. l'I.! I' ~., I.i I' Z: ~'J*h I:E I, CI = I LLI I uIj; LUIUJ aI — iI: CT ~ a.; * -' rz -'-, aWair _1 Im. %, ~ ~ ~ ~ ~ ~ I.1'..i... Z 1****.1':" I I...._1 LU~~~~~~~~ a aL; =! wi LIlu c If',J zI z T.a L 1= 1...1 Li I I I,, —, a naL i a: o a: o 3 — s: 11:* fjj o~ ~~,% II I I~~~ I.1 I I~~~~~1J'E' W.I- W I;!I W a a 5 I ~. -J.. J hILL] I Mli'. _J cI I':0W WW ~ LLI 1 ~~ l l.._, J (... )'lii 0 Ii IZ:.;U " \t~~~;::;^ __..-., ~ ~~ ~~~ In I W W tLdW,, L... -, -. o,xi 0 00_ i^: o oo, ~J~~~~~~~~~~~~~~~~~~L CZ,:0JZ iLU-i~~~~~~~~~~~~~~~~~~~~~~~~ oWjI r -r LIZJ-:,W. ILi CL I~ ~ ~ ~ ~ ~ ~~:, — o:i' —',~~~~~~~~~~ ~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ W J,,Ic.i - Liii r-II.-H W. LLJ I 1 Iir- Li I L r LJ'" IiZ I r 2 -' r-o C ~W''LU LUr r. I~ ~ ~ ~~~~c,I I-,-..,.-..,. I- UX" ~ ~ ~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~i-i',:-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -2'W =Z.'DU ^.:::'~~~...J'"<~~ I —m~~~~~~~i. -~~!-.-o~~ u ~ -,~ l~" --'~z~~~~~~~.'"' I-';, - Ld^.7.1,LU,'',z,'t L.. U'.l., — r-o/,^C-.C-4 ~'~ 0 J WD zI, z:-j'lo I.. ~,J I _ i H: h- C h-,Cf:z: I r" c —4 r-1- r-o. o c! ^ LU CT -J U-'l0: -Zf i **4" 0 **^!-<f -Ip II!.I b',.',..u c,',...'ja <-:'i ~,="~c4 j., [U.~' ~W.r,,~~~~~~.i I IiW -J LU h-.j I.::; - I Ir I.r ~L'.LJLr~ 0:~LL' 3=:LU~~,.,.u,o!in...... II-, = =.~~I,~ I LU-' Q_... i.- [2., 2;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~L' QL. U _. z'' ='='z:' z a.' l 0' o E LU' > ~ ~ ~ I zI zI z:ri: iL" Li,"'; i. *s LtU l L';LU rJ ~','.'.~,!'.'_", ro 0b~ LU r,:, C i 0 ~l~~~~~~~~~~~~ I I......WL.. h- ^ iM r"- r-'-i o o ~-~ o ^ i~~~~~~~~.~ n p;: LU.'~ LL I r-1'' LjZiL I-^ L W ~ ~~~~~~~~~~~~~~~~~~~~~'-, I',- I W o, -,',L: 0^ 3_-:c' t- (- iLUI - -r I...i, —, I- h~ Z~~~:'"L l i Lii ~:. i..tJ LU W W,Z ~".:, l..L..I-.L 1I 1 a~ ~~~~~~'- _Ji' I. ~ - LU Li. LJ or L- - IL.'- -L.:.- W fcr lW 0 l"-' J I0 Z I LU!. L L - a:. zLzq<H ^"= ^~~~~~~~~ ~ I-. LU o, 0LQh LU LL CQ in-a; o in u oxI L I

-259L~~~~~~~~~~~~ 0 O O 0 0 0:D O's rio 0 0 0 0'r - G, f- -j -0 t I.:- 1-4'.t f. IF W.'r C -r Jr) t r r) a r'I a IC1 I~~fCI I3 I~ I3 5I ID: C3 J ": 9 6t!lC —ia 0D Lr ji —~ r C."lPr) 0 CO LO - G — C3 M.t 1 O ~ ~ li t il t t 7L ~/ ~I I I i - I ~r-~ Ic~ ~1 iJW~IL)0~-I0~ r5JL4JI: J I0~IrI oyo~ s3 ~ b o ~311 obo~l a Ill- ~ crt ~ t if 17 Jr- ~. J l;.fi - 1m 5 rfr.-j,,,;:t~r31 -r~r,.. 5e rrcrlrt u OC7Jr Ccl, J r — r- 00 inr D11-rtCo1- Jr )j —r F-..I r p h,-7.... l~~~~~r-Il ~ ~ ~ ~ ~ ~~I Pu W i.1 C,~ I ibr,;r, i r-n.t r — u-) iiNq u) 1-10 C`'.Io.t. -D C, o r —:r r I —. r —.,- -.4 I.f.f 1 C I u 7 j D 0 r- ) ~f ii: i I III I ii aIIa~-a I~ Jr II II II III I* I I I 00:0 0:0 IJ II~ I~s LJIO U~J 1J LJ3l, J1UJ cI 010 ~J *i 0i r -0 J_ CJ CI 0 GO CJ 40 C i i- 6%. Lr): - f" M r —) CC, r~ ~ ~ ~ ~~~~Cj 4 r r-) 5 a t r — p lr.D.4 O 00:00:01 C — C4 c i')C lr. I l.l col (1r11I1 00:00:0 1... 0) 4 N N~~n~ C4r 11l)vir r r r-4r 144t l 17 C,w.Or-4 l4 U H. /~ "rsiar r — a 1:U lly. I:I~ IZ~- I:~~J r~r IPe rri J r r. I.1 I j ~ ~ ~ I:I' " I ~ ~~'I I II I I I'~ ~ I I. I -'"5 17 Irzi -: IIIUIOiJ'nIvCI ).JK.I.Jr JI.4 J r~5 ~ C~i ~5J:Q ~10 1 r.Co I:0 I 0 a I 0 II I0' ob r c- r-6 cr r C rI I Ir-,..9 o a. r — V) o IO I r —j: i-l l.. 7i op 0:0 0 0:0 0 0 1=1 o V n p 0m.D -2 mk.D r) rt- -.fi 1 - V-. J CO I I m W I..i..I..r~ ~I~. ~~~~~~~~~~~~I I i~~~~~~~~~. I I jc J- r 1.,'..t I-).11 ri4. 4i >- 4 rjri 0 I C1- r14 14 I.0ll IOIl lO Olo910 101 I LI lI J l LLf I P lIlrzl 1 l IU 0 O U If I ~ ~~ ~~~~~~~~~~~~~~~~~~ I I I ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ b.ILIWI *-II' l ~' iIt 145I-.4inI 14-1Ir'., 1LOLII.4inr0nicriINc ~-5i. - II-in10Tji~IIci ~L I' I~T ar- 0' 10 C il o L 0bI0f rib in i-,d Cr~r.- IC obobi 0 -I 0'0 r- C.D co ~ —i 0'l0 0 t;, C.4 IjpIfJ r;IIJ 0 Ic~ C'.1 in) 0rrjI,) -:' jr.f - l ri — r — inCt -7 t- I. I-' O I 0 l;C- C 010 1-CI-0 -.iCI CI. -~ - -li4 IV- C.7 I CvI..C 1 I.0 l ni Ir v 1*)l.4inI- I.. " I.:; sl l I - oa aOr ~I ~.I I I I I i..i.I I... I~~ I I~ I C0:Ol:l:JIOCI C.O:1COC1 0OCO:0IOC0C~llI i- Ij1*jF I fr-lJII..0 0fr.Ir40.Iu0ir C4 ~.0IJC3 i 00L s sI CII Cri 41 f. C~ C1 - - - I r 1 I I. rI IDID J, J Or v I I I I I - -: I- f.7 4I-7-4 -r — t U-P-).I I — t- "' "'.0`.,. c r t) "J' V-) -) LO LC I'F * ~f I- 1 I - I (.. I I I~ I-C"I; ~ C- - c1c"I". - "". - - ic -. a /I; r Li'i C-.. r."9 CT c17". -; ~jI ~ r~ r i ~ ~I I * I I I i I 1 II I I I I~~ ~ If I Ce. C. ~ ~ ~ ~ ~ ~::1 I~' C, ]- C. tr OS L ) j ]70 11 Cr.CoI.ir- r,- u-.-..o Z 1i-rl r- r.-04rLO....r co. l;Nr rLo rr- u-) r-.-II~-r'I.0004 V-4 0x I.- -— CI O 17i0ICOC'- *I -- n Lo In....- * -r 01inric I00I, 0 I-~IIOI CCI r~ r- 11).li 4-in T C -..O Jrfi r-.. I,: n IO.r0 l iC'. LO0 - IC x rO 4 o D r- N or in 4.- 1CC. Cin v)fl Cr4. 4T in C -, c' CH CI CT C I C - C''.I CICCI ik 0 4.r I') -- C14 T'-~ IIi~ 1111111~ II"rr~ Ii-"rr r-01= I -- l0I)r.rCIIlI I,4 I~~'I~I.I4..b ii. ~I I u, 4 - 4uI j.:u JiI 0CII ILIJ4..I.I p4 ~ C- uico I r "J LO P- r1-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.44r- I N Ilr- I r-.) Ir I n LIr-r0.. ilr iI-i. l-4.rI —f I I04.IuIinin JinOCl. iJ ininiliiv-) in I1IJru6nlr-in DI.cI cI -I —OC OC r 04 I,-D -D m -iOI-I.D - L r - (YI~I l 4ClJL.III..IrI.IL -llUT.D I b-rCII -. —,F.0 -D-LrI.i0LIC.iin1.10r. iO0.D c.r D4.-r, jrit.- rp m.0 cour-in -c -- -..-C) CL')LO LI..4 Cr,4 0Il.I W-)ItllIN -Ir-Q-J -- j.1 coI )C1 Il I cl.- o..C-Z c - jrT-r..-, JIO I I-r. 0,6 r- 4C, I OC 1.41.11-4 -J r.j.4 iC.I) rCC!4 i- hl- I- 1-j Co 1- U U iU'4 rl U U) U Ux 1) 4 co Co 4 4 4 III C I II 1 1 l I0J C CII IIl C C.J UI ) C III iL- II in - u)W)UIJUIU) iLO 4- U- iLg!..Dt I174r c I4 -O l9 J -4II,r o p).D - lt r —O I-. i. —. M-lU —It-i.. r —- UI)C) L a~~~ ~~ 41.. IC I~' -)H I; I.I.4t.I-.J.JC.J - mf. e U- -)l-)U) U)U.O U- u- I ) - O l-)h, - l- )V.. r- r- c-lo oq tt. -D C., ",ICN." r.-, v.C c,.- C%.-'7" C-,a'. 0 0 0 F ) -._e I-, Cc C. m r!..oCoxt -. O C- rr laI -, 1.. Ln: o n r- -'o il ),..t - C.4 r r - t 0 O -4co.D -- u-) r- r" U- 0 ". IC" Lrj Q O", - C' r — ico r — -. Lr) im c 4 j r — C C.. ci ~ I i i. —.4 re) Vj, Co L- r-e). a o r a -dt e I.r'.~.. I i i f I 1 1 I I I -C 1,0'1 -It'lzj -fr t t-:1~"~-rY3 Lf)~Ls~~ I05322-r sj ICO L J Pr 0 U1 N C - r. r It f).D -'" 0 Nr k I ~O 0 zr r- p,t IN 00LO C ISrC f" c Q U71 5? 1.0 O T) O U-) LO LO LT2 I'- i LO LO. cs C Lb,-)f r3 r3 r''~.r 5~~~~~~f I~~~f- ~~5 ~ t'5- I~~~~,i-1 r — r~~~~~5 Ir~~ ~~j Ii'S rg4r> c a - ~ r — O P, i'- cc. r-.4 rf- 7. jr -~- -/C4 cf C.". e' a a -- I — Y.-lm~~~~~lor~~l'-Lor~ ~ ~~C'-' N - i, ) r- COC. —cc n -k C4 c U- 111 r- C,-~.q re -o 11 -4 -) -t fj -:i:~-r- c c o OOj Ir

-24or — r ~- U)r — r-'.-2 - - r rx-: - il- 4.' r' - r ".) r —. 4 U-C r-' cc 4 o - O r o C,.*; r —;u~ *n'o * g*;3. TIO i*~ f" ) o:c-4 LIr ~- T"- r-'',6 r — **:t- c4 c ix r"- **~i 4-t — rOC- C O r- -t;c-.4 o T7.r- U-.j r"' -0* r —.4 i r-4 C 1o C D cr- — c —. o-. co- o- co)'oc CC, 0 of o r-'' r- 4 Ci.7' - -...r ~ r T, —'2 r — Co;0; Cr C 0 CC ) 0 Q ~ ~ ~ ~ ~ ~ C 2-, ~- -4N *ab - N ~- ***' *'2n ~ 2'7-' i 2'~ ic ~"'2''2''2' 2' " 2 7' c'2 u) 2' in'2 r.4 O.-n m no t..s3 O I.-o-%t- r..- i7 \<f U r/N *~ D r" r""*i 7~- IT'. ON 17.0 LO LO r) r)." ir" 1711 C) )o t O-:~ co -, o co - o * **co 6 r — ir- rc-4.3. *^ f LO~ or-Dc ID r- co i"b M7- r-'- c^. PQ- r" r- 7'. u") 1:- - r" ) -r Q)fc o'r; rer4.o \ -t- ooo r"" i^r cooI r- - ~ *'t 10 **~' ~ ~ ~~~~r- -O,03) r7e,0 -!c4 -4 C a4 ))-o r-.-. Loi ir —.0 r,-:f ** \-t) -ty. ~ -**D * m't I U. OT ^r- C U IT- " Fp" *r — - *r - 6.5 y ~i~-r-. o r~ C *"" *i~~ P ~ T co c -!T~ ^-4 I - r- pj- rt>" r — **XI C.** ~*4;* OCl - " 7. -*3'O0 i?-*''10 h)* 0 C~ 0 0 W U~~~~~~~i ~ ~ u (,%4 Ur' U. **t0 O C.3 N'.1' C i r C lO *-\ i'r~1 "- O;-*t D 0 u-i~~~~~~~~~~~~~~~~~r i- - ^ of~ o~ roI'~ r<-. riin u -. cr- K-e" 1% —T-' r"" co <?*' c'ti:o ot p *'t r-' -t ic -o cl r1 --...- r." 7-*~ r-: ^- co t * r ^ 17t!- it t - D o'.t I- o7'. (?t co I'r —.) -.o cjI 3 I * o~~~~~~~~~ in 1r- LO c^N Oi' I 0r' rZ"* o L- uiro -. o!" o * -N o-,-.in - r"- c V-1 Io U —., Lo 1.. - )~~~~~~' l"I.'ujj C' II *U-.) r4" 4-' I — r" * ID ~ ) N u, *! cN. u-) CO C- **s rZ Tc!-,*j L U'"'lt0 T.k -k:ri *t LO 0- f" C - *If-:** 0- iCO * rl 3 U": ONi* CO co*" r-<- D iC r- CO ~.- o [r -t' 03!-J3.4 o** O o r-. In c%- co i 7-. 03, vno r"" r-,i rnin ii7' q coc-.4* 1 -~1 7 o < r~ 7~io n r **3y.<74c c,'In U- ) 1co 1 c- O 0 * )r.. %.t *^ o Is' = i33 -- re..O - r.i in~ ~j r r- r")?*""* r-. r)r-. x".i-inr- >r'- a- un.- -4. U^ - ri** i4.n c i' r b, c!c'4r *d c n 4 r" - K D o U- 3 L —C~o -4.t r. —~. onU: r-.-rmtu")iTIntco.4. r'*.-'- c —r - c-,- I C, O I. T " "' lm x % I cr.1tUj -r-r r- -D n L rq 4 e r-.:i r-': **: t s!-%-r4!"* U-) Aiin U-) nU-) U-) b *~ -..3 {'.6.'3 *3.o **~>!.J3 *1j3!'.j3'*'- r"~ F "':o fr) *.j3 **d rr- Ir'U) i 1-t COcre)'...O N r- r- U C) OCO'L Irej rx 4 l-t r-'-4''4'T- "714'.4 C'. -4'0 p r —~ rD C ) r-.4) r r- kC t-4 rUlk' k **) n'r'' * r) Ir-..j). rjrJ..) r I.*.n r.r.-.c 0 0 - 0. i,''.l r U-) F T 0 *'. r-' 33t AU 0 U03 U.' C-4 04 q.t kU.' r-'. 0U' Un ohv' Ur k.,: C'-4 xt. b*sf.- u*-:i *r.3 F-o C co r-,"~' K)~ c-i54 ico P. ~' lr- ^** r"- V)n <''3 r.'.4C'C *.J3 _n 4 0 CO, r'-*.4 3 U"' mt. 4',C- i000 0 A'.. 74PC4GC. J 0 p *<1" r-0 I404N 11 C4 -. v^ - 6 — I- - V~ v^ — v- V- I, -- q ^-! I I1 -I % **j LO *O LO ID. n I i u -) Iu'n n in u") u-n u-n I 0 0 0 C 0 3 I 0 fp O j 0p 0 0 O -O I0 0 ~**4 N4 CN ~* C-4 rM%*4 N 04C l. *4 0 ~*4!c'r-4' C**4 4 C *4 IC. —4 CN 04 iC. —4 4 C**4 C**4 I*4 C-4 4c-4 r'*A^ O 0 C O O 0 3 00 0 b0p00p0p0 0 ci 0 b0 IN: 0 U-) r-s ON 7- {cs4 CIN ac' (p 0 *< CO r-e) <t C {4 -t- re). N.0 * *t- r"-,-, ai ON' }'0, as 03 *'r i - 0o. " r — t.- C4rr — C".. ir)~ U') P L[* c-U4rO I -' r-o 0 - IN rji ~:o n L.' - I 0- 02' o )'- cO}TCf Loi U")In - c co o A c". ir-,- - o V1'2'*' l-' r- r" -% L'co 0 C3 Co oD to ~* 4 UM. o o co r Fr)- 04 Ir-ocr 4oL. co Nq. - 4 iu 0) c,- 4o N (F')4 r*si3 D r"- iJ'> <?* }CO'7'' ^-D 3, U r C'e-4I'"33' CZ i03 C'-4 "t F' t U'4 r- O lC-4*<t t r —-q C, LN Ol.4.. -.u! I=- r —3 U-) *o Ly rnn \ 1rco *.r t n' *Irco- C l~C! co! r n r o-d 0 -q r-.-. *v un ^ r"- (33- a, IF> 0 k-r- (***4'N r-"j P r^r ^ i-*t -t *<vrt- INk V'3 O ~- T'.,- T-~22'C)Ci. T 0h~ 21 n'2T' p~ T'rC IN FN~N *4 C'4 ~'N i<'F''.4 ~''r iN C kc' 4C')4 C rO L I ~~~~~~~~~~~~I I AI I II I I I I I I I;I I III I I I I C —4 b in ^ C-4l^- o i- <- — 4 r-"i [1*1-4 Ic-j *- r^..iN:o - k4 V~r-o r —t [.: o ~Y- 3r 17 o- r. 0 O r 3 - 4 I r- a. I-.O - t r - 0. ) I, OF- O UC) N'N C-4 -4 V. I-4 5O4 ---,'.Ul)C4 N c r — C' re) C- " CT I" f- r [ — r- rr-:o r ***'in I * It o 6. -4 * Coo 1 *o ON Ul'*. ON r't c -4 17. I II j o rcu 4 ~N c-.4 0<3r r"" ^- 4 FN ci —4n 6- W-'~ ~ ^ t r.joc i.3i o r' Fr -N co I4M J'.'' r"-|cr.'I -I-co -; i cr-, ~~-t cui.' i'r' u. p r N in r c-'4 k o ~- 7-~ ^T O ~- n o eo^ -if ro -co "-r-" 11. c-4 }s4r-u: o Co" Kr 4 wr-*j - cr' c) - - ) Lo FO: M. o - 1 L -JK4 "'c' 4t'r- I No-%j kJll c-j**.o o r- v)-t "'Fo inU-) co v)'.J**..~! }k Co I I 1 o (% r-o. __.^. r.,~T r j 6 ^. 1. ^ r. -.- - P. p-.- Fr A' i I I-.1 I,1 [I I1I!l I [II 1-i;1'I*t I- I 03I -t- ~7. M- in -D c- 4o in- N 10 LO co *:~^ Ir-*l. r- *~-t- - aro 17~," - Cr'4CO 4J *.''~ p-'*, 3'-*3.-*-.- ~ O I'" — -- 1I4 FCU'.. F D' Cr. %'~. l'-ul.i.-_ U), W' F r.... - - UI,. PO U)C' v.1CO k..- U t C *. 4 r-:tU~r- m ~* ^ r'3 C) *-0 N *"fr C o C~ r N r'31 i " II I_-0 T CO -4 ir-) r-,-^.j- * 0o b'"O F')(4..''T-C'''R4 -4 r~i-F-k -.*.Dir "'~.' "- Uj*t'U. ^ - U'di1010Ui3 tnt t' ^0' 210T-p c^ -o r- i.^ *^ o b o r< 0 %r. Ir - C." c.o~r (3 C4**0 LO cl ^ <-.~ r-" r-) P9 t fc 1U — t oL uNr r-IJC-JL.L.biLt...i ru'L o ^'3.' r- L'r''Lo'r"-'r u' L -d V- Lo b ~7F'-. kF'^"CO.r' 4 ***'-4 ) F-07'. CO W ^-r — ^J3C4')F t -..U Lt ir~ V-. r't r-i -d. UI*t - CU. JIr — Co co r- rI - Lr3 Um " r — ^~otf ro*"p U3y*io -coc-4 co b'* "- -t Li a II Ia a a a a I a. a IIa I 1(- U'3 *j3'' r 4' 4 |- *<- 4-. (4.^ *23 4-CO 4 0 " UF') r''' 7'.' {r.'."'T.j r4 I c —' C —4t r- **. 3 r'. 0 I' * * r i * * ~ i. * I U;* i * t.. ~ ( * ip* * li — i m7 r-_ r,-, c r-. 03 tri — ~ r> -3 _ 0 0 C- D -1 rn r l-11I ~ or, o 03 r", -% m UI Ir-,~N r-

-241-.jo ~ " ~ ~1:1 r3 ~ ~ ~- C~s i — ~~ — r- i) t r, )'-4 if C., C0 0 I -- 0 r 53 C1 r3' ~3-1'' ~M15 I It _ -.,' _c r- - r- C': ~' 0 0) CO'C' 4 C;' 010O r") r~ - 0i~ Z 0i tc - C p.1 KD VI' 0t U C' r- CC' CC' r- O r- CO CT) C'4 *t t t r C C. 0 ~~I Ii~O ~I K~cl F':r lI, " IsI. N,. N i% ~~ / l I I I ~ ii rn, i I~~~~~~a _j,I — Li. t3~ ~ ~ ~~ I~ I II~ 2 3 IC) C CC'O c P -~I':'' H'I' * I-' q Li' i.'%4 IO Lf'i r ".tu e j', L~O:T -4-,':o ta-%.- t- ~ r~- c.-C -1. ~~-y13 ri3 -' r- 3 lf C I I i= 3 r-IoC-J3 )i:'C' 41 (' 4 a a 53 a ~~r a i=3 a ~~ a i=4 a 11=4 a a M Na a a 0 N,. a a v M M I I ('4 ~-' ~ ~~ -t'~' -w'C N 1' l'' i j ~- N) id) N)e ~I 0~ G~ I41- V O CO~ o Ni r CL'3fOI~ c.-lC'I0'-4.- F-~ 41 —~ 1 —a-U' JNrr —: fl')C'l -41-I~r'-i-'I5i.' -a -I 11r OF-C —I~~) ~S ~f~5 ~ ~ c41-N) On-41- — r —-COF —— r —I, —----- NIJ).lcr. c i.-; CI -a r-Ci.iII'iU. irx-a -flb')Ir>o n'I't'NFrIU')U')-T -,-O *~r ** *:~ *I. **:C F* * 1 ~ 1.1'C'ifr- F- U - (i IIJ i T-4 r. T- T 0..4 r 0 ~i. - 1 ia-. ia-c ('-4 r('4 ('4! ('-4 (- JN (' 4 i'4 (' - U)Ii- — h- - )0 CO C -I O (-4 r U't'''' O' r' rf -:' j C.-O t 0 co~4 1-L' In- F- n'1-''*fl p 0 ) 141 - r- N)r% CT, Lf ) -- F-* r,4 0;Y 0- r,' 0r 0) 6 r a-) a- -'4 i-'6 "4 P4NlrF'i'-1-L( r f l O'-F CO (C''%:I -' 0 0 6- N - 1' IN CN54- U-: U.'. vf -fl r- Lr'C - WI'A 8 it I R it a a 0 o 1 z':' 0 Ic' I I 0:'~ L.J Ii L. 010 0 N 0, 1t 0 "'. 0 0 0.10r 0 Lo L 0 r0 IT I:C I- I r 9ifC " T i a I c, r r I r Ic, I *- O I I~ ~~~~~~~" IG i~~ IC I'r ~ I I I 111 I's -r 1 I1 - "J -- t 6) u i r- kb r- - O r — f - t r- D I - I- r- Io I I I I0 a I I a a I a a I aI aI I I I ~ I ~ II~ Ir I- I. - ~ ( ~ 7 U')COCO) N) r- CU I U) lCF Ll') iLO L' N U CTl - N ) 0-r'rC' ('4'1- iNL N) *~1 - k. - IN~jF —'C' N)'1"'fi I —' - r- rl Ll').'C;'-' r- U' N)x ) ) - II"Q r- " U;'V)LO 10 P-. v- u-.i — O o.C. %. 1D - 1,':~.o % C 1 1 -"I Q i biD $. O!.0 % I) Is*fj i~C O k f Q) F F' P.$ J,.4 X. 1 *.I*- ** *U I';1.'-4 Il ).- Ll — F ll-: C (I"'-T- Ur i 1' T" 1 1: -a;N U w H-NI Ir CT'-1-':0 9 L. IK- -:- 41-N 1f` C i I - r ii It 1i rp,, i*Ii. Jill C 3 I' I. I'', i I~. I 11 11 I I. ~.. I I I( I I I.~ I I i i ] N) Ll') ri)'-fPT'i L'' -D'-r I- U~o a- ) N) ('4U-fi - N)'.i.O N IL ('4 - CT -fl'Z' r —' -U) CT- U' - 0 p" (' r- C' A h-fl'N O., 4 ~0'fi -a) 0 I'- f')- C;Il'-'-4 II' 4 4 1- Ii InCO 1'N1 Ij- -')-fl r — I-'fi IF1 F Ifl l' ) C3; iCO c~~~~~~~~~~~I i 1 -a-~fl('4't CT'- ti~'.r~l-4 —4i-,r — k1J-a i-T gF- 4C -iJFVC - IN'Ii)Ifl(.04U - 041-.i )~4n4-Ifli-4h)4i-'.fC I= ii-a-'4-41- cr —Ct. 4 -"i rt rSF N r-() C-41iI- xt -Lliii-4I. Lr 1Nj! -J-i)' — i jj iO('L 71 )t I4 co r' -J1- r p,' co ci lci) I:,, C1:1 I.7 I ID O - - -I"N ~, IC-4,r4 -4r:0 1 4P. II 9 I T- CD It U- - I I -- -- I I I v P 171CI C), cI i I ID C, c) O 10;I C D0 fP o C CI ICD'. C, 1-:5 I= I C O I-OOL a NI N, a. a ~I a I a a n v a I a M a Is a Ia I I a a... a a a a I~r *~I I~ I~ B C ~~~~ -'.. i~ 41- tCi i"iT..JU'Csl'iC "'4'i-a I"~ Qe3 rO g-. N.M I.:u- * *I * *. I. *-. * *- * I. I I I a r- ~ ~T N'"'-" -U'CC I S I Ij *. I -.. - I a r — Ii, -4 in --'4r'4 k"' N i Ni Ni a-a-tri-~'4p-4i'4I f t'I -aNI'-iit'"tFU~' ~L'.i'Ll h~j"Uii"i'' t, ~ i- F-arfl% " I- lo r-I III -in- -44). =.C In- - 04 1-D II;"''T~'4 i- I - L I I -a. ~.t'4L4 4 (4 L I4 4 4 IN r4_-;t" 4i ('4 4) i 4 h'' 4 I4 U., O II.,:I F' I,, I O I ~~C-0Ci "'4U' C-)-Li-Li-k 4 ei li i'i'ith t'i'''4-' ib-hi'.O D —. i~r- T-t CIDiU.t av- rx-ip FI- " -'-a) f-" C-. f."-4 -a -k - ca — a'-.rc c,- -% -' CN K K- "" 4' t44 ")'4'U 14 - CCI %.,:I F-4 Lrf."-4 N IIN -~- us- r-e: — d- -t U-jlo o 6 -%i4 -.%- i r6 - iT 1~~~~~~~~~.1 ~~~~~~~~~~.-1 l- re -- 1C?.4r r, - C 1=1 61J1,I.t (%-4 17:0 T- C -,- CC lr r- ci rt:i ccIIj OC t~: O O U- j F-,:-lr; r- i r - - CO r- tc- 0 10 0 Ic. c - 0 c C- c- C- o C:- 16 O o C, 1=1 0.0 C l 1C., C, 0 C, 3Li-S 117 C, C C) r,-j n ii.%-4 ire.. xt P-7- I c~I~~t - K r S IN xt O O -r c1hl:J r rc~ U J t f =' i 4lt,:L 1 I a1-CS r C I (%G- G I

-242".!:i I I':..i';I'i:::'::i I - -.3 1 p I I. I,Jd':::;.-,I i':: "i:4 -1:;:;.':;;:'";' 0;': r'J3 i;:':'i 0 2"" C la")'.::1"* I-r' (:;:':, i C:' iI: ** I'- ".'CO i! L - 33 I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~I''1i I I(:''~I i'- I.i'. i Ii, I i L.. o':.i..: I' I l -. ii I.. CJ C-1 O -Y I(:D L.. i fa:1:3~~~~~~~~~~~~~~~~~~~~ II >,;5,.J -"~ 3K; HU F::::i U ZI r i;:! LL 14?.: E: *~*: UJ ~iL....iJ I z,:I i l::::, i. iI-..LJ Lt L O i I: 1: D:I ii... I — i::!::J i: l. L I..r l II I-~~~1;- I. Ip -IJ f I: F I i C'F- I L I.': L C 1.1 r:JL L Ui.. Ii..]: i -'3I,' Iij L -" I.i i: C[ 1 l::i-" i z1. P. _ i I! —l'F- LI - r'o -[Z: Z: 2?Z' I r.1I I 333 ii LI i..3 L II -. —113I13.I3J 333 II i:-,. L.UI.":: fLU i-f U.J z:: z:!i',':..':~'' l',z a_ I... - I. i —:s.... -,:",.,: LU';i::: o:......:...;. r 0;.::::: It t. S..... ~-,.... I':!:'J Q,....." jjj l~4 1-i;-"(.... ~-1. ~.! i I:: ) L icr-..nI ~H,. h"i'." i^ " I I o " 1nL.j. ~ -- i:!: 10 I::::f IS L L: I 11"t I I'[ u'- z' I f,U in. LU,a, z:'~: c" a:~-; j-" c:!:;:' * -'-' CK: i~u c=, a:iaj i,,uij u-") ffl in- ii; i~j in c:. *x'!*::

-243-.............. I k Q —'I.'.I V.,?.t t- I- U. L -L j IC-)! 1) I:,-" CIC',I I" I I... II1 1 j if i ic- I — i lC if c 1I I i i- 4,Vi ".' L 1 1 4-4 iI t, 1 r r r { --,T 441::I II,....?1 i Li Li") U-) l4 L) LiJ.-. Li J II..4U C ":.,'...r-..C",ir 4rc inr-rll: C"rl.il.4 —- I.4........4 G' -,.11rl 4-'-U...-j-f2~4r — r'i r- C-)Ij4'tl.~ 4'.' 4 I'i11'I f-;.- 4- 44..4$ IIII(:::II C'ttl -4 C -' —' 1' 4t IE~l 4 414 4f I i LI 4I"''..I I'4 IU4.. I" I:~~~I I"r i. rI f -- I ). 1: I I... if I I I II 1:o I~~s tl~ i~:I -r —~ II1~I ~~- 11-;~1 G~ l:~;11111111 iII:IiII:I II ~ H ilJciiiiii IlIllsl II'~~ II LL LJ1 L JLJ~ICJ''-IU: ~: I.j I;: ~~j 1"" I'T" O" 1".-.1 — I..i: -: f. C-,.1 —i N 9 LI-) D %-,:J f)I - f'' K A 0'r- 17- I.4 I.-s ~ r-ri irv i I. ~l.~:. iU I r., I. r — ~i;.~ U-J r,,: r- r.i..O rr.:.'I C _- ~X I~.I V`4 cc P- U:l 1- k'Y. I. t 1-1:0 I.,'O.U")L I1'...I.J.I:I-.4-'iI I'~ <11111111~fr- ]i:!Ir ~ ~ I1 IN I' I I I I 4 i..". C-A I:,-I r - C;.. I I -..t I.. I -.t I- U-.- $..O4 — IlJ41 -..1.I.1l 11,:1, i~:I ias!Cj C~l!IS CS )L71 Cj 1 A)U' 1.t I LO r — 1.17.1 V. 1 I i 444,J-'-t.4 i k 1 1` I 4f44"114"I4.14i~~~f14114,1LII4II4I4144141I4IIIII4I1Li1 -.4f —~~~~~~~1-i'.-$ liii,, 4-414 I — t %l"I;t iIt.17t J1[ it'.1i It. I ~ ~~~~~ - 14-1-4 —i ~~~~~~~~~~~~~~~~~~.41-il.I F.,.~ I i..t4 1114- iiru-iijl..ir...-Il-i rq CI C - I'- I CII I _! T -.:::::1...... f 1 —..1 11,1 r- r I:3 ll::::- I -rr l... a:%t c cl:::1 1,::II-'.r 7 4-, 4 414 41 I- i -..I" ~i7..~~~I41,iLCIIL.,i1I'....II~~~~~~~~~~~~iII.,4.'..'I-4 i,71 I.:.-Ij.. 1414.-1 QN),,4i4-4..I-.9 ~ -.9 Q,f4,4 —'I 4-J Li-") -'J —4-~~:T i'.I,4'lii i144-1i34414.1" i-i, 4g14~~44 4L.L,44.4IC 1'4L 14 4jb),I.iIi.LL4 — Li''- -'::::I % -14- ri4l"1-I-L4-I.. UI..I-411 —.i-.I114,.4l.. - 4.l4. 1I. -.l..i. —." —IL44 -4-Ff P,. I-L. Li- I -I.J 1, t f:::i rJ 1:::11, 1 ~S 1.5 i c~ L II 4 1,'.IrTI)4-4~'Lu4 JJ44; im::iiii li..i 1711 Iii ii1. L IrUI.. FO7 9l$.f H:3'11. - Is -I.rC'.- 14- Cr:3 I.j-' 4U 4 4q h+ r..i r r - 4 I U",.. l% NI IJ. I I. -.; l - r,- TI, -D o lo O C. IC::.:1 11~.-. tIr I'~. o liD i:: II-::I I.- -1 1 -1 I(:*i C:~~ ID f;L — l - I a:- Z 1 —l C - C'......... )~~D IiI_-' - -I C ~1~I 1.~~11:~ o - 1 f i" rr"o II: c.l -I ii'~1 ir'-J D ic ~j:5 ~r ~1 I? ~~~ Ir::7~1 C;~l 11:;~~ 1 (:7~) ~~~~~.~ 1 (7 —: _ I- f —J IzI I O C.:) 1: f-", IIZI C I (Z.,I 1,I I I I IC ID -:I [-.I I -In - 1.... ~ ~ - II:I I I [:,:::I.::I I:- C....) D.... z! O 0'. - I - O. 1 t 7 -y:: r- Ir~J r —1~- r31F- b"5 i r~S r, tC'S r~~~~~~~~~~~~~~~~~5 CI C;~~~~!r — 13 (r~~~~~S ~~r?- c-! 4 IS4 f'-. 1ii P. % 1 b" ~I''IPt: - e ( I I I LI- bJ ii-i 35!.s~~~~~~~~l-jilr~~~~~l r~~~~r~~ fia ~~J- I~~~~~~~~ i~~i i~~~~~~..s ~~-!- iii I:~~J:.1.111~1! ~r~~~~~~~~~~~~~~~~~~~~~ k 5LI LI"~~J N I- - r fS 75 C. ~I ~I E.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~I.II r~~~~~.:111:~ti I:.~~~~~~~~~~~~~~~~~~~~~~~~~~~JIC~~~~~~~~~j 1:'~~I 1~- c ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-4I.-4 - i'-4- I -417 1. r,4ONI.. IAINI rr h. L, (. -i' - f: I..:-I. -c i C...I Ir.- 1' I, ~ ~ ~ ~ ~ ~ ~ ~ ~`Q KO-0K U —~Cf' 0C-4 i-j 0 -.7f IIr0!D I U L.:, -- IL 1:1- Lf-I I-P, I f,. I'-J j,, r —i i P-') IC 1 "j I- F" I- ib I~~t..... V- rq.! P r,.. El i I I r ii~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~JJ- LO Y CT- I I,"I -1 111 I fUn U-E I r ir' ( -q N... JB L t P I -1 U-1 V:, U-) U") Li-, I VI VI U-, I I-' a3 U", U-) Li-:' 11i'-' U-) U L1 A I r, C t. Ct. Ix -C' r- I %- EJrC CC, r -t e-4 r- r ~~ r,-d. JID C.,., El C t;- O (1e Pei?;I ~ fl i~~~~ r —t.'~c~!U I-. k. O 1~L: r — C,~ I,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~c'I ift U7.4 %l cc co' CCII:E I 17l'- t7 fS' -E, V Co f 5~ i iS IicLi il cc-~s~ C,.s5 - CO 1:5 fs c Li Ar..'.: I IC' - ~ l r 11 l IF -17,........ L~ c~~~~~~~~~~~~~~~~~~~~~~~~U N C' A C, -1 Cc.%4 t C 3'1 elf 1~~5 ~ Fs3 13, r~i " rT~s r~&C ~ ~~.J ~f ~ tT) 53 k, oP~~I ~- r~:12:5~' ri (kt U 0 %4 LO r — C' 4 U., C-,. Ln IIA -4 07%4 - % 11) -1- 1: -4 P. 1 C r,.. 1=. i,-. 1-4 I.1I-,. (. 1,,F.- -. - lo c or- r- r (% p F I- Ico 1- Li!la111 it i, C~J~~~~~~~~~~~~~~~~~~~~~:I~~~~~~~ 1.:llr~~~~~~~~~~~~~~~~~7!Z br U)tr,- C,-'(- Q U I.4 ~ i, ci~ r -4 cl 4 -J L. Q U.J 1. f.I- L U 4C - C., F'. C. t D, 11'JC.51 -J- 51r~1, J... 3 rl: c,: ~~ ~- D-J rs 1 I B T-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~I- -[-C,`, 1-r CI1.. D Y -.tI-: - -. o C( o O b-.4F 9 V.1i oK.' TQ J ( F "4C.N 1% - -, Ju:.z -: r C. %j1- k -prB.

-244~. i ") r- ~) 7 - ^.n 1 ~C-4 ("4A C('4 F-. b [ 0 I C:-.l' I(: i-; r: 4I -,O., ":":,:.':.r *i".1 r,- -,1a:::a, ":1 " = r-:,,:', -..1... r l.,r o 1:::,::- i." 0 Dp 0 M 0p 0 DiJp OiO 0C.*;*Ci0{:; iC ) CD,:' C. 0i:ip C I.''.4:'.. (,.-........ I'.........................,.-.: T.. j.. IC..; -,r1:?:":,:.:: r"- rr":', r-:: r_':,,' " "1 r' -'. r-.:,'"',: ", i": Ci: ~ {,""' 1:::::, I ~~~~~~~~~~I, a. 1 al-a-a a ala,':i r".-..-. i: —4..::.....'1"-'"" -: 1,:'*a..Ii C.O.:,'",r.[. ~,,"a..a 0:1.a..:r..j'i.......!-o i"1 - r " -.1 -!or 4ra *r:, r-r".. l a", r - 4- -- - ara'. I!'.' a- r.. I.. r"' a:..-: 1.:. "4 -..',::i- 1:: "'' a.: * ". a'.'.:;.'r.'.. 1 r- -4 ":, =' e:,'',,:'.- I"'..:, Lf':t, 1,; C.'.T C,.'( iji {r"." o r — It,-co':., r.'.,i,-:'> ci*r.". i.-: ir-*::i:.1 it.::, =: Ir":i.t': "'!0'., r.. -,- r'. - 1.::1m 1j:1:i....*c ra-.-.,::......:.oi... r-.-:1 Ic,-:a -.'. 1.-'::,:, "'.1,:,:....- -.,- ia a dw rTt II-4 4O U|., Li":il ii ~ oi "l- r "":' r,., 1.'...:i-. pl:::, L:':.,. lt.j:[; 0 I I —-O O O p o =ci C i = p cD Io Ci o I I,:o., ":'::1; O ~ 0:: i: O ":1:' " 1:''" " -::: i' " II: ~. c C I'D C 0. C" I~~~~~~~~~~~~I — a.,. " 1....'..... I I~~~~~~~~~~~~~~~~~~~~~~~~'DI_ l17 C0 0 a 0 a a 0 0 0 0 al IC)a I aCaDt l a _t a C' al a) aD! a. 1 ED IC D0 a D1 a a D a CDa a c,': I,".. ",,c",..... Io aatata.ataa..a t..aaa.aa t a t.'..aa a IOa,-:,.: c, ".C: 0 0 Ca I, I, a 0 a" 0 a " C a0 a C. a D Ia CD Ca 0 a a c-~~ ~~~~...... C 5 c ".; 0-'I liO1 C:: C)'-I.....ID-.D C...)D.............. C`.' CD CD 0Ip 0p C:ID D E I: i 0` J ~ C ~ C: D C::: I*: CD iC: D!~::i;~ )~ Db IQD IL"' " IT LI"B" f l-" " " 1O " " 0 b 0., C C)I I D I I D C: }bIaaalta ta a I ao 4 r-a.41 c Ir-6 %. a. 4 r-, o - -4o'44' L 0-. {*.~~ **~~"c ui f' lf: 1 f'" ifn":.'.:' iN':i' U1' 0.~ IL"'I r"~'"J in *:.tco!1c -4 r —-4 C-1 4 o c-41''.'., r",.it.,':1. co.. _e ty" ^ |,,.....' j.4 I.L'.: r If." ["~''i ") *D I,-:; 0 -i ~~~~~~~~~~~~~~~~~~~~~~~~I'..:l""'- O:'_.1- Ic- r...!.:ir-:f. r": n.,:...,,:::. —I,:",>,- o',:,,:o.:cicl;. c->,.":, r.-, "":'. c;-::.-.'.- -::''=' ~Z.'~~~~~~~~~~~~~-4'.O.1,.7', I =I,,a, I c | Ir - CO. r-t l —la ar".P Lja| la.."", ~-) (.. 0,4 r- P-lr.." ali..al l T a | arf t a:4 0 C) C) C.0.D 0 - bD 0:i0 p 0 0 T10**.-I- CD C::i CD O C 1:: I:':.- ^tattaaaa t7a 4 ^ p 7, l^ lal t...- l T-.... CI'.ST.- ITa.. a.- iT -.. Tt - J..a; C r-4 a': 4''.:-4-. 4 i',. —"'a ":4. -,:.4 4 4 4 4 - 4, v:, -4.`'. It' 1: 4 C-'. 4:Ar 4 -4 a -4a -4 II, -'r4:.4 C r': -.-,:'.4 C',. l-4:C4.,-.4,:. r al a: 1.."-4,'.4 a- ""'' "a-'.1 4 I 4- l CD I*.;. *..: a:a4 **{ a1:11 4r..i..1aa* aI 4 i. C-alla 4 a:-4l.`4a a Aa.t. a CA 0!i:a 4 aa Al.! 1 - Cr a4 ral -lt l 4 aa l'-. 1 I a it-CDc-4'".. ~ ~ ~ ll'all r i o 4: i- at~ that tat i i.. a r o ia — at i.. aj4rn.* o: ": i O t. r"'C I.:-....'Ia -.a. II'....O:'a- a — - - i -a 41 r" a o a a: oa a" a p at. a a0 t' aa a a a-.-:, -- r:..:. — 4 r.a a:i a,: a r — a.4 a.4a:p:4' 4 "' t":' 4: a: - 4 "-.4 -'4 ra.' I:.4 a.: a 4a:' 44 4 a 4- 4 a: 4 a 4 4 r at a I' U_. lh _. I l -.-1 -.1I - 1 - - - N T- T~ - T T- r — II I I I I /i-. I I t r. I ti I,t. r ro r-coa I C t r.-. N ".% aa.ri..ieaa.al.a a,, a',:. - r1:, =,1,:,,=,,,, o,: i,:, *o"'"::' U L~'::::1 1:= o C`.,. —' " r,-"..,'::, -,':" T4. EI" ",, "1:,,."", "" 1'":'" " "'4 I'T:)'::: r:,,:=. 1 I 1::' t=' c:,:1 -.11 1111111 a a:,' " I.a-.a-: - 1 "c.j1 a rit a.pl ":'; I"' a"-4aa ti'L' aa... IO i'4 - II. —...........D'a i - ~~~~~~~~~~~~~~~~~~~!'"I-I a -1 — ai~~.'b'a."a",~ aa.tt'4a'lI'"":1':'.a- ~"a~'."a'11-'1""'1;., aaJIi,':1 I.-aa.:1iII:: "1b1',a'.)I'::!'"' Ii.':1I.1I:!'1:.,?..1!::1 4^-= [aq I -r iF Ia. t a aat.'a. aI..' I a..I: t. -1u' 4l ai i, i -- I' o l: I'aTaaT.Ca Va'4,% t. - 1' 1 Ji- I, taa b a, ri.a.- I a.- t I1 a I — t.0 0 C)':,%4 I),-1ILi i.. a a a ra. fa- -4. 4 a 4 La a L- a 4 a c- a' - - r- a' a aT'' La " a l o,- a n: - LaU: a a Lai a ao aat bap.. co.4 - o.... raaa a-a Iar ra*. -t a oar )*a4 ta...I — r:-%4 U ab:i a, -D 1 II aaa ha r'a1(-: h at an ar at- ar a. ^ra F-'-'1 c r-'':1 F D 1'.^ a'.a "a a a* l.4 a-''a bn a a n b D a a ta LO a.a a':. a: aa a Li Fa.4 Ia- a....'1' a C'-4 CO r"a'.~*a * a n a ct i a -4 a &t a -o a7't: a. 4 I. a. a. tat a C at aa. r.:4:' l a: pa a ti p. a a a L U Ico~' t=1- or- Ij.: 1 I 1t = ~.::>'r 11 al'"1.11"::'i"1 I1"" I'""1 -~i 1"'" 1 ""1 11: 41:1 I.n:1.1: I: 1,::,::,,:o,::::,,,:::':,,:::, — T:, o,:: a'i"a...I a"= a_-. a =: a 1'-a I", a i "" a ": a I:j I: a 1 = a" a,= a =: I,:: a"!: a::a' aI:=:a:t aa a I:::a::a I..: a:=:a,":1,::1 a' "':' a:= a:' a 1: I:a Ln uaa a' La' t.1:1 a at a J- r r":::i.::... r<::o o h:',I'1a. i - 4 c 1rrr- 4 h o- a. cF'o.'' o:: o- Lf PQt' l 1 0 CD, ~'::,^ 0| 0 0 Qb O D*DC 0{0 0CD0 i,,!-~ DC~ ~ ]~~~~~~~~~~~~~~~ 0 p 0 0:: DO I:: DlOODCDpiDp0:i0p0 I o I" noS no noi''oi ii ic: u'c n0i no i c-4 r-(''*' r-? ** |r- ~~In *11 ) r- - l'i*l^ 1 **'* {r'' p'*~ c-4':4 r:)f-:i *:- -1In n*I:1I I:t { C-4 {[**4 C-4 i: — C-.jIN C4 S-4 C-4 -4 C- r-4 C —4 T-4 -4':-4'**:i -'") r-:i r —) r-.-) r-'-i r-':i r-i r~ r-: r —: *~:i r-':i r-:i i~-:

ii. I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.... C I I I I I~~ ~ ~ ~ ~ I ". 4 r'I. 1 I ( I4I I r I I.I....................1: I C D: I I I i I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~:-lII..'.- I 4 4 Li I Li *- *- 1.4'.~~~~~~~~ 4 r *i I i Li I *~~~~~*........ I I 4 r *~~~~~~ C i i i Ii 1 I I'-: i i 4.,-.- 7 ir r is"' I L Ci k* *) ri * 4 II. LI IjI,: rI) _ "4 LI) k: r 1j"I A~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Lii j I, Ij i I:-! F)I:: I: 111111 I " i. i "',i L Ji iiL I: -D::I c:::' I I LU * * i * * I * I ~ ~ ~ ~~~~~~~~~~~~~~~~~~~~~~:::I 11Ii-I ILILI* "4L" I III II-'I I l~iIIII1 111111 I IIIIIII~iI.IO.:" F1I1F11..11: ci.oI III1U IIILi ~ I'I'Ii II~iII 11 11 Ij I..'I I I 4, II 11.iI' Ii. IiI.. ii.4 I I'I 1. ll I. i. 4 I I i i. ii L.. I Iii, I I I I I IrIII I Ii II ". r- I.4 I I:' II I I iI i F. ": I. ii iiI i i i II I LiI 4 I I Il I I Ii I I Iii 1 I I I I I I 4 c- I: 111 If..I. -.- 1,. 1 I -"'I II V I 14114 L~~~i i i I i i"i~iaia aa"I.* If * -..IIII J I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ I~~~~~~~~~~~~~~~~~~~ I:"-4 Li") 1: L I L CO I I *1 I I p- r,-j r,, 1 U".) -t1!:1: r. i- Li")1.4r 4.4 411"I 04 I"') F- —::I" C; lu":i r-.- I~~~~~~~~~~~~~~~~~~~t 1:,..4 I% —- 1:::::I ~ I- i a.a %*. - I i") i") h "I II-_ ill.."I I I I I *1;.!: *-.!::I.14,1 I,..9 l " fo.1~~ C-4 Ili IIN I' A I`-j )"..I C..1.1 I J I J A -.3 I"-.J ~ ~ ~ ~ ~ ~ ~ I U.1 f'4 C-D r-,- —.- -1 1:1'- Li1' I I1j::)-.1)1, II1 r,:i i,, I" -- Li a r"a, IO 1 111 r.4 1 %t U-.4 1.3-.1li l r —4 Il — F.i 1' f.:; C. I I 4 Ii'.:: a.4 r.. i 4 i' F- I I 4,4 tII 3 3 i It-4 1. rI I I -i' I I c L) "i::),. 41 I.J I.4 ~. I I - I Ia 4' II I I I 4 1jI I I I I I l "; li il 4 v. III I- 4 IL.- a CD C CO LI") Li") -::I- 11CCI 1::;"l 1:I Ir::::1 -I- n — -I-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~. ~iiiFa~l~~h 7 a.a Li I'' I ~ III ha.4.3 lhhaaali.4a.4-baF-I.,.-.-h41ra 4.4..44L"I L.l1:Ihri K.lhla~ "A:.Il. —0:'-.,4 O:, I rDa %T 1 3 lb a La,. ra ~~~~~~~~~~~.a I ~ ~ ~. i...F..... 1..... q, ly......... 1 Il~.. ~...r.... ~. r~~.a~ia1'aa~~al...-p.r....F.. hi... ar i il I.~aI~1 1.4 ~~~~~~~~~~~~~.. I I~~~~~~~~~~~~~~~~ 1.4~ ~~~~~~~C 1 3,.4O) —.-C: y'I' 44 411 i "441L1 11 3 CD, C L~r,~I rr1, "ia4I1.. (" U: L!6 —' -) liii 6I [~i.L....- 11..... 4..Ii hb iI.i..4..iiI.. i.t4i * "I l 1 * 1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.....

-246Ij I-'- I C',:~~~~~~~~~~~~~~~'.41'. U.J I_ o c,,. r,~ i I i I, i - - I-'. C.,'If I I I I It ZE, I 11-I I i.e.II I I L I ~~~~~~~~~~~~~~~~~~~~i' I I IIx C),~: w CLI C I I.." I I I LLJI W Ct',D- t I _' "I',"' I. -... I I 01 CL''!.-I,. I7-. I-'~ i,'""'l: z:,ei I,:, a I=W I >i'J I I a a "aIa. I 0 a! in 1W~~~~~~~~~~~~,...Id c, lo,..r, o Ii-' I- I I W i -J I I c=~iI' 1 -J II II VI I 0 I 0:DI I E U~~~~~~~~~~~~~~~~~~~~~~~I I. I L.III -J -J~ ~~~h':a o -- I LU I I I I' I I1 IIIIIC, 7-1 U). INi I ~... Lu 11~~~~~~~~~~ Z.... I t"****j la~ *I I..~j I'.. IWI aL ai I 2[' II ~, " ",:LJl,-< rll ^n-J 2 2:,'X r-r-i- UJ:Ej ID~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~- (..) ~C*~- al a xa C COI W I VI~~~~~~~~ II I I I I a. 4 cn ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~II IIi in *I oL i~~~~~~~~~~~~L. IO i I I II X I - I 11~~~~~~~~~~~~~~~~~~~~~~ I, I1 1c - i - 3 i a I -J.0 i" I' 1 II — - I,.".,},',",[ IS:., r-,I 0:, 4,",,,::..-"' II::o wI a -j,,Lri I a ~.. F: 17.. 0'41, -.,:, I LU' V rIZ I I**"~ I I I I al miI m. ~ ~~~~~ ~~~~~~~~~~~~~~~~~~I. VI I I I* *I InI I -. 2-JJ' I- Ic Ijj I lIZ:1. ct o a' 1II, I WI; C o rW I * I I I C I I I I FEI II gL I I LU!~~~~~~~~~~~~Z U 2:: Z WIi. i C I ICLU i a a I L' L *W 2 I I. II i 2a U. "I u- o a i~a, Li IWI 4I " ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~I. W I-'. CIl -J CI I L i.; ~Z 3:! 2: O!IZI I I 0.1' I-;~~~~~~~~~~ IJ IOI 10 I1"i'ZIjZI! coltij 11- aI! I- Ir:e *- r- wim rinl 2 I M=I~j: r~ i cx zi' u.. ti- o r 4J iW.W LJ.Ja'I...JII..I I n 1cr- Ic I:. i' r-f i —I r —'J E l I ll::i *! o 2i o oao, r'-":oCM wMr 0Q LL a I" LU 0 I I r"4 -oe*:i ~ - c1cc li.J~~~~~~~~~~~~~~~~ HLH&E ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~I {2,, IJJI o ~ ~~~~~~~ I ix < *I i i I-o I G,I I o n.....I.'I'' ~,,, I I,-..-I::~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~I I-~,'. 2I -.. r * I - i I I I I In I~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~ I lll - I IQ I 0 I.r1 UJ Q IZ'c~ siJ7' 2; 0 LLL~I U ~.l,~a!.* * o r J UJ 0' Q I-"1 2. W IA i., WI1-.I2r:0Z:a 2 r: Is I U.' HU 0 1 1 i I.. 0. ILI W I I- " I 2i Uji ** i'' 0 0'"'0 "'-"{' ~L I I. II I H"i.'... 2I;LL ~ - Io! r — I- I"': 2I.J I L LI.u LL I: — o cin J < W Il I-: LL. I I~ I 3 I: -J 0O rim IJ I- LU IL S-J W J I I u o IL - aLI I o In I I 2H I-i acti nO tril WI Wi IU" It I 5 W WLU 2 LLU 0 ~-< &:*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ju I I:C. ch CLWO ^)|CL CCk:'t I UJ UJ EI 2 2: 0'OH'0.J 0 OUJI I I I I I

-247-,:,, ~ o i o o o oo o o m o,:, c c....!' 4 nr..:,i,o. n,.:,,r- *^l!''r- *:-7-!~r-" o c'*3 7!mr-jnc-4r'i~ co 01Co cz., C. 0 C. o: C. o: 0 rn I=. _,:_,c-io o Q( oo ID-c:', oi o',,:..-, o (..4 Li.: cn r...::..4 o', -., u-n c..4 r, — r- %-,..""- <.n'.;..I-'.-.0 r,:, lo r-. A'|.i"-, r — (, 0 0 i-D 0 l r —. (D I 0 0 0 O IO CI o 0 oo 4, rQ,,-,-,,i-4..iri r-'., r.';, r -I-.,' r —:' r<(r'. U -.-,.ir r r r — "'',,'c -'. r- r r'- 4 O, —,,,-, ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~ 4 ~4 ~;., ir,T',i C'4r'4')1 44N ~r4'-'', )r,;', c4 C, ro-, -i o 0o':4.,,-, o ID 0C, -, C o o oo... r —,-.,',j-,j.', - -,'4,- o.. o,...'j- Cr o ooo o-.10 oi oro~~~~~~~~~~~~~~~~~~~~~~. 1C.... -r- j 0.4 S,:,4"'' l 0 E -0. C,:,:'4 E t C -. r. - E 4- C.4. r r., - -r!r,:- r- r,') Jr'. r" I o,'C'''1:.- Crr,-j w" ) r, - r" ) r-qCO rtC!'j rC 0 -rjo o 1=1 0ii D, o cD44-'C in -C)'1'.,3iC C4- CC o.)-o tiOn t 4 r- r'-,i''o, i "- C, -' 3 -,4 j o 0 CR,, " " C. C,: I C C) O - Or-, r' -.OIor 44144411'-1r411't'trr'~~~~ ~ ~:,,:.)l> -.4:',,=:d,-,,,-, o'I',-',,-".,,:.',=o.,',:,'i, -,, o oi r.c oi,4..,l....n o 4,'..'.,ro-14~-yIr'tCC,4 "-~i'"".~~~~~~~~~~~~~~,I....:..........I... t4o 1*l''t*ii~ 4. i4 oir01121C)'.^-Cr'~4'r'" to'4co r"-'ii4'" i'' - ct,4 -!7- t — 4' r-'':ic'-I4 if 4l.[l**4',co *'-lo c'4'*4'r -,or-r'-4->-I o - **'-T —l -41 "4'''t4 - r-l'-r"ir c o;~- o C44C -\v Q ) o u- o o C C-' 413 I.74' _. 1 " V:"^ o, -- c —4 *tri'. i C4-4' "I CI r'".1. r' — - j- r -".'-C'o 44 4 -. co j I' —' C —4I' r- C', r -.41 I "I r-"c p. Lb'' CI'- - 4~jo-'1 CO't P- - 44') 044! i I 4-''"'4't'1 L4.'"'4 IIII I I Ii I I i~ ~ ~~~I i 4 i i'4 i i s: " i'!, cc-, *~*' c^ — 4 r- *t1' I- r -- Cq"i w.'o- ii~1 c r "" 1 r'- 6 -4!C". r-'" c r-"!- 1n C —.C c, D* ** -~.i~.'i~'! --- r**+**. *<t\' 4 1 *\' r -r-' r-o: ^*"^lc* c-r 4! - L-0 c r -**st4lc' rI- r'O U?*' i l-.t I r"-c'i "t 0c O 4 lr'- n'''I;t'l-". r".1, 4.- ID C),' O CiC) I Cq C ). _ I —41 rI -i r'C-.4i r-"'Lt r4-j'j4-4 I *-H<fOr C'1"4 *^{*t** l'~4 4*<") I'.rC 4]*+ d " ) 4-*'! ) )JC" ) *<.j *'jt ri'". 4 -. i r"'~ 4 C)r Cr'.44 "4 ~-C - I " |C-. 1.1 4:,Ti...' 4":i''I'*> I"*!'. *- 4.4 r"-!o c,l4 o r "-!o 1 o co co —.~ *4-!co.4, 7' H'!'.' r','C-'r'.1I4" C'_-,.44 64 I'-i-t I'l C'. 4-11114Cr'o41- 4- rt. ti o c4441"> C o r' 41, r"l r*.C"4 — 4 o 1r..o 1- c rti"'"-. c'C I 4-" i ".I 4r-" ~l-4'C)4". r -4 C)'0C r-1,40 I Cq r*) 4:"' CO CO r-".4 T C'''-ir C%4I U - C "' l t C r14" -Cr14: 4 -: c-4jb" b c*...41C4 (.)'4r- C' r — CC'"C r -4 —CO C'4r I 1-1. **C;!u;,**4-'s~i o~i'.a i~iio U"!1'.''"!.) C o **4-! CA u" I Lr I.D r~.i o o r4'i **ii' i r vi - c,, -'4cor r-!o 4c O4 r4'4 C"-'Tt'Cr. rC i r —u. c i'.4 r"-i — Cr',f 41". c'o 414r-o C,0 OCc r1 0 -( (, **4 C. CO10"C *cr -4J-CO re)UlC r4C<) r"i ** l1 **O 0 i T T~TJ..i-4. *4~*4C04!1b'|COr *< O~^ fj0 l il 0- r'- 0 0 -4-'-t C U ir-~. x; V. -Ir...-k 4-: -..t r,, m 1 r.-I 4'4 C C Ln 4 — C) Ci C) C)i" 4-" C)i' " *r J'"cI. I I I 4 4..4 Itj n i r* k 4IN -4 -" I - \'\.I i i" I't l'-..' r. 41.,.41,,.-r 411 - -r.'I.' 4Cr c- -4c.-4 r-o r r * r c4 o o o o' i "-) i' -'IC) o)ICo o 1 - C) o-Ir o o o o d'D i"'**Io"r- * o r-.l*rr'.-'!'*r"*li *-r" ^ ro *"i.ir'c'- * c C)-1: *- c r'4o'.01-Cr ct-4 ] [!.-! 1 1 r- rl i!. i. 4.4 4 c4 C'j'4">44 C>4[r4 C") *- 40 C(.' co I 0 tj...C-4. f"- C r,'f r C.-4 C 0 I 17.,: r,, r""c,... 0 *! "'"";' ":"'i? "':" "".....-'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~4 "' o ~':o o'~ooOIoo oQo ooo 4-'-<':* *._,,,-, -,,:...o*i- o -o 4- r -, -' o i o'oiooo oo o'i: o o o.: C., o r,:,:.:; T*......c4' I-^ rninc-4 r-o o *.:I c —. r-oir-4 ococo*- I c. -.';'j~ ~ ~ ~ ~ ~ ~~~rU U tr 44'44- C"'i'C' -14"144 1 C'4- 4 CO. r,: C,;4',4'-4C C- t)' " r- N.',U \ Cr' 4.. 0'.1. -1'. I C % r-4.orlSI4 4.4l4.., r-'4 41"' I o 4 o441. 4.. r~4.4 1.444.44o') c 4^1- 1- 47') r I _ 0 k-4 ^ r.-o r,r-. ^.i. c,4: ^ co" I ":' co','F',q,~:. U C,',, —.,,-P U'',',-,,;1,.',1',. C)C'4.:,:.".r r"'.OD r, )..o,- 4 r-,r --:- in n', 1`17- UlV,.- C... o 4 C -0i,' I... U:' I -.. _ J,.~j'^. ~-, ^,, j~.i -'. I - r- - r - -- -- i-, l C I C C4 I, - r..4 4'' o 0[0 0 00 o0C OCp 0 0 00 I ) 0 0 I 0 0 IOI 0 0 I O 0 O I I I I ~ ~~~~~~~~~~~~~~~ II 14)40!0.0r4- 4-i 41D\,.".t-\-t'.41. 44441 41-I'. 41-4"'^-co cos ii')'!- C) Cr' -l-o<f'-Cr' c' 4r'". "01Cr' -I^r-' 4-.T "4~ o~-I *4t1 -."'1- "-4-*<1~r) r'IC - r-'-Ico 41')I' coI 4- 4'oICO 4-''CrH- C lt) 41.. i-) C) 41')C o..iC 41') -.4. Cr or 01 41'";- 41"'),CQ Cr'C 41') 4 —r4-'CI4- 4, coi 44i C r'-? COIC)0 r)'4- - C o,' c o I Cr' 41' co)'Cr 4n- "/i 4c'41 *') r C)."4l> 14)41' 4n i -- "0 C'r.4 — ^-I~ 4.',4 4.-I..,'- r, -,:0'.*J' 41on ("li-.cr..'4',4,-o''.,4 r-C C...:, — c r' "c rj- t.-,Cr' C),:Co *sc o jo r" 4 ( j'.4~.cr'.4j'i-1C' r — 0'4 4 f'' *- Cr' Cr414- f ncI.4 " - oin',r- r — C -).,'r i Cr'V 1- C r; C'4 I T'"CI 0 0,4" " 1- In CrIr C1" 4"'.4 C-.4 4") C) 4 — 01C' 414 C'- Cr' c-44 "1 -14- 41")I -'4 co'. m' mOC Cr'.'- c'.C,4" 4''4 C)'. ",'>4C- (41CrP (" V )" 4 4'.C'".I4") C'~~~~~4'"". C', ~-j.4'-41 44 —C. 4C'.".,C OCICI:I4 -.-1''.C'.C 41-.,1''1 -'l'".:'-I."CJ'C oO 41)'r — W) ) J''I I 0 C 0 C 1 is.;cr I *.I'Ii I cI o.c140 <''''4 OH CI' I CIOCICCI''F-.4, -'44.4-'::O.,0:.o " -'.,'., ~.. -- co! rC"4-.4 4'".o4,:0 oc, r'.r L',Pr.'.,4 C" 4 1-4- "-4'..co 4" c41'Cr I rn - q q. 1 q- 0 In O 0 0 I'D C) 4 1)' 4:1' -[''- %_0 Co |-1> IIli- rl) r l'Ir O -- O.'4 C") ")'' 14 — ~'C' r 0 0.4") I 41'O 03 41i,41 ilIo 1- 0 441 1 1 i".'o oi 4 C1' 0L "0 CO 03 CO_ r' r14''C 4 I" " C0 C 4r0' r- 40 4 —.DIC.lit ~~,lr. 0' - 47C!) 0- 1') - 03''-C 4"4 C.4,'"' ) "n "1 4' "C 4" 0 CO C Cr4 I I',;.I:,,-,.,rCrr,-.',,C" T4'C' 4.. 4 C Cr'.r" 03C) *""' > r:'",C)'' —-I' — -'-'-,-,', -r-:.D r- C'-4,r1 4 I 4 4. I 7'-'-'-:' -'-'-I" I!! i I I r..,'!'. I j C. 031 7} o''- -r', o,- C IS r'',...,) I, O3 I'% C I C., O O o r4C"."- -.ii'7 c -— I —- -" 4 444-1 — *- -4- Cn f"4 —.o,%-,4'". o —'-,'4'- (..'.,- r'-. ri:,' CO O.'' - 44 T-r Ci"4-l'"".j3'-i r'4'CO'T-I' 4C. "0'.4."'- 444c-ir- - 1') 2^ O~ig: 0 o 4 —4 CO-: r "tICC3 C CC- 4 — C 1C4C 104C')-' 4C I i'-oijo. "0 ".o 4n " -. *.,4 0'3-40 C, 0 c^ csjc^ CIO., tzr. T.. p T -I i ID C 1r- 4 r r=ii r MII -D C c * *sr r"'-'1~oLI ~~!o y? *^ 03! Q iT-lr- c^ "- Q!'^i I o'-. o co in!'-<i- ^ic'-!. -<i- <?*u':'!'^-**j~i~r —~-ii- r4 01' )I4 — cr4 )"0 4r4 "4 mi4*.o Cr' C "4 -.'"""ir'? CO 1'"l":' in Cr"i'Cr 4"":.'4 —'1 —! o'1-,,'- o IC'".'1-I' 41" r-'C)I'4' — 4 C".' C.,r o i-4 c',4 CO r- r-o I 414,'-")!^ coir. o i41144,4 r -~,)i *< ~C'i i 41') 4... 14.,.4,:.'..., 4-.-..r,'1.-, I,: (,4' "~i'" n Cr414'" I 3 r-'-14 CO 4 - 01 c -.'4 co. r-'-1'Cr 4' o r- I *>4'>41'>4r- ('-I:.r"T-) Ci'O c'C1-'4,Cr" 41'' 4'1-~4i~'- 4CII <4''- C^")1uIli i'4ji ~in- 4."'-ni'nn''1[in,("I'4141' 4nii crni'in 414141 4'".ni' Cr.Iny3s' " "- r-[o'C ) 4'CInco. 4")~ oo'4I4 I U,) D41" o{ 43o4 — r'i -!''3' (t L'o' -,: r 4' " o, C',4 *"! o: r- r"4. "n-,41,) 41r4 - C',.0 4.,.1'..-, c —=,:-,-I 4- 4- 4 —.,:,', r-, c'.r,,-0 41).-,:"" r4~ "cr" C I v U OiO~ u-):'" ** o cf- Oj-<t 0 iJ-N C~IO- Lr'' r -i p: u, Lr * r-O **t vil C-.4 CCr'' jo COC 0i 0 Oj7 Cjr-'l~ -' TJcoi Co L')4|C;- — 4**j xti-j-d ~ r, mt 74L r r —,3 rijij0 *4 ren p~ — r-1 1 r- e r-,!^ J L0 U)! 0.c'l(\ r 0. r-N li r — I CO C3rO C,%'y re l -). 0 x ol0 m r-o ^ i -. C 0-4 * Q I *~ CO 4 J - k r-lr r 7 —! C — 4|r3r) o r-oC-l c1l7) 4 01C,; C D [*!*~ U') v r-3 O - (7 4-.Doc Lr. U~f.,.; xt r,-,)q I., c C. U ".I...'>, 4-,0 4 }.,. -,. -,, 1.-41C'4 04'"44.44r''ir'i.".3r1)*..".*f * *til" n n b^11 l~ b~l" i n ****t''l4*4{., <J - r-j-'I' I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ "4,,, "1I" ~4'".,," ('4- 4'". 4.41,:''4 4.44-'4.''4-'441 1,.''I 4. 4'11 41''~ 1 4111'411''1 4~41l"-,4I4 41,~ 01r"04.'4-r —4-IC-CIIC" C.0.-14 I I 1! I~~~~~~ I I y 4 0 1'3 rl("4'-4'". 4,' -4 r' cr (3 c -".' o r' 4'1-C)'-'4-IC"rWi?'-* 4)4 -1 i M.. C('j1-n''coI r- rr*:?' Cr 1 COIjr3 rr 4- C' 0' 14 i Co C wn[- CO Co Co c 4 (r * Co O \o O C o o,: r-c Cis. r- D,,_ %D I U. O-, cc I* co C"'. r o d. U- ) f4 Pr 1. in 0,, o, r-,4 IJ' D.,r). Cr" 014:' 4:t4i1'fi-iu "4 4 1r-, co,'4. 4u"~ co 04-') - 4.iC. r —co "4.o C'" 04 r-o)'4., L I'y' r- 4 c',- 104r'' i-j " 4' 41,.:'-'' r 414 o 03.DIr r- C") H.,' -',41,4-'Cr "3I- n 4r I r- o I-'Cr. r rjc'4'-1414 4:4"- 4:14-'~ ~ ~ ~ ~ ~ ~~~~~~~,~....'C 1 I.,..I,,:.11 * oio, co - -,'.4 C., c, C I C)'-1444'r V)r-'-1 4-' 41'-, 0',. CO c4.'"- 01 o4 e4: ("4 "4'4' 0 0 4 — C4'. xt')1co 410 4 —'.(4' -'1Cr" C4:U-) ix.4 C")~'-1- I l- I'- m r71c'1-4 IC) 4 Cr 4- 4- r"r-" P,- oI O o oo O 4 -- 4 4'- -- - O -4 O 1-4. C) 4 — r-I c, — -,. r,,- -jo..0:. C: rc.,r' r oc-oc; o - r —C. in, 4 - 0 1i JI, r"1.-',':' C"R"... ~ "*I"....N mto-Ir-," o, rJo" l C _,' C'..4 r — o~ —.'4' oF - o,,,o bII.,:, C I 1 I I Q'. E,;:.. I..'': "". 441-414'I - IJ'-2 N1:,,4 ("4,1 0:,,:(:, r-., Un-.j,, r-4- u,:.....'.-1.'-nC-,6, r l41 —-.,!4-Irr'0'.C rOD-.'.o-1'1'-,'- 4-i 4"'- C ) r — II4C'.'- 4 G I Cr ("''-) "0 L I r ijj o~o iooo ~oooo ooojo*<"^ i'!~-c^-^-ysoo<* 7-i-!-,c54 o3roo oJ,:, nin r j3.:, ooc'-,3.3coi ~~'4!1 310 o6., mi IN 4 14 cf. C, 4 Co l4"'-0 I N qC"-.) 1 Co>4''Iu' 4 — C ui Cro4','-j" 4: C., rnI'C 4-C"CO C ))I0 910 01' -1 4 LI),' 41') 41' Cr44' 4 — LC C C 4-4-4-,- - In n 4, 4 ")'4 L'4: C'04 C' 3 4 ")o o: 1'i ~- 4'1 4 1') o oC:o Co c C:o 1Co CIO CO- CC CCOC-O ccC,:'o - C:: -- U-1." U -": I' ~ i...' 1' ID C)- -r'itV 771W C ~C) C)IC)0 0 I I ". C ~ rIC 9 CI O 0f~''>DC CI-'I'4C "C4 InJD'> 41i) CO,4- CO C IO In44-4-0 1') 40 C I'Cr14"-'4- 4 —'4- COICO,',41,4.~~~~~~~~~-)j, I-, I._0' —I- -j(('4 ("41" ('44''4(.:'4 (";1''4l") r- o.C.)rI r~, x,,.- - "4 MI C I I = I 4 -'- -o- - 41t oo,,) o',:' r — cc-I I- Pro It oo-' —1 I. 1,, I I,0 o' i,o o o o, M,- C, oXo o, o IIf — v NOD01 CO Pr,' 0 6'. ('4-G- - 7 J% 0 P't, 1c',.D r,'"!O,:0 Ir — -0 1.1 %D I'I:'t -D,r?'cLocr (,~;,'.. D r, r- ol o lot ol; u o, u o r c o: l, m u o,:0',D 10 r-c.- -.1 eo (' ('t U) r-O cr c,4re,r, 6.,Jr - DIr -c o or-r -r-P-D L n 4ir —' ('.1'.'c, Io OI0 0. l0 C 0 1 CN'IV DI0 LiC) 1a,21 o: g,-'1 o i o-) o o,,j i' C., re oU)Q r 0 rl-lm % -, t.r.- Lp r IDr-'D%.:...,....I...;'.- "'.i."' Fc,,.:.: ~~~~~~~~~~~~~~~~~~~~1 t oNI (4' D O r, C4!o oiooL D -c,,, m':!co,,. 3 I I - 21 r I (~~~~~',-J(4 ie, J I', I I I I I I I I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ — "'QI(J JIJ "

-248tI r,7,) N DI I) I -1C -.,, r.1 -:,.I - -,I-0 f'4 0 n: co r14 0 co, =,I co -l':** cci 6-. r.co1.'T — U) I —C4 CAl3' - -': OIC r..!j.r~ -c, r —' it F C4 (C4i 0- C:'::'' C."'rx. a' c r.- r, - r- r — r-: r- r- r- r I I I~~ ~~ ~~ ~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ I I.-4 cIC4C..'C ".)0 C I I I~~~~~~~~~~~~~~~~~ 41v 6'.j- i.) co or- c" r-ah cv' achr- a r-') ai r-c t. rj-1 a ". Lu. co ).'..i.'1' Lo L-) I 1'- iti1' -31cc'. cc ~ c.' r-) co c., r-; Z" cun r- ci *..c o r-' mt Ci' I kCc u-C - c.iIL fx-.) -.6%Is W * Ic cc 11'i- 1 rw.i )'.A- PI cc ci! CID C L r- - c ce'C 0c (1 I rj,I LI- M4r- ~~' ~~I I v ml 0~~~~I'.. cliv a r- LI":' C'~ cc'~,- ci'.i" ccii o c _ c re) c i. c. %D C Fi',41-1'4I 1"t Xi "I t - I N)o -) u 1 I cc, cc C. Ci. C:' Ca' — 17% CA rCII'>-4 CNI'N4 rw- re) re) re) re) I r) r,-r e) tw r I I —- %-I I- - V I W r I — V W- — IT T IV- W I r ti rej a.D':-.~ "lc". r',r:i v. i..1 re'::-I "~,,' r o..b c,,-' ccl cc. ci.rI':'- c I i c Tutu 1 a.,%;4 re) cc: T': - - ar;* t r- F" 4 LI.hLI")'..D r re~r, C: e)'e.)r-.- I _ U.-:, c-.41, 0 co 0 F-.: r f -I LI":6 U- C F-'> -IU')- i Ixu. ccit L'iI I' Li "I c' ~:. N'I- c cc' c " I. ~ Ii" F- I- 4 - CO C I I Ii r- r- r-:01s En relF LI)'- FF'r, re' F 0 rj -U'L" re' ci. rct:'. U- LIh re) tq r_- of r_ VI I U )~~~~~~~~~~~~~~~~~~ a II i I 1JI'' co Foll CJ Ii, I r'~"~. LI ICl 11 ~ l -t - - I Io t.- r- -0 U,) r,- -."'a a,ta.1t u.-r" i,: LI"'-.~.''.ji' -r-a' D' I.,i u,.1- r-F 4 i o coLI") ON C r" I T 0 1-IL'L tr,)! r'o'.)ICO 0.4 *1" *j I.-"O''LI_"' r- I.7.:a"itI. - I I I~a U-LI.' 0% ol~ C'' LI U ti''''I) r. u' L.,I~''.- r, 65 i LI) -16 n I ZtIL~' 1-; LI) u-LI) &,DI'%-I' U' r —: ol. 1- uo -, — I-.)Lv-d i'4 r-i CA r -P U-LIa) co -,I- wvD c lc0 I v- I L r- r-col C CC CO ON! a- C. —I C., I" I=11= O vr o ONr- — ri rcr "I C I''r' C"o c-4r j: DC I U- ) i C I'i V''' I-' LI'C I'itL'AI L)L"'I v'.1U- - ci I'L I LI In I LI'L' I L LI LI' IS'I. C LI' LI' i LIT) LI"" I" LI) I i 4- C'l'. 4'ClILO a'''4 CaD'il''4''''''l''4., A O f111.'4 Vi' I'liii %t.'4 I 4 I *i* *71 Nt -i'-'**I"''*' - - 1. 1 1 C* * *IgCD I4.. - -1C 1r r- "I. %'I re i-. I.4 I* I.I. I ":Ii. LfI I I I~~~~~~~~~~~~~~~~~~~~~~~~~ IIc,1 c)I a c loc I- c CIC1I CC" I DI CD'-c i.On QF0F)Oa' LI a C" C" 4 F a ml c a. t j 1 "vL 1 -I~i a-~'11 V L") co r- o- o - 17'. PeL a'Cc I). aIi CH.4.C " r'ci.L-: afaiF CS''i1 C""- 1 -Il LIF't "'-r14 C' I. 1) C'll'' F-It' F' -IC aoIa. I4 F-'r- I''-"" Ia'A I F1'"'4 r-I —'"'-FIFI 4i *.% I. * *.*-t k- Ur- )r.4I**i.*r**c I.a Cia1r H- F T 1F"- F!o c e r-!'".I iI 41'''iu i't LI ").DIo - F —- r-co C.")I ci"Ia c cci.. LI")Ic' L~co LI' ci LI7C Lr) Q. I.LliL'I~ I ~ I)C"L~c I)c L")tci I"ic LI") c- Goi 0'~' ")"- i Ii" r-L")' "' F-,, F-I"'vI in Ci". r'' cii'"4 c-i Cl 6 r"-')F'14'II" I)'~~C

-249L.) U I'. ". G" r:......0j-.,", ". "..'.'!-`; ",.- L'.:' r.- - o',,-,' r.,' - CO,. I'-iI~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.......... r0-Ci q —'C,, (r'"i!..':. r r* *' *r. — f') l Ii..:: I"* t.]7,-r...11'-" *^;. r-:. r CO:I i;'';;; IO T-*t'.:...- J'''r 0 _'.::1 r~ - r; -: — -'.,;C.-I 1'... 0:,l~ 0". L~C'*r-'r:,'- *t *;'0:*'*'*i.'*);'..:jij:I-,"", ) -, "l,'."'," ".Ir.. G',:i [i",;,."r', LF,..*'= r (*.,i'.. -_".1; r. ("..1T7i.L. ~r-,-!,O: r"-', f';,:,: c,', o or" -,:.. Lr,: —.r-)4',y.N'.J.:* r.....,:,::::,,-...::O...:',LO.,_::=,;'..o'*:1'...-r-" r.,:,..,- r,-:':, 0:. t-:,"0'.::t':o,:;':*'***':'*.......'''*~<* c'-;.....r-i~~:r-i~r-"i,-1"T o L o i' 0 0..... Li... a... a j~~~l~~!^;i\~-qa,I, 1;' I' i i-! I I'I I 1' 11111 1 * i........... i I C D: irj I_ o: I.-D1 t 4 1. 4, Di C, JC4 c ** -- I'i.. II -***a I0 0II k o I r I"" * 0 I I!... I r r_ i C O I i I *Za a i ~a - ir:,;' I.r... Li::'-'":" "-:': -: ""'0 ia 0::::1 ":' ".i::'L"::':t 0'-4'")=: o'::::-,'-:,,=,:::: I.'::., ""'-, i 1!,,o " "',,,:'",1 ) - rrN;: rI'", ":,],''::j a-,'a0 o:r,[ rr "'.....': -",..-. C. C' r-!u: oI I.= ~ I *'o 1=i "~ 0:1 Cq, r"~ *4 o. #t o if' -r' %t" %t 11? o:", n O:':, T,4 o i -ro r" 1r "~.rj- r "-[r r. o c —.i o a *.+i:, [i-. I.-, = — i,,) ~,1,.. J,,[,... N.i * *[. ~ * *!* ~1............. w ~ ~ " I'1 {,])... "..i,')i ~71':,,-');,::,i'J[I"..- I' ~.' i'.4'* iN' I i:",':,,..,I'""41:,. CX4** ~* i:',4 i'~", I::,'"'),4[lrl:")i"-"ir~:J [.O I ~ I'.~jI"*-' )[ *4 *i]:. *t|IJ":.I:''i t 10(,,1.10.~7'll'" i~..')1..e- -.......... I~'"I.,-,,,,,,,....*t.,T-a!,.,,.]i,".."4:,jo:,i:i J 0:,**i1 0"!.'*Oi1r" *.ta -'.r.-_.",":.. L,,:,:'.'*II "J"S r- 0 01-: r".i,4i —.I -i'.1, 0r - r,. C: i,...,% 4r: r',. i o.-1'.41'. i 4 " a.0':,' "a r-'':i r- i i.. Oi -- _.I I'. i;":, 4 ".- a: a.';,.;': Li'. --: o,";, 0 1:i <._o~~~~~~~~~~~~~~~~~~~~~~~~~~, vi "i# LL r —: r,""'l _ Cqt' > r""S rn'"l' "-D0i*: Li; I 0 f'i.i. Lf'< i): r''~ O-i: *. ^i:-4i!'*''! 1.'! *-;-4- "i i. t'''^ ^ *- " ir':!1"., r~ r-.. q r-: -t,.t -,u",I sirml a a r.-j a a r'~ F il7 r -0 io |.1- a. 1!i i " a - F'r-. 1[a 0 **;j il" r- a 4iiIa.- c a F- Li, r-0- I0.-. - C — a t 0. 0 r - a0"41iaa a NJ. llaa.a ml a', y a*: i. 1f* I', Ia 0 i r Li " - iaar"ii *: r-a;.a- i..1-0. 0 L iaia - I* " O 0: J.! t. P-4C4rfi rf P- 4 *.:t ~ ":.4! *.!' fi r" 1'. I.Cl'4C- -!'4C4 CIl4 iaC1 4 F -F C-li. 4.jI4C4 C.4 4 C' - 4 - 4 a'-aar 4 -4 1 LC'a-, U J U l i- -1L L r'::' j':' a i F "-':' Lia" o:"''F'":::'i a- Li a.'" o r':" I"*a'= L:0,aa'a,a a, a,: Li:,: a: 1.4.,=a ra I a..:.,:.:..- ~ - ro 7 a~ a aa.....aF,..,' -I,,' - a~..-..aiaa~aa...,..,"lIII~aI a tt.,-tl!- r.': a, 1:-'.4 - F C: —, 11'': a F: —4'-I-:i.. r'-;i -- r,"-'r"a':'0:: i:-F r- -- a":,t4ia.-a-.- r-a:: j..a 0:,'1',:rt U-j C~~~~~~~~~~~~~~~~~q; U,-~~~~~~~~~~~~ ~ ~f.,.e~,. r D') o -.." I - La a at..!4a.4a.a41 41- I a Faal I ti rtF:o,I,'L.,'a Li4 iIr: I r., a., -: a..a F-I F lE a I-Ia * av:,.,.:.,..':r O — i l,:t 0 i O, y:o, C 40.4..,":, 4,L: I- -. -'I.:- I r -.".,'.,Di 0 lj":i.r'. C.U':..ii- o:,.-. o r- "i n U __ I N__ ___ I r N]- CO" r~ *r~ r- TI ZIi I —t`4 T~ r I r 1, a-I"''"v'T!'"',:-,,o,, 0ia l a.a 0 -{ 0. - i C —4aC""..U""i. i r: F-.-Li:!.j: M U CO 0:ij0- U 4iO <- C1 a4I C,4i. r,aI-;r:4t1 a Fiq U -i.a CO-a 4 -0 a0 a o! 0 01 aC4 a:~ a.0 a0 a0 a0O l ala ~ ~* m U" -. r1 -. a#4 n a o r'o ooo o- o oo::i o o oo i-.l - -l co o-.r"-1, - a'.o l. ii a. a a —o c u'4' I'iIaF 4 - [ ra'~":,-'..,1F F",,- F:',::.._,.,Iaa _.,:,-,,iaa.,! " l. ia....,:.-,..=,, ~ a~:4..4i.!4:,.4l.4 oa-.. ~. I.fF=,.j;'.I f.' ".Jt ('. IC'I 4'l.. a10 c"...jt!,'4 T'ai ) i.-aaa-'iaa " o r" Cu ir a'.a r -.. - F'").-1C4i'4 Lif4iIfT'r, 4[r..aa aoUL. T 0 **^! iN **4-i r- ~ ~~~':t**......J7.1;:*T'*' (-'"4'^ O r":-' 0'" (''**"4- O'4 * *-;*C "r"J':i*.l 0:J*"!'!..iJC: **ji -'nr':i ) - -i N, j % 1 i I! N IN''- IN"\ — u 1)'. r - 4 CO % IN! 0 o! % P- 4 - Q- C-4 j C` -4 r7-4:ij **itr"4 CNi r0 f-c4 **;:( i 7.U%4- *. C',.4,1 CO'.ri41: *; U l I r'c l j-a (4i. j.:r, r — L.....,:',,, a".,Ia...,a-a..:'.. r-:.;4 o_*r-Jii'.LI r, I LL "4 " c4 i'j i "S 3- - < *. D I r-oaa ai' **I ICIi *:t-II I I. ol O a. —-.a. — r-.- r — L r:~ — 0 C.-%Orla - i -'I ar"- -I I -. a -. r1 C. oi,,a~ r-i.' t.,'. I rl-ai o,:1,i r-Cr-.. I',r-' a0:1C, "Ia-4aU-' aO -.i'-'L. a..I I 0I{0 t C1 " 0 I I[0 0 O i "-r i ~ C'.4C F4-.:i r': r-:i *::t *: ci") U- 1-i I r! I'" I I -- % *^- ~7-.^.t ii":'! r'-r — co o:'!o o!'-^ o:'c'-4 o'r-'') Lj'i~c'-4u":<.'-i~ic:'...1-4 r.':.,J b":.,.,.-. J b":, r —,"-, c,:'.,,,"o r.,-,J,:r.,'{r'':,,:'...i -- ~ r.4 I I I I..9 I',' J.''":" ": ", r.' r.',... ~: 7,: -C. UI V ~ r " -- U"-. 0:o o o c I'.c, "I' -4' - I:'"~!:'i' r —,': Do.: I r C:,,', r., I=.-. r"-or-,: " 4 C) I I r a o l- *ma ela *~ r i.r-: c o i o.1* v: r ij.-:1 *(-4I c)i4 F- L aaa:i r-!tar.i -',: i i a "a -:'.ila al.''.-'- -, -a ih L i) F -iai.a c-4a'i aa r- II' (taltQ — ~ r': i4 L.f)'* C - **3 F''C -!*:' *t' *'r'i C -4 - i7 fl a>iC (-41'' >4: 1-'.j:0 i~ aj: 0I - - ~ I I "-I r.. Ij r - r -. i -.i(;IU..4c! ~ *1 -4 -- r'i *! *^. -: L: al'F.-' I - -i - I. I ~.....','.....! I ~ Il4S - a- a~-c l.a-ilir~~-I~i~ - a 1: I * r II.. r-aca -- ~ a r-!o:CF — 4 1:a L -.-l... a a.... a r.I aI I F..i, c, -'r.:i. c r..':I ('0,. ", r i."i r"'.:*i,'':',.r r"Q1 I'z', r:.''a.':,-, I-", I a:I 0 I O|4 C4 Ir I0-I ~ C a U r -.l ro I'I., a' -Dl.:..,*. LO: a:.4.4r C r, —:i.fi" r.4 " C'4" 1.0 r..-i.CO....'j4i * ri O C. I.ia... i:-' I'?.IlO..*D1D- r-A...r', r-: —,r':. j,:1:....0: r:,...':i:,[....-...:.-:,, " C':, l I: 0: CL r —~~~~~~~~~~~~~~~~~ ~~~~~~ ~~~~".o!..,. o -- -:q vi^!",^. *f'.r oij.J i v-:iu:, o'..io -'r:r-: r'.:l" (\j'.4.'r4- o: r".i'.r j:, r]'"i^ i-..rlcl C)- *^-j< ~-4CD - C- CT4'4 C-4 -4 r-~: r- U-ir~i rC:i *t *t *T *:- Ci:'i O O L ~ j: L {O l"' ** * \*t *t\' *t -:i r-,:< rO:,,l tf' - ib-. r":': C'".', lf':,O t}':" ir':~!.i o o i:':,,:_-',,.:,.r.O r i'.'' I",.C':' ",,"', Li,,"'. cFa4 L~ia1F-t -4! r-':i) i o coau.~lalala c a-4o:'i~i co ar-..:t.r1-i r1;:iio,',.r' -': ~.''4::. r':[ r:.':. o r:i I: "'-4 i-'.{,~.:':o i,. I,.,:.{ I 4;.....1... 1.,: I,j...,:..,:,:, -,..:1,.',1, C —- a ll a - I,- i0 IC 0a 1-:1 l.a i - O C 1":1 (- D l= 1 4-:I 1 ".1 I- Ft FF4 a.. I0: -41 a.aa 1- L L Z io LOILO ii~~~~~~~~~~~~itij~~~~~i~~:: "io i i *.ri.r o::,',ri'ri*r r- -- - **-^* r" —}r- ",;,,:yi',-.,,.i.. r'.!: L LO L,':'[i:o*t * r *.' r:, C 4 4 4 4 4 4 - 4 -4 C -4 -4 C- 4 4 aaa4l a C 4 L4 i a - a'::-4 F:-4 C-411( C.J4 aaa4iC a.l a4 4' 4 -a - 4 F -la'-'4 F -a CF-4J iY4l-j!1 i1 1 U a1l41 4LtaJa. "Ill. P~""N'D —,'''-u:-C) C,:,.,,,,.7 C."~~'. i::,!o: r- I-n,::,,,t',. r. -.,t,:n" r —r:.r —,. I-... re -....:..l%. r —c,..a0 ala.I:I.Il.lllal-a.c -. —6 l n.- -a. ca,4r- l 1aI. 40 1...h CI it CiOilaaa F IIIZ 7, -1U) -% 5 ca-lall~.l4aa.-aa l.3.-llaI.a. o.a. rl %D v * -.1'r cr- i cipr-: 1: ** tr i o: lo -. c%4%-4co nco1 l.ri' ~ c — cv 4 c o, Lo c-4 U')-4 %.4 % c-i ~ -.[r -- j j.:i:t- r-!r - L **i-oCT i~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~.- I'.... "..j I... ":I r" " i-'c' ",'j't"4..-kGNC"..r _ - -,' J."I"'.. - [c, r.',i I'..c,,:'.4 -r',''Ir''-~ C._, -- C.1' r —4. { L':',' r'-'' C4 r: -':i,, r", i r'O - cr. O 4 jl' "*' r r, -'r,,- - r-,rI,-,, r,"',-r-:-,r;-coico cocoeo o:,coo:'.,',1,:r, I'..., ^*>\c 4i,: I,:'..,: p.o o o - I.- aaQ 1L — iF- F 1 7;_ a.,a al 4a aF- aIiaaa - i.4L ia a.4Li1.J C:j i -.( -.J I I Ij I " U") II- - I- 1.7" U.- I " — 1U41111 FaIF. Liala F aaa.I aaa C." a.41auaa - " C L111Cr11 4- cI: ala -IF 14 -4 Li. 1.-Il I l Il-a —- -.x,, = -- j _, - a l, I- -.- i re'', - I-:%'(I%- u. D r..,4 IF-rFl -ja l la. J~~~~~~ ~~~~ a'"- q- r-'I Lia a -'' -— 4~i,'=, a,, 1.4-,,:a.4,,:.:;,,-:,aFa~4' l.a...a F a..... 4:': ra,,:'.1,FL",.-I...:',.: 0 0 I — 4_1 6 -%r r- - l.,, r C 11 t O U'F all N r - p- r-a a:1-14 -a — at L ) (.41". I- I 11: 0 0 I 0:0 0 0 Cli ("0-, rj r,-,, ",,, "tI a-a-, — FF -- U-.a Il:'' "- l- a~. a4.,:, a- a-l, I::,,::I::,., =:.F:F =,' - -''= —-'" - cc O c: —,_',1, -,_ —--—,".. C:.",,::: 4 D::, r.,_._',r... ",-o,:: or.,,, I_, "':,,j:,,....,,,,I.....,I. 41 --' " 4 ~~~~~~~~~ON r..t lC - N.,.t1D 1"4..I I I' -1: f2.1. ir'.irt.,:_,1_ -i~~~~~~~~~~~o'-4.~ =-,,,,:~.t -',!',5-t- c,,5i..:. o,:':: -,-j-:,_:,- - o U:::, C.4 OC.4-,..,.='':I'"' ":I':'..-'':,,",:: r'""J,:, c'-,,':: I.. r tj ~~~~~~~~~~~~~II a ~'- I..... 1 I I C- ) lal11-a1,41 1 F —la F-aaI~~~~iaa~aai(4Li1 F a.1 — a — F ~ I-a:L- F A I. 114 - al 1 t lI - a4 I~ F Li aJ.. 1411 a., lIa a- nI 11-?l" J ai'la i.a...a-ia.4a-4l..4l.4l~all-aalF-aaF- Faa -1It.% I- a.% a - ra a,- a e a.. ar,Ll itL l ia.l ma CII I.J I Il III II I all i II II q-I~ - I-\ 7-1 —a — Lila Q a.I. Faa aPea Li') 0-4 F — alaa *a~~ — It F- - a —k I -1 k14 a — a-f -ala 11-a- l a,- 1111 l.aa t 1. o r~ FalZi a ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~I CIC —-4 V') F- 0 %1,'.".J I U-.I 4 I i C 01:1- 4 I j-a-t -— a-I-.-D 1O1FU C-ail.a 0 -4 -'r-ION a.~ lO-,a a`-a 1.7-.1 r1 IF Li —- a. -ilI_).alalal aa COF'alaa1 I, I ll:0a a 1 al- - F -al i a - 1 4C% - 0.4117. 1P s PI...t.. L r U nf I- c —. ID IDC 0000I a- - I r,3 C',0 OI O CD,' Lt" O OD J: ) a oil.. 41v 8 a.4 1 4 a, F a a la Iaa ofaa axiF-a radr 1.144- a11 Fv aa i ar- a-I.11- I O:,' I o l I...-.. a I I,' bx l,,'",'I b",~ r',.~..,0 ~,:,,..c.,,,,'ip'-...' r —I tn- 0: rI- rt.~ Il Fa~ ~~ ~ ~~~~~,f F.,a-a-ri'a ", ~, a: a7.-l..'.1 OLi OF.!aj'F.!',la...O IF-a Il.IF-,i...-aa P —Il.laF-. —ll —ilLi..:,, F aa1 iII.4 a.aa..a..-,..m - C-..- ""1 Li. ~ F~ F.:, 1,,4.- rt —'a,t:-.: r,, a1-, Lia -iaI -aa,ia %ia. ia I I~i~I,= - IC:, (:I, r — F-. F-.. F.. -FF F F-aC i, r —'-C1l il.' -J.. - 1F "Li'414 J'4 14 11-1 1.4' r4.,4,1 ~ 414, 1 - 14'.4141 4 ~...'4,. 4.: 4 1 I 4 4...O I D i- I.tr,, U I:.. = C 4 ri r I Ir,- I4 I44 i I III-.-.... ed ~~~~~ ~ ~~ ~ ~~~~~~~~~~r...:o. r. co, 1,:"4.-,.,;,,oc.,.Jcr,:':,,,r'-rIa,.'* ~'i,' "::i"' qi' ala'; "':"a....a.a —"*ll a —' "''' ":':"ii'-"d...r~l~~~a-FLaiFl-F-ia..,, r1..4a 2: -I i- C- 4 F- %l F F.- aaa a..aa4a al a. aaaU —) Un 1 a It a -.' 0 -1 U- U —,,:a T)-.t -. -, -tI.t -t,)1) n I3 1 -I,~~~~~~~~~~~~~~,',, -a-.- a:.,:.,-,4a~~l...,,' a,::,,:,=,=,

DATA SET B RAPID FLAME PROPAGATION RATES -250

-251i ~ ~~~ I: I I 10 10' 7' 0 1 un ~00 2: 2O TK.:' K o. i' I I 1i Io oo!6 o~' ~ ~~~~ Ic'' VI 2ui o Z. Z UJ ~ I I I i' UO~~~ ~ ~~~ I I*Z II-I o j a.Q. > u I ~ 1f II.j ~-^aai ^ 0 O 110~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~I I1. Uj 0.4 I 4.1I I i 9j < c a o~ II I i I <- u LL4 a^ 1 1 Ij x I Z ~ ~ ~ ~ ~ ~ ~ II ad U. P I a wj I-' I I*I I I Ii i I I,. I -I I-a -t J0 I UCDJ I M uz 0 l9 co l 1: i.0 I 0 0 4 I I 1 afl~ ~ ~ ~ ~~~~~~~~~~~~~~~~~~~~.1 0 0.- 0 1J 0 1~ i I *i H o I 9 1 11 11 11. 3~~~~~~~~~~~~. Ot <MJ I ~ ~~~~~ IS I I II ~i~~~~u Hall el 00eel I ~- uI~~~~ I Io I I1 I i o" I L-4 %t %0 i 0 i:5)c -:3)~ ~~~~P rr O 0> ) IM V cel UJU UJUJ TJUJ II lexie. LU I I I I II I *.QCZ r.dI. o~ I M t~~~.y<.J <I I I II II 444L111' 1. I I I I I I ~ ~ ~ ~ ~~~I I i.! -J <^-* Xi O (/) 1 1. 1 1 <1 0010 010 1* Q ~~~ ).I.. I~ ~ I92j I-4 \ Io Is In I ~a~oI I*I IIi ^(DO J I 0 I I* * *>*I 0 1 _ I I I 0 I Cfc{~ < ~ < ~ i 21:~~~~ ~ ~ ~ ~~ ~~~~~ Il< III ( > I- * < I IZ I! I I- I I- I xi ~ ~ ~ ~ ~ I I Io I I Q I I1 I I'~i~u <} ~ ~ 1 1j I'1 1*~ 01uj 0, <jQ u4' z. I>!uj!uI Iu q ~ ~ 00W-V02Z Iiiz ^ Z ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~~I WI C, IL.h d -- a!!uj~ ~ aa IcoI 0li!. o x:a u js z1 Il~!~~a ou uj uj0CD408 3 0^ I ox I

-.252I I I I I I j~~~~~~~~~II 0 I I I I I ~ ~ ~ ~ ~~~ ~ ~ ~ ~ ~~~~~~~I I I I % I - o I% # 0 - I404V 1 1% 0 c I o 0 ci 0 0 0 010 0 0010 010 0 001IO010 NY N NiNyc~ n IMm N1 M, %t * %t %t - ot4~.4.4444 %t M MM M C0 0 0 00 0 0000010 00 00100009,10 010 0 0010 0100OO0000OO00100001 0 Z oqe 0 0 ogles 0~~~~~~~~I *I * 0 # 0 0 01 0 M M 0 P4 In *~ elF4. %* *) 011 -. Or -01* e-Ie e l. - * 4* *l e1ee- 0.1.01 -40 LM0t01 N 0* - * ** 4. -c -M H -e e0~.O~ l1a'lN0, 1 l 0vi4 I I I I II I 0 20 i4..00 U 0 0%NO0U1,t 0 4N 014.nint i ll% P.4 0It %raoM 40MaI y ~ a 0wM Nc f 4NV lenM' t1 t t% t- % 4 t — - t*Iw - t t * tj NC P4 "'1 - 4 P 0 ~~~ Ofo-.-. NN'0OO~~1A II I0eI II IoIeII I I I I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 2. ioqe.4 e.1000 e1'~~~~~~~1~~.0.1 001000010 el 0.6.10.~~~~~~1.. *0 0 V44 M -In 4 V NCO O jI 000CA 0 IIIII P- N N M %t U1''01% N I', I i 1 CY e..., iI(l IIIIIIII0 0a 00 O I1ClII 4I co Oin SIN 4NI L 4 I t t ItoN; (- maC qi oI I q C I I I 41 S 9 e01 e001e e. 0 a l4.4.0 di0 ~~~~go~~~~~~~g ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~0N0~~~~~~~~~~~~~N00"0~~~~~~4 -4 " 0.4 V4e 0 00001 N ~~~~~~~~0 o -,-N-4M4 a I 0 0 0 0 I.C. 0 0.0 O,1Q 0 e.1 * C O CC. 01 0 c Nc cofONC) VN.CY% r P 0 6 dor- InI I ~~~~~ ~~~~~~~~~~~~I co o o-l I o I I a I1 I I a I I I CII c 0 0. N,t c - Poo 0-dHV4 oOOOIO f*lO4 001 IP or-O 4 0 -WIP — * - N* P4-Oi- N N N ICYN CY0O0 N4 - 0200aco 00 oooooooioo 0 0l0,0 00eOI.oN-I'0.40e4010o0 10 ~0% 4C0.00 O1 00 00 all000I 010 00 00 a0 a. e 010.0el e'l a0P4 a 0I0n0 o0'.00 NU4o-W. U- MLA CYCYMo- O00 OI9O 99919O CYIN99I9999I N y99I99I" 0 M00 0000,I 4.4 tCin c I- 0 N1 nc i- I I, I I in I I I?-M I,-0 M (I. e 0,eqe U In *-N c - 4P40 0 & A% A 1P IP M0-0 I In - C N tt I e 0nM I III I I IA I IIIIa I M y iQ,. I I I I I I w co. M co, co co coN i400C0Vfo..1.0.-4'.- C.0o.i..-! -d'0 m0.d1'I0 I~- I O N04 * in 1 cu ~~ e 0 * e.~~~~~e eNAM0&lU n04n.10n.In eel. ** CO I 0 0 00N *I- W Io I I I tn' In in UN In U 0II I I II I I I~0~c Ik C II % Ok 0I I I% I' W0 ~M 0 ~ Y'0 %0 0 O I I I I1 I I I I I I I~~~~~~~~~~~~~~~~~~~0, I I' I I I I I I~~~~~~~~~~~~~~~~~~~~~~~~~1 0. I- I 4 PI.. -1z.: P 4H. - 4. I IM, ID I Im I IIco Ino- 0'c o iA N N 66 -4.01 t RI o14.4 c 04.ON1N t94. V41 N041P i I00' 0 MNN.r I0 % -t4in 0 ncolbo'5In004 co 0ee-e't HO - 40 in %f0 4 6 qo.q w,6 & 7 Pe4.100ml0f) o co R 000in m Po Ni AN ol0O-t 01elP -sO0%. In V* (NOCoNC nN tA n el N OD N CY iN o4. selee. le 0 000 -4 010 0 Oeee. 0 0 1. ~ l 00 ele 010 e o don e 14. 0 0 II Ic'oooII~ ~I Po coI. 0 *"' e re 0010 Ml co oletI!ol e. N Ml,1.0 * %ol 0100r- 0 000N O 01.01 ee 000 ode- tAI i II It 4 M I0 0c,0 C00 00000C II II II I 11o 0 11 11? 00 C o I4M Q4 I I P I4 I001c.(Y I M in 1 I I- t I0 IMV4 t I I40 t t m 10.-o4140 04f~0~..-f~00 el#-$ l'00IN4 00I.410NI40 40 000 0NIrO 4.0 IL PIV. -il 00N P:~ Ine-o.400nol0I-. 0 l NC.0. 004 -t r- rNf* c l N' 0DwC 4.y In 00 0'0P. I0.0i N- 4 ON C P.. 0 04 LA N NP00-, P. 00. 040 0001 -c, -oP),c.q 0 4LA4Inf0I %0 I N 00 In- V j 001I co.l4 "f - N co I*-~ 0" %4 0 - -4 0100 N f- 1-I" 010 N Int 44 MrW nt L..% 0e C O NN M.0 4 U- l4b I l" 0 01 X.-14..- r- n~I.- f.. - oc 01O Fc M' o o c co -IP' Ico I coC0.' an to o 1 o n,0 00,10Ifo- 0c. C PW % 0I -I el-N 0 N co0P(N -I a coOD ifC, e'.44.4 01 00 00 000 1 inO 0F o-l. in! In 414 Ico. I td en', ne 00.o. P~Ns~ n0 Ce'edo tl 60.040 Lu do C C; I G; I o Ivi o: Po I4 NNM"I M Ir - ~ Nm % - 0 C: C ~~ tf~~41 P'c~~~~4. ~00rP4 "4 0e V N0I S4l04 P4 PA rOOO1N 4In.0 PA0Iel Po. Po~.4.le.' 00 J..44 I.-4IN oON INO

-255o~~~ooo~~~~~o~~oolooooo~~~~~f- 01jo0 OjQO 00000:0 I i I I I I~~~~~~~~~~~~~~~~~~~~~~i0 7 0 0 o I I00 l 10 i 1 0I IO I CI >0000000O Ir r InNu!f4P40 M:P ol I4c'"u o0 N')O r o I I.~~~~~~~~~~~~~~~~ 9 # I I'I II I ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~"j %mI98.-c!0 NO. Qt tn1 41O; fI M 0 0'N N0:%o 0 a o: I ftV *JSt *O r~j w S OSIC 4P4NN01 n' *-* I I elg esS 0150I 9.1.01 t t t COI S I 0% 61 - 0 I i ~~ ~~~~~~~ c..1 aI 0r-' I- enI% - i 4 (010 4 c I0 I I - n c n % l -0-tMM IMV4L NU %10P44M0O I I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ S OS N O *l 01 *- *. * * N! S- so 0 S0 Y *M *. *h * i O Nil 0l 0 co MI coS0'I MI NO 0' 0'm P4 O ti r 0 10 00' I c 0'I co: NO-: rO 0'I0N 0~o, M N 0' Uj 64?. tn N' mi m m CM 4 % 4ThMI c- i. 0 tn "fiu"- N 0I 0'- " %t1 a I,.~~~00NF %,0 410 ON ~0i NI'l 00'N1 Q V (~ IOUNMNI ~~0!0 0I % 10 N ~ ~ 0 I% 0' el0el 0' N 0 e 0 1 I I g~~~~~~~(4 r- l", PI' P 1 * 1 - I en N 4~. 4'4 ~ 4d~4o4. I:~~~~~~~% I I I I I z -00'~ 0060 U.%'0'I~ 0' 0IO% nUmUAw 010L 1UoIUU% At!L 0'I0UnII0'00'0'I'0' CDo o0 0a 0 0I000000 01000OciOO OO fOO f00100 C0 01 00i CiNN NNN NNIN4NN N N NNN N NIN N N N N N N N N NN NiNO:1 coUI o a P I' I. j!C n -1In c I -- I I% nrII. O' o n' I Oc"' I S MO ON tN S4 % ~ T 1mN %OL N - I L nMI M N1 I. ~ UIN fI O0 O I7 olm N'4M -I IINMN'IM Nr I ~ In I I4 Io t 1 -N 04 oIr MI tn IioO ~L y 10 I-!N'1t-r n I I I Si' i0000q l0# 0 0Lt e UN 0I 01 I 4 0 el0 el0 C9ol0 %4.N;0%,0 - ~ -4O 0:0 %O 0' 0' 4 r,%+ N1 I VII OV-4' tN 4O 017~ U- NI tU~. I' U'- M I Is4 -4:1,4 P- oli-NNN1NNNNINNlNNNNlNNfNNNNm Ii MIc O v 0 010cl *!c:.I4U,-O m:1 1 rII N r ii I00 I ~~~~N: a "0F %O Uniwi*'MNi N P40 0' 0'0MI (- %-%O0 %40'lt I NNN N N N N N - "4 - -4 -4 P P- 4 - ~4 -4I -4 P-1.4I -.41 41.4 - - -,4 01 1PI -4 P-' P4 PI -4 -4 f- P 0-4. P-.41 -mr P — P1 P- P.41 P- 4 P-1 el P- P-1 P-1 r-4 P- P-41 - I I 1 V1 o ne I I O' I — U t MI O I-I.-t I I0 - — t1r-' I I IvN tO I I I I I64I I I I 00' f1 LO'%-40 0% XYN OsdU'N N O OI4 O P- (0'1 m -.4 0'(, ff-1 pN't1'?n. N tn 0'Cy I O Ok %' N %0, 00 P- %O FN-I - %O 0'I 0 U-% M r-4 %01,4(:) 01 Ui N?. Of0l4 I INII IN Co Lr:I% 0, Cnff tn fN a U' "I LI I % I 0'(~ I I 4 0. P c 4 P41 0' coiO4,cp'4 OMI 0~r'-IM I,,-Nr'00 11I ff1 It w r- - %M I N.I t.r it4M L P 0 IL I- O0 -1N M I t' FP-UIi I 4I 0'r4W'Pl 4.N N.'M I A'IU L'UUmUiUII O I ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~II~ ~ ~ ~~ I. 1 4 I % I 0 %t cy N:-' OO I- M - I I O oNc n M,, MI N 0 O~~~~ z.Isin 010 NLA I~f1 ff I i co t: 0 c LN ~41 ff1.! 0',0 N 4 IO rl ffN NCW1 4 -4 -4 I I I I

-254I I%~ I- M % CO04 0 % LA N P AI I' I I I~~~~0 n 0 *! %'t N It %O I0N L -Ic 7!M * oM I i4 -io "IUi %O % C - "'!P oc co! o c I coI I I I I I I~~~~~~I 0 g rf 0 010 O 0: NO 94 O 01 0% O! ~O. Co 0 0 %O0 0 40fOl 0o 0 000 01 0'O0'N 0110 0 0 9.4 0 0 0 h. 015 0 U' O Ui0I 00 0 ~~~.00~1. * I 000 100 I940 SIs *1 *.SIo0o.oo aoe * I0S 0 SI~S I j I I~~~~~~~~~~~~~~~~~~~~~~~I II (A I I ItI co 07 in 4 0 4 C P, 0M 0- 0 - 01 coo ON! 0 0 0 %0-10 Ml 0 0tC 0 * S 0 01 CDU- 0- 0N'41 0- 0t P 1 O I -4 I co I n c IMC1 N MCI Itln1A1 % - o. I* %olMI4 t ac:9 Ne I r. IJ SI I I S S ISI SII0 eSI V I I.1 N MlI % I o I-4 I It. I VI I M NI tN tC0 - 4 o~~ ~~10%1~~~~~IL~~~0 01 CN~0u,4N iNcoo N ir —- 4Of. U-11 l o1 P-N," Lo 0Nt L U I WO 40el 0 0 el 001.0 0.0.S.Sooio ioo elo I 0 0 0 * 010 0S010 S I 1"-t % ool4 N NNAlN N1NU N 0 t 4 N40N1N co IP1 N%1% L tI4N1 CO N' uO1.O I I I Im- c coI04 N l L I LA % I- -1co I,. "I I' I-1P O s I^, it MI I 2 I UkUV -iWI IA111 4 % 0 D -1-l4 0 0114 4 % C%5%I I IC % IO I04 O% a% 0. U5O P P mC3 - tco oMM * 0kn nL N%~IN I 0I.4Ui' aP0 MM iN co M l M.1. WU Z%O 1' 0% U * 4 0I01 0 0 0 S1 0. I 001 0 0 0 * 0 01 0 0 0 1 0 l * 0 0 1 1 4i0 0 0 S0N~ 110 1 I 0 I I 1 I0 41N 11 11N 110~N'- lco 4 lcoc f 1 1! m 4 0 % N L I -j - c 00 0%0N V01NF vl 4 NNI ~ fee F(t NNIUI t 4p%1+ i4- t 01 0% - -i -! t Mm C NNI~ U.I4AP4' F~% N 0N41 Poll 0%41P -1 - w- V'I4I —fI4 001P4 swP4f4 0-1 il -N0%4It 0%N 4 t t-M P'004 M %O 0I 0 NU f-U-Cl% %.40%.4NU 0 N -iO10% -4 nOO0 P~~40N M I w IN00O~~~~~~~~~~~~I I U- P- 0ko Mcy tn -4co.4 0%ON I * soI olUr.10 00010M L P co0 0.01. I 4r 00 0C o01 ( o 0 0,I 0NLA0%1N410 040%ii 0!01CO001 0 ol O i..40%4NIU9! I..J?"t~~Co0000 I I I l l0S 0 90 S0 0 0 IS0 Se %1)1'~~~~~~~~o I i -c - C I IMM'0 CH - N A (I( P4 -41 1 1 1 0 ~ 000 0c ~0 0-10000C -100% 1000In010010001001000100000 00 I I I D0 4 O n ON -blC 2. S @ 0 olel* * 00 0 1 0 00 00e 01 00 S0 e *I elooooIS l I I I I~~U* I0 P. o I 0: ( I I II I I II N — ti M O — t M? —I %O 4t N 0 ~ ~ ~ ~ ~ ~ ~ ~~~~~~~ II I.1I 0 VI % I a~Q lI I o- 1 1 1 1NCO% 11% i 0% CLIP 000 t-NU%00 0i(0%MP-0 I-tMP NO J% 0. %0 %I9.4Nw10o9N.40%N MtANIN0 MP- I I ~~~~~~~~~~~~~~~~P- I ~~0 0 V4 I 1S'' S I S 0.I -' S 1 I I I S (1 N44 P-, 00'V% Mr'0 IIt OI — NI r' c00(NLA0c 0 0 N.~4 coI0 NrO~o t0c1 a I,,- 0-4 f- 44, r- 0 CP~~ 0 Q~ NI -t- %t -t -4. 0% N I 44 % (Di co-..1 4 44.1c4a, c UiM1 00 N- oc Oy~: M fI %~ N- 4.4. M ~MM N ANI9.+ 00 N 7'401M OLA (0 U't o!014 M C P4~ % OD i 0%N:I ON NI I I- I I ~ 0 0 0 0 0 0 ~0 00 0 0 1 6 01N 00 0 01 0- 01 0t 0 94 LA0I 0 0 0 1 I 4 O P - 0 P-'-i MII 0 a a O N! I0 tIl -D - -4 - - N inN ~I (I4 *u a. I I il I I 19 I~~~~~ Il I 001 O. N rI IL C; C I' IM 0 N IIIIOIe- IIiM P-0 M N P-1 -4 -4P-1N I N' I 4 tI %+ L l FI Ur IlL A t -' in -I, I i N 0 0Ncr n 04 r4,0%,O0.N%+ Co4-N Nt M1 C)N' 44 U1 I - ml 1o44.1!' ( —~INc~ 71N4100r44.00 t 0 ~-44N 4.0' 4,0 ml 0Mr 4. st 01 % ft,.4 P4. rol' 01 N-0 0- M N1 41Ni,- Co P- M014 A NC M. 0 U1'0.. 000 N 4,- I%- 0 t N 410% fI% oP i 014.0019.94 co 0%s N14 NIM %O 0I.1CY,: 0 N -t1 M'4 Ln % 4i nM4 0 M 0 0 C00 0- 0.4 4"94N N N NJ M M14M M. M l,I t t t14n4, 010 000 0%I0 010w-I.-4-.C 9.41N01 fl 040a0000a0!0O!0ol **. I I.10 I!0a 00O >.I iI0 S lS 9 I SIel I e 10000S M0 *1 00001el0 el 0 0000 Il I O' S I el 0 I l O el e O #I I e O SI O I1 0 I I I ~ ~~ ~ I II I I 0. 0 MC~ Ns I -0 NQ CII 0 N I-4 O IN I 4 00 I-!r- I I-P-'AU-!t MI N':MPIMi Ne0N Nd IMfr04Ol.4r1I.0C0U)o0%I.Cl114.00 o-P,'4 v- t"' M%0N4. M Ml 4N1P"'% 41 t0 U%104tf A'%,U)0-!'10l'%0 l^ ~0%1UN1! C0%IU~

Xn. C..255 Pii2: i:::ID L.A ~~~~~~~~~~~~~~~~~Lii.J. LU Eff I I 1- C LA~~~~~~~~~~~~~~~~~~~~ ilL I~~~~~~~~~~iA It I. I DA~~~~~~~~~~~~~~~~~~ CO I I~~~~~~~~~~~~~~~~~~ Z.,~~~~~~~~~~~~~~, L Ll~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 1.- i: i I IL I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~1IL ij I i LiL'iLi Li I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ii III~~~~~~~~~~~~~~~f.:I itt~~~~~~~~~~~~~~~~~~~~~~~~L LLL i Lt r ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ i I i i i ii~~~~~~~~~~~~~~~~~~~ia. I IL- I i i i~~~~~~~~~~~~~~~~~~~~~~L - E * t-i I I i Li I Lii~~~~~~~~~~~~~~~~~~~~~C 0- " i I-q~~~~~~~~~ I I I~~~~~~~~~~~~~~~~~~~ffIP u IL. LJ

-2560 0 0d 1 0 0 0 0 0 01C' 0 C 0 1 O' Ql O a 0 o! 0: 0{ C-.4 ***'* r,-j:..0 -- 0 Iu.3*-) Cr —! COr: *c J.'(4 - -ib. **IIi -.*4 1 C-.4 ('*Io c0- **t COr_-j., **4 o CD r oi~ r c-dr cr r o ~' -4 r o o o o o c 01 r C o! -4-j-:f 14 44.4 *ti') r41-I r — r-l r — r*.-'i-'.- r — r-:i k4 1 Cci. r- c., -— 4.,...I r - r 4'Io c~o c c o c:do c c' c'- c r'1o o'1" IU ~ r'' co * 4 o c 1 r-4- injJ: f" c cil -o - - -rC- -- ~-'-r-' - - C-S -- 010 c.-7-. cor *cr 0 c{ 0 0 0 C::i 0: 0 i C::, 0 4''i-'''g o (".4 (".4.4.4 r --- rCr- r-: 4r- r-r-:ir- r:4 r- r-;r -r-:f j- -If'i-i' 4- - f i-f'4- rf *'r- i — r-, r —i P.-) r-f-,,,C), 0 i' n -o i-{.CII i I i 1-iir m r)-"*('('"* i — ii~r - ( i — IA' * r -'':'j 1' Q4A -j (7-'r'>i b-I C':ic u" r-l: * r1') i"'- clO *- r'- -I ") "' CO r- CO lCO'.i' 1 ~-r-: C -4l'-f -.r-: — ~ 0 m " ~i CO C- C- OA* - -Ic* or- iS.3u") r - 7 o.43 - **47 r —. — cif: I-'- r —'-.e ojc r —lU- r-1'j4. r-y c4'1i o!.o*d r"- NJ-i-c N r o~ -t4"o 0i47- A * 4- win —!r- liv 4- 4-ri r- oin - - o 4')4A 4 i n c-10 4ir - 0- * 4f 40,7 - 0C O *D ll 7 C * 0 C i ri C) C4 D C ( i C i C, 4 4 I1 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~C-, I0-. o x.L.,-. "f-C- i OI-f-1" c -^ ** 0*4 4 4 -"7'~- * " Ud co r *'. 0' >c.- ) r —. 1- 04 U") U")" Ur- U UI 4"% U.-i 4 I' 4o'-'4 o r Li-,-4 * 4j i I a cA r- o co r") 01 i r'-: I *r 4i *4 1. - r- c. t o C r.- o'o o. — o,,l r-'. r7 —.4..:,:: ":!''-:''','- -' - *.! c r- - - C ~..I';41l~4r'44~4;4 44'. D.'.-':,I1", 4.', -'-,. I.".,, I 4..Co.t I 1. 4"-'I C" I, %,,, jI-,, -, o,,:,:0- o -" ('4c o4 1'- C, C-',.'-;l' 4-, r -- - - t'-'i C —' r, -f r"g- r 4i ir i 0-, - i4t - U1"N I I o o c n n r.t r-Q L; co U*.o r"-I o i **1 r-r)i, -I o.c-j o")r.. co (7-~ *4 c -lrj ~- u"iT - re) ID r-io'. c -j re,'.!'u) in *r0 r-"c.4 %D *-r co - r.) - r"-C **ri. r"- 4r o W-4 C Co r", r-l o IDjr 1. * r-, P r,. 1o r -....:, ~,,.,.;.:.0,.'.I. C= I c N 04 C~i` C", r^ D c 4 r.4 - r4 Un -:.`-' o c IN'.5 0 "D)4 f Il )' 4co in1 r- - 47 4:T -' o r17-<. U") 444'.4)IU" i -- r U-" C r N- Ci.- l- -i U r — r — "i U") "Oif'c C*'.c'it ** 0':1r: ii c r i o co U") co" r-ir-'4)~> fj fC- U, Io r" V- Vo. u -.i, *.. r- r" *<f. i-ui r.r-444 -D..'-: -U ). 0,.- r-"i, I o A" -i r -! r a ) 4 -E ~ i~47-4CA,. — 4 C") 14"'.1 0o,' i-o- C)('I,:1 o ) A. ) oL 4. -,. o o -4I, r_, _:, o.. -T I P4 cII..t,.:. %,:'.:..t.,... r=....:.;,,..... -'K ~~~~~~~~~~~~~~~. I.4~~~~~~~~~~~~~~~~~..t -— t t'I r)rr X 0 U.,'1) U-4 I... -.D r- o' 44 r-U, 0 _ _ r'" 4 U'-' "' r'.- 41 1.-o %.",- r.,.. D. -. r",'iIr —,'."1 -i -.l,:,,:,::I -':'':,'='':".']':.'=, 0-1C re) cr~':,. III ll O l4 ic 0C%0c04 1447*<1ii)'* < r_. I -''- r r — *t cc,'.7 o-:.;,o....o =, o 0.o'"",=,l=, =,o, =,, r = co oe - o':io -.i.o o o0, o o o o o o.0 - o o-,r, o ao oo o oo oo o co oo oo oo oo oo oo o',o=,oo o,= o:=...... o..o ooloooo ")I ~I47IC)4lI~llII%.L.~ -I II. II I II: I ~)017000 ~I I ~I 4 ~ 0 ~ 0 0 0 0 0 0 0 0 _ 4000 41 0 011 1 01 0 00 0 0C0 0 0000000000 (D 44004 000 I C0 0000 01C 0010, ~ ~ ~ ~ ~ ~ ~ i I i i 1 1 I i cZI 0 1I I lcoo ooo oooooo ooooo oooo o I I I D o I 0 oo0o! c, ic0 io o!I I ooooooo o o oI ooooooooooo oo 00 0 0 o 000 0o 1 I 0010 o010,4o o o oI O I=) oI4L.44 iJ 40 o o'4 oI- 01 C_-)0000 o o Oo o o o jo I o o o Q o o00 a0 ooio, i I /H. ~ 11 0 0 0 0' 0 0ID00 0 0' 0 0 0 0 000I 04 010I- 04I)I 1 0000 fo 0 0i 0 0 0 ID 00 0 00 0010010, OlO 0i 0 0 i a 00 0 0L 4 0:0 0 00 I- I C 4 COj 0 0go 00 001 0OOO 0 0 0 0 0 0 0 0 O 0io 00 0 0 0 0 0 0 a 0 OJO (-n 0 1 1 D':DiC DCDC 0 D I nC I I i I i1,i,,, * I, ~~~~~~~, —:'u'I,..,:. 4'',-,- - — l-. I..4- i-.. I 4 —":,"-':1-:.,, (.,-.,,f,,,,:,:.,:.,.,:I,. - - fl -: ~ -U i:'' *f -.U -., o - -.:.. _:,.,-.','0~,-J' U" f''' " -l(. C i (I-.47- 4 i "r' r* -" ir-.. 4 r -c —-- co (;'*'l *J —4" -' i4 — 4 4 i 4 I l'-o- V) 0 0I.D'43:~" r,-'. ^C C." CC' C.' CI..-. L!'.'.' —.. I','i-li ri,3', -.::.'- ", "- i"" C,!. —,' C C-i-. 010'0.`.,C.100 01 —0 1 I - 0. j!'. 0 1.-I 4-~ -1 C-' - ( i- C- -E — i 40- ii, 41 r 4 ('-4 C-44C-44 -i( 4 ("- 04 4-i (,4 11 4- (i C, % l 41 o C C 0 C0C c0C': o0CCC or c oo 01C' ro IrC o o o o o o o',0o 4o-Ir o o1 o ii") Qo o SDar"- rNo U`),0,.t 0<f * Ci* q c r^ %t i * r'1) in o * o c4 i —4 r.- o. _, rl- _: O-:.., Co rvi! =. r,.. rl,,,.: r- c'""' c':'.i D r, o r r"-:: r': D'-: 0' "":'i Q- so ~- c in o 0 0uN" D- o u) -,t *r- G:o t o -*!* r — r'")- aN %, <.r** - ^f r —.t u- j *i nc-i u-. co r- r"- C7' 7- reo**) coor -ore co crh ci, rV- n -i- *; 7t n r, -o ^i r — N^ r" - r *- my - %o in) kn. N? (s' r — c, r""c c - r - * I- *D'U r"-.*D IN- o n r'- *- o c'-4 ID r,, o o co e - c'-, c- I- 4 I.-I 4 o **4t *-.D r — c'<4 r- o r- *- r~ji c0 r"- 7 co in 0x) c.,. * <f c* C*."4 o c.'.- co1 **.t i) Cr h C7-. o in I*** r-" *f C) GN- r — *.o 1.0 c-4 17-0 r r"- r"- LOin ***4 C(7-. J,* co co 01..o rM..t i;..i -.r re u) U, - r"- r,, m) crj", o) 0. cf r — **sf*<fo - mD us., r< oy s r — Di) cii *- r"- ci *1, *- o 04** CT.- i.-. i~~* M r — i^ r- r,-o (** **) *+t xti *.t **r-j - *< rl) pw". c,4 r- D C i-. r — in - D o.7 in 0 co 41 r~e -o I< -.0 i) i) *<f co I*.o 17, co (7-.- r.,o in Un in **t *" r"' 0! * cri 8 n (* T u; ) o' u; ***4 u4i **a r —' r'- co 0:5 7') C`- > N' - 17-. C7- c;%'c-i I:-' c,.i;' c r',". C 0' 1 -1 - c o co co *)*fc-ji"^ I.-; jin c.) c' — 1m co.- c'-<*j: r- r" " P.-) r->') r —) p<"/ r''-) r —) r,) rj IN4 i4 Cl IN'-,.- r- 0: 1, 4 r., r...., I:1'II I I'.. CO co0 c. Q) *co1) 0 CO co 0.) CO co1 co C0 co0 co co 03 C"I r,- *'* ~r * r"- o r"- Di:..: IN,, (7-. (7-. *frr) coi 1.7'*~). r — r'o *) -.t o: r.3 r"- o: IA *'*f in.D r"- o'-' -/ - c,4 (7^% c. ox-, rf, —4 ^-iI.-4'i-.4'-'-flU")U")TA 4"4i-T-C4i-.0) C. 0- l- (**sU * ^j3 0 C D r" - r l") - 7'.4 U r'U l"). — 0'3 y) D0 - 4- ")'('- ('4. 40- 4 U' fi rN 0 0 u4 f" — utif ir 7 0~ * — -D i uf) nu"C) An Dn u4) Lo nl -i Dn 0 U — iC A U > o.4 (%-) 4 co ri- - 0 o>. co..`340'.4 0"*4i'.o *I* r-[.i 7 o U r "-r )l.Dc *rI' cI r") - Ln U) 4 I o.D r-0-'O A") D") A")'i A U )i - D "V) ('n 4I) 41n in in in in D in u) Dn u4) in in in I.-, ir"- r- co(7 o o im -c,.4 r4 )f *tn.ri r-C co 0 -7 44o- c-4 r 4- *<..D Pn r -4 c 07oI" )447IN 03) %< 03 ^.1 *tif A"*4*T mr r~ 1'"- ID r r-";,v r,^ r-'-! C. ) r GN con.D 1.0 U`'Q ) in ii. *d r'- r-o *^ r-..t P n o0 Lr in 1 Un i 1.0+ tr q ro("4 N) C: 0- r<") *<f r-") 1o r-o 1n *4 c r - C0 G. y~i o ** —^ coco ro r"'*Q co *t N.D ** - r"- rm'n) %7 u oc4 r"- r —i e) r,, - - I.. - %D * I* c *-.D r"- **i Q C4 C`- 171 **.t t Nji **i r^ I C`u-ic 17 co - C`iroin i *- -7- P0- 1.0 r""-.- f P f r —c c" "' t.... CO D3 ". i C` *4 (I- N D) 04 *- 1 *4-t U) cri i r — I-,)o ** -'* co o "' C*if cri 17 * P!* *~ t r- C`. **i 171 in 4 c 0 (7i 4 (417 r — r"- co I- o r- in) *- vn,* D n o o in - o= r.,, oa co, 0 - P o o *4 *4 i c O co1 C% n r- IN *7) * in r- -,, cri c r- IC~ c trfi cr C,^ co cr rej: in -~03 o. i,.r.D3 r-...Dr i Crj~ co r"- *- IN% r — r — co r"- - ot ID Cr- ID -.D) -t ~- rin X **fi i r — Co r — 0 %t-*if _ y3 N C`i i. *~*i. C`i N*r re:i U,) Cri _n~ r —j Cri cri. 171..D Co **^1k re,) o r — 0 CA* C0-4 CV-4 0*4 0 CO %~ *t *- C(7i 1.n C ID C re) CO ~- PI P") 0-o o f-)i r- ID ID N** Cr r"- D*~ 0 *.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~"'.-l.:,'.~I'.,-..:"..I.,_.:',.D (,.'.,,*,,*.".D o.-',:.D re... *.4.... D.. C04'N IN *-0 i CO It^ 04* C-47-' U"). It 0 k** r - C 1 Cn*- C-N C`fi r"(-'- CP-4 *It,'~1i, C -4 a l."."..-''.OC' *if'~(7. P. *4. <. n. *~'.U D.^ %D **1*n * r-0 lo- r — **sf ID iN C %- 4 4' T " * i ~- Cj^ c q N)' re r — r,, r, rf).. *<f I< *< -..t u-j: Du"' Din *.5i *6'^'-n f- fr-i- r — r — coi 0:1 0:1 coi o:5 oi cc' j-r c'c co 0:1 n co lcc - jc r- r — r — I,4C ~*4 Q ll)Q y3 *0- Q,03 7 - C'4 1-.0 **^- **~* UNi Q-7 CZ r-.?i 0- **-) r, tzi r"- C^ <~ -.;i o u-j 0 U o":' ~*4 0 0'7 i M Q. i 0:' * cf I C`i0 (7i ** Ci *<f 4 -**4 t **C^ **f* r-O: 8- o co Ln~ b' ri **4-. **4r., o u cri "s t r-i- r- * o cri 171 co ur) *a n r"" c - - N co coW **^ *6 *n Xi> *~ r"- r — o 7a o o'0 N t **f-.0 -r-' -,r c;%,G4 *< -i*s 13t **at r —'3 *<f (7i in"1' r-'-3,'~r"-'IO N') r"I coI r — o G cri r Ni t - coin 1.0 PO i 1.0 * *- - 1i N o CO r — **43 ij'j u **'-, **j *i * t *',.r ***r **if **if *ift *if in in m- in) 1. r — 133 cr o ID v-': i r- o ID *kq - a- o *4 cr-I r"*<f \tf No.%-17 r- r" o D~> — 4 r"- 1 0 V,- u 0 (4 11r —.D3 *s0'^i) 10: in0 L U-n u L) u) in in U- ini n u") u") U-n u") D ) u L) i n n i i n n n'. 3 3.D3 r — r"- fr- Co- 133 co Io cr inJ W) in) U`n *<'*IT *f* r1): 1710 0-4 C —4T- - 0C Co C., oCo0oCooo'o oo o o o o o o o o o o o o o Ioo o o D Co o oo o D o o o.......:..:.................................. c~r. o 1N Cq Q Cq- C.-.r.jcr o *- r'*< **t coi o C, 0 Q r-"-) D.o- --'.j3 Ln" r — co **f v ~r — o *- o r-*-r ~co o j3o r — r'- 1n!c- r^ -- cP-417 o.. 0!.Co'~ 4.171 coj ***t o1 -7 * *41: *<fm x r" —.. o o 0 * cf0 (7 4 ^' ^fr- r A 0 co CO -,.Di (7'~ (4 CO wj.3' * r *~ -- co cc, (7i D~ 1(7i CO) COt*}**f r — CO *- i- (4 r-3 Cc, r — ic n ".iriCO r — I0 u-i/,:4.. aCL \ - ^ r C,4' Mrk~r I N 4r. ) un r — oD *- t r-C ICo v71..D' o-C. ID **-'*.r- N *< * % o o iN *ift -*ic **3**..D 0 *.D r — r — Ir — co cco r —"'*Do I' —D in fr *.' I I 7 " l' " 0l u-)'-I,;'.1.-).4 0 -p- 0 1-" ('1 4, 44- ("41 - I I- ("1 414 " ~) 4 -" IN) A N N 1 N c4-4 4 "1 U) " U") r -- 4 -'Ir-.*fl -4-''*-C'i * i — i — i — i — 07 n 071 17n7 C I n 0) 07 0 n (4 C n CO n 0714 (' i-n n *4- j-Ifl 4410 4-4.0 U") -fi dl~~~~~~~~~~~~~~~~~~~~~~-i- 44 -l) dI ") 4- 100 Cr1 A") dIn InV00)4 040 L If D i n CA L I) iJt1 ****- it Lf-., c-q4 r-:ir- r-o: r — **. o **tf r,-~: I4 r"- *f - -cr i GN - o rP- co iN 0 - Po (. - r — in!- r"- r-: r — V) Im.r- co **: ri I,-N iN -1 re) co **if *- C cri o (.n iN — 4..r!,.r o 1 c- N-4 ir'f03 in in 0 0r-C r': 4 %D —I r — r- fl'- f 01 *. II %- -Cr-4 cri CO re) 171 C, 44) v r N _0'.. U-i 0001r —0010in-k0 r-o cr * 3 * * 0 D 44 - r. - Itfl(i-I r C.1~~~~~~~~~~~~~~ 01170:f U") U") T-;3 C A'-4 T -. 001,41 in IN -N'~1 u3 -4 r-' — dl Cr" Cr1 C~b" ) r- 4-1U" i- -CO i — 4-i Cr- 0-fl *< f CO!o'-.4") C O I — i I 1 II r'"lll r"C- ('14 * r-7. ~-r — C.44 4'. 1 I'.i4 - C r1- i-, r [l!c'-.:.I...-.,:,:'I,.,:, o "'~~~~~~~~~~'I ~ ^ ^ *<fin ll' **J3 "- CO' Ci -4 r':D~ C *4y3*-i r- - C ri -r -k U-*3r)' 7i C 10 - Cf-4 r^ V%: *** n'~ — r r — C EJ7 cri7 7-.4 (7i (71 7i - (7-.Ci r CiCO C COr-*)' 4. r l - 1.- -~ b wf 1 -17 -I u I-'01 ) Dri'i' -1' r. -- D' Ic iI ~r-': r —) r-i rq r-.: r 11) 1"i rrjrr)'.t I I1 r-, 3 i'. - r-. r — r — r — 0r — r — r - co c o.4 i. —' ) co 0c co', -co 0 co 0 ro cqr- - o o Cc, 0~~~~~~~~~~~~~~~~~~~~~~~~~~Ioo oo' i A. i o - o o o 0-4 1 o o o o - r — r- 1 ID o1 4 u-iI.o 010: -1 Ici i-3 40 ('04oc1 co 4', r4 - r — IN) c t co u -i c-10 -- c-4 4 r — [r0-') c-f4-") 7o o in ar o I o Io o o o o o oo o o0 0 oo0 oI o o IC, *f i cr i DI r.:i (4171 ro..3-. k. o.D *C,- cot i, 171 j rC.-:, ret c-.4 j6,'r. C- r,)-'. r ":cc- ID r-,'- c. oL'~ r.- ri., L- C, 001, 0, C; C; C 4 AQ 0 ID 0 U0 0') t.1. I u- 4l, r 4_- 0r4 — CO 4 i C-0 0 - 1 -444 C-4 0)r- Iu- "4- GI',7 0 0 }-o i-n 0fl loi U")- A") C I I~ ~~~~~~ ~ ~ ~~~ ~ ~~~ ~ ~ ~ ~~~ ~ ~~~~~~~~~~~~~~~~'.'~ I, 0I.r.I' r, - 4 r -4 _) 3r — c - C 4, o - c- I-4'-I- CA-') 3 3 r- )-r r- r — Ur — " co Co co co'o co co)c ici- - Co C0 c 0 o P, I o o o 4- ^- 4- Ill- i.- 0'4 0I- - 4 Cr1 -7 -C u-''. -. _ U 0:. 4 -ui'Nt A") 10 4 Cr1 l u -i u- Ifi I -f C0 c.7 u- 4li 14J.:. i — 00 U") -'4 I ") ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~'410 4.O~~~~~~~~~~~1")~~~ 41-4 U~~~~~~~.b 1H 4l~~~~~~~~~ 41- 4 — ~ ~ ~ ~ I i-I i-I 4- ~~ ~1 "l r'-0 c " ~I 7 (A'-041C. CA l'.,4 0404 f.- u-i "" lILA r~~~~~~~~ ~~~~.1 00 0,A' lI." " " "l 0'9'' - 1-.'Cl" I,' 4-' ~.,.ri-1" r,("..I r0 0OU" ~~~~~~~~~~~~~~~~~~~~:I I I I' I._~l~~~~ I~.,: I. I I..l "i' ",...I, _".~ I. I%~,: ]O 1..1. i.:..,:: Il oo,_o,~~~~~~~~~ o Io:,?!:,o,=

-257I:- %t r - rI. I I IC J ( I I IL,,.,:. iCA C'' ij I%.t -- C.,-,.0 %: (".4 C. I IJ o. F Fo U j r.IF- - I I c- r'.` I 1 i**..I**Il*lUI' L Fe F' Ii4 C II I I cc, r,,- C.',, r..,, g.. I.7., 1.1.1 ~ ~~ ~ ~~~~~~~~~~~~~I I I I'O G%. I r-rj.:t (-%4 u-j ~~~I.-) - D",b CO v- COI I I -IA O O I I I I I I~~~~~~~~~ —:. - -- I,.. i - U ) 1-.1 "' C. c; I: n - - I I I,-,I IC C I,~ I,: IuI I I I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~- I I I I r r - I r-: I,, r.: Ir ( I I I II r -,FIIi.-L ~ II F I Li 4 C.4iCLirLi I U7 I -:Ii 4 r' I.I 41. I IiiI Fi *j I IIF-E I LII' I I %* IFrI I-I I4i F 4 LI::F-I Ci C 1 iii.1 4 I _jii II I r-'i C~ 4' ~ lli' Hi Ii Ir-i....-11l I~'1. F i ii I IIH. i F lIL i'r.1 I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~11 a x S F-i -.. C4 U..IlciI r- I4r- iF F 4'i.-.- Cei.:j C elJI dLe i 1 ~: I I'_' I C I.1D III I ol o 0 1=1 I 0 1 ~Ij I I Il I.I I. 1..,1D 1.I I CD —.1 I I. I- II I I:, c " 5 r.; o o 1- 1 I- I.J 11- 0 z.- il Ce C:::1 ID ID C I.. C 11 1 ".,:: C:. I —. I I I I I H I I iII II —.I, C I:~ I I C-1 I"1 22 C 22 I I.:::'I I I IDI::I ill "::II j i -i I I I-I I - I -i C ) ii I ID I I 0.. C Ii. C I C 1 I I i::: 0 1 21:2:2 IZ (:'.)I iI Ic- - I: I 2 Ii I: - I"' 1 I: (- I H - I i:-1i C)11 n I Ic I I'I'-IIc-,C. )0 I I ~ ~ ~~~.I 1-1Ij I I I1I IE- F.S c..i _ I- I1I I I IDI:1117.1 1:7.1 0 0 C5 I~~~~~~~~~I.1Ij I I ":I 1 1 - I --- i i I C D I I ID I II C"A.':::I C'.., I r;-, I 17. 1:I I I I~~~~~~~~~~~~~~~~~~~~~~~~~~~DL: i)b)L',IL I I *I" ill. 1 I I - I. j I I l I II I I I I I':,-:ll I I I III ll, I Z "'A 1`4.1 C`4~~ ~~~~ 17,4 C el I 4ci.111 I I I I'.4 %4 C. l. A i'. II IC,- C% I I I II-'.-.J I. I I-:, - I- I- J. I III I I I I I I~~~~~~~~~~~~~~c I I I Iot r- - 0. I,I I — I % I r O tI: i. -- r I -. r i I I.II I U —.I I t I- I C 0 " I6 it r 7. % I _ I I I..J, Cxj 1 1.C ic LI.I.- I I DI I * I~~~~~~~ I ~~~~. I I.t I CI.I.1.I~lL. LI IILq 1I L ii IL y I Li-I Li I LII LI I l I Li lii I I.I 4 III 1121 II I~I ii iii 11111 I ~ IUI I I,- r Q'-.C I 1 111 2:-1I..... I II2I..... I`7' I IIII I r.-I r,",Irq r.,-jC-4 7'. I I I (: C "I' C" I I-..,I A.~~~~~~~~~~~~~IIiI I I I 1 ~~~~~~~~~~~~~~~~~~~~~~'., ITI17:;. I. 7 I-.1 -,I I, I I ii1F.ie.iiijic.1- I FieleiIII4 F~~IeI..c~.ii~ III-..IIF i iiI I Lee! —- -4 F-i he ~~~~~~~~~~~ 2 III L 222 I- I I I-i,,4 o c1h L - I -r -iIII4ILI-I I I I I i - 222. elil-.. I I: L IIt FI,,. l r I I- i 1.-..Ii —I.- e~eel-...i- 4C.4eII~trI.J-l..I..-.I,.4II, r- ryee r.,ei,I I....I.I-II-, r c4 -.-r,:!Iji LiI II I 1.0 I *I 0* C- I I I CO W)CO U Ir I rII C IN1.IIIF CO b-,I1.IIIc %iue... riL I2 i1 2Ie rIiI1 C, I7 4 I rI, Cq r- IItI-, I I I'II I I rI I IUII - Iii II II I I II 111 11 kel r,-, r-.- U-7) cc- c. ~~~~~~I C LeIe e Iee h JNI 41114411141414 14 I- C4,..411.4 %.4 1c0 4 1411 -42 ---- — ~ 14.:' — liI I C -4IC'.4 r, r, -.I-..-... 4. 41. I.41. - -. I4i I.~~~~~~~~~~~~~~~~~~~~~~~~j I LI1.-I -*I * I — I I I iI. C%4~~~~~~~~ --- -- CO r, j I - o-4 C.,. r-,.,.. b- C —1.I I` U-jr.-)0- IC, IIr- ID - n cc V 0 c- "'1 ro or- Ico r- V. L I I.t lu r — LI 0 C.-, II,,, IX., co r D~~~~~~~~~~~~~~j U-) U-) In L~~~~~~j LI V. LI I C%.4 C-4 -.4 -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ IC 11~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ o i F 1. ieol'~ch i cc Li hlcN e c. -I4 liii i -l-i-2 C i ele''l

-258~- *- O i -. j~i *** -: 0 1:f o.i,. j -: [i-i - -G *~i O -.1: **" ji." 1,-1ii -:f **t r-. - r-4i'U" r -- i r-.! - - I I I I ~~~~~O IO,I,,, Ir-, I - (4 j I I C C_-J r^ -o co ~ r-:i r""- ***+ LO' cN-:fj i,:-.i r,"ji r-:i, a', ("A4 r:i,-j r-.- c,-i.1:t.j~{*.: ~ -: ~{.jii"...jN IiA r-, 0 r-},." iii"- r T -1 1F:;:;i | -, (:-.I 0:: ii::::i i:::;O I" 0J-;::0 I: i::::) 0 0 1:::~0 0 0:; oo 0 I"') d 1"') C.) C." O 0 1 D CII I.-.) C'.) 1,Z) ~ C) ID CI. "~ C. I I 1 ii I I Cii I I I I.-: I I —-*I'..i ID IZ I ID1 I Cf:0TIU": 01 ID00 0 5 0 E-60O'D00 00 0 I00 0 0 I 0= I0 "." 0 0! C)i0C I 0D ol" C, 0= 0= la I Iz U. o {.[N'* *-: 0: o r-:ij i n.j %. io'-q IN m 0 -I:: -— [**:f i E~ o.. r -:i*a.-.iIN ij": C:o 4.-^ r- o r,-:i*j i i-. - 4 iriiq j,-. I-f C)"i i C~ o i o i C~io o ]*r- ~i -~~ -4'I N r:]r:.Ar: *i *:- *:..I -tl u'O -U-, LI-,o' -'.j i. r"- i"" r "- r —:1 6 c.:0i-, co.'. I.T.,io |i i r... %.TJ II-,~t r4jj c,%. ".1". i,"; r*-.-4 C,I - I.. - O l I - - f -\: -.! I I L.L r- I:',. r - 11 -— I I I r Z O c f'jIT-. ~*'I - T -I:. l *i 1- 0 u.i6r"l i U " U 1 1 >;; ^. r —:ij *.j~~~~i cojo r -5: j: r'-;-co C.'[ -- - ID o:-4 -.i r.-:i r-'-.n *1'U~I...]ij " co *- %* 0 Cici' r-r- ir *f'L o N niu r",- i<'r.] i~ ~~~~~~~~~~~~~~~~~~~~~I.I.i~'.~'''Ii'I'''I'.'I i!' ii'' r r' c^' r"-4 r" r''-: 4 co4'.4 4 o:: o1 i".'': " - 4 o i:.7.' 1 ci-'4 o": f -."j- -o "'-:, U-,,, i U-.,!'"'. U -I r'' r'I''' ~ ~ ~ ~ ~ ~ ~ (I' 4("4Ir, r-j ~* r" — **it{ 10 **^ **:f *<- % r:-. UO-O.: IIJ:! -., **,) O *- ^ r'i*j:..~ *,: r -.-i o ) T- T. i;:0 r* *t IT i" r7-, i i,- i. riij- * u -. *; r ojr- i o ir- i'.i CIi. r ii oi"iii i i: lt I.,i;'I i:'Ii:-I I r"~ I EL r**., U,).: u'> u":ii L i:i;' — c'-.',4; r *.j4 i'j 4.i *.f -..|..l.- r"- r".. r-'-:i o i:- 1:04 r-'i I *;fJ CD Un oI r" (Z:0 f a r5 r- -:.-. o!I I-t C- cI r"- II.7 E **-o r- r"~ cri **y:'j N ii'c i' * r r"~{'*t 0-* c'-.'t CI.%, i i if"''.1I';'' i:' co''' o ~ re "'%4 II C:,I LL *..N, l i. N. a il i 1 1,,,, > 1, n i 1 1 ~ ~ " **~ ~ ~ ~ ~~~~~~r u":4 ii: i: n i'o u)i'i U':.!iu:i). **."'. 4;: *;:.:i'. -..:: 1.7 1:1 t. **i.. I.%.4:'.f* LI-.0.D ** 1", *.::i'.j: C'.ri*.! I.01" CC.o U-.' i %tlo r.'6.'i..4 1'.1.1 I..I.%~~I F'""''''''F- " i "r':iFr-" co m L'!i iii'' o,'r:f' -I —-- "':i o c'4''ii'U'..1 -U" F- rrs'-4.'>4hr" r-o'N | F-, u - I r a-. r-i'- *<- c'.'% I.".! r.,4i"q %4 I c' —* 4" co co r-4 co',.D i:-%-C%!%4o li4:i **t4 C1',! 4: %? 1 * i.%i 17%4 r" c;'.4 co...-%4 r C- 0 1 oC, *-41:f % I'% T~ - o % in4 IN f"-4 r?%4 C% N 17%4 *-.1 *"I D7 *%Q Q 4 I" L V *1 * * *. 1I - II* 1,... II -C IU, ij I.., U ll *,.,. i i i ". i.- r.i I) "r-""-i'-"' — %i4:u.4'i*,';i (,%'. r-:iJ " (,!::ir co r~** *- C r'~i, ".fii:i " r'i i.-. d,- **;:! cI *t * re):i.":i *;:!- *" ^ i-j ir - "'- I" i', -j * EL rei xt" I "I " " * " " " ~ ~ " ~.- U U ~ I IN 11111 Iii III, r,1 I, a-t. I cl) I' II11:.; O; 1 i.: *:: l I CI* | * *.D c- oi oI T.' r'II'''4 f'4 1: r"" I i' " Li *'I'''''.: co'''''''-'":i''I''"- I":: IN * *r" ci' ~ t*l b-i r - i::! "-j *d,f i?. r I'- I* ^ C~i C~i*''"" ***I't C iN *..:i C:: **! I`-: CI)- cQ LI-j11 *if I0 *ij qr"i CT,|":.. - r"-, C *fi:): f y i i, -,. l C''Z i..: - re) i-ir7,,/ir-4 r *I" r". ^ 0 0 0 0::i Q 4:i 0~ C:i'::: 4::I"- i::i'.ui::iu Li:i C: 4 C "i i Fi F-''O' "i::i Ci 0 ID C' i " 0; CLJ [' CU' 0I'''i'C 0 0~~ Cii'- i-1 0' I. *"., *: 1: -'.. 1.'''';' II,."'..' *^ 10 0 **: *si~ r^ -- i -. ij. r" **:f iM r-:i,- r-': o i:^ 0 - r-' io::i r-,-: 0 -- 0.- **q* CO -: 0 i'-1 O r - " "ir^ u i'. I I -— i —k.4.41.4"A ri1.t4 -j-inii tlI.ui',.41'I-4uu4inuuulF r FF.r'. iuuu I. L.L a lei 09 isi r'4'- F-i) Li' ri L.'iI r- in''' c"-.''''iF- Io r Li C::) 1f"0 f — >. >.j. r" - r"~ r-:i) o"4 1. P-) r-.I.. I`4 Ii: i 1) i. I.T I*I I o 1:I I. —' ". I'. r-,. o 0 - i) I i 0 * i r-.j'. u: 0 r"l I c I I I I r i F"i''i"I"r"'e" "1"'I'lL' LuL': i''''''' l-~ i.'5 V1 fI —lj F" F' r,, i LL~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ L'"I J-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ i i {i c-5 Fo F- I:i:.r.: i' ". 4i U"IF"I',Io', Io o 0:1. 4 o.10r"F rI- 1: L.. i::i':i:::.I -l4 r-' uF -FiF I I 1''C F'- LIF _" I 4 IF I t 0 " I I I F I U' I''IF. - IF - I'4 i - - F" -'- u- I"..;\ ('-4 L i:':''% I'""') 1 7 "' IC) C 4-i' C u iI *t'.4Ii'4'0 4 r'4:i" i" f rC''If o4' 0 ni. *u.:'' 4'II IN r Or -I 1-.1.1. M j -.')C " V' C -.1"*I **f- i~-. r_- lO~ U-JC".i- O r "- int. "**q rf -< *r,, i;' C') r -: o:ir-:.i. 1::::.j 1: r-:- r"-, O C * ID c —) m r-.,j.~ ip r"" *~r r r- C.j,- LI~ ) 1'." 0 - Cr *j i 40'* i... **^ r i r-: co r"~ LO* O *:fCO U".' >**r~ * orr" -: oP %.,;-:i fy o", cq — t re 0 **q i.~q r"-, PQ 0 r — ".1'*1* I r-'-j^ la r- 0- I%! C`,**f "'-d -~ C0-4 *j r 7- > r-~: i r-". *) O *-r,- U: i,'J *j: i r"-.. **:f C.7O`" I U - |u: i";o, ".j.o * r- " f". - I * r) rri r.,,, II I~l..I''''''i 4 Li-IF0 ~.. CI::: 01 1 I r- rI= II"- T.- Co -.'I., — 0 IJO? V) t CJ ~*4ID I.-jC.~ <:-4 0:1t l 10 O -.t - CO U. Cr- - *T * r: 011 CO If' **;f4I ~.% Lr.* r-:i 1 z..j, \ ^ " r i:r~, r rj *< r",-, l r-1-111 (. r — r —,, c r"- """ o.i r-"" oi" o:: I.ri -.o r — o- -: f r o. r-I. o 4h*fib'U-' h r-U Ir- r.) I N.f I rxi r,- r (X) C;,., I:"., 17,~~~~~~~I) I IC r0''"** ^ T 1;;''' ^'' 1:1:' 4''~ 17::1!:r't U'-I CO CO~'"**<'"**I 1^:1 I-1' O."0 O"'1:1 **.^1 O ro *I - C 0 r- rj - i.4 o r-:i r -:` ij-,- in r-.j' I I I ij Lo -- *t C T. T * i:.%-1-.: -tJ o v _': * U': 41 Li-"-: Lf., *.j-i I C CO U:iri. o T ij - ) rT) -- 0 ~* -:ir- O r.j1 i"-j O C O'- * *<f)'I 1L iCr:i*^ru4CO0N C: Z11..,i —.jii-. r: I.j7 o.- n*T IO iC-4 *.jijJr-o r -. LO CO'(' i-4 "J!:.!J! i 170 - Q) ~ ~ ~ ~ ~ ~ ~ ~ ~- -"- - cK-1'."**f C.** r —i **.t r,'J: [r' u'" ii't".4 in *j U-j --',"1 *."'<i.ir- r- r-' r -"r" ^,.,ol 0 * I' *' -]' jlX~~~~~~I I oID, i -.j ^, ^. ^..-% i -"- if-:, o **:f **:f o'*t'rI \i.:i 10, i;M 0: 1 i-:i r — - ***T4 r"- c~ I-T:. xiT - uji:^ *^ -.j~i o.;-;,.4 ~.,o C.-jr r- ) *r - - cc I I ^~~~~~~~~~~k" I.J o. - Co 0c. 0Co*0i:i0 000Ci00OO00:iQo': C.i -i 6r-i 0 0ri00 Li "..........^....^ ^... r%4 ('*oD. 1,'f l~ r "% c Li'., CC C C, p C"-4 r —: -— t % -"*:* Lo *.7o VI r "z-~ r -- D". r-: r -j r-j.4 r,- o rco *..i' i- - o.t r — i r. — r o -- xt~.* Lr — - un' k.i f- o -r-:Oi C.".f K %D: r-;i: 1:0 ijO 17-4 i:;-, r:: o.ji- uD*** r "- atCO,, r,, -: i:0 -ki Gn.j, T-i01 -i ~i. r"- 1:0 ~T-. IT-. 0'N *, *. r- O l; — 4 *-f,.O rr [o i —A *.~: N *:.: *-:'- -" r- *- *.0 >.' L^!eLO cr-" r- IT!.r! l rir-.L s-]' r- c"**'"* ** M' -i r: -. r: r-: i-.- INi..f - **+ u: r i.-i I: U: -i U: P.~ e": U ": IN ) 1. 0 r \T.i i U lO L i U - *^ **!C o ~tj:i rn-i I.-:*. j-Vf o. oj **jO 0 Vo ** o`:4 r- j *.c- ir. "j-: r' — -O I ( *.4.: - O: r, -:i10 r-r- **:~jf -~ LO" U- r -.j t r-it7,[... "1= %t. co - C.i-, r"- V Ih - 0 0~ *f - U: N r: -i -: r: u i *: -j o i-ir - u: -,:, r"- *.:i r" r -:i'.j41i r-j r -:i.j, rT-. i -. 4`r-. o r-%i cc'CO C?. Ir" r -: r C O - O CC, h - "- co r - - r-:i - rf. o t -r r U -i -C *.j= r -:i in *11 r.D C".. - r i 1 r "-I I iN i d-I I.7 IoO ~ ** - " r 17 r!0 -^ - N i 1I! rei it.i ii-i u" i:'i *ji*jI.;i *j:.:.j: *: -. r- - 1" rC " ~ "- r"r-.0, r-4 r i" " " - - r- r" r- r- r- r- ^! 5!i { " ~*4 -j c-4 -j i:j:-j:- i i' I iN -* ~ I: -.4 N rji:- r:-.[ IU *N'I.!-N-'N ~ *4':- N * I' —-*.EN j -j t V r - 4 r-j IN iN.T I'y r''" ^'ri'' ^ c:l^* j'rl:":'' " u'-T1 I":t e!0! r'1 "* ij " <- ^ cl' 0 I!!c ll *J 4CO 0- "O 0.~ r- LI —. 0:1 U. I" 0 " - i N C1 L!d;* ^ r"d d j- r- f u ^ * ^.{.-;,'!j! ^ *.ji *.~i r- r- i —r-C'Cr"-r r "- rr 1: 0:1eo co co ckc-Jo -:10:,cou-o)couo *,IIr!. u:rrr ij 17.rrcc10 o i6 o o o!, 1:+ 0 0 C, ^ ^ ^ ^. ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^_ ^ ^ ^ 0 1'Z. C%. % r, I,, j r ". j U

-259II F I NZI a I: al Iu ( 0 1 1!< %@ 0 z ol (iz o!N < Oc. |Z 0 | N r 0 co 1^^z, j < U.,i i: F I F F F F F F F F i O UJz. Cj >, t I t-4 0 -J t W t t ia,,, <* X Q U. 1<i ~ t < CL+ ~1e S: U! zt*l!!i 13 o Jt.j F o l O I FFFFF IU I J J IL 4 CD |o F F oO i', uJ,w I.~ ~""* [>'. LJ1i F F I FZF F F F F F F. I F F..=. Z I,l F= I F F FFi F I I~ I'U. i OFFF FF F I;J 0 0 ~0 I (!!4, I F o II I F F F F F F F Iw ~. F I 1 1001 Z 0"4OF0, 0 Z > =) I cc C - F N I 12'-u 4 IIt I4 o a M >I I o.,i. I- I I ^ ^^,~-lo 0^- ZQUOOilo I ZF!woo 2I uj uj auIc II. U.I'I. >CT~^oi(^oo ~~~ ~~I i.uj.-,IW 4;.0uo,I., - I I"~ I.,=l S I 0t I 0 I I I'm U!,..I. I q I U. I- Ii. = 0 el MIN QImiI 3 I UJI i I. 0 0' 1J:I = 1 I.-, 0L C3 0

-260I I i I o0 0o 0oo 0o 0o 0oo ol N Ao o ooo-Iloor!0' o 0W'4 0,0:,i Nn f::0 (In - Oic' 0 o co N'0' co0 oo oo 010 0 00 010 00 o 0:0o 0 o 0 0 01 0 0 1 oo o 00 o o 0 0 00 010o F4" o > o olo tin tin O iN. " ".- o M MIn Co t I I I N F O loo: [ NINO..:o. c.s ~4 }41 oo o o I- - o 0 o 0 in [ o ol oo cI?, I I= o! t I. I I I I! I I o. I I r 0 I j I, ~! sI 0 ~ I Ite I t | I 4 I I I I I I I; I I; I I I I I I I co o N. I N I Im M I 0min~t~OCO~00 0M0 ~0 ^i 0 ^ in I 0 %+i. %t t i 11A I0r1l"4NN i-t %t t -4- 0 44 st lt -4+ 4 10I: l Mll 0 n0 0, o i - 0, N,,.a' I' I i I IC) i N l'0 I.... I 4 0 0 O oN 0- 0 7.% IO mi 0'I- f-A.1Ni'l 00? CY N -5 N~D 0o N n 01 0 co M?1'.4 0'a N',0 0 I-5 05 co, I?I' - O M LOAIN N 0 LA %0O N 0 C "NO IM 0I.. r$0 4.0 LA,7'- o l. co N.... N LA { N 017. LA.?. O e M10 L 0 L' N v COl. LAO at,0' LA O' Mi' I0 0 0'00 L" l: el* o,o ** * *. 10 * o~elg~g 0 *.1. *I* * 0 el00 06, ll 6 60 0 l, N 1- 0 01 0 m19 Old N~~~~~~~~~~~~~~~~~~~~~~~I'l ial oof0if1tft^-o0c~mjoowoo~fM~ioo 0{( 0 aMi ~ Lnj0 ioc o ioeV PI'' *cII * I I'I%''',1'co'''j' IC l I(9 nj6 ~ 9: Ill' Ill I l I, I:I' I ~ I I I 0100 00 CIOi I0 C0 0.LnIu 1 0, I I0 I I o I~ o,~ o,[o,oooo o. o lo ooo o o _Io oio ~' ooooofnu~rI^f~o~fnco^^t~o~i~o~coj(Nip^{^o<T~o{^coMtlf(,........ gIacII~I~~g9,IIII I I I I I I ~! I IN- I' i Ioo IIjIoI IIooo oo 0 o L } 0 0,10 0 0 0 0 CIO C "ill' 0I - - C" C- -,jd' j1 m \. 4 C l cll N ~ ~'<".~N NI:~ ~!'l~ ~l~ O,~,,~,,,~:-,-Y N MN I.'I.. 0 0OOiO0O 10gI 000,00,000 0'0' 0j [' 00 010 01000 010 0100 0 0,0 *0 00 010 91N 4 L'9lo 01- N a 0 10'-'01 r'1LA N IO.5 0'0 N (5 0 CIO s 0 0''o nLA;t I;P4 A4 - lc Wcco WW PlI-P1- - n4 - 4UI I I I I c c o lo oco co ol o o oNo olo o o o o CY I c.* ooooo looo ooj 0 01 001 00 Ol ol oo o 1000010 o0 0l1 0l 1 Lo OILA,?' 40 fN.,4.:. N,0 0,N', oi- co i, 7' 0 7.~4. ("57'-0 ".7' -sfr4 00I4t 0001001000,o0 0 0 o:,= oy, o oI o o a o l o irin lo4if <o~oolo rso~ iolo'lO4.f,,0 01O0'N,0- -si-s -si-s - -scooo. - oo i. N'[ N.514. Lb' 00-10'>'< 0~ ~5-s f'0 0 l0 S * 0 0l6 e 00 0 el 60.1.1 66.1..A. o, o' 0 s".60..10 #I I00 l(~ ] ~ I! I 0I * I l,I P If- i M <M MlN -I?-Pl c I I-t - LAI 0 - co co c o N I PO i iy~ tn i(Y to i4 i;4 j7~ CY% jt co 0% 0 i ji i*, 0i o I%.!- i00;i CY, %M i c 1 o ie ~ - - m b..d,.s -c\ -\f\ i sb..s."s'in ~i. -.-s om~ b- ~ - p~ NbN 4.b7'. 0751 t'-l..s'0,,'.5'0.5'0i~'0-s 10 LAtaC 4. %t 7!' Pft 04 %t O pIN'0 4.0 NfrI5 I' I jI I I, I I b *b *b*< * 1 01 0 0,0 1,00 ~1o' 4.I0~N00el e l Si I 0 L 0 ("01 - ". - 0 O Ni7I I a el. N f0' NO 0 0(.1 CY,.1.o0 oCoY s Nsgo ig g W b oboUoB o 1,4 o oo 4 CO 6.010 600,- 0 N r> 10N CO!o *. N1o g 00 I 6,6 6,0 0 1 o.o o n.t 1 t 010i s! OOo 001 U, o!o 00olo.0 o o- -so N0 [ ooo'I oob ooo'- 0 - 0o. Nop o o l - o - so o-I LA LA LIL LIL L LAL LAiLA O L LALILAo oLA' 0o 7-1 OlO'04 NO O IA0 CO- a',0:. C0.40 LNIa'r 00 CO nO ('-("507'-'IM o o a'ob 0i0 0 0'b0 010 0O: M 0'!0 P-INO 0' a' o'b' I"!'o 000 O io -loo OiMoO Mi-s - sof M r..s- -Ai, -:sI -4 O i 00 1 I bo, ~ ol 4010j 61i 6 0 6,,60 *b! Lo ^* oo k ('N o M 06106001 * e CI( o ib.oo o o[o 0ll"'C00 U ll l' 01'00 o! of e l 0 SiI Ie l I I.. 0 I I I I I I I I Nbll a -,4.i~ L 00" LAt NCo, llf l o 4. IrilAM 4.7Ia 7 LA44 ~OIN (I,0N''0,Lr- O i(O NM o ao' boLAOfI'N 4MIl',o IN 00..5j^^jcsj~tN0"0iLA7-b0' 0-s-si 0'0',4.00fnjO^' Oia'^iONO~ir~lA'0'0^OLA ^0L N' I= obo N}f v"jnoor^ ojMio 0 ig. N oljO0i0,o60 Oio 00 16 0,000 ooo 0,0 o0o o00o1a6!0x*co 16 I e,. e - N OILA4 - ~ 0,0.,0 I 0-s LA 0- N -s (-4 -01A -40 —s4INO;0'L -s iO-sL oIo4.1No'N IN 0o o0 oN o' OlON; oi o o7o al o0o (lO"o1 0'0k' lOA 10 (-4'0f-4 -.o -{4 01. 7-10 ON. NN loNN -l' l( OI I,-01.-I i —gl, o liooo 0, 000 00[ 0 gIgjl l 0 000'| " j': 0 *: 1...{ 10: 00 000,0

-261| I II I I I I I I 10 ~"~ %o AM 0o!-4 LIOo'O co Nium knmQ^ o.- Nf 0 NlcO pMO? - oiO Mn~f" -- (-. o1o I I I a Io It %t 1 co{"4 mo a -4 co I I s IO14- I Ii ~i M co o o i ^ % oo' r M o{~Inl- 4 f% CM N -4 iF-4 o10 a (j t~!oo o 00; r- I-p- ( —If P.- r- o o' % o lo IC 1,4M M N fy N -(U N' Po, 00 0 0 0N0 01Oi 0 0 0 10~ ~~ o'o o o o:o o1o o o OiO o1o o o 010 o1o o o oO oi l I^ ^(!pr~ ^ 0 I t m r o ( ^ I 0! o 0I' MIOO I I I I I I iI,- %tir o <M P-4N colo fM o in co (Mien " -N< I. -i<m P40 *-4 P- m'%M 001 co m- m- U- nAm ICM COIN P- ~o cp'o CO ^ OIL L) 1.0 { <0 j (OM O() N! <Nipt f<( p^rQ p0 [M ro- r^ c f 2) I I i I I I^ I-j- I^ ~ -4 I I<~<f; - ~ |~<~4|- - ~ ) I I I ~~~~~~~~~~~~~~~~~~.I I I I I I II 1 0 4 I I 0 I # I I' I l I,'co <Ncs PM Cy,! co l 01-'oco r-'co -O m <-O r — o!^ 1,!in M o (Nr-! (NIOc N'O 0o ol iOD ODIO o r — M O!4 <% -. OILM fniP1- pN M\ %ti ~-<< CO 0% <4'1P- LnIrs co co a o II fim r k!< Poll~ co i~4 NoirN P-A o Ini< 4- to oo P M is NIN P- t Ln Prl*~ in!^ tr* o^ 010 I I III I II* IN -&Lr O,% No N I 4 1 14 0IO IN N NIP- q-1- LPiN4 ~.N f U-A U-% Ii tn oo lin Wk. nt %r~ %NO in c NJo j M nr " ON M ~ s'if OD< o loi I(M *I*d 0 [ M ~o m * IO 9 4 0 N0 N ** c 00 e"- 1 **"c 0 5 01 o0 r - 0 I I I PI 0 It[^ P- ^' < 0% O i~0 I 4 O,M M O co{^ i n r n4 M - I o r - I i( i I I Vol O I" — V) -t I co Ii I o P-4 M U I n co Ico Ic I i I I ~ ~~I II I I~~~~~~~~ 1 1v4 - - -' -4 P4 4 - - - 1r4 r41 - - - P- 1 t 1 I t I I I ~ ~ ~~~~~~~~I I I I I' M^ oo'h" %o Mt km M I n - C j COIN tnt t M o^ o ID 00I' i 010 ^> r-4f I ^rjn ^[i Nr-N % n ooic^ M 0 r*+ m LA ON w NIM f so %o rojm ^\ r^-~ rsj M s l(\ IM0 (7! -4 00 OM o!0 fCM V<11 ~~~ OO1- i4' co ifnl-r CO' " -1co I N {^ <MI" CY"< fsti~ 0^ (M4%O% 0{10 INd POIO co fN cnol^ <~<i<o r^ O OC 01N^. a < o ~I}- ~"<icyv io+ n (M. N woll P-4 v-4 oi 0s- <,U-'t M MIN< N00 f N o 1i~ -4 P-4" Pm oP -4 (i~ ^rirsinrtn -p ~ o0 Cio.0%1 a OOO ai,~O ~ l f 0 01P oo.4 V %* co M OO aM ior'ooiot %Mm} s o I M ool' %O~ ^N1 A icoU~UW - Io UfN] o0 o 114- U Wo t~l U j-4* U' f0~I A M L'M K N U'i^ kA - ~ Noo N N9 I I I gI *IN0N N 0N0 NN NIN N N NNN 1 0t 0OtO SS0 0 *I0, 10 0.010 *1- esCOe r*h ^o M N * fn0 r mI- s v- N C14 M N <!(A — t[~ N - N M C!^ -([1N 1- ~ tC r ft P-4 IP4! -,O ~-<tN - 4 IL0 Or- a~4N oa 4 nui t %%Ir- U PII- tO I *tIOU\4 osoIs" tI. - No- o'o o o- of o - r-r- o co c - o oio, ojo en o r — -4 co o. N~ N ~ o o+ I o0-0-MIoM NIN (M(t N f-s 1 CiM CtiM CM NM U-1C%'f rsJf A LA #-4 fst LniN CO CM4 N<M~M CM'CM (M CM 011 o, ojo M o ojo OI oo looo o o o-4o 0[0 o- o oj o0 Ml, U~j-A'O co M'So o o1s4 %t %+ ni Ior In % c% 1r-r-t-t. co co.,' cot oo co c-m o r, Cy ml, oi4 I I t I10 I P] rjo oo oo t \ 0 FQ -oj10 0MI 100 M M o I t t ~It M lo NMip't" N NM r*~io ld ct o tM tn] m t* c I *D in If7%.OI M r-4 N0 fIO"ul 1P4N 0 oIl.1 O",1 01%0IM N11 INN.-4!0 NMOM0 It t (7 ^*if< Co Co 0! COM. C COI! - f" P- I'o P\o o* P- 400" % t! % 01, (M ^'O 4 ~ c cS' I U-^ LAMO la, f<^ii t co ~o -4,1~~ u\ fn o t — - a, m n 4 o vr' ^-ifq tn oo ooo ooo o y f!1 4N 11*M 0n in7 N N i4410 n O N-4 CNO inI o o cOtit UU-,r- M co'O NIN o No "4 00o L4 f~ N M. en1 N^ co(~~ cot- wl N- r ulf -4 r -~^ 4 r-4 ~~11 o% u4 ~ Pj- 4 N ^ f0 i- ~0 t )* 0 n ^, r~( P~ ^l0'vI1 1 N~'L0'4'4 U)~ e I'IN M*I0c, "t'' M McI-INN1', M - 19I I N I I I I M I IM OtiM' r-4 N 40 c %o -tjio %in Mo fUip -iN^ P-~ CO ooim %o M N" %in% Moo mi %01( b -4~ NOC 0I 0 N 0 - 1 N r4I OU NI0M C I - — 1U O-4M1 0C IO N I-. Z I - O c -,N, - " O O I OI I I1 r4 N N M M M Is % I I I I II'II I I Ii 0 010000100 oo b MO s000100100im0 010 o'onin^ ooo0b^oo 0,0 00010 I N- - N NIN- NI N,- N- NINN4v-4 -i-1NNNNIN N IN. N C N NIN NIN N N Nb.1 co* 000M 0.o.0 0N.10 0 co 1000 (000M o 0001! CM o' g^ * oetc(jf m 010^ 0's 0 ^r! *o no ^IMCI "m( fQ't rn M) M >on.'O 0 0 -4 N~ <MJM r- a, t"[lo tit —o co? 0M c{p" N.o U),o^ M o IN o oono I(; <M U-\ I-~! a N oi %MO olo NM UN P-~r c!o 7oc -4N11M r^'o o't CM pr L \o (M elj 0 0 0 ^jCM eli s0 h- t0 O OMOI 0 0 0 el^ (M< (M $I ft 0 ~M4 04 0 0! oi in II I c I I j M co'm %to r N10 o 0c Nnh fMo ntlM mndM 0 No s Ino MS (^4 Oro^'O;~"'O[c o- o IN ^"'< 4 N mii c*io o cM n ^ m ><( iio r*!r~ Io oI, Lon 0s' Ln M o mi M N IN — 4 -4 ~ ~ ~ ~ I I I IMmiN r ^I ^ p([fn in~-Io 0 LreO" Ot kt rol (M %oinr%.,o'o N NtN (Mp i'4l0 %O >t' m "4<!O'tM o0 0o C'lMo 0s~ No f ^' 4.t4. L'In''0''0!^ ^*^ ^ 00 00 00 0[r Ii p -4 In — i? 00 m ~ ^[ nc dmC|M MortNc f4Md N'0 "4!'?0!o 0 I'o~ 0^ eg^ eo 0 steo eio.0(IO *l i"- ole 0 o e el.^ 0*9f gg ele *si g10 oo * I- I "4 "Ml<M -~'"<-Ij-"4I~^i "4 41^ 4I< "4"4l^ -<i~ "4.t<~f.f4l"4^ ^ ^.^i-41" *-I "4 1-4l * I I* * * * ~; *I I~ ~j I I * * * ~ ~ *; o I' In o In~ Ini Ino ii j n oii n~ n o U O m o i (M <MI< Io ^ 4jn (' ^ N[0o i^o o "<"'M( ~'"'-m i fM 0Mjf (M IM I\if.M1 Mrl<~< MC Mf nrO ^ r T ^ PI^ ^i ^P

-262* o *t -e< i oI0' en^ Cc 0 *4 a,. %O in foo ** r- r — lr< ^ rm. M opm LA ~ t!o M lo, c*1W F. 4 of..J ~4.0 < I0c lo' 00c' o M 0 0N IOI'< Oio<N.- * P- oo 4I co 0-? -o o;C 0' ~r o 04 o^, Nco cv 01 o *: -t Ur u1A tn.40 o o I- I-I*I I c 1>00 e* e 0^ oi 0 0 0U. 0 0 4 I 0 0 4'1O 00 0 4'O a0 0 N I Lfl!~ 0 N 4i! V 00 0 0 0 IL * -4 o o. Cy o- No oD ol o 10 op o o- Co "o!o or o o o oCT N.o ( o o4 ot It o o lo o. o' CO i-o o l oo a1 0 ol SI0 0 *0 SI *I0 00000 10S0S0000I 0 0.0, 0 S0 00010I0 00SI0 I U o U)i I-m 4 co "4 0 m n c o I0 ~>o I*0- I N I O I A I I o+D t i m I rh I I I04 o Q IZ O IO 4 I O ui co o o O I I inI I CI II( ^ s ^1'i n!M r~" co If% or m 10% oo1 IMif O.QI o No M - to 0 o oo 11'. o!m.q 4P (\t lo IM -4 0 ^ 100 10?I A I t I 1 1o I 4i1 SII i I S I i I O i ooolooloOOO C-IOM 01 o-1 00 000:4 M OOil p 0100 IN -4 CO IL o r- tf in 1.010 004 1 i I *o M^ LA f1 U' 00 CO co Pl N!~ 0001 co <^ 0 0 O1O O 0 hi 001M 00 0 1I io t I't Lmm 1 Pn in NT MIcontnoo co 10~ (M! co r-" ocor I~i rl(ocr- fl- fnooior 4 I LnI 0 mn O', i 00 pn I4"! i1iOI co %O I Ioob 4% f oif0 O S. in o o0 i0i0 tn'n 0"INIU LAII 000 10',.O'0, Lo I lo fcv ( N"fS (NfIN N~ <N Ni< C MN CMN NIN C~ N MN NIN'N <N lc NIN~ N (M NIN NIN'i N CNI<\f N CC<iNN NIN N {UJsT ^culu Vvrro "M P"'j r~ P " 1~ 1,11 %U kn;<y " Vw qn^ i;n WI! g~C j-4UJQ0 iro %Oy M~f ON r. ILJU 0. 101.co (M elooN a olloo 1. 1..*..^ aO m'too ^i O Mi~^4<co 0100109ONo0 Li M % 6 o I 0 I. O I D i I i O 0.a% - I- I I I Iy I'loI I cy I yr —P L I ON Cy co I I - 0 P Ic coI0P M C IM OIP- I I " I? Nav- I'cI I^ Irrl Uli N I I o- oI)OiIoIin N!0 O PM % I I: P- 00 C4 I) In I 1 1 1 Co 0_ I I 4 o I LA co I~ N l\ oo im PI-'~ (N< o io M o oo O co in N c O < ^ co ^i\< tn co m cpo 0% O^ oo',P F- P4 N^o N!Mi't<4 %t~ I-* rt st -t P —t -t — lm m i lm NJ No _I i %- 4 c OM M m% -,F4P " NI 0I NO-4I I I 11. Iv'- 1 P-4 K wmll r-4"4 P- r P-1~ P-| 1 V~41 f-4"wl F-4 ral-4~~[~ "4 P-4~~ P ~ ~"4 P-"( ~-< ~~1 P-4'!^ ^ ^< O N "01 N %ti 4 a Oiq^ ^ > tn ~4 0|N alo N 6 U,0, —ii (4'! iO0 o 0?I. ~iL0 04 LA M 0I'04, I CI o -i<4 C41 mico Zt tn oU-, m4o ir- r- oo co" ol - lo* 0 i 4 N*^ N Mo IM oo+ lin-i rO m0 F-ii co 10 0' o Os 0 0 00'U'0 011%a 0{0 CIO 0 0 Ui 0i0 0 0 0' Ol"0114410" i P40N N i 0 0 0[Op 00 0 OaO SICoo 0 0 0{0 001,0 0 O O 0 OjO 00000000 0 0 0. * * *11 I soI"[ IW II I I I 41 ~ Ico io a^ ~- ~ P i-# o t 0 ol!oo o oo N M Io I- 01 I I I0 F- oo c ~~~~~~~~~~~~~~ I~~~~~~~~~~~~~~~~~~~~~~~~~~ i.0" rI o O 00'4 4 N0 Zs r-i < Ni 00 LON M010 -N 4100 - I,'- 00"4.O41 %O N-< 0' Pt fr-s rIS 0'1 -1 1~. ~ ~ ~'I0' 000 "41 %+Ni- 00 f 1. r"1o"0 " LI CY. O PI'O 0I00 N 0% O0'k C % 0It 0% CO s I o >Q CM 0% 0 la VI cO'O r I(0IN 0L010 Io IM "4 1n,O!<t - A NIN "100 o o 1 I <'1~ C )O oo 1 SI I I l l II e I0 l INoo O M Lm c, I o o qI NNo N N1 I o!^ 0 o M N'l~I~'.' ______ N1 p- o I NIM M!< 4 im o o w I @ 1 9,00 I9 010@0 I 910A009 II10I 1 II I I 1 Ioe I o e 19 100I I I I m in ^!^o'O i Iff fs N *0 1 n'oo el < I. N f o fM oj) \ IN *" N y ~ i- coii'JI M n <Oii 0 MI st' -o o^' mi0 o-I — i U- o %t m o.!< 0 40 mi I f I- %t * rI!dn c o OIN 0 t I" 4 M 001 0'0 CO% 00 IINNIIOO rI o m I IN't oo c Cy, mOcM r-'t o 4 o- o r- M r!4 1o N 00 I N'I in 1M Uo~f P —ON co M Ic o I 1 0"I N j.IN -01 NOf' I M C I cON v 1 " w) O0 NI.o in ooo M - 0 c P- r s 0041" co4 No in 10C A oi@ as n.0 I a 000100 100 0 0101 olo 000100 0t"W o4I"4"4"P I "o 41!o CMN I7% 17! 10 r 0 o oo N o O ISI el 0 0 0 I I0. I 0 A Il, S el I ISI I I'. N N^ 0 o iNi co co o-oI N O', oN I.- PI " co!~ U) 0 co ifM t h —tO N. N, fim ^<o' I ^ U oi U ni N% Mlr 010 c o N \ M t o- o- r —!4 IIotiti o 1^0 F () o o - r~m oN co w i Cco F-i 1, co a, i m N m o IN - 0m co!o co"fo o (M u "{i- t I!oi-o - o >i F.I I I I~~~~~~~~~~~~ in ir-~ rM^-,1C (Ir,tn C* o1ic P- C) v-4 I (^ M N ()0 f1i M N^ ^' 0 ( " 4 % 0% %t v" 4 ripm N^ %j If*- %O ^ l o oN %O CO 0 I 0U 4 CO CO! 0i^- 00 N M]M %t U) v-1 v-.o iM' 14'-I~f ^- ^ M*i%' o-!40 a. LAIN 01i( % pn C' rs r-4 I I ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.I II I c^~~~~~1% r4- CC)ic Vn-o n r- <\m1 oo o^ v^ o n 4 o t c N,, r —( o!<40 in 0s 1 O' 0' N^r* — t jr- oo' clo^-t~C C)2.1'el I I I I I I II# 0 e I I I o INJ I-<!~-~ I~ 00 ('4 in I- c- I i n co i. 1-4 ( t o4 r oo o o 0n:!<- o C tn cL o4A1,0"4NA~.4N..01.AL o' 4!.\ LA1"4 o.l LA LA'c oko! LAIL ^I "4I[r4 in0\ Ioo ~c oi ^rit>i^r<i or~i' nr 00-"."4L'0!o0i0'"o 0 00}, 00[100, r 0 I4LC01oo c000' 0 j4 00P 0 N 1 000[00I0 0 IW. LA Lol.0 00N0000P0 I1 0 NI4. 4N LA'~N LAI7! o u) * 0% f-41 N %4 0 < m!(NJ 10 Co o c o 1l j co (M o r-100 0rip >Q M Oc4 M A,0C rac <-IP Nt rn ini, u)in P. a, Os(\ No' ft f* N^c 4 10 (41 la #- ^ LO^ ODo in (M -4u C)OII O NILA ) 1' 0LI0 4- ~41o,-1 N4. i t't - t+ Ai n1 no OLA 0INI'fILA 0' 00 * 0 * * * * @1 C @ 0 91 0 0 * * 0 *j * SI @ CI * * *CIO * 9 9 010 @ C) 0 *10 0 0 I II O ".4[- co Cy C)M o N M P.- I ir pr^ f^t <4{n LA st I 4 %O %n In inOi %n ldn inti in' in 00in- 1-li m!+ N4 N4 -a4 1< 0 -0t I I I I I I I I I I I~III ooo < h^oo M ^ooo io"4I4" iNcr^ o^1i4. o^ O<14.4.LA AILA'i'o t^..r.rin oo00I0 o 00'0'0'Ioooo f4"4NI? Io. 09 94' im 000 @I.oO,, n10,-* o0 019 OIN tlm 04 m N1,t U M Lm %O zliiO M NM 010 0 r00I4- @-0 I I o I N, N n M tn n oi o 4't 1 r~t't IL L I tn I U? U - I F J LA tn Vn [ln'n' <4' I N I ~ 1' IN'' %''! I I 0!" < n 4'ininCM ( C <ia ^(Mf^y- ^icLA i~ Oo0''0 04'~NL 00IN1" Ii^- 0 o I'0010 in'0L4,l00' 0I"4A^ oIs Ino IZ * *; 00 I * *! *i 0 *0o ** *i *1' 0**910 Cl ** *; *0 91** I; @9010 Ol @ C uj o o o<-?iinLoA-r"ico o 1N o 00i.!"CM|(M 4.'01 "' NO0LA"'00A o I~p *0r ^o< ~~ ~mi I I< Ij h! ^ r! rioo ooc I Ioo'oo ooloojoo ^ ^ir ^t ^o ~ i - ^ r-4 <-( r~4 1"41 r"4NNNI Y4 f4 <W4 1I4 4 I4.- - ^)4~>~- ^- -l-<^ 4l~.4.~ Ir ^ito r Mt \ 4.. IWIWMI" IM IN I

DATA SET C REDUCED FLAME PROPAGATION RATES -265

-264o'i jI e W. le I I c c I I 0 1 I I 00 I, Ik UJ o l, o oo o, i I W00 I O 0 -"I I |'0 00,}0 l| | |,II | i | 0I |_ 0 | NJ |:, u.. 1 I It f9 9 I i IJ I. I U 0i 3W C, IIMI 3 QI l- 3 J O t1 l 1 X LWl I Z5.*0 < OL 31 S: 2:lo LLI (^l^ l -J l l ll i1 WII J J I 0,, O I I, I 3 3' i-J IU3 - o dc -aj,!!! i 3 01 1 II 11 ~ ~ I0. 0, I Uj I -1mis r~e O o' o' I I 3 3 3 w I 03.11 23 3 I 3 3 3 3i luO 3z It I I ii 1<'1 1 1rs i v" I I I I | I 11 I | I -J' -J' i: ~ - <I I 33.3 4 i o IU. I. I!," s S! B!zo o 3 ~0 0! I! CO! *I C oI ~ 1 o, l O] 2 1 1 I I V c^~i 3 i NO It I Iti I I'~ I I zti I 3'1 W I' 11 1 4'' -I eel 1.3t.43! 000 0;,, "i,I, I30 100:. I ~-IC.~-I I c~Iz 1 I wWWIWW W-I Li I 0 - { > 1< 1 1 1 1U1J3 IU J% 0 U I 1W UJ u L 1 ~)<i I I 0 1 c i 0 I I' * I I II I I I PI I!!^5 ~~~~~~~~~~~~~~-' I',I.I I!^~a. 5!, 23 23 23 ~I 1l o I II 1I I I~. I [ I,o ~!,..3 3: 3,.. a u> 1 0 0 i I i 2IW>1o u. I 10W: -i U IJ I.'0 3 2iU3) >.-W l-W lUW i I=J 1 0 4'I0 X i 0' 0 I I 2 0 0 1 <-!==.J u 0,W 0 3 QfifX: QiUJ UJ X: <I3 I 3S,,! ISJ3 0 J

-265oC o!o o o o',o Io' o-.a CIO;o... o!+Ito,oo o M! C0 ooo!o o D ooo 0 o O i0o a c a o o ~f O C 00 0c s~ 0i 0 inN <Sic C^ en 0oist 0:0o' 00 o CIM'O 10 I'- CO 10^ 01-41 oo <1` f1|4'LMILo %n P- h-1% 1'f LA i - t o ti oo ro;o:0 c~n o te - no in. oo m Ia0 0 0 (MI^ r^'O 0 -i <0] oo if- <\ 04 u 0000 o01M0001 01 1 000 0t 0~O ^o?- f~}- mi c0o i010 0o ^ si0 ^ ^ oo0f josi r0 j' ro w I aS S S SI SI 0 I I 0 SI S $I 41 I IIS I S i s I * i Il C I tA C c%:N -O in I( N!<t M o P 1 4!c - t m'.4 1 - r- I I IN co n ro!( < IN U o!m 4 IN oo c o I I Mo lIon'-i oc4 I I1 i | I lit ( jr^ ^ (^ I}p r ^ - 1 I N I I -i4 4 0!I r i-m in o000NOc~,0, DUc~-'t in!-4t 0olo o os^o-i!t inioct^ iooi -u^ nfNi C7,O ii\ ^n ioo~i, r-. N ~in n~(:BMF'r-p iN 5 N Mo 0 M r oI o:l l', IS(a i fS of S It t I l S IoiI 000!00iOOO iO iOOOO!O~iOOOO!00!^^0<^OU^!^lftfSJ<^i~rsj[^0(^flO~n!^^{sOO(\J^!^tI I It It IM M I 000I00:0000O:00:0000I00 ~m 4' a 7~0 00t- C tl- 0' 0' N O 0 10 O — M ~O' 10 t1 1-4C tf'- N'-1,- 0" " ic L a oI o en 00 00 O 000a0 aO0 00 04 o 010 0{0 0i 0 0t 0 0 4 IA O-4 N C 00 -4 O-N U I -O: Nt Q't NO IfI- %O N I -t U., M I -NIC 0 00 1, O O 0 0:C - tS0 0 00 0001001000 01OIN0 NI-' N N'N 0I rcm r o 14 MVr (7 r4% ff'r %p 1'r 1, fc- e4 P- N 4 0N N cg o N 00oo S 0 0 0 0 00 0 0:0 oi eo 000 oo o 00! el o0 S e S Io 0 o S S n o S t S! n ^ SI ae l0 0 fi0000 0 000 ooo1 ooioooo=ooioooo *oioraooi~o~co^(^(\tcor~lco<~irk<^i.^r~i^^co^!^ooio^<~'<~if~iot~iiO %c O C OIl O loIO 0 0 o!0alaO000 OIOIO.lOji -O O<I-pOOO[0[ N O N P-N 0% LA I I co 0 [ Im M co co iN,.~~~ ~ ~ ~ ~ ~~~~~~-.iNO 0 S 0 J O SOI 0 0: l 0{0 00 of 0el 10 0O 0 0 0[0 OO 0 0 NII II I 0 0 el00 0 I 0~~N' ~J~ON.NCO.-4~ O~~ U~ 01(0 ~QiCO'4 ~ CO'O~~ e~ N1~010%0CON11 ~ Or'~~-4~%JCON p 4 0-C NNN 00 NrfI 0~ U~IO ~C'4'.4O.-N ~ Q%~~~'I4~ 0 "4I ~iNrf0 efi~~ ~~4. 0 0'u~ ON r — ~ Po r uul C NO'IO L( N'.4 I,,o gg g a'Da,O I 0 0' O c I IOO10 ul 0 10 I's~f i I^fjI^^iI I Ii i li ^o~ii I I i ~~w o If I ~rf I I II. I Ioj^' ~ ~ o l o i^ o io 0:100:0 1 000 010 00 00 0 00 0010 0,LC O en O'r NIMO O' N4r- r-IL&' t N O 0 - D I0% Q0I(0 Mi NO Q%. 10 % O N 0~ y%%0 "4.- 0 0 010 0 000 00IO 0 0010a0aa 0 0 0 010~ Oli0- 7 GI- -10 1 0LI, c10N1o UA% ~~ I' y *,. M'.44! aLCO 0 ~A4 oOI a, I~~ 00 ~~~ 0I0 0 0.0I00I0 001000I0 0 0000:99-j 4N 0i -,4O-1N0 0 01-N 4. i IA1 0 -O (1 0 N'0 N N MNWb.4- 00CO — 00010~~~~ ~~ ~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~1...o10< *ejM oo 01..oo}o oo o010 o0100.,...o! po..... I.. I I I I,, I I I IZ0 e lS 0 0 0 0 I0 0 S e 1. SI I Sr0*i l* $ o * III l i* I 0 *l - Ii s *1 (I NIII S I, I.....II I I I I. N....... Io.4 01%Q 11-I U-% 0fo fst %tM N\i( LM< t- -4 Mi - N i U in 7.,u,-'O00NNV~. tN01 in [- 7mL N in tl-fi~M fy -. N fo-joooMoa, iP 10001001000010010000P,01000010 %I l?-Wi -C ION 60,t O NI % 4CO 1CO r60 LA C-OIN MIN I-4 " 0 Oi (1,0 Nd COI 0M, N N LA1 NDC LA7 60.-lO 000 o 0 01t s 0 0oIOo0100001 01 U-MWLA IN01,-0 s C -, 60I1-60 a01 0-41. 6IIA601N(10 A o-0 (.0 i 00 1 j 010 i0 (0 001; CI - C M 1 i* i0 1 M M -.1. 4 0 001 I~ ~~~ ~ ~~~ ~ ~~~ ~ ~~~ ~ ~~~~~~~~~~ I II e I I e e I~~~~~~~~~~~~~~~~~~~',,+I I I,' I I iN I I I I i~ ~I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ I ei 0 el SI 0 0 I 0 O S I 0 I 0 el 0 0 O iO I I S, I II O el O 1 g ~ S < I III I I I I I I I 1 1 I I*~ oo Ir\[cr* I~jiCT~ In IM I It" I^*icy' In I^'l-^ ^iI N o'o M o N IC) CO -4 {.- u-, ~t O co U-i i co oo If\! Ln 4-I LA' 4p U\ in 4t-!c~o4-I o I.U' I-4'U 1 M l N Nt n 0 I U "4 10U"46OIIcoAOl N 0!co 4 o 1 o 0 s01 I C I- 0 10 r oo 4 n U'%U~in T U'\,It U'\cr U'\ o^ o^n (^In VA ~o i l o'~ kQ6 o rsj [U' w\n <a\ U, o 1% ^- <4'!oo fCj, 0% ro o- N ino' o! Lm %O - oflr -l- CO 01lo ON s0o V^fM4'' o l4<j 1o~ o~o~o~1o' ~III ~O ( 0' 0CioQa 0'I.: 0! 0, 0,, ~IO 0,0 0, 0,,0'i,,0I0 100 N'70. 1. o iO ol o 0, 0 oo 010 S 0 S 0 N N S e lNoNI a I' "i ".I.'I...'\ <Mf^ I olo o o l o!oM O~l O ol ~^^ o lo o!'\f ns r'o IM POn - oisj<-, (~ m^^<-~ 0<!o^S o^ ^o > o( (~~ ^r of 00II I' I1 I1 I1 0000.10010.001001g 0""'"'i"' I I0 c~j f~cs~i< f~ijf-< - r-4 ^iir- iji ^{~-~cs4[r>4 ft m fn fQ p~.4* *~t'4'4*i^' in[in in in nl~o ^o ^o ^o 4,o r* 4!*.4 j -4 in n 41n j n -4 0-4 m PP>rsjifsj ^ ^ i c4 io o* oolol oolooroo I IIoo IiMo O o N oI^- Ot n P.O O NM I I IIIoo L,ooI~,~1o~1o~I?~~ I1,0: I- I I 060 o LAinnj 60 I4' iO soJi -4 N" j^C~o o~ ~ ~o~iuirr! ~o h.N 0%ILA ^r~ o-^ 00 ~ f NI -N r0o fM!<N <Q'i0? LA N4 0%i^ LA ON Nn >^f o< p o'"o coOU.\01 N0% 1 0%NOC-OC 0%0%I0 ~ I COI C)0 0L CI LA4 O Nc 0IC N~o4ILAN LAZ 0%I LAM lF M V 01L (00.O I 4.NN"4 NI% — t0- n10M0,-4 N c 0 N o r n "4 0 N cN 0% ID NI,~.~. 4,m. 0 OIN (1., ~N -4'o"4A.0 N60L, ~ o.40dD"4N 60N0CY% 00OD 00: —O Nle-4 N 0% %OLLA N,10% OD N1N,-41CY- r4 0 olum 0sIst Colo 01 IN 0~16 A160,ico CO IN U)6 f-l0 O O a, 0 N. LA 01-4 Nb lu, -7, IN j~Cy 0%IN' 0 0I (0100(P4 0 601N't coI*O e0 0NI'' N CO "M%' 4r %1M. - e' It Ni,O 6 LA P- O LAL SA4'Of 0 004100 0.1.c 1 0001601S el0 S000 01SI*0 S0e01001l0 0 00.1 001 00 S 1. 0 10l 00 a l * Io.*I9 N,, 0 o,'t0'I LIN 0'% LA 0o %O' LA?- ~IC) 0' M L N N 60- N - -oILA COI' 1 0'-I' COI N —4.OI. 60 sl 04 - 1(0 LA- I 0 0l~g O io o!lo co!^n^tooo j o^lo inin^oloinoo oofi,~?!.,~!co NII I I I IL CO ( ( c COC CN I N N'- C) co U-\ LA j0 -'t I"'0 -1 -4 I 4 (4 j I -4 N OD 601 I N N % O I160 Cl O i 0 (M r< 1f1C NO I I's- sN 60 146 N''t co U, 0% iN I N 0600 * I M' LA ILA1LALALAlAI ALAA LA LA 601!011c 0 kN"'t h- 40 %1( coiAt0'O NO ( 016* s f!07 co.4'N0%IN.4'1N%' IN 0% -.4 0oLA, M!cOLA h4N I LALALILA LA1LA- LA LALIL LILAi LA, LA LAIO~LA-ILA LA LA L~1)U%~ nL AILA 6060N (1' %0'-4 N" U)UI V4ILA 60 N' NICO 0%I0 0 I- r A LAs c 16 0 I CYp' 00 P N MICo,'~ olo4 i o'[. o >ol o olo o^iirj~!o olo ol o o~i*-o ol,^'tmo,,01n ~tin nt ff ~'lf *y^ -'toino^^o'io~o~ ^ iroi a I N O N - oo o coI U co (~, I I I I oi~en-N- IC- 4- ODMI - - II- %O 4 - 4 I o IN f. P- ~t n In -4H Cy-4j I I I I I N IM! I I O O i I C!i I O O N I I 1 1 1 1 ~ ~ ~~ ~ ~ ~~~~~ ~ ~ 1 l I I a e II II el l a S l I * II el LA I 6 o00 o o- o o41 o(1 o o o (A l oN!m 4 L!i m - o I I -~ I.,O (0 o 01N o O -!~,..OI. iqi- 0' I 1 j >-lji-<.-4 — 1 -1-4 4-6'-1 N -4 N N1NA NIN (NI ( N 60 N< M r4 j1 A1N N t N F^ ~[- ~[ CM f^ M 60 (L IM IM LIM IM N N N N cO) LALl O,- N %I4Ni-M O,0( s PM l —ft% l- r:UI O NOI (A Ln,4 4CO'M -IN 060a MI(N (A (0( b. 60 O ON -Ol S 0 Oi 0 el0 0 1 0 e I 60 N10 0%Il0 0 0 N L 10' - 0 "e l S -4 el N 0 16 0 N (A 60 e001 0 L.L 0 CO NICO 0'0' 1 L 0 LA- ~ r-I N% -l NIU0CC'- I'4' 1,"M.'CyLA OY - C 6 1(0 ( 0,,!+ N M "4I 606 (I( Ln -"l4 M~ 60-4(0Y'OIM-16 N P-4' I4Ll A0.'N'4pdL OL 0 (.'6 1 (0(0(060 N-4 N 0 0 IA N0%AL 0 "O.I N N L 0 A M I LAO %IN 4 L NIM0 NAO I4 I I L I4 U-0'% 600% ~ C 0%i4't r'I LA CO 6 0 (A0 0%IP-0% N, 60 rb (0- 40 N iM -tU OIro- N0 I0% (A 6010 0NM1-.- N 0i LA "'tI LA M4 6066 M NY V- 40O0% N'4'l- 604' NO I~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~~-0 00OC o) co) co CIO CI a Ol a 0 i- 0001 0:00 0;10010000 I00 06 l 0010 6 l'1''] I il " Il I.II' Il I':I' el ~ el I I I I I ~~~I II II II IIII I I I I I LAAAL''.'4.4!I.I1,4~ I loooloooloolooo-NeIAO0 I I I I I I I I ~~~~~~~~ ~ ~~I I I I -I.- I l l -l r.I I Ii oIm, I0. 0 I l.' In0 l 0%0 16 N"4(A0 O"4(A.4.'(01060(A0 40%N AIA 0 A 0o- LIC 0 ( AI.'I% A 0.4IC 0I0 N60rbo(AINN I6 % A 4'Nt44O Ill~ t. Ie 1,-4:,..,I%'..4 -, 0m'I6~*0( ml....:, l 0(0.. 601.1,'I'4I0 mir.44 NI0 ~ N "'I.' No4 ~ ~b ~ ~6 I4 (A'4'60N10%.-4II'0'I 001 0010 ~~~~ir.'00*g 1 -4-4I-4.41-4-4-4"4INNI(AffILANIO.4'160NCO~ ~ ~ ~ ~ ~ ~ ~ 0%0~ A0O0-10IA 0IAdIfNooo% 6 rAN P' L. 0I~~~~,oo Io I, oooo; I"",:,:I.-44NINNN:, I4l.IFA6AAN~ I I I II I I I I II II I CO A OI (A 601 NIN(A (0010%.410LA ( oIN.4.4' NlN — 1[.4 NIL m~ 6(04LA'LA ALIN LA 0%rI[AN~4 —"' 0.'6 I I 0 0 I I I I I I I I~~O'0 1W 0 10 1 000 I~ ol 0l olo 010 ooooloo o 00 00 01 010 0i 0[.10 ol 0l 01 01 0o 1:~~: I 1:::::

-266It I Im N (7 O I en I I OI0 ICI -I I. c':m O I. I I I I(NI I ICy ~~~~~~~~0 1 1 010 01II I eel.0.0. *.O *i..910 Oil 0 0010 0I0 0 01. Oi I I I ~~~~~~IoI I co IP m0 7 N UAI I -I I- " I I In O cnI IMI # I I l 0 el 0 0 0 i I I el *. I I I I-1(A1. m m Ui t1 o N i C I I -I ItO f-0 I0 I I4 N NIN CZ I~ -1* O - - -!.(I I m f I M I' I I I I4 IPV- UM10 %MlomatA174 NN CI I I I 9 V~~~~ (* 11 I. loco ~ ~ ~ I a, coi fO U-N tAI~ U-m 0' m 16 NIO'4. N. 0041". 0'N QR O O O r.-1,0 - - IN L — 4 i -4 4 M0 0% NAt 0 U M1 I4I a, UA fnI I-%O (I I'- O c% r..I u~ co IM N 12% ft-.I IC* I 1. 010.90.1,I.u. t O(; s(3- I Ii' mlI I NI I I Ico a I IIm %+IO. 0 (. 01' 1 I iII~~i P~~ g ~ ~4-f I-$I t nUN Uio 01' O 1, I I I m lIen f t I t If I tI I I IN %O 0 rol P-4 I%- I cr~~~~~~~~ P41 I — -t I'0 N110 O O't IN O O co I.1. 0 * 0 I tU1 -a % om0 1I. OU1Mri oI. n' I 00 00 01 o4 S. 01 ole 0.1S'I II I I I I I I I I I I~~~~~~~~~~~4j I It IO% I NO % OUI WtUi 1 ~41UiWi60 I,Ui n i 6 I' I I I Iin in b 1 0If0 0'0 0 f"-1O 0N aC~ 01 I0'1 O 0' a' 0If 0I %0 01001' N~ NIN10 N N ItN NI0 N 0' N1f N IN N* No NI OI" N N 1c1IN ol 199 0 0 010 010 00 0IO 010. 001l 0 0 00CI001 Ie' 4 01AOC' 0', Cl Qt N -l %O N 00 %'i0 N110 In -4~ f I I I ~ ~ ~ ~ I ININO0 -m coIN d14o m - IN N M Iy I0 AN%. -40 fn I LA, I 0 el ~~r~410 Ni'O 00' 0tl *o~ N U4I 0 I~ IN'010 ol OS'II I N %+ I~I MIn'1%0%OP CO CO ~0 [O0 P- 4 - N I4 N 0 N M MI 0 M110' q - It 11' U01 I I " IM P410N - NM%. O' N4 4 1jUP u P- 0 N U9 9'C7 I N NN - ON W 1t — 0sU, - 410(1C. I' — -O "I"1" I St4 M" I4 m I I I O l I I II II N c 1 00 - W NI01-t0 nUMf,UN- " I' N iClM C~C- 0 I I I IN- NIN% NO N NIN% NiN- N N N0IN N-IN N0 N N nIN N1N N I. N NIN 01I 1,ft 0r- I U 010f-' 0001001000-. c, t.-0 I II I 4IfnrI I 0 1 0 100 I- % I I-coC. N1N m I' + I n u, O O O F, -F-1r-c o c I O I I II II I ~ ~~~~ I-1- -1- 4 - - 4 P4 - 4 r4 P v-4 i 41w I I4IvI I I IN 101%m IIn I N 1 0 N I0 N CO-4DO P4 % ON n 1P-4 4) -4 c f-.4 (N I I I I I I I~ ~ ~~I 1 - M Ut-'1 OP - 17 I I Oi II I 0% — 10 fn -4P I1 ( I PI'1 0 N - -4L I- I I I 4I P I l' -0 I1- 01o0 N mU-.Ioa O I II mI n t I I tIoLn IILIN N 0M N M0t 010% 4ONQO10L(111 unUcAInUn1 c-)I t1 a III ~~~~~~~~~~~~~~~~~~ 0 I 1 1I I I(- oLMeM N. ole.,O, O,, -i*, 010 01 *- oton I I- -,+ 0-. 010 01 1 I4

-26Ta I M o I O IIo N C L! r^ I- I O % to I r 4 4;! I-! t - 1 in N!I-. in I't <rf i O 0 I I I I -I I, O -'- "IIN I- I P4 I0 D1 - 1- I 4 I I I 0c0 0 Cy, N 0 0!0 cO 00 N N 0N ON "O' 0 0i 0 0 t OO OO 000 1>00 irn I a OL 0 0 o 4I —4 N O4I0 O 00 0 N % 01` 010 O4 N r vO' 00 Q0' IS! 1; i: 61. e!! i 1I^, ^4 ^ ^ \^ o. IIon n| o *!p o!- o co co o Ioa m!r M I I m o o 10 ID -- N IM -:t In nI IO I- I — I I-:I-D I ~ ~ ~ ~ I I I I I ico ~ ~ ~ ~ o I oooi oooo oooo ooo oo0 ~o ojoon{ — oo1ojo ^{fi{oo0ooo i lac 0010u~l o01000 0 10 c) 0olog 01000 0'0 0 00 00010 0,00010 010 00 Oi I I U. 0 f^ 0'oo o1 IfQ in r Mo 0< o {- Ns r^ co \^ ^. n o M r0 Cy, of!in o0* ^ ^ o o Im 0 i' in i~o C O o4 Qt i 0 CI 04;^ a p^ ^i^ PO ^C " ( r4 N N N im j( m s en i't pnf mt U- 4 Io s f!I — r- In-c oc ini miu0tn II 0 i i ~ ~ ~ ~ ~ i I!!!I I I I! I I I I'az csf ~o o I I i I co - o luj I I 0 P-1 NI II I I~~~~~~~~mN O 1* - lnP-0 Mm -4-tIm)1-1, Frc 00 A10 "410 P N' I4 o'm sO cUio mlO o N 00 "4 co co. 0i LA ^ 00 0%-Io' 0 NIU-04' 4 %ar ei 0"NI II i0 L 01M ~O I4 WI 0ir4 U~0 1I iU 401 fE'^"in!^ *<-lf^ 0 o~ o~ oo i0 0'0 N N r^ St II[^* 0 i r- lo 0' ip- " ~4 <m 0 "I N1 o 00' 1 4 u n 5c cNo}Il ~ in n t ie@ 1, { * el*0 el 0 @0,10 0 gIg gIg 006 1 I I I I I 0 I < If r I I\ F\] N (\ N N I I t I),. I LA I U; " I I I i s *0 PI- IN co I ct 0 QD m Io In in I i if0 I I I0[m m 0* ^ h o (J 0!~I I, I Nr II' I,. o I,.,I'':"i'1', I, I i I I - " 1. 0 N O IN 40 CO "4 -4I' 0'''' NCO -0' NO0NI0 * I0 "400,0 "oI"a N lc IP4N N 0I 0''40 OP I01 I I ^ n co I rIr1r mI U)in o en 1 t - o c1i I I 6 f Vh ico U-, m'017 f 4-' IN P'- N1"4 M fl"4'0 C 0 % tcof 01'00 I I 11.N %0 0I"4 0100 I% I* 0i0 %OVII"4'4 0 0 4 M 10.4 4' ff COIN %+IOr U1 0 NI. P- M I'0'0ff1 I Jim.CoIIII.I o''u' e11'42LA't "4 ",4 00 P IOo -0 %0I"4 "4 "4 %tIM p4 In 0 LAILIACli 0 co'0 0.'koL u1r'.. I 4 %tmllo-0'0ef 0' "4 en1 w ** *I**e** 9*0 * * *I0 SOisJO 90 ** *i. * 1"0I 0 01 010 0 *!x 10 0I`'o 0'4 0'M IN 010 N CO mf110 N1fo "-4 ot I Lf1"4 f%!<M I- 0o'41 0 r IN "40 co"4 1i nI %0 N T (UL. i *' (;! ~~~~~~~I I I I i t oto o oo olo o o no oo N Ni ~~ ~0,i0 0 irr 0 1 < in U) N N o U) 0 00 0L 4U'0 0 0 LA {I0 Iff1 0 %000N 0. 4 0 0 0'ff1 0 1~ 0 U' N f1 NIN4 %' %4 0 N0 "4lN Um ^u) V k It I~^o oo o o o o oo o oNo (I i~ 1 o *U 69619 * 1.'* 66 1061966 @1*0,6 6~ * I I1~ i~ I.,t' 6 r, 0'10,00 1 I I! 0 N NN 11 ~NIN'4' N t NiN 0N' f IN oo 0s Nfi N 0 oI"4 NlIs( s4 ff1 1"4mi0 UlO i"! "!Iff1 oN I0 N N..'.N IN'I'*~'"I0'N N N4f1N0NIN?'0N I N 014 "4 l ( cof1 l! c lel o "4If U - 4 "m' I - r' Oifli<'0 r10 0' OINI N'01 "n In 1 I0 001'0l N! I. 1`M( 0"4IO' o io P "0 0o 0 r- I O M Ui4M 01 No 00 M o as o o+ P im c n ^ o il M N mi0 0'o f 1Mi' r!"4o 10 N 1 o o000 cI001000010010000I00 o ^ I0 0 0 " "41"4 o"<i* ~ o( 4"4 oo ^.in"o"4(M4"4 "4 "4"41"o"4"4N1 1" I 00 010 o o o 0 0 04 010000M 1001000 ON st. - in 010,0- 0 00 10 C00000- 0100001 I IU 00 0 el 0el..1 66 1 * lel0 0... I e el *.. e I CO IN jfr'c e'; N I I I I I I I I U,N 4 CO 4 m P4 IN — t r1^ o. (M (\!~ o^c p1- r~- t-'o COl NO In %tjc M~o N\ o^ CiO %^j^ %t M P-4 \(m <^ o r oc o-a in 4 o cn o f-<'~t %o oo P-i IU[o N M rioi-Mo04nfo0* ^'"00 ~r<i _J I u"I %O 0 O.4 - f"- II -,COI I I I I I I I I I' I I I I, I co c I I' m I I I c I I IO I oo "4f m %t ~n o -10r inio o I I I I I Ioiin Imic te 0M c,, I I I I, I II I I I I I I I I I I I I II I I U') o o 0110 OO P-4 ^-4 NN f MiM %t! Lom('M 111 IC% WM OiO Oi- ( N ooMs~f *- My ~ -~}- 01ii U) oo No I.co oIaoo a, c^\ I M r ^!<< r a n a o c?* n r p 4 -4 o1 of1 P4 4 PI4 o oolpf4 I IIIIIN Nr $1 t sl! t et"'00I o0' f si'01"40'1iI r"I0Ifi 0'0ff1"41'4NOONo I I ~ 00 01. ****~ *1* @0106169 9 * l* * 91|06 Ole) ~>** *I | ~I0 I ~ O * I I~ ~ ~ I il IZ " 4 N l NI 0'0 f el'0 ell "40''0 I 0 0 A 01o0 "41f, L. 0" el 1N I f 00', N el 0 f' el I I " 0N 4'.1'1 N 40'-ff110 T'I*- " -4'. 44 h04 "4 0 410''0IN 04-chi 0 "- f0'0 L4 "4 stI-0k Ol-" f0' NA I 1 O 00 oo NI4 1". g N1' 0'ff n 0 410 "iLA 0' N'0' CM 0 ~j o1 iO N' 0'rff o' U in IU %*, <4' M o - C>o Co lo 1i 0,7A M oj4 % 0 fM, IM l o < In ~t I O N!M o 00 NN! I 00 - ~ ~ N 010 U- I" "4I N*t } 7 ff ff1 iff'Po 4L ( AI LO'- 0i'o %O co i t'.0 01ioo0 0' 0' IN OI-'j - o' o4, Ni CM~~~~~~~~~~~~~~~- <-M -4M|-4 <Ml<4 (M4 (M C1-t INIC NM C iMrs[M MMCiMC M M CM CMlS CM j(M VMC MI% CM CM I-M i M M~ CM l N~ ~-t m,0 _I-4'1t 1 ~ co,, 0' 1, r 0' U) a',, co c) 1v N o <'1' @6.69 o. * a,091 0 i0 O o16M M 00..'- 01 n o *'6''. I - Io.?. I I 0 IN O Io o I o Ij 0I I n M}I I I P'.4 I I^ m 0 I 1 1 I 4 I I1N I M IM tt- t 0 t ILM 0 I - - I COI 0 1"0 0 Ir I- I Ir~ I I I I ~~~~Im Im /I! 1 I I 1 -jr ^C!. i n-~ -- o ~ M P \f o > ^ c o o "" o~''i "'^'o o C'n r*o C'o o c n o I~ ~I..,.....,Io'~',~"'" ~" "'''~ "" ""i~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~N4''"0~0 II 4 A 4 MI 1 oI' ~ 0 Ie rf' 40'!'.''f1N1 0'10 ef1 0 el00 I I* 0x Ml, 0o N>f N^^ 0Q7 ao- f —a Oic oo C ooo co 0 r- -('0 oo oN CT>!( cmal oOo o1i — < v- 0-! 1,0 C C M -M U-1 i 0"I 0 0 ff110 lo LAO LA Ij "414 f 00 - ^1'0 410' 0'-0 l"'0 l AI,, N 0 Off'IM OMi'0 fM4 4 0 r j00 0M I4 kM "4 "C41 I cc t0>-"Ir.L- M' A 4N00i"I0''0L 0l I NI~h.IIV~ ~ 010 0'IN 4 CO CO f1ONLAICO'Lf'tof 9 6 9 ~. o, 6160 gg 0 9 *I I 019 69.-0 ie 0 60 9 66e 69 9 0 6 I. I.' I i I N I I I 0 I I0 0 1 0 -4 P- P-4 -4 N I N 1 M M 1M M M 4 t tft Uf~i U~ 41 O %1D I.- I — 1 co 0 O" 0 I-4 r-IIN M tn CO ION ~ ~ ~ ~ ~ ~ ~~~~~~~~,.,~'lL'...f~ 00 1 1,1 1 0100100 00 0CIO0 001"4NI"40 _ O f''4L 4I0 N'ANtI 001 I oI~~~~~~~~~~~~ I I "4lN'4'lT"' 0~I I~ LI' I 001010 0 0l0 0104 0 000 O 0 0 01*0 010 0 001000"I4"I4444 I I - " I- o - Im U) I co Io -,m t, * - I I -41 IP O UM N C I P In I41 I1 -4 -4 I4 N N, N N N N. IN'ml fn M M M t t t st 4 t t I I I I 1 It It N+ 1 III N N N: Io I tI I~ I Io' I I 0"',Ni-A~.'0L' *i"'eIO 0'! CO ff i *t' *f1' *1 e'I" eI'0 ff1 ~fi. *"I' "'~1''~ 616 010 6 6 010 619 0 0, o o. *l 66*O *0 9090.1. 9 o. 1 60* I~~~~~~~~ 1I I I I I I I I I I I I It I I I I I I ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~III II I I ~~~~~~~I I I. j'I.I' I~ ~ ~ ~ ~ ~ ~~l I I ti I i' i I " I 1I0 1 1 I *I C I 1690 O~~~~~~~~~~~~~~~~~~Il,1 9001 I 6J 10 0 I Il I I I.. I II I - II t =,,, I I I i I I II I~~~~~~~ ~ ~~~~ I' I I I

-268N, O O 0 O I O O W:o' * * * Y I I I' I1s _~|<<"<x sQ"I, I | | I I I I ~ 41 I I 1. i i I i i I. t- M i0ii I: ~ l o.I., I I I I Iuj U.J I I I, I IJ I WIN I I uzo $ II I I I I 4.I I I I c jI1 0 0 Z 1 1 0 I I 0 0 o1 go'I Il t o o t~lUI o IZ I i i o o i m o!o I o LA:IZ: Z: 0 I 0 l 0i I I I I 12 I I I1, I I i i Ij L I OLY i 3W, I I IU I,I - J |L LU -J, W! I'1 W Ij Il L a l X ~ j I us CL O O~ Cz1o 3 O < xu Q- a <i 2iO IQ gb J> I WQ i W U 1 I I I I~I I I I', 4ii ~ z. M I I M I I 01, — I I,,,, I *, >. I.'2 01 01 I I I I I oi ~ I I I. I I o z I i O 0 I:II ZIl/)i >10 I ^'U~U~i0 f^ 0 <\t rsi!^ 0 |< ~ a X i?02-I! 0 0 0 O'O 0 -j ~ W co l oI!I ^ ~ ~ ~ ~ -[ >uiuujuu ju u 4i-!u 1W!II1aI ~ ~ O 1Woc u~ 00Z1I04I I~~iI~ iN 10J.~ i.01 0 0~a'iL uI I i ~ ~ ~ da I ** Ijjo I~ {' 2 2" 2: O~~~~~~~~~~~~~~~~l *0 U~~~~~~~~~~~iO~ nj ~ ~ ~ ~... I I^ CA oI> 00.100100 & *! * * 1Q. uI I I I > >-^!2:2'3=?0 -I UI IQ0 14 I I I I IX Q UJ14 I I 2I

-269-',~~~~~~~ I i 0 0 OO 0 0 00 CIO 0 0 0 0000001iO-40OW-oc OO O i^ ^tlin t+ o lr — N in in N O WOOF Ot:m i N-Ifl Orn OPtOtOO 0:0 ~ ~~o %OU N 0- oo.~ oooioo~ooooloo Oo oo 00oo 1 oo oIo[i0%!foiN!'4 f%(\iN ^ ooop i 00 010 0o0 0000 010 0! 00:0 010 0 0 010 0tr~O O O t. r 0,N 1N! p 10 i I rN of o ui (f N 0% In1 M co % IO I0 0 0 0 0 10 00 0 10 0 0 0 00 0010 00 0 0 0,-1'aN - o110- N N N' MI0 I~ fflI 1'D% ~% I*'fE- 1'E%4 1, um~ ff tA I g't' t N NA 4 0 c N.- L oo o o oio oio oNo oNo oNo o o 0 o oo o o o,o oooo^!O i~^ C~irS\f~ o'~oo, ^ri~n~ioiO~o iN^!~o~ r\r~ io~c~i 00 010o 00010 010 00 00 010 0f0 010 010 00 010 0 1000 010 0n10 0,0 0010 o 0 0 l 0 000 0 000000 Io 0 o:o go 0:o. * 0. *n ri * 0 eM o0 0 010 gi g 00 ole *Ig t — r IL() <4^. 0J cy O^ -oif V Ioir- 1* 0 1000 P ooo I~........ I..I... I.o..'0O U 1;1N o-! i, i i 0) i I )! 0,.ll iN!.. I L 01U1N %,,.. lc:00:01 - N I00-% Nt INO MIN 0.4I o4,nr o. N cot, I M c.. 0 ~~ 0%~~ 0100 I I' U 1 A - NI0 N% M 00M. 0i U4 004 NRO -tI - t %t- N00O1ItN0Nrf M.1.0n MINNr N N 1 M M,- 0T~~~~ ~~ NiIO0% It00~~~~~~~OiCO~~~t~~O 0%"~~~~OiN~~~io~~O ~~~ 4i0%UA~~t ~ O In cr O I.d'~~~~~~~~~~~~~~~~~~~~~~~~O c (, —.IJM 000'un t N0co 04 o O lo 00~ NO U) L4'0 o0't O o% 0 00 en M I NI% co M 0'O N10 N I.-'0' 0M' 0t-. ~.0'1 in: ".0% N 1M 0'0 I o ** *I o oCoooiCI.CIO aC a 1 10 0 C0 i 0CI 010 0o0 f0 010 0 0 0* 010 C0 00 klm o Io I ~ ~ ~ ~ ~ ~, ~.. III.. ~I.~ I... O O O o 0 1 0 0 10 00 a 00 lo l 0 -i 0 1 U04 U0'0 I0'0 i 0% 1 00 a010 0 N1 0 % 0t 0 Io o 0% 0 0 0 0%J.4 e0''H 0 %5 o O O 0 0 u0 0 rooo0 0,. COIN 0, o 00100 - CIO I 1 1 -.I I I I I 0 rco.' I0'00CI010' 0 4 i oi ui10 4 o.CIOCIO 4'0 f0 10 UI 0 000 0% 0% N 0 0 0" Ur0 0 0'0 U~0 0 0%N 0 0, 0.i, c 0 10 AI.'NN10o4e 0 % 10 000' ~010 I7'01 010%0%11 0,0 0000J" 1 0~1,~~r00 %'"0~ 00o (N1! Inir. 0% N 00 n 100 o" CNO 0100I O [( 0 r 1 goor on 0 O IO OVjics NN ir'w!4.1.4".o"f'00oiO 0 )"n 0Lr4oo win' a00 op eg ole 010 0 0 o e oSo IS e o ee gig go o g o ojo 0l o 1 00 o g l og o *lo o0 g 0o0 01o 0I* 1 OO O 0 OI-O O O O 0 a 0 O O I 000000010p00000 lo I II Ii'.1 I,,!' 1'I'I'1 I' I II''I'~, I - II I I 000 1001000^^ ^^^^\ ^^^ olo I M I \{ I o^ I4 010~~o~r~^ oa'( > oo 00 I[* IMrs 00 I o! Irf I^ii i~o ojoip oopoo oooooooso010o oioooooloooololo0o 010001 i00ooooobpo oi o ooojo 00 OiOO!010 0001001000 olo 0100001000000100100001001000010010000!100o c0 000'u00 0^ 0001001000 Olo 0000-00010000,10010000O100100001001000010 oto00010000 015 0 0000 o 0100100100 o1000 010 010 000 0 (D. 0,001000 0 000 0 000 0001001000oo010 010 000100100001001000i< ot^lo 010000010000o00o1foooooooo ~~ 00010010 e g oie 01000 00 01000~~~~~~~~91 91 I I'01 0000i9 I I I 010 1 0 00 I I ~ ~ I Im II I~ I -.,,- II I 1 In.,I.,, I' I I I I I ~~~~ ~ ~~~ ~ ~~~ ~ ~~~ ~ ~~~~~~~~~~~~~~ I i I I I I i I oofft^^i~~010 ol o i00 01oloIoioooo oooiooloooopooIooo^o10o, p4 (4 -A~r (tp PO4 <M4~ rsj< *-41,4 ~-4 } (- P1 i- wi i- Pj i!4 N Ni N M M^ 1psj <M ifo Lft',. <d It P- }~o Mo 10 a> 10 4[0 + u 0%00(107 010O0 oloo o( o 000o1 00, o 0o jio(C00 00C0l0 0C0 0 o0, oooo, oI 000 0o 00 00o0 0 0 010 010 0 00 10 0 10 00 010 0 0 0 0 010010 00 Oi 010I0 0 0 010 01C0 00 I010 I 0 0 010 0 00 0 0 0 0000O In0 OO 0100 -ML 0 -401 N 0100 ol 01%M 4N0% 00 0 10 01000 010 01000100 0C 4I c,Ui00 1t0 *1-tM- v P40~ nNIn P- - f~~~~c:DOO 411 M ~t% ~% Min loioom oioo oo'o o0 o M Mo oNorolo 0c\ o oNf o-t i nr^ o e lo 0 O C0f1oco10o c go 01000 "I 010000 10fO 01000oo O*i O o 100 0 oo o e o oo 000 oO0 iO I~ ~ ~ ~ ~~~~~1 Ic IIo (^*j~io!^ c oot l oo^l oolool'-3 ool<o ~ < p o ~1or! (^too~m o~ t o~ru ^ t~~o~ oof^ io^^^o~oh^ r ~;,::~~~~~~~~~~~~~~~~O % No co P gl *^(^ iurol^ o lo ~,isio lO lio f oow^o'O~roi^o uoiooiio~ooioo.o I oI I ooI i o Io I o I I..., IIII i i I I I I I I I I I j I I I ~ ~~I I i I I 11ouI -- nu rlnLMU lnLiMI U-: ld' WNAU A N~IkN~ 01%0P - oC' 01 0 14 N lt4u~ Of-wc 0I I 1- N 1 1t % 0I — r~0" I I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ O% 0% 0%1% %lo' 0'cy 0% ON 10%j 07%10% 0% CY' oo0 0'10 0%~ 0% a 0%- 10% Cy, 10% C0IO 1 0~1910 0 0%0 010 O 0-%00O1OOOO- I-4-4- 000 V- N N N 0o" o.4io c -.gM M 4 o M M r I N.0 - I —- M a, - N O -41, CO % 1 1 -o o^ i. I 1o M0 F-! n Nc N -- %JnN Io o0001o0 N 4ooloo 0.010o-10o-4 000liO L oo } lo000 Oi 000000 N 0000 00 00 00 000 ~ l00 ~-40 0 eo!o i oo'rI I (oooo | ooS loo I I oI l0 010 SI 0 *! o.1 el0 * I e 0! 0 0 0 01 oo * l 0 ^oop r^ ijo io^ jpjNOolin^ o^^~ ^ oloolit i~w~to ioolo fcolo~ofo I I I ~~~~~~~~~~~~~~1~q I- N % In o 4! M L~- I I M I I% Im I- 0~[n0 % 4MP - N N NIN NI-I- -14N I M I 4 %,4 %t - nL I i 1% IO I% I-r- Bl Ir- 0 VN'tI I N.'0!L 0 1' 0 r-~ i4 co0 4"-IN N, " 0 % M o'0I 7 10% I0 N 0 en 0'0 010 0000 "01 01000 Jy o o'0C4 olor4. 000 COCO M I.- 00 %LA 1 0 P ~40 4 0 o Aon i 0 LA4 010N OILA+P. Pe4 0%0%O OI,00Ln 0. 0%I00 NIN- 0 r0'0,NI.4'1' 0 - l.4"IA 010 N 0IA410 0 P-'O0 M -1' % 4M M 0.c~ 4. - t ~o0F - Nm -o 0 M [ P 0 CY' M f-i coli(M M U <N P-c1i( ro4 0, 010% 01.4.'0L i'0 %000 i-;- co 0NN1 01L A0 M1'. LA C.4.N'. 0. f% P 0% LNr f- Nr M ^' iQt M^~ 0,01N r fm -l I 00' lv^ Nicy,!^ r^\<^o c^ tr, LA sotl~ m Lm o^1 kn!^ o<1V1 m At"!LML mI ~bI,. - -ao r* >6^ o! Ol~ No F4 M~s -jo^rtn os rioio^' tr f.jr 0%~ "0%0~.00N N 10 AI %7. 010Looo00o,I'10' 0 o0.' 0,oo0o o Nsl 0N'oo] 0SI k In' *', 010 20 10 0- *4 0041001010 0 01010 10 oe 00101000 0i0 01000 g0 010.000100100 oleP> o o %o L L oio olo o4o.o. LAoo o, 0 0 g I I oo oo N 1 N, aC P-01 ml,+ co O~ LA MAL LA LA'0,I100 ~' o0 o N )'. Li, 01 00 N!NIO 01. 0'01.4.M O'ing ~-.N 0 00 a- M4" n M I.LaALILAAILLALLAIALALALLALienALAILALA0-LALIL'01',t NM' -l l N%. I'. 0010 010 N (0 c 1~.4. if — 1A c 0 iO'-ON V4. r-'" o0 o 00.4N0 I 1 9 SI0 0%0 e10 0% 0% 0%I0 0%l0 0% 0 00%0 III 0 00%I 0 00%el 0%0 el 0 %a 0 0 0a 0 000100I00 a. z 0 1 0 0.- -' 4 -'4. -fI l (. 00N N N 4. OlO Olj~f~rn~f~fni^^i^^u~inj^^j^^Osor~i~f~i~f^^^^^jf~o,o,oooaoloo ~0~, 0o 0o 0o0o 00o 10ooloo o o00 0 oeift o o1'*1 0 0! *I ^!stin g! o 0 0 *1* olj e 000el0 e 0!000 00.0 o I I I I I I I I ~~~~~~~~~~~~~~~~if M oI - M "L A1 IL In Ht-t'' - I )-W -% Wo o oj CIO o o ojo Coj o o CIO CIO st ff oo % [~o pn1, Mo 0 U-6- Dooe M co 41jo~ mj*N ft<\(P -io~ N CY,!tn tn'co 0 LA LA W~. co ip n cyh rl 1 I'0%I00' 1'II' I eI''1''I "O'' o'l a o. NX 01oe o (ebe 0 0 N ol ol 0 0 g eI I 00 0r o o 1 co o 1Oecoc c, 0co OiCO CO 10 0 e lo0 0 10 01001000 N I''I1 1 [ ~II jr-4I r-I -4 ~-4 P-1 P-4,4 -< f-4 r-4 -4[i-4 -4 -4 -~if-< -41,~~ -4 -1 1 11- 1-4i- - 1- 4 -< - f-!'0'0NN N N N' N NLA N N N I ~~~I III I I I I I I I I OiLA~~~~~~~~i'0~ ~ ~ I.000I.~.00' %0%I000 00N 00..0'L000IA0~'N%0"4 >00 gIo001lIoIoelo~Ol 00 01 o e1 *I 0.0 gg 0 l 1 * oo eo 0 0 0 0 1 0 0. 0 gg 0 1 0.%0. oo.I...,0%.....,I...4.0..... I'.I. I I..........I. ~ Nl'0N~~~~~~~~~~~~c4~~, 0I'I0 %NAI0OLILIN'NN"I4 0 L!..'"~0..' %'L 0~~~~~~~~~~~~~~~~~~~~~~~~~~~mu F',.. ~ ~I~ [ I,2u..N 00f~ I 00~~~~~~~~~~~~~~o 00,- ole ole 00010000 l. I. I I I I I I ~., fI o I. Io I~ el'eo 00 l~ o eleo eI eo 0 0 0 i 0 0101e ego 1l 1o01 0 00 0 0 1 0 ole ~ 0 1' I I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~111 I N \ N N N I I I I I I, I I I I I I I I I I I I I I I I I I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~I~ ~ ~'Il ~:.' I...ii I: I. I.? Il.I I I I I% l I I I i i I I I I I I I'

-270%I C W Io e o 0 I m'^ol o;o m t o o oi I -. I lO -!,... -4^ ^ oq mCY,0. 4 NO O I CO O ".O IO 0 I N N rINj o H P i V ^ 4 M Mt4 4 ^ -4 P-4 P 4 I o oooP- I 0 I lo s00 O O0I O 0!0 O O C, 00:0 00a0o0lio010 40 ~ Oo' Io o o,o oto o o oo o,,o olo o' o o ao ol o ~i o,!:. i.. I',,j.. I I I i N I I I I I,:::::: X II I. I o l o; o c o 4.o o.o " o c, 1O A L - 4, -, 1^0 o.. ^-.:,',0,,],, c i. ^ oI,'.- o.. - o o,, a, ro!, p | 10. 1 I 1 0 * M IIN ~.I s* 1 * * * *l C If, cop O o moH NIN m om coj^.M LO ino^ f~ i o tLA8'l~-. *m. ~ O I' - _. _ N1_ c_ O _ 48 _t * liI CO.....4. 1 I o I o - I I I I o MI I l'0 o1jo 0 c ~)o oCIO o O CIO,j.o..' i o l O n m, o!o o!o^ s~cow t a: Ic:! ~1!.~ # fts <'s, r!.,~ uo ti. 1': o. ~. i i i! I I I g. 10000 OiO 0 100 0 00 O 1 o00 0O 0 iO Ol lO O 00 O 0 0 0 0 001000 0i 0 10 010 0 0,0 0 0 010 0 0 O0O 00 0 0 0010 O o4 o1o o o 1 oo olo ao o o olo o o oo o ol o el o o o o S.0 1.0 al o!o o o oio o oo oo I l 0 010 000100 0 0 00 I0 00 1010000 0 0 I ICa..' I I I, I I I I O I I ~~~~I I, ~ ~~ ~ ~ i II I Io elo! so o O o,-, o'o l I. o o Io o! o olo o co 0 0 o0 o'lo 000 01. 0'1 o 0o10 o oo0 o oI i~ U0 00001 0 o 0m 0 u o o o o olI 0:I Io I I* c I" I I t c 0-1- -' %P4c.,fo c.' I 1' O' olo o o o oNo: O o olo oo Io oo I oo.O ~mI c>N (aC( n N f[ oMO oio NOO o lo r v% wo 1 oo[ o0io ff " c'.co Ml n i I I I I I 0 I P IN rfPu'0 N N'0' 0'LA N o0 co 1o' 0010 o'o oo oo'oo o00P o^ - o~| ^1! 1~ oI loLo o ofr, O LA D o 0,0 r1.0 A, o o 0n ~1 o NU-L ~~,t oo o r o oo U)Io.!oL o oN oo......o UN c o!-*' U ^ Uin I In o!!! I e! l. 0 0 10 *!!e I' e|t4 ra Ir -~4 l p ~ P41 —4 w4jc^ -.4 P 4 | 41 4 4 ur -4 f uu4 u11-u4 -I *~4 ~4, | P4 1 o100! c O l' 0U- i- o' kO NO. co0 01 0 - O NO 10 01 l I rc o o o 1. lI I II u11 lo o L m' 0l% i OiLo'a o m o co i- O, coi m U) L UA N O LAo o1 jh- oos i~ n oo (f) D f 0 0! (- in n 4 oo 0 r4 1 o! 1 c[4 fn r 14 or4 O I'''' *' *I' *'*' * -^ I * 1' *';'' j''' * *' i I I irp (4 ^. 4 j oo ^ NP o i o oIU I co ~1o4 e. 4 a% m 41i N O I I I 1 CO, 1N 1IM I, l j I,,0, l -I Cl Q|'' | MI. 1N l.',O IM j o4 M~in I- CM dint <(lIn,M lo mo19 fo}*w ^ cr m't co ^ U-,,' co om o Io o, o.,oo o cM o ollo io o o[~ o M po inI 1 (Mr NM m mLn mim, t u t s4 4 U', t' t ] -i Ln u inUo VIt LAn u- 1 c a o[ IC',.I 0 N I * I t U c 1; oo o N 0 CM | (M{ i* ~ in Ni N C",,II N Noo, N m, J I^ 01.. 1 1 I, I',' I 00 i r^ fo N 1 0 I o co I- r.K O O O. Itn, U; LM t-i t-A 01 o olo 0 O o, Io o e ooo P|O o ole o1..o.I 0 1st 1ni ~ m>o l>lo X\ oo'oo oI o I c, ojo -lr M <M f r j^intI l I I I I' I I I i 1 t, l l, o l, I,. I,-, ~ I,. -.,,,-~, l I,,. 1. I I ~ u~,,0,0 0,,0!,,0 0,, 0 e,, e e elun 0, e *l 0 n e 1 e I 0 0 0 0 0I I I I I I 10 00N 0 0 010,, l, ~.4'',,.. ~ 1 N0 0 00 000 0 0 " i 0 0,' e e 1 * m4 e 0.,',, 0 *'. *1 * e 0 1 0l * 0,, e *,..,. O *.,...,..,,, IN ~,~ o m o,NIN N1 N NIN Nu'N, N l.,.. m., c,, lA' 0 1 I I I I t t,''oI,,,~,,J~,,,. I... ~1:, I,,,....,, I,-.I.,,~",, ~"'),1~ r'.-N~~,I,',,.r;

-271II I I I~~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ I a M 0 ol? Q1o 1- CM P-!o o!< inO m i-.401n' CM: N 4 s ot o!-; 00i -1 m! co A l ltc in <M!( 0 lo -.~ cr, o!i5 r l Z 3'^ N- Cy, ~fI- -i^ 1, oo (M'tO <!^- 0 m'4"n 010 P in U"o i s M P — If- + 3 - N i0 M P o c m ON r, ( Mi ^ in r-414' 0 icM m FqN o; t<4 asM,a!n o (70 10 oo M M~i <^- jcyn' O co Oi-4 IN|C M 0-4 o,~I I z I oI Il,o -o I Io o M' o C {m.' o a 01 0 0 0 $I e 1 10 ooo 0a'4if 0 IO.04 0 0 O 0 004 0 o0 N 00 010 N 0 V N 0 0 olo 0 l'o 0: 0 0I I I I I I:'*~ ~~: 0 o0 o o:o o o o o 010 0 010 o!i1 0o 0100o oo0o o0Io o00o o o 01 B- o'r-rf 0 co S oM so M (N Lm co, ^^ -oc oc no <-ir^ ~Qs ^cino! 4 loo I, o., o o o;^ r ^ co 1 i'~ F1 11000 O:O:; I I8 I' **:00:00 *1*^..19 0 0000 1 00< I,-, *,1-'r* O 0.10 I I I I.1' I'.I I I4 -t r-4 st'. I I' I.. I I I I I M I, I I I I, I.I I' I~~~~~~~~~~~~~~~~~~~~~~~' l: co!t%. t N f-N -% 10 Or4M 4 I I- C N 4 I*,.- I0 co'!4,* I11s a tP OI I I I I I I I ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~ ~~~~~~~~~I I I I I I 5 S o o~~o S oK Im I A O %0 M LM'< 4 M MC ^!fo In 1- o Ion N! 0 — 14 N ^[^ co r'IN LA P- o I I I I I I I I I o ix.4 M'0[ co p in M ) * co! a \r4 ( M M pst-'tji ^o r0 l^o't I1^ (7% P4 M[ I' o Ico a P4(s j-t tup 0Co o N I!~ N~ NI'I N N I I I'I I II!4l U)II* o5 1 S ~.1, - o, l!o n o ~ l'oinIo M o, Lm o. I - %3 o' 4 t- N.o fi 0S M< O1N co" I -t <~!''14 0%co oj NmI t, el. el ~s. c I I o 0. N 0 oIN ~,1 N 4- i -4 o! o4- 0 N 1 o o0 -4 CO O o -,n % o; en 0 Q, f K 0010 CM r -o o 4 o 0n ois0 o! 4N N e- NIN It Po r!o f^ n' 1o M r 0 aLn!^ N 0o IN o Jim'M co o I i 5 000%ni( S10.roo obIc0lo 0OIN CM r0{^ ^iLC in in m!0 CO if0 0 n ^ (N1'c 14,!N NoO I o 0I 0 P el t N 0 M. CMe el e' e el eM l e'I CY' a eM el U- lM'- eee~ (1,C~i'io00 0 00 Ni% 0Nei'I ^ 3fi! N0^^ 0~ 000 N 0o. 4NIq;'4 LII'000 N Li-i 0 0 o 01 *I- 0 f 0 0 ob lo 0 N10 0 0 01 I 0 * L t 00c 0 0 0No a 10 O N-00 0 N 0 INoo In %. r- S o! o (7. 0 co-< lm N NM c M o ti' m ON U- oo ^ M CMI M0 m N < -4 0' O 0 I %r0o P- <M 0 1 1^o ko ) oo LAU)coil 41 14oIo% o 0. 1f o 0M m. %O inu %O m'oinf''i o %0'I o CM i <4' CM 0 o % n in %O i s o'I U-A', C N N IN N N I N, I I I I I JIo 0 Ln!^ M!c ( %; M^ oo ow riNooh %r 4* ocM ^IcF c n*! ~io in 770 inrr r- io %P 0n N''0 f- -r c o MNc c 1 I I' I I I I I I I I I I I I I I I I I I I I I!',-! r,, U.1,-~10 *lO.40.~10','1",~~ 1 ] I, II ILA... I I I I~~~~~~~~010 000 II <N L P tU eIUN LFlt P - 4IffiI Srpf C,U,% fr4 -.41 I N.OIn In ^oj~o N> ^o ^o p4 p4 N N o o oW"O- CO CO M^ c l N N [00:lN0 CO'4o 00N0 0U Io W OO 0 0 010 0 0 0.0 0 0 0 0 0 1 0 0 0 *I 0100 0 9 100 10 09 Oil O 0 10 000 IM i o o1 oi-,' oi,,00 0lI o 0 N I CO Io o ol, N o I'm N o oI o Mi -I I oo N 0 CM 10 N! M o%! W 0i1 4 M N 00 N 0 - o o1o - - o o - iL. N In 0,m 0, N., m C)o M CM!? N f~M co lo UiII n co t o'tco Io co co f^\a 0 >< %O N M N ~ i oN< NIA itn NM co0!- OI( oN 0't I I I t 0 I I.In Om %ON m^!noo(m No f-4i Pa*!% o 1-4 p^!"o!<4 M% co ~ -.'o 00o. CZ) M W,'0 o!o^ s<r[~ w'o^ I CM i4o 10C'4.0 ft U-o oo-o N" (0% O' o' 4!IN ~0o io -o M o o m N l oo0 i co'IN IN4'IN co m 1in o~~~~~~~~~~~~~~~~~~j- o41- oi4 o-!5 PO o^- <M!^ <^!*I N N N4ic IN ~n II St %o+o pir IL WI NOif %n?%- 0 1^! no if I I I M Iw M1 olo Le 94 o60 1001-0 0 0 *I!*t 010t 0 1 019 iO % n N M <4 oI 00 r M!o "lno M I I N I oo v-4 OD C o 10 Ln N 0 Oin a n N- riNCO 1,t 0 o N c100 U OD'IN0 n 0' 4 00I IO I 1 I 40 IN co 4P.! I`n'M i0%I o 100 iN I r'.0%ji i0 I r is0 0 in4 ot r-4 co I cL oa en!P- Nr< P- <M N %O M IMI r^ ^0 %tio in~f-~1U^ Cy, N 4o l^o m -i-4 %t COI In lo -mic -.< oin 1- im oll WA CO N 00010~0.~d ~l f.I~'' e. l ~,.i., e I ct 0 e I e I I, *' OOIOOIOO 000I00I0000I1 I1,~H,~ 1. I M 1 0 m' i 001'Negig_ *i cot._rNi*t-I I *N g o gi I II I 4 a i co 0 01 0 co 0 0 -10 *I M * IM?M <*1* % i 0 o o* U I^M 0% f- f-4 M^ co ml f 0f No -.M f0 cr im I o r- cO! 0 tic P- o (4 mv st M' co^ o II - { o10 4 Q r-j JM o ~ II II. i.I I_.. _,i;*. I I I I I IM o I-4 P- IN ^ oN I I oo I'fU CM N oo o'I Io IcM I4t I in N I f O|( o i o In oI o o N!-M 00 Io fo M oc? <\j!0 CO oi1 0 ftiin ro o^ OD P-1 M f( fM o'- o M t CIM a, I r oo- 1 ^o^ rn oo' M co I I I0 0 0 I 0 Il # 0 I Of O O 0 I 0 I0 e0 0 I I I If CL~~~~~~~~~~~- N^ oo CO!o4 -!^ u"t f- 0- ~-~}<t Pr r^ co0 NM~ N/ Mor-^ n rn t (M!N o - 10 as P" -'sO:N <4 M [ M- c'o I N I N M M M M p-t r It t Is t I I I I I I n NMo en pr 0 n1- M oof- 00NM r (io CTlMO o7, COI- <T'ICn o -4 (~CMc;^ oo'4" o^1 I r4 <N!-4 co la -,t co f- INO %+ IN in Pi i f 01c t o U'~-, o o In -[ I o M I0 0 II N N -4 CO i4 IN{OM N I^ I. Io O!N i~ 1'0 o N O I I I I ~~~~~~~~~I~~~~~~l I I0 0 N-4! N Q; I r- oo00 —00N 0 0COP4IN %%OINNNNICAO LAo N~lf 0N C o I Pl-!n CO OD 1A IM 0 %N0 N IL S 0M 0M10 r0f (M NiN N~t <M? sM (M!M (M}M -M — M (Mits tnM~ 1<M %O oM IP- C^!coJ co (M- M1<M -M INM M (M tM ~ 0 - 4 a, N U) CD -0 0 Uil-N I 0 U) I1 O!^ C4 O N^[ N-[ C4 - -~M IL CM-4 -CMJCM tC!CO (M (a I'M fM JCM L~ fM (M- I I I I -0oI — I U* to r-r-I, M I 41'- IO*l* 0100 C O le r- 10 *-1 7i* 00 9,IN(10 1 916 000 II-I ~','.~I~' 1 " i~ I NNN'r 4I'1U'I''0"0 I I I I I ~ ~ ~~~ ~ ~~~~~~~~~~~~~I I II I'I~ ~~~~~~~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ I II I I I'-4N ~ ~ L' I I I IM'~I*?~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~c o1-, I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~I, ~='li I-, I,,, 01000.010 ool 010o o*o. o. o~0 0100.1.* 0: I I I I I I ~~~ ~ ~~ ~~~~~~~~~~~~~I I I II I II II III. I I I I I I'e~ I~.lu. 1.ol4 0'1o I,' I oIoI I I I I00IIAN 0. 00 ~N4O~.I0%~0AIINO I' III I I~t I, II, I I I II' I I'.I I' II II II I I I I I I I I ~ I I I I II I O N 01 mloA O'IA'" —. -.. 1 CO.QIN NI_.' 000 00''0I 40O~N40 0lN0I0r 0''''I''I''1~~~~~~~~~~~~I'0Ei''' I I II, III4I I II II II I' I I I I I I I. I I I' I I ~~~~~~~~~~~~~~~!I I 1 I, I'I~ I I I II I~ I, I I 4 I~~ rl,Io I- I, I-. I. I I I, ~i I. I'' I' I''~~ N 00 I Il er' I I I, - I!' I I! I, I-, I. I I II, LA~LANCO ".0 ~00%0I~000'N 0I.0I 040IN~'N4010~~1r A IlI~oI~"L oIN N.'.,I I ~ ~ ~ ~~I I II. II II II I I~ In ~ In ~ I o l II I ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ I'IN~ II'e* I I i I I II IIi II I I I I I I I I ~ ~~ ~ ~ ~~ ~ ~~~~~~~~~~~~~~~~~~I I I I -I

-272l o o o o e e eo I i 1>~~~i4~\~~l | \ i i I | I I I I,i I'iz lo l I l~jI I j j.I I I, I I iI IZ 0'.i ~"I I [1z o l 1 1 I < I I I I 10 Q. I I Z ic I,. I 1 I 1 1 1 IIJ I 01 z!> ~ II I C',M2t: Z O Z4 Jt t t o~~ U I I -J. o I LLJ I,=' ~J IZZII5'' I I I I IVt) 4 si c I t I ii Sol aI -: I< a I I I I! 0t t, WI I{ i o l I I I t,> - L *Q ~ ~ ~ ~ ~ ~~~_, ti * ltt= ~ itX I I I W o Y | | I I I J:: W UJI UJ LU O ow' < C II Ico t 2 I I 0I I I 01 i I I I' C w C niuz ttow X l — t Xt | ttl tt {C Ic e 0'I i-J) i-i 01 r i ItU I* ILL. I 1I I i IU IA I I LII I > 00 0 100 Q 4-< 00 UiO i I I! 1W Q(LUO<I0 -I0CAL. I I I IO U IS 2 <iI Z OO^Q-J~eQ OIJ1 uj u~~~~cQ~~~a^U(j~~~~~~ux]~ II i

-27500oo 0oo 00oo ooi looooioo!Oooo 0oo1NNNNNp ~ m x~^om^< en Fim^>~~utim MM MMt~ piMf ~o cy r CY CY CY C,,o0 0 0 1 0 0 O O 0 0 O' 0 0: 0 0 0 0 0o00 0 0 0 10 0: \e C^ (^ C^(> 0^ 10 f^ f^ f^ 10 r^ ff 0 <^ (^ (^ lo\ (o 0 o O <0 O~ C ^ I l l 0 0 SI 0 l 4 0 e I e I I f 0 * l0 e I I e S SI I: 1 (oo CY% oI o o Oi o0L:NNI +MFo 4o s awu o mI oo o:o oro o o- imoio o~o oo o- o: oo oIo o- om aj oo 4~nr-o o co o'o F.-oo po o o S0'o *"01r4 r-. -.4 o!in P. N M co~-co r- r-i N if 0^ O itNN+0t rr%- o iM!^ - 4! ~ tnACOIo 0IO N< (!ON 0 - If-o0 0 -! %0 -.IN 0 0 o P<' o llP- i^ P -o M?? o'oo +4 nin i~ (~ %O % M Coo!t ailo %t CO 011o NMJ*O N0 IN QM^ \!t N I% CY% o|< 01, <-D IO It o1j- n CY' IL'4000t %4O t- (NO P m-o Ln M M f^( i~ I I I I I I I I I I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-4 10 n % I n 0 o? 1 SIN lrico *. 0L or-N' In lt'0!0 %l0 e-?ofr ^if^ <o. r^ 0 co r- Ln s Io (o N o,in ^-4 Io. +, Ir <Ij t cl i N! r- o o< lv~!mr I f o ^M I- %nOp i-I~ ~ I I~ I* * I I *I I I I * 00010010001 0i0 00 TgO 0 0 LA 0!aL A f4'!t Nt ^!'t41CD 4t'1'0A N IN N 40 0,:%t 4 i4 0 I't 0%o Q~~~~~~~~~~~~~~~~~~~~m M m'ir o^tf (y> c oif olrs or - ot I <o+c ( t- fM<4 o!~ MINco isfs^ f^'4 o!^ (M,- -1 IIio fN~h Nr M %t(\ LIMcj 4*rnI I I I ~~~ ~ ~~~ ~ ~~~ ~ ~ ~ ~~illI I: I III1. II I I I I o 3 f\^< ooo i o~ o, Mt u" cnuo %4' IN o o- Clow nu^CK* - co tf IT r-IP oiWf^ h/i^s' fion fj - 4~^ -^ o 0000 01 000 00~ 00 10 10 01 01-'4 N tn 0%oO?'0 c1N 0%- I'+0 O CNo -10 ^r; c1N ol O 0N r 0 m 0% c ^ o I 00 10010000 4 100I n A1- t0000100100A'.40010 coILA'0~ Lm~ F I %.r-0 N'0 i4 41U %'i.'0' I- (n0 LAA4'4a 1 N N Cy 0) 0% wl 0- UN LA.0 000100100 010 0~ 00010 OO0O 0100'N NN NN N'~ r~e0~ ~ ~I1~ ~ ro ~ ~ t1~~ ~ ~ h N~~J NJ:N N j oo o00010010o00 01010oo0 1 0 ojo 00 jOIo o000 0 I 0 00l00 i i I (! 1 1! 1 1 1 I~l'!'' 1!! I I I I II I i I I IO %t U,% 4 %01110 %0 0 0 0 %0 %O 0 _t LA LA knio't 4 CIO ILM In M -1 %O 1-4'O l',,0m I kn IN N M O K ~o o oo oo o o,, o'o o~o ~oooo, o o~ or, o,,,o^^i~^o~nowO('<Or~o~n ^- p <o,~ o o o Io o o o o'o o o o4o oio o o oo o!m ti oj O ool i 4 M In In t-o Jo Joi n o lo M: p ~oi I I I l I I. N I I I I I I I I I I! 1 CO O 0t o joo;ooloooolooloo~oo,,oo looo ~',o': fJO ^ i~ias~~otooco ^~~^ o^oooJ I 0'4 lo' 01 o~ O 0u 0 o N 0% 0% 0 CD' 0%0'4 C 0%'0 NR 0N'10 NI'4 N141 0' N 0~0 CO'01r- n.4 o' 0INA InC 4m'v''ll110- N 0 p-.'0,LO P- t 0n 0 ~ %1C 4~ A ~0%l~0%1 N ICD CD1 0 1N' 0 r. -.1 P41' "'00 lN col. 0 -40% I0%'t 1-4 N0 N- ti M lo M oL NO 0% M K0 LA ( a~ 00 1'0NI% 0- 0IL Cir' N Li4 0i%'P~~'-~ I LA0 0% M %D r. Ln NI0 W N0%L 1'0 I.44 4 I % oL 0l4'0 N r'-1 N P- %t co' o.0 0 * 0 0 0 0 Oo 0.10 0 0 0 00 1' Ol.... o O..o.g.1...4''. 6 0.', 0o.Og l0 % -44 44I -4 NIN N IN M 4-4 00 0 00 " 4 M'U. -f1' 0% 0% ~t 0NNN r'. j I,-4 N I 0 000 OLAL 0 0 COD 0' O 0 0 CIO 0 0 0 0 0'0 0 LA %0 CO 0% N OO oIo 014 N.0 o0iro 0N[0n 00 0 cO 00 O N- M r joO 0 cDO O 00L~~~fr-4C~~~110 ~~-1LANILA-4 o,'4u~~~~~~~ CDI'0CDIlr. m LA%1l'-'IN AN'M0'010%01''0tf* 11- 1010%'000%I4LMk0N 4 A-..4'- C1'I N1C LA14'0NNC o 0 0 %0 LA OIC'0,C O 4 0' D0 % 0 10 0"ci- 4'0 N14 "p~0' 00' NIM.lp' L "o40'CD NItUA4ML 0 + I.-'0N O' 0 0~ p-0 M' co lOO ~CD%7o CIO tL 0If'0LA 0%... 000 1 -4s-i-4No 0N0 a - I III 0 00, *nl* W, 1 c g do,,**Io o c. c- r-I SI, I IIIII0 s 0l elI lilI I I I I I I I II I I I r^ ^ fn r^^~~I I i I I I I I I I I I I 1,,t"i! o r r"., oo'I'^ n r p ^ o ( i, 1 I I:I'-'I I I I I IN I:: IC!1- 00010010004 "o 004 0104IP4P4 - q" Olrl-1,- 00010 00001 01 0' 10 ol-4 4-41-0' 4W10N U C l~o "k-LA "4'0IcoN 0111 17 U-,10, I'co 0.~ %O 4 %!' fo4 wiw.w 00010010000100100 obo 01000010 O4 -' I 0NI CI.4 0.4 i jn 0%cl, 4p-.'0 cCo0% 0''- CD N 1 0n CO COO 000100 000 oo 0%1%oc~0 17 0%oa 0%0 IN01 0 01 000010010% NOa 1Cli f'-IL CD 0% 0%fr,'.1ol, 0% a, NIl'- 4CD% 11 CD LA 0 o"0 LA 0 0% COOP 0 ~-oo o~o ooIooo o o oio ooooo ooboo oooIool"L41'0LNDINAAL4LIoL 0%%0l'^' l'-04 H^o CponlM-r'^ooc ^!'c'(~oij noriM io^ofo oob~ %IfI I I I D j' || N,,0 1 I a el..-,,.0,:l, Nl..I 0,,t.0ir el. ~'I el, t"Ju" NIC S.i1'~u,.0',t 0 e.p0. e-l..,. ^oo ooii'ist'st 4'!~t ** " o~<'roi< mr~oo~rimrSrooin~ti~ o ~~poo~hoiiooolo.,,4' ^~ -^^roli SJ,,al" m\<~I~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~.". I.* I~ I I, - - I ~ I. l I~ I~ I,* I,'i'~~~~ ~ ~ I 1'I I' —I~ I, I I I I li I 0 ooo ~ob o 0io0'1'''!fO^ O"':'!'Io'o' I'oo'!I'0Coi'''! "404 0'A4A0%ci'i MI l 0001001WA.4000 Qt% 0N 00A 0 -4M0 000 10010 N %O UN41+W- m% t Or-I CO 4D LA' Ink 4oor.4 N ND17'00%COO ~'* V4 en P% M O U) tn N *-!< ^c If- O - 001ooM l c o 0s 1' o - (t M ~-t M ~I!~ *- 0 o M< M f- M'*o +o so %t M \ N - Oinn-4 t~ oio- V%- oo4 Rn 0 i0 St N O %O I 4'l I o 0 co001001000 c O" IO 4 m0100001001000 M 01001 N I- co CD'017 N1- a, 0I NM IC ON N co 01 f OP4 CDIN (10'0IL 4cl' 0 lA'17 4 V-0'0"CN %0 10 M010- 0 00 010 0I-11 N "4 I 0 I I_ I 10 0. f%4LD0N..h I 0 0 0 010 0 1 60 00010010 " 4N N 0 "4el4eNIN 07 4 el0 Si0% 0 a 07. 1 f^M M(Nr(< ~<-!- M, M( M-r M cN fQ NIi Foirn PQ0 Pos t^K m F4 ~o i F- NMm M:n t ^*tf ( 0 icj r — i 7' P4 - < 4f < I00 c 00coIocCO0 00 0001CID o 0 4I MgCOg00 60001.ft AM.106U ON- f e o 01*00I601M*0 Nt0 MW1*1c )%OI 00,66 00 co 010 I I ~I I' 0, i i i i i i i i rj i!! * j! j!!! \i,,,,e,'''~ IN[ LI W, A I A iLNU I In I U IW'%U ~U I I~U In I. O P -c y y I M Ir I IO I II o o ( I Cr% ~ L IM I I - I, II I0 -.t I l I "44-1""" I co14"14NNI"o0'0Io94'0I-.4'0-LILIL0IDI o"iLA 0%1117CD~oin'0~- 4k11teII%.-.4'00~oi~i~fsoo^^~oo~n p^nfp 1} I, m i1 10 %%,0 0IIoo o oo oo o 0oi 0 o 0 0000 0 0' 0 I I I "4"1"4"41"44"4"41"441~4"4"4~"441"4NN1N~k~, N rJ.NNIN',J.!..l9 e 0 0 0 0 0 9. I..! ~., 1..,:..,.4. lP, ~ 0"4 "4 "4I"4 "4I "4"4"4~~~~~~~~~~~~~~~~~~~~~~"4 I ~ ~ ~ ~ P "4l"4 "4I"4 P- i.4 4 -iP-1 — 0' "4I4 "4l6"414141~ 0(!00 o\o 0001 001 0101M00 0 0m! en!00000 l0 in 00 N00 4 r Mo0100001001000 00 oO! 0O co 00{o 004N 0co % N!~ 0 I LI I (7 W P Fn 1 o o 0 * 0 10 610 0061 U) y*!!f 0 g N o 0 0 0 Vr l- o leo N - 4 i o r00.1 M 0..M'0 00I6 10 Mn@ 00 000o 0 M Vol I I I I I I ~~~~~~10 I ~~P 1* I IS I I l I 0 e N j N. j a4 0;,'t Cy <0if cr-f (\j (4e -M fij ir-4 M P O f 0Nl^ - it- Of 00 -ti CO 4-j^ s %0 Ntfr I= Nf fn r7% pn1 r 0 t0N C N N N 1' I''''I1 Mi M i I I:I I IN i I i Ico P4 4i n M r t co O 0 cn MIn o IM I INo! In - ^ c I In I r'4 In s I No o~^<a,-j(O I- I4's(0tn 0 -4 4 I - I0 M Ir s I~4 a, wr r' o % O W 4 n o e I I I I I I I I I I I I! oI i I0' - A L 1 1UiL I U -tI Lmi i, I li k i I P 1, I 4 LA'0 0ntnI' -110 LA' "14 4N NLA-4 14 1471 " (170 o 1 r' 11 ol'0L 414 LCfIO'01740 o -I CD IO-1 LAI0 "4 0'01!'- " _4' N 4 "-4 P4f4 (I "4~NI!'.o4I-17 M' 0 A 0 %IN NI- N1!'.t CCO 1171'- M COICD 01 4!'- 4(171-1171-'N 0% - NL' ND 0 I"4 - 107i4'00 411 CO LIN4 U O4L "1LA 01 1%t 0 -4 11M17'' L n'0'N COO. D0 % 10%9 -IN OM C' i COI4 L 0 %40a' 0%I0 LA-4 CO t-LA Olt' N oI'- C mi'01!' - 0% N 070% iN CD- 0%!-0 "4 N'1400%a'014101 N70 C-417 %O r- "4N N N*ooeolo ol I o olo o ooo o o o o e I'0'0117I0% 4~~~~'t1' i'- LA014, r'10 4- "INo'"' - co1 0% o 00 4 m CO0 1'- 4 -.i'0 41' NI'08 oIN ~- 1-N'0 1' —t% IMr 0'0LA101k'-t CO LA%0717NW C,~@ O 1 1 1 1' 0'0, 4 4 1I 4 1 4OA t I'-,,,: -n I 107I'0714711171'071107107107N1NNIN"~~~~V4 -4"4i "4r4 —iNN IN M I I M 4ItN14717'44 7'0!o.IC0% N N O oX o o 1o N oo _psMoo o (i oro ol o CO M!o a I CO lt.o Ia,,c -N4 " M 4 0 NMc I1 I I 1 I I j t 1 r l I I co C CICO CICO CD. CD COC COICO- COr- WD COICO COICO "41'OI- 40ICO MA10 LA i 4CDIN" -4 CO' 0 1'0I%1 040 % 1- 4 M U% 10 LA'0Lr~i t Nt 0 I "4- I 7 Cp'0 LA41 I e4l" "I" 0 " "4i"el4 e "" "4 "" S 4I " Nl 4 01 0 %CI LA C 4',9 0 of1.0' CO.% 010% l 01C'0 Oel' 0%*44 *lA' CD I0C *11le 07JAN10 h,,-.j.....,..... 0,~..,,~:~ ~-I~~~~~~~~~~ Ir4. LAL IIL A I LLA C AILA LAILA 0 C4 I'0 -N J'LA i I 0"4 NIN 10 0 4 CO 0 0% 00 j, OoOOCOCOa0OOO l M0I 10( NNM 4N 4-4C6it C10 -4 Y,,I CM "C~ r-' Io- M 0.1 ~ 04 0% 0%CIO 0I0% 0% 0 0I0% 0%I0% 0 0% 0I0% 0%10 0 0% 10%0 0%1 0 0% o:0 M% 10%0% a' IO- 0001001000 r 0f10 0 0' "4" 1 co 40 "4'co0 4 o- H r 4-. P N4'W j~s 010 0 0 010 1, I - I I,I,I,1 I I CJ_1 O I 1 i I C IO "4'0 4 N:0 4 IooI 04 o0o o7o 1o,.L'01'-o o 0 C CDILA r-i0 "4 N t' 1, L I ~ ~'0irC oiCo17' o0IC oi'"4~o 00 o0N4 0%o4COODi"1o"44' CO, IN 1410'CiLA17O4 io~0 ~"40 LA r.~~ o COA oi o o1 o Il 00 0olo oI06 oN e ou 00 0N 10 00 0010o 0100 0 CO 0 1060 O. Ig 6,0 I, 1 0, 01-0 06 I NNNI"010%CO%~.iN0%iLA I 4"4ICD'0i0%NC17LAI'0!.I0%"4'1ONI400 I N CDI N(4 V LNN I NNINI"44"441o Ill "4i4NiI1717171171011044444IALAALA'0'i'00'00i'LAIA i 1070D ~jlIl ooo,o, oo o1 o1 I ~ oI o, I I LA4l7'7%.j.4-~.,.,.,~ I I I I IJ I I I I 44 414%I'I7:0Nl0LN0~''LLIAALLLLIAAL AAALLIAAA'i00!-I-'CIOCO H~4A%I I, I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~o.. IoII I I.-,o I, Ii1"I,.%47l4AN' *i~~ I 1' lOO'01. 0100I 100.....i. 00 010.i.~ 00..0. o.oleo.!..gIe*00 0I006.061 i i I''II I I I I I J I, I I I IJ 4-~~~~~~~~~~~~~~~~ L~" NJ0 J' (1JI0C1'1 40 o 11D'I%4I %N0i17NN.l0 I 44~i4-14'U 4"'. I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(10 I,..I4 I I I I ~~~~~~~'...t I I IJ t II e I I I! II I I I w~ ~~~~~~'' 000I000I000Il% LbD.4b04L'0!-'IDD0, "4L!'.i%-04'I CD'0p"4"!'-0=t —," I I I I I I I ~ ~ ~ ~~ ~ ~ ~~~~~~~~~I I i I I'' I I':'i' 1'i' i' "' I I i'' I, I.,, IJ

-274I- I r%- % r- O o oM:coP 0.tU~0I M I I I I I I I~~~~~ M c o oc I- I N la, I.-0 0 110U I I ICID ~~~~~~~~~- I ~~~~~ I I 0 I001 0 0 I i* Io I0 ISI SI I 1 0i 0 oil 0 0 0 Si SI 9 0 0~ ~ ~ ~ ~ ~ ~~~~~ I %O %O CO P,- I~~~~~~~ U. - I In I0 I Ii c c l I II %O I I II I — 4 I,-4~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~~~~~ 0 im -LMC *g gg *i* *@ 9, *1-. "" g %g gIg.0 M 1 I I~~~~~~~~~~~~~~~~~~~ INiO0IS 0:Ngt1 IV4 OOI -!M:4No co in00N0 OIo I I II I SI~~~~~~~~~~~~~~~~~~~~~~~~ 1o i.+ 0e oft g 1NI —U ~ 4c oM 0 - w4 I I I I I I InM - Is+ t A % m M s I-4 I m I %II% I~ O N0 - 1'I.4P4MloLA N 0Mc - - I LA r- 1-4 00 NP I *% Pf- 0% MU I I f r O 4-I, I1 IO lf -r IC OICOcI im c I 0 0 Ci 0 - -1 I ~ ~ ~~~~~~~~~~~~~~I I WI I %O M %I m % I A oN IM 94.+.1U..4 la U$. %. I'% I I I 0 I'm c IN Ae I?*IN - om 6 0 0 I IM P*0%0 %+ It- CO I%+ 4 W4 0 N %Olm 0. ol 4 1~~I I I IO61 I u A I U- - 1I Uik I 14 In n 49n i I L )I U LA' I WI I IONiN11OLAINNN INNN NNI N IN! 0010 I ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ I I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~I 1%0 gig gP g c N~ M~ M *% g -N gII g, g- g coMI In %' I I0 I4 I I I 1 i 0c %0% - 01 rIN 010 r OOP1 as ON, O10 I- 11.I I t 0 % II I el I C Z 4 SI 4 I I i IIZ I 1 f l' l III I I I I I I II. 0 0 I 0 COM -t I %I 0.4 NO U IOP.r 0' I I Ioo( oooIo, ooP aoooioC. 0 OCOI0 10000 It- -f I0-0-I.-00 o 0 M INN1NNNNNNINNNN1NNNONNNNNINNNNIO 4 I 1 0l~ 0O10%O 00t 0140 010% 00% 0%10 0110 0 0 010N010A 0 0 00M'IN 0 I-.4 N.41,4co.0I n I,- i 1r.',U,1 I g I I I0 I I I II I jr- InIP-I- %- o 1 1. O0 0 40 i o tC I I II I I ~ ~~ ~ ~ ~~I I I't,- la 00 0 Ico In I oM - ti i' A I CTi I I ~ ~ ~ ~ II M n'P- I I I II o ~ - o Mco r4-. 1IIN* 0ICO0-4NM - Ioi)0 P c o0M0I, NNIff Io MIWA1r*a0IN 0, OW0 1N e 1I-co1AI 0 %,0mM %oILA U1 I 1N1N INOr M 40MIO-LAt 0%I1or0 I oNA AIorI U' 1 I 1 L Nc c NiN NiN c Nv N N.4IN N iN I coo0 NN1N - MNNN I M I ~ ~ ~ ~ ~ ~ ~ I of~~~~~~~~~~~~~ I I0 O, n iI0 t1 t-ts tI - I ItMM r- -

-273I- t(,N1,O %OI0 0 II N~o N% 7 % l ~ I.4V40M P4 I 10 0M 0N1,!oN - I^ I>. 0 -4Mr-(n0 tML Z 0N4 -,-'0,,J% Cl LA r f1Colo'-.4 0''f klf-Coi4 ~ % %1N - O N I N t tIn I.4 rf -0 NO l 0 I-l4-I0-r-C oC,0,O,0 Y r a cr I lee 0" *i ole *.1 *100 *@ 0 0 010 0 0 0110 @1. *0 gi SI 0.0 OI@ 0i10 0 0 oi U.O O O I t O oOIM,, I Ir, Co I. atC I I' O044 r m % %I I U COI- 4], 0I I I 010 0 P-1 -40-1 -4N NI (""1M M S t!~ L 1 -',O t -I,-I I00 17, O' "om 0 0Ot 00 0 010 0 0o1 0 0II0 0 0 Oi 01 0 0'01 01000 000000 IZ 00 M I % - Nu -4 % ~0 N -,O Ln 4 C'-t~ 0 ff1 %O0'% NSLA* Cocy clml - 0~ 0 C' 0NiU 0'4 N~ M M, IAu P0 0 01 01 0 04P,4O r4 0 0- 0 *I 0 gI 00 +, -a 4lv1104 I )IA0 0U 0 0 I I (il CO1 II tj )P4NP.Cl. AM,,I ok. 0 *j*10 0100001' W 00 m1400M0010041%0000n 1 I II -4 %10 0 M -I I- 01% 1,4N H t 1,')%OI I- tI - I 4 0I I00 F- st UI, "-a 1 I- - - I-1P4N N N N N NI iM M f 4s s In I Ln I I In U I I I I~~JA ILM O M - I a t IN U- 1, Ii I %O P-IN OL o 4 M F4C I WIN U I II II I CO~ 0~ M %0 0 1L ooN ( M N'fc a 0IO I- N 7% N - P-o N1ff IN IN t 1 lm~ 0IO -4 I4 N * I, f -t 0 ob r dI0- " a 0', O~I U- t km 0 I, t "4 N CIO Vi'0 ~0~1" ~~ tILI00U 0~ iW 00 01m 0 0 0n- 0 @1 -010i 0 04 010 1O0 0 *r C N I.1.'O 0 0 N1 g-A * * a, ** 0 M N OOf 1 I I ~~~~~III Il i ole Iel el O *I f el el Ie II 0 I I I M I III I 1 I I I I I I ~~~~~~~~~~~~~~~~0 ~ O I P I,0' I II I. A I Ii u" Iini u ~ 00 1 O O NoINOZ1 O4%DOI (OLI'O 1 10O % r 1's41 nIL)U I UrI)U I I *a N 0,N NI N NN NI0! I! I I i I I I I o0( oN!~'~0'~''''0 1"4NN""1N IU 0 N ~'U -Io "4O MI ~In of'-0 iM0W %0 M 4MP4- %t St 0' s - 0 P% Co M N.I I ~~~~~~~~~~~~~~~~~~~~~~~~ I I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 1W 0 M 1 0 IU' M "4 v 4- f4 I MN ff10 iN 00~if M~o ON fIN al1 ff- 1 P f0 00L1IO UIO N t U) %'I' 14P N %0 - 41 I 1W 0 0 01 0'I 0 0 0b 0~ 0 01 * l 0 el 0 * 4* * * 0101.41 0 * 0 II Co N N IN M 4M - 0 Lri00 U-,C s N tO 00~ U fI' 0 I c! M0 ~ I II I~~~ NI~~~ ~ ~ ~ ~~OH o1 010'OD Ji -40 CIN MI 0IN O% U~ 01I_5i U, OI O OI', - - If. I-',o C Io C I I 1 Co I I - if - O I I I 0 0"4N 00N0 I'0f4f14 IN I0'+i knS~Iz O % ON'I(II"4iIPf10IN i00otI0%OLnNo %0L(- "4Io O,.0%'0 I IC)00 CO0 100000000000010 "4"4N1 -.1r4 4.4v- III 10O IO IO O 10CI 00010 010 0 0 010 CIO.00 glO 01 0 I10~1~0g I I I I I I I~~~~IO a I l I I I I I~~~~~~~# I e I I 1 0olOe I I I I I I I I I I I I I I I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~I ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ I I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~I o~ 00 *I M M 0000100 7NW410 — 0 *I(7NC *O gI0 *N 0 010'- 00 IMft 01066M *l 00 10 100"" IMPI A InC N I ~ ~ ~ ~ ~ I I I I~~~~~~~1 -4r I M'I' C I 0 O,+ t C t1 - I- I II ~~~~~~~~u - N 0 * eI Ie IA 0 0 01 0 01 0 0 * P- *O *I 0 * I 0 01 M * Ln N 01 0, 01 It O Co %O.-4"4M4I I I I I I~~~~1 I 4 - I-v- I- - - P4P I M1 n'tIti 1 00 r-0.10 61.0 0 IN I r, 0.t'~~~~~~~~~~~~~~~~ I" I I 9 01 -4P- I II ~~~~~ I I IA~~~~~~~~~~~~~~~~~~10coI. I 0ff 10"4!"I0 0 rI41-4rfIN N M Ilm It t I m I IAF. I ole II UMNl' I 00 01 *I 0 CoOl M 00 -010 -010 0O 0 0)1"0 401000 C 1O 0 01 01DM 1 I 1W. I].4r1,0 lM P M M UAN r4 10 % n I.l i "0 l+.C l -l oi V!M ml V-4~~~I ~"4ff'l 0 0 N 1 Co ImtI I410M - 7 I 0ul0-MI N I UI I M I(SU~ — 40 i I M N -~0OMlj I 1 4 I.4 M Z. I7,4I ( U)..f C I I I1a,-4r- - I N I' I-, I 1 Nf1'I4N0''0T~~ 0I"0O'N N4IN CIN NNN- rI0"-4~'~1' ~ II I I>.. *I 0.100.01001000010010. I I I ~ ~ ~~~~~~~~~~~~I mIn I MI. I L 1 0 I-4 I N O MUa In I00 c - I —l,- 001 1,V 10,,0.CoM 000IV -' # 010010 000 I u I I %MM I4',tU IuNpOOr,-f-"C Ca', MN'0 I.- 0' I I I 0 00-4-4t4- - - 10 *I0 0 0 010 01) 0 0 0 0,0.10 * * I19(l 1> el,'O.-1f19' Ir 4 0 I1 I ol 1 6 10 1 0 01 0 010 0 0 01 c I I I I C I I I I I 1' I- NI J I~I I'- 0 14 IN AC IM 01 A rII IM I I I, I LA'I N0 N0r- t ~ CYr%" N0 O L( n 001"4' 01N 1 r — 1-4ff "4'- f1 N I0' If110 1, 4 NO M 0I Cr fIff10 "40 CO0 1.4 O I CN' 0' N I II S D S...... 1. -1.. 1.. I- - I I- I I - - - -

DATA SET D FUEL-AIR CYCLE ENGINE CALCULATIONS -276

-277W. a, ~4 Ii.ii I. C Ir-, 0' 0 I iCM;i.'.'.,O I I co! o o 1 1{~~~~~~~~~O' -'~ z: I'-J:' I - I~~~~~lx Ci: OC)' -I a:.= l k 0!'', I I 0 ODOD01-I I; ~..~.,'~4 I I an ix; C IxS: Q~!' O!,.-,.,! go,, W O r —,.,io S O \,0! (c I',-l, o - I -' Wj sCZ. 2: (Di^ o'c~ I-~ -o o! =?; ^ I "i I- r'!W I ( *0 i I I I i W UI oI'....Ij L.::I' W I,'.co",. r-.. a. I'' II 3.I o {. o p! j[,,;c 0 I ~ ~ I! I I. S!.,o'!.I' l:I!'' I p WI'!L) ooiooD':In ~ai *1l,, I' I o l w ~~~~' ocrt~~~~~~~~o' I?' 0 ml'!! W', I0 oN I'Z W' OD N'4: O IM'.. N.'N Q a! S o^ O!co IM r-q to. <r xIa. iCNI [lo o L W X. W2U0: r.,:,o CO i- - cr' i, _ ~-IwL ) M 1 I -.rI'- im.-' ON uI; ~I. U ~ i V r',~ll.',..i —, I- I I C WI =_I I ~r-! ao 3 z oln'-o ^o-oo^g!~ oo iT~~ I'-o 3In L,o -~ I" I;,l,~~% r~~I It.I W. 01 uS. a' W w.u I. t W i5 - I,: I i U IIm.1 crrO oI oo0o ol,o o i, ^~~~~~~~~~~~~~~~~II ^\' tt 2 11 i 11 itnH ~. _jj' - I,<: I Lgi O. 4I I c 3 ~ in I. OJ0OOIX I,.. ~ ~ ~ ~ ~ ~~~~ 2 o'i,,?~ I!^ * O. I I 5 ~CSL-o'. Cii.n i n I,.e,b allI aS. o. W I. I, 0 i...I ^ 01L.,,.-.;'.. Io U iCii I' I: itLc W, W-It Z!r W'S W IJJ: S''uj. - n ~- S~ ~ ~ ~': " ^s;LQ; —. 5 {~~~~~~~~~~~~~~~~~~~~~~~~~~!::S~': crto', er~ o I', Q Q Ce i I I 03I LA:N D 0 1iO C S< M 2I A. [W WJ {3 Lr I( X4r') c L Iq W. X L_- a, _I C5 a W'it i' W io -rtt1o Z I p ~ 3 I- U- U c1 S W' IM z - H wN I0 0I Q S S 0 0 i 0 10 0 Wi - J S I0 fI'I * *'' LU 0'': I I- In>*U10~* I''^. f W] Q Q0r 01 iinPU'S il H Ill I: - I LJ w! —' i =, W 1inwI I T o i'aI G%~-' (.3 EC~ Iit h- i0.^.I i 0:n 4: I I I W I ~I I~ I'~' LU'L WI "1 ~~~~~~~~~~~~~~~~~~~~~~~ I I I I IininI~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ I I I..J~~~~~~~~~~~~~~~~~~~I~~~~s~~~~~~I I I -~~~~~~~~~~~~~~'o~~~~~~~~~o~~~~~I~~~~~e I I Ic~~~~~~~~~~~~~~~~~~~ I~~~~~~~ i —~~~~~~I1

DATA SET E NORMAL RATES OF FLAME PROPAGATION AND HEAT TRANSFER - 12000K EXHAUST TEMPERATURE -278

-279 I I I I i I41Il:. < 0 I 0 0I ~ SiZ Jl*:X1la!:: * *:l X l l l | } l L W; C ~ I W.l < < X: r C: l, I I I O 0;W I 1 F I ~I I I U COOO ^OB 1 I"';.1. 0 0 t- 1,.I~Z 1 I I I I I I I U) i - < C. i I, CC II- I'i II I w I I I I o L|O j I I i:zl Z 2: LU iz I I I I z, I O I CI O lZ lZ~i llu2~o I I I I ~ I I iU I!0 I. 0 I I I a. I II I i oj< N1> e c oi j: I! uj ia<!U w!z ij. U S; j i C 1 1 1- 4z jt,!, l % r3 < % 0,, m Q i O I j I I/) I I i! <! < 1 1l I L I. U't I i I I I!'I I I I I I I i W)1Y WIS e eQ 0 UJ I:: I: IX I U I, LU1 S ^-i0 I ~ I 0 I I I I 1S3U 0 X?Dj 1:: I i, j I I I IJ!! o i! O! I I I I I I I;~~~~~~~~~-. jl', I.I' I i U I I 1 I z I I x I I <; 1lu,1' 1,~ I I 3 ~ IoSS I uuu~x!< <x " i 1hI: I?^fc^ I1" oI ~ lM~ I I i l I I I,J <~~~~~4Z I I I g~~~~~~'N1~~~N 1" I II N~'4IN3O 01. 14WI I 14I, Io= u Oi~ IO 1.) I I I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

-280o o0 o o lo o o o O o o o a o o"Oa0Ooo w o ol oi.o co If* <o! 4 C yl <^<M^~ <C~* r o~!o4 0 <0 %t o o 0% O~. o0o ~*~ <M cm * 0%'- 04 (r~ oijm 1 3 Colo o 0 o 5 1 o 0 o0 o o oa o o o Coloooo 0 in1 %O?-l~<>o 0%10 P4 Cy Mt UN Io P- Co ~!o~ 0%.Io a0 06 010 O-0 j Colo*w I-^ f n 9>1 ~*<-~ co "O a O' 0 0 0{0 Oi 0 000 C OlCiO 0 0 O'O O 1 N( c C yJ iMf" m m, I"I mic men~ mlm l ffWf^^<' 4 4 < *If" ff I fW{ It MW (* 4" <i 1 I 11 1.1 1 11 11.''!~~~ I II II II 00101~~~~~~~ ~~~~~~ 000 I I I I.0 00 0 i 0 3 i 0101 0001001000 0 C0 CI O oCIOO N00 a 000IOCIO co I0O CIO 00 CI 009 9iNco 00 00 0000000000'0O!~~I 1o'o~~~"' 0-10 j * *~j' *' o t' I I a Io <~o^ slo ~ (o< o t >inNo'rQof-S~o o <! (io o o' o~io o!fo o- o o ol2_ * o o ol olo m-..~ ~i.' O,,d',q!t'" o, o ql oq o,m~~tdIql I ~..~,oIS 0 0 0 00en00 0mi mom 0o0 0o N00 olo 00 %oloo ooPO - om o, o, 4 o O*m *1 % mN O * C0N n C 4 00 001IAN90001r0f @69 991000 @019A0-00r W,?IOP- o ocoItI*' 11" 10111o &" o ot m~o co *. <t 0 um in M -t Mpn r- I- P41,41 0% 4 N "4o ^h^ M OiNO!: M^ 4 ^ m* m!<o P oo Md'" in f~-l' col,0 in ", l',.'.,,,,,,,1- coi s I P- 0 I% 0% M N I otI-oo1r4 -!i c P) 0 m Z o M C- P- M oo oMir- ~o i no'ao ool o o,~.` fo _ —- 100 _o I olo Ioo oI o o!,ol o oI o I0 o, O3S53?3oS~inSS~o o! S o m M n %O cO co 0! < tmcoo l -O ~il*-< o38 * ~~~~~~~~~~t~~~II'o i (kl'' 3' I I' I ~ 0IN 00 0000 co 4'1 L N0 I f1I0 O 4I f10 0 10 C% N 04' LA0% PN 0 P 0 00co NN c 1o 4 P1folI1t m4 414' 0 O Nin o - N'0Co 0%I N 00 co a0 0001 0 *00 cooMbI N- c 4 M"4P o 0 PM to w00 L- 00 ff14 P0 0 m 0 t'.1 In 10 P0o 00104'<4'f o 0 M In 0tin40 %O-N 11 0 04 M'L U'n LA f1 P414 f10' P0 P0 %4t' 0%t N in I 01 o~ N 0im N 04+ m M4P l1 a, MfI%'0 LA A P0In4 IN..eu'i %-I t 0 1"4PCY c'0L f0 0P1%N 4 0 LA P01 N 0%N. P00 t N P010 Ur" In LA 01'.t 4 olo t ff 1 4+Oin0 P0I 4L P' LA O0% 0 P IN C P04 L P0 t-1' %OIN04 LA' 01N0co %1.4CY0% P0~. (V 0 0OIN'IN r- 0% N4' LA 40 P0Ou N 4' LA -4 N' 0 % ff1 M - 1 N "0 0 010 010 0 P0-'0I LA P.i"4 0- P0 LIN" P-0 fNO at 0N i 1' 0" N0%o o o 0 Oi4' LAd P 0.1 0 0 00 0 0 0000 90o- f. m<W<f*1 l o o o o ooooooooooi; nI o o -. mm i I mncM^I I.I'I< I' I I "4k f1NO0 0 a0I0 0000 1 010 % 0 1o ~0 i N0%ff1P0A0%'010%P00%"4No 1L O 1OP0N0%t ~ I N1~ go li 0In'I0 0 OP 0 "O co in 0 04' LA 4'I'0 P0'0000% LA LA P0.-hO 0%' 0P0 0 4' 4' NiL P00- M Nt I c 4' N4- co r- co.4' 0% r0 aP,- %'0 f14 N r-L co' 0 ~ LA *P 4' 0% P0 Nb -c 0 0P0NOL'0 P0"4 OA0 ILAP00 0 P04 "0% P0 4 N 0 14' 11l %OI 00 "4. c4Lo 0% 0" UN0 I4 0 4' P0' N LA co 4 O P01' NI0 in1 0% N 00 N ~ILA P00% N LAO ff1 04' N "40 ~e N 40% 0% ~ 4' LA N.-4f0ei0a"4. "4 0" N II a P0'00 N LA N... 00 0 0 f04 40 0 2000 ~~~~Io 600000099 e~~~~~~g.......9 sie gig 00~~~~~~~~ 0 -000 "O9 0 ee... V g O P 0 0 0 ** *, *gt 0 - O~ ii Ii Io.4e4N~~~~~~~~~~~~~~~~~ff14'LA.LA'0NI~~~~~~~~~~~~. 11 1: I I. I LP1P Io.,:,'I III II. I NN'N,,4,,', 1, i4 1' 1',-,,o I I II _ l I,&" Il" 00a00000 00 0 0 00 0 0100 0'1"0 Nso'O 0 LA 0% LA ff1 0% 0 "00 olo N l N-'04 0 01 co ""0 4' 0 In1 L 04' 00000000000000100000000..,I0 ff104" ol 4I00P0000"4""'0~ P0 P04' P00% ~"40 P0000,,,g4'0 4I",' P0,, P0'0 00 000000 000000000000000 N l -. a 0:n N f1 4'I0 l0 A'0,P0 P010% 0 "4 N ff LA oN N o " - N -0 N,40 N L'- Nv:::'!''i?,,'''' 1'' i'''''''!'''' "''',,,,,,,~T'^^ f!,"'f,, ~, t,,i,, ~,,, -o^ 0~~~~~~~~~~~~~~~~~' I II 4 " 4"44 "14"4"14" 4N",00ON4"0 0%" 44 14 "4"140~ i nNNN~,4.-4 -4o4,4,'".4-4INN ooooooooooooooooooo000000''0 0%1LA 0%1P'0P00'00"N00%LA0%4.'0'off10%00LAn^otOP'0 4'NINPjr in LA~ ~~~~~~~~~~~~~~~~~~~~~~~~~.. -,, ~ ~,0, Vl,,, lN W)I1o'o411In I,,'n,,,~!,,,,% nW NN =lo n oP,'...-,.O',,,"'l4UNOi nOi't' -F4W o 0tf-N 000 0% r N0 0000 0 0 0 00 cMM0 M0 0 0 1%00 0 0 ff1L%4' P4'A 0P004 01 f f N Mm. + ptI 0 0 LA'0I NI0 0'.0 0%IP P0 N P0I'N'01 I 0o 1000000 000 000 o 0 o0 C 00 c0f 0,0,.,,, 0,, MN'0i", N,,01' mi"% A "'4 ff a 1''0 0-N 0% 10 q 0 10 LA"!~ 0i% 0% C ooooooooooOOOOOOOOO o looo P4 "4F<4 P4 F4 oo^ " 01 0% IP P 0' 000 N 01-0 P0,4' N1.4 CY0 CY N ff1 z 6I Io MI.: i N o ooooo o ooo Noo oo o o M 0 O-o'4 0"MLAOLAOLALNAOmLANOLA NP0'1 r lnO in O - U,%~~~~ ~~~ M~-,0NNM4.,I P, 1 "4.-.4 [o NO"m,:n a M% UN. o[: l-!l- PO.:V- %ri O~N% - nNm0F -P-4 c0 te, co~ _ IO -, -N ~!~ M P4! M! IN, ~., at~~~~0 f't't1 unOu 0,,-,[ %'t M. ~!o m nOC 0 tPIplWMN% OMI 1-P414% mr- t0f4% O0N0 l y94M c.-4 M-M IN~ ~ ~~~~~~4 m[.-, VI " " af,,'ll~10 % f O OM O O O O 0 l,-I %a-I!,-',-1.- N. llZI Olin - I I ~~~~~~~~~~~~~~~~~II. V4( I,% t0p-c LA LA LA LA LA LA0LA LALA LALA A k0LALA LA LALA0In 0 wLALAM o NN o OA I- Nn Nj. O N 04LA P0 coc0o% oc c oc I0co0% 0% 0 co1co co1 co0 co co10 co co co M 01 0% 0100mOI"4 "4stIN N- ff1 rf1' LA LA'0# c'O P00N0000f- 00N10%O 00".4 co IN0 N C) r- 4'44a n 0000 0 0 00.010000000100%0 %0%011%00 %0000 %100% 0% 010% 0% 01000001000I P. 00001IN.I~.~~~~~~~~~~~~~~~~0 fi" ~, *, c'I:..,,,,,.,:,.,.,.,. ~ "4"4"4"4"4 "4 "4"4'"4"4"4"4 "4"4"4"4"4"4"4"4"4"4I"4"4"4" ~~~~~4I"4 P4I 4 "4 "4"4"- 4 " 4"4" P4"P4 "4"94 "4"I 4"44 4NNN.N NNNN. V.~~~~~~~~~~M ti'O NO r-w %.( M (^ M c N %m 0000000O000 00 01 0 000000000 XOOOOOC<~OOOOOCC< O i<(^^O ((0(0~^J0~^~OO<000000000000 0 0 0 0 1 0 000 2 9 * 5 5 5 * * * 9 * * * * 0 0 0 0 * 0 0 ~ ~~ * 0; 0 51 0 0 0 0 0 0 0 0 0 0 01 5 0 0 9 * * * 0 91 00 I~~~~~~~~~~~~~~~~~e4 I' I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[ I II ~ eI' $' l! LANL~~~ff1P00'%' 1 1''i, I! NLa wr i'0 + Of 0%P0N"M4"4'ffN O+Iff'00 N.IO %IL co 4' "' NO ON _4' 0%r$ N,'0 0.4Nf1014'% 0% LAOLAP0(LAAMM% O"401"4 LAN ffIP0 O N 014 co N N O OO 01"44 O "4 LA co4.1 0%I0 en 1' LAI N P0IP0. "4 NWm 010 P00%'00 NO'P LIN ff10 U"4P0~N P0 4'00% 4' P0100L -, 4 enf1 P-0 Im LA ffI" COff11 plN P01 4''0U% P0 00%'000.4 Oi 4'1 "4I'0%+ 0%tI m 11 i N 4'A'0 DP P04.'0 II C P0%4' Q "4I'',.0% N 0% P-P0IN"4 It 0% N4c 0 "4%tM004' 0N "4- 01%4 LAN P- 0'0NN,I O OI, LA'0'P."40 Ini LA LA1LA 4IN 001 A LmI nLA ff1 P04'"4LAOin n i LA ol% 0 "4 N 0P P0 P0 0I- -c o0%'0I0 0% 01. 1 0o0ooooooo..'oNN o o oo 00 0.0 0 O1000 10.9 0* ff1 I0 N N10. "4010 01P0'0~ff1 0'0,IP0'-414''0, 00110010.4.4 ~i"4.4I"4.40 0100100101 0110 P0'040 0 0 O, 0 O4 Vfo'LI0 LA LA LA LA LA L NA LA LL LMAI -LA LA A 10% 4ON'N. 01 LA o"IL N'0ol.N NNic. ico 0,1 P, n LA I o 0,' ON 0L NIo L O 00. o fI, L.L"Ao 0000010000010000000100010000001 ~I4' 01 L "4I'0 4i" P0 La- co" 0'LA0 c 01 P04' I NN N 0I'4. N0f 0P0L 0%M'40I N4 4'.S4ID SS'4'4S'44 AIALA0PiP0 0010%00"4N a, NM 4 P 0f.if1 f L' P 0 0 I,,,-I e 00 010%10101l0100000 " 0,-lC r.-000100oo,,,00.0.".la'1".I'"-,4,a.d!m 1 NN 00 OOO~~~~oOO@0 *1miraIkn IC,~,-... 00 ~ 0'", 19 * 101 4' P00 LA f1- 01 N P0.44' 0 00 o4i'0 000% r L'LcAI ^ 0N 4m' O4 0 NJ 4O c I' T 014'1 N fIN >0 0 0 ff1 I'0 N 0-O.4 I0 C fy- 00 00 P0 N'01%' 00014' P0 LA N ~P0 4 0 P 4P cf41. -f04' f1 NP fNfN N N0. ~IN vme MMI+.'0.L 1 4' "40 P 1. ILA 4' N ff1.414' 0I'0' LA I0ILA VU)U4'10.+. I N N I O oN l o lA O' 0 o I Om N "'A 1'0%4' "n LA rf 4 If iN N o 4 Lrf 0 0 I 00o o00o %''0 O o..4.40 m L P r4 "410N N- P0 0I0 f1- 0 0 NI"4 N * cm % m m \!M<jc <- ^ ^ ^ ^}^ ^ ^^,( ( *i <^M m ftno" 00%'0"4ff ~ ~~~ff1 I f1 0 0LA"OLA'4'1'0,NNel f14'e l ff1 01Pel90 ff1 elA'.4L01 414' 4' N 0;LA1P0 4' 0 0 q el 0 #P010 oooooocooocoaooo~~~~~ofloooooooflooooooooooococ^^^4*o~~~~~~~~m~^^^|m~~~o~f~~tf~m~~oo^^c~~l<^tf^ P- rc^ r ^^o I- co w co o, m wm w I!~~~~~~~~~~~~~~~~~~~~~~! I OZ 0 0 0 16O IO0 0 0 lo 0 0 0 cO01 00000010 N lunO 01 0 90000060000000 0 -I.0.0010ko <* i 00 co O' 011' N10 I0..4.,,,d001 NcM IN 01.. N.,, 01 m1' 0. 0O 0 t 0 f0, 0 1'4 N" 0m,"1 014'. 01 - I. 0i,, N.4"44.m4..mcorII I 4Nmcf1rf1^mm'4i4'LAILALALA'0 mm'mr0oi0PoP0mb mi'. i:oI "' "''"' ""'" (sicsi0 o nino sio0c^^ st'~ It oN1 e 0 l"',., Me I',,,,,,Oc, o o Ol " o,,0[0 co r el o i1 ~sio 0 o 01of^N~ ^%~ ^x o f mlU"NoN~,,d,. knmool. yo io^^^^\~~n^ssm ^ m orm ^ rmI0.010 oii OlOim ftnniiinnntimiimm ^^^ r OlO' co o oo ~ o~o ~l',.-. o,,,,,,,iM"Cl 01NO 0 010 0 0 00010 0 0'0'001 0 P0 00 P0 f14' N i'0" 0 N ff""o'"'' 1, N,,,ff L 0'' 01 P0N N'0N 1 P0 LA 0 -1','LA Oir"" m 01",4" ~nnmn^ ^^.m fs(M-f (oo~oo~oooo~oo o o o o o o o o o o o o o o^ r > ~ ~ ~ ~ ~ ~ ~i.o.[...o... j.-:............................... 010"4N"000,N0N4'.','A"I~N 44040 j0fffO0 j 1f4.O~fL.4N.Lj N0P0P'0LA4'4'14'~cj<\(\ 4'I4'4 4' LALLL mlt ~~ I A'0It' 0'OP0 01.41f1LA1P00NLAIP04'i4' 4~*'> ^m LL 4IN n 4 o!iUn O i-, c.,,l' Xi O'o I' N"- 0.-,' C o! 00 00 00 0 I C 0o0 0000C 0 1O 00100" C Oc -l'" - 4 m o 4 o ~co P01^ o clco 4 Pmcolco m c o - o4o -!' -i oN oioN'o-4ioN 0~!oN o-ioNo! Ol l - l l- c-i N N N o M ^^{mmm^^aio^ moo i^ o ~ -^ m ~~o^ ~~im ^~oc~^ cowo 010^ 010^ 0. in: 0 006 00 0 6 1 06.1 10' 00 ON I0 iN 4 mO I41 0 1 L ~~~~~~~~~~~~~~~~~~ooo!o oloolo oo oo oo o {o o oOo rm fi ci^ f^m fs moo-in n o~i-ifm^'noo o1'""'m'' N, o 01io'I Noo.ooio4 1 foN o Io }mooi 010110Ni'0'0'P.0 P0 1 1 1 o 6o0601 ojO 0 1 0 0 00 0 0 0 0 16 1 0 0 1 0 0 1 0 00 1 1 oio''oo^ ~'pfo ~ ~ M ~' mi^^ moo~^^M m~o -m^jo oom'..41.4.41.4 "4 i "M N1N m oo-ff1 ff1 LAP0 014''0P0 0o~o 01.4 1f14"0 011N4''0 aoION~f1LAP OIe.4 N 4'4'4' a1oooco1o aN.410 4' P0'iP 4 P' o'0ff1^fI. 0101'f N{0 f 0 N 01' 0 "41 0 0 0^i- l P010 P 1 N f1l o ro- ON,,0 4.0,..slI P0 01101 P01'l/P (M. olL LA'01.4 N 4'~~~~~~~~~~~~~~~~~~_ 4',ALiA'P 11"4f1'0 NIl,,,,,00101.4 -I f~ LA'iP0, 0,..0'-' N~f'LAL 0P14" oo 01101010 PIP P0' A l'N4 I~~~~~~~~~j II ooobool 4",oom,-,olo 00,4'0OjLP0IA04,J% 4'0fPI 0010100 00 00 001 010 0011 4'~ N0 0IL LA4''0"4IA I4'0 r,,.. 4 " 0LA0114.,4IN4'-AI0 JI 010 4 0 010 010 ff1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ r',-"4IP0. f'0,'104 4 0"N,-,,,LA',,'N 01'l ~'i "0!'.'1 ~ I. ~. ['I.'I' l''I.'[ I I ~ ~ ~~~~. I., -i.'-''- l,i i i0 I,; I,,,,,,.,,.

-281In Ico z colu-~ I o Ii, ~~~~~~~~~~I I 01'co4 %C %t oo in Lnim r;s N!o Co r^ ~o( oomo o im~o Ln~% r*-SM~ OjO O'r, < o oor )i o fn N M -4.ci o, a' o.-C (5 M.o'! c o O I.. CO MriS CM CM CM P-~ *-<| V-4~! F-4;-4 V- q-41 V -4 0 OiO0 0; 0 0.0 OiO 0 0 OiO) I%^^or- 0sM O, o'i o t 0 in-00 m co,inm i-io NMO NM- 0w110 rC- o o)o ^ioo in CO U1 Lnlfn o 4n M0 Mo (N zi^- r-4 o fri<^'. P-4 m^ o' o in in IL NMin oo co ".7 cr, 4!~- %O Ln Mi oo P-( co 0 in omi r- }* NO NCMooim inlf- Ns. o o o C71M N L ON %t 11-4 -A; 0 - -* "o0 mn I CO LA M O^ co C.s coO i 1~h r^ M 0 f-( -.4 <1* ^*n ^0 f 00 00 a, o 0 r- P-4!< fN N M M^.(Pf~i ^j t -t't I 4 ^-[t>f^-* OiOOOO.,..,..~.OI o.o o.~~ o~!I I I It ~ I ~ IaI ~ Ic Ln IN c 1NNO.c4oor.Of^^Aoi r^ CO M u'A M 4Oo osiM ooiN.O co oi N O r.QNfno~iOUO (1^oif IcrnrONopniNfQirrit-rco~Oo IMW Mc C7% P- 0s -$'Ir- I cr, c oo \ o (N - r — I"- a,'t!o co la^ %Or I [ Il oo%. In'o o 4 M1rM rn M^ Ln ~o (MIN O o mi.-4 r-irn ayso O Mo 00}^o M^ -4 oir — Lini^ Ns o 0 o el I i e S i S N uv cr. oo o, co 0100 <M~' rn oi (4"i4 N- Nor or <y in,- 04' ri no c~ I cro tvM (m 00. O~r.. m sO i i't O M -4 1, co- o mo No o ^ c ij %0 o o^ o^ N Um O't o ( O!4 o Mt- r0v U- ^o %OQ oo< o 0 M^ M" LA~ (N I -- asi^ ~~io o l as: M\ ONC0 In U,) M1 0%' I-4ir l — (1s 101,1 U)* 42 \ ^'' N OM4( MI 0 0 ( *O <5{m N i't M 4 M 4 ON I [ * I I I I C -rt 0 co r^4 1 M 0 r- 0s o NM U1,0- ai O^ c^ o. I fMi ^' in.O!P c o o0I O ~-. r-41 M. Mrn~r -t 1 <-t't~^ -t tin Ln I n mjir k Lnn O,., ^ O 1o,Oj''O;^ ^O l O is O s D * % O o!,n!'<< co O^'r co0 M f*-h rS"4 If )* 4 L N 10 PSUN do >o roj colm 0, en o o0 co; 00 t ol~ o0 Moco U') 4 in IallI OM co M co It co in N Cioo'Oin mM N o N0(MC 0 %O CMN Orco P.- >0 m^ M, (M N^ N~ ~^ 0- 010'O a" 0s C' a 0 110 <^[f<^~ ~~~ NM f1 OJ(M <N 4^ r-4 r-4 -4rII P-4 ir-4 P- "-O f-4 r-4 it f-4 ~~4,-4 <^ 1 ^!-4' ^ ^ ^- ^ ^*'*4- ^ *<f ^*S^" t 4 4 4 <t *4 t 41 4 4t! -t <h %[ ^r!'t -t't LA O 00N0 0O' C 0 c O OO O. 0 0 0 0 N s I NNNNNI NN(N<COINM?4JN(Nj NI O NI NI} N N Nip Oie *O O 0000 O.O CI 01000 9 0 0 010 090 0;0 0 0,j,,...,. ^..,.. j. *, ~.., I.S. e l I.S..;:~., ^oIr c^ LA NM U) (7| O M,= *~f - "l + 0U oo CYM 1%-sOl^ %0^ M'^ o 0a cr%~ % s IN..,O 7'. o'( M 4 0ir-<a M %O rl- %t fI.,, co (7,,~k,i? crf- co M n In.-4:r, M 0% ^ 0 100 c o! l c o o r4 OfF P- in 11%,-W fn ~^ in m I' U1 M M C?% 0s [so co a, co r.~.^ I co O o r^.I — coi on o r,- N\ Ln <4i1-4 in; r. [i I — d 1 U-, 0 t o co 1O'. I t 0 e l.. 1 S 9 M 4I I S I S S 1 Q.o~~'~-~ ~ I.I I o OIc N st in UI IO NI1 O'I c U M tN %O C I 0 0Mn I ~ - N n N o ~~~~~~~~~~~~~~~~~~~~~~ I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ CDJ~ rI1-4 M 4 u),, f~-<~~ co |7, C7 }( 0 C;o N M N M <M (MI~sM U) U) rsJ O',( IM(M I ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Ih o 0 t I- 4 I - ri M,O' N PI I I- N i r t o M I so Mir 0 o o -4 N (M roi M -4 M 1 o, -41, f, o'~ O, i o O,~i7 co 1-' ^O I n M*-i NM r-q 01o oo 0 I% f C* a) 1tn s<t I N4jf NsS( ~-41 o 10 o C oo CO oM OjC 0M 0N O', 0N ^1 0 C, 7 0, C, ) Cco aoco co *0 co oI co 001CO00 co0o oo Co CO P- f* - f* - pnM ( 1\JI ^ 4 -1.4 r41 4 m4 - >^ ~; ^ ^ r-4 -4.11-4 — < {"4 -( -4(l r-lr(r-' — ( — p-4 (s I r.4r — o4 <^ in o -4 I..01^ rn c t- (' -4o- in o i^'o4*'i rsj 41o~> 1 4-4 -4 -41 P-4 r-[4 - I (MJ 4 O o O *<M oo 01 ~oo ft rIn U ni-, N! OOIsO -M -4.1 fin M oj 0^ oo COis -4!-U C3n o C Z COf-m rN cN LMNO Ni < - o1'-410 N I 0 M- o 30 - I I I- N4 0 I Ij IYi O ( t M o O ( V -i Un in N ^ r t CO U'0 M %O O o^ Ln O I~~~~0, I 1'I otN 0o N< CO 0% in-r~ NM o }M 1-4 ~ o' co so or *~!,O s c c o N. -.4- r^'aQ r^ Cy, (M " i~fio I %r' o^ 0% V ON r- i 1,U c o~p._4 0CICM PI- N^ in 4* L-rn V) M oir1, -4|T 1 M - M -~ % O 1 c7,I\ — re **^ rN +n ^iO on -~ r~ji^ror rc0 o ~4'r n co I xo ^ C) 1,4 M't o O*t I fji fI' *- c 0 * P< ro Pr- N CM I*\ or io % M r1U- i %D In r — Icol 00c o co~ (If co! c ^'4 a, 0 M %O In I,,..., "'. -I.,.....-... 0~i0000i0'^Oi0000ri0010000'^oi0010000os~i00I0000^oo 9 9 919 ol ** i 0 0 9 9 9 0 *I e *91 * * * * * I c n t 7'I M l I,,-' n N 6, I,0 - I I, 4, I- 10 - 4N -,O CO I N st- -i o cMt coIIfI Io, I ro ^o | (M4, M M\-< I- rUl^ - O CO C) Ni)Mm 4cL o t - ot 7 jv. ts.%0 %> "~r co N M c M o CM o n i4 "o ~o.-'... i. V) I I I I I i (M I t M s C ) M - ^I -t -4 %O < -(f- M)1- N~ m- i-t all M-j- co~ 4- co(- I IlrM -4',7~ rco O - ^0 c ir co t [ O 00 OI-O O I II I n I 4 - - ri M I I I i I I,,, r~ ~CK.0'"'-' ~'"""""019. 11;" 00....... I. ~ I I'2.1L2 I ~ o,,J.. II.,I,,..41,...4 I''~~~,~- I I ii'1 II i I I I I,,t I i i l ~~~~~~~~~~~~~~~~~~~I,,**,. t~t. I ~ ~ 0 0' [I'" -"!4... II I I I I I I I I I 1 1 I I l I~~~~~~~~~~~~~, I l I I I I I I I I~~~~~' ~ I~ ~ IO IO' U'I I I[0I I OIO 9.41C0 %01LS1 a'1%tL(~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ LO NII~~~~~~~~~~'OI%0 ~~~~~~~~~~ 0~~~~'~~~~ II110 0 ~~~~~~~~~~~~4 ~~~~Q~~~~t~~~'-4ILO 0~~~~~~~~~~~~ 0 ~~~~~0IO~~~~ ~~~~~~~~I II0 " N i I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~reO~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~O I I N4- I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

-282I j..J ON %O rl-r_ r-0 4- N% OO0%1 t V-d:0 %+!U,)% m4P.MM In Ni CNO F O I o > C 0.4mi- M0% 1 p.4l0 LA041-v4,.P o" N14 010 (Nma -c 0IV4Nlm +. - ot-( I i~~~~~ I0 @10 010 0.4.4 0I* ml 0 @1. - *I 0-c' oc oc 0c % N1' ~00 I10 e,0 9 0 0 e'. * I I * * I 00 @1 0 0 0I I I. I I I I 0 0 0i 0 0 0 0 I CIO 1 I! 10 01 I 10 1 $,-4 0 ooooo'oo0oo0oooo0o oooo 000 1o000 1oooo: 000 1 000 o 1 I cc O oo I 00o 00ooIO 0 00 1ooo o00.Ojl o o o ooooooo010ooooooO1 II 100o 10co 040 I IMI Mc MI f I UA I I * 01 *i 0la e 0 *I# 0 0l It 1 0 0 0 0 II el 0 el 0 I 1I: I 0 M'r11co-t11M 00 4 001 P* 0 0 0 10 N p4 m100001. Ic 0 I l I I I II e lI I I N I I I I IN IN N i I I I I NIN Ni I IN INN N, N I IN if CY I I V0 %O PI P- C P0 - M N %Ot ~ L tA1 in M -.~CO NL - 1P4CO N M -4 I-C 4I~ OD00 -O %O 4 CO;..0 M M 1 I 0 I1 0 In CO o, LA 1 otc' tc n OI% N p CO- NI%0 cr0 co CO. 010 r1II F, in a, FI 4 F- c% N o CO 5I m -c %Ir. I W 0 *I 0 01 o 0 6~~~~ ~ el 0 0 1 e 0 01 II 0 0 1 0 0 0 0 0 g 0 0 100 t. 0i 0 II el1 0 o 0.0 0 01I I 0 a 1k 0 0COCO ON~- N0 I %tP-0 N~ UIA P I4U No -%0 0:C 0%~ I O'tCON(4 O I N NNI~~~~~INIII J I N - U. II 1 0 CO'0% ~Q0 0% CO,-40 NIM M Nt N, 0ICO CO1, — C ja 1 1 4 -CNI: IIr n 1O O -c0 1o% % 1 I I14COI"CO 00 CO1%0 % 0 0t10 0%10 % CO0%II( 01 0 1A 1 0%~ 0 C10 10 O 0 I'I I.1.. e.' 1016I0 of g *I 01 0 el l a el0 el I I I Il I I i I I I I I *I@ @10 *00I00~~~~~~~~000 1 1 0 10I I I IN0 - P4I-40% CO L PN 01LOt 0M -4N tI0 N0% OCOCOU,. CO W4 0 0 L I'N~r — *+ m -rNU Qt 0 IO 120010~~~~ ~ ~~ I M I M I0(~ OF4I CO -...M M L @o 0 0A 0 gmui4 00.co0.1 *n.1"r- *l I I I 1~~~~~~~' el l0 l 0 I0 I I I I I I ~~~~~~~~~~~~~~~~~~~~~~~~~~~.4r4r IvNI N N MI M I..LmUiN I I I I I I I I I I ~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~I I itI1 I I I I 1 IC, -1IN N I7 I II N O It Oto% %t fn I M II 0~~~~~~~I~~~l ~ ~ M c MU10 NI% 1 0~~0Ie.IICO~I0 1 0 0 0 0 N N M M M 1,t t t L 4I I00t O P-t F ococ 0% 1e~ 4r%0 0IN,"4 f-e1 I oolooloo* II ~ ~ ~ ~~~ ~ ~ ~~~~~~~~~I I I 1t4 I- P4I. M I'm I NI tII I0 M III U - CO I a LA~ ON -, I* t co4 I N1 N4I,' 414 co UN 4 O Ln I IN NC' I P-1 Ik 0 lo oIP-'4I,.. Ir- 5511O %I I'M V I I I I I I I I~~~~~~~~~~~~~~~~~~~~~~~~~C U L Ln P O ir- I IM'I I I N?0% r 0 IN N N1 u lo LIl0 0) M c s0 f~IL* %o I CO O M1I c c 41 N0%, I CO[C 0 I %Nir-i I- Ch.O UI0%%0INO U L)IO tfC OIN%00I %0C104IO M.tf -L m e014NIO I0l'tOIN n0 M' Poll I ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 1~~~~~~~~~~~~~ y' 1/) * ole ole 0 0 Ole~~~U Ole 0LooA1 0 *1* 0o * o 0.1 el,10 b0of b.. e I I~~~~~~~ I I I I I I I~~~~~~~~~~~~~~~ ON N1-. -0 n14 I n % II.I-x 0% 4.- M I.O''1,N I0%%0CO N4LCI I 1 0 0100 01 0 0 ol 0 l. 0 9 I10 010 * 0 Cli0 0 10 0 0 ole Ole 9 0 0Ole 11 CIi CNLi%1I0 Y40%Q'.I > 0 el 0 0 II el, 0 oil.0 1 l' lIo I l l N INtIM M -4P- 0 tVA c.,I, I, In0 +l,, I CO N %OI% I Io o1 L, 0 fnNIf 0I4 _4 I. MC (I1I4r4- r401~1~ 0U NC O1,1 OL OC)N 0i 1% 4% - I I~~~~e I IeI 1 of I I I Iof I I,' NIOI,7I-!t 4 MIN -!0 (-!F' 4 I w4 I.

BIBLIOGRAPHY 1. Clerk, Sir Dugald, The Gas, Petrol, and Oil Engine, John Wiley and Sons, Inc., New York (1909). 2. Donkin, Bryan, Gas, Oil and Air Engines, Griffin and Co., London (1905)o 3. Committee of the Institution of Civil Engineers, Proc. Inst. of Civil Eng., 163, (1905), 241. 4. Clerk, Sir Dugald, Proc. Inst. of Civil Eng., 169, (1906), 121, 5. Clerk, Sir Dugald, Proc. Royal Soc., A77, (1906), 500. 6. Hopkinson, B., Proc. Inst. Mech. Eng., Part 1, (1908), 417o 7o. Tizard, H.T., and Pye, D. R., Automobile Engineer, 11, (1921), 55, 99, 134. 8. Goodenough, G. A. and Felbeck, G. T., University of Illinois Experimental Station Bulletin 139, (1924). 9. Goodenough, G. A, and Backer, J. Bo, University of Illinois Experimental Station Bulletin 160, (1927). 10. Hershey, R. L., Eberhardt, J. F. and Hottel, H. Co, SAE TransO, 39, (1936), 409. 11. Hottel, H. C., Williams, G. C., and Satterfield, C. No, Thermodynamic Charts for Combustion Processes, John Wiley and Sons, Inc., New York, (1949) o 12. Nagel, A., Mitteilungen ueber Forschungs Arbeiten, 54, (1908). 13. Rosecrans, C. Z., University of Illinois Experimental Station Bulletin 157, (1926). 14. Endres, W., Der Verbrennungsvorgang im Gas und Vergaser Motor, J. Springer, Berlin, (1926).e 15. Hottel, H. C., and Eberhardt, J. F., Chem. Reviews, 21, (1937), 439. 16. Rassweiler, G. M. and Withrow, L. C., SAE Trans., L5, (1938), 185o 17. Rassweiler, G. M., Withrow, Lo C., and Cornelius, W., SAE Transo, 46, 18. Withrow, L. C. and Cornelius, W., SAE Trans, 47, (1940). 19. Rabezanna, H., Kalmar, S., and Candelise, A,, Automobile Engineer, 29, (1959), 547 3577. -2853

-28420. David, W. T., and Leah, A. S., Journ. and Proc. Inst. Mech. Engo, 143, (1940), 289. 21. Leah, A. S., Engineering, 168, (1949), 665. 22. Edson, M. H., "The Influence of Compression Ratio and Dissociation on the Ideal Otto Cycle Efficiency", SAE Paper, 380C, (1961)o 23. Edson, M. H., Ind. and Eng. Chem., 52, (1960), 1007. 24. International Critical Tables, McGraw-Hill, New York, 1, (1928), 393. 25. Hougen, 0. A., Watson, K. M., Ragatz, R. A., Chemical Process Principles, II, Thermodynamics, 2d ed., Wiley and Sons, New York, (1959). 26. Kobe, K. A. and Associates, Petroleum Refiner, 28, (1949), 83. 27. Spencer, H. M., Ind. and Eng. Chem., 40, (1948), 2152. 28. William, M. H. "High Temperature Heat Capacity Equations and Thermodynamic Properties of Combustion Gases", U.S. Naval Ordinance Test Station (NAVWEPS Report 7609), (1961). 29. Rossini, F. 0. (ed.), Am. Petrol. Inst. Res. Proj. 44,(1953)o 50. Hilsenrath, J., net al., NBS Circ., 564, (1955). 31. Hildebrand, F. B., Introduction to Numerical Analysis, McGraw-Hill Book Co., New York, (1956). 32. Weber, H. C., and Meissner, H. P., Thermodynamics for Chemical Engineers, 2d ed., John Wiley and Sons Inc., New York, (1957). 33. Lewis, G. N., and Randall, M. R., Thermodynamics, 2d ed., McGraw-Hill, New York, (1961). 34. Clark, J. S., "Initiation and Some Controlling Parameters of Combustion in the Automobile Engine", SAE Paper, 279A, (1961). 35. Brown, G. G., Ind. and Eng. Chem., 17, (1925), 1229. 36. Gaydon, A. G., Flames their Structure Radiation and Temperature, Chapman and Hall Ltd., London, (1960). 37. Lewis, B., et al., High Speed Aerodynamics and Jet Propulsion, II, Combustion Processes, Princeton University Press, Princeton, N. J., (1956)o 38. Lovell, W. G., and Boyd, T. A., Ind. and Eng. Chem., 17, (1925), 1226. 39. Daniel, W. A., Sixth Symposium (Int.) on Combustion, Reinhold Publ. Co., New York, 886 (1956).

-28540. Vickland, C. W., et al., "A Consideration of the High Temperature Thermodynamics of Internal Combustion Engines", SAE Paper, 380A, (1951). 41. Huff, V. N., Gordon, S., and Morrell, V. Eo, NASA Report 1037, (1951). 42. Zeleznik, F. J., and Gordon, S., NASA TN D-473, (1960). 43. von Stein, M. R., Forschg. Ing.-Wes., 14, (1943), 113. 44. Schmidt, E., Thermodynamik, 6th ed., Springer-Verlag, Berlin, (1956). 45. Taylor, C. F., The Internal Combustion Engine in Theory and Practice, John Wiley and Sons, Inc., New York, (1960). 46. Penner, S. S., Chemistry Problems in Jet Propulsion, Pergamon Press, New York, (1957). 47. Wohl, K., Sixth Symposium (int.) on Combustion, Reinhold Publ. Co., 335, (1956). e 48. Bolz, R. E., and Burlage, H., Jr., NASA TN D-551, (1960). 49. Semenov, E. S., Inst. and Exp. Techo, 1, (1958) 102. 50. Propulsion Chem.Div., Lewis Flight Propulsion Lab., NACA Report 1300, (1959). 51. Scurlock, A. Co, and Grover, J. H., Fourth Symposium (Int.) on Combustion, Williams and Wilkins Co., Baltimore, 645, (1953). 52. Mickelsen, W. R., and Ernstein, N.E., NACA Report 1286, (1956). 535 Evans, M. W., Chem. Rev., 51, (1952), 363. 54. Hirshfelder, J. 0., and Curtiss, C. F., Third Symposium (Int.) on Combustion, Williams and Wilkins Co., Baltimore, 121 (1949) 55. Hirshfelder, J. 0., and Curtiss, C. F., Fourth Symposium (Int.) on Combustion, Williams and Wilkins Co., Baltimore, 190, (1953). 56. Semenov, N. N., NACA TM 1026, (1942)o 57. Tanford, C., and Pease, R. N., Jouro Chem. Phys., 15, (1947), 431, 861. 58. Dugger, G. L., and Simon, D. M., Fourth Symposium (Int.) on Combustion, Williams and Wilkins Co., Baltimore, 536, (1953). 59. Dugger, G. L., and Grabb, D. D., Fourth Symposium (int.) on Combustion, Williams and Wilkins Co., Baltimore, 302, (1953).

-28660 Heimel, So, and Weast, R. C., Sixth Symposium (nt.) on Combustion, Reinhold Pub, Co.,, New York, 296, (1956). 61. Dugger, G. L., NACA Report 1061, (1952). 62. Clarke, J. S., "Iniation and Some Controlling Parameters of Combustion in the Automobile Engine", SAE Paper, 279 A, (1961). 63. Longwell, J. P., and Weiss, M. M., Ind. and Eng. Chem., 47, (1955), 1634. 64. Lanchester, F. W., Inst. Mech. Eng. Proc., 141, (1939), 289. 65. Janeway, R. N., SAE Journal (Trans.), 61, (1938), 371. 66. Pye, D. R., The Internal Combustion Engine, Vol. I, 2d ed., Oxford University Press, London, (1937) 67. Ricardo, Sir H. R., The High Speed Internal Combustion Engine, Blackie and Sons Ltd., London, (195). 68. McAdams, Wo H., Heat Transmission, 3d ed., Mc Graw-Hill Book Co., New York, (1954). 69. Pinkel, B., NACA TR 612, (1938). 70. Pinkel, B., and Ellerbrook, H. H. Jr., NACA TR 683, (1940). 71. Pinkel, B., et al., NACA E-131 APR E5J31, (1945). 72. Kinghorn, G. F., Schroder, A. Ho, and Hagginbothom, W. K., Jr., NACA L-782 MR-L5D03, (1945). 73. Brimley, D. F., and Breevoort, M. J., NACA L-685 MR-L5A17, (1945). 74. Taylor, C. F., Inst. Mech. Eng. and ASME, Gen. Discussion on Heat Transfer, Inst. Mech. Eng., London, 397, (1951)o 75. Taylor, C. F., and Toong, T. Y., "Heat Transfer in Internal Combustion Engines", ASME Paper 57 -HT-17, (1957)o 76. Dahl, 0. G. Co, Trans. ASME, 46, (1924), 161. 77. Oberbye, V. D., Bennethum, J. E., Uyehara, 0 A., and Myers, P. So, "Unsteady Heat Transfer in Engines", SAE Paper 201C, (1960). 78, Carslaw, H. S., and Jaeger, J. C., Conduction of Heat in Solids, 2d ed., Oxford University Press, London, (1959), 79. Jakob, M., Heat Transfer, Vol. I, John Wiley and Sons, New York, (1949).o

-28780. Schneider, P. J., Conduction Heat Transfer, Addison-Wesley Publ. Co., Cambridge (1955). 81. Eichelberg, G., Engineering, Oct.-Dec., (1939). 82. Oguri, T., Determination of Rate of Heat Transfer Between the Gases and the Cylinder Walls of Spark Ignited Engines, Bulletin of the Faculty of Eng., Yokohama Nat. University, Vol. 9, (1960). 83. Nusselt, W., VDI - Forsch., 264, (1923). 84. Nagel, A., Engineering, 127, (1929), 59, et seq. 85. Vincent, E. To, and Henein, N. A., Thermal Loading and Wall Temperature as Functions of Turbocharged Compression Ignition Engines, Ph. D. Thesis, University of Michigan, (1958). 86. Baker, H. D., and Laserson, G. L., Inst. of Mech. Eng. and ASME, Gen. Discussion on Heat Transfer, 334,(1951). 87. Hottel, H. C.9 and Egbert, R. B., AICH.E., Trans., 38, (1942), 531. 88. Livengood, J. C., et al., Trans. SAE, 66, (1958), 683. 89. Taub, A., SAE Journal, 356, (1935), 159. 90. Curry, Shelley, "A Three-Dimensional Study of Flame Propagation in a Spark Ignition Engine", SAE Paper 452B, (1962).

UNIVERSITY OF MICHIGAN 3 9015 03483 0979