TECHNICAL REPORT NO. 293

SIMULATION AND ANALY~lS OF [HE

U~ l-JiG EFFECTIVENBgS ANALYS IS-TIOV (TEA-TOW)

FLIGHT DATA

PATR I(.K E. CORCORi'l

A PRI IL 19,80

APPPCNED FO PUBLIC RELEASE, DISTRIB3UTION UNL-It'! TED-

t~ ~ ~M( ~ATRI~ S~~MSBest Available COPY

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DISCLAIMER

The findings in this, repot are not to be construed an 'n)ficlal Depa.rtmv:t of the Army position unlei-s so specified

.) or.heor official documentation.

WARNING

Information .c1 data contained in this document are h:ised onthe input available; at the time oi preparation, The results may besubject to change and should not be construed as representi ng theD,,dCOM position unless so specifled.

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ThC use of tra&. names in this report does not cons;titUte anofficial endorsement or approval of the use of such commercialhardware or software. The report may not be cited for purposesOf advertisement.

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REPORT DOCUMENTATION PGE BEFORE COMPLETING FORMP T NUMBER 12. GOVT ACCESSION NO. 3. RECIPIENT'S CATALOG NUMBER

S, TYPE OF REPORT & PERIOD COVERED6 SIMULATION &JANALY.SIS OF THE,-jRAININGEFFECTIVENES.NALYSIS-TOW (TEA-CW) FLIGHTDATA z

6. PERFORMING ORG. REPORT NUMBER

7. AUTHOR(*) 8. CONTRACT OR GRANT NUMBER(&)

Patrick E. Corcoran

9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT. PROJECT, TASKAREA & WORK UNIT NUMBERSUS Army Materiel Systems Analysis Activity

Aberdeen Proving Ground, MD 21005

II. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE

US Army Materiel Development & Readiness Command/ Ar-5001 Eisenhower Avenue .T7- U MB A

Alexandria, VA 2233314. MONITORING AGENCY NAME & ADDRESS(I" different from Controlling Gilce) S. SECU F. )

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16. DISTRIBUTION STATEMENT (of this Report)

Approved for public release, distribution unlimited.

17. DISTRIBUTION STATEMENT (of the abstract entered In Block 20, It dlfrant from Report)

Ill. SUPPLEMENTARY NOTES

19. KEY WORDS (Continue on reverse aide It neceesau- and Identity by block number)

Tracking errorSimulationVerificationLive-fire trajectory

120. ABSTRACT (Canfbzue am reverse e * ft necmesa.- ad identity by block number)AMSAA was requested to provide an independent third party analysis of TRADOC'sTraining Effectiveness Analysis-TOW (TEA-TOW) live firing data when neither thetester nor the TOW Program Manager's Office agreed on the cause of the largemissile excursions and reduced frequency of hit. By making use of the AMSAA TOWmissile simulation it is concluded that the missile excursions were the result oigunner tracking errors in all but one casp. The excursions in flight 2407 arenot the result of gunner tracking error.

In addition, these flight data are compared with the simulated trajectornis ,

DDJA i, 3 1t I Fo5 UNCLASSIFIED7-.7 SOLETE SECURITY CLASSIFICATIONOF THIS PAGE (When

sacuRITYCLaUSIrIVATL OF THIS PAGE(Ohm Date 80M4O

'20. ABSTRACT (CONT'D)to demonstrate that the AMSAA TOW missile simulation is a valid representationof the real system especially when engaging the accelerating target.

UNCLASSIFIEDSECURITY CLASSIFICATION OF

THIS PAGE(Wh.e, Data Ente?.d)

ACKNOWLEDGEMENTS

The contributions of the following individuals areacknowledged* Dr. Gerald Nielson recommended and calculated

the spatial differences used to validate the simulation.Messrs, Arthur Gordon and Everett White conducted thesimulations. The missile trajectory plots appearing inAppendix A were generated by Mr. Douglas Finley.

kJ

The ssil traectoyNpl t aparge ilnk

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g-~

Next, page is blank.

¢3

TABLE OF CONTENTS

ACKNOWLEDGENTS . . . . . . . . . . . . . .. . . . . . . . . 3

1. -INTRODUCTION. . . . . . . . . . . . . . . . . . . . . . . . 7

2. PROCEDURES . . . . . . . . . . . . . . . . .. .. .. .. .. 9

2.1 Tat goniios ... n d.. i ti..o n...s .. 92.2 Data Acquisition . ....... * . . . . . . . . . . . 92.3 Tracking Error Analysis .. . . . . .. . .. .. .. . . 9

2.4 Trajectory Simulation and Comparison ....... . . . 92.5 Simulation Verification.... .. .. .. ... .... . . 10

3.* RESUL.TS* . . . . . . . . . . . . . . . .. .. . .. . . . . . 13

3.1 Tracking Error Analysis . . . . . . . . . . . . . . . . . 13

3.2 Trajectory Comparison . . .. .. .. .. .. .. .. .. 13

4.* DISCUSSION . .. .. .. .. .. .. .. . .. .. .. .. 23

5.* CONCLUSION .. .. .. .. .. .. .. . . . . . . . . . *. 27

APPENDIX A . .. .. .. ... . .. .. .. .. .. . .A-i

DISTRIBUTION LIST..... ... .. .. .. .*. .. .. .. .. .*.29

Next page is blank.

5

SIMULATION AND ANALYSISOF THE TRAINING EFFECTIVENESS

ANALYSIS-TOW (TEA-TOW) FLIGHT DATA

1, INTRODUCTION

The purpose of this report is to analyze the TOW

Training Effectiveness Analysis (TEA-TOW) flight data, andto validate the Army Materiel Systems Analysis Activity's(AMSAA) TOW missile simulation,

The TEA-TOW test program had been designed tomeasure the effectiveness of alternate TCW trainingprograms* The first training alternative was the minimum

phase wherein each trainee received eight hours of informaltraining, After this training period, Pach trainee firedone TOW missile (with an inert war headI at a remotelycontrolled M'7 tank. The tank moved . a cunstant velocityand was at a range of 2800 to 30C0 meter.- If the frequencyof hit equalled the historic TOW frequenc,, of hit, theprogram would be accepted. If not, eothez training programwould be tried. The minimum prograa f, ings rsulted inlarge missile excursions and unexpectedly lo- frequency of

AMSAA was requested to provide -r ndependentthird party analysis of the TEA-1CW liv- 'iring data -the-neither the TOW Program Manager's Offic' nor the tstragreed on the cause of the large missile !yrrsions andcorresponding reduction in the frequency n' hit. Thetester, the Training Doctrine Cki'mand'l ViRADEC) Corr:,inedArms Training Activity (TCATA), blamed the ano'a , .nfaulty missile guidance sets since several sexs failedcertain tests on the Land Combat Support System (LCSS) afterthe missile firings. Personnel from tte TOW Progra'Manager's Office reviewed the video tapes of the f'rings andthey concluded that the anamolies were the result of poorgunner tracking.

AMSAA proposed to solve the controversy with themethodology whereby measured ounner tracking error is usedas the input to the TOW computer simulation and theresulting trajectory is compared to the actual trajectoiy.If reasonable agreement is obtained, the live-firetrajectories are attributed to gunner tracking error. If noagreement is obtained, the actual trajectory is probably dueto faulty equipment since the missile is not following thegunner generated line-of-sight.

TCATA supplied AMSAA with the tracking error and

the time correlated trajectory data for 84 flights. Aftersimulating these flights on the computer, only one simulatedflight did not agree with the corresponding live-firetrajectory, Therefore it was concluded that the TEA-TOWmissile trajectories were the result of gunner trackingerrors.

Since the simulated and live-fire trajectoriesdemonstated qualitative agreement, the data were used tovalidate the TOW simulation in a more objective ffanner. Inparticular, these data were used to show that the simulationis valid against the so called "highly" evasive target.These are targets accelerating at O.3g's (normalizedgravitational units) or greater In a plane norffal to theline-of-sight (LOS).

The validation of the simulation is an importantoutgrowth of this study since the validity of the simulationagainst t1.a evasive target was questioned. The validationissue wns vi;ry important to the success of the ArmoredCombat Veht:lQ Technology (ACVT) program. The ACVT programwas wil1ing to provide the funds for a fiele test so thedata necessary to validate the simulation could becollected, Because of this analysis a considerable amountof mone was saved by using existing datay rather thanacquiring additional data, to verify the simulation.

8

j. PRCCEDURES

The target was a remotely controlled M47 tankmoving at an average speed of 13.5 mph. The tank wes movingat a 45 degree angle toward the gunner at a range of 2800 to3000 meters. In all cases, the target was moving from thegunner's left to his right. This target speed resulted in ahorizontal LOS rate of 1.5 mrad/sec and a vertical LOS rateof zero.

The tracking error and missile trajectory for eachfiring were recorded on video tape for post flight analysis.From these recordings, the tracking error and missiledisplacement were measured relative to the center of thetarget as a function of time. The tracking errors weremeasured in milliradians and the missile displacements weremeasured in feet. These values were mea~ured 10 times asecond to insure that the significant frequencies of thetracking error and missile displacements could bereproduced. These data were supplied to AMSAA on computercards.

For each of the tracking error time histories, themeanvariance and normalized power spectral density (PSD)function were obtained. These quantities Here obtained byusing an existing computer program, FTFREQ, from theInternational Mathematical and Statistical Libraries(Ref. 1). The mean and variance are computed byconventional means and the PSD function is obtained bytaking the Fourier Transform of the autocorrelationfunction. The normalized PSD function is cbtained bydividing the computed PSD function by the variance of thetracking error. These measures provide estimates of theamplitudt and frequency content of the tracking errors.Additionally, pooled statistics such as the average of themeans, standard deviations and normalized PSG functions werecalculated to obtain the average performance of the TEA-TOWgunners.

1. IMSL Library 3, Edit ion 6, 1977,Volume I of 2

The tracking error data were used as input to theTOW computer simulation along with target motionrepresentative of a 1.5 mrad/sec constant velocity target.TCATA Indicated that perhaps 10 percent of the data werenot constant velocity. Howeverpthe trial numbers of theseruns were not recorded). In all cases, the target motionwas simulated as moving from the gunner's left tc his right.

The simulated traJectories were recorded on stripcharts for uick look" analysis and on digital uzgnetictape for future processing. Since insufficient resolution

was obtained with the strip charts, computer plots Here madefrom the magnetic tape which allowed for a bettercomparison. Two computer plots were generated for eachtrajectory. One plot contained the actual and simulatedtrajectories in azimuth and the second plot contained thecorresponding elevation trajectories. The trajectories wereplotted from six seconds into the flight until target impact

or, in the case of a miss, until the missile range equalled

the target range. The data prior to six seconds werequestionable since the first four seconds of the actualtracking data were usually missing and had to beficticiously generated. The remaining two seconds appearedto be a reasonable settling time for the simulation torecover from the ficticious input. These computer plotswere used to subjectively compare the actual and live firetrajectories.

The TEA-TOW data validated the simulation in amore quantitative manner. In particular, it shows that thesimulation is a valid representation of the TOW missilesystem over a range of LOS inputs that include the LOS

motion due to an accelerating target. This is possiblesince the input to the simulation and the actual missile isthe LCS motion which is the total motion of the tracker.The LCS motion is made up of two components; gunner trackingerror, TE, and target angular positionG t . Thisrelationship and its first and second time derivatives aregiven in Equations 2.1 through 2.3.

LOS =TE + 8t 2.1

LOS= TE + 8t 2.2

LOS = TE + 2.3

From Equation 2,3 it can be seen that large LOS

io

accelerat ons can be generated by large, oscillatory typesof tracking arrors even in the absence of acceleratingtargetsp i.e.#t 0 O. It is possible to obtain estimates ofthe LOS accelerations resulting from the tracking errors byusing PSD tectiniques.

The output PSD PSD(W)o , of a system having atransfer function, G(W)Y and input PSD, PSD(W)i_ is given byEquation 2.4.

PSD(W)o= IG(W)12 PSD(W)i 2.4

In the frequency domain, the transfer function relatingacceleration and position is

G(W) = _W 2 2.5

where W is angular frequency. Substituting fcr IG(W)12 inEquation 2. gives

PSD(W)o=W 4PSD(W)i

where PSD(W)oand PSD(W)i become the LOS acceleration and LCSposition power spectral densities respectively. Theintegral of the acceleration PSD with respect to cyclicfrequency, f. equals the variance of the LOS acceleration*This relationship is given in Equation 2.7.

-2 f (27rf) 4 PSD(f)idf 2.70

Since an average normalized PSD function was obtained,Equation 2.7 becomes

cc tef (27rf)4 PSD(f)ndf 2.e

whereot~is the tracking error variance and PSO(F) is theaverage normalized PS0 function of the tracking error. Inreality, the upper limit of integration in Equations 2.7 and2.8 wes set equal to the frequency %here the amplitude ofthe PSD(f) equalled 0.5 which is the half-power point of the

11

tracking error. Seventy-two percent of the t-acking errorvariance is 3ccounted for over this alf-pv'4er bandwidth.Therefore, the effects of low aiplitude, high frequencynoise are eliminated from the acceleration calculation andonly the significant frequencies and amplitudes of thetracking error are considered in the calculation of 2 .

GCCThe live-fire and simulated trajectories were

quantitatively compared by computing the average spatialdifferences between the corresponding trajectories. Theaverage spatial difference is given by

n

Z[(DYi )2+ (D~i )2] 1/2 2.TD= i'=l .

n

where DYi and DZiare the trajectory differences in azimuthand elevation at time t and n is the number of points pertrajectory. For all of these flights, n is on the order of80 since the time-of-flight considered in the analysis wasfrom six seconds to about fourteen seconds. The spatialdifferences were plotted as a function of azimuth trackingerror standard deviation in order to obtain an estinate ofthe goodness of the simulation as a function of the LOSinput. The goodness of the simulation as a function of theLOS ac(eleration Is obtained by making use of this figureand Equation 2.8.

The combination of the spatial differerces and thesubjective comparison of the trsjectories provide confidencethat the simulation Is a valid representatior of the TOWmissile system.

1 2'

3. RESULTS

Table 3.1 presents the mean and standarddeviation, in milliradians, of the azimuth and elevationtracking errors. The mean of the means is -0.061 mradlagging in azimuth and O.COB mrad high in elevation. Theaverage standard deviation, which has computed bytaking thesquare root of the average varianceiis 0.257 mrad in azimuthand 0.070 mrad in elevation. This value of azimuth trackingerror is 2.6 times larger than the standard deviation oftrained gunners tracking the same target. Trained gunnerswill track this target with a standard deviation of 0.1G0mrad in azimuth. The elevation tracking error is about whatis expec-ted of trained gunners yet when coupled with theazimuth tracking error it is smaller than expected. Pastexperience gained with TOW tracking errors indicate thattrained gunners will have elevation tracking erroramplitudes that are about 60 percent of the azimuth trackingerrors

The normalized PSD functions of the azimuth andelevation tracking errors are given in Figures 3.1 and 3,2,respectively. The accuracy of these estirrates is on theorder of 15 percent at the 95 percent confidence level. Thebandwidth or half-power point of these signals is between0.6 and 0.7 HZ in azimuth and 0.5 HZ in elevation. Thepeaks in the PSD functions occur at C.2 HZ in azimuth and0.1 HZ in elevation. These bandwidths and peaks areconsistent with tracking data analyzed in the past.

In accordance with Equation 2.8, the averagevariance of the LOS acceleration Is computed to be 2.7 mrad'sec4 . The corresponding standard deviation of theacceleration is 1.6 mrad/sec2. If targets uere prov~dingthis LOS motion, they would have to be accelerating at peaklevels of about 1.4g's at a range of 2.85 km. This level ofacceleration is greater than the acceleration capability ofa ground vehicle. Therefore, on the average, the angularaccelerations resulting from these tracking errors aregreater than those generated by evasive or maneuveringtargets.

Computer plots of 84 missile trajecto, ies arecontained in Appendix A. These data were used to

qualitatively compare the live-fire and simulatedtrajectories. Supplementing Appendix A are Table 3.2 and

I

Figure 3.3 which present the spatial differences anddistribution of these differences of 80 flights. The fourflights not contained in the data are 1119, 1150, 1241 and1337. Flights 1119,1150 and 1241 were removed 4rom thetable because they had a limited amount of live-fire data

but the live-fire data that exist compare fauorably with thesimuited trajectories. Flight 1337 was removed because the

simulated trajectory apparently exceeded the look-anglethe 'eby causing a breac In the guidance link. 'The look-angle Is the angle between the tracker and the missileflare. This phenomenon rarely occurs, but, when it doesp itis the result of high frequency noise being present in themissile system.

A review of the computer plots, Table 3.2 andFigure 3.3 indicate that flight 2407 does not agree with thecorresponding live-fire elevation trajectory. The live-fireelevation trajectory is flying erratically below theIntended LOS. Additionally, the spatial difference for thisflight Is 13.3 feet. A review of the trajecto:y plotsindicates that this is the only live-fire trajectory thatdoes not demonstrate reasonable agreement with the simulatedflight. The actual flight 2407 was attributed to possiblyfaulty equipment.

The spatial differences of the 79 remainingflights are plotted as a function of the azimuth trackingerror standard deviation and are given In Figure 3.4. Thereis a trend in these data that shows an exponentialrelationship between the spatial differences and thetracking error. This relationship is more pronounced Ifseven flights are removed from the data. These flights are1143,P 1152t 1201. 1206y 1217, 1304 and 1362. A review ofthe trajectory plots of these seven flights shows that thelarger spatial differences are the result of biases in allof the flights except 1143 and 1304. Flight 1143 exhibits alive-fire elevation excursion of 5.0 to 7.0 feet near theend of the flight which is not apparent In the simulatedtrajectory. Flight 1304 exhibits a lerge spatiol differenceof nearly 5.0 feet with smaller than average trackingerrors. This is the result of the actual missile 5tillrecovering from tracking error transients that occurredearlier in the flight.

A review of Figure 3.4 shows that the averagespatial differences between the real missile and thesimulation are about 2.0 feet for tracking error standarddeviations of 0.,)00 mrad or less and exponentiallyincreasing for larger tracking errors. It is shown In thenext section that the larger spatial differences are due to

14

I LOS motions forcing the missile to its acceleration li mits.

15

TABLE 3.1. TRACKING ERROR STATISTICS

AZIMUTH ELEVATIONFLIGHT MEAN SIGMA MEAN SIGMA

0 -.1669 .1530 .0195 .07621109 -.0248 .1068 .0406 .07071117 -.1392 .1140 .1591 .04901118 -.0685 .1221 .1611 .04581121 .0980 .3041 .0363 .10301122 .0377 .2211 -.0435 .04581124 -.2065 .1221 .1373 .0954

1127 -.1814 .1476 -.0245 .04001128 -.1192 .1480 -.0849 .04361129 -.1175 .1578 -.017 .02001130 -.0641 .1619 .0041 .06561131 -.1640 .1841 -.0393 .04691135 .0315 .2249 .1281 .04801136 -.1622 .2195 -.0027 .08721137 .0691 .1526 -.0143 .05001138 .0080 .1761 .1273 .03321139 -.0611 .1897 -.0339 .03321140 -.0588 .2642 .0488 .0663112 -.1918 .1533 -.1121 .07141143 -.0009 .1673 -.0480 .08891144 -.1513 .1175 -.1128 .05291145 -.1170 .1183 .2302 .05661146 .2439 .1652 -.0333 .06081151 -.2531 .2841 -.2157 .03461152 -.4777 .2304 -.4419 .02001153 -.0264 .1327 .0917 .06321154 .0007 .1371 .0178 .05101155 -.1869 .1393 -.0050 .06081156 -.2727 .1606 -.0684 .0548

1157 -.1281 .1010 .1417 .07551158 .0019 .1421 .2505 .07811159 -.1768 .1192 .0516 .04001201 -.5490 .2112 .4597 .05921203 .0585 .3464 -.2062 .07211204 .4339 .3762 .4399 .09221206 .0534 .1975 .4308 .06781210 -.0381 .3081 -.0971 .1304

212 -.1587 .2202 .1532 .05921217 .0448 .1910 .4580 .03161234 --.0171 .5442 .0561 .14281235 -.1749 .2865 -.1029 .04471236 .3404 .3782 -.0399 .07141237 .3644 .3887 -.0590 .05001239 .0361 .1868 .0560 .05391240 .2579 .3464 .0180 .0927

1241 -.4226 .6054 -.0991 .07071304 --.0586 .1428 .0190 .0400

16

ITABLE 3.1. TRACKING ERROR STATISTICS (Continued)

AZIMUTH ELEVATION

FLIGHT MEAN SIGMA MEAN SIGMA

1314 -.2197 .1490 -.1167 .03321317 .0697 .2066 .0742 .05741318 -.1563 .1229 -.0186 .05741324 -.0525 .1992 .0853 .04001327 -.0929 .2095 -.1405 .02001336 -.1481 .1407 .0661 .03001338 -.0165 .1546 -.0786 .06161339 -.1661 .2447 .0715 .03611340 .0241 .1349 -.0213 .03871342 -.3222 .3341 .0033 .07351360 .0185 .1345 -.0891 .08001361 .0527 .1703 -.0349 .04241362 .3925 .1105 -.0845 .05101370 .0994 .3764 -.1211 .06562407 .2231 .2126 .0096 .05572409 -.0634 .2579 -.0503 .04472410 -.108 1389 .0373 .06402412 -.1123 .3750 -.1300 .21472413 -.0818 .1732 -.0867 .05742428 .0409 .1849 -.0134 .04362434 -.0076 .1323 -.1221 .04692435 -.0549 .9608 -.0006 .20642436 -.0843 .2587 .0720 .05102437 -.1546 .1594 -.0555 .03002438 -.2233 .1513 .0522 .04802441 -.0554 .2076 .0160 .07752442 .0980 .2646 .0321 .07212446 -.3256 .4712 -.1517 .10392447 -.1733 .1830 -.0389 .07002449 .2381 .3028 -.0754 .05202451 -.1767 .194 .1010 .05392453 -.2624 .2366 -.1303 .04362454 -.2251 .2345 -.0957 .04122457 -.0231 .1513 -.0538 .0346

POOLED STATISTICS

MEAN -.0612 .2566 .0080 .0698SIGMA .1765 -- .1439 --

17

TABLE 3.2. SPATIAL DIFFERENCES BETWEEN TRAJECTORIES

AVERAGE AVERAGESPATIAL SPATIAL

FLIGHT DIFFERENCE FLIGHT DIFFERENCE

0 1.52 1235 2.851109 1.63 1236 2.861117 1.60 1237 5.481118 1.68 1239 2.661121 2.63 1240 5.381122 1.94 1304 4.841124 1.96 1314 1.591127 1.80 1317 2.131128 1.64 1318 1.751129 1.72 1324 1.381130 1.26 1327 2.091131 2.53 1336 1.411135 2.65 1338 2.001136 1.54 1339 1.921137 2.36 1340 2.211138 2.45 1342 4.161139 2.21130 1.13ot

1140 2.22 1361 1.691142 2.30 1362 2.701143 3.23 1370 2.431144 1.51 2407 13.231145 1.76 2409 3.301146 1.68 2410 1.761151 2.24 2412 7.551152 3.33 2413 2.211153 1.77 2428 2.391154 2.00 2434 1.261155 2.04 2435 7.751156 1.58 2436 2.781157 1.71 2437 1.671158 1.97 2438 2.001159 1.11 2441 1.891201 5.32 2442 2.701203 4.37 2446 5.791204 6.35 2447 2.611206 4.13 2449 4.481210 3.33 2451 1.871212 2.34 2453 1.491217 4.37 2454 2.831234 3.72 2457 1.63

18

2.0

18 AVERAGE OF 81 PSD'S

1.6-

T1.4-

4

V6 1.2-

01

.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

FREQUENCY, H -

Figure 3.1 Azimuth Tracking Error Normaliized PowerSpectral Density.

19

2.2

AVERAGE OF 81 PSO'S2.0

1.8

1.6

S1.4

d 1.2

L Ujw1.01

8 -

.6

.4-

.2

0 I I I I

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0FREQUENCY, Hi

Figure 3.2 Elevation Tracking Error Normalized Power SpectralDensity.

20

0

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Ito0

c

CIR

- a.CC/)

III-

In~~co 00n0 In 0 t

kD~gno3N

21-

(3)

z

zi

z

0 CY

0 z0

00

0 0 Y00 T

0 z0

00 C04

K ) X

vGor 0 0

.

0~

22

4. DISCUSSION

The overall results of this study show that themissile trajectories of the TEA-TOW prograr are the resultof gunner tracking errors except flight 2407 which does notfollow the gunner tracking error. A more important resultof this study is the agreement demonstrated between theAMSAA TOW missile simulation anq the actual system. It isshown in Figure 3.4 that the spatial differences re on theorder of 2.0 feet for tracking errors balow C,2CC mrad.These differences can be atttibuted to the following! (a)measurement errors in the tracking error and live-firetrajectory data (b) differences in the off-nominalconditions between the real system and the simulation (c)the actual missile still recovering from tracking errortransients earlier in the flight and (d) modeling errors.

For tracking errors beyond 0.200 mrad, the spatialdifferences show increasingly larger values. By making useof Equation 2.8, It can be shown that these differences arethe result of the larger oscillatory tracking errorsrequiring missile accelerations that are not available ifthe missile Is to follow the LOS. Using Figure 3.1 andEquation 2.8, and assuming all gunners exhibit a PSDequivalent to the average PSD, the resulting averagestandard deviation of the LOS acceleration is

°'acc - 'te [j (2'f)4 PSD (f )n df]1 2 4.1

Evaluating this integral, using Simpson~s rule, over abandwidth of .65 HZr gives

0acc = 5.7-t 4.2

The lateral missile motion required to follow the LOS motionIs given by

Ym = Rm Sin LOS

where Rmris the missile range. Successively differentiatingEquation 4.3 and using small angle epproxiffations give

Ym- Rm LOS + Rm LOS

2 3

anA

Y'yrmLOS + 2RnL6S RmLES Rm LOS L6S2

Assuming that

Rm=O 4e6

and for this example

Rm LOS>>2Rm LOS -Rm LOSLOS2 4.7

Equation 4e5 is reduced to

'm Rm LoS 4.

From Equation 4.8, it can be seen that the maxiffum requiredmissile acceleration will occur when the missile is near thetarget provided the LOS acceleration exhibits stationarityIn a statistical sense, By combining Equations 4.8 and 4.2sthe peak missile acceleration required to follow the LOSresulting from the tracking error Is given by

"m= 3 (5"7°'t ) (2.85) 499c

where 3 (5.7 Ot.) is the 3-sigma or peak value of the LCSangular acceleration in mrad/sec and 2.85 is the targetrange in kilometers.

The maximum lateral acceleration capability of themissile Is shown In Figure 41,. as a function of range. Ata target range near 3.0 km, the maximum available missileacceleratLon is just over 1,0g, Substituting this value ofacceleration into Equation 4.9 and solving for the trackingerror standard deviation, gives the value of the trackingerror standard deviation which forces the maximumacceleration capability of the missile. This value is 0.200mrad which Is where the larger spatial differences startoccurring in Figure 34,t However, there are several flightswhich still show reasonable spatial differences above this

24

value.

These results imply that the simulatior is a validrepresentation of the TOV missile system up to, and in somecases beyond, the point where the LOS inputs are such thatthe maximum available missile acceleration Is required. Interms of validity against maheuvering targets, the resultsIndicate that the missile simulation is valit againsttargets accelerating up to the acceleration limits of themissile provided the gunner tracking errors ore small. Thislevel of acceieration is greater then the accelefationcapability of a landborne vehicle.

25

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9 < CLL

0LIJ 3-

ILIC1 26

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5. CONCLUSIONS

The results of this study show that all but one ofthe TEA-TOW flights followed the gunners' tracking error.The live-fire traJectory of trial 2407 is not following thegunner tracking error and may be the result of faultyequipment.

The average azimuth tracking errors are 2.6 timeslarger than the average performance of trained gunnerstracking the target angular rates presented. The elevationtracking errors are about the same as those of trainedgunners but are smaller then expected, since the elevationtracking error is usually 60 percent of the azimuth trackingerror. The TEA-TOW elevation tracking errors are about 30percent of the azimuth tracking error. 'It is thereforeconcluded that adoption of the minimum training programssuch as that tested, would result in a degradation in TOWperformance over that which could be achieved with the fulltraining program.

From both a quantitative and qualitative analysisit is shown that the AMSAA TOW missile sirulation is validover a wide range of LOS inputs. In terms of acceleratingtargets the simulation is a valid representation of theactual missile system and is capable of providing reliableperformance estimates against targets accelerating up to1.0g at a range of 2.85 %,m.

27Next page is lank.

APPEND~IX A

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