(C71~

No. 13556

COMPUTER-BASED SIMULATION AND ANALYSIS OF M116A3 AND

M116A2E2 CHASSIS TRAILERS TRANSPORTING FIRE FINDER RADAR UNIT

NOVEMBER 1991

Michael K. PozoloU.S. Army Tank-Automotive CommandATTN: AMSTA-RYA

By Warren, MI 48397-5000

APPROVED FOR PUBLIC RELEASE: ~4 0 /SDITqRTRTUTIONq TS UNLIMITED

U.S. ARMY TANK-AUTOMOTIVE COMMANDRESEARCH, DEVELOPMENT & ENGINEERING CENTERWarren, Michigan 48397-5000

NOTICES

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Destroy this report when it is no longer needed. Do not returnit to the originator.

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1. AGENCY USE ONLY (Leave blank) .PORT 1991 3. REPORT PEnaX ANO DATES COVERED

4. TITLE AND SUBTITLE S. FUNDING NUMBERS

Computer Based Simulation and Analysis ofM116A3 and M116A2E2 Chassis TrailersTransporting Firefinder Radar Unit

6. AUTHOR(S)

Michael K. Pozolo

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) B. PERFORMING ORGANIZATIONREPORT NUMBER

U.S. Army Tank-Automotive Command 13556System Simulation and Technology DivisionWarren, MI 48397-5000

9. SPONSORING/ MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORING/ MONITORING

U.S. Army Tank-Automotive CommandSystem Simulation and Technology Division (AMSTA-RYA)Warren, MI 48397-5000

11. SUPPLEMENTARY NOTES

Unlimited

12a. DISTRIBUTION/AVAILABIUTY STATEMENT 12b. DISTRIBUTION CODE

13. ABSTRACT (Maximum 200 word)

This report presents a comparison of the ride dynamics andperformance of the M116A3 and M116A2E2 chassis trailers transporting theAN/TPQ-36 Firefinder radar unit. The M116A2E2 trailer has a set of sevenleaf springs and uses the M101/M116 hydraulic shock absorbers. TheM116A3 trailer has a set of 11 leaf springs and uses the M103 hydraulicshock absorbers. The comparison of the performance of the two trailersis drawn from a computer-based simulation of each trailer and its primemover using Dynamic Analysis and Design System (DADS) software. Thereport details the simulation of the High-Mobility Multi-Purpose WheeledVehicle (HMMWV) as the prime mover towing the subject trailers andpayload over bumps, potholes, slaloms, side slopes, and cross-countryterrain at a variety of speeds. Time history responses of importantdynamic characteristics are analyzed and plotted for each simulationperformed. Conclusions and recommendations are given for the use ofeither trailer for the transport of the Firefinder radar unit or similarhigh center-of-gravity payloads.

14. SUBJECT TERMS 1S. NUMBER OF PAGES

Computer-Based Simulation, Dynamic Modeling 36Vehicle Performance 16. PRICE CODE

17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION 20. LIMITATION OF ABSTRACTOF REPORT OF THIS PAGE OF ABSTRACTUnclassified Unclassified Unclassified

NSN 7540-01-280-5500 , 1 Standard Form 298 (qev 2-89)

p•miwbed by ANSI Sid 23t 0s

2

TABLE OF CONTENTS

SUMMARY . .. .. .. .. ... *. .. .. .. .. .. .. ..... 5

INTRODUCTION/OBJECTIVE. . . . . . . . . . . . . . . . . . . . . . . 6

PROCEDURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

RESULTS AND DISCUSSION . . . . ......... . . . . . . . . . . 9

CONCLUSION/RECOMMENDATIONS. . . . . . . . . . . . . . . . . . . . .11

APPENDIX A. TIME HISTORY PLOTS OF BUMP COURSE SIMULATIONS . . . . A-I

APPENDIX B. TIME HISTORY PLOTS OF POTHOLE COURSE SIMULATIONS. . . B-I

APPENDIX C. TIME HISTORY PLOTS OF SLALOM COURSE SIMULATIONS . . . C-I

APPENDIX D. TIME HISTORY PLOTS OF SIDE SLOPE COURSE SIMULATIONS . D-I

APPENDIX E. TIME HISTORY PLOTS OF APG ii CROSS-COUNTRY COURSESIMULATIONS . ........... . . . . . . . . . . E-I

LIST OF TABLES

TABLE 1. MII6-SERIES TRAILERS . ......... . . . . . . . . .6

TABLE 2. COMPUTER SIMULATIONS PERFORMED . . .. . . . . . . . . .8

TABLE 3. MODIFIED SUSPENSION EFFECT ON TRAILER CG HEIGHT. . . . .10

3

4

SUMMARY

This paper describes the computer-based modeling, simulation, and analysis ofthe Ml 1 6A3 and Ml 1 6A2E2 chassis trailers. The simulations were performed by theAnalytical and Physical Simulation Branch of the US Army Tank-AutomotiveCommand, System Simulation and Technology Division. The purpose of thesimulations was to determine if the M 11 6A2E2 and/or M 11 6A3 chassis trailers wouldbe capable of sustaining the mission requirements as transporter of the AN/TPQ-36Firefinder radar unit and also to determine which of the two trailers would be best forthis mission.

Computer-based dynamic models of both trailers were developed using DynamicAnalysis and Design System (DADS) software and all computations were performedon the Cray 2 supercomputer located at TACOM. A series of simulations were run ofeach trailer with the High Mobility Multi-Purpose Wheeled Vehicle (HMMWV) as theprime mover. The Firefinder radar unit was selected as the trailer payload. TheHMMWV/trailer combinations were simulated negotiating bump, pothole, slalom, andside slope courses at successively increasing speeds. Time history responses ofseveral dynamic parameters were recorded and plotted. The primary areas of interestanalyzed and compared were the roll, pitch, and yaw stability of the two trailers whileperforming the above mentioned simulations.

The results of the simulations indicated that the M1 66A2 and M 11 6A3 wouldlikely sustain the mission of transporting the Firefinder radar unit from a stability andride dynamics standpoint. The modified suspension of the M 11 6A3 trailer led to amuch improved performance in ride stability over the M 11 6A2E2 while negotiatingsevere vertical obstacles such as bumps and potholes. The results were most likelydue to the fact that the modified suspension of the M1 16A3 contains a set of leafsprings with a lower spring rate and greater allowable spring travel than those of theM 116A2E2, and also a set of heavier-duty, M103, gas shock absorbers. The "softer"springs and increased spring travel of the M1 16A3 suspension reduces the frequencyof jounce stop impacts when encountering vertical obstacles. The drawback to the"softer" springs is a reduction in roll stability when performing sudden lateralmovements. The differences in the two trailers was not significant in this areabecause the M103 shock absorbers effectively damped out the roll motion of theM1 16A3, thereby negating the adverse effect of the softer suspension.

5

INTRODUCTION/OBJECTIVE

In an effort to improve the mobility of the M1 16A2E2 trailer, the suspensionwas modified with a new set of 11 leaf springs and heavier-duty shock absorbers. Theresulting trailer configuration was classified as the M1 16A3. The purpose of thesuspension modifications was to increase the allowable spring travel distance andthereby reduce the frequency of jounce stop impacts with the trailer frame. Thesuspension modifications have led to the increased mobility and durability of theM1 16A3 trailer, and also allow for transport of payloads in excess of three quartersof a ton. Both trailers utilize HMMWV wheels and the offset axle developed by theTurtle Mountain Manufacturing Co. Table 1. lists the differences in the M1 16-seriestrailers.

M116A2 8740054

M116A2E1 Improved Springs (7 vs. 5 Leaves)Improved Frame (4" vs. 3")

M116A2E2 Offset axle

Increased Track Width to 72HMMWV Wheels and Tires

M116A3 Improved Springs (11 Leaves)Reinforced FrameAdjustable Wheeled Landing LegTwo Rear Landing LegsM103 Shock Absorber

Table 1. M 116-Series Trailers

The Analytical and Physical Simulation Branch of the U.S. Army Tank-Automotive Command, System Simulation and Technology Division (AMSTA-RYA)was asked by Product Manager Trailers (AMCPM-T) to determine if theM1 16A2E2/A3 trailers would meet the mission requirements of the Firefinder radarunit and to analyze the performance of the two trailers to determine which would bemost suitable. As a result, the System Simulation and Technology Division developedcomputer-based dynamic models of the HMMWV pulling both the M1 16A2E2 andM1 1 6A3 trailers supporting the Firefinder radar unit as the payload.

Each HMMWV/trailer combination was simulated negotiating a bump, potholeside slope, slalom, and Aberdeen Proving Ground course number 11 (APG 11) at arange of speeds. The purpose of the bump and pothole course simulations was to fully

6

exercise the suspensions of the M116A2E2 and M116A3 trailers. This meantproducing maximum leaf spring travel and forcing jounce stop impact between thetrailer axle and frame. The effort here was to determine how much improvement inride stability was witnessed in the M1 16A3 due to the increased spring travelallowance and lower spring rate of the 11 leaf springs, compared to the M1 16A2E2with the original suspension. The main drawback to the increased spring travelallowance of the M1 16A3 is an increase in overall center of gravity height. Also, thereduced spring rate of the 11 leaf springs, 680 lb/in, compared to the 720 lb/in rateof the six leaf springs used on the M1 16A2E2 results in a loss of longitudinal rollstability when encountering sudden lateral movements. For this reason, theHMMWV/trailer combinations were simulated negotiating a 120-foot longitudinal by11-foot lateral transition slalom maneuver, and a 20 percent right and left side sloperoll course. The purpose of these simulations was to determine how much the changein leaf springs deteriorated the roll stability of the M 11 6A3 as compared to theM 11 6A2E2. The trailers were also simulated traversing the APG 11 cross-countrycourse. The APG 11 course has a root mean square (RMS) vertical amplitude valueof 1.37 inches which can be considered as hilly cross-country. The purpose of thesesimulations was to determine the overall stability of the two trailer configurationstraveling over a high amplitude, high frequency road profile. A variety of each trailer'sdynamic parameters were recorded, plotted, analyzed, and compared for everysimulation.

PROCEDURE

The computer-based models were developed using the DADS software packagedeveloped by Computer Aided Design Software lnc.(CADSi). The leaf springs andshock absorbers were modeled using translational-spring-damping actuator (TSDA)elements which incorporate the respective spring rates and damping characteristics.The trailer chassis, axle, payload, and wheels were modeled as independent bodies.The mass and inertia properties of each body along with the longitudinal, lateral, andvertical stiffness properties of the tires were also included in the models. Severalmassless links , or distance constraints, that do not appear in the actual trailers, wereincorporated in the model. These massless links limit the trailer axle motion to verticaltranslation and roll about the longitudinal axis relative to the trailer frame and alsoaccount for the roll center and roll stiffness properties of the trailers. A computer-based DADS model of the HMMWV, created for a previous simulation project, wasused as the prime mover for the trailers.

The HMMWV/trailer models were simulated negotiating a 12 inch bump, with20 percent approach/departure angles, at speeds ranging from 15-25 mph (allsimulation speeds were in increments of 5 mph; i.e. 10, 15, 20 mph, etc.). The

7

models also were simulated negotiating both 9- and 12-inch potholes, with 100percent approach/departure angles, at speeds ranging from 5-15 mph. For both thebump and pothole courses, the HMMWV/trailer combination was simulated travelingon flat, paved road for 20 feet, encountering the obstacle with the driver's sidewheels of the HMMWV and trailers, and then traveling on flat, paved road until asteady state response was again reached for each dynamic parameter recorded. TheHMMWV/trailer combinations were simulated negotiating a slalom course whichconsisted of starting in the right lane of a flat, paved road and maneuvering into theleft lane around a pylon 120 feet forward of the starting position and returning to theright lane within another 120-foot transition. These slalom maneuvers were performedat 20-30 mph. The next set of simulations consisted of the HMMWV/trailercombinations traversing a side slope course. The side slope course requires thecombination to travel 20 feet of flat, paved road, 100 feet of transition to a 20percent right side slope, 100 feet of 20% right side slope, 100 feet of transition toa 20 percent left side slope, 100 feet of 20 percent left side slope, and finallytransition back to flat paved road. The roll course simulations were performed atvehicle speeds of 20-30 mph. The APG 11 course simulations were run at speeds of15-25 mph. These speeds were chosen to be five mph above and below the Firefindermission requirement of 20 mph maximum speed for this type of cross country course.Table 2. summarizes the simulations performed.

COURSE DESCRIPTION SPEEDS

BUMP 12" HEIGHT, 20% APP/DEP ANGLE 15,20,25 MPH

POTHOLE 9" DEPTH, 100% APP/DEP ANGLE 5,10,15 MPH

POTHOLE 12" DEPTH, 100% APP/DEP ANGLE 5,10,15 MPH

SLALOM 120' x 11' LONGITUDINAL/LATERAL 20,25,30 MPH

SIDE SLOPE 20% RIGHT & LEFT SIDE SLOPE 20,25,30 MPH

APG 11 400 FT. X-COUNTRY, RMS 1.37 15,20,25 MPH

Table 2. Computer Simulations Performed

For every simulation, the driver's side leaf spring's deflection and force wasrecorded, along with the roll, pitch, and yaw angles of the subject trailers. The timehistory responses of these dynamic parameters were plotted against each other foreach trailer for comparison purposes. In all, 30 simulations were run (15 per trailer)and a total of 240 time history dynamic parameter responses were recorded.

8

RESULTS AND DISCUSSION

The results of the computer-based simulation of the HMMWV/M 116A2E2 andHMMWV/M116A3 combinations are presented and discussed for each type(course/maneuver) of simulation performed. The primary dynamic parameters ofinterest analyzed are the roll, pitch, and yaw angles of the M116A2E2 and theM 11 6A3 trailers while transporting the Firefinder radar unit.

Bump Course (15-25 mph); (See App. A, plots 1-9.)

The bump course maneuver showed the most significant difference in theperformance of the trailers. The M 11 6A3 was able to negotiate the 12-inchbump and remain upright for all speeds simulated. The M116A2E2, on theother hand, showed a roll over situation at the 20 and 25 mph speeds. Thereason for this difference is the increased allowable spring travel and reducedspring stiffness of the M 11 6A3 allowed that trailer's suspension to absorbmost of the impact of the obstacle whereas the M1 16A2E2 was forced into amuch more severe jounce stop impact. This resulted in a much greater rollmoment to be imparted to the M1 16A2E2, thereby resulting in the roll over. Itshould be emphasized that encountering a 12-inch bump at speeds up to 25mph would be an unlikely occurrence during the Firefinder mission. This typeof situation would probably only occur rarely during an evasive maneuver orpanic situation.

Pothole Course (5-15 mph); (See App. B, plots 1-18.)

The result of the pothole simulations, for both the 9- and 12-inch holes, show

that the roll angle of the M1 16A3 is much less severe than that of theMl 16A2E2. This difference becomes greater at the higher speeds. At 15 mph,the roll angle of the M1 16A3 is as much as 50 percent less than that of theMl 16A2E2 for both pothole depths. This shows much greater stability in theM 11 6A3 compared to the M 11 6A2E2 although neither trailer came close to arollover situation. The reasons for the improved roll stability are the same as forthe improved performance of the M1 16A3 during the bump course simulations,reduced spring stiffness and increased allowable spring travel. The pitch andyaw angles of each trailer remained insignificant throughout all of the potholecourse simulations.

Slalom Maneuver (20-30 mph); (See App. C, plots 1-9.)

There were no significant differences in the roll, pitch, and yaw angles

9

throughout the slalom maneuver simulations. Both trailer configurationsremained stable.

Side Slope Course (20-30 mph); (See App. D, plots 1-9.)

There were no significant differences in the roll, pitch, and yaw anglesthroughout the side slope course simulations. Both trailer configurationsremained stable.

APG 11 Cross-Country Course (15-25 mph); (See App. E, plots 1-9)

The APG 11 cross-country course simulations showed the most drasticdifferences between the two trailers in the area of roll stability. The Ml 16A3again out performed the M1 16A2E2 in this area. The 25 mph simulationshowed as much as an 80 percent reduction in the roll angle of the M11 6A3compared to the M1 16A2E2. Although neither trailer reached a rolloversituation, the M116A2E2 appeared much less stable. Again, the improvedsuspension of the M1 16A3 is most likely accountable for this difference.

Another area of concern in the transport of the Firefinder radar unit is the highcenter of gravity of the trailer and payload configuration. In the case of these twotrailers, it has been determined that the increased spring travel of the M1 1 6A3 willnot significantly affect the overall trailer vertical cg height because the reduced springrate of the leaf springs allows the trailer to settle at a center of gravity height onlyslightly greater than that of the M1 16A2E2. Table 3. shows the relative difference incg height of the two trailers with the fire finder radar unit as payload.

Spring Jounce JounceRate Clearance Clearance

(unloaded) (w/firefinder)

M1 16A2E2 720 #/in 4.485 in 2.93 in

M116A3 680 #/in 5.25 in 3.60 in

CG Height 0.765 in 0.67 inIncrease

Table 3. Modified Suspension Effect on Trailer Center of Gravity Height.

10

One final note, the M103 gas shock absorbers used on the M 116A3 showeda considerable improvement over the shocks on the M 11 6A2E2. All plots indicate theM1 16A3 damped out considerably quicker than the M1 16A2E2. This is an importantfactor in overall system stability since this most likely accounts for there being nosignificant differences in the overall trailer roll stability in the slalom and side slopecourses.

CONCLUSIONS/RECOMMENDATIONS

Based on the results of the computer-based simulation, ride dynamics, andstability analysis of the M 11 6A3 and M 11 6A2E2 trailer/Firefinder configurations, bothtrailers would likely be able to perform the mission of transporting the Firefinder radarunit, however, the M1 16A3 would be the better of the two.

The simulations show an improvement in the performance of the M1 16A3 overthe M1 16A2E2 when negotiating severe obstacles such as bumps and potholes. Thedifference between the two trailers in this area becomes more dramatic as the vehiclespeed and/or severity of the obstacle is increased. The reason for this improvementis the increased allowable spring travel and reduced spring rate of the 11 leaf springsused on the M1 16A3. The increased allowable spring travel and reduced spring ratewas expected to lead to a decrease in the longitudinal roll-stability of the M1 16A3during sudden lateral maneuvers such as a lane change or slalom (obstacle avoidance).The reduced roll stability is caused by a reduced roll stiffness due to the "softer" 11leaf springs on the M 11 6A3 compared to the 6 leaf springs on the M 11 6A2E2. Thelongitudinal roll stability of the M1 16A3, however, was not significantly different thanthat of the Ml 16A2E2 during the lateral maneuvers. The use of the gas shockabsorbers from the M103 trailer on the Ml16A3 greatly improved the dampingcharacteristics of the M1 16A3 and were most likely the reason the roll stability of thetwo trailers was not significantly different.

11

12

APPENDIX A

Time History Plots of Bump Course Simulations

A-1

12-inch Dump att 15 mnph

0.6-

0.4-

0.2-

0.0-

-0 .2-

0 10

___M116A2E2 ROLLT JUIGL- (radiatns) vse TIME (se-conds)---- M116A3 ROLLa ANGL-E (radi:a~ns) %rs TIME (sftcond.g)

12-inch Bump aIt 20 mph1.5-

1 .0-

0- 8 10

M116A2E2 ROLLZ AUNGLE (3radians) -.s TIME (sle-cond.)e---- M13.6A3 ROLL, AN4GL.E (ra~diafns) %Ps TIME ( scons)

2

12-incxh Bxump a~t- 25 mrph1.5-

1.0-

0.0--

-0.5--T

o 4 6 810

____ 116A2EC2 ROLLT ANGLX.E (radiafns) %vs TIME (secoqnds)---- M11GA3 ROLa LWAGLýE (radi~ans) vso TIME (secomnds)

3

A-2

12-incl-h Buimp a~t 15 mph

0.2-

0.0-

-0.*1-

-0.2-

0 2 468 10

M__ M1EA.2E:2 PITrCH ANGLýE (radcilas) vse TIME (sieconds)---- m116At3 PITCH ANGL~E (rvadi~az-x) V's MTIMTE (meocondsl)

4

12-iLnch B3ump ait 20 mph

-1-

-2--

0 2 4 6 810

___M116A.2E PITrCH A.NGLEM (radia~ns) Nvs TIME (osecopnds)M116Ak3 PITWCH AN4GLE (.radcILa~na) Iv' TrIME (secondmcs)

12-iLnch B~ump att 25 mph

0-

-2-

-3-

-4- I

0 2 4 6 810

M__ IMI 6AV2E2 PITWCH ANGLýE (radia-mn.) N's TIlME (secondsxa)M11l6Az3 PITCH ANGLEM (rdan)sTME (seýconds)

A-3

12-iLnc-h Burnp att 15 rnph

0.20-

0.15-

0. 10- ____

0 .05 _ _ _ _ _ _ _ _ _ _

0.*00-

-0.05 ---- r

0 2 4610

___M116A2E2 YAW ANGLE (radL6ans) vsr TrIME (semcondns)---- 116A3 YAW ANGL-E (.radla~ns) %rs TME (sem4condsf)

-7

12-in-ch Sumnp att 20 rmph4-

3- ----

2-

0 2 46 a 10

___M116A2E2 YAW ANGI..E (radi:a~ns) %re ITIMTE (gfeconds)c---- m11EA3 YAW ANGLIE (r7adi:ans~) vs TIME (0sacondsa)

12-;inch Bump at- 25 mph4-

3-

2-

0-

0 2 4 6 810

___M116A23E2 YAW ANGLE (radians~rj) vs TIMI-E (0Secondls)---- 1116A3 YAW ANGLýE (rmadlmns) vs TIMME (se-condse)

A-4

APPENDIX B

Time History Plots of Pothole Course Simulations

B-1

9-i~nch Poitho~le atý 5 mqph

0.4-

0.2- _____

0.0-

-0.2-

-0.*4-02 46810

___M116A2E2 IROLLT AN4GLE (radiaLen.) %re TIME (secondscl)---- 2116A3 ROLLý A.NGLEX (:radilakr) .re TIME (secondls)

9-inch Pot~hole atý 10 mnph0.4-

0.2-

0.0- -

-0.2-

0 2 4 6 a 10

___ 4116A2E2 ROLLT ANGLE (r7adians) xus TIME (selcondns)---- M116A3 ROLLT AýNGL-E (rWfadians) Nvs TIME (secondscl)

2

9-Iinch Pot-hole4 att 15 mrph0.3-

0.2-

0.1-

0 2 4 6 8 10

___Ml16A2E2 ROLL. ANlq=E (rvadians) WsTmE= (seconds)-M-- 1116Aý3 ]ROLL. ANGL.E (radiantrs) vs TSIME (seco nds)

3

B-2

9-inc-h Porthole! atl- 5 mrph

o0.05-

0.00- - - _____

-0.05-______

-0.*10- -

0 2 4 6 8 10

M116A.2E2 PITMCH ANGLE (radi:a~ns3) vas TIMMM (sec<>cnd)---- M116A.3 PITWCH jkAGLEr (rfadians) %re TIME (secondsl)

4

9-incx-h 3Ponthole atl- 10 mph0.*10-

0.*05-

0.00- - - - -- -

-0 .05-

-0.10-

0 2 4 6 8 1.0

M116A,2E2 PITMCH ANGLTE (=qadlLansx) N's TIMME (eaconds)l---- M116A,3 PMITCH ANGLaE (=mad-Lfns) -re TIME (seondls)

5

9-iLnc-h Potlhole4 a-t 15 mnph

0.10-

0 .05-

-0 .05-

-0.10-

0 2 4 6 8 10

M116A2E2 3PITCH ANGLE (radiaLfns) %re'sTME (sem.conds)M11A3PITCH ANGLE %raa rn e W TME (stco-nds)

B-3

9-inch Po~tho~le att 5 mp~h0.08-

0 .06 - _____ __ ___

O0.04 - _____

0.*02-N

0.00-______

-0.02-

0 2 4 6 a 10

___M3146A2E2 YAW AVGLýE (ra~diano) Ivs TIE (:eco~nds)---- M116AL3 YAW ANGLýE (r.ias) .sTeIM. (seconds)

7

Xio- 9-inch PotZhole at- 10 mrph

1.*00-

0.75-

0.50-

0.25-S ___

0.00-

-0.25-

-0.50-------r

0 2 4 6 8 10

MI I6A2E2 YAW ANGL1.E (radians) %re TIZ- (seco-nds)---- M116A3 YAW AN4GLE (adia4ns) %rs TImz (oftcondls)

8

9-inch Po)tholeo at 15 mrph0.125 -

0 .100 -

0.*075-

0.*050- _____

0.025-

0.000------

-0.025-

02 4 6810

____ 116A2E2 YAW ANGLaE (radiafns) %vs TXMM (seoCndsm)---- M116A3 YAW ANGL.E (radians) vso TIME (seconds)

9

B-4

12-Inch ]Poýtholmekat 5 mph0.4- _____

0.2-

-0.*2-

-0.4-

0 2 4 6 S10

___M116A.2E2 ROLL ANGLýE (3radil:ans) N.s TIME(scd)---- mii1ý63 ROLL, ANGLE (=madia~ns) %rs TIME- (seaconds)

10

12-iLnch Po~t-ho~l at 10 mph0.8-

0.6-

0.4-

0.2-

0.0-

-0.2-

-0.4- -r

0 2 4 6 810

___M116A2E2 ROLLT UANGLE (radil:ams) %vs TIM?. (se~condcs)---- M116A3 ROLLT AkNGLE (radi:a~ns) -,re ItME (aftcondsl)

11

12-i-nc-h Po-tholef at- 15 mph0.*6-

0.4- _____

0.2- ___

-0.2-

08 10

___M116A2E2 RkOLLT A.NGL.E (.radi~ans) %vs TIEb (seMconds)---- M116A3 ROLLý ANGLEM (=adia~ne) %vs TIM-E (secondls)

12

B-5

12-Inch Potlho~le a~t S mnph0.10- I____0.05- _____

0.00-

-0.05-A

-0. 10-

-0.15-

0 2 4 6 8 10

__I_ M16A2E2 PlITCH ANGLEX (radia:Lmn.) %re TIME (seacondcs)14116A3 PITCH ANGLaE (waiansm) xrs TIZ4E (seconds)

13

12-inch Poýthole4 att 10 mph0.1-

-0.2-

-0.3-

0 2 4 8 10

___M116A2E2 PITCH ANGLýE (rqadians) -.r TIME (Setcmnds)---- 116A3 PITTCH ANG~LE (.rmadiamn.) xva TIME (sec=onds)

12-inch Pomt-holt at- 15 mph

0. 10-

0.*05-A

0.00-- ____ _

-0.05--_____ ___ __

-0.*10-

-0.15-

0 2 4 6 a .10

___ 116A2E2 ]PITCH ANGLE (radiatn.) vrs TrIME (sea4conds)---- 116A3 PITCH AN4GLE (rvadiaLens) %re TIME (se4condsI)

B-6

12-inch Po)thole a~t 5 m-ph0.15S

0.10-

0 .05- ___

-0.05-

-0.10-

0 2 4 6 8 10

___M1.16A,2E2 YAW ANGLýE (radialj-ns) NV5 rVIE (se0conds)

---- M116A3 YAmW AýNGLýE (rAadiaens) Nrs TIxmz (seco~nds)

16

12-iLnch Po~tholef aot 10 mph

0.*15-

0.*10-

0 .05-

0.*00--

-0.05-

0 2 4 6 a 10

___M116A2E2 YAW ANGLE. (radiansLr~) %rs ITI (eons---- Ml16A3 YJAWP ANGLE (r=adi-a~ngs) xris TIME (eco4=nds)

17

12-i~nch Pcotho~le at 15 mph

0.15-

0.*10-

0.*05-A

0.00-

-0.05-

0 2 46 8 10

____ 116A2E2 YAW A:NGL.E (.radci;ansi) %s TIZ4E (s~econds)---- M116A3 YAW uANGLE (.ra~dians) xvs TIM3E (seq.condsg)

B-7

APPENDIX C

Time History Plots of Slalom Course Simulations

C-1

Sl-talom Courst a~t 20 mrph0 .04-

0.02- ____

0.*00-

-0 .02 - ____

-0.04-

0 2 4 6 810

___M116A,2E2 ROLL ANGLýE (r:fadians) murs TIME (seconds)---- M116A.3 ROLL, ANGL-IE (rad~lafne) Nrs TIrME (seco0nds)

Xl 0- Sla~lom Co-urse at- 25 mph

2

Sl-alomxr Co~urse alt 30 mph

0.*10-

0.05- '

0 .00--

-0 .05-

-0.10-

0 2 4 6 8 10

___M116A2E2 ROLL, AUNGLE (radcijanS) %re TIM-E (semconds)M116A3 ROLLý A6NGLE (radians) vse TxmE (Sse~conds)

3

C-2

X102 Slalom Couame at- 20 mrph0.4-

0.2-

0.0-

-0.4-

-0.6-r

0 2 4 6 8 10

___M116AM2E2 PITCH ANGLE (3radlan.) NV. TIZME (aeondpcs)---- M116A3 PITCH ANGL-E (radiafn.) '.'u TIME Cuaconds)

4

X10o 2 Slalom Cc-urue a-t 25 mnph

0.50-

0.25-

0.00-.- _ _ _ _ _ _ _ _ _ _

-0.25-

-0.7--

-1L.00-

0 2 4 6 8 10

___M116AI23E2 PITCH ANGLýE (rvadciano) %re TIME (so,=oncdu)-M116A3 PITCH ANGLýE (%din. ev TIME (oooonda)

5

Slalom Courom at 30 mph0.02-

0.01-

0.000

M116A2E PITCH ANGLýE (radilan.) %e TIME (se=ond.)

6

C-3

Slalomn Ccourste a-t 20 mph0.2-

0.1-

0.0-

-0.2-

0 2 4 6 810

___M116-A2E:2 YAW ANGLýE (ra~dia~ns) v'S TI1ME (s~econds)---- M116AL3 YAW ANGLE (raMd.LanS) V's- TInE (Sccondls)

7

Slalocm C~oursie alt 25 mnph0.3-

0.2-

0.1-

0 .0-

-0. 1-

-0. 2-

0 2 4 6 8 10

___M116Aý2E2 YAvW ANLEa (ra~dians) V'sa rTIME ( se.conds)---- M116AL3 YAW ANGLE (r7adi:a~ns) N.'s TIM~E (se4-condsa)

Slalo-cm C-urses art 30 mph

-0.44

APPENDIX D

Time History Plots of Side Slope Course Simulations

D-1

S~ide4 SXlope Co0Urse atl 20 mph0.05-

-0.05-____ __

-0.10-

-0.15-

-0.20-

- 0 .-- -- -- ----

0 2 4 6 8 10

___M116A,2E2 RtOLL ANGLýE (radians) -.s TIMME (sea-conds)M16A RL AGL .radiafns) %rs TIlME (setcondcs)

Sidce Sl-~ope Co-urseý at* 25 mrph0.4-

0.2-

0 .0-

-0.2-

-0.4

0 2 4 6 8 10

___M116Ak2E2 ROLLT AkNGLIE (radcians)vse rTIME (secopnds)---- M116Aý3 ROLL AN2GLE (radi:ans3) %r TIXME (3seconds)

2

Sidel- SlopeD Co~urse avt 30 mph0.4-

0.2-

0.0- -

-0.*2-

-0.4-

0 2 4 6 8 10

____ 11GA2E2 RkOLL ANGLE (radclles) vs 'TIME (Se1-ccnd)---- M316Ak3 ROLL.T AN4GLE (=adians) 'vs TIME (seco.nds)

3

D-2

X1o-2

Sidem Slo~pe Co:urse at- 20 rnph0.75-

0.*50-

0.25-

0.00-

-0.25-

-0.50

02 41 830

___M3.16A2E2 PITCH AN.1GLE (.radi:ans) vso TIZME (seconds)---- M116A-3 I-ITCH ANGLEX (3radi:atns) X-s TIlME (0eondBe)

4

X10o2

Sidet Slopeo Courset atý 25 mph

1.0-

0.5-

0.0--

-0.*5-

-1 .0-0 2 4 6 a 10

____ M16A2E2 PITCH ANGL (rdins 3Cvs:mrx TIME-W (secondsw)---- M116A3 PITCH ANGLýE (radiafns) %rs TIMM (sekconds)

5

X10-1 S;Lide Slcope Ccou~rse at 30 mnph0.10-

0.*05-

0.00---

-0.05-

-0. 10-

0 2 4 6 8 10

14__ 116"2E2 PITCH ANOMLE (raians) s~r TIbm (seconds)---- 2116A3 PITCH ANGL.E (%dan)v TIME (se~conds)

D-3

X101 Sidet Slo~pe Co~urse at- 20 mph0.25-

0.*00-

-0.*25-

-0 .50-

-0.75-

-1.00-

0 2 46a1

___M116A.2E2 'YAW ANGLE- (3radla~ns)m. WsTIMEm(secoDnds)---- M116A3 YAWm ANGLE (rfadians) xs TIME (se0aonds)

7

Sidel Slo~pe Coxu=04 aLt 25 mph

0.10-

0.00- _

-0.05-

-0.10- T-0 2 4 6 8 10

___M116A2E2 YZAW ANGLýE (.radci-anrs) x~a TrIME (s9condrxs)---- M116A3 YAW ~ANL.E: (radi:a~ns3) Xvs TME (seM-condsI)

Sidel Slopep Co~urgse alt 30 mph0.2-

0. 1-

0.0-

-0.2-

0 2 8 10

___M11l6A2E2 YAW ANGLEX (radija~ns) %rs TI:ME (se04condsl)---- m116An3 YAW ANLEa (rfadiatns) %rs TIME (seconds)

D-4

APPENDIX E

Time History Plots of APG 11 Cross-Country Course Simulations

E-1

.APGC- MI Crossm-Countr-y Co-urse a-t 15 rnph0.*04-__ ___

0.*02-

-0 .02 -

-0 .04 - ri T T TT rTl T ---

0.0 2.5 5.0 7.5 10.0 12.5 15.0

___M116k2E:2 ROLLT A.NGLE (3radclLans) vs ITIME (seco~ands)---- M116AL3 ROlL.T ANGLýE (radiajns) '%,s TIMEM (setco)nds)

A.PG 11 Crosws-Co~untr-y Co~urse avt 20 mph0.2-

0.0- A

-0.2 1-____

0.0 2.5 5.0 7.5 10.0 12.5 25.0

___M116A2E:2 tOLL JANGLE (=mcd.ans) vs TIME (SeD-conds)M116A3 ROLANGLE (-radc:a~rxs) vs TI=ME (sa49_cond~s)

2

AG11 CroDss-Count-ry Co~urse atO- 25 mph0.4-

0.2-

0.*0- ~-

0.0 2.5 5.0 7.5 10.0 12.5 15.0

---- M116A3 ROLLý ANGLE (radija~ns) -.s TIME (ses=rcnd)

3

E-2

0.2- ~A.PG 11 Cr:oss-Countr=y CoDurse att 15 mrph

0.1- ____

0.0- V~.ý /"

-0.1- . _ _ _ ._ __ _ ._._.._.

0.0 2.5 5.0' 7.5S 13.0 12 .5 15.0

____?116A2E2 PITCH ANGL.E (r:'aditas) vsr TIXME (seaconds)

M116A3 PITCH AkNGL.E (radlians) XYs Trlr4E (ts4econdis)

4

AIPG 11 Crossm-Ccountry Coursef at 20 mph0.2-

0.1-

-0.0-

-0.31

0.0 2.5 5.0 7.5 10.0 12.5 15.0

___M116A2E2 PITrCH ANGLEM (rvadianes) vse TIME (secocndsm)--- M116Az3 PxITCH ANLq~E (ratdians) se TIME (se=condsm)

5

APG 11 rosCuryCo-urse atl 25 mph0.2-

-0.1-

-0.2-

0.0 2.S 5.0 7.5 10.0 12.5 15.0

___M116A2E2 PITCH ANGLýE ( radciatns) Iva TIME (sercondsm)---- M116A3 PITCH ANGLýE (radiamns) %vs TIME (semcnds)

6

E-3

A~Pc 11 Crossm-Coun~try C'ourse at 15 mrph0.*05-__ ___

0.*04

0.03-

0.02-

0.01-

0.00-

0.0 2.5 5.0 7.5 10.0 12.5 15.0

_____ 16A2E2 YAVW ANGLýE (radlamans) %rgs rZXM (Sdbco(ndls)---- 1116A3 YAW ANGL.E (rmadiams) N70 =:ME (seaconds)

7

A.PG 11 Cro~ss-Co~untr.y Caourse a-t 20 mph

0.05

0J00

-0.0-

0.0 2.5 5.0 7.5 10.0 12.5 15.0

___M116A2E2 YAW ANGLXE (radi:a~ns) vsg WIM a (seoaCnds)---- M116A3 YAW ANGLE (rdins Ws TI (seconds)

9

0.E-4

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