AF TECHNICAL REPORT NO. 54-405 September 1954 FINAL REPORT INVESTIGATION OF THE PRINCIPLE AND MECHANICS OF THERMAL CYCLIC ICE REMOVAL Myron Tribus Stuart W. Ghetohill H. E. Stubbs M. P. Mbyle Otto. Reuhr Joseph R'utkowski T. J. Herrick Paul Wing J. A. Nichols Engineering Research Institute, University of Michigan Project No. 2128-7.-F-Contract 33(600)-23549 United States Air Force Air Materiel Command Wright-Patterson Air Force Base, Dayton, Ohio

PREFACE The work reported in this paper was done cooperatively by the Icing Research Staff of the Engineering Research Institute, University of Michigan. The program was initially supervised by Dr. Myron Tribus and later by Dr. Stuart W. Churchill and was under the technical direction of Mr. H. E. Stubbs. Dr. R. B. Morrison also had supervisory responsibilities. The thermal analysis was done by M. P. Moyle and Otto Reuhr and the force analysis by Joseph Rutkowski, J. A. Nichols, and T. J. Herrick. Measurement of water thickness with the ice condenser was done by Paul Wing and experimental work by Roger Glass, Ao E. Wood, Joseph O'Brien, and Frank Vogenitz. AF 54-405 iii

SUMMARY Thermal-cyclic ice removal from aircraft has been investigated theoretically and experimentally. The theoretical criteria for ice removal were generally confimed by the experimental work. The procedure developed for predicting whether ice will be removed by a given heating cycle under any given meteorological.conditions can be outlined: as follows: 1. Calculate the removal pressure from the velocity of the aircraft and the aerodynamic characteristics of the aerofoilo The removal pressure is the difference between the stagnation pressure and the average pressure on the ice. The average pressure on the ice may be approximated moderately well by taking the pressure distribution over the clean airfoilo 2. Calculate the equilibrium temperature of the ice as given by Messinger (Reference 6). 35 Calculate the thickness of water that will be melted from the ice temperature, the heating rate, and the time the heat is on (Eq. 5). 4. Calculate the retaining pressure on the ice from the water thickness (Eq-. 11)o 5. If the removal pressure is greater than the retaining pressure. the ice may be expected to come off. AF 54-405 iv

TABLE OF CONTENTS Page PREFACE iii SUMMARY iv NOMENCLATURE vi SECTION I: INTRODUCTION 1 SECTION II: THE GENERAL PLAN OF THE INVESTIGATION 2 SECTION..III: THE LOCATION OF THE HEAT SOURCES 3 SECTION IV: THE RATE OF MELTING OF ICE SECTION V: THE INTERNAL FORCES 9 SECTION VI: EXTERNAL FORCES ON THE ICE 15 SECTION VII: EXPERIMENTAL PROGRAM 16 Test Series A 17 Test Series B 18 Test Series C 20 Test Series D 20 Test Series E 21 Test Series F 22 Conclusions from Experiments 23 APPENDIX A: EQUATIONS FOR ANALOG COMPUTATION Al APPENDIX B: THE PROBLEM OF MELTING ICE AT CONSTANT HEAT FLUX A4 APPENDIX C: RELATIONSHIP OF ICE REMOVAL FORCES TO WATER FLOW UNDER THE ICE All APPENDIX D: EQUIPMENT AND PROCEDURE FOR MEASURING WATER THICKNESS A15 Equipment A15 Operation A17 Errors in x A19 APPENDIX E: DEVELOPMENT OF A TECHNIQUE FOR THE FABRICATION OF MODELS CAPABLE OF DELIVERING APPROXIMATELY 100 PERCENT OF THE GENERATED.EAT:IAT: THE. SURFACE:..F.OR: THE..EXPERIMENTAL INVESTIGATION OF INTERMITTENT DEICING A23 APPENDIX F: MISCELLANEOUS NOTES A25 Calculations and Data A27 Some Properties of Water and Ice A55 REFERENCES A54 FIGURES AF 54-405 v

NOMENCLATURE c = Heat capacity of solid. L = Heat of fusion of solid. U = Melting point. relative to ititial temperat.rxe iof spsQid. to = time for ice to rise to mielting point. K = Thermal conductivity of ice. 0 = Heat flux per.unit area suipplied: by liter. p Density of ice. X = Thickness of ice melted. t = Time after melting starts. F = "Function of" or force pLX a. = 0to Pice W =.i X = thickness of water layer formed on melting. Pwater a = Thermal diffusivity. _ 2= 2 -Pw2L. nw a = distance, length. U = Temperature. P = Pressure. y = Surface tension constant. R Radius of curvature.u = Viscosity. A = Area. b = Width of ice. _ (^ 2 ~1/3 FAb2p2L2 AF 54-405 vi

NOMENCLATURE (cont,) W B =. k k = ( -fi 1/3. 2FpL ) S = - +2 t tanr t/to) (/to)2 S Q = t/to C = Electrical or thermal capacitance. R = Resistance. e = Dielectric coefficient. AF 54-.405 vii

SECTION I INTRODUCTION Although thermal anti-icing systems which operate by keeping the aircraft structure clear of ice at all times have proved effective in protecting aircraft against icing conditions and permitting them to fly in all weather, such systems have high power requirements. In contrast, cyclic deicing systems, in which ice is permitted to accumulate on the aircraft surfaces for a period of time and is then removed by melting the interfacial bond between the ice and the aircraft surface so that the ice will be blown off by the aerodynamic forces, offer the possibility of much lower power consumption than an anti-icing system. It should be noted at the outset that the aerodynamic performance of- an aircraft protected by deicing equipment will be inferior to an aircraft protected by anti-icing equipment since the aerodynamic surfaces will be covered most of the time during icing conditions by a thin coating of ice, whereas with an anti-.icing system the aerodynamic surfaces are kept clean at all times. However, the total power the aircraft required to perform at a given speed and rate of climb is a better criterion for the effectiveness of an ice-protection system. The significant effects on this total power caused by ice-protection equipment are the power required to carry the weight of the protective equipment, the.power required to operate the equipment, and the added power required by the aircraft because of increased drag and weight due to ice adhering, to the aircraft i.Although anti -icilng systems require n6 power to overcome increased drag, it may well be that deicing systems compare favorably by the test of total power consumptiono (In comparing different systems, it is of course assumed that both systems meet the primary requirements for keeping the aircraft airworthy and capable of pilot control at all times.) The purpose of this investigation was to determine the principles of thermal deicing so that they can be used in a rational design of aircraft ice-protection systems. A qualitative picture of the ice-removal process can be obtained by considering a piece of ice attached to an aircraft surface that is protected by a thermal deicing system. The piece of ice is firmly attached to the aircraft surface by a solid bond} the exact nature of which is not necessary Jo examine for the present problem. It is sufficient to realize that even a small area of the solid bond will be strong enough to hold a piece of ice to an aircraft structure. Suppose now that the heating apparatus is turned on. The temperature of the ice and the structure to which it adheres will rise until some part of the ice comes to its melting point. Then as heating continues the ice will begin to melt and the heating process will be altered by the absorption of the heat of fusion. Since the heat source is inside the aircraft surface, the: ice will always begin to melt at the ice-metal interface. As long as some parts of the solid bond remain intact, however, the ice will remain firmly in placed Finally, all the solid bond between the ice and the metal will be melted and the ice will be free to move under the influence of the forces acting on ito These forces are first, the aerodrna'mic forces from the air stream passing over the outside surface of the ice, second, the hydrodynamic forces in the water layer lying between the ice and the structure, and third, the force AF 54-405 1

of gravity on the ice. It cannot be assumed that the ice will immediately fly away from the aircraft as a result of these forces. Other possibilities that must be considered are that the ice will slide back along the surface, or that it will shift only slightly and find an equilibrium position in which it is more or less floating on the film of water. This phenomenon is possible because the surface tension forces existing in a thin film of water may be sufficient to counterbalance any aerodynamic forces tending to remove the ice. If the ice does not fly off from the aircraft surface immediately upon destruction of the solid bond, the influx of heat continues to melt additional ice, and the water film between the ice and the metal grows thicker, causing the forces of interfacial tension to change. Eventually the forces of the airstream will no longer be counterbalanced and the piece of ice will be swept away from the structure. The picture outlined above may be complicated by water which melts upstream, flows back, and refreezeso The details of the process described above thus depend on a number of parameters and the central problem of this investigation is to obtain a more precise and quantitative description of the process. SECTION II THE GENERAL PLAN OF TEE INVESTIGATION The parameters which are important in thermal-cyclic deicing may be grouped in several general categories. The first is the meteorological conditions. This category will include air temperature, liquid water content, drop size distributionand air density. The second category pertains to the design and the performance of the aircraft and includes the geometry of the aircraft surface and the velocity of flight. A third category concerns the specifications of the ice-protection equipment and in the case of thermal-cyclic-deicing systems involves the distribution and strength of heating sources. The primary problem of this investigation was to determine under what conditions a piece of ice would be removed from the aircrqft surface in question, Decomposition of the overall problem into a number of simpler component problems is of considerable assistance in determining the criterion for ice removal. A method for doing this is shown schematically in Figo o Considering the lower part of Fig. 1 first, it is supposed that a piece of ice will be removed when there is an unbalance of forces acting on it so that it will be accelerated relative to the aircraft structure, The forces on the piece of ice will arise first from the aerodynamic forces associated with the movement of air over the outside surface of the ice, and second, from the pressure distribution in the film of melted ice which lies between the ice and the aircraft structure. The forces in the water layer will depend on the thickness of the water layer, the motion, if any, of the water, and the amount of water surrounding the ice but not under it. The water thickness will in turn depend primarily on the method and rate of heating the ice and on the initial ice temperature. The equilibrium ice temperature is determined primarily by the rate of impingement of water, the flight velocity, and the air temperature. The rate of impingement of water is determined by the flight velocity, the water contentand drop size of the clouds, -and the geometry of the wing or other aircraft AF 54 -405 2

surfaces. The aerodynamic forces acting on the ice will be determined by the shape of the ice and the wing and by the density and velocity of the airstream. Thus, in Fig. 1 the variables appropriate to the cyclic-thermal-deicing problem appear at the top. Below them appear a number of boxes, each of which represents the relationship between several of the primary variables. The new parameters in the boxes are in turn used in further analyses until it is possible to determine the criteria for the removal of the ice. Several of the component problems represented by the boxes in Fig..1 have already received attention by other investigators and been ateat leastpartially solved. The determination of the rate of impingement of water drops from their trajectories has received attention from Langmuir and Blodgett and many others. The methods of Langmuir and Blodgett have been mechanized by Tribus and Rauch and somewhat simplified by Tribus, Sherman, and Klein.8 The determination of the equilibrium ice temperature has been given by Messinger6. This leaves the determination of the thickness of water film as a function of time, the determination of the aerodynamic forces on the outside of the ice, and the synthesis of the results as the major problems which must be solved before the dynamic behavior of the ice can be described and predicted. It is to these three problems that the attention of this present study is primarily directed. SECTION III THE LOCATION OF TIE HEAT SOURCES A thermal-deicing system gives promise of providing ice protection with less energy than an anti-icing system only if it expends nearly all the energy in melting the bond between the ice and the aircraft structure and very little in melting or vaporizing ice elsewhere or in heating the airstream. In order to avoid wasting heat, the icing system must heat the ice immediately adjacent to the structure rapidly so that its temperature will rise above freezing before large quantities of heat flow outwards into the airstream. The system must also avoid expending large quantities of heat in raising the temperature of the structure. It is also desirable that an aircraft surface protected by a deicing system cool rapidly, since any water which impinges on the surface after the ice has come off, but before the surface has cooled below the freezing point, will run back and freeze aft. A heat source consisting of ducts carrying hot gases, such as are used in many anti-icing systems, has serious disadvantages when used in a deicing system. On any particular cycle it will be necessary to heat the ducts and the metal skin of the aircraft to rather high temperatures before the ice will begin to melt. After the heat is turned off, the thermal energy which has been stored in the metal skin will be conducted outward and prevent the surface from cooling rapidly. Thus a deicing system which uses hot gases will require considerably more energy and will have more difficulty with runback. These objections to a duct system become even more important in the new aircraft which use thicker skin and structural members. Furthermore, it is anticipated that some of the future aircraft will be designed with movable sections in the front parts of the wings. With such design it will be very difficult to construct ducting to distribute hot gas to the leading edges of the wings. AF 54-405 3

In contrast to the difficulties inherent in the use of ducting for cyclic deicing, electrical heating appears to offer a much more suitable method for the distribution of energy to accomplish the removal of ice. Wires can easily be run through movable sections and it is possible to generate heat in a resistance elecment on the outer surface of the aircraft structure just- where it will be most effective in melting the bond between the metal and the ice without wasting energy elsewhere. In view of these advantages, it appears that deicing systems should use electrical power as their source of heat and the present study primarily considers such systems. One method which has been used to produce heat in a deicing system is to embed electrical resistance wires in a boot of neoprene which is then cemented to the surface to be protected: The wires are positioned in the boot so that more neoprene is below them than above them, Since the neoprene is a good insulator, it impedes the flow of heat into the air frame. At the same time} but to a lesser degree, it impedes the flow of heat to the icecap and causes rather high wire temperatures to develop during operation of the heater. When the heating wires are turned on, the surface of the boot is not heated uniformly. There are hot spots over the wires and relatively cold regions in between them, This nonuniformity of surface temperature wastes heat because an excess of water is-melted over the hot spots before the cold spots are melted at all. The excess water is also undesirable, since it runs back and freezes aft~ An investigation was undertaken of the temperature variations which occur in a deicing boot under normal -operation to see if they were large enough to be an important factor in the deicing 3rocess. The constru.ction and dimensions of the heater boot are shown in Fig. 2, The thermal transients in the boot were analyzed by dividing a section of the boots into thirteen -cells and writing difference equations between the cells approximating the differential equations which actually govern the heat flow., The equations were then solved on a differential analyzer. The method of dividing a section of the boot into cells is shown in Fig, 3 and superimposed on the picture is a diagram of the thermal network. The derivation of the equations is given in Appendix A. Figure 4 shows the temperatures in different cells as a function of time in a typical run on the differential analyzer. The heaters were energized for thirty seconds and the temperat.ure in the icecap rose about 60~F during the cycle. The difference in temperature between Cell No. 4^ which is directly over the heating element, and Cell No. 6 which lies midway between heating elements, is plotted in Fig. 5. It can be seen that the temperature difference is greater than 20~F through a large part of the heating cycle Since the calculation method is rather csmde (because the division into cells is coarse), the numerical value thus obtained cannot be relied on to much better than 20 percent. However, the results clearly indicate that sizable temperature variations can occur along the surface of a boot using wire heaters. Further confipnation of this conclusion was obtained by making interferometer pictures of a thermal deicing boot of the same construction. For these pictures the boot was not covered by a layer of ice but was cooled by free convection. In the photograph fringe shifts indicate temperature differences with each fringe being equivalent to approximately 8~F. Figure 6 is the interferogram of the bobt two seconds after the power at seven watts per square inch had been turned on. There is one fringe shift between the hot and cold parts of the surface of the boot; indicating temperature variations of about 8~F. Figure 7 is an interferogram of AF 54-405

a boot in which the heating elements have twice as great a spacing, i.e,- the structure is the same as shown in Fig. 2 except that the distance between heating elements is.01 inch. The interferogram is taken again two seconds after the boot is energized at seven watts per square inch. The fringe shift between hot and cold spots is two or perhaps a little more; indicating temperature variation of 16 to 18'F along the surface. Thus- both the computations on the differential analyzer and the interferometry studies indicate that considerable variations will. occur in the surface temperature of a deicing boot using wire heaters as shown in Fig. 2. It: is therefore: desirable that deicing systems be built with a more uniformly distributed heat source. The ideal situation, of course, would be to have the heating element distributed uniformly over the whole outside of the aircraft surface that is to be protected. SECTION IV THE RATE OF MELTING OF ICE The preceding sections have discussed the desirability of having a uniform heat source which is close to the surface of the structure. An analysis will be made in this section of the melting process in the ideal case in which heat is generated uniformly at the surface of the aircraft structure and no heat is conducted backward into the structure..This idealization can be realized to a fair approximation with certain designs of heater elements and the analysis will also serve as a basis for understanding the process of melting even in systems where the idealization is not so well realized. In order to simplify the mathematical treatment it will be further supposed that the icecap frozen to the structure is infinite. This supposition will not introduce a serious distortion in the results. if the square of the ice thickness is greater than the product of the time of heating and the thermal diffusivity of ice. If this condition is not met convectiv heat transfer must be considered. heating element 0i _ t n nt \ +^< ^ o \:ice (to infini'ty~ --- to infinity AAF 54-4o55 5

The idealized problem is shown on the preceding page, The heat generatedper unit area by the heating element is a constant and all the heat is conducted to the right. For a short time after the heater is energized the only effect will be to raise the temperature of the ice. Soon, however, ice will begin to melt and there will be a water layer adjacent to the heating elementO Beyond this, ice will extend to infinity,. As time increases, the temperature increases in both the ice and water layer, more ice melts, and the thickness of the water layer increases. For purposes of deicing, interest is primarily in the thickness of the water layer as a function of-time and secondarily in the temperature throughout the system0 The analysis of the melting process Can be considerably simplified by considering the disposition of the electrical energy. Until melting starts, all the energy developed in the heating element goes to raising the tetrperAtur-::,bo:the'icecap. After melting starts, the energy goes to raising the temperature of the ice, raising the temperature of the waters and providing energy for the heat of fusion at the interface. Since in practical deicing systems the water layer involved will be quite thin, perhaps a few hundredths of an inch, the temperature difference across the water layer cannot be very large, even though the thermal gradient is quite high. The analysis of melting will therefore be simplified by neglecting energy -expended in heating the water and supposing that all the heat flux generated in the heating element will appear at the ice-water interface and be expended either in melting ice or in raising the temperature of the ice. The eror resulting fromthis assumption will be examined later. An extensive study of the problem of melting solids as formulated was made by Ho. G. Landauo4 Landau introduces two parameters into his analysis: m, which is proportional to the ratio of heat energy required to raise the temperature-of a piece of ice to its melting point to the energy to melt it and is defined by (1) m ='. 2L where c = the heat capacity of the solid, L = the heat of fusion of the solid, and U = the melting temperature of the solid relative to the initial temperature (Uo is thus positive); and to, which is the time required for the ice immediately adjacent to the heater to rise to the melting point, i.eo., the time in which the heater is on, but before melting starts. The value of to is 2 (2) t it K-c P 0 - 4 02 where K = thermal conductivity of ice, 0 = heat flux per unit area supplied by heater, and p = density of ice. AF 54-405. 6

With a change of notation and rearrangement Landau's results can then be expressed (5) (1 + 2/ m) cr = F (t/to, m), =here p L X 4 where L= --- =X, t~o' KcU U2' - 0 X = thickness of ice melted, t = time after melting starts, and F denotes "function of". t is measured from the beginning of me:ltings The time from the initial application of power is to + t. For deicing the important quantity is thickness of the liquid layer formed rath:er than Xy the thickness of the ice melted. The thickness of the liquid layer, W, can however be easily obtained by the relationship density of ice (4) w = (4i) W~ = ~density of water For the special case m = 03 the differential equations become linear and it is possible to obtain the following analytical expression of the results. (5) = 2 (1 + t/t) tan'l (t/to)1/2] - (t/to) The equation is plotted in Fig. 8. The present investigators analyzed the melting problem for m = 0 before discovering Landau s worko Since this work has a viewpoint somewhat different from Landau's and gives certain details that Landau.omits, it is presented in Appendix B. For m % 0, the differential equations are nonlinear and Landaul therefore used a digital computer to obtain sol:utions which he presents graphically..However. for ice at temperature above.-40F. which is the lowest temperature at which aircraft icing occurs, m does not exceed 0.2. For m less than 0.2 the values of a do not differ from those for m = 0 by more than 10 percent, so that for practical design calculations Eq. 5 is sufficiently accurate. A special case arises when Uo = 0, i.e., when the ice is initially at the melting point, for to and m also equal 0y and Eq. 5 becomes indeterminate. However, if Eq. 5 is multiplied by to it becomes (6)p = 2 {[(to + t) tani ( t/to)/2] tt).(6) ~ ~ ~ [(o+ a AF 54-.405 7

If to now becomes 0% this reduces to 7P L X (7) = t indicating that. the amount of ice melted is proportional to ( t ~ t), the total energy supplied,,which is of course to be expected since it has been assumed that the heat expended in raising the water temperature is negligible and when UO = 0 no heat is required to raise the temperature of the iceo When U0 is equal to 0, however, the melting problem is susceptible to a more exact treatment in which it is not necessary to neglect the energy expended in raising the water temperatureo This problem is analyzed in Reference 3 and with a changed notation the results are (.8) w = ~'l, - 1 ~.+.5 P2.513 + 827 o ). (8) w = L (l-4 p + s PwL \ 2; 5211 4! 5; where W = thickness of waters Pw = density of water, 2r t X = X- 9 and n2L2. a = thermal diffusivity of water. No method for calculating.. the res id ue of the infinite series resulting from using a finite number of terms is suggested by Evans', Isaacson- and McDonald in Reference 6, so that the practical applicability of Eqo 8 is somewhat doubtful. Settling aside the question of the accuracy obtained from any finite number of terms in the series, Eq. 8 can be compared with Landau-Ls solution for Uo = 0 to obtain an idea of the error introduced by the more drast'i.c mathematical assumptions needed to handle an arbitrary initial temperatureo Comparison of Eqs. 7 and 8^ and consideration of the relationship of Eqo 4 indicate that neglecting the heat required to raise the water temperature is equivalent to using only the first term of the series in Eqo 8. The second and subsequent terms of the power series may then be taken as a measure of the error in calculating water thickness (9) E 82 2' 3' 4'. 5' Taking typical values of the parameters 0 = 1.2 cal/cm2 = 1 g/cm3 L = 80 cal/g AF. 54-405 8

Qw = 0.00144 cm2/sec t = 1 sec E can be calculated as E = 0.04 = 4% It should be stressed that the error discussed above is only the limit of the error in Landau's problem when the initial distribution approaches zero. A more practical method to account for the energy used in heating water which comes from melting is to consider the temperature gradient-heat flux-average temperature relations for the water layer at its maximum thickness, compute the -energy required to reach this average temperature for the volume of water present, and spread this energy uniformly over the computed time interval as a correction of the heat flux, Although this procedure may not be conservative, the uncertainties involved are not so great as those involved in the estimation of some of the design conditions, Equation 5 is rather abstract and recapitulation of its application to the problem of deicing aircraft appears worthwhile. The dimensionless quantity a is obtained by multiplying the thickness of the ice melted by a number of parameters which describe the meteorological conditions and the design features of the deicing system, namely, the rate at which heat is generated, the'physical properties of ice, and the equilibrium temperature of the ice, Therefore, for any particular design.and particular icing condition a is the measure of the thickness of ice-melted. The thickness of water can be calculated by reference to Eq. 4. The expression on the right in Eq. 5 is a function of time together with certain parameters which again are determined by the design of the deicing system and the meteorological conditions. Thus, is essence, Eq. 5 gives the relationship between thickness of water layer and the time that the heaters are on for given conditions, design, and weather. SECTION V THE INTERNAL FORCES This section will analyze the hydrodynamic forces acting on a piece of ice which is separated from a solid surface by a thin film of water and the extent to which they can resist external forces tending to remove the ice. The forces acting in a direction normal to the interface will be considered first. The normal forces required for removal of the ice are first calculated assuming that all the water under the ice comes from melting of the ice. With no excess water present, the static pressure in the water under the ice differs from the pressure in the surrounding air and is a function of the surface tension of the water and the-total curvature of the surface between the water and the air at AF 54-405 9

the edge of the ice. The difference in the static pressures on the two sides of the air-water surface is given by the following equation: (10) AP= + in which AP is the pressure difference, y the surface tension and R1 and R2 are the principal radii of curvature of the surfaceo If the edge of the ice is reasonably straight, the curvature in a plane parallel to the solid surface can be neglected and the total curvature taken in a plane normal to the solid surface. If:an external force acts on the piece of ices the ice will move to a position of equilibrium in which the force resulting from the pressure difference given in Eq. 10'counterbalances the external force. Since'when the water film is very thin,very slight motion of the ice will produce sizable changes in the curvature of the ice-wat.er interface, the ice will need to move only minutely and will, for all purx* poses, still be attached to the airfoil surface For any given water thickness there is, however, an upper limit which the curvature can assume, for the radius of curvature cannot be less than one-half the water thickness. In fact. the minimum radius of curvature can be equal to one-half the thickness only when the contact angle between the fluid and each solid material is zero. The contact angle of water with metal surfaces is greater than zero and a function of the material of the surface, the kind and amount of dirt on the surface, and whether the wetted area is increasing or decreasingo Thus in practical deicing situations the minimum radius of curvature will depend on many uncontrollable something greater than onehalf the thickness of the water layer. This maximum curvature then determines the maximum AP which the water layer can produce and consequently the maximum removal force which the system can resisto In estimating the maximum pressure difference,. AP, however.. it was assumed in this work that one of the principal radii was one-half of the thickness of the water layer. This assumption leads to low estimates of the pressure in the water under the ice, therefore high estimates of the water thickness required for removal of the ice and high estimates of the time required for removal.o EThis gives an equation 27 (11) (A^)max = W - There remains some question as to the effect of corners where the curvature parallel to the solid surface cannot be neglected. It is obvious that the liquid under the ice cannot extend clear to the sharp corners because this leads to a total surface curvature in the wrong direction to balance the pressure differences.o The water film retreats from the corner and rounds it off. The result is that the total curvature becomes the same as at places far from corners, but the wet area is decreased. For large pieces of ice, such as on wings, the area decrease is negligible compared to the total area, but a correction must be made on small models like those used in the present investigation. The force thickness rela tionship corrected for corners is shown graphically in Fig. 9. AF 54-405 10

The thickness of water melted can be expressed in terms of the heat flux, the initial temperature of the ice, and the time, as explained previously, and it is therefore possible by using Eq. 11 to establish a relationship between the force required for removal, the heat flux, the initial ice temperature, and the time. This type of calculation can of course be applied to a specimen of any shape or size on a flat surface and probably equally well to a curved surface with constant radii of curvature. If the surface has a changing curvature, as for instance, the surface of an aircraft wing, then the shape of the water under the ice is a function of the position of the ice on the surface. It therefore becomes essential to consider the possibility and the effects of motion of the ice parallel to the surface. An aircraft wing, for example, is ordinarily a surface with straight-line elements in the span-wise direction and with curvature continuously decreasing with distance aft of the leading edge. If a piece of ice with a water film beneath it slides aft on the surface of the wing, then this water film must become thicker at its center and thinner at the fore and aft edges until some point is reached at which the fore and aft edges of the ice are both in contact with the wing surface. (See the accompanying sketch.) At this point one of several things can happen: ice in initialice after it position - as slid back water (1) the ice may stop (held in equilibrium by surface tension andpressure forces). (2) The ice may flex and continue to slide aft, bending continuously in such a fashion and amount as to keep a constant water volume beneath it, (3) The ice may break, due to the difference in pressures above and below it, and the fact that it is supported at the fore and aft edges as a beam. (4) The surface tension effect at the sides of the piece of ice may no longer be sufficient to prevent the entrance of air under the ice, therefore, the ice may continue to slide aft while drawing air under it as it slides, Of course, all these effects may be complicated by continued melting of the ice if the ice is sliding on a warm surface, or by a refreezing of the ice or the water beneath it to the surface of the wing if the ice should slide from a warm to a cold surface of the wing. What actually happens will, of course, be a function of the relationships between the strength and the stiffness of the ice, the surface tension in'-the.'watier:.layer.- and the relative;mag.itiudes:of';he foresla.-..-!-. ing oon thecice tangent:ad.nOr'mal to- the w.ng (.surface:. The situation is too complex to be definitely analyzed, but some qualitative conclusions can be drawn. First, tangential motion will not remove the ice by itself, Second, the ice will eventually stop sliding either because it encounters some irregularity on the wing, or because its rear -edge moves behind the heated section and becomes frozen fast. If the latter happens, the small frozen part will offer very little resistance to a bending moment caused by removal AF 54-405 11

forces acting normal to the surface. Observations of deicing tests conducted as part of this investigation indicate that the ice does leave the wing with a motion hinged on its aft end. Figure 10 is a sequence of photographs taken from a high speed motion film and shows the ice shortly after it separates from a model wingo Finally, it can be seen that if the ice slides aft to a position where it doesn't fit, the average thickness of the water film, which is associated with energy expended, can become greater than the thickness of the front edge, which controls the retaining forces. The heating requirements of the deicing system are thus increased. Another complication must be considered in more detail. A cyclic-thermal deicer on an airplane wing will normally have a leading-edge parting strip which is kept continuously hot to prevent bridging of the ice over the leading edge of the wing, Water which is melted on this parting strip must run back over the cyclically operated sections of the deicer aft of the parting strip, This runback water may flow under the ice and considerably reduce the time required to remove it. With no excess water present, the pressure difference between air and the water under the ice is a result of surface tension. With excess water present, the pressure in the water under the ice is a function of the flow velocity and viscosity of the water. Stefan9 has derived a force-time relationship for the removal of a round solid disk from a flat surface when the disc is immersed in a fluid. His equation is: (12) t= 3 i 1 _ 1 4 F/A W2 W2 in which R is the radius of the disk, p the viscosity of the liquid, t the time to separate the disc from the base surface, F/A the separation force per unit area, and W1 and Wz are the initial and final distance of the disk from the base surface. In Appendix C a similar relationship is derived for a piece of ice which is infinitely long in one direction, and has a width b in the other, A simplified form of this equation, sufficiently accurate for the values of W encoa:ttered in deicing, is (15) 4 e C 4 - F/A where t is the time to remove the ice from initial separation Wi. The development in Appendix C also yields an equation for the rate of separation (14) dW 2F W3 dt b2 AF 54-405 12

The separation resulting from flow and from melting can now be combined for the case when the ice is initially at the melting temperature (15) dW 2F dt pAb2 W3 +0 pL' This equation can be integrated by separating the variables. Performing the integration and introducing symbols for groups of parameters, (16) T J =.2647 [ L 2 in (1+B)2 +/ 3 tan" (l+B)2-3B 2B-l] + ~3 -,240 where (17) and (18) /= ( Ab2p2L2 F02 A) N)/3 W W B = W = W k ( Agb220 1/3 2 FpL / Equation 16 is plotted in Fig. 11 together with the equation for melting alone which is obtained by dividing Eq. 7 by J and will give (19) t/J =.794 W k Examination of Fig. 11 shows that a conservative and simplified design procedure would be to( assume that Eq. 19 is correct except that the presence of a sufficient quantity of excess liquid water, for instance as runback from forward deicing heaters, limits the value of t/J to t/J = 1 or t = J. When the initial temperature of the ice is below its melting point, the equations cannot be solved exactly, but some qualitative conclusions can be made. Considering the equation developed for melting when heating starts at an initial temperature below melting, i.e., (20) X = t S pL.s = -1+ t A t Oeto or W = - S pwL tan (-) oo (t~o. 0 d in which (21) AF 54-405 153

it can be seen that this can be written:pLW (22) Qt = -- where S (23) Q = t Equation 22 can be divided by J to get (24) Q = ~794- J k which aside from the factor Q is the same as Eqo 19. A more useful form for this equation for design is (25) St = -794 J k since here only S is a function of t, while all the other factors in the equation can be calculated from the design conditions. Thus S can be calculated and t/to can be found from Fig. 12 and multiplied by to to get to Without excess watery W will be calculated from the surface tension and pressure data, With ample excess water present there is reason to believe that Qt/J ands therefore- Sto/J^.will not exceed 1. The basis for this is the following. The difference between this case and the one in which the ice is- initially at its melting point lies only in the loss of some heat to the ice in order to bring its temperature up to the melting point~ In Eq., 15 this effect can be accounted for by multiplying 0 by the factor Q, which is always less than lo This means that when the initial ice temperature is below the melting pointy the effects of heating are relatively less and the effects of flow relatively more than when the initial ice temperature is at the melting point. Therefore, since the curve of Qt/J vs W/k for melting only and Uo < 0 is identical to the curve of t/J vs W/k for U = 0, it follows that for melting and flow the curve of- Qt/J vs W/k for Uo = 0 must lie to the right of and below the curve of t/J for Uo = 0. Therefore the equation->. Qt Sto (26) - 1,0 7T =-J =zo AF 54-405 14

will still give conservative, or high, estimates of the time required for removal of the ice when sufficient excess water is present even though the initial ice temperature is below the melting point. An interpretation of these results is that when no excess water is available the length of the deicing period is determined by the time required to melt sufficient water to remove the grip of surface tension on the ice. On the other hand, if excess water is present around the edges of the ice, the first part of the deicing period is spent in melting sufficient ice to produce a channel underneath the icecap Once the channel is formed a relatively short period of time is required for water to flow under the ice and permit it to be removed. SECTION VI EXTERNAL FORCES ON THE ICE The forces acting on the outer surface of ice on an aircraft arise from the air flowing over the surface and the water impinging on it. The aerodynamic forces can be divided into pressure forces acting normal to the surface and viscous drag forces acting parallel to the surface. The forces due to impingement will be approximately tangent to the surface except at the leading edge of an aerofoi.l, and they may be of the same order of magnitude as the pressure forces. All these forces tend either to hold the ice in contact with the wing or slide it along the wing surface. To be removed from the surface, the ice must have a component of motion normal to the surface, and this requires the building up of a positive pressure under the ice sufficient to overcome the external forces. If the ice has been deposited on a nonporous surface, the only possible source of this underneath pressure is the external pressure communicated to the water film at the leading edge of the ice. As was shown in Section V, the pressure at the edge of the ice is not communicated with full force to the water film but is diminished by the action of surface tension at the air-water interface. In order to effect ice removal, the pressure at the edge of the ice must be large enough to overcome the effect of surface tension and the pressures acting on the outer surface of the ice cap. Since an icecap extending around the stagnation point of the wing will have no edge exposed to a high pressure, it will not be subject to any removal forces. This shows why a parting strip is necessary for deicing systems. The parting strip should be wide enough to cover the stagnation point for all angles of attack, On the basis of these considerations, an ideal method of deicing would be to force hot air under the ice through a porous wing surface. This would achieve the dual purpose of melting the solid bond between the ice and metal and providing directly a high pressure under the ice cap. A minimum of melting would be required, only enough to break the solid bond. Against these advantages must be set the difficulties of controlling the hot air system. A porous wall deicing system offers attractive possibilities and minght well be.the subject of fttrther study. It is necessary now, however, to return to the calculation of the external forces in a more conventional system. AF 54-405 15

If the shape of the ice cap is known, the pressure distribution over it can be calculated using the theory of potential flow and analog devices which are applicable to the forward parts of the wing where ice accumulates. If the shape of the ice cap is not known, the pressure distribution can still be obtained with moderate accuracy by taking the pressure distribution over the clean airfoil. This procedure is applicable if the ice cap is not too thick and is a reasonable approximation to the pressure on a piece of ice that forms between heating periods in a cyclic deicing system. It is not a reasonable approximation for obtaining the pressure on ice that deposits over an extended period of time on an unprotected surface. A special problem arises in calculating the pressure acting at the front edge of the ice cap, and as discussed above this pressure is very important in the removal process. Two possibilities seem reasonable: 1. The pressure at the front edge of the ice is approximately that which would be present at the same point of the clean wing. 2. The pressure at the front of the ice rises to the stagnation pressure of the air stream as a result of the bump caused by the ice deposit. Theoretical analysis does not offer a simple method of determining which of these hypotheses is correct, but part of the experimental program undertaken in this investigation (described as Series E below) indicates that hypothesis (2) is more nearly correct. On the forward portion of a wing the pressure decreases with increasing chord. One effect of this is to produce a moment on an ice cap tending to hold the front edge of the ice against the wing and tip the rear edge up. This action is just the contrary of that desired for the removal of a piece of ice floating on a film of water. However, the tangential forces acting on the ice cap cause the ice to start sliding back, and, as explained in lubrication theory, the ice will then tip the other way with the front end up. Thus a small amount of sliding assists the ice removal by increasing the thickness of the water film at the front of the ice and thereby reducing the effect of surface tension, but greater sliding as was shown in Section V carries the ice to a part of the wing with lower curvature and thus impedes the ice removal. It appears then that fortuitous surface irregularities can be a factor in ice removal by affecting the amount of sliding of the ice cap. To recapitulate, the most important external forces are the aerodynamic pressure forces. Acting on the outside of the ice this pressure tends to hold the ice in place, but the pressure which occurs at the front edge of the ice is communicated to the water layer under the ice and provides a force tending to remove the ice. In the absence of special devices such as porous wing surfaces, ice can be removed only if the pressure at the front edge is greater than the average pressure over the ice cap. SECTION VII EXPERIMENTAL PROGRAM In order to check the theoretical analyses which have been described, an experimental program was undertaken. Six types of experiment were set up, each designed to supplement or verify one or more parts of the theory. A table summarizing the AF 54-405 16

conditions of each series is given below followed by a detailed description of each series. Series Heating rate UO Load Water thickness Flow Deicing A slow <32F measured measured no no B measured <32F measured calculated (force) no no C measured <32F measured calculated (weight) no no D measured <52F measured ---- yes no E measured (32F wind ---- no no F measured 32F wind —? yes Test Series A Series Aof the test program was designed to verify the relationship between the thickness of the water film between two solids and the normal force required to separate the two solidsu The chief difficulty encountered was the measurement of the thin film of watere Previous investigators have attempted to do this by making a heat balance in which the energy which went into the icecap back of the heater,.etc., weresubtracted from the total energy input. The difference thus obtained was attributed to heat of fusion which could in turn be interpreted as the thickness of watero Since the heat flow to various parts of the system could not be calculated very accurately, and since the heat of fusion was obtained as a small difference between two larger quantities, this method has not been successful in distinguishing small layers of water, As the problem is studied it becomes evident that accurate measurement of this minute water thickness requires a technique not dependent on heat balanceso The present investigators, therefore, developed an ice condenser as an instrument for determining the thickness of thin water layers adjacent to ice. The ice condenser can be operated in arapid and straightforward manner and gives results which are closely reproducible, The theory behind the "ice condenser" is quite simpleo It is based on the phenomenom that the dielectric coefficient of ice is 35 whereas that of water is 81o Suppose now a condenser is made up with ice as the dielectric instead of an oardinary dielectric such as mica or air.(see sketch)o As the ice is heated from one sides the capacitance remains constant until melting begins at which time water, water,///C ___ ice = C = 100 cwf ie e = 130 4f having a dielectric constant of 8, appears at the boundaryo As the ice melts.-to. water the total capacitance becomes greater, due to the higher equivalent dielectric constant of the condenser. To measure melting thicknesses, a device need merely be constructed that measures the capacitance of an ice dielectric condenser and detects capacitance changes of 20 to 200 percent.accuratelyo This equipment can be called the "capacitance change detector," Then by making the ice sample to be tested part of a condenser, connecting the ice condenser to the capacitance change detector, and measuring the change in capacity when the ice near the heated surface melts the thickness of water present at any time can be calculated. AF 54-405 17

A procedure based on the above principles is as follows. lo Freeze ice between two flat, horizontal, copper disks to have an ice condenser. 2. Connect the ice condenser to a capacitance change detector after determining a, the initial ice thickness, and Co, the initial capacitance. 3o Load the lower platewith a weight. 4, Uniformly heat the upper copper plate. 5o Melt the ice near the upper plate to a depth Aa and then the ice and. lower plate will fall, 6. Monitor the capacitance change during melting and record the total capacitance change ACo 70 From AC C,.and a, compute Aa, the melting depth. 8. Repeat with a series of weights to obtain th-e relationship -of force. to Aa. A schematic representation of the equipment is illustrated..The equipment required and the procedure are discussed in detail in Appendix D, I-^ $ 1 heat $'icokp [ - ~'per i;,: 3 a'I d ^^ \isk.^ o a d~ 3 ^capacitance change detector..load It has been predicted by surface tension considerations that the relationship between. water thickness Aa and pressure P should be one of.appro:imately inverse props:ort.ionality or Aa = 29/P, where, is the surface tension co;nstant (75.5 dynes/cm). This relationship is verified by the ice condenser experiment as indicated in Fig. 35.The heavy line is the predicted curve while the crosses are the average values of Aa obtained at each particular normal pressure. Test Series B Series B tests were designed to verify the relationship between initial temperatures heating rate and removal force. -Pieces of ice approximately 2" x 2" x,25" were frozen on an electrical heating element and were removed by heating at a known rate, starting at a known initial temperature (<0oC), and AF 54km4o,

under a known normal force. The time required for removal was accurately measured. The setup for this test is shown in Fig. 14. The heater element consisted of a piece of 2" x.002" nichrome ribbon 2.5 inches long with.25" x.03" copper strips soldered to its ends to make electrical connections. This made a 2" x 2" heating elemrent which was cemented to a 6" x 2" x.,.5" piece of varnished balsa wood in order to have a rigid backing which would take up as little heat energy as possible. The force was applied by weights through a string and lever system as shown in the photograph. Not shown in the photograph are the autotransformer controlled a-c power supply, the electric clock timer, the microEwitch used for automatic power and timer cutoff, and the lead weights used to hold down the balsa wood heater backing. The automatic cutoff microswitch was mounted at the top of the framework shown in the photograph and was actuated by a less than one-quarter inch movement of the lever. The microswitch in turn actuated a relay which cut off both the electric timer and the power to the heater. In early tests the timer was only accurate to one-half second, but in later tests a different timer was used whose accuracy was limited only by the actuating system and was probably good to.05 second., The test procedure went as follows. 1. The 1.75" square x.25" thick ice blocks were made in a mold and wire loops fastened to the top by melting them into the ice and then refreezing. 2. These ice blocks were removed from their molds by melting, mounted on the chilled heaters with the aid of about.5 cc of additional ice water and frozen into place. 3. The ice and heater were placed in the test framework with a thermometer lying adjacent to the ice, all connections were; made and the whole setup allowed to come to an equilibrium temperature; a matter of twenty to thirty minutes, 4. With the load and heater voltage adjusted the timer and heater power were turned on with a single switch, the heater voltage and current were read during the test, and the timer and heater power were turned off automatically by the microswitch. The above procedure yields the following data: the normal force for separation, the initial temperatue of the ice, Uo, the heater current I, the heater voltage E, and the time required for the ice to be separated from theheater, (t + to). AF 54-405 19

From this data the following can be found, EI 4.185 (19.75) = the heating rate t - It KcpUo = time for melting to start t = ~t + t 1 = dimensionless time. to W = water'layer thickness required for separation based on calculations of the force-surface tensionarea relations for the ice sample. (Figo 9). For comparison with theoretical results the quantity p'W/fto. is plotted against t/t,, In the theory the results should be approximately pLW- 2 t) (t/to) /2(t/to) -+ tan'(/t The eermental results are plotted as open ci es n Fig 8 The for The experimental results are plotted as open circles in Fig. 8a The forcethickness relation used should lead to high values for the thickness'and the locat.ions of the circles seem to bear this outo This series of tests indicate that the theoretical results are substantially correct and will'be slightly conservative if used as the basis for de~ign.i Te.,t Series C This series of tests is in fact a part of the B:series in which- one extra set of measurements was madeo TZhe. extra meastrements consisted of weighing the ice plus heater and heater base before each test~.Then after the test th-e: hheater and heater base and the ice were wiped dry with a sponge and again weighed..he object of this procedre was to obtain another estimate of the amount of water melted. It is believed that this process should usually lead to a low estimate of the amount of water melted, chiefly because of the.refreezing of melted water' on the ice sample after its release from the heater0 The value of W so estimated was used to compute a new value of pL.W/to and these values are plotted on Fig. 8 as the filled-in circles. -The locations of these circles tend to substantiate.:the belief that the estimate of W is low. Conversely, if the judgments that W is estimated too low in test series C and too high in test series B:is acceptedl then these two series of tests show the theoretical curve to be substantially correct. Test Series D This series of tests was designed to verify Eqo 26. Test series D was like series B except the heater was mounted on a- larger balsa woodbase and was surrounded by a piece of one-quarter inch plexiglass to provide a reservoir of AF 54-4.05 20

of excess water. (see Fig. 15). The excess water, slightly above freezing temperature, was added just before the heater power was turned on to simulate the pressure of runback.water in an airplane deicing system, In calculating results from these tests the value W/k = 10 was arbitrarily chosen as corresponding to the release of the ice. A different choice would produce a negligible change in the results because of the rapid increase of W with t. The results of this series of tests are plotted in Fig. 11.and show that the analysis leading to Eq. 26 is substantially correct. Test Series E In the series E tests it was assumed that series A, B, and C had demonstrated the validity of the analysis and that a test in a wind tunnel could be used to get some estimate of the forces available for the removal of the ice, provided of course that the first motion of the ice was predominately normal to the wing surfaceo In particular, the tests were designed to decide whether hypothesis 1 or 2 of Section VI gave a reasonable estimate of the forces. The tests were run in a 4" x 6" single-pass wind tunnel operating in a refrigerated room at about 100 fps test section velocity. The heater in these tests was a 3/4" wide by 5" long strip of silver paint (manufactured by a General Cement Company) sprayed onto a hollow plexiglas airfoil 12?2" thick and with a chord of 7o5"o (Approximately NACA 652-016 profile, see Fig. 16), Pieces of ice 3506" x.56" x, roughly, 1/8" were frozen in place on the heater strip with the airfoil in the wind tunnel and the fan on to hasten freezing. When the ice was frozen, the mold was removedthe sharp corners removed from the ice with a soldering iron, and additional time allowed for the ice to reach an equilibrium temperature. The test was then run very much as were the series B tests, except that the removing force was aerodynamic and shutting off, as well as the starting of the heating and timing, was manually controlled. The data taken included: the initial temperature, the voltage across the heater including the leads, the current to the heater, and the time to remove the iceo There was, of course, some voltage drop in the leads, but space limitations prevented measuring the voltage drop across the heater alone. The loss in the leads was less than 1 percent of the total voltage drop, Tn analyzing the data from this set of experiments the pressure on top of the ice was assumed to equal that at the chordwise station corresponding to the midpoint of the ice on an NACA 652-015 airfoil at zero angle of attack as given by NACA Report 824, Summary of Airfoil Data. The pressure on the front surface of AF 54-405 21

the water layer, i.e., at the leading edge of the ice, was assumed to be equal to the stagnation pressure, i*e., hypothesis 2 was employed. The difference of these two pressures was taken as the F/A which had to overcome the negative pressure in the water layer due to surface tension effects before the ice would come off the airfoil. With these assumed pressures J, k and W could be calculated. The dimensionless time, Sto/J = Qt/J and the dimensionless thickness W/k, were then calculated and plotted in Fig. 11. The points correspond reasonably well to the theoretical curve, but indicate that the pressure difference used for the calculations should be reduced by about 25 percent. Points obtained with a 30 percent lower pressure difference are also plotted in Fig. 11 and show good agreement. The 25 percent difference is not surprising when it is remembered that the airfoil shape has been altered by the ice accretion and that the angle of attack was not precisely set at 0. In contrast, the values of AP that would be obtained by using hypothesis 1 are about 2 percent of the values required to give agreement with the theoretical curve. Thus, this series of tests definitely supports hypothesis 2, that the pressure at the leading edge of the ice is the stagnation pressure. Test Series F This series of tests was made in the University of Michigan icing wind tunnel which has since been destroyed by fire. The wing model consisted of a 6" span, 7,5" chord NACA 652-016 airfoil section made of balsa wood and overlaid with copper foil on its forward portion. The development of this model is described in Appendix E and its dimensions are given in Fig. 19. The heaters used were the forward ones on each side of the airfoil between approximately the 1.7 percent chord point and the 11.7 percent chord point. The tests were run at several heating rates and several tunnel air velocities. The test procedure consisted of turning on the heaters for a predetermined time, then turning them off and recording whether or not the ice had come off. Tf the ice had not come off some time was allowed for the system to cool to equilibrium temperature, then another trial was made using a longer heating time. The longest time not causing shedding and the time which caused shedding were then recorded. The equilibrium temperature of the ice was between 3515 and 352F with the heaters off even though the tunnel temperature was 280Fo This was due to aerodynamic heating, plus heat given up by the supercooled water as it froze. The results are plotted directly in Figs. 17 and 18 and in the nondimensional forms developed for test series B, C, and D in Fig. 20. The data do not match the theoretical curve nearly as well as the other series of tests, This can be partially attributed to poor control of time intervals and angle of attack of the model as well as some uncertainty as to the actual profile of the model. Comparison of Fig. 20 and Fig, 1.1 indicates pretty clearly, however, that the ice on the model is not surrounded by a great deal of excess water and, AF 54-405 22

thereofre, that surface tension is a controlling factor in the amount of water which must be melted to get shedding of the ice. The difference between the stagnation pressure and the local pressure on a clean wing at the leading edge of the ice is not great enough in these tests to make a clear cut decision as to which is the correct one to use in computing the forces on the ice. Use of the clean wing local pressure will give more conservative results and would be about right for some of these lists, but could be way off for the aft heaterso Conclusions from Experiments Taken as a whole the experiments show that the theoretical treatment is substantially correct and may be relied on to predict the influence of various parameters on the performance of deicing equipment. The numerical values obtained from the theory were of the right order of magnitude and usually within 20 or 50 percent of the values obtained experimentally. There were two questions which the theory could not resolve and for which alternative procedures were offered. The experiments gave evidence that runback water did not play an important role in ice removal and that the pressure on the water at the forward edge of the ice was the stagnation pressure. However, the alternative should not be ruled out finally until tested further on larger models. AF 54-405 23

APPENDfIX A EQUATIONS FOR ANALOG COMPUTATION The difference equations governing the flow of energy in the network of Fig. 53.have the form (Al) Oy-n (-U un) y-n = c dUn dt I where n = the cell at which the heat balance is being made y = an adjacent cell G.n = thermal conductance between cell pairs C = VpCp = the thermal capacitance of the cell Btu/~F dUn - --- = rate of change of temperature of the nth cell = ~F/hr dt K = thermal conductivity = A = area of heat flow = ft V = volume = ft3 a = length of heat flow = ft p = density = lb/ft3 energy/time-distanc e-temperature 2 In addition, Cell 7 receives energy from an external source. The energy balance then is given by (A2) Power in + G y ( Uy- C dt L M ~Y dt The values of the physical properties of the system are given below The values-of the physical properties of the system are given below. PHYSICAL'PROPERTIES OF BOOT MATERIALS AND ICECAP Specific Thermal Dens it t. -Material Ib/cu fl Heat Conductivity Btu/lb-F Btu/hr-ft-F Aluminum 160 00,178 117 Neoprene 75 O.40 0.073 Nylon 66 0.55 0.145 Ice 57 0o46 1.28 Nichrome 515 0.193 --- AF 54-405 Al

When the materials of adjacent cells are different. the thermal conductance Gy..n is obtained as the reciprocal of the thermal resistance between the n and y cells. This in turn is calculated by adding the thermal resistance of one-half the n cell to one-half the resistance of the y cell. An example calculation for Cell No.1 will illustrate the method. For Cell 1 the dimension of the cell normal to page (in Fig..3) is taken as one foot. KA (1.28)(0.067)(12) G2l l a = (0 a (o0.o00975)(12) = 9.02 Btu/hr-F 1 1 a) 1 a ) 2 lkA)1 2 kA)4 1 (0.033)(12) (1.28) (o.oo65)(12) + (0.o11)(12) (0.073) (0.0065) (12) 0..0368 Btu/hr-F C.= Vpc = (O.067)(00065) C =vp (12)(2) (57)(0.46) = 7.92 x 105 Btu/F Then Eq. 1 becomes 11.390 + 104U2 + 0.0463,x 104U4- 11.437 x 104t = dU1 dt Making the substitution T = 104t gives 11.390 U2 + 0.0463 U4 11.437 Ui. = -.. dT The complete set of equations for the thirteen cells is given in the following table. These equations were set up for simultaneous solution on a differential analyzer and voltages:corresponding to temperatures were plotted against time t;o glve the. curves of Fig. 4. A2 AF 54-405

DIFFERENTIAL EQUATIONS FOR HEAT CONDUCTION THROUGH RUBBER DEICER BOOT Td1 = 11.390 U2 + 0.0463 U4 - 11.461 Ul dT ~dU2 = - 5.919 U1 4.502 Us - 0.463 U5 + l0. 514 U2 dT dU3 dT.4.502 U2 + 0.,0465 U6- 4.595 U3 + dU4 d- =- o 0.1235 U1- 0.5676 Us- 0o144 7 U + 0.8359 U4 d U = 0.2951 U4 + 0.12-4 U2 + 0.2242 Us +- 0.1115 Us - 0.7543 U5 dT -dL = -0.2243 U5 o - 0.1234 Us - 0.1115 U6 + 0..4592 U8 dT dU? = 0.0742 U4 + 0.5180 U8 + 0.0204 Ulo - 0.6131 U7 + q./0.5817 &.. _ = 0.,7353 U7 - 0o.1558 U5 + 0.3676 Us9- 0.0515 U11 + 1..310 Us dT u = 00.3676 U8 + o.]558 U + 0.0515 U12 0.5749 Us - U - = - 0.0110 U7- 0. 5665 Ur - 0.0110 U13 + 0, 5885 Uo1 d0T -.dU1 = 0.~2948 Uo + 0.0101 U8 + 04.2241 Ui2 + 0.!090. U3 " 0.5399 Ui.d -. -.0.2241 U.-. 0.0101.Us - 01.0109 Uis + 0. 2451 U12 dT dU'3 = o0015 U-o.+ 0.0026.U]L + 0.0029 U12 - 0.0073 Us13 dT AF 54o405

APPENDIX B THE PROBLEM OF MELTING.ICE AT CONSTANT HEAT FLUX Consider a one-dimensional semi-ininiite slab of ice at a constant initial temperature,.UQ, corresponding to that of the air and with a constant heat flux 0 applied at the finite boundary. After a time to the boundary reaches the melting point which has temperature O0 and an ice-water interface begins to move through the material. The problem to be considered is the determination of the position of this interface as a function of time and the parameters 0 and U0. Problems of this type have been treated by Stefan and others:- but the boundary conditions in the case considered here are such that it appears unlikely than an exact solution can be found; however, it is possible to "linearize" the temperature equations in a manner which permits a good approximation for the ranges of the variables which are important for aircraft deicing.. It is assumed that the loss' of heat energy to the water is negligible compared to the total amount introduced; that is, the heat flux i goes into two places, to melt the ice and to raise the temperature of the ice. The determination of the temperature distribution in the ice at the time melting begins is a liniear problem and its solution by use of the Laplace transoformation is well kndwn. If the time t is measured from the instant melting begins and distance x from the finite: boundary, i.e.. the place at which thei. heat is ap-: plied, the boundary value problem is as follows: (B) u = av X(t) X x <, t >, (B2) U(xO) = — O ierfc ( "'' k''4t"o (B3) U(X(t),t) = o, ( lti.' U(x,t) = -Uo, (~B5) dX~0 = PL d+Kl a >d.(B.}) 0: pL- + K -U (X(t) t) t dt'x where U(x.t) is the temperature distribution in the ices Th- act K, L'and p are the diffusivity,..conductivity, heat of fusion, and density respectively of -ice, to is the time between power on'and the start of melting: and ierfe is the integral of the complementary error function, AiA 5k.-405

The position of- the ice-water interface is X(t) and consequently gives the thickness of ice melted as a function of time. By making a transformation of the space coordinate z = x-X(t), the position of a point in the ice is related to that of the moving interface and the problem takes the form: -2 U 6U dX (B6a)a A = a a d (B7) U(z,0) = U + NJ t. ierfc (-; )= F(z) K'Vao (B8) U(ot) = 0 (B9) lim U(z,t) = -Uo z --- CO (B10) 0 = pL X. + K a (O"t) (Bll) X(O) = 0 An examination of Eq. B6a shows the nonlinear property of the system which makes it invulnerable to the various methods of attack known in partial differential equations. At this point a second major assumption is introduced which will "lineariz'e" the above system, and hence, give a suitable approximation to the solution for X(t). Because of physical considerations, only the values of X(t) for a small range of t, say 0 < t < 20 seconds, will be necessary here. Thus, if the term -X(~U/.z) is small compared to the other quantities in Eq. B6a, the solution obtained by dropping this term will be close to the exact one.* If this is done- the rest of the problems i.e,, satisfying the boundary conditions and calculating X(t), goes through quite readily. Using the results obtained by this method, the quantity -X(PU/.z),can be evaluated and in some degree the plausibility of its neglect deter-mined The solution to the linearized boundary value problem can be obtained by use of the Laplace transformation as is stated in Reference 2, The problem is to solve (B6b) Uzz' =Ut (B7) U(z0O) - F(z) (B8) U(0,t) = 0 (B9) lim U(zt) = U z oo00 Let U(z,s) = Laplacian {U(z,t)) * Dropping the term is equivalent to setting Landau's m = 0, AF 54-405 A5

Then sU(z,s) - F(z) = CUzz (z,s) u. -a U = - F Uzza a U(o,s) = o rim U(z,s) = - U:Z - -> 00 s sz -z U(zs) = Cle + C2e + U*. The U* is obtained by the method of variation of parameters.fz = c1e + c2e U(z,s ) x(z 2s X X a.d, + e"' - ) d a a After lengthy, but straightforward calculation, the expression for U(z,s) becomes 01 Frf X) 7~(x %) U(z,s) =e -' X.l ee,-e 2 s 0 From a table of inverse transforms 2 K Inverse Laplaclan' -zs i = e F (k) d (K ) (K.O 0) Applying this formally above I U(z,t) = i - e 2oa.irt 0 (x.^.)2 1. vic iX~t, >,)2 -. ( x. ).a. )X 4at - F(..)d.. (B12), ^ (x+X)2 U(z,t) =.r e.. -e'44KQt 0 - This result is easily verified by differentiation to be a solution of the equation. Then U(Ot) = 0 is obvious, but the other boundary conditions are more easily seen to hold by a change of variable, eg., x +: =. Equation B12 can be differentiated with respect to z; z is:set equal to zero and expressions B10 and Bll are used to find X(t). *Dropping the term is equivalent to setting Landau's m = 0. AF 54.405 A6

g Pi t ) 5 - 00 1 aU (,0t) 0z F(5) (t-z)2 2 (- z e44t 4a0t _ -+Z )2 ( ep. <zt!,2 + 2 (.-z) Se dt 4at 00 -_ _ j-,to 4at e.__ t Integrating by parts (313) a (0t) i z -1 NIVt 2 _ 00 _2 F(oe )j F- (t)e 0 0 00 1 From Eqo B7. F1 ) - 1 2 0 e d e d% Changing variables and collecting terms Z~ ( Ot) bz~ = K 1 4 f -. -r QI 0 0 t.e e d~d'r.. o0 0 Expression B13 can be simplified as followso Define t2e gy) = j e U f(y, t)dt and f y,t) = ty 0 e.d. e dX where y = V to 2 2 -t y = te and ag by 00 0 2 2 2 -t -t y te e 00 = -I -2te.0;t2 (2l+y2) -1 I dt -t2(ly 2) _ e. 2 (l+y2) I00 0 1 2 2(l+y2) AF 54-405 A7

Integrating: g(y) = i tan'y+c, but since it is easily seen that g(O) = 0y = 0. 2 The simplified expression for B13 is ((Ot) a.) tan (t/to) 6z K' From Eq. B10 dax(t) aJ pL dt = K (O,(t) + Substituting Eq. B14 dX t 2 1-i2 pLdt = 0 ( tan (t/to)/2) + 0 pL dt= 0 tan (t/to) /2 dX:= L J tan (t/t) /2dt + c x(t) = L [(t/to) tan-' (t/to) - (t/to) + = pL.e last step can be verified easily be differentiation.) Since from Eq. 11 X(O) = 0, c = O0 and the final result for X(t) is (B15a) X(t) = (tt) tan'1 (t/to)1/2 (t/to)1/2] This is the result sought. So X(t) depends on the ice properties p and L and the parameters 0 and to. Incidentally. to can be eaily calculated and is given in Reference 2 as U.ZK21~ (B15b) to u 4 It is now possible to calculate the neglected term X(/U/z) and compare it with the other terms in Eq. B6a. Since the remaining terms are set equal for all values of z and t, either one is suitable for the following definition.6U.-x (B16) R(z,t) = 2,ju z^2 AF 54-405 A8

Of particular interest is. t ef x(t) 2 4I4at(t+to), I(t) } (B17) R(X(t),t) X2 2(:X e 4a(t+to).2,, e'.4a (t+t_) erfc Nf-t, 71at00 I where t I(t) - 0 0 x2 (1+ 2) - 4Ga(t+to) e(t + (t + X) (The above results were obtained from Eqs. B12, B15a, and B16 by tedious integrations.) Equation B17 now gives R as a function of t alone. Calculations showed that 0 < R(t)<10 for t < 20 seconds. It is important to note here that this bound on R(t) does not guarantee a definite limit on the error in X(t). but only gives a strong indication that it is small. A possible way of improving the result for X might be to approximate the term - X(6U/6z) by the expression B17 and to use a successive approximation attack. However, there are other reasons to believe that this will not be necessary for the range of quantities of interest. After the work of this paper had been substantially completed, an article by Landau4 was discovered which contained these results as part of a larger undertaking. Landau considered the problem as stated in Eqs. B6 through Bll but without dropping the term - X(~U/6z). Instead he defined the problem in the following way using the parameter m = 4ic(-Uo)/2L where c is the specific heat of ice: (Bl8) (B19) (B20) (B21) (B22) au a_ u 6u t = z2+ m(t) az z > 0, t > 0 U(z,O) = ierfc (j) lim U(z,t) = 0 z -- oo (t.) = 1 + 2 u (Ot) az 1 U(O0,t) = t 0 N/30 Equations B18 the variables change of the through B12 look somewhat different from B6a through Bll, because have been made dimensionless and pJ(t) corresponds to the rate of interface position. Using the facilities of high-speed computers. AF 54-405 A9

Landau was able to obtain solutions for several values of the parameter m, In particular, the solution for m = 0 (a physically nonrealizable case) corresponds exactly to the approximation obtained here. Actually in deicing problems m will seldom exceed 2. Lanau's results show that the solutions for m = O.and m =.2 are close enough for the ranges of the quantities considered here and B15a will be within-10 percent of the solution for the exact value of m* It is important to note here that the quantity X(t) is the thickness of ice melted, not the thickness of the resulting water layer. This difference is important in computing the forces required to remove the ice from the surface. AF 54-405 A10

APPENDIX C RELATIONSHIP OF ICE REMOVAL FORCES TO WATER FLOW UNDER THE ICE If two parallel, flat surfaces submerged in a viscous fluid are being separated by forces normal to the surfaces, the relationship between the forces, the time since their application, and the distance between the plates is a function of the size and shape of the plates and the viscosity of the fluid provided the motion is slow enough so that inertia forces can be neglectedo.Also, if vertical motions are small, gravity forces can be neglected as well. In deicing problems the conditions for neglecting gravity forces are likely to be met and though inertia forces may not themselves be negligible, the increments of time during which they are important will be extremely short so that their effect on the time and energy required for ice removal will be negligible. It also seems likely that surface curvature will have little effect so long as the radius of curvature is large compared to the dimensions of the piece of ice under - ons iderat ion. Stefans gave a solution with experimental verification for this type of problem in 1874. le dealt with a disk being separated from a much larger parallel surface while submerged in various fluids,. one of which was water. His solution is A 4 t W12 W22 where R = radius of disk p = viscosity of fluid,.t = time, Wi = initial separation distance, W2 = final distancee, F = normal force on disk, and A = area of disk. Considering other uncertainties involved, this should be a sufficiently good approxiat:ion for a square specimen and other shapes with roughly similar dimensions in all directions. Since some pieces of ice are likely to be long and narrow, however., another expression has been derived based on similar assumptions, except that the piece of ice was assumed to be infinitely long in one direction and of width b in the' other. The derivation follows. The problem is simplified somewhat by making it symmetrical, that isP two similar plates are used which are of infinite length, of width 2a, and are separated by a distance 2h. The axes are chosen as shown in the accompanying sketch with velocities in the fluid of u and v in the x and y directions, respectively. AF 54.405 All

I I.0 A uI * - I 1IZZrjI7Z i 1 - in y direction: force per unit length in Z direction -a - a r-11 With "b-ody" forces and inertia forces fluid motion in two dimensions reduce neE to (C2) The boundary conditions are (C3) aP 6x. P by U = 0.u = 0 v is not a F Slected, oax2 \ for for Navier Stokes, equations for the. 6 2ud W-.. ay2 a2 EJ 1 J = + h for x = 0 function of X for y = + h by the following It can be seen that Eqs. C2 and C3 are completely satisfied equation. P = C(x2+y2) (C4li) u =- h 2.h2) v =C (Y3. h2 * ~ - Y ^ *. h - v -5 The value of F can now be found by integration of P over the surface-. y = h, thus a F = * 2 C(x2 + h2) dx 0 Ca3 5 * (C5);}i A4F 54-405 A12

and the average force per unit area is F/A = - +h2) 3 from which c = -- F/A 2 a + h2 3 The notation can now be changed back to its original form by substituting a = b 2 W 1 dW v = for y = h 2 dt to give F 3 2 -W A = (b2 + W2 ) (c9) dW dt In this equation the variables are separable and integration is easy. T~7 o W2 W1 b2 + 3W2 w5... 2 dW = - 4 t A 0 dt (Gclo) 2 -b - —'-'- 3 2W W2 log W] W1 2 F/A P t b "1 1 2 rl2 2 2 Wi W22 W2 _ + 3 log Wi~ 2 F/A t t~5 For round pieces of ice of radius R.(C )l t =. I ( 4 F/A V 1 Wi2 11 1" W W2 while for very long pieces of width b (C12a) Ft F/A.b2 4 21 W2 2 5 W2 + log-j 2. Wi AF 54-405 A13

in which t is the time required for the water-: layer to change in thickness from W1 to W2 due to surrounding water flowing under the ice. When b - W2 > W1- which is the case for any deicing situation, Eq. C12 simplifies to (C12b) t = l 4 F W1 in which t is the time to remove the ice..AF 54-405 A14

APPENDIX D EQUIPMENT AND PROCEDURE FOR MEASURING WATER THICKNESS Equipment The ice condenser consists of two copper disks 3 inches in diameter (see Fig. Dl). The top plate is 1/4 inch'thick with a small lip around its upper edge ~I _ 1/4 inch ~I ~1 1/8 inch Fig. Dl so that it can be set in its holder. The bottom plate is a plain disk 1/8 inch thick. A wire is soldered to each disk so that an electrical connection can be made with the capacitance change detector. Since the top plate is to be heated uniformly over its surface, its wire is soldered carefully on the lip away from the main body. The placement of the wire on the bottom plate is not critical. It is important that the top plate be of uniform thickness'with a very flat, smooth, unblemished bottom surface to avoid having hot.or cold spots appear on the ice during heating. The ice must be melted uniformly over the surface for accurate results. The jig (Fig. D2) for holding the condenser is a plexiglass disk with a hole in the center the size of the copper disks. Around the hole are cemented three spacers on which the lip of the top copper plate rests. Figure D3 shows how the I0071 spacer top view side view Fig. D2 spacer. [plastic jig l - * -No -r'r ie *,,, \ b.ottom plate Fead wire Fig. D3 AF 54-405 A15:

completed assembly appears after the ice dielectric has been frozen between the plates; the hole in the plastic is just slightly larger than the disk. Note that everything is so dimensioned that the lower plate is still in the hole itself; thus when melting commences the ice and lower plate cannot slip sideways due to any slight tilt of the jig., but are constrained to remain in position by the edge of the hole. This is important in that any slipping would cause a spurious change in ca.pacitance and lead to an erroneous result. Three components make up the capacitance change detector, a 1.8 mc/oscillator, a calibrated variable capacitor in parallel with a potentiometer, and a good vacuum tube voltmeterO The frequency of the oscillator must be above.1.5 megacycles because the dielectric properties of ice are functions of temperature and frequency. Fortunately, however, the dependency of the dielectric coefficient on temperature and frequency decreases as the frequency of measurement increases and at radio frequencies it is effectively constant with respect to both factors. An experiment showed that the dielectric coefficient of ice is constant within 0.75-percent at about 3.0 right up to the melting temperature, while the resistive component decreases linearly with temperature. The 0.75 percent variation is easily accounted for by experimental errors. Thus at this radio frequency an easily discernable discontinuity in dielectric constant occurs precisely at melting. The variable capacitor and resistor are used for a substitution method of measurement and will be described briefly. The ice condenser can be represented as a pure capacitance, C* in parallel with a pure resistance, R*, as represented in Fig. D4. Since ice is a poor dielectric, any ice condensr will have a relatively low parallel resistive component. The usual capacity measuring devices are useless in this case because the resistive component is so low compared to ordinary dielectricso However, a substitution method can be usedo The ice condenser is R* ice actual equivalent Fig. D4 loosely coupled inductively to the RF oscillator. Then a calibrated resistor and capacitor'are substituted for the ice condenser and adjusted until they give the same response in the oscillator circuit as the ice condenser. The resistance and capacitance must then be equivalent to the ice condenser. Figure D5 shows the three to, oseillato swl s\w 2 -- -e -I R Fig. D5 AF 54-405 A16

components pictorially, It is important to calibrate and keep low the capacitance of the leads from the calibrated condenser unit to the ice condenser; other stray capacitance being unimportant as long as it is kept constant during the experiment, A schematic of the capacitance change detector is given in Fig. Dll. A good capacity bridge capable of 5 percent accuracy or better is required to calibrate the variable capacitor since it may be necessary to bias the variable capacitor with a little fixed capacitance at times; depending on the different dielectric thickness being used. A heater capable of uniformity heating the top plate of ice condenser is necessary. An ordinary heat lamp about 6 to 8 inches away from the plate worked quite well. Furthermore, by adjusting this spacing, the melting rate can be increased or decreased. Finally, a deep freeze unit is needed (a) to freeze the ice dielectric to the plates initially and (b) as a cold place in which to conduct the experiment. Operation In preparing the ice condenser it is necessary to obtain a thin sheet of ice frozen between two parallel electrodes. It is also necessary that the electrodes remain parallel after melting starts instead of tilting as shown in Fig. D6. The procedure for producing such an ice condenser is to put the electrode which will be heated upside down in a pan of distilled water. Several small chips of insulating material are then placed on the electrode near the periphery: Three or four short pieces of copper wire are placed on the plate with their ends sticking out over the F~~~ gF~ F ~~water weight dowice - tilting effect Fig. D6 edge and the other electrode is set down on the copper wires as shown in Fig. D7. The diameter of the wires thus determines the speacing between the plates, and since hips of insulator c/opper electrode vcire e l wire copper electrode Fig. D7 AF 54-405 A17

this can easilybe measured it provides a convenient way of determining spacing. The several parts are then lifted out from the water as a unit. If the plates are lifted out horizontally, the water remains between the plates due to the effect of surface tension. With reasonable care, water can be maintained between plates which are separated by as much as 1.5 mm, The assembly is then placed in a freezer and a weight is placed on top of the upper electrode. This weight prevents the water from raising up the top plate as it freezes.After the water has frozen, the wire spacers can be removed by pulling them out with the fingers. The heat from one's fingers is conducted down the copper wire and melts a film of ice surrounding them so that they can be removed very easily., The ice condenser is now ready for test. The action of the little insulator chips in preventing tilting is illustrated in Figo D84 After melting starts, the bottoms of the chips are still supported in c hips of iLLnslatr copper electrode - water Fig. D8 the ice,-.but their tops bear against the heated copper surface and prevent it from tipping, The equipment is set up as shown in Fig. D9 and the initial capacitance, Co is measured by using the technique of the substitution method. The ice;condenser is coupled to the RF oscillator by closing switch 1 and opening switch 2, Next, the oscillator is tuned near resonance as shown by a maximum on the voltmeter and the voltmeter is read. Then the ice condenser is removed from the circuit by opening switch 1 and the resistor and calibrated capacitor substituted by closing switch 2. The C gnd R are then adjusted to obtain'a maximum on the voltmeter at the same voltage as before, C and R must then be equal to C0 and Ro. The ice.condensery which has been placed in its holder and adjusted so it is horizontal, is loaded with a weight, the weight of the' lowoer:plate' add the additional weight cofstittutg te.he;ttal'load On.the.ice. Then the heat lamp is turned on. The tank condenser Ct in Fig. D5 is continuously adjusted for a maximum reading on theVTVM1. When the lower plate falls, the reading on the VTVM just prior is noted and Ct left alone, Next the calibrated condenser and resistor are substituted by throwing a switch and adjusted so the VTVM reads a maximum of exactly the same value noted. The values of C and R must now equal C' and R*. AC = C* C. r I___ calibrated to simrple condenser i ce 1 tube - and pot and cond, Fig. D9 AF 54-405 A18

Knowing Co, a, and AC, the ice melted, x,, is computed from the equation, x e 1 a E -e e1 + (Co/AC) where e is the dielectric coefficient of water and e of ice. K C1 = x K =constant The deviation is: aKe a3 iix I a a Fig. D10 1 1.1 1 C CI C;. x a - x Ke Ke ex + ea- ex Kee ae, _ Kee e - e C(e - e) When x = O, C = Co so K aC e X e C - Co _ _..- = 1..Co/c> a - e C e - e 1+ (C0/C) Errors in x The errors inherent in this system manifested by an error in x can be estimated using the previous equation. x 1 a C0 1 + AC E - e AF 54-405 A19

dx da e e CO 4dAC dCo\ +,.... +.. —..x a E e e Co + AC AC C The factor e/E - e is small. Therefore the dielectric coefficients of ice and water need be known only approximately. This explains why no determination of them was made. The usual values of 3 and 81, respectively are sufficiently accurate. Neglecting errors in the dielectric the equation reduces to x a Co + AC AC Cy, An estimate can now be made of the total error. da 5.d r a (error in determining wire size) dAC AC Co Uo Since was about.7 the total error is about 7%. CO + AC A calculation of the thermal expansion of ice showed that its effect on the capacitance of the ice condenser is insignificant. AF 54 —405 A20

OSCILLATOR ll _ lL 6AC7 XTAL _ _ _ _ L Fig. 700 m f h0 50 K R150 MO; — IL 504 8hy 3 I _____ _ _20_j.f _ _20 f _ 16_ f __ | 150 \ I I Fig. D. Schematic o Capacitance Change Detector. I___ __ c__ - _ j~ ~ ~ ~ Fg +l Sceatcof aaiac h eDtcor CALIBRATED COND C- R Zi -- Sk -F e_ JT- E

Fig. D12. Close-Up of Ice Condenser in Its Holder. Fig. D13. Capacitance Change Detector. AF 54-405 A22

APPENDIX E DEVELOPMENT OF A TECHNIQUE FOR THE FABRICATION OF MODELS CAPABLE OF DELIVERING APPROXIMATELY 100 PERCENT OF THE GENERATED HEAT AT THE SURFACE FOR THE EXPERIMENTAL INVESTIGATION OF INTERMITTENT DEICING At the beginning of this investigation the various types of models being used by investigators in the field of heat transfer were considered for possible adaptation to this experimental program. A model was desired capable of dissipating high power densities at the surface. At the same time, surface temperature measurements were desired at a number of points over the surface in order to correlate analytical results with experimental data for the deduction of the amount of ice melted at the time shedding takes place. Nichrome ribbon heaters bonded to the model surface appeared to be the most common method of model construction and the most suitable for the high intensities desired. However, difficulties experienced with bonding the nichrome ribbon to the model surface and at the same time avoiding surface imperfections resulted in a search for a better technique. Conductive carbon coatings applied to plastic models which had thermocouples imbedded 0.005 inch from the surface were tried and found to be quite successful for heat transfer studies at a low intensity level up to 10 watts/in2. This was considered insufficient to.:garry out the experimental program desired, and the search for a better coating was continued. It was discovered that "Silver Paint," a product of the General Cement Company and used for printed circuits, could be used as a conductive coating capable of very high heat and generating capacities limited only by the temperature limit of the coating around 300 to 400~F. (Dupont Company makes a paste which can be diluted with amyl alcohol to perform the same function.) Pastic models were again tried, but model failure occurred from burnout at the high intensities, due to local hot spots which formed since the uniformity of the coating was of the order of + 10 percent. It was decided that a model consisting of a poorconductor for a base covered with a thin copper foil would eliminate this problem. A 6-inch balsa airfoil (NACA652-016) was fabricated and a copper foil.005 inch thicka which had thermocouples spotwelded to the inner surface, was bonded to it with Cox's* heating element adhesive No. 28. Slots.005 inch deep were milled at 3/4 inch intervals around the airfoil to within 1/2 inch of the edge. The entire surface of the foil was then coated with a thin plastic film and baked to insulate it electrically. The silver paint was applied to each strip separately by spraying, maintaining electrical insulation between the strips with masking tape at the time of application of this paint. Two coats of paint were required, each coat baked one-half hour at about 200~F. Bus bars and lead wires were attached at each end of the heater strips by screwing copper bars down onto the silver paint using plastic shims to isolate the screws from the copper bases. This completed the fabrication of the model; then all elements were checked for electrical isolation from each other as well as from the copper base. The finished model was placed in the University of Michigan Icing Wind Tunnel and preliminary tests indicated that it was capable of delivering-the desired *Cox and Co., New York, N. Y. AF 54-405 A23

intensities without burnout. The initial tests also indicated that consistent shedding result could not be obtained, due to bonding of the ice at the edges of the model. This was remedied by the installation of guard heaters at the edges. The performance of the model in this form was highly satisfactory.' Power densities up to 43 watts/in.2 were obtained. No higher densities were tried due to the short time intervals required for shedding at this point. These tests are discussed in the body of this report as Test Series F. Fig. El. AF 54-405

APPENDIX F MISCELLANEOUS NOTES The following two notes are included as matters of some interest which are not directly related to the main subject matter of this report. A series of tests were initiated wherein it was intended that heating rates approaching 1000 watts/in.2 would be used. The areas of particular interest in this phase were: 1. Establishment of the minimum amount of energy required to remove the ice for a particular systems 2. determine if the mechanism of removal might change radically at high heating rates, and 3. establish the effect of heating rates on the thickness of the water layer. A number of flat rectangular elements, consisting essentially of brass shimstock attached at the ends to copper buss bars, were assembled in a walk-in cold storage room held at about 15 + 2*F. After freezing a block of ice to the heating elements and allowing time for cooling of the element to room temperature (+ 15~0F), the desired voltage was applied to the element. A very slight spring loading on the block of ice caused it to be displaced,.after sufficient melting had occurred, and to engage a micro switch which shut off the applied voltage. The voltage and amperage were recorded on an oscillograph. Several difficulties and a few conclusions resulted from these tests. 1. Extreme care was required in attaching the ice block by freezing to the heating element uniformly and with no overhang on any side. 2. As the heating rate was increased and the ice released more rapidly, the amount of time required for the ice to move sufficiently to interrupt the power became a larger percentage of the power on time. That is, a tare, presumed to be roughly constant, of unknown quantity was included in each run; thus indicating higher total energies than was actually required to free the ice. 3. Heating rate of over 100 watt/in.2 were employed for this first series under conditions described above. The total energy required for removal appeared to have almost reached a minimum, for this system, of about 4-1/2 watt sec/in.2 at rates;of 125 watt/in.2. AF 54-405 A25

4. Calculations were made of the average water film thickness using the simplifying assumption that all the energy went into either heating the element or melting the film of ice. The values obtained varies from.0006 to.00198 in..with the thinner layers resulting from the higher heating rates. This would necessarily follow under the assumptions made for these calculations. Because of the tare mentioned above, a number of tests were made at increased heating rates wherein the power on time was pre-set for each trial and the success or failure of the test recorded as well as volts and amps. The thought being that the time required to just barely remove the ice with a given applied voltage would establish the minimum time and energy for that voltage. Unfortunately,. difficulties in recording the data and apparent discrepancies in the results were such that a modified recording and control system would be necessary before useful data at higher heating rates could be recorded. Heating rates approaching 1000 watt/in.2 were supposedly used, but inaccuracies in the data left some question as to the actual heating rate reached. At these higher rates the ice appeared to be freed. from the model instantaneously. The program was discontinued at this stage mainly because of increased emphasis in other areas of deicing. With proper models and. recording techniques it appears that further tests at heating rates in excess of 100 watts/in.2 should produce interesting and meaningful data. Ice Characteristics From a very few samples of ice collected from aircraft in flight it was found that the ice differed little from ordinary ice. However, the grain structure was very uniform and the C as of the xicrystals was normal to the surface More samples were not collected because the authorization for collection came very late in the icing season. AF 54-405 A26

DATA FOR TEST SERIES A Plotted on Fig. 13 a C0 AC Aa P.0865 cm 202'pF 173.P4F.0415 cm 2.65 gm/cm2.0865 194 234.0485.0865 202 177.0420.0865 197 169.0420.o865 200 196.0445 Avg..04357.0865 198 125.0345 3.75 gm/cm2.0630 255 298.0350.0865 201 132.0355 Avg..0350.o0600 258 150.0230 4.85 gn/cm2.0600 256 145.0230.0600 259 161.0235 Avg..0232.0600 257 127..0210 5.96 gm/cm2..0600 262 131.0205.o0600oo 259 119.0195 Avg..0203.0600 264 64.0125 13.7 gm/cm2.0600,263 93.0o60o.060o 262 66.0125.0600oo 246 65.0135.o0600oo 257 76.0143 Avg..0137.0865 208 345.056 2.13 gm/cm2.0865 208 281.052 Avg..054 AF 54-40'5 A27

DATA FOR TEST SERIES B AND C Plotted on Fig. 8 Test Data Water p Test u 0 t + t Force Melted Area to WB WC t/to Test 0 Tts + Force Meled (cm2) UO/ (sc) (cm) (cm) BFo Me (C) (cal-cm-2-sec-1) (sec) (gm) (gm)cm) (gm) g LW/Oto C A -25 B -26 C -23 D -24 E -24 F -24 G -24 H -24 I -25 J -25 K -23 L M -23 cD N -24 0 -25 P -8 Q -8 R -8 S -13 T -13.2 U -13 V -15 w -16 x -14 Y - 6.2 -.8 AA -10.6 AB -10.7 AC - 1.2 AD - 2.5 AE - 3 AF - 1.5 AG 0 AH - 4.5 AI - 1.5.145.142.146.685.685.639.583.627.645.607.655.655.649.363.398.279.267.275.266.266.251 1.265 1.185 1.22 1.24 1.19.598.451.587.587.560.605.280.284.275 83 80 73 16 19 14 21 17 17 19 2 3 16 32 44.5 8.55 19.25 21.0 26.0 23.3 22.95 4.87 5.24 3.08 2.14 2.8 4.67 6.70 1.53 6.22 7.05 6.23 17.76 17.85 12.97 32 86 86 36 35.0 56.2 35.6 36.7 35.5 55.35 69.8 70.3 69.1 69.9 70.6 35.3 35.8 33.6 35.9 35.7 34.7 37.1.9 1.0.7.6.55.75.8 ~7.7.5.25.5 1.1.72.93.52.65'*7 25.8 172 183 158 34.9 35.. 0 37.6 41.1 38.3 38.8 41.2 19.75 35.1 35.1 35.4 66.0 67.8 28.6 29.9 29.1 48.9 49.7 51.8 11.87 13.5 11.47 5.01 6.71 17.7 23.2 2.045 4.27 5.35 2.48 0 15.84 5.45 56.7 64.2 47.9 2.33 2.35 2.71 3.24 2.81 2.89 3.26 2.36 2.36 2.40 8.35 8.80 1.57 1.71 1.62 4.58 4.73 5.15.27.35.252.0482.0864.600 1.030.800.035.055.0118 0.481.057.112.033.033.077.079.076.077.075.077.077.o47 040.041.0405.0395.077.076.082.077.078.080.075.0456.0507.0355.0304.0278.0380.0405.0355.0355.0253.0127.0253.0557.0364.0471.0263.0329.0354.482.246.524 5.87 7.085 4.166 5.05 4.88 4.88 4.83.271 5.67 2.83 4.06 4.45 10.26 11.96 4.68 3.93 4.04 17.04 13.97 11.3 45.58 31.4 6.8 5.50 18.12 177 127 527 38.6 226 1.09.983.916 5.61 5.57 5.18 6.86 5.09 4.81 4.53 1.71 1.71 3.96 2.03 1.76 14.0 13.5 14.2 5.88 4.90 4.64 18.1 14.9 12.25 53.5 31.9 9.01 6.8 13.1 296 213 864 37.8 383 8.19 3.70 2.26 1.88 6.50 7.36 10.55 47.5 27.6 5.64 2.19 4.31 217 94.6 528 19.3 181

CALCULATIONS FOR TESTS OF SERIES ID Plotted on Fig. 11 Test Uo t + to F U0o/ to t/to S J Sto/J AK -17.2.629 12.75 35 27.3.295 42.2 54.5 1.55 6.56 AL -12.617 1.79 35 19.45.084 20.3 15.5 1.57.76 AM - 8.4.604 2.60 55 15.9.076 33.2 27.0 1.60 1.28 AN - 8.6.259 5.56 38 33.2.4355 11.78 8.4 2.74 1.34 pL = 79.-71 2 (.01794)(19.75)(l.75) 3iAb = 980 But this is for long narrow pieces use 32 b) in place of b2.'. pAb2 = (.01794)(19.75)(1.75)2(.75) = 8.0510 3 980 Test F Ab F J K t/J.6 FT F k AK.629 35 120.7.237 ~ 10'3 1.55 AL.617 35 129.1.237. 10-3 1.57 AM.604 35 132.0.237 ~ 10O3 1.60 AN.259 38 308.0.219.10"' 2.74 AF 54-405 A29

CALCULATIONS FOR SERIES E Use (7) v from 652 - 015 airfoil in NACA Rept. 824 % C 13.3 20 Ave. (\ 1.18 1.,74 1.346 2 22 =.0821 psi at 100'fps Pair = 1.346 (.0821) =.1104 psi = 7.57 jgm 2 cm W = 2__L req air = 2(.000432).1104 =.00782" =.01987 cm DATA FOR TEST SERIES E Test V tto vo/0 to t/to S AP -16.1.374 12.86 43.1 3.6 2.57 1.27 Q -16.1.233 27.2 69.2 9.2 1.96.90 R -16.,1.68 14.7 4.8 3.8 2.87 1.47 S -16.1.368 17.0 43.8 3.847 1.87 T -16.1.385 13.0 41.9 3.4 2.82 1.45 pL.L\./3 23 t S f f}'3 k J W/k toS F j AP 213 5.96 4.81 * 106.00224.598 8.86 7.63 Q 342 6.99.01685.00191.823 10.38 10o06 R 217 6.00.00223.607 8.90 9.2 S 217 6.00.00223.607 8.90 11.70 T 207 5.91.00226.588 8.78 9.37........!,, i.~i.. _..l...... i, i!.1. T.... i.... cortected by using F/A = W =.0774 psi.0284 cm = m2 = 530 cm2 toS J AP 6.77 Q 9.40 R 8.15 S 10.15 T 8.31 k.00253.00216.00251.00251.00255 W k 11.20 13.13 1130 11.30 11.13 AF 54-405 A30

DATA FOR TEST SERIES F Heater area.70" x 4.5" from NACA 652 - 015 aerofoil PRESSURE ESTIMATES (Linear interpolation)' C 1.67 11.67 Ave. 2 v.980 1.299 1.14o V use 1.140 1 pU2 V = 230 fps pV2 =.435 psi 2 1.140 (.435) =.496 psi = 34.9 gm/cm2 TEST SERIES F1 I -r Time Watts Test - in.2 Shed No shed L pL/3 7-" W k J shed no shed t/J -- ~ II. r. i. -. i 1 3 FA 1. FB 1.25 FC 2.5 FD 3.5 FE 4.5 FF 4.75 FG 6.5 FH 12.5 FI 22 FJ 44 20 18 4.5 4 4 3.5 2.9 3.0 2.0* 1.0 15 15 4.0 3.5 35.5 2.0 2.5 1.0.5 2150 1720 860 615 478 452 231 172 97.7 48.9 12.89 11.97 9.50 8.50 7.87 7.67 6.13 5.55 4.60 5.65 11.29 10.48 8.33 7.45 6.90 6.72 5.38 4.86 4.03 3.20 1.055.910.574.459.393 *.373.239.196.1345.0847 19.0 7.83 10.2 9.4 12.1 15.3 14.9 11.8 14.2 16.5 6.97 7.63 8.9 8.4 12.8 7.4 5.9 *sliding back Ab2.,01794 (4.70 )2 F 980 (34.9).00504 k.. 3 \ 0 ) L2/3,.00635 ( p() - 2 - 2(75.6) AP 980(54.9) w =.8 ( /3 _'877 (pL..6 =.257 * 10 = (.006355)3 =.oo443 AF 54-405 A31

TEST SERIES F2 Test Watts el F pL v e1/3 (iAb iAb2/ In.2 fps A - IF) FK 1 83 7.037 4.53 2150 12.90 1.98' lO"e.01253 L 1 145 11.5.037 135.8.65 10,.00865 M 1 230 20.037 34.9.257 108.00655 N 4.8 82 1.05.178 4.53 448 7.65 1.98 ~ 10'".012553 0 142 2.7.178 13.3.675 ~ 10e".00876 P 230 35.5.178 34.9.257 o10-6.oo635 Q 8.3 142 2.307.13.3 259 6.37.675 106.,00876 R 230 3.307 34.9.257 106.00655 S 230 1.5307 34.9.257 10".006355 J t t/J k W W/k FK 2.09 7.335.000772.0341 44.1 L 1.44 11.5 8.0.00053553.1118 21.0 M 1.057 20 18.9.000391.00442 11.30 N.735 1.5 2.04.001300.0341 26.3 0.513 2,7 5.26.000909.01160 12.75 P.5372 3 -5 9.41.000659.00442 6.70 Q.355 2:5.62.001092.01160 10.60 R.258 3 11.62.000792.00442 5.58 S 258 1 3.88.000792.00442 5.58 AF 54-.405 A32

SOME PROPERTIES OF WATER AND ICE Water (32'F) Ice (.2'F) lb Weight b62.41 57.50 ft3.97.92 cm Spec ific Gravity, p 10 Specific Heat Bt 1.00 (.504) lb~F cal1.00 (.504) gm C Thermal Btu Conductivity hr ft F. 1.294 cal K cm- C 1,44 x 10o3 5.55 x:103 sec cm C Thermal ft2.66 Diffusivity hr456 cma S 1.69 x 10'3 11.8 x 10'3 sec Latent Heat Btu 144 L lb (heat of fusion) cal/gm 80 Viscosity (1 atm) Cpoise 0.01793 Conversion factors: 1 Btu = 1 Watt = 1 lb 252 cal = 1055.2389 cal/sec = 453.6 gm joules = 775 ft lb 3.413 Btu/hr AF 54-405 A33

REFERENCES 1. Carslaw, H. S. and Jaeger, J. C., Conduction of Heat in Solids, Oxford University Press, London, 1947, p. 227-228. 2. Churchill, R. V., Modern Operational Mathematics in Engineering, McGraw-Hill) New York, 1944, (a) p. 106-109, (b) p. 117, problem 4. 53 Evans, Isaacson, and MacDonald, "Stefan-like Problems," Quarterly of Applied Mathematics, VIII, No. 35 313-314..4..uarterly ofAp.4. Landau, H. G., "Heat Conduction in a Melting Solid," uarterly of Applied Mathematics, VIII, No. 1, 84-94..5 Langmuir, I. and Blodgett, K. B., A Mathematical Investigation of Water Droplet Trajectories. AAF Technical Report 5418. 6. Messinger and Bernard L., "Equilibrium Temperature of an Unheated Icing Surface as a Function of Air Space," Journal of the Aeronautical Sciences, January, 1953. Also, Energy Exchanges during Icing, Lee. No. 6, University of Michigan Airplane-Icing Information Course. 7. Paterson, S., "Propagation of a Boundary of Fusion," Proceedings of the Glasgow Mathematical Society, I, 42-47. 8. Sherman, Po, Klein, J. S., and Tribus, M., Determination of Drop Trajectories by Means of an Extension of Stokes' Law, Engineering Research Institute Project 1992, University of Michigan, April, 1952. 9. Stefan and J. Stizber, Akad. Wiss., Wien (Math.-.faturw. Klasse) 69, 713 (1874). 10. Tribus, M. and Rauch, L. L, A New Method for Calculating Water Droplet Trajectories about Streamlined Bodies, Engineering Research Institute Project 1992, University of Michigan, December, 1951. AF 54-.405 A34

HEATING LOCATION AND RATE AIR TEMP WATER CONTENT AND DROP SIZE OF CLOUD AIR VELOCITY GEOMETRY OF WING AIR DENSITY K1 Li INPINGEMENT RATE 1 1 ICE TEMP I I Mm I WATER THICKNESS IL AERO FORCES - ] I 1 DYNAMICS OF ICE " IZ I -a - - CRITERION FOR REMOVAL Fig. 1..Schematic of Ice Removal Criterion.

NEOPRENE ICE CAP I \N~ DIA. WIRE / / ALUMINUM SKIN NEOPRENE SCALE 4:1 Fig. 2. Dimensions of Rubber Boot. AF 54-405 A36

z 0 Wu C- a 2o < z~L 0 Ol r-_ j 4~Cj 0...i.06 a: 0ra LO 2 2 0 2 rc 3 SO NO - <^.0 I: -,: N' o < 0 0 0 ~i*0 ** a , $. 644 * a * Q*, o*c' a 4 O U ** 4 a r -~rrr*rrr *re a an brQ*oQ'hD1VVg(\ 4'CQ a O "U* U' i c0 UU ZQt a *r 4 a o a "1 * *oa ~3~ ~, o ~,,*9 * O 04 LC rrb a a 1) py q UI 4.~d3U *I I'a. 4U 40 **qi) 4 Y rc a O. C rS i a 4 a *O a a u r * U' ir O a i, *rC i)li i 4()(* U 4 I..Y' 0*bU Q i U oU "o, i> ct o Ucrd qCY a 5' i, U 4 C " "v i:C. O'i "'"ir*Q Uq rg+ * j: a.I,. d ir 4 *a * ai U prlDL., r g,41 4 oq *C 4 V "e YVIljI CUO*OII I O a c U UQ Y c*aa crra O 3rrrrrr Ibr*.u a;$ a 1) gd O.,arr 4 a 4 * ad a OQI i * 4 UIDq*r6 a Q *,U*g "U i r 4 I-a CY UU **Cr P"a i." U a2'4 4* 8 4 F "**r r*,, i*O *q,.*. U a i **il o, *P O 4 i,* i-i-a IL"r *p rLZ * Il IU. I i) * 4 a sirir a.,u 4 q a 4 jp*e n.:Ot.,,+ n db 00 qa,., * C a ES a O C-I Cz.lw w1~ Z! =i ~Z. z o Co C,o 4-O 0 O - FS Crs; > s - Cco * 0 -H r -_S ^.- <.<4~'-D"~L*L~II~")*V"I~~C* ' J Jr**(ri, a 4"444 * " i:* n* 4 c*i)" ar a = 4 L C* h* 4 if * gU. 4 *icln"cJrr*r~tr, Yrbrrrry*C t no " u,r ~f a * * a. ~I o " 4 O" *Qg,* -*n, " b z, r *r r i**, aaU4 IP,* Ec"h* * " UirOO * 8u a FU4 DI))) i***" i ". 6ya ii _:i I )) U .i~ .Y.a'* )Z*e X -----— -; — nct-. in o.* 0'. * * o 4* nb.r bfVr i 4 U* 4 O a 4 4,, Cru r, *r n"9'.. *an Va* ~j" "i Q a i; " 6u,Q, U, a 6*t 8?r.I=b g** dnh""G*)i 3 "6 a gtlOc*cr 4'iO* *O, a " O 8 aa r *: —-- 4I _ N -A~~~~~~~~~~~~~~~~~~~~~~ - o S W - - - -5 -~~~~~~~~ ~~~ —- --- "3 nlp a' n*a i' og r~ * * 14* * 4 7 ~.g Q " O OPC RC ~" " i? 4 *,( * a a o, * a i 4 * o *oo V4 a Q *r ai 3,* ak a *(O b UC****,:rQ, v Q6 4 j.: F a a a n i 5~'-~- , " o 4,4 Lrrr, atl-eT* ic a * Q 7.. 50 r *ib* * o * U C', 6"U b* 4*4 bkY***(i 94 c 4*,)4 a a I gs a". 001 9 * O Iao * 9 a T. a a a 4 a 4 9C*0 * 5 r?' * a r o 4 i a ~*e sr * c *?r,-r 2sslrr*cs Ibrm*C ** 14 6444 *,,i) 5 aO 8 a g'' .q~gLI *. gBL a.o.. ~ *C,,n O; n a

I n I 0 \J1 IL 320 280 s 240 )) onn I[ > -d RUN I 10 WATTS /IN2 30 SEC. ON TIME c 160. 120 2 so, 8 0 --- --- __.. — --- --- --- --- - o I -- ----- 40 40 0 10 20 30 40 50 60 70 80 90 TIME IN SECONDS UL 320 280 - 240 200160 u 120 TIME IN SECONDS 320 w 280 240 - [ 200 160 0 120 - 4 80 0 10 20 30 40 50 60 70 80 90 TIME IN SECONDS 5L 320 j 280 - 240 -. 200 - r 160 - a 120 - w 80. OV ^ - - -^ - - = - =: o 320 w 280 I 240 t 200 i 160; 120 2 w 80 ~ ~ I -- I -- I - - I I - - c IR {? 320 w 280 240 200 u 160 0 120 w 80 e, 0 10 20 30 4 T 0 50 60 70 80 90 100 ME IN SECONDS o 320 w 280; 240 a 200 i 160.,f - 320 w 280 a 240 $ 200 2 160 8 120 2 a 8C a I i 80 I __ —. 0 10 20 30 40 50 TIME IN SECONI'L 320[. E ___ I —3 II v2 L - - - 0 70 8 9 0 I I- - I- - I- - I- - I- - I c I- - c M D 30 4 1 D 50 60 70 8 IME IN SECONDS 0 9 f\ 7. 10 30 4 1 0 50 60 7 IME IN SECONDS.. 80 90 100 u 0 w 280; 240! 200: 160 - 120 w 80 4C 0 I - I c I I - - 0- - I 0- - I- - I c /' 320 w 280 240 * 200 160 - 120 w 80 I- 3 10 20 30 40 50 60 70 8 TIME IN SECONDS 90 100 0 90 100 0 50.( IME IN SECONC 0 70 8 S ~ 320 w 280; 240 i 200 ~ 160 w - 120 w 80 I. 8 t 320! 280; 240 i 200 ~ 160; 120 80 w 80s A^1 / 0 10 20 30 40 50. 60 70 80 TIME IN SECONDS 90 O 50 60 70 80 90 100 TIME IN SECONDS 0 10 20 30 40 50 60 70 80 90 100 TIME IN SECONDS I- 320 u 28C: 24C 20C ~ 16C o. 12C w 8C - 4a 0 10 20 30 40 50.60 70 80 90 100 TIME IN SECONDS Fig. 4. Cell Temperatures of the Idealized Heater Boot as a Function of Time During a Typical Run.

IL 0 w bIJ 0: l&J I. CL) Z U 60- _ 50 40- _ 30- I 10 _ / I.,. I _ _ i I i..~C ~ I.. I I I 0 10 20 30 4 0 50 60 TIME IN $SECONDS 70 80 90 o00 Fig. 5. Temperature Difference between Cells 4 and 6. AF 54-405 A39

Fig. 6. Interferogram of Boot Two Seconds after Power is Turned On - All Wires Energized. AF 54-405 A40

Fig. 7. Interferogram of Boot 2 Seconds after Power is Turned On - Half of Wires Energized. A41

600 200 I TEST RESULTS 0 THICKNESS COMPUTED FROM SURFACE TENSION THICKNESS COMPUTED FROM WEIGHTS.2.1I I 2 20 40 60 80 100 200 400 600 1000 t to Fig. 8. Comparison of Theoretical and Experimental Melting Rate. AF 5-4405 A42

1.0.10 E I U) en LrJ z CD II-::.010 II.001 10 100 F= FORCE - gm(NET) 1000 Fig. 9. Force (gm) Thickness (cm) Relation for Excessive Water. 1.75" Square with No AF 54-405 A43

Fig. 10. Ice Removal of Heated Ice from Model in Wind T unnel. AF 54-405 A44

40 D> X <n 0 O3 4(n 10 k I - F i I00~~~~0 2 pL >I V TEST SERIES D < y / I i + | + " " E (ORIG) o 0 " E (CORR.) B=W/k 0i F "s>,Qt/J =.794 W/k (MELTING ONLY ) ASSUMED CONSERVATIVE r ( +B)2 - 2B-1 13 DESIGN WITH AMPLE Qt/J.2647 /2 LOG + + TA +240 WITH AMPLE RUN BACK I-B+B 2 02 h________r __ _\ _ _ — fRUN BACK WATER.____ 2 ^ - o, \,, -,,, A - A AA A IAIv m U e/ 9+: W/k W/k lU Ie F' l0 Fig. 11. Time, t, vs Water Layer Thickness W.

\J1. 0 VJ1 I.( Q t/to ~ t/'to [ ( I +t/to) TAN V t/to-J-/to] Fig. 12. Q vs t/to.

I r% I.g.9.8.7.6.5 4.3.2.I.09.08 I.07.06. \.05 I.7 —------- - -- - ---------- -- — \ 6-04 —- -- -- - -- - - _ ------- -- - - -I 2 L) Uf) Lii z C-) Ld I-. tN2 0.0.012.01- - I I - I II- - I- I I- I -I I I I I 2 3 4 5 6 7 8 9 10 20 PRESSURE GM/CM2 30 40 50 60 80 100 Fig. 13. Separation Force vs Water Thickness. Series A. AF 54-405 A47

Fig. 14. Device used in Experiments of Series B. AF 54-405 A48

Fig. 15. Heater Element used in Excess Water Experiments. Serie s D.

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. ( z a 0 w.C,) 0 LL a,C w cr w Ul) w z 0 16 * EITHER SLIDING BACK OR MELTING I 7 \kl H-J 12 8 4 ----- -mm m m m mm —m w 0 4 Wa~s/~ K ~~~~~~8WTSi i 0 75 125 175 225 VELOCITY (FT/SEC) Plot of On Time Required for Shedding vs Velocity for Various Pewer Densities. Fig. 17.

0-pU.) II CJ VIZ Uf) 0 %-. z 3 a w m Uf) w uw z 0 I 20 16 12 8 4 n 4 i RUN I -0 - SHEDDING -X - SLIDING BACK RUN 11-A - SHEDDING RUN M-0- SHEDDING ALL RUNS-* - NO SHEDDING Uo = 230 FT/SEC To = 28~F Lw=.207 GMS/M3 p=20 MICRONS I a I t I i - i - I 0, 0 a x x 0 0 5 10 15 20 25 30 WATTS/ IN2 Fig. 18. Plot of Power on Time vs Power Density. 35 40 45

HEATERS ARE.70" WIDE, 4.5" LONG 1/8 -,^S^ -\ ~ \ ^ 21.67%, in /t 611.67 % \5A / 1.67% iL — --------------------- 7. 5 Fig. 19. NACA 652 - 015 Airfoil.

>. 20 0 ICE CAME OFF - ICE SLID BACK, 16 Qt 12 I 4 — t l | — - 0 2 4 10 12 14 16 0 2 4 6 8 10 12 14 16 18 Fig. 20. Results of.Wind Tunnel Tests.

kD1.40 \J1 \3n Fig. 21. View of Wind Tunnel

0