DISl,)S.,)7O 4

A j

MEMORANDUM REPORT BRL-MR-3870

N BRLUSE OF THE MAGNUS FORCE IN

THE MODIFIED POINT MASS TRAJECTORY MODEL

ROBERT F. LIESKE DTICELECTE fl

OCTOBER 1990

APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLI)AIfED.

U.S. ARMY LABORATORY COMMAND

BALLISTIC RESEARCH LABORATORYABERDEEN PROVING GROUND, MARYLAND

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1.AGENCY US ONLY (Lesti ave 2.. REPORT DAT a I REPO YPE AND IDATES COVEREDIOctober 1990 Final______________

4. TITLE AND SUBTITLE S. FUNDING NUMBERS

Use of the Magnus Fore. in the Modified Point MassTrajectory Model IL16261BABOO

9. AUTHOR(S)

Robert F. Lieske

7. PERFORMING ORGANIZATION NAME(S) AND XODOPSS(ES) 1. PERFORMING ORGANIZATIONREPORT NUMBER

9. SPONSORING / MONITORING AGEN4CY NAME(S) AND ADDRESS(ES) 10. SPONSORING / MONITORING

U.S. Army Ballistic Research Laboratory AGENCY REPORT NUMBER

ATTI: SLCBR-DD-T NLM37Aberdeen Proving Grounds ND 21005-5066 3 -67

11. SUPPLEMENTARY NOTES

128. SISTAROVUTIO / AVAILAIILITV STATEMENT 12b. DISTRIBUTION COON

Approved for public release; distribution is unlimited.

,:wA method is presented for determining the Magnus force coefficient for use withthe Modified Point Knee Trajectory model, to improve the simulated time of flight,based on the firing table experimental range firing Impact and time-of-flight data.A comparison Is made with the Magnus force coefficients determined from aerodynamictesting for the 155gm, RE, M107 and 8-Inch, RE, RA, M650 projectiles. The Magnusforce coefficients contained in the firing table data bass for artillery projectilesare presented.1/ /

11. SUBENT TERMS 15L NUMBIR OF PAGES

~-"Magnus Force 1 4 Flight Simulation t-) 1(! 25Trajectory Modelingi IL. WEE CODE

17~ ~ ~~~~1. SECURITY CLASSIFICATION ilSCRYCASIIA1N1. SECURITY CLASSIFICATION 20. LIMITATION OF ABSTRACTOF REPOfRT I OF THIS PAGE I OF ABSTRACT

UNCLAiSSIFIED UNCLASSIFIED UNCLASSIFID SARNSN 7540-01.2100.3533 Standard Form 298= g.25f

UNCLASSIFIED PrIubdMy10I1 g i

bizromoINALLY LIFT suAm.

Acknowledgement

The author would like to express his appreciation to Messrs. James W.Bradley, Robert L. McCoy and Charles J. Nietubicz for their very helpful com-ments and suggestions during the preparation and review of this report.

""YDT IG

1.C I (IAccesion PO

NINS IIA&1DTIC TAB 0Unarnounocd 0JustifioatL@n

ByDltribution ,

Ava ilab ilitY Codes0-11. and/or

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J.N-rhTioNALLY LIFT ULAxK.

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Table of ContentsPage

List of Figures ........ ....................... vii

List of Tables . . . .. . . . . .. . . . . . . . . . . . . . . . .. . . .. . . . ix

I. Introduction . . . . . . . . . . . . .. . . . . . . . . . .. . . .. . . .. . . . I

II. Discussion and Results .............................. 1

III. Conclusions . . . . . . . . .. . . . . . . . . . . . . . . . . . .. . . .. . . . 4

References ............................................ 15

Distribution List ...... ................................. 17

IN7991IONALLY LMl BLANK.

List of FiguresFigare PaLe

1 Trajectory height versus range for projectile 155mm, HE, M107, fired withpropelling charge M119AI, charge 8 .............. . .........

2 Estimated yaw of repose versus time of flight for projectile 155mm, HE,M107, fired with propelling charge M119A1, charge 8. ............... 6

3 Difference between observed and simulated time of flight (A time of flight)versus simulated time of flight for projectile, 155mm, HE, M107 fired withpropelling charge M3AI, charge 1G ......................... 7

4 Difference between observed and simulated time of flight (A time of flight)versus simulated time of flight for projectile, 165mm, HE, M107 fired withpropelling charge M3A1, charge 3G .......................... 8

5 Difference between observed and simulated time of flight (A time of flight)versus simulated time of flight for projectile, 155mm, HE, MI07 fired withpropelling charge M3Al, charge 5G ........................ 9

6 Difference between observed and simulated time of flight (A time of flight)versus simulated time of flight for projectile, 155mm, HE, M107 fired withpropelling charge M4A2, charge 5W. ... .............. ... 10

7 Difference between observed and simulated time of flight (A time of flight)versus simulated time of flight for projectile, 155mm, HE, M107 fired withpropelling charge M4A2, charge 7W ......................... 11

8 Difference between observed and simulated time of flight (A time of flight)versus simulated time of flight for projectile, 155mm, HE, M107 fired withpropelling charge M119Al, charge 8 .................. ... 12

9 Magnus force coefficient for the 155mm, HE, Mi07, projectile (Figure 26 ofReference 3) with the effective Magnus force coefficient added ........ .. 13

10 Magnus force coefficient for the 8-Inch, HE, RA, M650, projectile (Figure 9of Reference 4) with the effective Magnus force coefficient added..... ... 14

vi'

LvmriomyLmr ULANK,

viii

List of Tables

1 Significance of Magnus Force Coefficient (CNPI ) for Projectile 155mm, HE,M107 Fired with Propelling Charge M1gAI ....................... 2

2 Firing Table Data Base Magnus Force Coefficients (CNP. ).......... 3

ix

1I%,rI!NllNoxM Y LzFT sLA1c

I. Introduction

The Modified Point Mass Trajectory Model 1.2 is the primary method of trajectorysimulation used in the preparation of Firing Tables. This model requires three typesof input data: projectile mass properties, aerodynamic coefficients and the performanceparameters determined from experimental range testing. This report discusses the sig-nificance of the Magnus force coefficient and a method of determining the Magnus forcecoefficient for trajectory simulation using the Modified Point Masi Trajectory model. Italso compares the Magnus force coefficients of the 155mm, HE, M107 and the 8-Inch, HE,RA, M650 projectiles with results based on aerodynamic testing reported by MacAllisterand Krial 3 and by Piddington, 4 respectively.

II. Discussion and Results

The 155mm, HE, M107 projectile fired with propelling charge M119A1, chaage 8 (684metres per second muzzle velocity) is used as an example to show the effect of the Magnusforce on trajectory time of flight. Figure 1 shows th- trajectory height versus range forprojectiles fired with quadrant elevations of 400, 800 and 1200 mils. Figure 2 presentsthe Modified Point Mass Trajectory model estimate for the yaw of repose versus time offlight for the three trajectories. The yaw of repose is the steady-state angle of attack dueto gravity-induced curvature of the trajectory.$ The nose of a spinning projectile is to theright of its flight path; therefore, the Magnus force, which is perpendicular to the yawof repose, results in an acceleration in the vertical plane with the acceleration increasingproportionally with the yaw of repose.

Artillery projectiles fired at quadrant elevations up to approximately 1300 mils willnormally function properly; however, projectiles fired at higher quadrant elevations exhibiterratic flight performance, such as drift to the left, base first impacts, large range anddeflection dispersion, etc.6 A yaw of repose limit of .6 radian (34.4 degrees), based onexperimental range firings, has been included in the Modified Point Mass Trajectory modelto determine the maximum firing quadrant elevation used in the preparation of aimingdata.?

The form factor, a multiplier on the total drag term, is the parameter ubed -in theModified Point Mass Trajectory model to achieve a match with the experimental rangefiring impact data. Therefore, to obtain the same range with and without the Magnusforce coefficient, the form factor was varied. Table 1 presents trajectory simulations tothe same range, with and without a Magnus force coefficient (- .75), for the 155rmm, HE,M107 projectile. The same range was obtained by increasing the form factor by 1.0, 1.2and 1.3 percent for the quadrant elevations 400, 800 and 1200 mils, respectively. The valueof the Magnus force coefficient was determined from experimental range firing impact andtime-of-flight data for the projectile fired with propelling charges: M3A1, charges 1G,2G, 3G, 4G and 5G; M4A2, charges 3W, 4W, 5W, 6W and 7W; and M119A1 charge 8at quadrant elevations from 200 mils to 1250 mils. The inclusion of the Magnus force

coefficient increases the time of flight .15, .35 and 1.11 seconds for the charge 8 simulationsat quadrant elevations of 400, 800 and 1200 mils, respectively.

The precision probable error in functioning time for modern mechanical and electronictime fuzes is less than .30 and .05 seconds, respectively. Therefore, the Magnus forcecoefficient is included in the Modified Point Mass Trajectory simulation model.

Table 1. Significance of Magnus Force Coefficient (CNpo) for Projectile 155mm, HE,M107 Fired with Propelling Charge M119A1.

Time of Flight (Seconds)Quadrant _

Elevation(Mils) CNP. = 0 Cjvpa = -. 75 A

400 39.31 39.46 .15

800 67.91 68.26 .35

1200 89.75 90.86 1,11

The Magnus force coefficient is difficult to determine by aerodynamic testing and is

not normally available. Therefore, an alternative method based on experimental rangefiring impact and time-of-flight data has been developed to determine the Magnus force

coefficient for use with the Modified Point Mass Trajectory model. The Magnus forcecoefficient is determined by varying the coefficient until the overall difference between thesimulated and mean observed times of flight is acceptable for the applicable propellantcharges (muzzle velocities) and quadrant elevations. The Magnus force coefficient (- .75)was determined for the 155mm, HE, M107 projectile using this iterative process. Figures3 through 8 show the difference between the mean observed and simulated time of flight(mean observed minus simulated) versus simulated time of flight when a constant Magnus

force coefficient is used in the trajectory model. The figures present results for projectilesfired with propellant charges: M3A1, charges 1G, 3G and 5G; M4A2, charges 5W and7W; and M119A1, charge 8. The approximate muzzle velocities for these charges are: 208,

276, 376, 397, 568 and 684 metres per second, respectively. Each point represents the

difference between the mean observed and simulated time of flight for a group of five toten projtctiles and each symbol represents a different firing program. The variation in theresults is probably due to the difficulty in measuring the time of flight with stop watches,since it is difficult to determine the zero time and impact time needed to manually start andstop the watches. Figures 3 through 8 demonstrate that the method can be used to obtainan acceptable mean difference between the observed and simulated time-of-flight resultsfor the M107 projectile. "Acceptable" here implies that this mean difference has no overall

bias and thitt individual charge bies can be compensated for by a simple correction to the

2

computed time-of-flight. This method seems to have the capability of extracting a goodapproximate value for the MagiAus force coefficient from the data, even though there arelarge occasion-to-occasion differences between the observed and simulated time-of-flightresults.

Figures 9 and 10 show a comparison of the Magnus force coefficiein determined fromexperimental range impact and time-of-flight firings with values of the Magnus force co-efficient determined from aerodynamic test data. Figure 9 is Figure 26 of reference 3and Figure 10 is Figure 9 of reference 4, showing the Magnus force coefficients based onaerodynamic testing for the 155mm, HE, M107 and 8-Inch, HE, RA, M650 projectiles,respectively. Also shown on the figures is the,.Magnus force coefficient for the projectiles,based on the experimental range impact and time-of-flight firings. The comparison showsthat the value of the coefficient determined from the range firing data is in good agreementwith the subsonic results obtained from aerodynamic range testing for the 155mm, M107projectile as reported by MacAllister and Krial (Reference 3) and the 8-Inch, M650 pro-jectile as reported by Piddington (Reference 4). The Magnus force coefficient determinedfrom the experimental range impact and time-of-flight firings would be expected to repre-sent the subsonic value. This is because the effect, of the Magnus force on the trajectoryis proportional to the yaw of repose and normally subsonic velocities and large yaws ofrepose occur simultaneously for artillery projectiles.

Table 2 presents a summary of the Magnus force coefficients contained in the FiringTable data base for artillery projectiles. These values are based on ballistic analysis of theexperimental range firing impact and time-of-flight data.

Table 2. Firing Table Data Base Magnus Force Coefficients (CNQ,,).

Projectile Shape

ProjectileDiameter Mh Long Range Cargo

Projectile CNP Projectile C.p., Projectile CNP.

105mm M 1 -. 76 M548 -. 40 - -

155mm M107 - .75 M549AI - .50 M483AI - .50

175mm - - M437A2 - .68 - -

8-Inch M106 - .38 MOSO - 1.00 MS09A1 - .50

3

III. Conclusions

The inclusion of the Magnus force coefficient significantly improves the trajectorytime-of-flight results of the Modified Point Mass Trajectory model. The Magnus forcecoefficients for the 155mm, HE, M107 and 8-Inch, HE, RA, M650 projectiles based on theexperimental range firing impact and time-of-flight data are in good agreement with theresults based on the aerodynamic testing. The Magnus force coefficients determined fromthe experimental range firing impact and time-of-flight data are of similar magnitude forthe different shapes (M1, long range, and cargo) and sizes (105mm, 155mm, 175mm, and8-Inch) of artillery projectiles.

4

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1.5

0.0 D

0.0 2 - -• 120.....

-1'0

The symbol. represent different firing programs..

0 20 W4 60 80 100 120 1W0

Simulated Time of Flight (Seconds)

Figure 8. Difference between observed and simulated time of flight (A time of flight)versus simulated time of flight for projectile, 155mm, HE, M107 fired withpropelling charge MU1 1, charge 1G,

7

2,-0

1.0 x

x

X

SI:] X

X B

-1.0

The symbols represent different firing programs-2 0 -__ __ __ _ __ __ __ _ __ ___'_

0 20 40 60 80 .100 120 140'

Simulated Time of Flight (Seconds)

Figure 4. Difference between observed and simulated time of Rlight (A time of flight)versus simulated time of fRight for projectile, 155mm, HE, M107 fired withpropellink charge M3AI, charge 3G.

8

2.0

<1.

1.0 C -"

___ ~~ C_ _

bo

-0.0 . .

B W

- B

-1.5

The symbl ierant different firing programs..-2-0 11-

0 20 10 60 I0 100 120 140

Simulated Time of Flight (Seconds)

Figure 5. Difference between observed and simulated time of figiht (A time of flight)versus simulated time of flight for Prolectile' 155mm HE, M107 fired withpropelling charge M3A1, charge 5G.

9

0,

2.0

1.5

1.0x

A-. x

_x

-04

B ~ x

C

-1.5 -

The symbols represent different firing programs.-2 ,0 ' " .........

0 20 400 so e0 10o 120 0

Simulated Time of Flight (Seconds)

Figure 6. Difference between observed and simulpted time of fliIht (A time of fMlOht)versus simulated time of flight for projectile, 155m, HE, M107 fired withpropelling charge M4A2, charge 5W.

10

S.. .... .. ..M I I I I 1II

2.0x

1.0

X F5x

AD0.0 -'-L--- -

-1 .0

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The symbols represent different firing programs.-2.0 a - I _ _ _ _ L_

0 20 40 so 80 tOO 120 14+O

Simulated Time of Flight (Seconds)

Figure T. Difference between observed and simulated time of flight (A time of flight)versus sinmulated time of flight for projectile, 155mm, HIE, M107 fired withpropelling charge M4A2, charge 7W.

11

2.0

1.01 .5 - -_____ ____

1 0-. .. ..__ _ __ __ _ _

y yI

a BC HF

H@H

-1.0

C

-1-S

The symbol. represent different firing progrzuna.-2.0 I , __

0 20 '0 80 80 LOO 120 14O

Simulated Time of Flight (Seconds)

Figure S. Difference between observed and simulated time of flight t tie o fLht_)versus simulated time of flight for projectile, 1'5mm? HE, M10? fired wit •propellinx charge M119ALcharae 8.

1.2

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14o

References

1. Lieske, R.F. and h. her, M.L., "Equations of Motion for a Modified Point Mass Tra-jectory," BRL Report No. 1314, U.S. Army Ballistic Research Laboratory, AberdeenProving Ground, Maryland, March 1966. (AD 485869)

2. NATO STA NAG 4355 (Draft Edition 1), The Modified Point Mass Trajectory Model,February 1988.

3. MacAllister, L.C. and Krial, K.S., "Aerodynamic Properties and Stability of the155mm Howitzer Shell, M107," BRL Memorandum Report No. 2547, U.S. ArmyBallistic Research Laboratory, Aberdeen Proving Ground, Maryland, October 1975.(AD B007930L)

4. Piddington, M.J., "Aerodynamic Characteristics of the 155mm Model of the 8-InchXM650E2,"BRL Memorandum Report No. 2538, U.S. Army Ballistic Research Lab-oratory, Aberdeen Proving Ground, Maryland, October 1975. (AD B007751L)

5. Murphy, C.H., "Gravity-Induced Angular Motion of a Spinning Missile," BRL Re-port No. 1546, U.S. Army Ballistic Research Laboratory, Aberdeen Proving Ground,Maryland, July 1971. (AD 730641)

6. Collins, W.Z. and Lieske, R.F., "A Study of Artillery Shell Drift at High Angle ofFire Using Solar Aspect Sensors," BRL Memorandum Report No. 2244, U.S. ArmyBallistic Research Laboratory, Aberdeen Proving Ground, Maryland, March 1966.(AD 907598L)

7. Matts, B.J. and McCoy, D.H., "Maximum Quadrant Elevation for Artillery Firing Ta-bles." An Appendix to "A Study of Artillery Shell Drift at High Angle of Fire UsingSolar Aspect Sensors," BRL Memorandum Report No. 2244, U.S. Army Ballistic Re-search Laboratory, Aberdeen Proving Ground, Maryland, March 1966. (AD 907598L)

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