T H E UN I V E R S IT Y OF MIC H I G A N COLLEGE OF ENGINEERING Department of Electrical Engineering Space Physics Research Laboratory Scientific Report No. 1 AN ACOUSTIC WIND MEASURING TECtHNIQUE W. W~ Bushman Gd Mo kakli G0 R, Carignan ORA Project 05911 Under contract with: NATIONAL AERONAUTICS AND SPACE ADMINISTRATION GEORGE Co MARSHALL SPACE FLIGHT CENTER CONTRACT NO, NAS8-11054 HUNTSVILLE, ALABAMA Administered through: OFFICE OF RESEARCH ADMINISTRATION ANJN ARBOR30 July 1965

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TABLE OF CONTENTS Page LIST OF FIGURES AND TABLES j NOTATION Id INTRODUCTION 1 II BACKGROUND 2 - III e THE EXPERIMENT 4 3. The Measurement 4 3,2 Theory 6 IV, DATA ANALYSIS 10 V. COMPUTER SOLUTION 19 VI, THE WIND PROFILE 24 VII, ERROR ANALYSIS 28 7 1 Sound Arrival Time Error 28 7.2 Errors in the Speed of Sound Profile 37 7.3 Noise Source Position Uncertainty 39 7.4 Error from Plane Wave Assumption 39 -VIIII:- CONCLUSION 43 REFE RENCES 44

LIST OF FIGURES ANDrJ TABLES Page?ig, 1 Microphone Array 5 Fiqg 2 Block Diagram of the Sound Ranging System 7 Fig, 3 Oscillogram of Microphones 1,2,3,4 & 5 8 Fi g 4 Geometry of the Wind Experiment Showing 15 Time Relationships for the j th Noise Event lilj, 5 F low Diagram for Wi.nd Coimputation 2 0 Fig, 6 Convergence of the Solution for Determination 21 of Time and Position of the ith Noise Event, Fig, 7 SA-9 Wind Profile, Altitude vs. N to S Wind 25 Component Figo 8 SA-9 Wind Profile, Altitude vs, Vi to E Wind 26 Component Fig. 9 The Arrival of the jth Noise Event at 2'9 j-1 j-1 k=l;' k=J I Figo 10 Expected Maximum Wind Error due to,5 ms 33 Error in all Microphone Times Fig0 11 Expected Maximum Wind Error Due to 2 ms 34 Error in all Microphonc Ti.mes FigJ 12 Wind Error Due to Error in V(z) 38'V.' 13 Wind Error Due to Source Displacement 40 Fig, 14 Spherical Wave Front Intercepting 3 41 In-Line-Microphone s Tabl.e 1 Sat:urn SA-9 Wind Results 27 Table 2 Wind Errors Due to.5 ms and 2,0 ms. 35 Errors in all Microphone Times,

NOTATI ON Am Sound arrival time at the mth microphone measured relative to the arrival time at the center microphone and corrected for horizontal and vertical departures of the microphone location from a horizontal cross0 Measured arrival time at the mth microphone. A(x) Functional relation between the arrival times at microphones 4p5I6p7 and the x coordinate. A(y) Functional- relation between the arrival times at. microphones 2 3,8p9 and the y coordinate. 6Ah Correction- in the arrival time for horizontal displacement of a microphoned 6Az Correction in the arrival time for vertical displacement of a microphone4 AA Error in the measured time of arrival for microphone 4d5p6 or 7 AA, Error in the measured time of arrival for microphone 203 8 or 9o /a/ (-b Coefficients of the powers of x in A(x), b) Coefficients of.the powers of y in A(y) d c dQ e East IF\ Symbol for the functional representation of a G ) system of equations used in the error analysis. IH/ Index of the noise event0 J Jacobian of the system of equations used in the error analysis0 KxcKy Characteristic velocity in the x and y direction.

KxOK Approximate characteristic velocity in the x and y directiond L M Counters used in the computer solution to indicate the numbers of trials t.i2ie for. converm eof the solutiond n North Propagation velocity vector8 P Magnitude of the propagation velocity vector. (P7) x zyz components of propagation vector, Position vector of the noise source in the x~ypz system8 T Time measured along the trajectory of the vehicle referenced to the launch time8 Tj Time of the jth noise event measured along the trajectory of the vehicle referenced to the launch time "t Travel time of a sound wave from the top of the jth layer to the center microphone8 Ati Time interval spent by a sound wave in the ith layer (i < ) 6T ~ Initial estimate of the time difference along the trajectory between the (j-l)st and jth noise event. YV Velocity of sound vector~ V Magnitude of velocity of sound vector8 Vx, (RVy) Components of the velocity of sound vector Vavgj Average speed of sound in the jth layer8 Vj Speed of sound in the jth layer calculated from the sound refraction8 AV Error in the speed of sound8 W' Wind vector8 11i

Wx Wy Horizontal wind components in the x,y; Xj#Z, and WXZQ npe direction, respectively0 Wz/ Wn We..... (AWx\ Error in the x and y wind components, AWy/:x \Coordinate system defined by the two legs of the microphone array with origin at the center micro-,z/ phoned z points up. ix\ZX~ii Coordinates of the jth noise event in the (x,yz) system0 ~ Z/ XQX Coordinates of the vehicle in the earth fixed 1Y2a coordinate system of' the trajectory0 The origin \Zyj of this system is at the launch site. Xm\ Coordinates of the mth microphone in the (xy,z) (Ym system0 m z coordinate of the top of the ith layer (i < j), Axi Increments of horizontal range of the sound ray Ayi in the ith layer in the (xoyz) system. Direction cosines of the wave front normal ()B with the x y and z axesd ~1 The tolerance within which Vj and Vavgj are matched. Increment in Ta 0 Elevation angle of the wave front normal at.-the center microphone 0 T~j Total elapsed time from lift-off to the sound arrival of the jt -noise event at — the center. microphone. Azimuth angle of the wave front normal at the center microphone 0 iv

qotation for Computer Output: (Tables 1 and 2) DWX = AWx DWY = AWy J = j KX = Kx KY = Ky TAU = WE = We WN = Wn WX = Wx WXL =W WY =W WZL = W Y = y - X Z = Z ZAVG Zavg Vr

INTRODUCTION A technique for measuring winds using the Saturn exhaust noise has been successfully employed to determine the wind profile over Cape Kennedy from ground to 85 kilometers0 The technique is an extension of the Rocket-Grenade Experiment, utilizing as its sound sources rather than the grenadep the acoustic noise of the Saturn rocket exhausto In the Rocket-Grenade Experiment discreet sound events occur at accurately known positions6 and the times and angles of arrival of these events at a ground microphone array are used to determine the atmospheric temperature and windsld The use of the rocket exhaust to provide the noise events leads to a substantial difference between the two methods0 The purpose of this report:is to describe the technique and to present the wind profile determined during the flight of the Saturn SA-9o The method of data reduction is described and a preliminary error analysis is presented0 1

Ig BACKGROUND The RocketsGrenade Experiment is described in the iterature2 3 and the meteorological results of its extensive application form the basis for a large part of man's knowledge of the atmosphere between 30 and 85 kilometers0 The grenade technique is based on the dependence of the velocity of sound in a gaseous medium on the gas temperature and mass motion. By measuring the time required for a sound event to traverse from its source of known position to a microphone array on the ground and measuring its angle of arrival6 the average temperature and wind between adjacent grenade detonations can be determined0 When rocket exhaust noise is used, because of its continuous nature the time and location of a given noise event is not known, except that it occured along the trajectory. If, however the temperature is determined independently, then the arrival angles of each of the many noise events that characterize the exhaust can be used to determine windsd A ground based array of microphones intercepts the acoustic wave front of a noise event and the time of arrival at individual microphonesT is used to calculate arrival angle0 The noise event is traced back by an iterative process until it correctly intercepts the trajectory0 Each noise event so traced leads to a wind data point, giving rise to a wind profile in a stratified atmosphere with the average wind in each layer between selected noise events The assumptions made for the approach described here are: 1) The vertical component of wind is negligible compared with the local speed of soundd 2

2) The source of sound is considered to be a point located at the nozzle of the engine or a known distance behind along the flight patha The sound wave is approximated by a plane wave at a large distance from the source,. 3) The atmosphere remains in a steady state for the duration of the measurement

I o THE EXPERIMENT 3,1 The Measurement A cross shaped array of nine microphones was set up on the southeast point of.Cape Kennedy to monitor the SA-9 flighto A minimum of three microphones are necessary to determine the arrival angle of the sound; the additional microphones provide a method of improving accuracy and afford redundancy0 As shown in the error analysisp the proper use of the additional microphones eliminates first order sphericity errors from the plane wave analysis0 The size of the microphone array shown in Fig6 1 is about 1200 meters on each crossed axis0 The size is based on consideration of the accuracy with which arrival times can be measured and on errors introduced by the second order sphericity term which increases with array size0 The microphones are located in heavily vegetated locations to minimize local wind noise, At each microphone locations a concrete box is sunk so that its top surface is level with the surface of the ground6 These boxes contain the microphones and serve as permanent survey markerso A survey was performed which defined the local geodetic network position of each microphone location to within 6 incheso The microphones are hot wireo single chamber Helmholtz resonators tuned to about 4 cycles/seco This low frequency characteristic is particularly well suited to extremely far field measurements since the atmosphere tends to be a low pass filter over long distances0 The microphones and their amplifiers were designed at Texas Western College for use in the 4

-C LP \n y 3 EQUIPMENT VAN \ SCALE:METERS 0 100 200 300 400 500 MICROPHONE ARRAY X Fig. 1 5

Rocket Grenade Experiment4 Figo 2 is a block diagram of the sound ranging system0 The electronic and recording equipment are housed in a van located near microphone 4, Although a location near microphone #1 would require about 2 1/2 miles less microphone cableQ it was considered desirable to keep the van removed from the array to reduce the possibility of reflective interference, The microphone outputs are recorded from before launch until 10 minutes after loss of signal0 On the SA-9 flight, the microphones were located about 10 km from the launch pad0 The exhaust noise was audible to the microphones from launch to more than 100 km slant range0 A manually operated variable attenuator was used to maintain- a proper signal level into the recording system0 Fig0 3 is a 2-second record made at about 55 seconds after launch0 The correlation of the microphone outputs is showno 302 Theory In the absence of local interference the acoustical wave front of a noise event appears essentially identical to microphones at separated locations If identical microphones are used; the output wave form of one microphone matches that of another shifted in time0 This time shift is a function of the sound arrival' angle the local speed of sound and the microphone placement0 The arrival angle can be calculated by measuring the time interval and the local speed of sounds After the angle of arrival of a noise event is determined, the sound is ray Ltraced backwards towards the source0 The first 6

MICROPHONE MAGNETIC TAPE RECORDER.3 AMPLIFIERS ATTENUATOR 2 Sp-~I |- BJ r | CHANNEL 3 h: ss 1 p- CHANNEL f 4 CHANNEL 7 MICROPHONE | CHANNEL ARRAY' CHANNEL 9 UINARY CODED TIMING I ___________13_____ - I I 111J~m ~ODLD tlMINO, U I ICHAN HNE 2I PRtOM RANG. 1VOICE IC 4 11 H-+S A CANNEL I BLOCK D R''OF TnlBO CHANNEL 9 Ja G~INA S CS.TBM CHANNEL 13 OSCILLOGRAPH Fig. 2 AMPUFIERS OSCILLOGRAPH

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noise events are ray traced through layers of known temperature and windd Eventually an interval is reached between the top of the last layer of known wind and the source of sound, At this point, conventional ray tracing procedures must be abandoned since the wind is unknown; howevero two independent require-: ments are availabled 1) The sound ray must intersect the trajectory, 2) Any intersection chosen will yield a wind value, The correct intersection point must satisfy the criterion that the time of arrival of the noise event measured from launch equals the time of flight to the intersection plus the time required for the sound to travel: from the intersection to the array. These two conditions uniquely determine the coordinates of the source along the trajectory and the average wind in the interval. 9

IV0 DATA ANALYSIS The first step in data reduction is the cross correlation of the microphone output wave forms in order to determine the arrival times0 In the analysis of the SA-9 data, this cross correlation was done manually using the method described below' 1) A group of at least ten successive waves is selected from the output of microphone 16 2) This group of waves is identified. on every other channel,, The identification is made by comparison of wave shapes and periods0 3- The wave form-with the sharpest peak is chosen from this group and its time of occurrance on each microphone is recorded0. After the arrival times are read, the arrival angles are written in terms of characteristic velocities along each axis, Kx and Kyo The characterisitc velocities Kx and Ky are defined as the velocities of the intersection of the wave front with the x and y axes respectively0 - In terms of characteristic velocities, the elevation and azimuth angles of the normal to the wave front are Vo K2 + Ky21/2 0 = cos-1 MW -.-~-uc p~kr*-O_ (1) Kx Ky Kx Wyo - Ky Wxo = tan-1 Kx (2) y where VO is the velocity of sound and Wxo, Wyo are the x and y components of the wind at the ground, Along each axis the arrival times at 5 microphones are measuredp In the calculation of Kx and Ky all times are measured 10

with respect to microphone Noe 1l reducing this to 4 non-zero arrival times. Only one of the 4 times is necessary to define the characteristic velocity for an axis1 but errors can be reduced by averaging or by writing the arrival times as a function of the distance along the axisd A(x) = ax + bx2 + cx3 + dx4 (3a) A(y) = a'y + b'y2 + c'y3 + d'y4 (3b) Any polynomial of 4th degree or less can be used, The coefficients are computed by imposing a "least square error" restrictions The nine microphones do not lie exactly on the two legs of a horizontal cross0 Corrections in the sound arrival times due to their displacements in the horizontal and vertical directions have been derived by Otterman5a For horizontal correction m ( Ahm =x7 - a4 (4a) (m = 2#308#9) 6A m (A3 Ag) (4b) Ah =' Ym (4b) (m = 45,#6,7) For vertical correction: 6Azm Pz (5) (m = 2,3.,..,0o. 9) 11

The corrected time for the mth microphone, Amy referenced to microphone #1 is: Am Aum mAhm Azm (6) (m = 2#3 ~~6~. 9) The characteristic velocities Kx and Ky are defined as follows: K = = 1/a (7) X 0 Ky = (Y) = l/a' (8) y ao Milne6 has shown that the wave front normal of the ray reaching the microphones remains parallel to the same vertical plane throughout its propagations For a plane wave then, the characteristic velocities of a specific sound ray are constant6 Since the temperature and wind are treated as constant in any layer, the segment of the sound ray in that layer can be approximated by a straight line, The wave fronts assumed plane, is refracted at each layer interface in a way analogous to the refraction of light waves6 This refraction is due to a change in the magnitude of velocity of sound between layers6 Further refraction occurs if wind direction and magnitude are not identical across layer boundaries Before the wind can be computed in any layer (jth) the sound is ray traced through the previous layers where the wind has been foundA The equations used for this ray tracing have been derived by Otterman for the Grenade Experiment5 The components of the sound velocity of the jth noise event in any 12

previous layer(i th) are in terms of known quantities avgi Yi Kx. (9ba) Kxj Wxi Wyi t =V (10) V Kyji - W xi (Xla. 2 2 -2 1/2 Yi = ((Vi + Vyi) (9c) iavg xi iy. k1 1 The time spent in the ith layer is CtXk (10) 1 z BYk And the distance traveled is The total time and distance through the (j-:l)St layer is then i: Atk k=l. Ax (12) k-l k k=l 13

Next to determine winds in the last layer~ The rocket position versus time function is obtained from the trajectory: X = X (T) Y~ = Y2 (T) (13) Z= Z (T) where T represents flight time or time of emittance of a noise event measured from lift-off, The coordinates XzRYQ Z~. are then transformed to (x0yOz) the coordinate system at the center of the-mricrophone array6 From the geometry of Fig, 4# the following time and velocity equations are apparent6 Time Relationships for jth Noise Event = T + t (14) j~1 t = Atk + Atk (15) where Atj = the increment of time in the unknown layer6 t = total travel time of the sound from (xj# yjr zj) to the array6 Velocity relationships: j. j2l 2 2 12 [x Axk) (yj z Ak 2 + (y. z j 21 l/2 k=l k=l p == " ------------------- (16) p (17a) z A.tj j-l x k (1 7b) 14

— ~~ (T,xyjzj)' ) ( T1.,,Yij,,yj,,Z317) z y'-) \ Z ((J-) ST LAYER, Vovg i-1 i,_ ij'tVXI~VySV:j-2 LAUNCH! SI TE z MICROPHONE ARRAY GEOMETRY OF THE WIND EXPERIMENT SHOWING TIME RELATIONSHIPS FOR THE j TH NOISE EVENT THE SOUND IS HEARD AT THE ARRAY AT TIME'. Pig, 4 15

j-l y- E AYk p = k=l (17c) Y At. where P = magnitude of propagation velocity vector of the sound ray. and Px, Pyo PZ are components of P in the x# y, z directions, respectively, The propagation velocity is the total velocity of the wave front traveling along the straight line path from (xj,yj,zj) to j-l j-l F, Axk, Z Ayk, zj_1 k=l k=l It is composed of the velocity of sound and the wind and is, therefore, not in general normal to the wave front. Thus # equations 17a 17b, and 17c can be written as: PZ VZ (18a) Px = Vx + Wx (18b) Py = Vy + Wy (18c) Wx0 Wy are the ce!-~onents of wind in the layer under investigation for x and y directions, respectively. (Wz is neglected). Vx, Vye Vz are the velocity of sound components in the layer under investigation for the x, y and z directions, respectively, For the unknown, but constant wind field in the layer between j-1 j-a (xj, Yj, zj) and( xkk, Ayk, z j)t-here can be only one = k=l k=l ray path from the trajectory that will satisfy the equations (14) through (18) and the condition that characteristic velocities are constant for a given ray. Otterman5 has derived the following expressions for Vx and Vy,. These equations exemplify this 16

directional dependence of V in any layer on the measured characteristic velocities at the arrays 2 V V x Y T~1 IK x (19a) Kx Px Py V 2 V Vy =.......... (19b) Ky - Py Px Kx The magnitude of the velocity of sound can be found from: V' =(V 2 1/2 (20) From these eight equations (13) through (20), position (Xjr yj, zj, Tj) and an average wind can be determined for the layer under investigation. These eqtations are solved by the procedure outlined below0 A sound is heard at the time, T, from lift-off at the microphone array0 Characteristic velocities Kx and Ky are. determined and the ray is retraced to the' top of the level-of known temperature and wind, This point of intersection is j-l j-1..li:,:' ( Axkr Ay, ZYk z ) k=l k l Z Atk is determined-:during the ray tracing calculation, Next: 1) A reasonable value for T. based upon the velocity of J sound and winds in lower layers is selected, This determines coordinates xj, yj, zj along the trajectory. 17

2) t and Atj are determined using equations (14) and (15)d 3) Using Atj and the position coordinates chosen$ Pz * Px0 and Py are determined from equation (17)d 4) These in turn are used in equation (19) to obtain Vx and Vyd 5) From equation (20) the magnitude of the velocity of sound is calculated and compared with the known velocity of sound for that layer, If these values agree, the selected Tj defines the true position of sound emittanceo If they do not agree, an iteration process is carried out, until agreement is achieved within error limita-_ tions o With the correct value for Pxo PyO Vx0 and Vy the horizontal wind components can then be found from equations (18b) and (18c) d 18

~V COMPUTER SOLUTION The solution for winds has been programmed for the IBM 7090 computers Figure 5 shows the flow diagram for the wind solution, The speed of sound profile is obtained from radiosonde and rocketsonde data0 and above the altitude of these measurements, from "standard atmosphere" valuesd For the computer input the profile is piecewise linearized using 22 straight line segments, The vehicle position data is entered at intervals of 0X.5 seconds0 Linear interpolation between these intervals agrees within 1 meter of the position determined from Lagrangds formula or Aitkin's method of iterative linear interpolation even at the highest vehicle speeds0 To insure convergence of the iterative process, e1 (the value within which Vj and Vavgj are matched) and &2 (increment in T)must be compatible (Figo 6) Counter parameters L and M assure that the solution has converged and indicate the direction of modification of the initial assumption of 6T. The relation between c1 and e2 is found as follows: For the jth noise event: x (21a) T 7At T k=l 3-1 p =k. (21b) k=l 19

COMPUTE THE TRAJECTORY READ SPEED OF READ ROCKET TRAJECTORY IN OF'THE NOISE SOURCE SA SOUND PROFILE EARTH FIXED CO-ORDINATE SYSTEM: AND TRANSFORM TO (x,y,z) READ THE CO-ORDINATES OF MICROPHOE V(z) vs.z T, Xg(T), ~i(T), Z,(T), d X (T, d Y X(T YSEMWTHMCRPON m, Ym, zm (m 1, 2,~~ 9) dT dT dT XI AS ORIGIN SET K-I J-1 ~~~~~~~~~~~~APPLY CORRECTION TO I A COMPUTE CHARACTERISTIC VELOCITIES MICROPHONE TIMES FOR APPLY CORRECTION FOR FOR jth NOISE-EVENT, READ 7x K-1k' KXIKyj BY LEAST SQUARE SOLUTION HORIZONTAL AND VERTICAL MICROPHONE RESPONSE REDE.p~iAND SOUND A~RRIVA~L TIMES F&I ALL 1-1 DISPLACEMENTS OF TIMES, REFERENCED TO.I MICROPHONES REF"RENCED TO I AykzO MICROPHONES MICROPHONE *I K-1 L=M= M YES 1 T~~~~~~~~~~~~~~=89~~~~~~~~~~~~~~~~ " a~~~~~~~~~~TR ANTj' j jz I. CORRESPONDING TO Tj OMPUTE zi i~~~~~i ~~~~DETERMINE THE POSITION CORRESPO DtGT CMUTE~ COMPUTE I OFNIS EEN (iY Z) zj-, DETERMN I Ml j- X-1 V f~ Vt z dz' V~~~~~~~~~~~~~~~~~~~~~~~~~~j ~ ~ ~ ~ ~ ~ ~ ~ ~ ~'~;t =~ ~ START )ji FROM THE ROCKET R' j, Kxj Zi-y =tj+zj-iYE Z ovgx 2 P2 Vj, COMPUTE IsCOPT COMPUTE COMPUTE 1 M=M*I I.nKxl~-y Ky - /YJ, a LM(y i - IA YK)/ >0 NO K+l COMPUTE STORE AND PRINT Wx1 P P _vxj STORE AND PRINT rj, Kxj, Kyj, Tj, Xj, yj, Zj COMPUTE AND PRINT TR Wyj Pyj-vyj xj, vyj, Pzj Vi, Vavgj, avgj, Wxj, Wyjl 1 W jtWje Wz.....,,~,. COMPUTE COMPUTE COMPUTE ADD V V.2Vg ~iVy = Kxj COMPUTE zi-zi-I COPUT V 0? (rv,,VVg Ati= At!TO IAtK AX i Ati (W-~xi+Vi VxrKXj Wxi Wyi K"j yi xi Ky. VXV2T I K~ ~ ~ ~ ~~,-x -,,P Kyj PRINT i-I -I -i ES P C ~~~~~ZtKe 3AX K ZAyK K-1 K-1 K-1 PRINT ADD ADD i, vX I, v i, Pz I Ayi TO 1: AYK COMPUTE iT A? Atiiitl.VX AYr KP-1 Ayi = Ztl(Wyl+Vy,) ~xi TK-C:XK Fig. 5 FILOW DIAGRAM FOIR WIND CONPUTATION 2O

(Tjc) (2) (a2 T9tj j - -- J- 1 (T_- - Ij TN LAVY, V.,j.,K v. (v'. v2.vz'~,/, (J-l) ST LAYERVavg i.-' f(e oI) LAUNCH SITE ~~~~~~~~SITE - ~MICROPHONE ARRAY CONVERGENCE OF THE SOLUTION FOR DETERMINATION OF TIME AND POSITION OF THE j TH NOISE EVENT THE CONDITION Iv;'- VwgjeliX,, DETERMINES THE POINT (Tj,x;,y;,z3) Pig. 6 21

and z. z. p- =(21c) T'E Atk T k=l Now j-1 j-1 dPx Xi- Ak + (Z Atk T) dx =~:~jj~~ __~~__ k~~ (22a) ~ - d AQtk T) k=l j-1 j-L (225) dP- Yi ~ >; c +( T -, j zl Qtk_ T)2 ( A Atk - T) j-1 dPz zj zj-1 + (I'E Atk - T) dz dT j-2 (22c) {T 2: Atk - T) k=1 To simplify the computations it is assumed that the velocity of sound in the upper layer is constant and wind is sufficiently small so that the approximation Px Vx and Py Vy is justifiedo So dP2 dP 2 dP 1/2 dVi idP 2x 2 dP T'UOT + a + (dY)} (23) c 1 ~= I~1 c2 (24) Taking the case of j = 27 as an example, = 3OO sec0 dx = 104146 m/s 22

j-1 E Atk =182a4245 sec. = 422,09 m/s k=l T = 12008481 sec. 11131 /s T = 1118.o31 m/s xj = 21878.1 mO yj - 169409 m. zj = 49280,7 m, j-1 j-l Xk = 211474 Yk = 164526 474234 m k=l k=l these values give: -1 = 280 C2 Based on an evaluation of overall system parameters, a criterion of 0,2 meters/sece has been established as the value for F1 and equation (25) is used to determine the appropriate tolerance for C2. 23

VI0 THE WIND PROFILE Figures 7 and 8 graph the wind profile determined during the flight of the SA-9d Also plotted are the rocketsonde and rawinsonde measurements taken near the time of the SA-9 flight0 The agreement between the methods is consistent with the results of the error analysis, Table 1 lists the input quantities in the first four columnso The time and coordinates of the trajectory to which the solutions converged are listed under Tj (Range Zero = 14037:00Z) xj yj and zjo The remaining columns list the wind values in three coordinate systems: (1) the system of the microphone array (2) the system of the trajectory, and (3) the North-South, EastWest system The data points were computed at intervals of 10 seconds Tr 24

ALT (KM) 80 75 SA-9 EXHAUST NOISE 70 MEASUREMENT WIND PROFILE 65 $A-9 LAUNCH DATE: FED s,!lis TIME, 14.a7O03 Z. 60, EXHAUST NOISE MEASULREMENT 14.t726Z- 14.45t4Z -55 X RAWINSlOND DATA AL 14'45Z -li'2SZ 1-'A ^ _50 A ROCKETSONDE DATA I S 4 z - 16:4S Z 35 30 25 (M/ 5 2K10 x 25

ALT (KM) 80 SA-9 EXHAUST NOISE - 70 MEASUREMENT WIND PROFILE.65 SA-9 LAUNCH DATE' FEB 16, 1965 TIME: 14.3703 Z 60 0 EXHAUST NOISE MEASUREMENT 14.37:26Z - 14.45s:43z. s X RAWINSONDE DATA 14:43 Z - 1421Z I,50 A ROCKtT/ONDE DATA A' l634HZ- 16S45Z 45 Pig. 8 40 K (MIS) 26 S r 10 - 100 -80 -60 -40 -20 0 20 40 60 80 1 00 W TO E WIND COMPONENT (M/S) 26

J [AU KX KY T X Y Z ZAVG HX MY HXL HZL HN HE SEC M/S M/S SEC METERS METERS METERS METERS M~ M/S M/S M/S M~ M~ 1 50.00 399.361 — 651.696 24.0539 — 7340.5 4766.8 871.3 435.6 -9.00 — 4.83 — 10.2 1.1 1.6 -10.1 2 60.00 412o678 — 651o740 33.6927 -7271.5 4793.3 2015.5 1443.4 — 2-12 -3.51 — 3.3 2.5 -1.5 -3.8 3 70.00 446.360 -654.368 42.6771 -7029;7 4892.3 3593.0 2804.3 3.95 -1.24 3.2 2.6 -3.4 2.4 4 80.00 503.751 -664.680 50.6690 -6614.2 5064.0 5411.9 4502.6 -.16 2.37.7 -2.3 2.0 1.3 90.00 595.671 -680.373 57.1450 -6071.5 5301.6 7336.3 6376.1 -.82 7.69 2.0 ~ -7.3 6.5 3.9 6 100o00 749.997 -703.672 63.0445 -5411.7 5589.3 9315.2 8325.8 13.94 6.21 15.3 -.5 -3.4 14.9 7 llO.00 988.429 -721.932 68.1878 -4668.9 5909.0 11263.3 10289.3 17.36 15.06 21.7 -7.5 1.6 22.9 8 120.00 1352.509 -732.422 72.6964 -3867.4 6263.1 13163.8 12213.6 10.48 24.72 19.0 -19.0 13.4 23.2 9 130o00 2018.866 -739.287 76.7159 -3016.6 6641.9 15026.3 14095.1 15.85 26~53 24.6 -18.7 11.6 28.6 10 140o00 3531.482 -750.593 80.3869 -2108.7 7041.7 16876.4 15951.4 12.64 18.35 18.6 -12.3 7.0 21.1 11 150o00 9973.709 -767.034 83.7945 -1139.2 7462.5 18734.4 17805.4 5.93 9.37 9o0 -6.5 3.9 10.4 12 160.00 -15921.402 -788.305 87.0341 -93.0 7910,4 20631.3 19682.8 2.01 2.53 2.8 -1.6.8 3.1 13 170.00 -4893.866 -815.274 90.1443 1060.7 8390.1 22579.5 21605.4 -6.51 -5.86 -8.2 3.0 -.8 -8.7 16 180.00 -2906.231 -841.160 93.0844 2239.8 8893.2 24539.1 23559.3 6.85 -6.81 3.8 8.9 -9.6 1.4 15 190o00 -2140.038 -861.576 95.8604 3496.6 9417.5 26497.7 25518.4 4.25 -1.17 3.5 2.7 -3.5 2.7 16 200.00 -1733.195 -876.660 98.4837 4806.5 9963.4 28441.9 27469.8 2.18 3.33 3.3 -2.3 1.3 3.7 17 210.00 -1475.187 -888.456 100.9837 6171.3 10528.8 30387.7 29414.8 4.36 7.22 6~7 -5.1 3.1 7.8 18 220.00 -1301.153 -898.791 103.3697 7585.9 11111.9 32331.8 31359o8 2.75 7.49 5.4 -5.9 4.3 6.7 19 230.00 -1154.535 -901.329 105.6036 9015.1 11699.3 34227.8 33279.8 30.67 20.82 36.2 -7.8 -1.8 37.0 20 240.00 -1048.201 -902.960 107.7538 10492.1 12305.0 36123.9 35175.9 28.75 22.52 35.1 -10.1.7 36.5 21 250.00 -965.721 -903.942 109.8247 12012.1 12926.9 38017.1 37070.5 31.56 26.18 38.3 -10.6.3 39.8 22 260.00 -903.289 -906.961 111.8477 13593.2 13572.7 399'31.8 38974.5 24.'77 20.01 30.5 -9.3 1.1 31.8 23 270.00 -850.222 -910.599 113.7947 15208.3 14231.2 41837.2 40884.5 32.75 17.84 37~0 -4.3 -5.5 36.924 280.00 -805.303 -910.123 115.6550 16840.0 14895.3 43716.5 62776.9 39.39 28.05 47.0 -11.2 -1.3 48.3 rO 25 290.00 -767 938 -908 376 117.4494 18498.3 15569 5 45586.9 46650.7 39 99 31 76 49.0 -14 5 1 3 51 1 26 300.00 -734.054 -906.412 119.1639 20163.8 16245.7 47423.4 46506.2 52.35 32.40 60.7 -10.6 -5.6 61.3 27 310.00 -708.860 -902.945 120.8681 21878.1 16940.9 49280.7 48352.0 31.68 37.55 43.4 -22.9 10.9 47.9 28 320~00 -686.617 -898.718 122.4709.23605.0 17640.5 51119.8 50200.2 34.01 40.50 46.7 -24.8 11.9 51.5 29 330.00 -669.506 -892.483 126.0535 25363.5 18352.1 52962.2 52041.0 17.41 47.51 33.9 -37.5 27.5 42.5 30 340.00 -655.064 -885.162 125.5856 27137.3 19069.0 54793.1 53877.7 11.03 52.02 29.7 -44.1 34.9 40.1 31 350.00 -638.614 -877.417 127.0187 28860.6 19766.9 56548,5 55670.8 39.07 55.45 57~0 -36.8 20.8 64.6 32 360.00 -620.848 -871.198 128.3649 30539.1 20462.1 58236.9 57392.7 69.15 51.31 83.3 -21.7 -.6 86.1 33 370~00 -607.293 -863.655 129.6932 32251.9 21132.7 59941.1 59089.0 43.11 57.11 61.6 -36.8 19.7 68.8 34 380.00 -595.009 -857.846 130.9856 33972.9 21826.1 6[635.6 60788.3 41.64 49.75 57.2 -30.5 14.7 63.2 35 390.00 -583.196 -850.393 132.2139 35662.3 22506.4 63282.4 62459.0 50.16 59.55 68.8 -36.4 17.4 75.9 36 400.00 -571.441 -843.046 133.3821 37316.1 23171.9 64880.6 66081.6 64.26 61477 82.7 -33.2 10.7 88.5 37 410.00 -561.000 -836.270 134.5225 38976.6 23839.6 66471.7 65676.1 58.59 59.75 76.7 -33.4 12.5 82.7 38 420.00 -550.751 -829.120 135.6070 40600.2 24692.2 68015.0 67243.3 70.63 64.95 89.8 -33.8 9.4 95.5 39 430.00 -539.671 -824.547 136.6314 42173.1 25124.0 69499.4 68757.2 102.36 52.62 114.6 -10.4 -19.6 113.4 40 440.00 -531.907 -827.416 137.7362 43914.0 25822.9 71130.2 70314.8 63.10 3.58 41.3 12.8 -23.1 36.6 41 450.00 -523.882 -830.045 138.7898 45617.9 26506.4 72716.5 71922.6 57.12 2.74 54.0 18.9 -32.2 47.3 42 460.00 -519.086 -831.615 139.8757 47419.9 27228,9 74377.6 73566.0 8~77 9.33 11.6 -5.4 2.2 12.6 63 470.00 -515.010 -831.464 140.9367 69226.5 27952.9 76032.7 75205.1.23 15.0! 5.8 -13.8 11.8 9.2 44 680.00 -510.463 -830.989 141.9483 50998.0 28662.4 77643.9 76838.3 10.87 16.83 16.4 -11.5 6.9 18.8 45 690.00 -506.611 -832.588 142.9602 52808.6 29387.4 79279.4 78461.6 o46 3.43 1.7 -3.0 2.5 2.6 46 500.00 -503.674 -833.101 143.9613 54661.3 30120.8 80923.9 80101.6 -13.39 8.29 -9.3 -12.7 14.7 -5.7 47 510o00 -501.319 -837~799 144.9798 56532.3 30877.5 82610.7 81767.3 -22.28 -15.49 -26.5 6.0 1.0 -27.1 48 520.00 -500~249 -841o668 146.0120 58472.5 31653.5 84331.1 83470.9 -60.88 -11.04 -42.0 -5.1 15.8 -39.3 SATURN SA-9 WIND RESULTS Table 1

VII ERROR ANALYSIS Four sources of errors are considered in this analysis. 1) Error in the measurement of sound arrival times at each microphone0 This introduces error in the derived value of characteristic velocity Kxa Kyo 2) Error in the speed of sound profile. 3) Uncertainty in the position of the noise source with respect to the vehicle0 4) Error from plane wave assumption0 7ol Sound Arrival Time Error It will be shown that error in characteristic velocity determination is the most significant contributor to wind error, The errors in the jth layer winds due to a characteristic velocity error arise from two distinct sources6 First, an implicit error is introduced in the winds because the result of the ray tracing to the top surface of the (jl1)5t layer is displaced from the actual point of penetration0 Secondp wind th error is introduced explicitly in the j layer from the error in Kxjp Kyjo Both types of error can be studied from a consideration of Figo 90 The following equations are derived from inspection of this figure0 j-1 j-1 { Z AXk j Wx( Tj - Atk) } k=l k=l j-1 j-1 2 + { Z- AYk Yj W (t - T - Z Atk) }) k=l Y J k=l (26) zj)2 = avgj ( j k T- k) 28

(XJ,yj,j,Tj ) I-i,/ wX(Tj-T. - AY,) / J WY(j TJ-1 ZA1K), K1u Kiu b// Kul Ki- I Kul THE ARRIVAL OF THE JTH NOISE EVENT AT J-1 J-1 i-x i-YZ-l) Fig. 9 29

This is simply the expresTsion of an expanding spherical wave in a moving medium. j-1 j-1 The direction cosines of the ray at ( AxkI Z Ayk# z.1) are k=l k=-1 j-1 x. + Wx At. - ~ Axk 1 = 3 ] k=l (27a) avgj j j-1 y + W At. z Ayk = _ Y 3 k=l (27b) V.At. avg atj Z - Zj Y,.._.....,....~~_.~.... _.(27c) V At. avgj J j -1 where Atj = T Tj - Z Atk The characteristic velocities are then K av -+ a + W +/a (28a) xY~ x'' For simplicity in writing let j-1 j-1 V Vavgj; x =xk etc; to Atk ag k=l k=l Keeping in mind that the trajectory gives Xj = x (T). Yj = yj (T) (29) z. = z. (T) and that t = T - Tj - to the above equations can be rearranged to give 30

F(KxOKyWxWy.Tj,totxovyOrV) = (Kx'Wx) (xj'Wxatj-xo)+v2 Atj-W (yj+ t -y ), O ('Yo G (KxrKyWxrWyTjtofxoyov) = (Ky-Wy) (yj-Wytj-yo)+V2Atj-Wx(xj+WxAtj-xx ) = O (31) H (KxKyWxWyTj,toxoyO)v) = (xj+Wx4tj-xo) +(yj+WyAtj- o) 2 (32) J = a (FGH tj) t= GW G GT (33) x f x Kx W0 T Treating W W a nd T as deptbe Ja' bian awa K WV T (34) aKa T X-X y F FT |Ft FH FT -a- _ I w T (35) ax0 j atO F FF F and similarly for aWx W aW ^ W W and GK' G, T aKy ay0 aX a7 X W ay xO Wy T o;' y "~T AW)x'W au o Jw ao J ~W ~

The partial derivatives of W with respect to xo, yo, and to give,an indication of the first type of error, mentioned earliero The derivatives of W with respect to characteristic velocity are a measure of the second typed The total error in jth layer winds due to an error in the jth characteristic velocities is: Wx (X) AK + X AK + Ax+Dx AKy + ~+ Aye Wx (y. (xW) Ax0 y0 + 0 J KX j aKx j J y j j ay o A similiar expression can be written for AWy J In order to evaluate AWx, it is necessary to evaluate Ato0 Ax_ and Ayo These parameters are computed by ray tracing each value of Kx and Ky to the level Zj l, The error in the characteristic velocities can be related to errors in the measured time of arrival at the mth microphone by Am x (37a) AKy mAAy (37b) Calculated values of AWx and AWy are shown in Fig, 10 and 11 and are listed in Table 2 along with actual differences from wind computations for errors of d5 ms and 2 ms0 These computations were made for - = 100,150,200,250 etc, These time of arrival errors are introduced into every microphone pair and in the same direction to maximize the resultant wind errors - An interesting observation from Table 2 is that the errors in the jth layer winds caused by errors introduced into the characteristic velocity for that layers result in a nearly equal 32

90 ALT ( KM) 80 70 60/ 50 EXPECTED MAXIMUM WIND ERROR 30 DUE TO.5 MS ERROR IN ALL MICROPHONE TIMES 20 Altitude vs. AWX, Wy * AWx Fig. 10 10 0 1 2 3 4 5 6 7 awX*AWY (MIS) 33

ALT (KM) 8070 60 40. 30 EXPECTED MAXIMUM WIND ERROR DUE TO 2 MS ERROR IN ALL MICROPHONE TIMES.,AWx x AWy Altitu4e vs. AWx.AWy 10 Fig. 11 0 2 4 6 8 10- 12 14 16 ~ 18 20 22 AW,,AWy (M/S) 34

WIND MEASUREMENT —ERROR ANALYSIS (SA-9) ERRORS DUE TO.5 MS. ERRORS DUE TO 2. MS. COMPUTED ACTUAL COMPUTED ACTUAL TAU ALT DWX DWY DWX DWY DWX DWY DWX DWY SEC METERS M/S M/S M/S M/S M/S M/S M/S M/S 50 436.00.00 -.00 -.00.00.00 -.00 -.00 60 1443.00.00 -.00 -.00.00.00 -.00 -.00 70 2804.00.00.00 -.00.00.00.00 -.00 80 4502.00 *00 -.00.00.00.00 -.00.00 90 6374.00.00 -.00.00.00.00 -.00.00 100 8326 -.33.48 -.32 *48 -1.31 1.93 -1.32 1.93 110 10289 *30 -.56 *33 -*51 1*25 -2.28 1.55 -2.25 120 12214 -.01.01 -.01.01 -.25 *18 -.23.22 130 14095 -.01.01 -.00 *00.00.01.01 -.00 140 15951 -.00.00 -.00.00 -.01 *02 -01.01 150 17805 -.71.86 -.71.87 -2.84 3*46 - -282 3.44 160 19683.62 -,90.80 -.98 2.47 -3.57 2.94 -3*54 170 21605 -.16.10 -.10 *16 -.19.11 -.10.16 180 23559.02 -*31.C1 -.02 *00 -.00 -.00.00 190 25518 -00.00 -.O.0o0 o00 -.00 -o00.00 200 27470 1o57 1.28 1.56 1.28 6.28 5.10 6.22 5.05 210 29415 -1l82 -1*40 -1l59 -1*30 -7.32 -5*60 -6.39 -5.37 220 31360 -.00.00 -.00 -.00 -e13.09 -.02..04 230 33280 -.00.O0 - 00 -.00 - 11.06 -~03 *09 240 35176 -.00.00 -.00 - 00 -.01 -.00 -.01 -.01 250 37071 2.37 1'87 2.35 1.85 9.46 7*48 9.28 7*32 260 38975 -2.79 -2.00 -2.34 -1.91 -11.15 -8.02 -9.45 -7.53 270 40885 -.04.06,04.10 -.04.06.02 *09 280 42777.00 -.01.01.00.00 -.01 -.01 - 01 290 44651 -.00 -.01 -.02 -.03 U00 -O00 -.ul -,01 300 46504 3o24 2.54 3.24 2.52 12.98 10.07 12.52 9.74 310 48352 -3.76 -2 74 -3.01 -2.50 -14.99 -11.00 -12*.56 -10.43 320 50200 -.01 -.30.02.01.03.07.05.06 330 52041 -.02 -.00.01 *01.04.01.03.02 340 53878 -.02 -.01.01.01.04 -.02 -.01 -.02 350 55671 4.00 3.40 3.99 3.38 16.09 13.60 15.21 12.96 360 57393 -5.96 -4.08 -4.85 -3.71 -23.72 -16.30 -2U0.6 -15.67 370 59089.03.00 -.01 -.01.37.07 -.19 -.11 380 60788.03.00 -.01 -.01.42.09 -,18 -.10 390 62459.03.01 -.01 -*01.46.08 — 22 -.13 400 64081 5.97 4.69 5.79 4.58 24.18 18.80 21.54 17.22 410 6-5676 -7.38 -5.16 -5.97 -4.75 -29.05 -20.57 -25.90 -20.36 420 67243.06.03.02.03.94.19 -.46 -.29 430 68757.07 -.300 -.03 -.02.99.28 -.56 -.29 440 70315.07.01 -.06 -.05 1.08.38 -*22 -.08 450 71922 6.25 4.32 6.04 3.90 258.7 16.30 22.09 14.37 460 73546 -5.68 -3.99 -4.49 -3.64 -21.76 -15.67 -19.63 -15.66 470 75205 -.03.01.08.06 1.07.34 -.11 -.08 480 76838 -.06 -.04.02.00 1.14.36 -.07 -*05 490 78462 -.06 -.04.02.01 1.09.33 -.15 -.i2 500 80102 4.30 3.34 4.36 3.87 18.59 15.87 15.71 14.20 51'0 81767 -5.03 -3.61 -4.00 -3.31 -18.61 -13.75 -17.09 -13.91 520 83471 -.09 -.01,07.05 1.07,36.01.02 WIND ERRORS DUE TO.5 MS AND 2.0 MS ERRORS IN ALL MICROPHONE TIMTES Table 2

and opposite error in the (j + 1) layer and practically no error thereafter, Thus, averaging 3 successive layers can reduce the percentage error approximately by a factor of 3d This however has the undesirable effect of decreasing resolution by 1/3d This suggests the possibility of varying the initial layer thickness, (thereby changing single layer errors) until both the resolution and the accuracy are optimized0 Some effort was made along these lines but no significant gains were realized, In order to simultaneously improve accuracy and resolution of the result it is necessary to decrease the error in the input datao Repeated reading of arrival times exhibit a scatter that indicate the uncertainty in the arrival times is between 2 and 2o5 msd The system parameters were chosen on the basis of uncertainties of about half this value, This larger error is attributed to slight differences in microphone characteristics, differences in local background conditions, and to limitations in manual reading of this type of data presentation, To the extent that these effects are random the errors can be reduced by using a computer programmed for cross correlationo In such a program the time difference between two channels is determined by an integration over a preset segment of the data rather than from a single wave forms thus reducing small random errors Automatic cross correlation has not yet been used because of prohibitively high computer time requirements, but recently acquired equipment,0 and an improved programming method hold promise for this technique0 36

The use of higher frequencies of the noise spectrum also offers the possibility of increased precision in determining arrival time. Experimentation with wide band microphones is planned to evaluate this possibility. 7.2 Errors in the Speed of Sound Profile The temperature up to 30 km is measured by radiosonde and an accuracy of + 1~C is claimed for these data, Above 30 km the temperature data are estimated to be in error by a maximum of 10~Co aw aw x- A V and A.V AV for a single layer can be calculated av av readily by the analytical technique described above, However, to account for the speed of sound errors in lower layers a different approach must be followed. A straight forward way of estimating these functions is to modify V(z) and compare the resulting winds. This was done as follows: Using the speed of sound profile as given in the trajectory a "standard" wind profile was determined. Then V(z) was replaced by 1) V(z) + 2 m/sec, for z > 30 km (2.70 3,3~C temperature error) 2) V(z) + 5 m/sec, for z > 30 km (6.8 - 8,3~C temperature error) and new wind profiles were derived, These should represent a"worst case" analysis since a constant displacement gives largest errors in the integrated speed of sound, Fige 12 shows AWx and AWy as a function of altitude for these two cases, 37

90 ALT (KM) 8070 60 * AW 3,} 2M/S DISPLACEMENT OF V(Z) x AWJ Aw' 50 x [X Ai Wy 5M/S DISPLACEMENT OF V(z) WIND ERROR DUE TO 40. ERROR IN V(Z) Altitude vs. AWx, AWy Fig. 12 30 1 I I 0 1 2 3 4 aW u, AW (M/s) 38

7,3 Noise Source Position Uncertainty The mechanism of exhaust noise generation is fairly well understood, but there remains an uncertainty in the precise location of the noise source with respect to the vehicle. For the SA-9 data, the source was assumed to be on the trajectory 150 meters aft of the nozzle. To determine the sensitivity to an error in this,estimate, the position of the source was displaced 100 meters and a new wind profile determined. Figure 13 shows the results of this displacement and indicates that this error is probably not significant, 7.4 Error from Plane Wave Assumption The wave front deviates slightly from planar and to estimate the amount of error this induces, a spherical wave is considered Figo 14 is a schematic of two microphones equally spaced about the origin of a coordinate system6 A source of sound is located at (x', yo z') in this system0 It is assumed that the temperature is constant throughout (Constant speed of sound, V) and that the winds are zero0 Since R is large compared with yo a plane wave approximation at the array should be nearly correct, The time required for such a plane wave to ctoss the array is: t-yo t+yo (38) -yo V R The time interval for a spherical wave is,I tay - t+y0 = V {x'2 + z.2 + (y' + y0) ] - Lx'2 + z'2 + (y' - y) ]) (39) 39

ALT(KM) 80.. 70 60 50 40 30WIND ERROR DUE TO SOURCE DISPLACEMENT 20- \ AWx "' X AW. Altitude vs. AWx, AWy Fig. 13 10 O.1.2.3.4.5.6.7.8.9 1.0 AW,.AWJ (M/S) 40

(x, y" z') R WAVE FRONT SPHERICAL WAVEFRONT INTERCEPTING 3 IN-LINE-MICROPHONES. x'~ ~ The Atmosphere ig AssUmegd Isothermal and at Rest. Fig. 14 41

Substituting R2 - xo2 + y 2 + z e and expanding the square roots 3 t o t+yO = V [2y~ i Yo. + d] Yo Yo 3 V (R.-y + o (40) The first term is just the plane wave term" Note that the second order term in yo/R is absent, This is due ito the symmetrical use of the two microphones about the origino This term always disappears if microphones are taken in such pairs6 A three microphone array therefore could not be used in this manner and the error due to the non.plane wave would be correspondingly greatero For the array used during the SA-9 launch yo for the extreme microphones is about 600 meters, After the vehicle has reached maximum rawinsonde altitude R is at least 30,000 meterso In, - this case Yo/R 2 x 10=2 and (yo/R)3 8 x 10~60 Since the time tyo0 t+yo is on the order of 2 second sov V o5 x 1020 The spherical term is then about 1/2 ms6 Therefore" this size array is compatible with the accuracy (1 ms) desired in the reading of microphone times0 42

V'" CONCLUSION The agreement between the wind profiles determined by the Rocket Exhaust Noise Wind Technique and other simultaneous measurements during the flight of the SA-9 is evidence of the validity of the acoustic technique described herein, On the basis of the error analysis, the maximum errors in the SA-9 wind profile are estimated to be about i 20m/s at 85Km6 and decreasing to about-+ 7m/s at 30Km6 These errors are attributed principally to inaccuracies in the reading of the microphone arrival times and should be reducible to about + 5m/s at 85 Km, to + 2m/s at 30Km6 by the use of improved data reduction techniques6 At locations where large booster rockets are launched regularly, a rather modest ground station can gather wind data from the ground to, in some casest 85Km8 These data measured concurrent with the rocket flight have important engineering value0 and the upper atmosphere wind profiles measured-on a regular basis would be an important supplement to the data available to meterologists6 43

REFERENCES 1) Nordberg, W, "A Method of Analysis for the Rocket-Grenade Experiment," U, S, Army Signal Engineering Laboratories Technical Memorandum NRo M-1856, February 19570 2) Stround, Wo Ge, W6 NordbergF W, R~ Bandeen# F, La Bartman, and P0 Titus, "Rocket-Grenade Measurements of Temperature and Winds in the Mesosphere over Churchill Canada," JJ Geo h sical Research, 65, 2307-2323, 1960o 3) Stroud, WO Go, Nordberg, W, and Walsh, Jd R61 "Temperatures and Winds between 30 and 80 km," JO Geo hZsical Researchh 61 45-56, 1956 4) "Ground Support and Data Analysis and Associated Research and Development for the Rocket Grenade Experiment," Final Report-, September 1962, Edited by At Md Parra, Schellenger Research Laboratories, Texas Western College, El Pasop Texas, 5) Otterman, J J I"A Simplified Method for Computing UpperAtmosphere Temperature and Winds in the Rocket-Grenade Experiments" Univo of Micho Tech, Report 2387-40-T, Army Contract Nod DA-36-039-SC-64657, June 1958d 6) Milne, E0 Ad, "Sound Waves in the Atmosphere," Phil, Ma 42 96-114, 1921. 44

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