ENGINEERING RESEARCH INSTITUTE UNIVERSITY OF MICHIGAN ANN ARBOR Publication Reprint ROCKET MEASUREMENTS OF UPPER ATMOSPHERE AMBIENT TEMPERATURE AND PRESSURE IN THE 30- to 75-KILOMETER REGION Report No. CS-2 H. S. SICINSKI N. W. SPENCER W. G-. DOW Project 2096 AIR FORCE CAMBRIDGE RESEARCH CENTER, U. S. AIR FORCE CONTRACT NO. AF 19(604) -545 December, 1954

Reprinted from JOURNAL OF APPLIED PHYSICS, Vol. 25, No. 2, 161-168, February, 1954 Copyright 1954 by the American Institute of Physics Printed in U. S. A. Rocket Measurements of Upper Atmosphere Ambient Temperature and Pressure in the 30- to 75-Kilometer Region* H. S. SICINSKI, N. W. SPENCER, AND W. G. Dowt University of Michigan, Engineering Research Institute, Ann Arbor, Michigan (Received May 19, 1953) A method for determining ambient temperature and ambient pressure in the upper atmosphere is described, using the properties of a supersonic flow field surrounding a right circular cone. The underlying fundamentals stem from basic aerodynamic principles as combined with the developments of the aerodynamics of supersonic cones by G. T. Taylor, J. W. Maccoll, and A. H. Stone. The experiment provides the necessary cone pressures, velocities and Eulerian angles, such that a Mach number characterizing the ambient space conditions may be computed. A description is given of the requisite experimental equipment and related techniques. Experimental data from two rocket-borne equipments are presented with the resulting calculated pressures and temperatures as experienced over New Mexico to approximately 70 kilometers. I. INTRODUCTION overcomes certain disadvantages of the earlier proceT HE University of Michigan Department of Elec- dure. Essentially point-by-point values are obtained in trical Engineering has been engaged for the past a manner that does not require an averaging process. several years in the measurement of the ambient tem- That is, each temperature point on the curve is deperature and pressure of the upper atmosphere. These termined directly from the experimental pressure data measurements have been carried out in high altitude independently of other points and gives the temperature rockets, in particular, the "V-2" and the "Aerobee." at a particular location in space, as contrasted with During the period in which V-2 rockets were em- values obtained from the barometric equation which ployed, temperature measurements were-implemented represent an average over a rather considerable altitude by application of the "barometric equation" to a mterval. measured curve of ambient pressure versus altitude. The experimental data required for a temperature Although curves of ambient temperature versus altitude computation by the new method include in general: a were obtained,' the computational procedure for ob- ratio of the nose-cone tip (impact) pressure to the taining the temperature is primarily one of differentia- pressure at some point on the cone wall, a determination, and hence yields only very approximate values of tion of the instantaneous angle between the rocket's temperature. longitudinal axis and a space-fixed reference system, In an effort to improve the quality of the measure- and the magnitude of the missile velocity vector in the ments, a more exact method has been developed which same reference system.2 ---— _______s,~~~ a e m h e ei The required pressure measurements are accom* The research reported in this paper has been sponsored by the plished in the missile through the use of "Alphatron" Geophysical Research Directorate of Air Force Cambridge Re-.... search Center, Air Research and Development Command, under ionzation gauges, which are utilized in equipment that Contract Nos. AF19(122)-55 and W33-038 ac 14050. t Department of Electrical Engineering, University of Michigan, 2Another temperature measurement method, similar in that Ann Arbor, Michigan. correspondingly fundamental pressure measurements are em1 Rpt. No. 2, Upper Air Research Program, Engineering Re- ployed, has been utilized bv the Naval Research Laboratory. See search Institute, University of Michigan, July 1948. Haven, Koll, and La Gow, J. Geophys. Research 57, 59-72 (1952).

162 SICINSKI, SPENCER, AND DOW P' l P P in the range of Mach numbers and yaw angles expt^T ^-perienced. N,\ M^^ -^1..,. The principal limitation to applying inviscid theory v, M' mi - 1occurs for large yaw angles (e-0.80,) where boundary T., P-', A layer separation occurs.6 B. Non-Yawing Cone The problem of supersonic flow around a cone has FIG. 1. Physical quantities appearing in non-yaw conical flow. been successfully analyzed by Taylor and Maccoll,6 Pressures measured by the experiments described appear inside of the subsequent embodiment of their results the outline of the cone. (For physical significance of symbols, see th list in paper.) in tabular form by Z. Kopal.7 These results are applicable to cone-pressure measurements in order to has been developed by this research group. The data compute ambient upper air conditions for given conical obtained is telemetered from the rocket to ground sta- geometry and the characteristic Mach numbers. Altions where it is recorded. though surface pressure measurements alone do not The fundamental information required for angle com- constitute sufficient information to deduce the characputation is similarly determined in the missile through teristic Mach number, knowledge of the total head the use of a single gyroscope. In this case, the data are pressure will, when taken concurrently with the surface recorded in the rocket on film, which is later recovered pressures, define the characteristic Mach number. A when the missile reaches the ground. schematic representation of the experiment and the Velocity information is obtained by triangulation physical quantities appearing is shown in Fig. 1. Quanemploying ground based instrumentation which tracks tities with subscript "one" are the upstream conditions the rocket during flight. or so-called "ambient values." The dotted area about Temperature measurements have been made on the cone vertex defines a subsonic flow region existing several rocket flights utilizing the new method. The because the cone is truncated to permit total head following sections of this paper present the data result- measurement. This deviation from purely conical ing from two such flights of Aerobee rockets, a discus- geometry affects the flow locally; however, a windsion of the theoretical basis for the measurements and a tunnel analysis demonstrates that the conical flow description of the particular equipment developed to regime is established ahead of the cone surface pressure obtain the basic data. measuring port. The computation of the ambient conditions proceeds IL THEORETICAL CONSIDERATIONS through a combination of the Taylor-Maccoll relations A. General and the Rayleigh total-head expression. P' and P, (cone-tip and cone-wall pressures) and cone velocity V Temperature is a typical "intensive" magnitude3 relative to the ambient air are measured experimentally. quantity, which, for its determination, must be corre- The theory presented leads to a relationship (Fig. 2) lated with phenomena measured "extensively." Although the usual laboratory thermometric systems can'[' i - _ measure temperature in extensive terms, these tech- MACH NUMBER VS RATO OF CONE PRESSURES niques cannot be directly extrapolated to supersonic i ___ missiles for upper atmosphere ambient temperature I.-1 — _4. J. __ measurements without producing questionable results. [ L___ — - --- i- -—.- 1..__ —. The chief difficulty arises with the formation of a -- boundary layer about the instrument, which perturbs- -- - the temperature experienced. A more promising datum- - is pressure, which, unlike the temperature, is very nearly constant throughout any boundary layer sec- _'._ I i I J-i l _. tion, being nearly equal to the value just outside the o! 1 1! i boundary layer. The pressure datum thus "neglects" P /Ks the boundary layer, approximating an inviscid flow. FIo. 2. Mach number versus quotient of cone pressures for non-yaw For the practical case of a cone with a semi-vertex case of a 7.5~ half angle, supersonic cone. angle of 7.5~, very good agreement exists4 between the angle of 7.50, very good agreement exists' between the'Franklin K. Moore, "Laminar boundary layer on a cone in inviscid theory and experimental data from viscid tests supersonic flow at large angles of attack," NACA-TN-2844. 6 G. I. Taylor and J. W. Maccol, Proc. Roy. Soc. (London) For definition of extensive and intensive properties see F. E. A139, 279-311 (1933). J. W. Maccoll, Proc. Roy. Soc. (London) Fowle, Smithsonian Physical Tables. A159, 459-472 (1937).'Cronvich and Bird, Pressure Distribution Tests for Basic 7Z. Kopal, Massachusetts Institute of Technology Tech. Conical Flow Research (Ordnance Aerophysics Laboratory, Report No. 1, 1947, Department of Electrical Engineering, Daingerfield, Texas). Center of Analysis.

UPPER ATMOSPHERE AMBIENT TEMPERATURE AND PRESSURE 163 between P0o/P, and the Mach number M1, thus permitting a determination of the Mach number from the - ---- - experimental data. The dependence of Mach number and cone-wall pressure P, on the ambient pressure P1 appears in the course of this determination. The am- t. bient temperature is determinable from the familiar Eq. (6) relationship between Mach number and 1.6velocity relative to ambient air. / It is convenient to initiate the theoretical analysis / by stating that ratio Po'/P, of the measured pressures, - --- / in the following identity::$ I/ M, ~~~PtP _=- _(1)' / - \ P, PPP, PoP ~, The theoretical treatment consists in expressing eachof the right-hand factors in terms of the Mach number2 - -- - and the known ratio of specific heats, thus leading to the Fig. 2 relationship. To accomplish this for the first factor, energy con-' ~ — siderations permit expressing the ratio of pressures across the normal shock wave in terms of the Mach_ number and the ratio of specific heats as follows:t I 2 3 M 4 5 P1 2yM12- ('y- 1)] (/(,Y-,) (y4+ l)M12 I/(1-) FIG. 3. The relationship between the unyawed surface pressure -_= - _(2) and the ambient pressure as a function of the free stream Mach Po/ (-~\+ 1) 2 number for a non-yawing, 7.5~ half angle supersonic cone. Similar evaluation of the remaining three factors on The third factor on the right-hand side of Eq. (1), the right of Eq. (1) requires use of the theory of the the ratio of static pressure behind the shock wave to conical regime. Taylor and Maccoll8 determined the the stagnation pressure, is found directly from the pressure ratio across the shock wave using a lengthy Bernoulli integral and the assumption of adiabatic flow graphical procedure. Kopal7 derived an explicit ex- behind the shock surface.7 This ratio, in terms of the pression for this ratio using purely algebraic procedures; local velocities provided by Kopal's tables, is he also prepared tables providing values of the local ve- P,/Po= [1- (u,/c)2- (vw/c)2]7/(T'). (5) locities (radial velocity Uw, tangential velocity V,, and sonic velocity, a) for any given cone angle as a function Lastly, the ratio P,/Po of cone surface pressure to of the Mach number. By using values from these tables stagnation pressure behind the shock wave follows from in his expression, Eq. (5) on setting the tangential velocity (vw) equal to zero. Pw (Y2- 1) (C2- -u2- vw2) The results from using these four evaluation proceP1 4 2'yv_2- (y- 1)2(C2-uw,2- vw2)' (3) dures in Eq. (1), expressed in terms of the Mach number for the non-yaw case of a 7.5 half-angle cone, are shown the second factor on the right of Eq. (1) can be evalu- in Fig. 2. ated in terms of Mach number and y. With the requisite Mach number known from Fig. 2, The quantity c, appearing here, is a useful reference the ambient pressure is available from Eq. (1) after velocity, sometimes defined as the maximum velocity dividing both sides by Po'/P1. The result of this proattainable by converting all the heat energy of the fluid cedure is shown in Fig. 3. into uniform motion. In terms of the local sonic velocity, Computation of the ambient temperature depends on a, and the velocity V relative to ambient air, the the definition of the Mach number and the adiabatic reference velocity c is defined as sonic velocity relationship. These express the ambient temperature explicitly as V2[1+ 2a2 1 (4) T= (V/M1)2(Ry)-'. (6) L V2(y-1) The velocity V appearing here is the relative flight speed. In the experiments presented, no provision was t See list of symbols at end of paper. made for estimating local wind conditions; consequently 8 G. I. Taylor and J. W. Maccoll, Proc. Roy. Soc. (London) mie v e t ati wa t as A139, 288-292 (1933). the missile velocity relative to the earth was taken as

164 SICINSKI, SPENCER, AND DOW;~~~~~~~~2 ~P, is the surface pressure for a zero-yaw angle (e=0), while the perturbation coefficients rn and Pn are avail~, —-; B^ - I ~~~~~~~~able from reference 7. Stone's analysis demonstrated that all the second-order yaw terms except n=0 and ^ ~' /; X.lt' ~,__ XMZ n=2 vanish under the boundary conditions on the - -..^',,'^^,iiflrn' t I ao, cone, while the Rankine-Hugoniot conditions reduce all the first order terms to zero except n= 1. /3 -— ^ ^ / ) In application of Eq. (7) the perturbation coefficients 2/_ _____ las given by Kopal need to undergo a transformation by means of a Taylor expansion for utilization in the desired reference frame." Kopal's tabulation presents CONEt~\ ~these coefficients relative to arguments of the unyawed / XIS CN reference system where the desired coefficients are perturbed by angle (<a. Thus the pressure at any perturbed position 0 is given by the relation P(0) = P(8+ (a>) = P()+P' (8)< ( +P" ()(>/2- ~*, (8) END VIEW OF CONE where the barred quantities are with respect to the unFIG. 4. Coordinates describing the yawing cone. yawed reference frame. The primes refer to differentiation with respect to 0. With Eq. (8) we still need an the defining velocity. Tacitly, this statement assumes expression for the yawed conical surface with respect to that the winds present are negligible compared to the the unyawed reference frame. In the region between relative flight speed. the shock wave surface and the yawing cone the These data have given the temperatures through variables will be constant over surfaces of a generally which a reasonably smooth curve could be drawn conical nature. If it is assumed that these surfaces re(Fig. 11). The departure of the measured temperature main cones of circular or elliptical section, rotated from the smooth curve are of the nature that would through the yaw angle e, the equation'2 for any of these result from the presence of a wind field varying in speed surfaces is and direction. Uniform wind fields, on the other hand, would yield temperatures, continuously higher or lower 0.+A0=0,+~ cos- (1/2)e cotta sin * *, (9) than the actual ambient temperature. where the particular surface is defined when 6, and AMs are stated. Using Eqs. (8) and (9) in Eq. (7), then C. Yawing Cone collecting terms to the order e2, and evaluating the Under the conditions experienced by high-speed derivatives gives the pressure at the yawed solid cone vehicles missiles are fundamentally yawing bodies; surface as, that is, the missiles longitudinal axis does not usually I / 7 \ /P2 /U8 maintain coincidence with the free stream relative P, I -cos e2cos2 +-(-) velocity vector. Consequently, the experiment must P, \P, 2 a employ a yawing-cone theory for its analysis. /P /\2 A theory for yawing supersonic cones was developed - )2 -' *I (10) by A. H. Stone9 which included second order yaw effects. \P 2\ a Stone's analysis led to Kopal's's tabulation of the per- The experimental data provide values for P, e, and turbation coefficients for use in the solution of supersonicantities along with Eq. (10) permit computaThese quantities along with Eq. (10) permit computaflow fields about large-yaw cones. Of particular interest tion of, the unyawed pressure. Having the experiis Stone's expression for the cone's surface pressure, since ment reduces to the non-yaw case for which expressions it provide te s the basis for a pressure experiment on a involving the ambient pressure and temperature have yawing cone. In terms of the coordinates of Fig. 4, the already been given. P, are surface pressures measured surface pressure Pa is by suitable gages located in the cone, and e and q are computed from a combination of the trajectory locus P5=P.~+ E 7n cosn+c2 E Pn CO.. (7) and data from a missile-borne gyroscope. From the P,=P,+ f F l,~ cosn&+ ~' P,, cosrub.... (7) n=0 n=- definitions, the yaw-angle computation makes prerequisite an assumption regarding environmental winds. t A. H. Stone, J. Mwath. Phys. 30, 200 (1952). "'Z. Kopal, Report No. 3, Massachusetts Institute of Tech- In both experiments presented the wind velocities are nology Department of Electrical Engineering Center of Analysis and Z. Kopal, Report No. 5, 1949, Massachusetts Institute of n Van Dyke, Young, and Siska, J. Aeronaut. Sci. 18, 355 (1951). Technology Dept. of Electrical Engineering Center of Analysis. 12 A. H. Stone, J. Math. Phys. 27, 73 (1948), Eq. 34.

UPPER ATMOSPHERE AMBIENT TEMPERATURE AND PRESSURE 165 assumed to be small compared to the missile velocity. ROCKET The yaw angle is then determined with the wind vector SUpR tangent to the missile trajectory vwhile the missile aspect is taken from a gyroscope.ALPHATRON III. INSTRUMENTATION The instrumentation that has been developed and FIG. 6. Elementary used in Aerobee rockets by this research group to ob- block diagram of Alpha- ALPHATRON.C tron pressure measure- LOAD D tain the fundamental data required utilizes an Alpha- ment system. RESISTANCE AMPLIFIER tron gauge as the basic pressure sensitive element, and a I gyroscope for missile angular position determination. rhis section of the paper will describe briefly the CHANINGG manner in which each of these devices is employed. CIRCUIT OUTPUT TO A. Pressure Measurement TELEMETER SYSTEM An Alphatron is an ionization gauge wherein the ionizing energy is obtained from alpha particles emanat- order to obtain a reasonable definition in the ultimate ing from a small quantity of radium, generally of the pressure data. order of milligrams. Figure 6 is an elementary block diagram illustrating The essential external characteristics of the particular the circuit developed13 to meet these requirements. gage chosen for use in this investigation are illustrated The Alphatron current is passed through a resistance of in Fig. 5, which presents a typical curve of output cur- sufficient magnitude to produce a voltage equivalent to rent versus chamber pressure. The lowest measurable the desired information signal. Because of the very pressure is determined fundamentally by the "dark small current, this resistance may be as high as 250 000 current," the value on the curve to which the lower megohms. portion of the curve is asymptotic. The upper limit is The voltage obtained across this resistance is applied determined by recombination of ionized particles before to a 100 percent negative feedback dc amplifier which the ionization products are collected and measured, as acts essentially as an impedance changing device. The evidenced by the bending of the curve at the higher first stage of the amplifier employs an electrometer currents. tube in order to provide an input resistance that is large Two features important from the standpoint of cir- compared with any probable Alphatron load resistance. cuit requirements are immediately apparent from the The following sections of the amplifier are, in sequence: curve: the very small current that constitutes the basic a voltage amplifier, a heater voltage regulator, another information signal, and the rather large ranges of cur- voltage amplifier and finally a cathode follower stage. rent and pressure which must be accommodated in an Inside the feedback loop the voltage gain is high, of the instrument which utilizes the device over its useful order of 4500. However, with feedback, the voltage range. The small current implies either the use of a rela- gain of the system is unity, whereas the current gain tively small (few megohms) load resistance and very s significantly high. Since the output voltage is equivalarge voltage amplifications, or the use of very high lent to the input voltage (100 percent feedback) the values of resistance, with the consequent problem of current gain is numerically equivalent to the ratio of the impedance matching. The extensive useful range on the input load resistor (Alphatron load) to the cathode other hand demands the use of several subranges in resistor of the cathode follower. The voltage obtained from the cathode follower cona.< ---,______ ___stitutes the desired data and is accordingly applied -— ~ Xto the recording system, in this case the telemetering system. gn:~~~~ /~~~~~~ -In order to provide for the several subranges, differ=, /ent possible values of Alphatron load resistance are 2' — --- -- -^ -. — -— /provided, one for each subrange. It is the function of the range changing circuit to select and insert the par-,i___ --- __ -— / __ticular load resistance appropriate to a particular range XJi~~~ ^^^/ ~~~of chamber pressure. To accomplish this, the amplifier i ~-." ~____ _ _______ output signal is applied to the range changing circuit "'I ~ which uses two thyratrons to control a bi-directional l| ~ ~ ~ ~ r nrvrotary solenoid. If the information signal voltage ex* -- —'- rlff —-IEIYO~*LtEU R..'- ceeds a predetermined value (in either direction) the FIc. 5. Variation of output current with chamber pressure for a 1A Developed from an original design by J. R. Downing and G. particular Alphatron pressure gauge. Mellen, Rev. Sci. Instr. 17, 218 (1946).

166 SICINSKI, SPENCER, AND DOW. - I | II | I v- -_. __-7 L - Lperhaps in regard to choice of pressure subranges as _ L_-. ___ [___ I - 1 _-__ may be required by particular gauge locations, for ex|... _..._......_.._.__ 1 _ >ample, cone-wall or cone-vertex mounting. -..... __ Th I B. Angle Measurement s ^^^^-?ip ix, -"! _r —_-.. F —' —... --.... -The gyroscope used for missile angular position 8o __ -r -r —-t it ---- _ -_ _ measurement is a modified Sperry type F4A unit. The -__.[| — i L _L \ j _ modification was accomplished primarily in order to!. ___ j_ \ i _allow operation under free fall conditions. However,._._.. _ i _ —-L......~_ —- _4_- i_ __ in addition, an attachment was developed that enables 0;...456 I I91.0 3 I 6 the establishment of zero position prior to rocket flight. I1. 2 3 4 S 6 7 1~91.0 2: 4 5 6 7? 6 e. rK PR ESSURE L Recording of gyroscope data is accomplished by FIG. 7. Variation of Alphatron pressure measurement system photography of the gyroscope sphere (gyrostat) posioutput with pressure for a particular sub-range. next lower or higher value of resistance is inserted, thus returning the information signal to an "on scale" 290 value. An automatic range selection device is of course necessary because the equipment operates unattended 280 through the total pressure range encountered during a - rocket flight. 270 — - 1 Figure 7 illustrates the variation of output signal with - 1 pressure for a particular subrange. In this case the 2 60 Alphatron load resistance is 5000 megohms. The complete Alphatron equipment in a particular ROCK- I DET PA1NEL_ W ADOPTED rocket includes several nearly identical, independent | VALUES units similar to that described above, differing only 24 2 1- 1 —- - - I I' —- _ __ A.' ~ P, AMBIENT RESSRE 2 ~ P ACTUAL CONE SURFACE 2 PRESSURE x Po ACTUAL CONE IMPACT PRESSURE_21)- - --------- - _ ALTITUDE IN KILOMETERS x PRESSURE IN MILLIBARS __.____...., tAo || | l i l l | | _ N 1 i s 1 l -, ALTITUDE (KM) 1'|l - -| -| ||I _^.J I — I —-— FIGr. 9. Ambient temperature at various altitudes above AlamoFIG. 9 Ambien teme\e *a - u- e o - g ordo, New Mexico. These temperatures are computed from z1 1 1 1 | 1 1 1' 1i' -\ l Aerobee rocket data of June 20, 1950 at 0838 hours using the ola^ __ __ __ __ __ _ __!_ ) l,.- I <~ O assumption of a limited wind field. -41\ ~~~x - tion in reference to a missile-fixed coordinate system. ---— 3 — | | | — -- -- --' ".,The film on which the position is recorded is recovered,-I- ---—. — i at the end of the rocket flight. 7' I. -~ I IE II;I I. 1-+- -=E 1\. I= =IV. EXPERIMENTAL RESULTS --,Z ~t Two experiments based on the above theoretics have I - I -I... I- - I - -I I been successfully completed. Pressure equipments were ~ J'i I. L - --! — j ___instrumented in Aerobee Sounding Rocket type missiles ol 0 0 -I5 1 1 io- 5-s 60 65- 7 for launching by the U. S. Air Forces at the Holloman ALTITUDE{K1M Air Force Base at Alamogordo, New Mexico. The first FIG. 8. Actual cone pressures, total head (cone tip) and surface, experiment on June 20, 1950, carried one impact prescompared with the ambient pressure for Aerobee rocket of June 20, sure gauge and one cone-surface pressure gauge. For com1950 at 0838 hours, at Holloman Air Force Base, Alamogordo, parison purpoes the two experimental pressures and New Mexico. parson purposes the two experimental pressures and

UPPER ATMOSPHERE AMBIENT TEMPERATURE AND PRESSURE 167 the resulting computed ambient pressure are shown in - - -- - - -- - - - Fig. 8. From this first experiment, the ambient pressure data is reliable to one part in thirty-five. - -- The seemingly relatively large scatter in the cone surface pressure is a result of the missile's rotation as 2 I it assumes increasing yaw angles with altitude. The 1 impact pressure is generally without such cyclic varia- - tions since it remains independent of the yaw angle for- - - _ - X values up to about thirty degrees. Although not showni C in entirety, maxima in the ratios of both cone surface - and impact pressure to ambient pressure occur in the l _ X - - neighborhood of 35 kilometers altitude. These maxima F - |MS are presumably the result of the combination of maxima /" I IZ _ 1 IU in the Mach number and the missile velocity; as such / - \ they can only be construed as caused by missile be- havior, not representing properties of the atmosphere. __ The temperatures computed from these data are shown in Fig. 9. No comment is offered on this curve 21-_ _ I other than that the maximum probable error is believed to be -eight degrees Kelvin to about sixty ROET (K.) P o 40 I 60 L0 kilometers and 4-thirteen degrees Kelvin above about I A LESD 2317 262.5 270 1252.8 218.0 sixty kilometers. SMOOTHED.9, - -- - VALUES 230 2t1 268 238 1j89 The second experiment was completed on September _ OBSERVED 13, 1951. The Instrumentation represented considerable | improvement over that of June 20, 1950, in having two 1o cone-surface gauges and a greatly increased information *LTITUDE (K reporting capacity. The increase in sampling informa- FIG. 10. Ambient temperature at various altitudes above Alamotion rate resulted in a reduction of the overall probable gordo, New Mexico. These temperatures are computed from error of the final temperature data. For Fig. 10 the tem- Aerobee rocket data of September 13, 1951 at 0437 hours using the assumption of a limited wind field. peratures up to fifty kilometers have a maximum probable error of -:five degrees Kelvin while the probable O error above fifty kilometers is ~ seven degrees. The ambient pressure resulting from this flight has an im- - }I T ^ E @wfsm proved accuracy such that it is reliable to one part in i ___ X I sixty-five. These data are shown in Fig. 11 as the "experimental points." V. SELF-CONSISTENCY IN THE RESULTS It has been pointed out above that each experimental point, for the temperature curves of Figs. 12 and 13, is evaluated from the experimental data independently - of other points. Furthermore, in the non-yaw case, the temperature calculations leading to Figs. 11 and 12. employ only the ratio of the measured total-head- 1 pressure and cone-surface pressures, not their absolute values. Thus, the absolute values of the pressure meas- urements are not employed in determining tempera- - tures. It is obviously possible to employ the experimentally-. determined temperatures in the familiar hydrostatic - equation1 thereby determining the absolute values of4 the ambient pressures by a method that does not directly use the pressure measurements obtained by the rocket instrumentation. In such use of the hydrostatic,l _ I, equation an inverse square variation of gravity is as-,o 00 00 U ooo ao T oo 7,O 14 S. K. Mitra, "The Upper Atmosphere," The Royal Society of FIG. 11. Pressures calculated from hydrostatic equation Bengal Monograph Series (1947), Vol. V, Eq. 3, p. 5 (dP/P (dP/dh= -Pgm/RT) using experimental temperature of Fig. 9, — mgdh/kTi). compared with ambient pressures for the same flight.

168 SICINSKI, SPENCER, AND DOW'II -X two sets of points are less than the experimental errors of the method. Of course, self-consistency as between ==-~ -======,~, EXPERIMENTAL PTt _ these two different rocket flights and observations by.- _-_ —- - - -4 other methods16 is also of interest. However, seasonal — _ -_ -- Azz_ 3 and diurnal variations of the temperature curve cer-'____ - — 2tainly exist and must be taken into account in comparing the two sets of results here reported with one %~~<~~~ ~~~~~another and with results obtained by other methods. _._ _ _ _ _-__-_, 1xO We wish to take this opportunity to thank Mr. ~x-AIZ EE ^ 1 _ =Ralph E. Phinney for his interest and valuable discus=- ~ == -~ sions involving the basic aerodynamics of this problem. a -- -- - - -- -- -- -- -- -- -- 3 ~LIST OF SYMBOLS: - - --- -.- - - - Pa Cone surface pressure of yawed cone, along ray'x,\s>~~. ~at angle 0 from plane of yaw _=_"_ -% - - - _ I xI P1 Ambient pressure _~ _ - = -:F= =-e —:~_^ PO Stagnation pressure behind conical shock wave == == =- === X- _-~ Po' Stagnation pressure behind normal shock wave ~_ -_- - - - __I X P2 Static pressure behind normal shock wave - - - __ - - - - - - \- Pw, Static pressure at shock wave surface on downt~I~~ ~ _ _Nl> ~~~stream side of a conical shock wave L - - - - - - A — P8 Cone surface pressure when yaw angle is zero (e=0) ~lo'3 35.Qo 0S0 5. o o~xo'" Tl Ambient temperature ~30.0 350 40~ 450 50.0 5O0 600 ALTITUDE (KM) M1 Free stream Mach number FIG. 12. Pressures calculated from hydrostatic equation using M2 Mach number behind normal shock wave experimental temperatures of Fig. 10, compared with ambient V Free stream velocity pressures for the same flight. Vw Tangential particle velocity Uw Radial particle velocity sumed, and a mean molecular weight of 28.966 for air u8 Cone surface particle velocity is employed. Balloon observation results are employed O, Cone half angle to provide the absolute value of pressure at 30 kilo- c See Eq. (4) meters, which serves as a constant of integration. E Yaw angle Figures 11 and 12 present, for the two data sets, 1/p, Stone's first-order perturbation coefficient Figs. 9 and 10, respectively, the absolute values of P1/p, Stone's second-order perturbation coefficient ambient pressure determined by Po/Ps Stone's second-order perturbation coefficient (a) As shown by the circles, by direct point-by-point 4 Spherical coordinate determination from the data, using Fig. 3, in this' case Spherical coordinate the ambient pressures are obtained practically speaking, k Angle of rotation about cone's longitudinal axis by applying an appropriate correction to the cone-wall measured from plane defined by cone's longipressures. tudinal axis and the wind velocity vector V (b) As shown by the crosses, by employing in the a Local sonic velocity hydrostatic equation the Figs. 9 and 10 temperatures h Altitude obtained point-by-point from the data. g Acceleration of gravity m Mean molecular weight The very good agreement between the two sets of R Universal gas constant points in each case provides a rather satisfying self- y Ratio of specific heats consistency check of the system of instrumentation and data reduction employed. The deviations between the "I The Rocket Panel, Phys. Rev. 88, 1027 (1952).