P HE UNIVERS IT Y OF MI C H I G AN COLLEGE OF ENGINEERING Department of Aeronautical and Astronautical Engineering High Altitude Engineering Laboratory Interim Technical Report SINGLE-STATION DOVAP-BALLISTIC CAMERA TRACKING REDUCTION FOR GRENADE-EXPERIMENT ROCKETS S.S, 12.50 —S.S. 6.58 Submitted for the project by Melvin G. Whybra Approved by: F. L. Bartman L. M. Jones UMRT Project 2387 under contract with: DEPARTMENT OF THE ARMY PROJECT NO. 3-17-02-001 METEOROLOGICAL BRANCH, SIGNAL CORPS PROJECT NO. 1052A CONTRACT NO. DA-36-039-sc-64659 FORT MONMOUTH, NEW JERSEY administered by: THE UNIVERSITY OF MICHIGAN RESEARCH INSTITUTE ANN ARBOR March 1960

TABLE OF CONTENTS Page LIST OF TABLES v LIST OF FIGURES vii THE UNIVERSITY OF MICHIGAN DATA-REDUCTION PERSONNEL ix ABSTRACT xi 1. INTRODUCTION 1 2. TRACKING INSTRUMENTATION 3 3. MATHEMATICAL STATEMENT OF PROBLEM 5 3.1 Basic Solution for Position 5 3.2 Correction for Variation of Refractive Index with Altitude 15 3.3 Guam Geometry Correction 21 3.4 Computation of the u Values 24 4. THE LGP-30 PROGRAM FOR GRENADE BURST POSITIONS 25 4.1 Table of Average Refractive Indices 25 4.2 Description of Computation for Position 25 4,3 Program Constants 26 5. TRACKING DATA 33 501 Ballistic Camera Data 33 502 DOVAP Data 34 6, COMPUTED BURST POSITIONS 37 7. ERRORS 39 7o1 Resolution of Horizontal and Vertical Coordinate Errors 39 7.2 DOVAP Errors 40 7.3 Ballistic Camera Errors 42 8. CONCLUSION 45 REFERENCES 47 APPENDIX A. AVERAGE REFRACTIVE INDICES 49 APPENDIX B. BC/DOVAP POSITION PROGRAM CODING SHEETS 51 APPENDIX C. GRENADE TIMES AND DOPPLER COUNTS 63 APPENDIX D. GRENADE BURST POSITIONS 67 APPENDIX E. RESIDUAL VECTORS FOR GUAM FLIGHTS (METERS) 77 iii

LIST OF TABLES No. Page I. Guam Range Survey Data 28 II. Program Constants for Guam Range 30 III. Reference Frequency Log for Guam Flights (Mc) 32 IV. Average Frequency and Vacuum Wavelength for Guam Flights 32 v

LIST OF FIGURES No. Page 1. The Guam tracking instrumentation. 4 2. The relation of the (X, Y, Z) and (x, y, z) systems. 6 3. The ellipsoid as the affine image of a sphere. 9 4. Plane section containing n' and xl. 11 5. BC/DOVAP program flow chart. 27 vii

THE UNIVERSITY OF MICHIGAN DATA-REDUCTION PERSONNEL (Both Part-Time and Full-Time) Bartman, Frederick L., M.S., Research Engineer Harrison, Lillian M., Secretary Jones, Leslie M., B.S., Project Supervisor Kakli, G. Murtaza, B.S., Assistant in Research Kakli, M. Sulaiman, Ph.D., Assistant in Research Mosakewicz, Mary C., Secretary Titus, Paul A., B.S., Associate Research Engineer Whybra, Melvin G., M.A., Graduate Research Assistant ix

ABSTRACT A detailed description is given of the reduction of the tracking data for the nine USASRDL grenade-experiment rockets fired at Guam during November, 1958. Included in this description is the derivation of a mathematical solution for position in a single-station DOVAP-ballistic camera tracking system. A computer program embodying this solution together with corrections for the variation of doppler wavelength with altitude is discussed, and the grenade burst positions obtained from this program are listed together with the tracking data used to compute them. The observed errors in the horizontal coordinates and the estimated errors in the vertical coordinates satisfy the required tracking accuracy for estimation of temperature and winds from the grenade-experiment data. xi

lo INTRODUCTION As a contribution to the International Geophysical Year effort, nine solidpropellant rockets were fired by the U. S. Army Signal Research and Development Laboratories from the island of Guam in November of 1958.1 These vehicles carried aloft the rocket-grenade experiment to measure temperature and winds above 25 kilometers. This series of experiments at Guam represents a logical continuation of the series involving ten grenade-experiment Aerobee rocketsl fired at Ft. Churchill, Canada, during the I.G.Y. The flights at Ft. Churchill were also conducted by the USASRDL working together with the High Altitude Engineering Laboratory of The University of Michigan. In this series the U-M group was responsible for both the construction and operation of the rocket instrumentation, and subsequent reduction of the DOVAP tracking data.9 Tracking instrumentation for the Guam flights was constructed by personnel from the High Altitude Engineering Laboratory under the direction of Dr. Harold F. Allen and Mr. Elton A. Wenzel.4 This same group was also responsible for operation of the tracking equipment at Guam, where complete data recovery was achieved For each rocket, tracking data consisted of a single-station DOVAP2 recording and two ballistic camera plates. Direction cosines for each grenade burst were obtained for both east and west camera plates by the Ballistic Reduction Section of the Physical Science Laboratory at the New Mexico State University.3 These direction cosines, together with the corrected cycle counts obtained from film transcriptions of the DOVAP recordings, were used to obtain grenade burst positions. The reduction of these tracking data, done under contract DA-36-039 -sc-64659 at the High Altitude Engineering Laboratory of The University of Michigan, is described in this report. 1

2. TRACKING INSTRUMENTATION The tracking instrumentation at Guam consisted principally of (Fig. 1): (a) A 37-Mc transmitter radiating 1750 watts from a right-hand wound axial mode helix. (b) A 37-74-Mc transponder in the vehicle with linearly polarized, transverse-mode loop antennas for receiving and transmitting. (c) Two receivers with oppositely polarized helical antennas for the reradiated 74-Mc signal and stub antennas for the 37-Mc reference signal. (d) A single receiver with a dipole antenna to record polarization nulls occurring with rotation of the rocket. (e) Two ballistic cameras working in the visible region of light, one with an f:ll and the other with an f:16 stop setting. At the DOVAP receivers the 74-Mc signal from the rocket-borne transponder is heterodyned with the doubled reference signal. The resulting difference frequency, recorded for both helices along with time references, constitutes the DOVAP tracking data. The ballistic camera plates record the images of the grenade bursts and both pre-shoot and post-shoot exposures to obtain star trails which are interrupted at known times by opening and closing the shutter. These interruptions in the stellar images provide the plate calibration against which the burst directions are measured.

-P: I FREQUENCY MONITOR TRANSMITTER LAUNCHER I-~ Fig. 1. The Guam tracking instrumentation.

3. MATHEMATICAL STATEMENT OF PROBLEM 3.1. BASIC SOLUTION FOR POSITION The total change in the "transmitter to missile to receiver" path length during the interval from lift-off to grenade burst time is proportional to the spin-corrected cycle count accumulated over this interval. This spin-corrected count is obtained by differencing the total count of the two receivers, and then using this difference to correct the total count of one receiver. Using survey data, this same path length can be determined at lift-off and thus the path length at the instant of grenade burst is known. Now we do not know the "transmitter to missile" or "missile to receiver" distances, but only their sum; however, this sum serves to define a prolate ellipsoid (with the transmitter at one focus and the receiver at the other) on whose surface the missile must be. The position of the ballistic camera, together with the direction cosines of the grenade burst obtained from the ballistic camera plate reduction, define a ray through this surface and thus the grenade burst position is determined uniquely. This situation is represented in Fig. 2. In the cartesian system indicated by Fig. 2, let the coordinates of the ballistic camera be: X1 = (X, Y, Z1), and let those of the transmitter and receiver be, respectively: X2 = (X2 Y2, Z2) 3 = (X3, Y3, Z3) We are interested in solving simultaneously the equations defining a prolate ellipsoid and a ray through its surface. A simplification in the solution can be had by transforming the coordinate system to one in which the origin is at the center of the ellipsoid, and one axis (say the x-axis) is aligned with the major axis of the ellipsoid. By so doing, we will eliminate both the terms of first degree and the mixed terms of second degree in X, Y, and Z in the equation of the ellipsoid. Suppose then that we define a new cartesian system (x, y, z) whose origin is at (1/2)(X2 +X3), i.e., midway between the two foci determined by the trans 5

z z I I/ / y - - ON Y X3 X \ Fig. 2. The relation of the (X, Y, Z) and (x, y, z) systems.

mitter and receiver. Furthermore, let the x-axis be defined by the unit vector: x = - X2 X3 x- x() X3 - X21 2c where 2c = 3 - X21 (2) = (X3- X2)2 + (Y3 - Y2)2 + (Z3 - Z2)2 Because of the symmetry of the solution with respect to y and z, it is not necessary explicitly to define the unit vectors j and k corresponding, respectively- to the y and z axes. The coordinate transformation, defined for rowvectors, is then given by: x = (t+)S, (3) where T is the translation: T = - (2+ (X + ) (4) 2 and the rotation is S = 0\ (5) with the prime indicating transposition. Let us now define u as the "transmitter to missile to receiver" distance. In the (x, y, z) system the transmitter is at one focus (-c, 0, 0), while the receiver is at the other focus (c, 0, 0). -Since the sum of distances to the two foci is equal to twice the length of the semi-major axis of the ellipsoid, 2a, the semi-major axis is simply a = u/2 (6) and the semi-minor axis, b, of the ellipsoid is then b = -c (7) 7

The ellipsoid is then defined by the canonical form (Ref. 5, p. 366): X2 Z 1 a2 b2 b (8) Rather than solving explicitly for the point of intersection of the ray on this surface and then applying the inverse iransformation to the (X, Y, Z) system, we will determine instead an invariant under the orthogonal coordinate transformation, the distance, R, along the ray from the ballistic camera to the point of intersection. In the original cartesian system the point of intersection will then be = X + R N, (9) where the direction cosines L, M, and N, relative the unit vector to the (X, y, Z) system, form $ = (L, M, N). (10) Let us rewrite Eq. (8) in the form x2 +:, y2 + z2 a2 = b2 b2 0 (11) This suggests that we can think of the ellipsoid as the sphere6 affine image of the x12 + y,' + z'2 - a2 = 0 under the transformation (Fig. 3) (x', yl, z') - (x x', y = y, z (X = X'~~ = b z') a Suppose now that the camera direction cosines relative to (x, y, z) aye the components of the unit vector t = (It m, a) m t s, while the position vector for the ballistic Gamera is xl in the (x, y, z) system. 8

y a x DIAMETRAL PLANE CONJUGATE TOn' A yI a Fig. 3. The ellipsoid as the affine image of a sphere. 9

Then both n and xl will have counter images n' and xl in the (x', yt z') space. Consider now the plane section through the sphere containing xl and n' (Fig. 4). Let R' be the length of the line segment which is the counter image of the line segment of length R along the ray from XI to the surface of the ellipsoid. Then R' = -q+ -a2,- p2 (12) where -> ->. q = n - S |nt | and 2 In' x ll 2 2 = J — n ---1L x =2 -n hence,-. ->. n' * xl |n |' I/ 1". + 1 I2 /v |^|n (12a) n * xi + / a2 ( n ' ) - +'n x 'X 1 Under the affine transformation we are considering (Ref. 6, pp. 161-162), a parallel family of lines is mapped into a parallel family of lines; furthermore, the ratio of the length of a line segment to the length of its image is a constant which has the same value for all members of a family of parallel lines. Consequently, to determine R we need only observe that I - -L - I InR' |^ |'l (153) hence -. - — 1. 4. n' * n' -nf. xi I/a (n ~ n ) - I, x2 n. ~ t

Fig. 4. Plane section containing n' and x1. 11

Now we can write n' (= b m, b =) [ - (1 ) ( ~ ~, and similarly R b = a ) = a - (1 - b) (xh oa Remembering than = 1, we then have Remembering than C ~n - = 1 we then have (15) (16) n * n4 n, - n, a2 [ 2 b2 = a2 1 - 2 ( + 21- 2 a b a2 1 = L -A - } (1 _ b) 2] (17) and similarly n a b After some manipulation we also obtain b2) ] (18) In' xil2 a2 I —. >. 12 a 2 X11T + be b2 b 2 (n (n -> 2 Y.- 1) I (19) where Kn X X)X = (mzl - nyl) Substituting (17), (18), and (19) in (14) and observing that In x xi2 = - * ( ) - (n * X = (xi ~ X ) -(n. xi) we then have 12

a2 (> * b2 -- n x - =1x b2 a2 R = - -I -- a2 [ 22 I _12 a2/ -,ja2 L2 _ ( l r^12 b 2).. 1 2 2 2\ 21 (XI XI ) (n.x1) + n V. XI )X a2 - 2 a2 b2 - Lxx)-nX')"l ^JK -)K XJ\ 2 -/- r i2 a2 -f - $b2 b L a-j j which can be written as - ( -4 1) + (l - a2) Ixl + b2 i a2 b - 2i I / 2 2 - +2 1 + 1 2 2 2 _l(~ x l) + ] (n ~x)x ~ a27X a2 X1, )+a2fl1a2- a} - )X [1 ( - b2) 22] (20) We already have a2 = u2/4 and b2 = (u2/4) c2 So that - (- ~X) + 4c2 4 X2.( 4 2 i)2 \ U2 J + U - - 42c ~2\ l 4 - 42 - ( 21 162 (4 s ) 23 - - c1 L tC2 1 +Xjj - x - C4 ( —n> (1 4 2 22 U / (20a) Now in this expression for R there are terms involving scalar products and vector components. Since scalar products are invariant under coordinate rotation, we can make the following substitutions Let X = X+ T Xi = X1 +T; (21) then X I~ X? -> - Xi * Xi = Xi ~ Xi 0 13

Also 1t * = n x In addition + - = i * N and X1 = i * Xi We also have (n x xx = * ( X1 = * (X1 ^ i) Thus we can rewrite our solution for R in terms of the parameters = i ~* 1 = X 5 = Xz * X1 xl*x = X1 - xl * xl (22) 4. " +, I v = Xi X i and the auxilliary variables q = i ~ N = ~ a = N X = n * x 4 = N v ( - n iT = N * v = (n xl )X (23) as follows - + 2 c Q + J( uaJc - c2)[( 4 c22 u2 4 _2 42 4 2 U2 U2 U2 1 - C 22c U2 (20b) Equations (9) and (20b) then constitute th complete solution for position in the original cartesian system. 14

3.2. CORRECTION FOR VARIATION OF REFRACTIVE INDEX WITH ALTITUDE It has been shown elsewhere7 that systematic errors of the order of several doppler wavelengths in the "tttransmitter to missile to receiver" path length can result if the DOVAP propagation velocity is taken as the mean of the sea-level and vacuum velocities. Consequently a correction for the variation of the propagation velocity or the index of refraction is indicated. An adequate approximation. particularly at radio frequencies, for the functional dependence of the index of refraction,., on atmospheric density, p, is given by p. -1 = kp (24) for some constant ko Thus, if 0o is the refractive index at the standard sealevel density, po, k = (po - l)/po and (24) becomes p.-1 =4 ( -l1to ) p (25) Po Now we wish to determine an average refractive index 1((Z) such that the average propagation velocity of radiation traversing the altitude interval from Z1 to Z is Ei(z) = (26) ~i(Z) where co is the vacuum velocity. Since p = p(Z), the propagation velocity at any altitude Z is c(Z) = (27) 1 + (po. l) p(Z) PO Suppose that the ray defining the direction of propagation makes an\ angle of 0 with the vertical; then for the infinitesimal altitude interval, dZ, the distance propagated is ds = sec 0 dZ. Thus the total time to propagate from altitude Z1 to Z is z 1 + (p -1) p(Z) t = L P0o- see dZ (28) Z1 Co = sec (z Z) + (o -1) p( ) dZ Co I Zz Po f 15

whereas the total distance, s, propagated.is simply sec 0(Z - Z1) average index of refraction is Thus the Co 41(Z) = (s/t) = 1 + (z - z1) z Po() dZ z -1 (29) or.1(l(z)- 1 o - 1 1 Z - Z Z 7 p(Z) dZ Z1 Po (29a) It should be noticed that the tacit assumptions of straight-line propagation and small earth curvature relative to the atmosphere's effective thickness have been made. We would now like to express (29a) in terms of the average refractive index relative to sea level, given by 7i(z) = 1 + ( 1) S z. 0?(zaz P(Z) d po (50) To do this we rewrite (29a) as follows:;i(Z) - 1 o - 1. z - Z1 i p(z) Po dZ - f p ( dZ 0 Po Z Z - Z1 L o Po J Z1 1 Z- Z1 Z1 Z p(Z) o Po or jt (z) - 1 = 1 [z( (z) - 1) - z1( (z1) - 1)] Z - Z1 (31) To evaluate the integral expression given by Eq. (30), it is necessary to know the functional relationship of density versus altitude; however, such a relationship is at best an average determined for one locality on the earth's surface. To make our equations of more general applicability, we will adopt a simplified static model of the earth's atmosphere. 16

At every point in this model there will be no acceleration and Euler's dynamical equation will require that the gradient of pressure be everywhere normal to the equipotential surfaces defined by the earth's gravitation field. Consequently, pressure will be constant-along each equipotential surface. Furthermore, to insure hydrostatic balance, Euler's equation would also require that density (and hence also temperature) be constant along each equipotential surface. Thus it follows that by adopting such a model a single density versus geopotential altitude profile will be everywhere valid. Now it has been shown elsewhere that a very good approximation to geopotential altitude, H, in terms of the actual or geometric altitude, Z, is given by the expression (JIQ\ rZ H = r+) r(32) where go is the local acceleration due to gravity at sea level. G is a conversion factor depending on the units of H, and is numerically equal to the standard acceleration due to gravity when H and Z have the same units. Also, r is the earth's effective radius given by (Ref. 8, Appendix M): r - g0 zJ (33) If Z and Z' are altitudes at two separated locations on the earth, then the geopotential altitudes of these points will be the same when (go) rZ r= *Zi (54) \ G r + Z \G ro + Z Here g* and r* are values at the location which corresponds to the primed altitude. Thus H(Z') = H(Z) when?.(go/g)Z (5) 1 + E' Z/r where e'= 1- o. (36) gOr* Similarly, - (g* /g0)Z' Z = + Z/, (37) 1 + e Zt /r* 17

where g*r* C = 1 - -g' gor (38) Let us now evaluate the integral Z p(Z) f dZ o Po in terms of the primed altitude Z' which we will assume corresponds to some location relative to which the density-versus-altitude dependence has been established. From (37) we have dZ =.(go/go)dZ' [1 + e(Z'/r*) ]2 (39) Also, because (Zt') = H(Z), we have p(Z') = p(Z), and as a result Z p(Z) f dZ 0 Po Z' (Z) p(Z') o Po (go*/go) dZ' [1 + e(Z'/r*) ]2 (40) Now when c(Z'/r*) I < 1, we can write: Z / p(Z) dZ o Po z (z) 0 = (gg/go (g /g ) p(Z') - 2e - + -....... dZ Po.,.. Z ' P(Z) o 'oZ(Z)rf - -3 [ Poo, Po0 This expression is an alternating series so that the remainder after any truncation of this series is less in absolute value than the last term. Let us now evaluate each term of (40a) successively to establish where it can be truncated with sufficient accuracy. If we assume the atmosphere is approximately isothermal, then we can write p(Z') Po = P e(Z' - Zl)/h Po (41)

where pi is the density at altitude Z1 and h is the scale height. Since the term of nth order in (40a) contains the quantity (Z/r*)n, the higher-order terms become more important at higher altitudes. Instead of evaluating the integrals of (40a) over some interval from sea level to the highest altitudes of interest, we will evaluate them over a small interval near the highest altitude to be considered, so that the relative importance of the higher-order terms will be more evident. Thus from (41) we have Zf 7 P(Z') dZ' Zz Po = ~i e-(Z' - Z4)/hd Po Z1 = - P h e-(Z' - Zi) Po /h] Z' -k Z, (42) = h iP P. Upon integration by parts we also Pobtain Upon 'integration by parts we also obtain zt Z1 po ()j dZ' p- P h z e-(Z - z)/h p0 r* + h -(Z' - Z3)/h Z + h Z1 = h a.pl Po (Z + h) p, p r* pO (Z' + h) r* Also upon solving (41) for scale height, h, we obtain (Z' - z7) (44) loge Pi/Po - loge P/Po Now let t Zi = 155 km Z' = 140 km 19

Then from the ARDC model atmosphere we have P/PO = 3.5071 x 1-9 PI/Po = 5.8886 x 10-9 Substituting in (44), there results h = 5 = loge 1.67905 9.6484 km. Let go and r be defined for 0~ latitude, and go and r* be defined at the reference latitude of 45032'40". Then by differentiating the Lambert series (Ref. 8, Appendix N) for gravitational acceleration as a function of latitude, 0, and altitude, we have Z=o az- Z=o -=.0 2 x cos 2- (se 2 =.085462 x 10 + 2.27 x 10 Cos 2 (se ) (45) Using the values go = 9.78039 m/sec2 g9 = 9.80665 m/sec2 we then obtain from Eqs. (45), (33), and (38) e = 0.0061295 r* = 6,356.77 km Now and also (z P p/ r(Z + h) _ r* Po 2.3815 x 10- (Z- + h) = 0.051432 x 10 v - v Pl Po 20

so that 2c x 0.051432 x 109 = 0.0006305 x 10-9 Thus in the altitude interval from 135 to 140 km the relative importance of the first two terms of the series expression (40a) is indicated by the rati 2.3815 x 10-9 0.0006305 x 10-9 Since the relation of refractive index to density, given by (24), is not valid for ionospheric propagation, the resulting equation for average refractive index, T(Z), given by (30), is not valid for altitudes greater than ca. 100 km, and consequently this last result implies that we can truncate the series expression (40a) to the first term within the region of applicability of (30). Thus we will have Z P(Z) Z'(Z) P(Z,) f dZ (g/go) f dZ 0 Po o Po or from (30) and (35) -(z) = - 1 1Z (z) dZ' Z= 1 + z- (Z/r) ] o zP (46) + [zt(z(z)] 16) 1 + C' Z/r where Z'(Z) is given by the relation (35). Equations (46), (35), and (31) now allow us to compute an average index of refraction at any location in terms of a single standard table of average indices of refraction at our reference latitude. For any latitude we need only first to evaluate the sea-level acceleration of gravity, go, and the earth's effective radius, r, via Eqs. (33) and (45). 3.3. GUAM GEOMETRY CORRECTION At Guam the transmitting antenna is a right-hand helix; consequently the left-hand receiver will normally see a phase shift of ~1 cycle every missile rotation while the right-hand receiver will see a phase shift of ~53 cycles.9 If we designate the total cycle counts from lift-off as NLH and NRH, respectively, for the left-hand and right-hand receivers, then the difference N = NRH - NLH (47) 21

will be entirely due to missile spin when the two receiving antennas are coincident, and will increase by ~2 cycles for each missile rotation. For this situation the spin-corrected cycle count is simply 1 N1 = NLH- N (48) If the antennas are at different locations, the separation of their phase centers will result in a phase difference which will contribute further to N'. To be quite precise, these helical antennas lack a fixed phase center because of the variation of phase over the lobe; however, if we assume that the phase center is located at the center of the ground plane, we will in no case make an error of more than a quarter cycle. Since both cycle counts are used to obtain a spin-corrected count, the counts from both receivers must be referred to a single location by making an equivalent phase correction. Suppose, then, that we refer both counts to the location of the left-hand antenna. Let X be the position of the missile and -L and XR be the positions of the left-hand and right-hand antennas, respectively. Because of the separation of the antenna phase centers the left-hand count will be higher than the right-hand count by the amount = A Ix - XLI, - XRI ) = _, (49) where A indicates the total change in the bracketed quantity from lift-off, and x = ~o/%i(Z) (50) with \o as the vacuum wavelength. For the Guam range geometry, a very good approximation is given by 1 - XL - XRI X (R- XL) = ~ N (51) where s = (IR - aL) and, as before, ~ has as its components the direction cosines determined by the ballistic cameras. As a result s T~[ ARo N* = _. _. (, (52) 5A ko 22

where ARo = (IX - XLI - IX - XRI at lift-off, and. 1 is the index of refraction at the mean altitude of the ground array. Since the difference in phase between the left-hand and right-hand receivers due to the separation of their phase centers is then N*, the right-hand count corrected to the location of the left-hand antenna is simply NRH + NV (55) and consequently the difference N5 = (N + N*) - NLH = NA + N* (54) will be entirely due to spin, whereupon the spin-corrected count becomes = LH i (LH N - N) - -N = N - 1 N N =NLH 2 - LH 2 2-L1 2 (55) Equations (48), (52), and (55) are tion. In particular, it should be the spin phase shifts are normal. over some interval, the correction 49-53): then the final form of our geometry correcnoted that Eq. (55) is applicable only when When the spin phase shifts are anomalous is, in general, of the form (see Ref. 9, pp. AN = ANLH + + Corr.) or AN = [ANLH + 1 A AN = [ANLH + 2 AN' + (Corr.)] +2 AN* AN2 + A AN* 2 (say) (56) = (AN2 + AN*) - AN* 2 where A indicates the change in the quantity over the interval in question. The quantity AN2, in particular, will be the result of the application of anomalous spin corrections to the cycle-count data over this interval. Thus if we wish to use the same form for the geometry correction as given by (55), we must correct the quantity AN2 by the additional amount AN* in this interval. In general, the correction AN* will be insignificant when anomalous corrections are applied over short intervals during all but the first few seconds of flight. This is especially true for the Guam range since the motion of the mis

sile is almost entirely radial and consequently the direction represented by N is virtually constant. 3.4. COMPUTATION OF THE u VALUES Suppose that at lift-off the Sum or the "transmitter to missile" and "missile to receiver" distance is uo; then the value of u at any other time will be u = + N~. _ (57) L /%o 7)1(z) where, as before, N is the corrected cycle count, ko is the vacuum wavelength at the doubled frequency, and p1 is the index of refraction at the average altitude of the ground array. Substituting Eqs. (52) and (55) into (57), there results Uo 1s. N _ 1 AR0 No u =4(i — I + Ni - - ~ 1 j ji1(z) 2 Uo = 1(uo + ARo) (59) and s has been previously defined as 1 1 s = (XR - XL) (60) Equation (58a) will then be the expression used to compute geometry-corrected values for u/2 in terms of the spin-corrected counts: N1 given by Eq. o r writing thi equivalent sum inng corrections of u/the (AN2 + AN*). The value of u/2 is, as a consequence, referred to the phase center of the left-hand helre Uo = ~i(uo + ARo) (59) and s has been previously defined as s = (xR - XL) (60) Equation (58a) will then be the expression used to compute geometry-corrected values for u/2 in terms of the spin-corrected counts N1 given by Eq. (48), or the equivalent sum involving corrections of the form (AN2 + AN*). The value of u/2 is, as a consequence, referred to the phase center of the left-hand helix.

4. THE LGP-30 PROGRAM FOR GRENADE BURST POSITIONS 4.1. TABLE OF AVERAGE REFRACTIVE INDICES A major aspect of the computer program for burst positions is the inclusion of a standard table of average indices of refraction versus geometric altitude, Z, for the reference latitude of 45032T'40" The actual tabular values are the average index of refraction less one, j-(Z)-l, as given implicitly by Eq. (30). The density ratio p(Z)/po versus altitude profile used to evaluate this integral expression is taken from the ARDC model atmosphere (Refo 8, metric table II). The value used for the sea-level index of refraction less one, (po-l), is 2.882 x 10-4, and represents a recent experimental determination at microwave frequencies.10 The integration of (30) is performed in a stepwise fashion by assuming the atmosphere is isothermal over each tabular interval of one kilometer in the ARDC table. This is equivalent to assuming that the scale height, h, in Eq. (41) is fixed over each altitude interval, in which case the contribution to the integral is given by Eqs. (42) and (44) with the integration being performed between the altitudes defining each interval. The actual computation was performed by a separate machine program, and the resulting values are listed in Appendix A for altitudes from sea level to 127 km. 4.2. DESCRIPTION OF COMPUTATION FOR POSITION To compute the grenade burst position from the spin-corrected cycle-count data and the ballistic camera data, we proceed as follows~ 1. Input: a. The spin-corrected count, N1. b. The camera direction cosines (j) (j = 1, 2 for the east and west cameras, respectively). 2. Bring the last computed value of 41(Z) and compute u/2 from Eq. (58a). 3. With the good approximation R ' u/2 compute the altitude Z as in Eq. (9), i.e., Z = Zo + N(j)R where Zo is the altitude of the camera. 4. Compute Z'(Z) from Eq. (35). 5. Look up the tabular value [Z'(Z)]-l. 6. Compute and store a new value for 1z(Z) using Eqs. (46) and (31). 7. Recompute u/2 from Eq. (58a) with this improved value of l11(Z). 8. Compute the "camera to burst" slant range, R, from Eq. (20b). 9. Compute an improved value for Z as in step (3). 10. Repeat (4) through (8). 25

11. Compute the burst position X via Eq. (9) (relative to the center of the geophone array). 12. Translate X to the system with the launcher as origin. 13. Repeat computation for the remaining camera. 14. Compute the average positions relative to both origins. 15. Compute the standard deviations. 16. Print out results and return to (1). The manner in which these steps are accomplished in the machine program is depicted by the flow chart (Fig. 5), and the actual coding of the fixed point program in machine language is reproduced in Appendix B. Existing LGP-30 library routines are used in conjunction with this program for both data input and output. Routine 11.4 is used to input tracking data. This routine converts nine decimal digits to 30 binary bits with a maximum error of one in the lowest-order bit. Results are printed out using data output routine 12.4. The print-out format consists of eight (or possibly nine) decimal digits with the proper decimal point location followed by a minus sign if the number is negative. 4.3. PROGRAM CONSTANTS With the exception of the vacuum doppler wavelength, \o, all the program constants depend upon a range survey. Such a survey was conducted for the Guam range by the Navy Public Works Center, and the results of this survey are listed in Table I for all relevant points. The elevations listed at all the stations are referred to mean sea level and were obtained by measurements relative to a station whose altitude is known very closely by barometric readings made over a long period of time. The surveyed point on the antennas is the center of the ground plane. The top of the mounting pedestal was surveyed for the ballistic camera positions, and the actual position of the optical center of the cameras is 1.52' higher than the survey point. The position of the launcher was taken as the center of the blackened circular area made by the rocket exhaust on the concrete runway. Since all the launching angles were close to the vertical, the initial position of the missile antennas on the centerline or axis of the rocket is assumed to be directly above this point. This vertical distance is three meters for the Aerobee 75 rockets and six meters for the Nike-Cajun rockets. Since the position data are used in conjunction with the sound-ranging data from the geophone array to compute temperature and winds above the array, it is convenient to refer the burst positions to some point in the geophone array. This point is taken to be the intersection of the two diagonal lines defined by opposing pairs of the four outermost microphones, and for this reason we list their positions in Table I. Since these lines are skew, we make use of the generally known solution for the least-squares intersection of two skew lines 26

START SWITCH NO.I Ia -< SWITCH NO.3 Fig. 5. BC/DOVAP program flow chart.

TABLE I GUAM RANGE SURVEY DATA Rectangular Coordinates Geographical Coordinates Stati on Elevation East North Longitude Latitude 1* 488021' j 199369.85' 214216023' 144~50'54" 13~ 36 '38 2* 488 31' 199365o06' 2142135 21' 144 50 54" 135036'38' 3 465.78' 201985 65' 214443 70' 144~51 20" 13~ 36 41" 4 484 34 199219042 214213.40' 144~50'52" 13~ 36' 38 5 4835 20' 199286.71' 214247,17' 14450'53" 13~ 36 539" 6** 475 55' 199770 96' 214510 34' 144~ 50'58" 13~ 36'41" 7 491.40' 199472534' 213531 51' 144~50'55" 13~ 36'32" 8 499.44' 196826 95' 214452 83' 144~ 50 28" 13~ 36' 411 9 519.92' 197898 62' 217195 72 144~50' 39" 13~ 37 08" 10 461o 76' 200238.21' 216367,57' 144051 '03" 135 37 'oo 1 f:ll, east1 1 f 116, west Ballistic cameras 2 f l 6, westJ 3 Transmitting helical antenna 4 Left-hand 5 Rght-hand -Helical receiving antennas 5 Right-hand 6 Launcher 7 No. 1 8 No. 2 9 No. 3 Microphones (geophone arra] 91 No. 4 10 No. 4 Y) *Add lo52? to elevation to obtain position of optical centero **Add 9,84' for Aerobee 75, and 19o68' for Cajun, to obtain antenna.o (identical in form to the solution for position from two fixed cameras). Let (0)(j = 1,..., 4) be the position vectors of the geophones, with the index counting clockwise from microphone 1. Define -> = X(2) -(1) Xi 2 x - x X193 (3) - ) = X - (61) 4-(4 ) -) ( X2y 4 x - and 28

,1 = (Xi1,2 X2,4) * (X j3 A X254) IX ] ' X2,4)| (62) (X1,2 x X1,3) ' (X1y3 x X2,4) P2 = 2 (P = 3 x X2,4) 2 then the point of closest approach on each line is X = plX- ) + (1 - pP1) ) (63) = p2X( + (1 - p2)X and the least-square solution for the point of intersection is X* = 1 (x1 +x2). (64) + = (64) 2 Using the positions from Table I and Eqs. (61) through (64), we have the result = (198639.59', 215470.08', 492.96'), which we will refer to as the center of the geophone array. Let us establish a right-hand cartesian system by orienting the x-axis eastward, the y-axis northward, and the z-axis vertically. Then with the survey data from Table I and the relations developed in Section 3, we can evaluate the range parameters necessary for the machine program. These parameters, together with a reference to the equation used to compute them, are listed in Table II. The quantities have initially been computed in feet and then converted to kilometers using the conversion factors: 1 foot = 3.04800610 x 10-4 kilometer 1 foot2 = 9.29034116 x 10-8 kilometer2 In these computations the position of the ballistic cameras is taken as the position of the optical centers, and the initial missile position is taken to be the location of the antennas along the missile axis. The positions of the ballistic cameras, X1, are referred to the center of the geophone array so that if Xo are the survey coordinates of the cameras, then X1(2) = X( ) - X (65) 29

TABLE II PROGRAM CONSTANTS FOR GUAM RANGE Vector Quantities (km) X Y Z t ~ Eqo (1)* -o 996530013 -o 082965213 0o006686211 Xi (1) -0o 375725 -0o034235 o 004471 (2 Eqs (4), -0o577185 -0.055156 0.004502 'v(1) 1 o o000142 -,o001944 -0.002944 / ^ 2 53rd Eq. of (22) v(2) rd Eq 0o000138 -000o1964 -0,003741 s Eq. (60) 0,020510 0.010293 -0.000347 X~i( ) ) 0.222584 -0o382174 -0,000985 Eq. (65) X1 (2) 0.221124 -0o383095 -0o000954 AX Eq. (66) -0o344842 0.292529 0.005307 Scalar Quantities c2 Eq. (2) 0 178964742 (km2 0,377291 (km) (.2) 3 1st Eq. of (22) 0 (km) 0.378823 (km) 6(1') 0o142361066 (km2) 2nd Eq. of (22) b(2) J 0o143524457 (km2) Zo 0o 149285 (km) Zz See text o 146581 (km) (go/g*) 0 997609581 (e'/r) Eqso (33), (36), (45) 0,85818269 x 10-6 (km-1) [jT(Z1)-l] Eqo (35)and Appendix A 0o00028622 Uo/2 Eq. (59) 0o439007 (km) (Aerobee 75) 0o439035 (km) (Cajun) * i is dimensionless, 50

The vector 4X is the translation which transforms a position vector relative to the center of the geophone array to a position relative to the launcher. Thus if IL is the survey position of the launcher, we define =X -. (66) ZO is the average altitude of both ballistic cameras used to compute altitudes above sea level for interpolation of j1-(Z), as in steps (3) and (9), Section 4.2. Z1 is the lower limit of the integral expression for jl(Z) and is obtained by taking the average of the mean sea-level altitudes of all the DOVAP antennas at lift-off, i.e., the average altitude of all the ground antennas taken together with the mean position of the missile antennas at lift-off. The quantity j(Z1)-l, used in expression (31) to compute 41(Z), is also listed as a constant. The values for g* and r* were taken from Ref. 8 and are identical to those used for the computation in Section 3.2. The sea-level acceleration due to gravity, g, at Guam was computed from the expression for the latitude variation of gravitational acceleration which appears in the Smithsonian Physical Tables: g = 9.806160 (1 -.0026373 cos 20 +.0000059 cos2 20) (m sec-2) At Guam we take 0 = 13036'38", in which case g = 9.783208 (m sec-2) In addition to the constants which appear in Table II, we also require a value of the vacuum wavelength Xo for each missile flight. Since the reference frequency varies by less than 1 part in 107 during each flight, we can for all practical purposes assume it is a constant. Let favg be the reference frequency averaged over the period of the flight; then Co ~ = 2f ' (67) avg where the value for the vacuum light velocity is taken to be that given by Dumond and Cohen, i.e., Co = 299792.9 + 0.8 km sec-1. Table III lists the reference frequency readings logged from the frequency monitor during each of the flights at Guam, and Table IV lists the corresponding frequency averages and the values for %o/2. 31

TABLE III REFERENCE FREQUENCY LOG FOR GUAM FLIGHTS (Mc) X-Time SS 12.50 ss 12.51 SS 6~.52 SS 6.53 SS 6.54 0 36.939918 --- --- 36.939725 + 30 " 18 36 939764 36.939774 " 26 36.939711 + 60 " 18 " 64 --- 26 11 + 90 " 19 " 65 36 939775 25 " 10 +120 " 19 " 65 " 74 " 26 " 10 X-Time SS 6.55 SS 6.56 SS 12.57 SS 6.58 0 36.9385531 36939732 36.938542 36.938968 + 30 " 29 " 33 " 41 " 68 + 60 30 i 34 " 41 " 69 + 90 1 30 " 33 " 42 " 68 +120 " 31 " 32 " 42 " 69 Note: Rockets numbered with 12 prefix are Aerobee 75's; others are Cajuns. TABLE IV AVERAGE FREQUENCY AND VACUUM WAVELENGTH FOR GUAM FLIGHTS Rocket favg (Mc) %o/2 (10-3 km) ss 12.50 36.939918 2.02892234 SS 12.51 36.939764 2.02893080 ss 6.52 36.939774 2.02893025 ss 6.53 36.939726 2.02893289 ss 6.54 36.939711 2.02893371 SS 655 36.9385530 2.02899858 ss 6.56 356939733 2.02893250 ss 12.57 356938542 2.02899792 ss 6.58 36.938968 2.02897452 32

5. TRACKING DATA 5.1. BALLISTIC CAMERA DATA Reference 3 contains: 1. A description of the measurement of the Ballistic Camera plate coordinates of the grenade bursts and star calibration images. 2. A description of the method used to compute direction cosines from the plate coordinate data. 3. The resulting direction cosines of the grenade bursts, corrected for refraction. The direction cosines in this report are listed, respectively, as: cos E sin A, cos E cos A, and sin E. Although no explicit identification is made for the angles A and E in Ref. 3, it has been established that E is the elevation angle, and A is the azimuth angle measured clockwise, from north, so that with the coordinate system we have defined at Guam we can identify the components of N as follows: L = cos E sin A M = cos E cos A N = sin E It will be noted that direction cosines are listed for Cajun ignition in all the Nike-Cajun flights. It was discovered not only that the images of the ignition flash are well defined on the plates, but also that the sound returns from the ignition are of good quality. For this reason a position was obtained for each of the ignition points. The direction cosines published in this report for rocket SS 6.54 are incorrectly identified and the designations "east" and "west" should be interchanged. Because the west plate of SS 6.56 had fewer than six stars from which a plate calibration could be made using the Herget solution, no results for this plate appear in the report. Subsequently, however, a reduction of the west plate of SS 6.56 has been made, using a solution for which a plate calibration is defined by three constants for each standard coordinate. The results of this reduction were made available for computation of burst positions in a separate correspondence. 33

5.2. DOVAP DATA For each of the missile flights the recordings of the doppler signal for both helical antennas along with the time reference signal were transcribed from the magnetic tape onto 355-mm film. These transcriptions were made by the Ballistic Research Laboratories, Aberdeen, Maryland, and are of excellent quality. On the film the doppler signals appear as half of an amplitude-modulated envelope while the time reference pulses are recorded both as y- and z-axis deflections, i.e., as sharp spikes and dots. The time signal consists of two distinct pulses with repetition rates of 2 per second and 100 per second, respectively. To establish grenade burst times, signals from two ground-based flash detectors were recorded, along with the time reference signals and the lift-off pulse, on a Consolidated Electrodynamics recorder (not shown in Fig. 1). The times of these events, which were read separately and recorded, serve to define the intervals over which the corresponding doppler cycle counts are to be made. Whenever possible, the event times are established by observing on the film transcription the modulation of the doppler signal caused by the grenade fireball, and the times read from the CoE.C. record are considered as supporting or back-up information. All the cycle counts are made by hand on a light-box or film reader using a pair of dividers set at an interval corresponding to some convenient multiple of cycles, usually 5, 10, or 20. A detailed description of this counting process is given in Ref. 9, Section IV. The cycle counts start from lift-off and the total counts are interpolated to the nearest hundreth of a cycle at each grenade burst time, including, in addition, ignition time for the Cajuns. Counts are also interpolated at each half-second to provide sufficient time resolution for the analysis of phase errors. Every record is read at least twice and the counts are then compared to detect reading errors, whereupon the two sets of readings are averaged. Each successive pair of average half-second counts are then differenced independently for each receiver, and the resulting difference, AN, is plotted against time. Similarly, the pair of half-second counts corresponding to the left-hand and right-hand receivers are differenced, Eq. (47)9 to obtain N'. These values of N' are then corrected for the phase change due to the separation of the antenna phase centers by evaluating expression (49) in terms of the approximate trajectory given by the rough counts and the direction cosines of the lowest grenade burst. The corrected values of N', given by (54), are also plotted versus time. On this same plot the times of each field strength maximum versus the total number of maxima accumulated to that time are plotted to the same scale. Be 54

cause Ns normally accumulates two cycles for each missile rotation while two field-strength maxima occur every rotation, the two plots should differ at any time by no more than one cycle. Any discrepancy which does occur (care being taken to account for change of rotation which happens often upon separation of a two-stage missile) indicates the presence of anomalous phase shifts at the doubled reference frequency. Anomalous phase shifts at the reference frequency, on the other hand, are evidenced by discontinuities in the slope of the AN plot. Consequently, careful examination of both plots will indicate where normal and anomalous spin corrections are to be applied. The method by which these corrections are applied are described fully in Ref. 9, Section VI. The final spincorrected cycle counts are listed in Appendix C for each of the flights. 35

6. COMPUTED BURST POSITIONS The grenade burst positions computed from the ballistic camera data and the cycle-count data by the computer program appear in Appendix D. The point identified by A* is the Cajun ignition point. Positions are listed with the center of the geophone array as origin, and with the survey position of the launcher as origin. These results are given in kilometers with the least significant figure corresponding to millimeters. For each grenade, the east camera positions are printed on the first line of the group, and the west camera positions are printed on the second line with the average of these two positions printed on the third line. The corresponding standard deviations are printed on the third line in columns six through nine. 37

7. ERRORS 7.1. RESOLUTION OF HORIZONTAL AND VERTICAL COORDINATE ERRORS Let aX/MN mean the limit of the ratio of the change in X to the magnitude of an infinitesimal vector displacement AN of N. Since N is a unit vector, any infinitesimal change AP must be at right angles to N, and we can set AN = K where K is a unit vector perpendicular to P and e is some small scalar. By Eq. (9) AX = RAN, so that lim |lA|-K AX IANI = lim ->0 RKe + -- = RK E (68) Furthermore, 4. ~u+ - 6u 2aN 6u aR Now N and u are independent aR/6u = 1/2 and as a result so that 6A/6u = 0, and if we set u = 2R, we have _x 6u + ax aR 1 2 1 2 (69) N is always close to the vertical so that relation (69) implies 0 aY 0 6u and (70) 6Z ~ 1 1 1 au 2 Similarly, since K L N, K will be nearly horizontal in which case K = (cos C0 sin a, 0), where ais the angle made by the direction of AN and the X-axis. Thus (68) implies 39

R cos a R sin a and (71) at Thus we conclude that errors in altitude are primarily due to errors in the u-values obtained from DOVAP data, whereas errors in the horizontal coordinates arise mainly from errors in the direction cosines given by the ballistic camera data. Survey errors will propagate errors into both the slant range, R, and the direction cosines, A, in addition to affecting the position of the ballistic camera, %l, directly. For the type of survey conducted at Guam, one might reasonably expect an accuracy of one part in 5000, and since the maximum interval in the triangulation net containing all the relevant points is of the order of a kilometer, the maximum error in position.dueto survey errors would be 20 centimeters. 7.2. DOVAP ERRORS As we have already indicated, errors in the slant range, R, are due almost entirely to errors in u while errors in the survey, not affecting u directly, and errors in the direction cosines both have only a second-order effect on R. The value of u depends in turn on (Section 3.4): (1) the initial value uo of u determined by survey data; (2) the spin-corrected doppler count; and (3) the average doppler wavelength, X(Z) = Qo/Il (Z). With regard to item (1), an assumed survey accuracy of one part in 5000 would result in an error no greater than 20 cm in u since uo is less than a kilometer. Item (2) represents the most serious source of error affecting the u-value. An error of one cycle, for example, would produce an error of one doppler wavelength, or 4 meters, in u. Experience has shown that it is extremely improbable that counting errors involving an integral number of cycles will remain undetected. In every case at least two independent readings of the film are compared and rechecked until the agreement is within a tenth of a cycle. Consequently, it is felt that systematic counting errors can be disregarded, and that random errors are less than a quarter cycle.

An important error source affecting the doppler counts results from the phase shifts due to missile spin. Extreme care must be exercised in the examination of the AN and N' plots versus time, and an occasional inspection of the film transcription is necessary, to insure that an accurate determination of the phase corrections is made. In particular, anomalous phase shifts on a single antenna at 74 Me, or anomalous phase shifts at 37 Me, are often difficult to interpret. Because of such difficulties it is not unlikely to accumulate a total error of the order of a cycle in correcting for spin phase shifts. In addition to this systematic error, a random error of the order of a half cycle can be introduced into the data by both the normal and anomalous spin corrections, although the methods outlined in Ref. 9, Section VI, tend to minimize this error so that they are generally substantially smaller. If we take into account both counting errors and errors resulting from spin, the total estimated error in the doppler count will be a systematic error of a cycle and a random error of three quarters of a cycle. The corresponding error in u will be a systematic error of the order of 4 meters and a random error of the order of 3 meters. Wavelength errors, item (3), arise from errors in the quantities: (a) the vacuum propagation velocity C6; (b) the sea-level index of refraction vo0; and (c) the average reference frequency favg. The uncertainties in the vacuum propagation velocity and the sea-level index of refraction (or equivalently the propagation velocity at sea-level air density) are of the same order, which is about one part in 105. The corresponding error in u would then be about 2 meters for an altitude of 100 km. Uncertainty in the average reference frequency should be less than one part in 107 so that errors arising from this source are negligible. One might consider at this point the possibility that the solution for the burst position has implicit assumptions which are as yet unjustified, and, as a result, the computation would be in error. One assumption that has been tacitly made is that propagation is straightline. A discussion of the errors incurred by this assumption is given in Ref. 7, Appendix B, where it is concluded that they are completely negligible. It has also been assumed that the point in space to which the doppler count defines a u-value is coincident with the grenade burst. To be precise, this point is the common phase center of the missile antennas and is separated from the grenade bursts by an interval of approximately 8 meters. As a consequence, the slant range R can be in error by an amount which is less than or equal in 41

absolute value to 8 meters. The actual magnitude of this error can be estimated only if the aspect of the missile is known. By examining spin phase shifts we can usually determine the aspect sufficiently to establish the sense of this error. In all the Guam flights, the true slant range for each grenade burst should be greater than the computed value by an amount not exceeding 8 meters. Excluding precessional effects, the magnitude of this error probably varies but little during each individual flight because of spin stability. Excluding this last error, let us summarize the errors affecting u as follows: (1) A systematic error of 20 cm caused by survey errors; (2) A systematic error of 4 meters and a random error of 3 meters due to count errors; (3) A systematic error of as much as 4 meters at the highest altitude due to errors in the doppler wavelength arising from uncertainties in the propagation velocity and refractive index. Assuming each of these error sources operate independently, the total error in the slant range, R(=u/2), will be a systematic error of 4 meters and a random error of 1-1/2 meters. 7.3. BALLISTIC CAMERA ERRORS Systematic errors in a plate calibration can arise from uncertainties in the local sidereal time and the elevation angle of the celestial pole. Universal time, on the other hand, can be established very accurately so that most of the uncertainties in these quantities are due to inaccuracies in the geographical position of the camera. It is felt that the latitudes at Guam are known with good accuracy while the error in longitudes, though larger, can be no more than 30" of arc. This latter error implies a possible systematic east-west error of this magnitude in the direction cosines. As a check on the accuracy of the plate calibration, the plate constants were used to compute positions of each of the calibration stars. These computed positions were then compared to the positions originally obtained from the star catalog, and the resulting residuals provide an estimate of the accuracy of the calibration (Ref. 3, p. 2). The maximum residual for all the plates, with the exception of SS 6.56 west, was 17.415" of arc, while the average was much less. Assuming that the calibration stars were distributed uniformly over each plate, it would be reasonable to conclude that the residuals for the grenade burst positions show the same statistical distribution as the residuals for the calibration stars. Consequently, the total systematic and random error in the direction cosines of the grenade bursts, due to calibration errors, should average much less than about 20" of arc. Since 20" of arc is equal to 9.7 x 10-5 radi 42

ans, this would imply an error of less than 10 meters in the horizontal coordinates at altitudes of 100 km or less. In general, the east plate calibration will be independent of the west plate calibration because of differences in lens distortion, camera orientation, and the selection of calibration stars. Thus the burst positions determined from the east and west plate reductions represent two relatively independent estimates of the same quantity, and the residuals of the burst coordinates will be indicative of the average error of each estimate. A plot of the residuals of the horizontal coordinates of the grenade bursts appears in Appendix E for each of the Guam flights. Since the corresponding residuals for the two cameras are necessarily equal in magnitude and opposite in sign, only the east camera residuals have been plotted. The angular error in radians associated with each of the residuals is simply the ratio of each residual to the altitude of the burst. Upon examination of these residuals we discover that, with the exception of the residuals for S.S. 6.56, the corresponding angular errors are all less than 20" of arc with the average considerably less. This corroborates our previous conclusions. The calibration for the west plate of S.S. 6.56 was obtained by a more simplified method involving fewer plate constants, and, as one would expect, the residuals are noticeably larger. Despite this fact, the corresponding angular errors are at worst very slightly greater than 20" of arc. Examination of the residuals for all the flights suggests that there is a small systematic difference between the positions given by the east and. west plates. In almost every case the position given by the east plate lies roughly in the northwest to northeast quadrant relative to the position given by the west plate. To summarize, the ballistic camera direction errors are primarily: (1) A systematic east-west error of 30" of arc or less; (2) A random error of the order of 20" of arc or less; (3) A small systematic north-south difference between the two cameras.

8. CONCLUSION The ballistic camera-single-station DOVAP tracking system makes the best use of camera and doppler information since positions are determined by a nearnormal intersection of a ray and an ellipsoidal surface. This is contrasted to an all-camera or all-DOVAP system where positions are determined, respectively, by the intersection of two rays or three surfaces. In both cases the included angles between the intersecting geometric elements are small, making the position sensitive to error. The experience gained with this system leads us to conclude the following: (a) As in any ballistic camera system, care must be exercised in making the plate exposures to insure that images of the grenade bursts are small and distinct, and to provide a sufficiently large number of identifiable stars on the pre-shoot and post-shoot exposures. (b) A check on doppler errors should be provided by back-up or supporting data. This might be accomplished by providing an additional ground receiver with an antenna placed some distance from the other receiving antennas. (c) With regard to grenade experiment, some method should be devised whereby a correction can be made for the uncertainty in the positions resulting from the separation of the bursts and the missile antenna phase center. Considering (b), one might say that any modification of the DOVAP scheme which would serve to reduce systematic count errors due to spin or provide a check on such errors would be desirable~ This, of course, can also be said of an all-DOVAP system.

REFERENCES 1. Siewert, J. R., The United States I.G.Yo Upper Atmosphere Rocket Operations, Final Report of the Special Committee for the IoGoYo Working Group on Rocket Operations, United States National Committee for the I.G.Y,, March, 1959, pp. 91-97. 2. deBey, AoLG., and Hoffliet, Eo Do, DOVAP-Instrumentation and An Analysis of Operational Results, Report No. 677, Ballistic Research Laboratories, Aberdeen Proving Ground, NoVember, 1948. 3. Chavez, R. B., Good, E. W.,and Gardiner, A. H., Direction of Grenades in Rocket-Grenade Experiments on Guam During November 1958, The Physical Science Laboratory, Ballistic Reduction Section, New Mexico State University, New Mexico, September, 19590 4. Allen, H. F., et alo, Atmospheric Phenomena at High Altitudes, Univ. of Mich. Research Insto Report No. 2387-51-P, Ann Arbor, March, 1959, ppo 1 -47. 5. Lehmann, C. H., Analytic Geometry (John Wiley and Sons, Inc., New York, 1942). pp. 150-151. 6. Doehlemann, K., Geometrische Transformationen (Walter de Gruyter and Co,, Berlin, 1930), ppo 133-136. 7. Ottermann, Jo, The Effect of Atmospheric Refractive Indexes on the Accuracy of DOVAP, Univo of Mich, Research Inst. Report No. 2387-42-T, Ann Arbor, August, 1958. 8o Minzner, Ro Ao, and Ripley, W. S., The ARDC Model Atmosphere 1956, Air Force Surveys in Geophysics, No. 86, Air Force Cambridge Research Center, Bedford, Mass,, December, 1956, pp. 5-10. 9. Titus, Po Ao, and Whybra, M. Go, DOVAP Data Reduction for IGY Grenade Aerobee Rockets S.M. 1.01-SoM. 2.10, Univ. of Mich. Research Insto Report No. 2387-50-T, Ann Arbor, February, 1959, pp. 47-48. 10. Essen, L., and Froome, K, D., "Dialectric Constant and Refractive Index of Air and Its Principal Constituents at 24,000 Mc/s,"Nature, 167, 512 (March, 1951). 47

APPENDIX A AVERAGE REFRACTIVE INDICES

TABLE OF AVERAGE REFRACTIVE INDICES Altitude (km) Altitude (kn) Altitude (km) PJ-1 Altitude (kn) 1L-1 O 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31.28820 (10-3).27465.26181.24959.23798.22695.21648.20654.19711.18817.17970.17168.16399.15660.14956.14290.13662.13071.12517.11998.11511.11055.10628.10227.09852.09499.09167.08855.08562.08285.08024.07778 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63.07545 (10-3).07325.07117.06919.06732.o6554.06386.06225.06072.05926.05786.05653.05526.05405.05288.05176.05069.04966.04868.04773.04681.04593.04509.04427.04348.04272.04199.04128.04059.03992.03928.03866 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95.03806 (10-3).03747.03690.03635.03582.03530.03480.03431.03383.03337.03292.03248.03205.03164.03123.03083.03045.03007.02971.02935.02900.02866.02833.02800.02768.02737.02707.02677.02648.02619.02591.02564 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127.02537.02511.02486.02461.02436.02412.02388.02365.02342.02320.02298.02277.02256.02235.02215.02195.02175.02156.02137.02118.02100.02082.02064.02047.02030.02013.01997.01980.01964.01949.01933.01918 (10-3)

APPENDIX B BC/DOVAP POSITION PROGRAM CODING SHEETS

LGP-30 CODING SHEET PREPARED FOR: PAGE OF High Altitude Laboratory 1/9 JOB NO. PROGRAM NO. PROGRAM PREPARED BY PROGRAM CHECKED BY: DATE M. G. Whytra PROBLEM: TRACK Ballistic Camera/Dovap Position fc_____ INSTRUCTION CONTENTS PROGRAM INPUT CODES g LOCATION OP O ADDRESS OF ADDRESS NOTE S _ _,,OPERATION uADDRESS OF ADDRESS WI^ I I I i;00p0o0oo, ' _,.1/oopoyxy / ^ ________________i,___o_3, ' ~~I~p I, I031' 1 zO504 loc. of il -' O j ~ pI,, l, I, yO l ' -~ p|02i, O h 1 'o zO539 loc. of ~3, __ i O' 71 ' I, |04,,1 t b o05' 1 z0537 loc. of', 1111111 ' i___________________ 0t 16 i p6, I I 1 061' i | 1 zo21_5 I,~ ~ 0, 7, t;,1 1 ~ I 1,.I, i,i I8, rhI ' I IIt- Data Input I,,,,. ~,09,1,, u ), 0 # 11.4,1,1 ffI1 1 3l07r ' i0 z00_32 I l, -__ _ bO^ \ L t. l |12 b 408'' | z0209 _I I _ I I - I 3 8 1 10 1, T I b 09ii __|, 14i |bO 1. e,' i z0501 loc. of L 5 - jt0019' _I I _I ii I I I, c I 01', I, 117, 1 c00' '1 o0->6300 _ 1 - 118, 4 2 9O |/ I [0504] etc., 191,, i, mC |, I_ 5I | | [0501] etc. 20, 300',,, 22 1, 18,' ~__________~__ ~ __ 16', i, 29 1. 11 1. 31, I I I i I I I9, i i i p W, /_I _I I I.1,I I, I, I I. I.,3,i | I I,0919 19 I, |____ 1, ____|__ OOL,' > X| |02 mO5t04 II r 1~~~~~~ 1 8' I,1 3I0! L, I I b 31 ' |, I 0000)~' I [ 0032] etc. FORM ~ ~ ~ ~, ~ LI ARAERTR 0 >Y o o: z z 8 I P FORM LP-14 C CARRIAGE RETURN I -- CONDITIONAL STOP CODE PRINTED IN U.S.A. j 553

LGP-30 CODING SHEET PREPARED FOR: PAGE OF 2/9 JOB NO. PROGRAM NO. PROGRAM PREPARED BY: PROGRAM CHECKED BY: DATE PROBLEM: TRACK I0_L. INSTRUCTION 0 CONTENTS PROGRAM INPUT CODES 0 LOCATION OPN O T E S OPERATION J ADDRESS OF ADDRESS I I I I I i I ______________ ______ 0032 ao413' @ 2, ~ 5 xc66305', 0 ' ' '~ I I~ ' 4I I I - 563014' @ \ \ \ ~ \ \^T | \ l,41 136 l s 1 31,363031 @8 1@1 -,,, ^ y3', ' o, @-@ 8__? 14 u0454'~! I I I L, 02', I2'-2 @ 15,II i I I I I.j....... 2~ I,,.9.., ', r'003 1'____ I i i I I, - u 0 ^ o14', i /________,____,,34 1 d i I 1 @ 1 44 1 3xo ' 1 2T @ 715 44,, 1 _,o 1x ', 1'_2 @ 15I 4 ~,,, 111 u 0 | ____l,, 7,, x i l2' 4, N @)s. u @7 g | 0 I I I I 19 I I A - @16 '49 I ' -8 L, i _3_1 1 5 I' L 1 @ 1 i r O 0 ~I I I '~I I I _ l15~ I I 1 I 31 1,4}15 1 5 Z) ( @1 ii -I I II I - 5635I 1 I I I' (1 /4)s-N 7u/2 @ 7________ _ _ __i,, 1.,,____l | 1 156,,,O 1. Z _____ _, ____,?0|1 15, | x h (63081 @ Z@7,,,,,,____, d? 2II ' IY03 1 i| +( '/ @ 163____r _ I______i, l,, 6_41', _ X _ @ Oijjj,, I I I I I,,_ _____I______ ____ __ ZI7_____ ______ _ I _._ 0 o 4 - 0 d x 0 o sn I2 c3 I O O FORM LP-14 PRINTED IN U.S.A.:.-.j, 7;ftll' Ir~ l ~ CARRIAGE RETURN --- CONDITIONAL STOP CODE ROYAL MCBIE, J13541 X

I LGP-30 CODING SHEET PREPARED FOR: PAGE OF 3/9 JOB NO. PROGRAM NO. PROGRAM PREPARED BY: PROGRAM CHECKED BY: DATE PROBLEM: TRACK SL._ INSTRUCTION CONTENTS PROGRAM INPUT CODES 0 LOCATION OF A ESS NOTES OPERATION ADDRESS OF ADDRESS: I I I I I I 1 - III __I I I:0 I0100 m0532' 1..Z(Z )-i @L1 I _I I I -.2I....1 I I xc6(Z z)(3(z 1)- @1 ~~I I I I 02 b14L2' I I 11. 11, ~03 x16314'1 ' z z @ o 0,,, | ~4 412' 1/2 @0 05 xd63507'1 - z/Z i @0o I I I I'1,06,6308' Z Z@7 -^ ___0I I I I I I Iel - @ LW_07 08 xd6311 / \ \ \: ix; 6 0 _ _ _630 Z' 3@7 0 ii10 0 ' 1 @ 22 Z' @29 1i1. I o1 a I 410' I z 0800 12 1yd21' \ \ | \X \{ \ ~ | ^ \ ~ \' '| i 0 | |d416" @2 I1 1 1 @ 29___ 14 1 24' 15 x6301' @7 I I I, I,i I, i - i 14 ' i 1@ 6.. ''- 20 12',' 1@14_,'/ I I I *l I I -\OIOO' 7 022 xc6308' I I, I I I,,2 I I6369' 8 I x 630,',_ _ _ _ I -Ifa toI 1,, _,,__ _, 1_____________ _I I ____I~I I I I Ia I 1 @ 2____2 _'_2 i i I _ -I I [ I 080.I, I J i I i,b6,9,, I ia o i3 I I(,0 I1I, I' 0'___ - '. 0 -3 2d y o o 0 - Oul I _ O Pi FORM LP-14 PRINTED IN U.S.A. (A.4 W CARRIAGE RETURN / = CONDITIONAL STOP CODE 55

L LGP-30 CODING SHEET PREPARED FOR: PAGE OF 4/9 JOB NO. PROGRAM NO. PROGRAM PREPARED BY: PROGRAM CHECKED BY: DATE P1OBILEM:.TRACK IL INSTRUCTION CONTENTS PROGRAM INPUT CODES 0 LOCATION OF ADDRESS N OTE S I/~ OPERATION ADDRESS OF ADDRESS I I I I I ]I I _,, h 5 ioo',, i u/2 0 7 I I I I I.A, ' J '.IL.. i. ~ I I I 6 110 xc63 ' (u2/4 -4 ),,,,,,, ^7, 1 1, DO~pO',, ~ S ~ I0539U o54o3 1, i,, I,, x 62,, 15, I''', 14 1 - 91 _,__, i i i ~ i ^o, 111T______ - 2 d6 '(4/46 ' ~ iIb 0 5 6 I c @5, _ 1 51 i,,,f I I y6?0' i u2/4 ~ 14 __,,, ~9 6 o-,, uc6 '(4/4u2 0. I I - V 1)0 ' i h06' ' (/u ' 2)2 2 1 1' ' ',,,! ' i 1 1 1 ~ 0io ' i ' ~ ^ 14 L A I I - c61' '6 (4/u2)c2(/ ) IqI 6 0172' 1@1 1,,,_ 9 1 1 3o6 ' i c ' '~~ ' ' Ic3 4 '4u,,(4 )c 1 ~ ____, p, 6o, 5i _I I __,,,,,,,' ' 6o6,,, (4/ ) 2 I4 6! 0 4 ~2 i,_ c 1 ''_ IL,,I 2' ' 0 1, - 1_____ _LA82. ________ LLL Li_2 L_ - II I4#_, ' _ -(4/u2)c:2 i FORM''-14N CA, R, RIA T R, ' 6~~lpl~,,_To,3 C: 0 *3~ cc 2 5 o o "0 u Q a > 0 j w Q11 Ow - 0 V 8 P '^3 ~ t &it I c* u CI 0. 0-4 0 ct a. 1> - 0r FORM LP-14 PRNT E 1N U. S. A. t-v5~ I C ARRIAGE RETURN I CONDITIONAL STOP CODE 56

LGP-30 CODING SHEET PREPARED FOR: PAGE OF 5/9 JOB NO. PROGRAM NO. PROGRAM PREPARED BY: PROGRAM CHECKED BY: DATE PROBLEM: TRACK INSTRUCTION 0 CONTENTS PROGRAM INPUT CODES LOCATION OF ADDRES NOTES OPERATION ADDRESS OF ADDRESS I I I I I I - 1 ' II ' - I | 020q0 _0 enter sq. robt, #15. 0 _____ 01 I - m0 5 ' u/2 @7 _______. I ll _ [02 1 0 xc6321 u 8 03- xb6SL' _ @1 T 10o4 moooo r1 ' 6@7 [0537], [0538) K 05 xs6 0' I a o-@8 ____0_ _ 8 I0 I I I I I -, I\ I~, I I', 8 1 I I - R@7 i I, i1.-.I uOOo i [0209]. [0211] 09 r0208' o 10 uOO 4/ h05' X R@7 111,1111,i12 - m05 1 | '1| L @ 1 I I 'I ' I I I l | I 11 4 1 1 1 ' L 14 uoobot [ I 215 I,, i, I I -, 7 _I I I I I I I I 18 _555 _ I I I ix- @ 7I 1 t Z 1 b0551' R @ 7 T204 m0502 0 0 I M @_,,, 21 ao4iT - r1 11 ________ Wilil, l, _ _ ____ __^5I I I I I __ __ 22 a05421 L 7 1L L^^ ____L__ __- j LL I,; @_ Y @_ _ _ __ _______________ L 4 1 i..._1_ _. 1 1 ---...I I L.|. I L L5 _ I Z @8 7 | I. I I. I-..__1 _.LOL._ | I I -' N @ 1 7 I S ~ ~ 2 I I04 i 1i 1 @ 0 8, I I i- — L... i..... 29,mO5 3 r 0 20 _.. I _.._...l.^ _ _......... L.! I I i. Io 5 5;,,.,'. Z @ 7 i I I0 I I I I I 10 aO ut4 2 ', 7 3.12 m0501' L @ 1 Li...A._.. _._... i 59. - i ______ _I I -i a059 ' AZ@7 ____I! 0. _ fj Y O o C; >. _ O eS W w W 0. C FORM LP-14 PRINrTrJ IN U1.S.A. `-..;n \/ CARRIAGE FtETU.RN I CCONDI T'IOCNAI_ S. OP CODE 57

LGP-30 CODING SHEET PREPARED FOR: PAGE OF 6/9 JOB NO. PROGRAM NO. PROGRAM PREPARED BY: PROGRAM CHECKED BY: DATE PiROBLEM: TRACK INSTRUCTION CONTENTS PROGRAM INPUT CODES 0 LOCATION I O F ARESS NOTES U I __ OPERATION ADDRESS OF ADDRESS 11.,, i0232 3 2 g i ||z @ 7 33 5 b b j7' | b 0539 I 1 11 a43634 1 t@ 1 29 1._| 1 131 I I y 7 I | b 0540 i, l I l l lI6 0,: b 4I - 4 m 0537 Li _ I I |1 37,1 a l46' ' 1 @ 29 i i i 1, I 38 2 i'i tm 0538 I i I I Ii i ir 2 1 r 12 r' ______ _j ___, 1 14 | i a 'i | ' | X( @, 7| 43I 8 lIli I I I4I I I i a5%' T 2 I___ l _______ - h58~ i /' _ IX@7 'X@7 illlllll,,ll48 1,1 i O4l'4 c Y1 _ XI @ 7_ ___________ i~ b951'' R@7 I 5,I7 118 a55' I2) I I I l l 1491I I I - i 7 -,,11. h59 ' _____@7,____ ____, 0 a58' Y ' @ _ _i i I [I I I - c5 LY' @71 _ A | _ _ - _- L.I __521 1 I I _ b_ LI R@ 7__|________ L___|,i17 I I i,, 4' @1 @ ___7__9 t- -l - 7...~Li~.tL A..L 1_551 zW X59b@71E __ |._ L.I x_6 I ___ _ _ _ ______ __- - _ _ _ Z @ | 11 _1L —.- 6 + 1. _bp5, 3' X(W) @_ _7 M63, 1 p42'I _ 0538 L.~~~ ~ ~~!1 {.J4L-.L.l.__________ - IJW3~Q,,L] _ __8 FORM LP-l4 CARRIAGE RETURN~~~~~~~~~~~~._. 0., > O3 U. W W QC 8 m a U I, O C FORM L-P-14 C CARRIAGE RETURN I ' CONDITIONAL STOP CODE PRINTED IN U.S.A. - '.-.',., -~., C' 58

LGP-30 CODING SHEET PREPARED FOR: PAGE OF 7/9 JOB NO. PROGRAM NO. PROGRAM PREPARED BY: PROGRAM CHECKED BY: DATE PROBLEM: TRACK L) INSTRUCTION CONTENTS PROGRAM INPUT CODES LOCATION OPERATION ADESS OF ADDRESS NOTES I I 1 1 1 717 1 -: 1 x_ I _ I T I I I I I __, I I,.o - o, f_ _IIX a v g _@ 7_1 1 I,,, I I I -! I I, I, I______, 1021 1 1 1 a0,5i7' ' AX@7 I I I I I I I - i04| ____3'1 1~03 ' E) X avg@ 7@ I i I I - |05| 2 I 1 iI 'I 1/2 @ 0 ~96, x 6 21 1 ' _ ____|_ 1-ol I 5 1', I, Y Y avg @ 7 I,,0, i I,, c | I 12 | Y' avg @ 702 1 113, 1 5 I ' '|04 I | Z(E) @ 7 I,,,,,,m 4,04,, 1 2 ml,' 1/2@ 0 I1,, Im 2' 1 112@ 1 1 1 ) 1 1 1II! | 1 1161_ i I b '~' Z(W )@ 7 11 _____,17, i,,,,,L o1/,@ _, 17 1 m' /2 @ O 18xa63o5' ' _I I_ _ I |I _ + 190 _ _71.h0. h602'fi ' L-_. __ Z avg @ 7 | _ _ _____ _. |_.....L..j22 __._. I__! 5i ^_ l _0a AZ @ 7 l l 21 co~o~I I I, @ | I_ _ _ j ^|21, | LL c0605' ____ Z' avg@ 7. _.22 bO521' X(E) @ 7 IL -.LV__JL_ _..... i r0 L2J 51 1 - X(W) @ 7 L L I__ _f Lf....._.... 1 12 6 I.... 1u,......j269'1.,, _,^ 529O ', L | | 1 _ ________ I I _L.. 1...1. 1.....~..L...^..._.. _. a.. i. L -,.... iI..I......._ -- - - - - - I II - 1.+I I L44_a_2 I I - I..0 1 LLL I.. l'.. c696.__ i, Ii3,, sQ591, i i' IbVY~w, 2I _ L..4LL_.....L.._ L _ ~1 _ L 1.Z l bi.?5231 ' Y(E)_@_ 7 __ 11,, iii i 9 L sp _9' < Y(W)7 ) @ 7_____MRFI__1AI Cz z o * _ L? w 0 1 O U U z Z A I - o FORM LP-14 N CARRIAGE RETURN CONDITIONAL_ STOP CODE ROIIIL M- BE. J 1354 1 X PRINTED IN U.S.A. "',':f. i.P...,$s 59

LGP-30 CODING SHEET PREPARED FOR: PAGE OF 8/9 JOB NO. PROGRAM NO. PROGRAM PREPARED BY: PROGRAM CHECKED BY: DATE PROBLEM: TRACK ) LINSTRUCTION CONTENTS PROGRAM INPUT CODES | LOCATION OPERA OF ADDRES NOTES... ~I I I IU) OPERATION ADDRESSI I I I I I I I ________ ___ I I 2 - 032 m104, 2' ' 1/2@ 0 __,5, 3, t0335', I ' I: I! I I t l l: 24t | _ I -t ' ' ' t __I I z _, L i, I 9u03 7' i t 4 I II II II t ~51 '4 C697' I I I6~ so0697',,,, I,,, 7, I I c6 7', 1 Y 7 | 1111, 1, I I,?8, 1 ', I L5' Z(E)@ 7 I I l l l I l I 1 591 s0560' I Z(W )@7 1,I 0 m 2' ' 1/2 @ O 42i., i,0 6 tp^ I/ 8,,,, Qt8', ' _ I.". s 08'! | z ~I I II~I 43-II I_, _ I1 14.7,,,1 x'32 o00' delay 4 il-8,, 1, r5l93'3, ________| | Data output I, 9, I II, i I #12. 4 i 1 11 0, I 0 z0512' 1 I loc. of 1st word I I ii ^1|_i,| xz0607,' It jj 7j I no. and q,,,, |16|38', | |163C. R. | 9_ i 2 I! I, i53 IX 300' Idelay 4 1 4. r 53' u |I enter I_______55,, ________ 5 ' 50' IJ #12.4 Iil_ I Iz5 I I I P |/_________|loc. -of lst word I I, I I }, 1 157,, x ~0~71' i _ _no. and q 1 1,, 1, 1 I 8 I xpl ', I L |4 c. R. 1 1 1 15 1 59 1 1 x 3200,' 1 delay I _ j i _| I I -i 0 r ', i' 503 enter 1 1 1, 1 1 1i, I, _ _ _ uL59^ O' _ /_ _J #12.4 I _ 1 63,1 xkOo071' I_ x no. and q._ C0 - Y' d ax O o I a 0^ P 5 FORM LP-14 PRINTED IN U.S.A. ~lj~~ C N CARRIAGE RETURN I r- CONDITIONAL STOP CODE 60

LGP-30 CODING SHEET PREPARED FOR: PAGE OF 9/9 JOB NO. PROGRAM NO. PROGRAM PREPARED BY: PROGRAM CHECKED BY: DATE PFROBLEM: TRACK 0. IL QL ___ INSTRUCTION CONTENTS PROGRAM INPUT CODES 0 LOCATION | ADDRESOF ADDRESS NOTES __ __ ) OPERATION ADDRESS OF ADDRESS I I I I 1 I - __~____|, - 1 x16_' C. R I I I I I P1! I I ^ O.' I. I___ _irelay_ - 1 xz32,00 i _ ___ 2 1 1 12 1 uI 000' i transfer to start I I i _ I I 9,, 50 1 't I loc. of i I '_ -_ 1i4. I I 5P, I I z 'loc. of I I I*~ I I I I - 9,, i I d e,, 1 i i i i u OOO 1 1 1 Ow 1 1 ' t I | | ^ ____ _ 98I, i I I 8 z|020' - I _, 9 9 i i | z5 o' ___ __loc. ofL - 10 ~I1 0 z80' i / r l oc. of 1st wd. of (Z) table II 1 I - 1 I 12Op090' ' ___ 1@,,opooooIt I I 1 2 I I Il -1 1 1 @6 1, I i i [, 1, 20i, 1 @ 2 I,,,z ~I I I 1 1 @29 I9,. 41 - 1z.5o29 I7 1 -,,w wyw', _ mask, 1 1.I I I - OI I { I ' I I I I l I I I l 2 1,2110 l 1 11 1 1 I I, 2 - L o -, I I! I I I - 1-1,- I,,,,,,7 li - 1 -,tL 2, A.i 1 -_________ I I g___.L_..._1 1 1___I I ___ A _ --- —_ --- —_. _.III I l I-I 1 V_1. L__ I___III, 1 @2.I I._______1, I,,.| " l I I 0 * y 0 o c> > C, U ~z z ) I Q < I, 0 a. C FORM LP-14 PRINTED IN U.S.A. r'-S,.Nl-. CARRIAGE RETURN I - CONDITIONAL STOP CODE ROYAL MCBtr, J13541X 61

BC/DOVAP PROGRAM CONSTANTS (Addresses are relative to 0500) Location Contents Location Contents Location Contents -- 0500 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 I r, N1 @ 16 L M @1 N i1 i2 1 i3 x% Yl zV o 7 91 (East Camera) v2 23' s1/4) s2/4 7 si~t @7 s3/4J i1 i2 @1 i3 xi Y1 YV (West Camera) ^2 ^3 si/4 s2/4 @7 s3/4 Uo/2 @ 8 o/2 @ -8 Zo @7 Z1 @ 7 I i R 0532 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 /,(Zl)-l @1 A(l(Z) @ 1 (go/lg) 1 (e'/r) @-6 c2 @ 15 (1)) @7 (2)) (1) @ 15 s(2)) xy(1) Zl(l)? z1(1) @ 7 X1(2)f Y (2) z1(2) AZ R @7 X \ yt Y z @7 X' (West Ca Y, Z' o6oo 01 02 03 04 05 06 07 08 Xavg Yavg Zavg Y avg @ 7 Z Z avg os y a, z unera) unera) I- - -- I L 1 62

APPENDIX C GRENADE TIMES AND DOPPLER COUNTS

GRENADE TIMES AND DOPPLER COUNTS S.S. 12.50 Time Count S.S. 12.51 Time Count S.S. 6.52 Time Count Grenade A* l17.238 4231.72 1 47.199 15629.10 32.383 10066.55 44.073 17428.00 2 38.472 12649.89 3 57.414 18883.55 70.298 25023.63 4 88.347 28093.75 5 108.380 29664.70 S.S. 6.53 S.S. 6.54 S.S. 6.55 Grenade Time Count Time Count Time Count A* 17.459 4236.50 18.770 4517.30 17.383 4348.95 1 39.650 15307.90 36.626 13670.00 49.086 18971.65 2 54.947 21063.45 3 51.950 20269.65 4 59.140 22814.20 55.978 21586.82 5 66.232 25075.57 63.082 24014.58 70.488 25790.92 6 75.330 27619.13 71.206 26484.15 78.449 27758.73 7 83.564 29577.15 79.252 28608.33 86.289 29396.97 8 88.253 30603.65 93.035 30568.78 9 1101.700 32753.72 99.060 32485.85 102.899 31892.50 10 114.978 34096.55 109.888 33811.02

GRENADE TIMES AND DOPPLER COUNTS s.s. 6.56 nk CCount S.S. 12.57 Time Count s.s. 6.58 mi Count Grenade Time Time I I r I I"........... - J A* 1 2 3 4 5 6 7 8 9 10 17.678 42.930 50.336 58.922 66.179 74.373 83.858 116.438 128.349 4515.90 17566.80 20766.14 24131.94 26693.85 29280.21 31870.21 37498.03 38326.77 78.307 87.234 99.402 108.222 134.832 24840.22 26506.86 28173.43 28948.31 29099.97 17.878 56.038 60.966 67.786 80.804 87.414 95.140 109.090 122.680 T- - -- 4708.68 22972.72 24787.18 27104.95 30911.88 32534.50 34170.77 36413.56 37736.23 __III_ _I..1.. I I _-,

APPENDIX D GRENADE BURST POSITIONS

SS 12.50 Grenade Burst Positions (kmn) (Origin Ctr. Geophone Array) (Origin Launcher) x 3.047583 -3.o44369 -3.045976 -4.023545 -4.020260 -4.021903 - y.257401.255595.256498.381063.377360.379212 z 31.926032 31.926433 31.926232 38.459181 38.459645 38.459413 x 3.392425 -3.389211 -3.390818 -4.368387 -4.365102 -4.366745 - y.549930.548124.549027.673592.669889.671741 z 31.931339 31.931740 31.931539 38.464488 38.464952 38.464720 Ax.001606.001642 Ay Az.000903.001851.000200.000231 (x is positive East, y is positive North, and z is elevation above the origin. Positions obtained from East and West camera plates are printed on lines one and two, respectively, of each group with the averages on the third line. Ax, Ay, and Az are the corresponding standard deviations which, for two estimates, are equal to the absolute value of either residual. The position of the center of the geophone array is (198639.59', 215470.08', 492.96') relative to the Guam survey origin.)

SS 12.51 Grenade Burst Positions (kmn) (Origin Ctr. Geophone Array) (Origin Launcher) x y z x y z Ax Y A 1.236779- 1.859000 20.653055 1.581621- 2.151529 20.658362 1 1.236377- 1.857459 20.653255 1.581219- 2.149988 20.658562 1.236578- 1.858229 20.653155 1.581420- 2.150758 20.658462.000201.000770.000099 1.709457- 2.541324 25.830423 2.054299- 2.833853 25.835730 2 1.708595- 2.538430 25.830823 2.053437- 2.830959 25.836130 1.709026- 2.539877 25.830623 2.053868- 2.832406 25.835930.000431.001447.000200 (x is positive East, y is positive North, and z is elevation above the origin. Positions obtained from East and West camera plates are printed on lines one and tWo, respectively, of each group with the averages on the third line. Ax, Xy, and Az are the corresponding standard deviations which, for two estimates, are equal to the absolute value of either residual. The position of the center of the geophone array is (198639.59', 215470.08', 492.96') relative to the Guam survey origin.)

SS 6.52 Grenade Burst Positions (kn) (Origin Ctr. Geophone Array) (Origin Launcher) x y z x y z Ax.267385-.191148 8.950263.612227-.483677 8.955570 A*.266636-.190721 8.950358.611478-.483250 8.955665.267011-.190934 8.950310.611853-.483463 8.955617.000374.000213 2.297385- 2.545263 35.554302 2.642227- 2.837792 35.559609 1 2.296746- 2.544102 35.554448 2.641588- 2.836631 35.559755 2.297066- 2.544683 35.554375 2.641908- 2.837212 35.559682.000320.000580 0 3.886005- 4.449707 50.778033 4.230847- 4.742236 50.783340 3 3.884703- 4.448812 50.778227 4.229545- 4.741341 50.783534 3.885354- 4.449259 50,778130 4.230196- 4.741788 50.783437.000651.000447 4.887833- 5.672308 56.849681 5.232675- 5.964837 56.854988 4 4.887628- 5.671816 56.849753 5.232470- 5.964345 56.855060 4.887731- 5.672062 56.849717 5.232573- 5.964591 56.855024.000102.000245 5.999316- 7.039998 59.802935 6.344158- 7.332527 59.808242 5 5.998789- 7.038772 59.803144 6.343631- 7.331301 59.808451 5.999053- 7.039385 59.803039 6.343895- 7.331914 59.808346.000264.000613 (x is positive East, y is positive North, and z is elevation above the origin. Positions obtained from East and West camera plates are printed on lines one and two, respectively, of each group with the averages on the third line. Ax, Ay, and Az are the corresponding standard deviations which, for two estimates, are equal to the absolute value of either residual. The position of the center of the geophone array is (198639.59', 215470.08', 492.96') relative to the Guam survey origin.) Az.000047.o0oCo4

SS 6.53 Grenade Burst Positions (kn) (Origin Ctr. Geophone Array) (Origin Launcher) x y z x y z Ax 2y.319129.164430 8.998568.025712-.456959 9.003875.319051.163938 8.998592.025790-.456467 9.003899.319090.164184 8.998580.025751-.456713 9.003887.000039.000246.360300- 1.608670 31.411616.705142- 1.901199 31.416923 1.359329- 1.606606 31.411776.704171- 1.899135 31.417083.359814- 1.607638 31.411696.704657- 1.900167 31.417003.000485.001031.779525- 2.386843 41.441860 1.124168- 2.679372 41.447167.778717- 2.383982 41.442072 1.123559- 2.676510 41.447379.779021- 2.385412 41.441966 1.1238653- 2.677941 41.447273.000304.001430 1.032907- 2.857167 46.580552 1.377749- 3.129696 46.585859 4 1.031476- 2.834023 46.580814 13,76318- 3.126552 46.586121 1.032192- 2.855595 46.580683 1.377034- 3.128124 46.585990.000715.001572 1 280639- 3.2754653 51.143542 1.625481- 3.567992 51.148849 H 5 1.280231- 3.273511 51.143715 1.625075- 3.565680 51.149022 1.230435- 5.274307 51.143628 1.625277- 3.566836 51.148935.000203.001155 1.604432- 3.842526 56.268229 1.949274- 4.135055 56.273536 1.605275- 3.838718 56.268480 1.950118- 4.131247 56.273787 1.604854- 53840622 56.268355 1.949696- 4.133151 56.273662.000421.001903 1.905511- 4.351550 60.204810 2.250553- 4.644079 60.210117 7 1.904052- 4.348665 60.205091 2.248894- 4.641194 60.210398 1.904781- 4.350107 60.204950 2.249624- 4.642656 60.210257.000729.001442 2.566003- 5.467886 66.556526 2.910845- 5.760415 66.561833 9 2.567075- 5.464562 66.556765 2,911917- 5.757091 66.562072 2.566539- 5.466224 66.556645 2.911381- 5.758753 66.561952.000535.001661 3.045057- 6.281413 69.197364 5.389899- 6.573942 69.202671 10 5.045827- 6.276127 69.197830 35390669- 6.568656 69.203157 3.045442- 6.278770 69.197597 5.390284- 6.571299 69.202904.000385.002643 (x is positive East, y is positive North, and z is elevation above the origin. Positions obtained from East and West camera plates are printed on lines one and two, respectively, of each group with the averages on the third line. Ax, Ay, and Az are the corresponding standard deviations which, for two estimates, are equal to the absolute value of either residual. The position of the center of the geophone array is (198639.59', 215470.08', 492.96') relative to the Guam survey origin.) Az.000012.00oo80.ooolo6.000106.000131.ooCC86 0C00125.000141,cooi4i.000119.000233

SS 6.54 Grenade Burst Positions (km) (Origin Ctr. Geophone Array) (Origin Launcher) x y z x y z Ax AY A.157593.000577 9.571398.187249-.293106 9.576705 A*.158357.000299 9.571442.186484-.292829 9.576749.157975.000438 9.571420.186866-.292967 9.576727.000382.000138.000022.771946-.662643 28.112239 1.116788-.955172 28.117546 1.771918-.660602 28.112312 1.116760-.953131 28.117619.771932-.661623 28.112276 1.116774-.954152 28.117583.000014.001020.oo0036 1.800386- 1.358396 44.129549 2.145228- 1.650925 44.134856 4 1.799438- 1.354838 44.129740 2.144280- 1.647367 44.135047 1.799912- 1.356617 44.129644 2.144754- 1.649146 44.134951.000474 o001779.000C95 2.180066- 1.608965 49.035981 2.524908- 1.901494 49.041288 5 2.178805- 1.604744 49.036219 2.523647- 1.897273 49.041526 2.179436- 1.606855 49.036100 2.524278- 1.899384 49.041406.000630.002110.00c119 2.614824- 1.903152 54.022105 2.959666- 2.195681 54.027412 6 2.613979- 1.899911 54.022289 2.958821- 2.192440 54.027596 2.614402- 1.901531 54.022197 2.959244- 2.194060 54.027504.000422.001620.OCCC91 3.043328- 2.194481 58.305418 3.388170- 2.487010 58.310724 7 3.043012- 2.190307 58.305616 3.387854- 2.482836 58.310923 3.043170- 2.192394 58.305517 3.388012- 2.484923 58.310823.000157.CC9087 3.528274- 2.513392 62.320837 3.873116- 2.805921 62.326144 8 3.526543- 2.508967 62,321157 3.871385- 2.801497 62.326464 3.527409- 2.511180 62,320997 3.872251- 2.803709 62.326304.000865.002212.C00159 4.660585- 3.294513 68.733478 5.005427- 3.587042 68.738785 10 4.660831- 3.290723 68.733662 5.005673- 3.583252 68.738969 4.660708- 3.292618 68.733570 5.005550- 3.585147 68.738877.000123.001894.C00092 (x is positive East, y is positive North, and z is elevation above the origin. Positions obtained from East and West camera plates are printed on lines one and two, respectively, of each group with the averages on the third line. Ax, ny, and Az are the corresponding standard deviations which, for two estimates, are equal to the absolute value of either residual. The position of the center of the geophone array is (198639.59', 215470.08', 492.96') relative to the Guam survey origin.)

SS 6.55 Grenade Burst Positions (kn) (Origin Ctr. Geophone Array) (Origin Launcher) x y z x y z Ax Ay.132180.157343 9.220663.212662-.449872 9.225970 A*.132667.157052 9.220702.212174-.449581 9.226009.132423.157198 9.220682.212418-.449727 9.225989.000243.000145.0.741977- 2.531822 38.792546 1.086819- 2.824351 38.797853 1.742067- 2.530680 38.792627 1.086909- 2.823209 38.797934.742022- 2.531251 38.792586 1.086864- 2.823780 38.797893.000045.000571.0.909964- 2.956431 43.013761 1.254806- 3.248960 43o019068 2.909287- 2.954432 43.013941 1.254129- 3.246961 43.019248.909626- 2.955432 43.013851 1.254468- 3.247961 43.019158.000338.000999.0 1.372320- 4.071676 52.536879 1.717162- 4.364205 52.542186 5 1.373205- 4.070100 52.536979 1.718047- 4.362629 52.542286 ^2 ~ ~ 1.372762- 4.070888 52.536929 1.717604- 4.363417 52.542236 000442.000787.0 1.618198- 4.642573 56.488751 1.963040- 4.935102 56.494058 6 1.619351- 4.641692 56.488783 1.964194- 4.934221 56.494090 1.618775- 4.642132 56.488767 1.963617- 4.934661 56.494074.000576.000440.0 1.858712- 5.204802 59.768495 2.203554- 5.497331 59.773802 7 1.860334- 5.202163 59.768675 2.205176- 5.494692 59.773982 1.859523- 5.203482 59.768585 2.204365- 5.496011 59.773892.000810.001319.0 2.067782- 5.681521 62.104871 2.412624- 5.974050 62.110178 8 2.071427- 5.680224 62.104840 2.416269- 5,972752 62.110147 2.069605- 5.680872 62o104855 2.414447- 5.973401 62.110162.001822.000648.0 2.369726- 6.380169 64,723278 2.714568- 6.672697 64.728584 9 2.371798- 6.379149 64.723283 2.716640- 6.671678 64.728590 2.370762- 6.379659 64.723280 2.715604- 6.672188 64.728587.001036.000509.0 (x is positive East, y is positive North, and z is elevation above the origin. Positions obtained from East and West camera plates are printed on lines one and two, respectively, of each group with the averages on the third line. Ax, Ay and Az are the corresponding standard deviations, which, for two estimates, are equal to the absolute value of either residual. The position of the center of the geophone array is (198639.59', 215470.08', 492.96') relative to the Guam survey origin.) Az )00019 )00040 00089 00050 00015 00089 00015 00003

SS 6.56 Grenade Burst Positions (km) (Origin Ctr. Geophone Array) (Origin Launcher) x.183816 -A*.185628-.184722 -1.944081 -1 1.949038 -1.946559 -2.462368 -2 2c467854 -2c465111 -3.069534 -3 3.076692 -3.073113 -3.585286 -L4 3.593039 -3.589163 -4.167136 -5 4.175615 -4.171376 -4.840867 -6 4.850606 -4.845736 -7.140589 -9 7.150051 -7.145320 -8.041641 -10 8.051121 -8.046381 - y.180962.178882.179922 1.989911 1.982346 1.986129 2.515829 2.508051 2.511940 3.114003 3.105743 3.109873 3.619693 3.609001 3.614347 4.184249 4.172684 4.178467 4.841879 4.829463 4.835671 7.074088 7.060703 7.067396 7.881965 7.866343 7.874154 9.538604 9.538571 9.538587 35.905073 35.905214 35.905143 42.355547 42.355678 42.355612 49.133532 49.133579 49.133555 54.284492 54.284677 54.284584 59.475053 59.475251 59.475152 64.657017 64.657196 64.657106 75.756252 75.756594 75.756423 77.277066 77.277663 77.277364 x.528658-.530470-.529564 -2.288923 -2.293880 -2.291401 -2.807211 -2.812696 -2.809953 -3.414376 -3.421534 -3.417955 -3.930128 -3.937881 -3.934005 -4.511978 -4.520457 -4.516218 -5.185709 -5.195448 -5.190578 -7.485431 -7.494893 -7.490162 -8.386483 -85.395963 -8.391223 - y.473491.471411.472451 2.282440 2.274875 2.278658 2.808358 2.800580 2.804469 3.406532 3.398272 3.402402 3.912222 3.901530 3.906876 4.476778 4.465213 4.470996 5.134407 5.121992 5.128200 7.366617 7.353232 7.359925 8.174494 8.158872 8.166683 z 9.543910 9.543878 9.543894 35.910380 35.910521 35.910450 42.360854 42.360984 42.360919 49.138839 49.138886 49.138862 54.289799 54.289984 54.289891 59.480360 59.480558 59.480459 64.662324 64.662503 64.662413 75.761559 75.761901 75.761730 77.282373 77.282970 77.282671.000905.002478.002742.003579.003876.004239.00oo4869.004731.001039.003782.003888.004130.005346.005782.006208.006692.007810.000016.000071.occo65.000023.000092.000098.000089.000171.000298 (x is positive East, y is positive North, and z is elevation above the origin. Positions obtained from East and West camera plates are printed on lines one and two, respectively, of each group with the averages on the third line. Ax, Ay and Az are the corresponding standard deviations, which, for two estimates, are equal to the absolute value of either residual. The position of the center of the geophone array is (198639.59', 215470.08', 492.96') relative to the Guam survey origin.)

SS 12.57 Grenade Burst Positions (km) (Origin Ctr. Geophone Array) (Origin Launcher) x y z x y z Ax a 3.730513 4.810209 50.470150 3.385671 5.102738 50.475457 1 3.731089 4.810159 50.470119 3.386247 5.102688 50.475426 3.730801 4.810184 50.470134 3.385959 5.102713 50.475441.000288 24.000015 4.163173 5.489903 53.778067 3.818331 5.782432 53.783374 2 4.162409 5.490904 53.778012 3.817567 5.783433 53.783318 4.162791 5.490404 53.778039 3.817949 5.782933 53.783346.000382.000500.00C027 4.745076 6.417000 57.043638 4.400234 6.709529 57.048945 3 4.744536 6.417081 57.043666 4.399694 6.709610 57.048973 4.744806 6.417040 57.043652 4.399964 6.709569 57.048959.000270.000040.000014 5.163004 7.084760 58.518592 4.818162 7.377289 58.523899 4 5.159950 7.083170 58.519027 4.815108 7.375699 58.524334 5.161477 7.083964 58.518809 4.816635 7.376493 58.524116.001527.000795.OC0217 6.418576 9.080205 58.431407 6.073734 9.372734 58.436714 5 6.418620 9.082666 58.431006 6.073778 9.375195 58.436313 6.418598 9.081436 58.431207 6.073756 9.373965 58.436514.000022.001230.OOC2CC (x is positive East, y is positive North, and z is elevation above the origin. Positions obtained from East and West camera plates are printed on lines one and two, respectively, of each group with the averages on the third line. Ax, y, and Az are the corresponding standard deviations which, for two estimates, are equal to the absolute value of either residual. The position of the center of the geophone array is (198639.59', 215470.08', 492.96') relative to the Guam survey origin.)

SS 6058 Grenade Burst Positions (km) (Origin Ctr. Geophone Array) (Origin Launcher) x y z y z Ax Ay.465442-.277967 9.900413.810284-.570496 9.905720 A*.465314-.277775 9.900440.810156-,570304 9.905747.465378-.277871 9.900426.810220-.570400 90905733.oooo000064.000095 4.268112- 3.917662 46.593490 4.612954- 4.210191 46,598797 2 4.266439- 3.916485 46.593298 4.611281- 4.209014 46.598605 4.267276- 3.917074 46.593394 4.612118- 4.209603 46.598701.000836.000588 4.757927- 4.378795 50.216804 5.102769- 4.671324 50.222111 3 4.755426- 4.377630 50.217180 5.100268- 4.670159 50.222487 4.756677- 4.378212 50.216992 5.101519- 4.670741 50.222299.001250.000583 5.442285- 5.017310 54.833213 5.787127- 5.309839 54.838520 4 5.439749- 5.015047 54.833713 5.784591- 5.307576 54.839020 5.441017- 5.016179 54.833463 5.785859- 5.308708 54.838770.001267.001131 O4 66.760444- 6.230092 62.373496 7.105286- 6.522621 62.378802 6 6.753548- 6.227777 62.374550 7.098390- 6.520306 62.379857 6.756996- 6.228934 62.374023 7.101838- 6.521463 62.379330.003448.001157 7.406463- 6.822767 65.567053 7.751305- 7.115296 65.572360 7 7.405594- 6.821510 65.567297 7.750437- 7.114039 65.572604 7.406029- 6.822138 65.567175 7.750871- 7.114667 65.572482.000434.000628 8.186701- 7.531182 68.756663 8.531543- 7.823711 68.761970 8 8.184420- 7.531491 68.756919 8.529262- 7.824020 68.762226 8.185561- 7.531336 68.756791 8.530403- 7.823865 68.762098.001140 o 000154 9.581136- 8.811387 73.040121 9.925978- 9.103916 73.045428 9 9.575537- 8.807240 73.040768 9.920379- 90099769 730o46075 9.578336- 8.809314 73.040444 9.923178- 9.101842 73.045751.002799.002073 10.929251- 10.044161 75.415981 11.274093- 10.336690 75.421288 10 10.931831- 10.044331 75.415561 11.276673- 10.336860 75.420868 10.930541- 10.044246 75.415771 11.275383- 10.336775 75.421078.001290.000084 (x is positive East, y is positive North, and z is elevation above the origin. Positions obtained from East and West camera plates are printed on lines one and two, respectively, of each group with the averages on the third line. Ax, Ay, and Az are the corresponding standard deviations which, for two estimates, are equal to the absolute value of either residual. The position of the center of the geophone array is (198639.59', 215470.08', 492.96') relative to the Guam survey origin.) Az.000013.0000ooo96.000188.000250.000527.000121.000128.000323.000209

APPENDIX E RESIDUAL VECTORS FOR GUAM FLIGHTS (METERS)

Y(N) — 3 -2 3 c -4 -3 -2 -I 2 3 4 I! I IIl I lI I I I X ( — 2 SS 12.50 E)

Y(N) — 3 2 - I -4 I -3 I -2 I -I I I 2 I 3 I 4 I X (E) — I — 2 SS 12.51

Y(N) — 3 — 2 5 -4 -3 -2 -1 1 2 3 4 1 I I I I I I I X (I — I E) SS 6.52

w X It - 2~ I As A OJN - It —

Y(N) 8 — 2 1/O D) r\) -4 I -3 I -2 I -I I I I 2 I 3 1 4 I X(E) — 2 SS 6.54

Y(N) — 3 -2 7 2 8 -4 I -3 I -2 I - I I I 2 3 I 4 I X(E) I — I -2 SS 6.55

/0 Y(N) — 7 -6 -5 -4 -3 -2 - I 9 6 3 -I I I I — I,A* SS 6.56 2 I 3 4 I I X(E) 84

Y(N) -3 -2 - I 4 C? -4 -3 -2 -I 3 2 3 4 I I I I I I I ) 2 5 -— 2 S S 12.57 ((E)

Y(N) -35 9 — 2 I 1 E 6 4 — 4-1 3 4-a — 2 SS 6.58

l Ev u1