THE U N I V E R S I TY OF MICHIGAN COLLEGE OF ENGINEERING Department of Aeronautical and Astronautical Engineering High Altitude Engineering Laboratory Technical Report THE MEASUREMENT OF UPPER-AIR DENSITY AND TEMPERATURE BY TWO RADAR-TRACKED FALLING SPHERES by J. W. Peterson K. D. McWatters ORA Project 03598 under contract with: NATIONAL AERONAUTICS AND SPACE ADMINISTRATION CONTRACT NO. NASw-138 WASHINGTON, D.C. administered through: OFFICE OF RESEARCH ADMINISTRATION ANN ARBOR March 1963 (Revised May 1963)

The revised version of this report was issued after an error was found in the data processing which had the effect of eliminating the altitude variation of gravity acceleration. The corrected density profiles are one to two percent smaller at altitudes less than 90 kilometers, at 100 kilometers the corrected profile was 10 percent smaller for 10.50 and 20 percent smaller for 10.43. Tables III and IV and Figures 8 and 10 have been changed.

TABLE OF CONTENTS Page LIST OF TABLES v LIST OF FIGURES vii LIST OF SYMBOLS ix THE UNIVERSITY OF MICHIGAN PROJECT PERSONNEL xi INTRODUCTION 1 I. DETAILS OF ROCKET FLIGHTS 2 II. DATA ANALYSIS PROCEDURES 4 III. DISCUSSION OF THE PROCESSED DATA 9 IV. ACKNOWLEDGMENTS 10 APPENDIX A. SOURCES OF CD DATA 11 APPENDIX B. CHOICE OF SMOOTHING PARAMETERS 13 APPENDIX C. EFFECTS OF WINDS 15 REFERENCES 18 iii

LIST OF TABLES Table Page I. Nike-Cajun Rocket Flights, Wallops Island, Va. 19 II. Velocity Ratio vs. Altitude 20 III. Processed Data, Flight 10.50, 1-m Sphere 21 IV. Processed Data, Flight 10.43, 1-m Sphere 22 V. Processed Data, Flight 10.50, 7-in. Sphere, Upleg Trajectory 25 VI. Processed Data, Flight 10.50, 7-in. Sphere, Downleg Trajectory 24 VII. Drag Coefficient Function 25 v

LIST OF FIGURES Figure Page 1. Ejector pods on tail of Cajun. 26 2. Grenade Cajun nose cone, uncovered. 26 3. One-meter corner reflector sphere. 26 4. Altitude vs. distance down range. 27 5. Horizontal trajectory coordinates. 28 6. Altitude vs. time. 29 7. Velocity vs. altitude. 30 8. Density profiles, Flights 10.50 and 10.43. 31 9. FPS-16 radar AGC voltage. 33 10. Temperature profiles, Flights 10.50 and 10.43. 35 11. Mach Number vs. Reynolds Number of falling spheres. 37 12. JPL drag coefficient data. 38 13. /po vs. L/H. 39 14. Velocity vs. smoothing parameter Azv. 40 15. Velocity components vs. smoothing parameter Azv, 80 km. 41 16. Velocity components vs. smoothing parameter AZv, 105 km. 42 17. Density function vs. smoothing parameter AZv, 80 km. 43 18. Density function vs. smoothing parameter AZv, 105 km. 44 vii

LIST OF SYMBOLS A sphere cross section area c speed of sound CD sphere drag coefficient D drag force E energy g gravity acceleration at altitude go gravity acceleration at altitude zero H scale height in the atmosphere KE kinetic energy per unit mass of sphere m mass of sphere M Mach Number M* molecular weight of air PE potential energy per unit mass of sphere R* universal gas constant Re Reynolds Number r radar coordinate slant range re radius of earth s distance along sphere trajectory t time T temperature, Kelvin V sphere velocity Vs sphere volume a radar coordinate, azimuth angle BP angle from line of sight to vertical A difference C radar coordinate, elevation angle p density of air viscosity of air ix

THE UNIVERSITY OF MICHIGAN PROJECT PERSONNEL Both Full- and Part-Time Allen, Harold F., PhoDo, Research Engineer Bodine, Margie S,, Secretary Bonfanti2 Giovanni, B.S.(AeoE.), Assistant in Research Chapelsky, Orest, B.S.(Ae.E.), Assistant Research Engineer Fischbach, Frederick Fo, M.S., Associate Research Mathematician Hansen, William Ho, BoS., Research Engineer Jones, Leslie M., B.So, Project Supervisor McWatters, Kenneth D., B.S.E.(Aero.), Assistant Research Engineer Mosakewicz, Mary C., Secretary Peterson, John W., M.oS, Research Engineer Schaefer, Edward J., M.S., Research Engineer xi

INTRODUCTION On NASA Contract No. NASw-138 the High Altitude Engineering Laboratory of The University of Michigan's Department of Aeronautical and Astronautical Engineering has been engaged in the development of rocket techniques and instruments for measuring the properties of the upper atmosphere. Two major lines of investigation have been pursued: the measurement of neutral composition with mass spectrometers, and the measurement of neutral density with falling sphere S The purpose of the work described in this report was to develop an inexpensive technique for probing the atmosphere at relatively high levels using a lightweight sphere to be tracked by radar. It was anticipated that in order to satisfy the cost requirement, the sphere deployment system should be compatible with rocket payloads designed for other functions. Two such systems were developed and successfully flown on Nike-Cajun rockets, The first system employed dual pods, which were arranged on the Cajun tail section for rearward deployment of two inflatable spheres. The nose cone payload of this rocket contained an instrumented 7-in. sphere for air density measurement equipped with accelerometer and telemetering. The second system employed a single tube in the Cajun nose cone for forward deployment of a single inflatable sphere. In this system, the nose cone also carried the principal payload of the rocket, 11 grenades for the measurement of winds and temperature, an experiment of GSFC. 1

I. DETAILS OF ROCKET FLIGHTS Table I summarizes four rocket flights at Wallops Island, Va., two of which resulted in data which have been processed to obtain pressure, density, and temperature profiles. Each of the sphere envelopes was manufactured by the GT Schjeldahl Co., which also provided the isopentane capsules for releasing inflation gas. Two sphere designs were used, l-m-diam sphere with metallized internal corner reflector (see Fig. 3), and a 4-ft-diam sphere with metallized envelope. Studies of the radar characteristics of the two targets did not conclusively indicate which one should be selected, so both were tried. The corner reflector design has had extensive use in the ROBIN program directed by R. Leviton and J. Wright of the Air Force Cambridge Research Laboratories. Figure 1 shows dual pods arranged on a Cajun tail for aft deployment. Each sphere envelope was tightly packed in its tube between staves of phenolic material. Envelope and staves were ejected through the end of the cube by a charge of black powder ignited 110 sec after launching by a pyrotechnic fuse. The ejection system was manufactured by the Zimney Corp. Rocket 10.50 carried one each of the two sphere designs. The two ejections were made at approximately the same time. The radar acquired the corner reflector, which was the larger target, and it was tracked until deflation at approximately 38-km altitude The second sphere was then acquired but not tracked. Rocket 10.50 also carried The University of Michigan 7-ino sphere equipped with accelerometer and telemeter.1 This instrumentation was developed under the direction of H. Fo Schulte; the work was supported by Air Force Cambridge Research Laboratories. The 7-in. sphere was ejected at approximately 48 sec at an altitude of 57 km. Upleg data as well as downleg data were obtained down to an altitude of 46 km, at which altitude the telemetered signal became too small for recovery of datao The difficulty was believed to be due to antenna breakdown caused by the formation of an ionized plasma at this altitude. The second application of the inflatable sphere system was an integration with rocket-grenade payloads. The rocket grenade program is presently under the direction of W. Nordberg and W. Smith of the Goddard Space Flight Center. Wind and temperature are measured by the rocket-grenade system, which is based on the principle of sound propagationo2 In the current version of this application, 12 grenades are carried in a Cajun nose cone. The grenades are ejected from the rocket and exploded at intervals on the upleg portion of the trajectory. The time of arrival of the sound at the ground is detected by an array of microphones. The grenade nose cone (see Fig. 2) 2

has nine short mortar barrels in the outer circle for small grenades and three long barrels in the center for large grenades. In the present application the sphere package replaced one of the large grenades. The design and testing of the sphere package for the grenade payload was done under the direction of H, Fo Allen of our laboratory. Difficulties were encountered with sphere deployment on the first two flights. On 9-16-1961 the sphere was tracked but was apparently in an uninflated condition, On 3-23-1962 the sphere was not acquired by the radar. The apparent source of trouble in both flights was failure of the gas capsule to release isopentane. The capsule release mechanism was modified and a successful deployment was achieved from Rocket 10.43 on 6-6-1962. The grenade system telemetering failed on this flight but it was possible to recover the information needed for grenade data reduction from radar data. The sphere in this case was again the corner reflector design. No data were obtained for the metallized sphere design. 5

II. DATA ANALYSIS PROCEDURES The aerodynamic drag equation is fundamental to the falling sphere system for air density measurement: A D = 2 (CDp)V2 (1) The velocity V in Eq. (1) is the velocity of the sphere relative to the air through which it falls. A method of deriving atmospheric density based on this equation for a sphere falling through still air will now be developed. The energy dissipated by drag on a sphere falling from upper altitude zu to lower altitude zj may be found by integrating drag force, Eq. (1), with respect to distance-along the trajectory: s'T h 5) A AE = Dds = 2 (CDP)Vds (2) tJ SU Su On the other hand, energy dissipated can be equated to the change of the sum of kinetic energy and potential energy of the sphere between altitude zu and AE = m(APE + AKE) (5) In Eq. (3) both PE and KE are the energy per unit mass and m is the mass of the sphere. These equations are used to compute mean value of the product of drag coefficient and air density between appropriately chosen levels Zu and zj: P^ A o A __ ^ A _ (CDp)V2ds = CD s = CDp V2As (4) AE (CDP ds - CDP V ds= DP2 su Ju where V2 = 1(V2 + V2) (5) As = VAt, V = (Vu + V~) (6) The mean square velocity given by Eq. (5) is exact when acceleration is con4

stant; when it is not constant, Az should be sufficiently small to insure a satisfactory approximation. The density formula is derived from Eqs. (3) through (6): 2m APE + AKE CDP =A V2VAt (7) In the presence of a force due to gravity the change of potential energy per unit mass is equal to the force, g, times the change of altitude. The buoyant force is also vertical; consequently its effect on the sphere's motion can be accounted for by an additional term in the potential energy formula. The buoyant force is equal to the mass of air displaced by the sphere times the local value of gravity acceleration. The formula for change of potential energy then becomes pgV s APE = (g- ) Az = g Az(l - p-) (8) where Ps is the mass per unit volume of the sphere. Buoyancy is an important effect only at the lowest altitude, where air density becomes as large as 80 of sphere density. Since air density appears on each side of Eq. (7), iterations are required. Gravity acceleration at altitude is derived from gravity at zero altitude by the inverse square law: 2 re = eo + (9) where re is the earth's radius. The drag coefficient CD is a function of two aerodynamic parameters: Mach Number and Reynolds Number. In order to compute atmospheric density profiles CD data are needed over a wide range of Reynolds Numbers and subsonic and supersonic Mach Numbers. The sources of these data are discussed in Appendix A. The application of Eq. (7) involves double differentiation of radar position data since the derivation of velocity requires one differentiation and a second is involved in AKE. Velocity is derived by a least-squares fit of a parabola to each of the radar coordinates-range, azimuth, and elevation,which are functions of time. The extent of the data used to determine velocity was defined by the altitude 5

parameter Azv. The spacing of the energy levels zu and z~ is defined by the altitude parameter Aze. Different values of Azv and Aze are used at different altitudes. The proper choice of values was studied in some detail and is described in Appendix B. Altitude was preferred over time as a smoothing parameter since its physical significance is more readily interpreted. The ability of the system to resolve fine-detail atmospheric structure may be improved at the expense of increased scatter by decreasing the amount of smoothing. It was felt that an appropriate amount of smoothing could best be chosen through a consideration of the altitude and altitude interval. Since the sphere velocity varies so widely in different parts of the trajectory, the specification of time interval was thought to be a less satisfactory approach. The FPS-16 radar data were provided at a rate of 10 data points per second. At low altitude the sphere falls at a slower speed so that a larger number of data points appears within a given altitude interval; therefore more data were available than were needed. Since a considerable amount of computer memory is required for storage, the data were condensed by taking 1/2-sec averages of the 1/10-sec data below 57 km. Equation (7) was used to compute a list of values for CDP at approximately 1-km levels from the lower level,where the sphere was collapsed, to the highest level where results could be obtained. The precise level of the CDp determination was the level of the radar data point which fell nearest an integer kilometer altitude, the differencebeing at most 50 m. Drag coefficient CD was then found by entering the drag coefficient function with Mach Number M and the product of drag coefficient and Reynolds Number CDRe V M = (10) and (CDp)Vd CDRe = (11) The speed of sound c and the viscosity 4 were derived from U.S. Standard Atmosphere, 1962. Using the drag coefficient found in this way, a list of density values at approximately 1-km levels was derived. The pressure at each kilometer level was then found by integrating the barometric equation AP = -pgAz (12) The mean density between levels zn and Zn+l was calculated using the logarithmic formula 6

Pn+l - Pn P Pn+l (13) on Pn The integration was downward from the highest level of 110 km where the pressure was assumed to be zero. A temperature profile was then derived using the gas equation of state M*p T = M (14) R*p Where R* is the universal gas constant and M* is the molecular weight also assumed to be constanto Except at the highest levels, the temperature profile obtained in this way was believed to a better source of speed of sound and viscosity data than U.S. Standard Atmosphere, 1962, which was used in the first determination of CD, Therefore iterations were performed. Above 90-km altitude, Standard Atmosphere temperature was used; for altitudes between 40 and 90 km the derived temperatures averaged over 4 km were used; and below 40-km altitude the derived temperatures were used without being averaged. Iterated drag coefficient, density, pressure, and temperature profiles were then computed. Iterations were continued until the largest temperature change at any level was smaller than 1~Kc The influence of atmospheric wind on the sphere trajectory depends on altitude. In order to discuss wind and other factors it is useful to define (roughly) three regimes of the trajectory of a lightweight sphere falling from a maximum altitude of 150 km, 1. High altitude, Above about 95 km drag accelerations are less than 1 g. Above about 80 km, velocity is greater than twice the sound speed. Maximum Mach Number is 3~7 at about 95 km. Subsonic velocity occurs only at an extremely high altitude, where the system is insensitive to air density. 2. Middle altitude. Maximum drag acceleration is about 4.5 g at about 80 km. Sonic Mach Number occurs at about 70 km. 35 Low altitude. Below 70 km drag force and gravity force are approximately equal. The velocity is subsonico The second sphere deployed from the lower altitude of 120 km follows a similar pattern. More specific details of the two trajectories are plotted in Figs. 4, 5, 6, and 7. In the high altitude regime the sphere velocity is large compared with expected atmospheric wind velocityO At the more extreme high altitudes gravity has a greater influence on the trajectory than the drag force. At high altitude, therefore, the sphere is not a useful sensor of winds, and the 7

total velocity of the sphere is used in the density formula [Eq, (7)]. At low altitude, the lightweight sphere tends to be carried along by horizontal wind so that the relative horizontal wind tends to become zero. For this regime, therefore, the vertical component of sphere velocity is used in the density formula [Eq. (7)]. The vertical component of velocity is calculated by the formula z = r cos P + r C sin 5 (15) where P is the angle between radar line of sight and vertical at the sphere. -i cos c sin -1 COS (16) + -- where re is the earth's radiuso Table II shows that there is a relatively broad range of altitude in which either method is applicable since the total velocity and vertical component differ by less than 1%. The favorable geometry is due to the large drag accelerations, which tend to annihilate the horizontal motion and leave the sphere in a vertical trajectory. Although the lightweight sphere is a useful sensor of horizontal winds, the analysis of winds on these two spheres is incomplete and is not reported at this time. The presence of variable horizontal winds has a slight influence on the vertical motion of the sphere. This effect is discussed in Appendix C. At low altitude, the influence of vertical wind on the motion of the sphere is larger and cannot, unfortunately, be separated from density effects. The error in density measurements due to vertical wind depends on sphere velocity and is also discussed in Appendix C. 8

III. DISCUSSION OF THE PROCESSED DATA In Fig. 8 the density profiles derived from flights 10.50 and 10.43 are compared with those given in U.S. Standard Atmosphere, 1962. Tables III and IV exhibit the tabulated valueso The smoothing parameter Azv was varied from 1 km at lowest altitude to 6 km at the highest altitude. The same variation of Azv was used for each flight. In each case Aze was made equal to AZvo No absolute standard for choosing smoothing parameters was found. As altitude increases, the derived density data tend to become more scattered, An increase of the smoothing parameter sufficient to control the scatter at the different altitudes was selected after examining the results of alternate choices. Some general considerations applicable to the choice of smoothing parameters are discussed in Appendix B, and specific examples are given. The density profiles showed no radical departures from those of the U.S. Standard Atmosphere, 1962 except at altitudes in the neighborhood of 105 to 110 km. At this extreme altitude it was felt that the system could not be relied upon because it lacked sensitivity to the small drag forces that perturb the trajectory. It is of interest that the data yielded by the 10.43 sphere, which fell from a peak altitude of 120 km, were comparable to those yielded by the 10.50 sphere which fell from a peak altitude of 150 km. At low altitude, the sphere finally descends to a level where the ambient pressure is greater than the internal pressure maintained by the isopentane gas. A collapsed sphere appears to have much greater drag than a filled sphere, so that there is a sharp departure from the normal density profile. This departure can be readily seen on the plotso A second indication of collapse appears on the chart of radar automatic gain control voltage (see Fig. 9). The chart of an inflated sphere whose reflector is erect has a characteristic pattern. Smooth and irregular portions alternate as the sphere rotates and changes its aspect with respect to the radar. At 500 sec, the 10.50 sphere can be seen rotating at a faster rate than the 10.43 sphere. When the sphere has collapsed, an irregular pattern is always seen. The automatic gain control (AGC) charts indicate deflation at 770 and 970 sec for Flights 10.50 and 10o43 respectively; these values agree well with the break that appears on each density profileo Figure 9 shows the AGC trace for each of the two spheres when normally inflated and when deflation is believed to occur. It should be noted that deflation time need not be pinpointed very closely in order to get good results since an error of the order of 40 sec when the sphere rate of descent is 25 m/sec results in an error of only 1 km for altitude of deflation. The AGC method has the advantage of being independent of aerodynamic effects. If the sphere were caught in a severe gust of vertical wind, the calculated density profile might be sufficiently distorted as to be unreliable. 9

Flight 10.50 also carried a 7-in. sphere equipped with accelerometer and telemeter. This sphere instrumentation which is described in Ref. 1, is similar to the instrumentation described in Ref. 3 except that basic changes in accelerometer design and data encoding were made in an effort to improve sensitivity to small accelerations. The data were processed by the methods reported in Ref. 3, except that the new drag coefficient data reported in Ref. 4 were used. The processed data for the 7-in. sphere are shown in Tables V and VI. The density profile derived from the 7-in. sphere (see Fig. 8) shows an increasing departure from the standard atmosphere as altitude increases. The data appear to be abnormal. There were no indications of malfunction of the sphere instrumentation that would influence acceleration measurement. Unfortunately, two other spheres of this design were lost due to rocket vehicle failures. Since the 7-in. sphere was the only one of its design to perform in flight, the data associated with it do not have the validity of those associated with a proven system. In Fig. 10 the temperature profiles derived from Flights 10.50 and 10.43 are compared with those given in U.S. Standard Atmosphere, 1962. The temperature profile derived directly from the density and pressure profiles shows some scattered data. Average temperatures are also plotted from the derivation of an arithmetic average of five temperatures bounding a 4-km layer. Also plotted in Fig. 10 are the temperatures derived from the grenade payload of Flight 10.43. Eleven grenade explosions spaced at approximately 5-km levels yielded the ten average temperature points ranging from 46 to 93 km. The spherederived temperatures from 46 to 60 km are 10 to 20~ higher than the grenade temperatures. From 69 to 85 km the agreement is better. The sphere data points are spaced closely enough to permit measurement of fine structure such as the minor temperature maximum at 78 km. IV. ACKNOWLEDGMENTS We are indebted to the Office of Space Sciences of the National Aeronautics and Space Administration for encouragement and for the financial support of the sphere program. We also wish to thank the personnel of NASA's Wallops Island Station who assisted in the flights. 10

APPENDIX A SOURCES OF CD DATA The drag coefficient of a sphere depends upon two aerodynamic parameters: Reynolds Number and Mach Number. Figure 11 is a plot which shows how these parameters vary in the trajectories of the two inflated 1-m spheres of Flights 10.50 and 10.43, and in the trajectory of the 7-in. instrumented sphere of Flight 10.50. At high altitude, where the Mach Number of the inflated spheres is supersonic, measurements of drag coefficient show little if any effect of Mach Number. The recent measurements of Ashkenas5 and Ashkenas and Wegener6 were especially relied upon for the supersonic drag coefficients used for sphere data processing. Figure 12 shows the measurements reported in Ref. 5; the curve drawn through these data is the one selected by the present writers for the purpose of sphere data processing. At low altitude the motion of the sphere becomes subsonic. In this regime, very extensive falling-sphere measurements have been made with the ROBIN system developed by Air Force Cambridge Research Laboratories under the direction of R. Leviton and J. Wright. Determinations of drag coefficients for this program have been made by H. Heinrich.7 Important Mach Number variations are indicated in this regime. The supersonic and subsonic drag coefficient functions derived from these sources are believed to be quite accurate. In the transition area from subsonic to supersonic Mach Number, the drag coefficient increases by a factor of two. Unfortunately, data for this area are more scanty. The measurements made by A. May8 at low supersonic Mach Numbers were used here. Fortunately, the transonic Mach Numbers occur in a relatively narrow range of altitude near 70 km. The Mach Number and Reynolds Number are defined by the equations V M = c (A-l) c Re = p (A-2) In the case of falling spheres, the unknown quantities are speed of sound c, density p, and viscosity i, since the velocity V is derived from radar data and the sphere diameter d is known. Density and viscosity can be found for Eq. (A-2) by an iterative procedure. An alternative scheme is to introduce the new dimensionless parameter CDRe defined by 11

(CDp)Vd CDRe = (A-3) The product CDp can be derived directly from the radar data and a fair approximation to the viscosity can be derived from a standard atmosphere table. If more precise values of c and 4 are needed, iterations are required. The parameter CDRe was used in the present data processing. All CD data were crossplotted in order to introduce CDRe in place of Reo Table VII defines the CD function. Linear interpolation was used to derive drag coefficient at any Mach Number and Reynolds Number. 12

APPENDIX B CHOICE OF SMOOTHING PARAMETERS A number of general considerations govern the proper choice of the two smoothing parameters Azv and Aze, which must be specified when the energy method is used in calculating air density. In the low range of altitudes, the choice was not difficult since 1-km values of AZv and AZe were sufficiently large so that the scatter was not severe. On the other hand, the 1-km value is sufficiently small to reveal fine structure of the atmosphere. At high altitude, the smoothing must be increased in order to suppress scatter in the processed data. Some criterion of a reasonable upper limit is needed. Atmospheric density profiles are, of source, approximately exponential. In this case the density is given by the formula z0-z e - (B-l) Po H where H is the scale height. Typical values of scale height in the atmosphere, which depend on the temperature, are 5 to 8 km. It is of interest to compare the average density p over an altitude interval Az with the density po at the center of the interval. The ratio, derived from Eq. (B-i) is given by the following formula: p 2H (Az\ o = Az sinh (B-2) Figure 13 is a plot of Eq. (B-2), which shows that if Az = H, p exceeds po by about 4%0 When data are recovered from trajectory analysis, the product CDp rather than p is measured. Since the variability of p is much greater than the variability of CD, the product CDP is also approximately exponential so that Fig. 13 is applicable. An exception to this rule is near Mach Number 1 where CD changes quite rapidly. It was decided than at high altitude, smoothing parameters as large as one scale height could be used. The sphere velocity can be found by resolving three orthogonal components associated with the radar coordinates range, elevation angle, and azimuth angle. 153

dr Vr = dt VE = r dt (B-3) da V, = r cos dt Each of the angle derivatives were found by a least-squares fit of a seconddegree polynomial to the position data using all the data within the altitude interval. Az centered at the required altitude. For deriving range component of velocity, an altitude range of 1/2 Azv was used. The smaller altitude interval was selected because the FPS-16 range data are more precise than the angle data, particularly at long range. Accuracy specifications often quoted for this radar are 5 yards in range and 1/10-mil in angle. These specifications imply that the range component of position error is independent of range, that the angle component of position error is proportional to range, and that the two are equal at a range of 50,000 yds. The range of the sphere at the altitude where greatest smoothing is required is more than 100,000 yds. On this basis, the smaller value of 1/2 Azv was selected for the range component. In order to study the effect of the AZv parameter on the derived velocities, data from Flight 10.50 were examined in detail at two specific altitudes: 80 km, where the drag is largest, and 105 km where the drag is small. The frequency of the data was 10 data points per second in both cases. Figure 14 shows that the velocity changes little for a wide range Azv. A practical minimum value for Azv at 80 or 105 km would appear to be somewhat greater than 1 km. The sphere falls quite rapidly at these altitudes so that only 8 or 10 data points are provided by the radar in 1-km altitude interval. Figures 15 and 16 are similar plots in which the range and elevation angle components of velocity are shown. The azimuthal component of velocity is very small at 80 and 105 kmi Figures 17 and 18 show how the computed values of CDp vary with the parameters Azv and Aze at altitudes of 80 and 105 km. The final choice of Azv and Aze as a function of altitude was made after examining several density profiles computed using different values for these parameters o 14

APPENDIX C EFFECTS OF WINDS Analysis of the motion of a sphere falling through still air of constant density and velocity z into a layer of uniform horizontal wind w, although a simplification, will yield a number of points of interest. Above the shear layer the drag is D = 2 ACDpz2 (C-l) Below the shear layer, the drag is larger and is inclined from the vertical an angle 6: D = - ACDP [z + (w-x) ] (C-2) where x = 0 when t = 0. The vertical component of drag is D cos 6 = ACDP z |z +(w-x) (C-4) The effect of a horizontal component of rela-Uive wind is therefore to increase the vertical component of drag. If the wind is small compared with the rate of descent of the sphere, the change of drag will be small since the function is a square root of the sum of squares. For example, a horizontal wind component of 14% of z is required to increase the vertical component of drag by 1%. In addition, the perturbation on the vertical drag is a transient condition that tends toward zero as the sphere responds to the horizontal wind. Horizontal components of drag force and acceleration are equated in order to derive the transient equation nx = - ACDp /z + (w-x) ( w-x (C-5) ACDP z(w-x) 15

The time constant of this first-order equation in x is seen to be 2m tc = ACDp (c-6) Below about 70-km altitude, where wind effects are most important, the equation for time constant can be simplified by the approximate equation mg = 2 CDpz2 (C-7) Equation (C-6) becomes tc = g (C-8) The change of altitude associated with the time constant is'2 AZc = ztc = g (C-9) Below 70-km altitude and above the altitude of sphere deflation, z varies from about 250 m/sec to 20 m/sec; therefore the time required for relative horizontal wind to decay by a factor l/e varies from about 25 sec to about 2 sec. The altitude parameter Azc varies from 6 km to 40 m. It is believed that only an extraordinary field of horizontal wind would lead to significant errors in the computed density. The effect of vertical wind on the determination of air density can be seen by considering the drag equation for a vertically falling sphere: D = ACDpz (C-10) 2 By differentiation, dD dD dp dz D = C + - + 2 (C-ll) D CDQ p z For small errors, then, the percent error in density is the same as the percent error in drag coefficient, and is double the percent error in vertical velocity. If the error in vertical velocity is due to an unknown vertical 16

wind component wz, then dz = wz. At high altitude where the sphere falls at a rate of 1000 m/sec, the density error due to a 1-m/sec vertical wind is 0.2%. At 70 km and 30 km, the errors are O.8% and 10% for typical sphere velocities. If large vertical wind velocities are present and persist over a broad range of altitude, the possibility of a significant distortion of the derived density profile is present. At higher altitude, where larger vertical winds might be expected, the large sphere velocity tends to decrease errors due to wind. 17

REFERENCES lo Schulte, Ho F., D. A. Robinson, and J. L. Wagener, Falling-sphere experiment for upper-air-densityO instrumentation developments. The University of Michigan, Final Report ARCRL-62-662, 03558-6-F, 1962. 2, Nordberg, W., and Wo G. Stroud, Results of IGY rocket-grenade experiments to measure temperature and winds above the island of Guam, J. Geophys. Research, 669 455-464, 1961. 3. Jones, L. Mo, J. W. Peterson, E. J. Schaefer, and H. F. Schulte, Upperair densities and temperatures from eight IGY rocket flights by the falling-sphere method, IGY Rocket Report Series No. 5, 1959. 4. Jones, Lo M., and Jo W. Peterson, 1961 Review, Upper air densities and temperatures measured by the falling-sphere method, The University of Michigan, ARCRL-803, 03558-5-T, 1961. 5. Ashkenas, H. I., Sphere drag at low Reynolds Numbers and supersonic speeds, Jet Propulsion Laboratory Research Summary, No. 36-12, Vol. I, 1.962 60 Wegener, P. P., and Ho Ashkenas, Wind tunnel measurements of sphere drag at supersonic speeds and low Reynolds Numbers, J. Fluid Mech. 10, 550-560, 1961o 7. Engler, N. A., Development of methods to determine winds, density, pressure, and temperature from the ROBIN falling balloon, Air Force Cambridge Research Laboratories, 1962o 80 May, A,, Supersonic drag of spheres at low Reynolds Numbers in free flight, NAVORD, Report 4392,.1956. 18

rd () -P l-I H.U CH X U) U C O O O U) ci) 4 4) c) H CH O C C PC t 03 a ~ 0, a) 0 0 Q S. c Q- " f 0 N "d,x:i CO p3 co CO CO () O c (. ) () a),C- r,- rd rd d PI CI) Z I (_! bDa*,, be 4:C- O U) O,.-1 0 r-~ 0 ~ 0 i P- ( r-l r-l p, -ph -p C\J c CO t-O bO' 0 (U, 1 01 Q, m I c o P-I.k CO rl C " a)'" o - I co C),S 1H r1-1 ft 03 r-9 CO * \ 1 o U) f I I 00 o H ci)U \ I I H H Hcci \1 T -zi- iLn ^ I t^ H 1 oH "0 I r ON 0,O r -0 r O C0 19

TABLE II VELOCITY RATIO VS. ALTITUDE o0.50o 10.43 Z vz v. 80 2296 2241.976 1933 1873.969 79 2104 2057.978 1822 1774.973 78 1869 1832.980 1736 1694.976 77 1662 1638.986 1600 1561.976 76 1453 1439.990 1456 1430.982 75 1235 1226.993 1321 1307.990 74 1061 1058.997 1161 1152.992 73 912 912 1.000 1017 1017 1.000 72 810 810 1.000 913 913 1.000 71 767 765.998 826 824.997 70 731 727.996 799 793.993 69 685 678.990 751 742.988 68 673 661.983 743 731.984 67 631 623.988 705 692.982 66 595 585.983 687 671.976 65 577 565.979 644 629.978 v - total velocity, fps z - vertical component, fps 20

TABLE III PROCESSED DATA, FLIGHT 10.50, 1-m SPHERE NO ITERATION PERFORMED ABOVE 90 KM. UNSMOOTHE[ TEMPS USED BELOW 40 KM. ALTI1 T ENSITY PRESSURE TEMPERATURE VELOCTY MACH CORE CO OEG.KELVIN KM. OM/CU.M/ MILlBARS RAW SMOOTH;/SEC NO. [Lu 10.0000G4.000000 0 0 2979 2.81 8 3.494 109.00003.000004 36 0 3000 2.85 7 3.623 108.00C0).00000) 34 39 3036 2.92 16 2.857 107.JOId8.000021 41 65 3058 2.97 26 2.432 106.00016.000037 81 84 3090 3.03 24 2.478 105.00014.000052 130 115 3128 3.10 22 2.550 104.00C1.000066 134 13o 3156 3.16 2f 2.409 103.00015.000082 191 155 3176 3.21 24 2.476 102.00622.00009 ) 155 157 3202 3.28 34 2.241 101.00026.000123 163 155 3215 3.33 39 2.148 100.00031.000151 141 140 3239 3.39 53 1.919 99.00C55.000197 126 136 3267 3.45 72 1.817 98.0007.000257 116 131 3278 3.48 96 1.689 97.00088.000331 131 131 3292 3.52 108 1.640 96.00106.000422 139 136 3302 3.56 127 1.578 95.00132.000541 143 146 3298 3.59 154 1.507 94.001O 5.000674 152 153 3303 3.62 177 1.460 93.00115.000823 165 156 3311 3.65 198 1.424 92.00213.001010 165 158 3294 3.67 235 1.380 91.00283.001258 155 162 3271 3.67 302 1.319 90.00360.001552 150 156 3243 3.95 421 1.262 89.00399.001932 169 151 3233 4.00 473 1.244 88.0056d.002382 141 151 3172 3.92 657 1.199 87.00756.0029'97 138 158 3131 3.79 788 1.176 86.00634.003779 158 162 3083 3.69 833 1.169 85.008760.004597 183 171 2984 3.47 806 1.173 84.01016.00485 188 180 2858 3.24 852 1.167 83.J119.006541 190 183 2742 3.08 941 1.156 82.01U517.007891 181 182 2616 2.95 1125 1.138 81.01897.009413 173 178 2483 2.83 1339 1.121 80.02263.011513 177 176 2295 2.63 1479 1.111 79.02843.013905 170 177 2096 2.39 1664 1.096 78.03282.016840 179 179 1895 2.16 1704 1.082 77.03772.020239 187 181 1671 1.89 1674 1.059 76.04688.024134 179 185 1467 1.64 1723 1.023 75.05400.02-9036 187 192 1272 1.40 1613.988 74.06187.034603 195 193 1084 1.19 1508.950 73.06/39.040696 210 198 946 1.02 1353.917 72.08676.04d04 193 200 842.91 1117.666 71.09700.056767 204 198 769.83 1021.591 70.11962.061330 19o 201 724.78 1076.544 69.15020.080136 186 203 688.73 1186.508 68.14465.094113 227 210 648.68 10C3.486 67.18748.110152 205 219 616.63 1148.468 66.18895.128328 231 238 583.51 1004.459 65.21128.14/216 243 243 558.54 1045.455 64.20931.167436 279 259 540.51 942.450 63.26163.190035 253 263 518.49 1095.442 62.26281.215366 285 273 492.45 1008.440 61.32991.243569 257 274 464.43 1176.433 60.32773.275381 293 279 439.40 1085.431 59.38446.309463 280 276 421.39 1221.428 58.43728.348908 278 278 393.36 1286.427 57.50714.394371 271 275 368.34 1405.427 56.57969.446097 268 276 339.31 1475.426 55.63540.506330 278 218 319.29 1510.426 54.69221.568180 286 281 304.28 1558.426 53.77247.638165 288 284 288.26 1639.427 52.87628.71d649 286 282 271.25 1757.427 51 1.00714.810048 280 281 252.23 1886.428 5b 1.17198.913910 272 280 233.21 2040.429 49 1.29430 1.034633 279 278 218.20 2130.430 4d 1.44004 1.164/06 282 271 208.19 2271.432 47 1.64620 1.310366 271 277 194.18 2433.434 46 1.35990 1.48286 278 276 181.11! 2590.436 45 2.157o0 1.67631 271 274 168.15 2816.438 44 2.43163 1.891367 272 212 157.14 29P7.440 43 2.73504 2.150584 274 270 148.14 3213.443 42 3.16779 2.429521 267 268 137.13 3474.446 41 3.61219 2.1/5/994 266 263 127.12 37(7.449 40 4.18540 3.145530 262 254 118.11 4189.453 39 5.03837 3.584469 248 237 106.10 4701.458 38 6.29106 4.135129 229 213 94.09 5646.465 37 9.30749 4.872131 182 190 76.09 8444.419 36 14.62074 6.006366 143 115 59.57 12978.489 35 17.72509 7.578454 149 167 53.07 13601.489 34 19.06564 9.386127 112 0 51.06 12334.488 33 20.64552 11.297326 191 0 48.05 11631.487 21

TABLE IV PROCESSED DATA, FLIGHT 10.43, 1-m b-rlIRE NO ITERATION PERFORMED ABOVE 90 KM. UNSMOOTHED TEMPS USED HELOW 40 KM. ALTIr DENSI Y PRESSURE TEMPERATURE VELOCTY MACH CDRE CD DEG.KELVIN KM. GM/CU.M MILIBARS RAW SMOOTH M/SEC NO. 110.00009.000000 0 0 1640 1.54 9 3.386 109.00011.000009 29 0 1699 1.61 11 3.165 108.00010.000019 67 67 1757 1.69 11 3.198 107.00007.000028 130 92 1817 1.76 9 3.390 106.00012.000037 107 110 1868 1.83 13 3.007 105.00013.000049 129 111 1914 1.90 15 2.915 104.00019.000064 117 112 1961 1.96 20 2.625 103.00044.000092 72 119 1998 2.02 39 2.143 102.00034.000129 133 123 2052 2.10 33 2.259 101.UU004.000163 143 134 2102 2.18 39 2.151 100.00047.000205 150 158 2141 2.24 46 2.054 99.00052.000253 170 174 2180 2.30 50 2.002 98.00055.000304 192 178 2216 2.36 54 1.965 97.00057.00u355 216 177 2238 2.40 57 1.940 96.00092.000428 161 174 2278 2.46 85 1.743 95.00125.000530 147 168 2310 2.51 110 1.632 94.00150.00066L 154 155 2333 2.56 130 1.569 93.00177.000820 161 153 2357 2.60 152 1.511 92.00234.001005 150 154 2371 2.64 193 1.432 91.00287.001264 154 158 2376 2.67 233 1.383 90.u0362.001560 150 155 2382 2.91 324 1.307 89.00387.001915 172 154 2400 2.94 347 1.294 88.00551.002381 149 156 2385 2.91 473 1.244 87.00708.002966 146 158 2369 2.87 577 1.216 86.00793.003667 161 157 2343 2.84 636 1.203 85.00989.004527 160 163 2305 2.74 740 1.183 84.01141.005556 170 169 2241 2.62 799 1.174 83.01304.00o691 179 174 2183 2.52 859 1.166 82.01617.008111 175 182 2107 2.37 973 1.147 81.01805.009722 188 192 2027 2.23 992 1.139 80.0208.011526 200 197 1937 2.10 1023 1.130 79.02184.013579 217 199 1837 1.98 1033 1.117 78.02687.015823 205 200 1714 1.84 1152 1.091 77.03528.018792 186 197 1603 1.74 1389 1.058 76.04643.022420 193 190 1466 1.62 1472 1.035 75.05031.026805 185 188 1311 1.46 1604 1.001 14.06207.032174 181 194 1177 1.28 1654.963 73.06751.038271 198 197 1045 1.13 1531.934 72.07329.045227 215 198 927 1.00 1423.906 71.08898.052762 207 199 854.92 1233.705 70.11319.062436 192 211 785.82 1139.585 69.14050.074663 185 212 742.77 1234.542 68.11198.086832 256 219 717.74 923.513 67.15722.099973 222 225 700.71 1139.498 66.16912.115864 239 238 668.66 1071.478 65.210U4.133689 222 237 634.63 1233.465 64.21286.154081 252 245 600.58 1138.459 63.24529.17o252 250 250 573.55 1215.454 62.26938.200844 260 261 543.51 1204.446 61.29790.221981 261 263 517.48 1238.440 60.32570.258158 276 270 492.46 1253.436 59.38506.292062 264 273 464.43 1371.432 58.40321.329832 285 275 438.40 1338.429 57.47436.372356 273 275 414.38 1480.426 56.52654.419587 278 278 388.35 1526.426 55.60321.475216 274 277 363.33 1637.427 54.66610.534911 280 279 341.31 1691.427 53.74447.602953 282 281 322.29 1777.427 52.83501.678021 283 281 303.28 1882.428 51.93288.765822 286 281 285.26 1978.428 50 1.10788.865000 272 280 263.24 2186.431 49 1.20715.973509 281 280 246.22 2234.431 48 1.38367 1.097613 276 278 233.21 2448.434 47 1.52543 1.240621 283 280 218.20 2514.435 46 1.74985 1.398556 278 280 205.19 2727.437 45 1.93894 1.576430 283 279 192.17 2852.439 44 2.22806 1.778487 278 275 180.16 3125.442'3 2.58611 2.010547 271 273 165.15 3376.445'2 3.00675 2.278055 264 270 153.14 3685.448 41 3.35564 2.587341 269 267 143.13 3916.450 40 3.79961 2.935885 269 265 135.13 4223.453 39 4.43974 3.329899 261 264 124.12 4621.457 38 5.08949 3.795622 260 261 115.11 4965.460 3- 5.78227 4.318292 260 256 107.10 5286.462 36 6.77239 4.930118 254 252 98.09 5859.467 35 8.01532 5.641495 245 245 90.09 6562.471 34 9.45873 6.484120 239 239 82.08 7282.475 33 11.51830 7.502120 227 234 73.07 8349.479 32 13.04915 8.686329 232 223 69.07 8715.480 31 15.52169 10.067806 226 0 63.06 9705.483 30 21.80934 11.860705 189 0 52.06 13197.489 22

TABLE V PROCESSED DATA, FLIGHT 10.50, 7-IN. SPHERE, UPLEG TRAJECTORY Processed Data Seven Inch Sphere Flight 10. 50 Up Leg Trajectory TIME DRAG VELOCITY VELOCITY ALTITUDE ALTITUDE DRAG DENSITY DENSITY PRESSURE PRESSURE TEMPERATURE SECONDS ACCEL VERTICAL HORIZONT. FEET METERS COEFF. SL/CU FT KG/CU M. LB/SQ FT DYNES/CM2 F C 189.76.000 950. 494342. 150676. 78.13.088 3428. 980. 303550. 92522. 1.499.00001067.00000550 77.35.100 3453. 981. 3oo866. 91704. -.465.00001225.00000631.00744 3.564 -106. -77. 76.62.100 3475. 981. 29833557. 90933. 1.466.00001209.00000623.00840 4.021 -56. -49. 75.97.117 3496. 982. 296071. 90243. 1.434.00001431.00000737.00933 4.468 -80. -63. 75.30.134 3517. 982. 293723. 89527. 1.412.00001644.00000848.01046 5.009 -89. -68. 74.52.123 3541. 982. 290970. 88688. 1.428.00001474.00000760.O1181 5.652 7. -14. 73.74.190 3565. 983. 288198. 87843. 1.355.00002370.00001222.01345 6.437 -150. -90. 71.74.187 3628. 984. 281005. 85650. 1.560.00002249.00001159.01865 8.928 23. -5. 71.31.220 35642. 985. 279442. 85174. 1.333.00002682.00001382.01985 9.505 -29. -34. 68.12.323 3742. 986. 267666. 81585. 1.271.00003923.00002022.03191 15.279 14. -10. 67.80.365 3752. 987. 266467. 81219. 1.251.00004483.00002310.03349 16.036 -25. -32. 67.41.365 3764. 987. 265001. 80772. 1.251.00004454.00002295.03555 17.021 5. -15. 67.05.439 3776. 987. 263644. 80359. 1.219.00005465.00002817.03766 18.030 -59. -51. 66.69.505 3787. 988. 262282. 79944. 1.196.00006375.00003286.04019 19.240 -93. -70. 66.32.400 3799. 988. 260879. 79516. 1.237.00004854.00002502.04265 20.419 52. 11. 65.97.526 3810. 988. 259548. 79110. 1.190.00006599.00003401.04503 21.558 -63. -53. 65.34.566 5830. 989. 257141'. 78377. 1.178.00007103.00003661.05021 24.038 -48. -45. 64.94.554 3842. 989. 255607. 77909. 1.182.00006884.00003548.05358 25.653 -7. -22. 64.58.677 3854. 989. 254221. 77487. 1.147.00008617.00004441.05694 27.264 -75. -60. 64.25.653 3864. 990. 252948. 77099. 1.154.00008219.000042356.060351 28.878 -33. -36. 63.88.719 3876. 990. 251516. 76662. 1.138.00009127.00004704.06422 30.746 -50. -46. 65.53.706 5887. 990. 250157. 76248. 1.141.00008886.00004580.06807 32.589 -14. -26. 65.o07.710 3902. 990. 248366. 75702. 1.142.00008867.00004570.07307 34.984 20. -7. 62.47.882 3921. 991. 246019. 74987. 1.107.00011262.00005804.08047 38.527 -44. -42. 62.06.992 3934. 991. 244409. 74496. 1.o94.00012756.00006564.08654 41.436 -64. -54. 61..76.990 3944. 992. 243227. 74136. 1.095.00012641.00006515.09126 43.695 -40. -40. 61.46 1.031 3954. 992. 242042. 73774. 1.092.00013139.00006772.09607 45.997 -34. -37. 60.25 1.245 3993. 993. 237234. 72309. 1.077.00015782.00008134.11791 56.452 -25. -32. 59.55 1.301 4o06. 994. 234431. 71455. 1.075.00016351.00008427.15209 653.245 11. -12. 58.90 1.502 4037. 994. 253184. 70657.. 1.063.00018893.00009737.14660 70.192 -8. -22. 58.55 1.586 4048. 995. 230399. 70226. 1.059.00019921.00010267.15526 74.5336 -6. -21. 58.32 1.690 4056. 995. 229467. 69942. 1.054.00021259.00010957.161531 77.233 -18. -28. 57.90 1.710 4070. 995. 227761. 69422. 1.054.00021373.0001ooi016.17278 82.728 11. -12. 57.51 1.935 4083. 996. 226171. 68937. 1.043.00024281.00012514.18421 88.199 -18. -28. 57.16 1.945 4094. 996. 224740. 68501. 1.044.00024268.00012508.19509 93.409 9. -13. 56.78 1.967 4107. 997. 223182. 68026. 1.043.00024403.00012577.20705 99.137 35. 1. 56.48 2.278 4117. 997. 221948. 67650. 1.031.00028479.00014678.21733 104.055 -16. -27. 56.20 2.291 4126. 997. 220794. 67298. 1.031.00028514.00014696.22772 109.029 6. -15. 55.69 2.429 4143. 998. 218685. 66655. 1.027.00030117.00015522.24722 118.5368 19. -8. 54.67 2.829 4178. 999. 214442. 65362. 1.015.00034923.00017999.29070 139.186 25. -4. 54.31 3.072 4190. 1000. 212935. 64903. 1.008.00037962.00019565.30802 147.480 13. -11. 53.97 3.184 4202. 1000. 211508. 64468. 1.006.00039235.00020222.32542 155.808 24. -5. 52.14 4.238 4266. 1003. 203760. 62106..983.00051882.00026740.43619 208.848 30. -2. 51.87 4.574 4276. 1003. 202607. 61755..977.00056118.00028923.45587 218.268 14. -11. 50.90 5.355 4511. 1005. 198443. 6o485..965.00065239.00033624.53559 256.440 19. -8. 50.54 5.589 424. 1006. 196888. 60012..962.00068190.00035145.56838 272.138 26. -4. 50.00 5.752 4344. 1007. 194548. 59298..960.00069666.00035906.61940 296.558 58. 15. 49.75 6.213 4355. 1008. 193461. 58967..953.00075456.00038890.64434 308.511 38. 3. 49.42 6.793 4366. 1008. 192022. 58528..946.00082698.00042623.68031 325.730 20. -7. 49.02 7.202 4581. 1009. 190273. 57995..942.00087506.00045100.72740 348.280 25. -5. 48.68 8.759 4394. i010. 188781. 57541..924.00107788.00055554.77334 370.272 -42. -41. 47.99 8.602 4422. 1012. 185739. 56613..927.00104223.00053716.87539 419.135 30. -2. 23

TABLE VI PROCESSED DATA, FLIGHT 10.50, 7-IN. SPHERE, DOWNLEG TRAJECTORY Processed Data Seven Inch Sphere Flight 10. 50 Down Leg Trajectory TIME DRAG VELOCITY VELOCITY ALTITUDE ALTITUDE DRAG DENSITY DENSITY PRESSURE PRESSURE TEMPERATURE SECONDS ACCEL, VERTICAL HORIZONTAL FEET METERS COEFF. SL/CU FT KG/CU M. LB/SQ FT DYNES/SQ CM F C FT/SEC FT/SEC FT/SEC X1000 189.76.000. 950. 494542. 150676. 502.66.128 -5468. 981. 299168. 91187. 1.418.00001607.00000828 505.38.101 -5491. 981. 296665. 90425. 1.464.00001215.00000625.01087 5.202 62. 17. 504.06.151 -5512. 982. 294285. 89697. 1.415.00001609.00000829.01191 5.702 -29..4. 505.47.142 -3555. 982. 289501. 88179. 1.404.00001719.00000886.01451 6.946 32. 506.81.194 -5597. 983. 284510. 86719. 1.552.00002586.00001250.01757 8.409 -31. -35. 507.92.243 -5651. 984. 280499. 85496. 1.515.00005019.00001556.02095 10.029 -56. -49. 509.54.290 -5675. 984. 275512. 83915. 1.287.ooo000600.oooo00001856.02632 12.602 -4. -37. 310.02.249 -5696. 985. 272806. 85151. 1.514.00002995.00001544.02891 13.841 103. 39. 311.13.357 -5750. 985. 268685. 81895. 1.265.00004144.00002136.03349 16.033 11. -12. 311.51.322 -3742. 986. 267265. 81465. 1.272.00005910.00002015.03528 16.892 66. 19. 311.94.302 -3755. 986. 265654. 80971. 1.285.0000609.00001860.03718 17.802 141. 60. 312.50.416 -3773. 986. 263546. 80329. 1.229.00005149.00002654.04005 19.176 -7. -22. 312.85.386 -5783. 986. 262224. 79926. 1.242.00004700.00002423.04210 20.154 62. 17. 313.23.384 -3795. 987. 260784. 79487. 1.244.00004644.00002393.04420 21.164 95. 35. 313.52.460 -304. 987. 259682. 79151. 1.205.00005962.00003073.04603 22.039 -10. -24. 313.91.502 -3816. 987. 258197. 78698. 1.198.00006237.00003214.0888 23.402 -4. -20. 314.25.514 -5387. 987. 256898. 78303. 1.194.00006373.00003285.o5146 24.67 11. -12. 314.70.476 -3840. 987. 255173. 77777. 1.208.00005794.00002986.05475 26.215 91. 33. 315.31.639 -3859. 988. 252824. 77061. 1.158.00008044.00004146.05982 28.640 -27. -33. 315.69.603 -3871. 988. 251356. 76613. 1.168.00007478.00003854.06340 30.355 34. 1. 316.03.603 -53881. 988. 250038. 76212. 1.169.00007438.00003834.06650 31.837 61. 16. 316.78.819 -3904. 988. 247119. 75322. 1.118.00010442.0000582.07463 35.731 44. -42. 317.10.876 -3914. 988. 245869. 74941. 1.108.00011221.00005783.07889 37.773 -51. -46. 317.44.805 -3924. 989. 244537. 74535. 1.124.00010111.00005211.08356 39.912 21. -7. 517.80.914 -3935. 989. 243122. 74104. 1.104.00011634.00005996.08820 42.228 -18. -28. 318.10 1.028 -3944. 989. 241940. 73743. 1.092.00013168.00006787.09280 44.434 -50. -6. 319.17.977 -3977. 989. 237703. 72452. 1.099.00012244.00006310.10975 52.548 63. 17. 319.58 1.029 -3989. 989. 236070. 71954. 1.095.00012863.00006630.11621 55.639 67. 19. 319.90 1.039 -3999. 990. 254792. 71565. 1.095.00012932.00006665.12140 58.125 87. 31. 320.24 1.300 -4009. 990. 23355451. 71150. 1.075.00016397.00008451.12766 61.123 -7. -22. 321.31 1.811 -4041. 990. 229125. 69857. 1.047.00023105.00011908.15421 73.834 -71. -58. 321.79 1.642 -4055. 990. 227182. 69245. 1.057.00020611.00010623.16758 80.238 14. -10. 322.13 1.856 -4065. 990. 225802. 68825. 1.047.00023420.00012071.17715 84.819 -19. -29. 322.56 2.010 -4072. 990. 224866. 68539. 1.040.00025449.00013116.18456 88.271 -38. -39. 322.71 2.125 -4082. 990. 22440. 68104. 1.056.00026890.00015859.19613 95.908 -35. -38. 323.47 2.322 -4104. 990. 220529. 67156. 1.029.00029267.00015084.22567 107.094 -15. -26. 323.71 2.359 -4111. 990. 219345. 66856. 1.028.00029664.00015289.25284 111.483 -3. -20. 324.14 2.625 -4124. 990. 217575. 66516. 1.019.00055107.00017063.25056 119.872 -20. -29. 324.84 2.676 -4144. 990. 214680. 65434. 1.019.000553450.00017240.28075 134.424 29. -2. 325.21 2.903 -4154. 991. 215145. 64967. 1.012.00056351.00018755.29766 142.519 17. -9. 325.56 3.114 -4164. 991. 211689. 64523. 1.007.00059057.00020120.31498 150.814 10. -12. 325.90 3.260 -4174. 991. 210272. 64091. 1.005.00040832.00021045.553286 159.571 15. -10. 326.23 3.522 -4185. 990. 208895. 63671..997.00044212.00022787.55136 168.232 3. -16. 326.50 3.602 -4191. 990. 207762. 65526..995.00045150.00025260.56752 175.870 15. -10. 326.99 3.904 -4204. 990. 205706. 62699..989.00048950.00025218.59786 190.494 14. -10. 327.32 4.196 -4215. 990. 204517. 62276..985.00052694.00027159.42015 201.165 5. -16. 327.65 4.294 -4222. 990. 202925. 61852..982.00055788.00027722.44557 212.381 21. -7. 327.99 4.570 -4232. 990. 201488. 61414..977.00057505.00029534.46879 224.456 17. -9. 328.34 4.864 -4241. 990. 200006. 60962..971.00061051.00051466.49652 237.732 14. -10. 328.73 5.057 -4251. 990. 198550. 60457..969.0006563.0005o32657.52908 253.324 27..3. 329.35 5.641 -4268. 989. 195709. 59652..960.00070821.000o6501.58505 280.122 22..6. 329.83 6.014 -4280. 989. 195658. 59027..955.00075482.00058904.63250 302.839 29..2. 3550.18 6.508 -4289. 989. 192159. 58570..948.00081931.00042227.66982 320.711 17. -9. 550.57 6.939 -4298. 989. 190485. 58060..945.00087465.00045078.71467 342.183 16. -9. 350.93 7.110 -43507. 988. 188955. 57588..942.00089418.00046086.758053 62.946 34. 1. 331.22 7.513 -4314. 988. 187686. 57207..957.00094655.00048784_.79443 380.371 29. -2. 331.44 8.192 -4520. 988. 186756. 56917..929.00105812.00055505.82424 394.643 3. -17. 332.22 8.955 -45538. 987. 185560. 55888..925.0011424.00058459.94026 450.193 23. -5. 332.56 9.501 -4545. 986. 181884. 55458..918.00120577.00062145.99494 476.377 21. -7. 332.94 10.521 -4554. 986. 180252. 54955..911.00151516.00067783.o6o86 507.937 10. -13. 335.29 11.015 -4561. 985. 178706. 54470..906.0014o662.00072497 1.12659 539.409 7. -14. 333.69 11.641 -4569. 984. 176961. 53938..906.00148138.00076350 1.20642 577.635 15. 10. 334.00 11.979 -4375. 984. 175606. 53525..906.00152038.00078361 1.27089 608.499 27. -3. 355.09 13.797 -4596. 961. 170826. 52068..906.00173595.00089471 1.51716 726.414 50. 10. 335.54 14.655.4404. 980. 168846. 51464..906.00183775.00094718 1.62930 780.109 57. 14. 557.12 22.356 -4425. 975. 161872. 49339..906.00277938.00145249 2.13271 1021.141 -13. -25. 557.54 21.524 -4429. 974. 160013. 48772..906.00267142.00137685 2.29350 1098.126 41. 5. 5537.87 23.967 -4432. 972. 158551. 48326..906.00297108.00153130 2.42427 1160.739 16. -10. 339.62 28.542 -4443. 965. 150787. 45960..906.00352557.00181708 3.22298 1543.162 73. 23. 24

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160.... 140 - 120 - 100 /! -.I8O 0I w w 60 O 0 20 40 60 80.50 20 O 0 20 40 60 80 100 DOWN RANGE DISTANCE- KILOMETERS Fig. 4. Altitude vs. distance down range. 27

V) 0 0 iri Ou L ~ 0 0? ) tO c) LLW LH C WJ Q<N 10 W Q0 - 0 o^ ro 0 -— _ W 0 4Ie I^ z \ 11 ~o~- In LL h) \ a o OW II <0 W — 9)8 (0 0 \ <00 U) ________Z 0 -o i ro 0 0 0 0O W F-\ N ^ 0 r 0 HION S331/10" 1 28 -JFL~~~~~~j ~ ~ wLJ O~~~~~ 0 ~ 0 ~ 0 H.L~~~iCN~ S~~VIOI> O i~ c I28b

0 0J 0 0 0 0 0 0 0 L_ co 0 - 0 0 IV ~~~Q 8~~ rd _I-_ - r~~) 0 w I0 UJ - -- - -- - -- - - -- - -- -0- - - 0 H LL 1io LC): O / / *o-l ~~~~__ _ _ _ _ _ _ _Z Z _ _ _ _ _' W" 0 0 0

o 0 o O3 ~L0) r O O |Y o\, —- -4 - -------- -^ - - 4sI =_ __ - I _ __ t _w H ~Wo v o 3oO~~~~~~~~L o I I < a A^(-i ( L~~O 0 0 ~0 liJ < P-\ 0 | 0- i 0 Io w a — J o 6 a0 a.0 00 ) W _N N ro to (\j CM - - 03S/iJ A113013A 50

I0-7 10-6 10-5_ 1 0 - 4 _I0 $I0- 2 i-4 1.0I %0 -___, UNIVERSITY OF MICHIGAN FLIGnTS 0' tl0>s0 ore Y,' (qJcAT WALLOPS ISLAND, LAT 357.9,'N 0" o^^ X.v~ 10.50: 6 JUNE 1951., 1648R 10 0 100 ^ ---- --- -~ —9^- --- -------- 10.43: 6 JUNE 1962, 19JOR I00 ^,,Ck,, -)_> ~FLIGHT 10.43 0 I METER SPHERE ^^.I METER SPHERE ~ 7 INCH SPHERE UPLEG ~90 -_-__! | ___ _ _ _ __ __ _ _ _ __C __ _ _ _ I___ * 7 INCH SPHERE DOWNLEG 90 - - - >*^^c<' 0 ^^ C ^Q () + RADIOSONDE;~*^ ^^^ ^^SQ -— US STANDARD ATMOSPHERE,1962 (EACH CURVE SEPARATED BY 8 0 T0D^ "^o ^Q<^^ ALTITUDE,km AZv,AZe.,km oc I 90-,5 6 " 70 FLIGHT 10.50, FLIGHT 10.5.____8 0 I 1 1 ITllI 1 I 1 Tl 1 80- 89 4 iI 7 INCH SPHERE I METER SPHERE 70-79 2 60 50 ^^_ Qsl^ 0-6 40 3 0 20 10 I 06 10-5103 io-4 0r Iu- 10",O!O: UPPER AIR DENSITY KG/M3 Fig. 8. Density profiles, Flights 10-50 and 10.43.,d ^(j^ ^^. ~ 4 0.._ _.. __ _.. __..._._ ^< __.... QQ"'.. " — ^^~~~i~ ~C~.,, I0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~'h - I0-6 I 0-s 10-4 I 0-3 10-~2 I 0-~ 1.0 1.0 1.0 UPPER AIR DENSITY KG/M$ Fig. 8. Density profiles, Flights 10.50 and. 10.45

LO LO 0) Uf) co 0o 0 0 r N H rf) Z N- IC) Z o ) 0 (~Z 0 0~~~~~~~ w C;S^ 00 C) SU / *n ~?~10 z (L L co rd IC) I 0 0z IC) N (0~~~~C LO If)LO ) C LL UN )a 0 0 0 0 0 LO 0 LN ___ I a) 0I r 00 ^* I a5 ________t0____________/ 1s- ____ ______'O______________, 0 r -Z) II I 55

ruj u ^ 00 __ LL ~~~a. Z< O C) CD ( ) OD 0) 0) W cbr + _j- O < ^ t~ I ~f U) z z a Q: ) < t I -j D Wa ~O Wi 9^ CD W- M < 7 Wx O Pr ( >g o^100Lc) I F-|- _- -y 1111 ^ --— _^ ~; C CQ r 0 o 0 Y / \?/0 o, o eu -^-^R{ z E Y > 71 0I0C\\ WCM Pi O ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~+ ILr 00 0 +\ a Pi 0 P~~~ = OOF ) Wr CU Q 0 +) fIZ~~~~~~~~~~~~~~~~~ CL.a Ih~~~~~~~~~~~~~~~~~tQ C\j CM Id -0 <^ Q7^ 0 \~ 0 u *^ ~ ~~~~~~ a __~-._N ^zzz-^zzzzm~zzz \ ^ooo "~~~~~~~~I co~~ o -- -- T3 -- - -- - -- - -- - ---- -- -- - -- - ---- u _^C _ _ _ _ _ _ _ _ -L -i_ _ -J -~~~~~~~~~~~~~~c 8 08~^~^^^~ 0 0 ~D ~ u ~ Sd3J,31^011M 3Gnill~I 0~~~~~~~~~~~~~~~~~~~~~~o

0 O w J I I I o t LOIX~~ O I 0 _ I -= —— a - I i _ ---------------.2 - s i | ------- Z g ---------- Z —--— 0 -, ~ M 5 I l |. l C —!! I- -- 0 co J 0 --— LL I "- ------ - - --- CD c s LO 0 <3 ~,,~,~ / <] ^.SC!^^(. 0 c n. CH:_ —: 5 < -<l0)^ _ ^ 5 o io < < <3> < " zO~~~ U wO~ P~~0 o o st o 37 —- J wI~~0 0 c %- -------- o <> -- -~ = -^ 0 - )LO Q() \ " =d Z tJf -a- - ~ -- IU 2 Q; --- 0 0 < 0

0 0 II- CQ 0 (0 I _ _ O o o i ) 9 9 < Q ____ __ 9____ 0 __ ______ ___ ___ ___ ___ 0c t'~ ty t. Ll CM D 0 O - z Fo rF -pZ - F * 0 )' C,,>- - w -! O.0 0. C.H?~.. LL'.- e\ii ^^-^NN' o o a... 0 0 0 0 by^ C) rd o F' /b N 0 R (0 C N 0 o (0 Q N 0 c (0 p N 0 --- -- - N - - - --- - - 0 0 0 0 3'ilN3iidW300 -)OVN 58

N \ _- __ _ _____ 0UJ N Ol^ a) N - z ~ Z < O LU IX I- < > W <~ O' z 0- H> zd Q ml 0 0 0 0 0 0 0(LiIL6 r( C 59

~/" ~ ~ ~~ I I,! I I -1 - I: L::: ___ |___ 0 8 ~ol~ ~ ~ ~N o0 c 0 o ~ o - O - N LL La. -- ^ ^ r<) N N C~ l CtII -- |J ~I Cl. rjI rJ N P) 2 CD (D - O(M - o ro ro roP Cj C\J J OJ C\ oJ COJ C\J CM Cj ~oes/l4 - 1k11013A 40

__- -I _ _ _ I _ _ i tt -- - — J _- O - -- - - - o - - - ~ CD 07 1 n - 1 04-1 0 O coW hc! - LO r -, 0Lu L5 <__:__ U 0 0 B-. ILl 0 0 0 0 Q0 0 0 0 _r~~~~~~~~~> A r-] fr) N N N O oCoo - <0 o oes/44 A1iO13013A

z Wj ID lr\ Lw 0 I __. 1 /''_u. _ _ _ _,_ C'0 a)C t- LLJ - zz d < ow -- co -z Lo PA 0 I 0 WO LL N ) _ H w a j o~~~~~~~~~~~~~~~w -) i\\~~~~~ I \\ I.u ~~~~~~~~LL.r-,0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 LO, ri N - 0e ) Q tN (0D LO N N N N CI N - - - OeS/4; AJ.1 30I3A 42

- (0 _ — e'____ ^- - b o ~o7rc C\J co 0LL / / S II~~~~ L. o 0 22! o o ^"N\VN/i O- bI __ I) ~ - ------— f^-~ - - - ------------' ~ rr) CD o LO n -- 0 —-- C- -J- Cj C- C — CJ ~w1/9)190 1 X d 43

1.3 —FLIGHT 10.50 1.1 _____ Z = 105 KM AZe -/5KM 1.0 — -- -/ 4KM 3KM.9C 2KM.80 wo.70 ------.60.30 - AZV -FEET Fig. 18. Density function vs. smoothing parameter Azv, 105 km. 44

UNIVERSITY OF MICHIGAN 3 9015 03483 3536