aerodynamic coefficients of the m483a1 determined … · april 1991 final, jan 90 -jan 91. 4. title...

AD-A235 620lilI ~iI lllilI 11111 II i

CONTRACTOR REPORT BRL-CR-659

BRL

AERODYNAMIC COEFFICIENTS OF THE M483A1DETERMINED FROM SPARK RANGE TESTS

ROBERT H. WHYTEARROW TECH ASSOCIATES, INC.

APRIL 1991

APPROVED FOR PUBLIC RELEASE; DISTRIBUTION IS UNLIMITED.

U.S. ARMY LABORATORY COMMAND

BALLISTIC RESEARCH LABORATORYABERDEEN PROVING GROUND, MARYLAND

06 05

NOTICES

Destroy this report when it is no longer needed. DO NOT return it to the originator.

Additional copies of this report may be obtained from the National Technical Information Service,U.S. Department of Commerce, 5285 Port Royal Road, Springfield, VA 22161.

The findings of this report are not to be construed as an official Department of the Army position,unless so designated by other authorized documents.

The use of trade names or manufacturers' names in this repo;t does not constitute indorsernentof any commercial product.

UKC LASSIFIEDREPORT DOCUMENTATION PAGE oI11 A40

1. AGENCY USE ONLY (Le~'e bdan•) REPORT DATE I .. REPORT TYPE AN.', DATE S COVERED

April 1991 Final, Jan 90 -Jan 91.4. TITLE AND SUBTITLE S. FUNDING NUMBERS

Aerodynamic Coefficients of the M483A1 Determined from SparkRange Tests

6. AIUTHOR(S) DAADC5-90-P-1903

Robert H. Whyte

7. PERFORMING ORGANIZATION NAME(S) AND ADDR[SS(ES) S. PERFOPMI•G ORGANIZATIONREPORT NUMBER

Arrow Tech Associates, Inc.1233 Shelburne Road, Suite D-8S. Burlington, VT 05403

9. SPONSORING MONITORING AGENCY NAMEkSI AND ADDRESS(ES) 10. SPONSOR!NG MONITORING

AGENCY REPORT NUMBER

US Army Ballistic Research LaboratoryATTN: SLCBR-DD-T BRL-CR-659Aberdeen Proving Ground, MD 21005-5066

11. SUPPLEMENTARY NOTES

The Contracting Officer's Representative for this report is Dr. Rao J. Yalamanchili, Launch andFlight Division, US Army Ballistic Research Laboratory, Aberdeen Proving Ground, MD 21005-5066.

12a. DISTRIBUTION AVAILABILITY STATE.MENT 12b. DISTRIBUTION CODE

Approved for public release; distribution is unlimited.

13 ABSS RACT 1 r '.,rj 2I 0 - . orus)

The aerodynamic coefficients of the M483A1 have been refined based on the analysis of 65 BRLTransonic Range tests. Both the original M483A1 tests (1975) and the latest tests from 1987-1989 were analyzed utilizing a six degree-of-freedom technique during September-October 1990.The Magnus moment was found to be extremely nonlinear with angle of attack and Mach number.The size of the slow arm limit cycle was computed along with the region of dynamic instability dueto a large positive Magnus moment at moderate yaw levels. The values of the axial force, normalforce, pitching moment, damping moment, and Magnus moment are presented.

14. SUBJECT TERMS 15. NUMBER OF PA'5ES

Projectiles Aerodynamic Characteristics 41Computer Programs Ranges (Facilities) 16. PRICE CODE

17. SECUIR;7Y CLASSIFICATION 18. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION 20. LIMITATION OF ABSTRACTOF REP•T OF THIS PAGE OF ABSTRACT

UNCLASSIFIED UNCLASSIFIED UNCLASSIFIED SAR

UNCLASSIFIED

INTENTIONALLY LEFT BLANK.

Table of Contents

List of Figures ............................................ v

List of Tables ......... ................................... vii

I. Introduction .......... .................................... 1

II. Procedure ......... ..................................... 1

1. Test Facility ......... .................................. 1

2. Test Projectiles ......... ................................ 2

3. Data Reduction ........................................ 2

III. Results and Discussion ...................................... 4

1. Axial Force Coefficient ................................... 4

2. Normal Force Coefficient .................................. 5

3. Magnus Force Coefficient .................................. 5

4. Pitching Moment Coefficient ................................ 5

5. Pitch Damping Coefficient ................................. 6

6. Spin Damping Coefficient ........ .......................... 6

7. Magnus Moment Coefficient ................................ 6

8. Stability Considerations .................................. 7

IV. Conclusions .......... .................................... 8

References .......... ..................................... 33

List of Symbols .......... .................................. 35

Distribution List ......... ................................. 37

L j - -:.. . , ,- . .

iy ....~. .

AI;! :-i, i t,2,. y C' o de8

ii'i


/ iv

List of FiguresFigure Page

1 Configuration for 155mm projectile, M483A1 ..... ................. 17

2 Axial Force Coefficient vs Mach Number .......................... 18

3 Normal Force and Pitching Moment Coefficients vs Mach Number ..... .. 19

4 Pitch Damping and Spin Damping Coefficicnts vs Mach Number ...... .. 20

5 Magnus Moment Coefficients vs Angle of Attack at Mach No. 0.65 ..... .. 21






11 Magnus Moment Coefficients vs Angle of Attack at Mach No. 0.96 ...... 27






" ~V


°' Vi

List of TablesTUkk Page

1 M483A1 Physical Properties ................................... 2

S2 Single Fit - Six Degree of Freedom Results . ................... 10

3 Multiple Fit - Six Degree of Freedom Results ...................... 11

4 Magnus Moment Cp vs. Angle of Attack vs Mach Number ............. 12

5 Muzzle Gyroscopic Stability Factor .............................. 13

"Vii


/ viii

I. Introduction

The M483A1 projectile was the result of a modification of the XM1483 configuration.This modification consisted of shortening the boattail length from 0.5 calibers to 0.25calibers. This was determined to be neccessary as the XM483 exhibited a very largepositive Magnus moment at Mach numbers less than 1.0. This large positive Magnusmoment caused the projectile to be dynamically unstable (fast mode) at fairly low anglesof attack (yaw angles) resulting in projectiles falling short of their design range. Reference1 presents the analysis of spark-range and yawsonde firings of the XM483. Also presentedin Reference 1 are the results of yawsonde firings of a modified XM483 (Mod 21B) whichis now the configuration of the M483A1.

Figure 1 is a sketch of the M483A1. The M483A1 (20 each) was fired in the BallisticResearch Laboratory (BRL) Transonic Range (TR) Facility in the mid 1970's along with105mm and 155mm models of the XM795. The results of these tests are given in Reference2. Non-linear Magnus moment data are obtained from reductions utilizing the Eglin Six-Degree-of-Freedom (6DOF) Aeroballistic Range Facility Data Analysis System (ARFDAS)program. Referegce 2 discusses the very non-linear Magnus moment discovered duringinitial attempts utilizing cubic and quintic expansion (with angle of attack) terms. The6DOF model was changed to perform a table lookup of estimated values of the N%'Iagnusmoment derivative (C,,,,). This change produced satisfactory analysis results. However,with only 20 projectiles tested between Mach numbers 0.65 and 1.91, the many data gapsin Mach number and angle of attack resulted in a partial aerodynamic data package.

Recently, the exterior shape of the M483A1 has been selected as a baseline for thedevelopment of several new projectiles. The aerodynamic data base of the M483A1 wasdetermined not to be of sufficient quality when the importance of development programsis considered. The BRL designed a TR test program, consisting of 45 additional firings,to supplement the 1970's data. This program was carried out from 1987 thru 1989. Thisreport discusses the results of these new tests in combination with tne earlier tests whichwere re-analyzed in concert with the new test data.

II. Pi'ocedure

1. Test Ficility

The projectiles were fired thru the 207 meter long, spark-shadowgraph instrumentedsection of TR. Reference 3 describes the details of this facility. The shadowgraphs takenare then used to determine the position and attitude of the test projectile as a function oftime and distance. There are twenty-five shadowgraph stations in the range. During thetests conducted in 1975, only eighteen of the twenty five stations were timed.

The expected measurement accuracy is 0.1 degrees iii attitude and 0.003 meters inposition.

Table 1. M483A1 Physical Properties

Period Diameter Leugth CG CG Masw Is Ymm mm mm Cal. kg kg- m2 kg-rm 2

1975 154.74 898.0 565.0 3.65 46.88 0.1585 1.6951988 154.74 896.7 562.9 3.64 46.861 0.1575 1.687

2. Test Projectiles

The projectile configuration is shown in Figure 1. Actual projectile hardware wasutilized for the tects. The dimensional characteiistics and physical properties of eachprojectile tested were measured prior to firing. Key characteristics are given in Table 1.

As shown in Table 1, only minor differences between the 1975 and 1988 projectileswere measured. The reference CG for the data presented in this report is 3.64 calibersmeasured from the nose. The stability computations utilize the 1988 physical properties.

3. Data Rtduction

Data reduction procedures were formulated by using epicycles to fit the spark-rangedata (Ref 4). This method is often called the linear theory. The data analysis techniqueand system utilized for this report is fully described in Reference 5. Slight modifications tothe baseline system (Eglin-ARFDAS) were made for compatibility with in place proceduresat BRL. Some notational and scaling differences exist between References 4 and 5. Thesystem used in this report allows for the simultaneous reduction of up to five experimentaldata sets. This is a powerfull technique as the only additional unknowns, required to bedetermined, are the initial conditions of each added data set. The aerodynamic coefficientsto be determined are common to each data set. A total of sixty-five single shots andnineteen multiple fit groups were reduced during this activity utilizing the six-degree-of-freedom methodology.

The analysis process is judged to be adequate when the resultant fits to the data setapproach the measurement capabilities of the facility presented above.

The standard method of modeling the expected non-linearities with angle of attackfor each coefficient and its derivative is given below:

e = sin(a)

a = Total Angle of Attack

Axial Force Coefficient

Cx = CXo + Cx2 2 + Cx 4e"

2

Normal Force Coefficient

CN = CNoe + CNQ3e3 + CNa,5e5

CN0 , = CNgo + CNa3E2 + CNCSe4

Magnus Force Coefficient

Cyp = CyPoIF + CYPc3e3

Cyp= Cypoo + Cypot 3 2

Pitching Moment Coefficient

C,, = Cm.coe + Cmf,3 3 + C,5,s5E

C,,- = C,..o + Cm,,•,3 2 + Cmcse4

Pitch Damping Coefficient

Cmq = Cq, + Cmqo,2E2 + Cmqcr•E4

Magnus Moment Coefficient

Cnp= Cnpao6 + Cnp,•3E3 + C•,nsrS

Cnpa= Cno + Cna3e 2 + Cp,5e 4

A lesson learned from Reference 2 was that adding additional polynomial terms toaccount for M483A1 non-linearities in Magnus moment was not sufficient. The 1975 testscontained data with projectile yaw exceeding fifteen degrees. The technique chosen forthe analysis contained in this report (different from Reference 2) was to create a tableof Magnus momen-t (Cnp) as a function of angle of attack (ac) and Mach number. As theprojectile motion is numerically integrated in the 6DOF code, a two way table interpolationis done to determine Cp at each angle of attack and Mach number. This value of Cp isthen added to the standard C,,p equation by the following technique.

CnPi6. = i-

3

now:

C.p = Cn 0 baa. + C,1pC•ba.. * C9 + Cnpo + Cnpr3E2 + CnpaSf 4

where: C9 is to be solved for.

1I. Results and Discussion

Each test projectile was initially subjected to single fit reductions. The aerodynamiccoefficients of the projectiles are determined by individual reductions. Following the sin-gle fits, projectiles with similiar Mach numbers are grouped together for a multiple fitreduction. These groups usually contain the extremes of mean squared yaw (low and high)available at that groups Mach number. A maximum of five projectiles can currently beutilized. In some cases, more projectiles (greater than five) are desired. However, thisanalyst is content with five data sets, reducing more data sets is mind boggling. Thetabulated single fit results are given in Table 2 and the multiple fit results are presentedin Table 3.

The precision of the single fits are seen to better the stated range accuracy. Thisanalyst believes that the accuracy of the calibration and film reading has been considerablyimproved in recent years. The quality of the multiple fit validates this premise in that theyalso better the stated accuracy.

The 1975 rounds can be identified as having ID's of T13XXX and T14XXX whilethe 1988 series have ID's of T30XXX. The multiple fit groups contained combinations ofrounds fired in 1975 and 1988. The rounds contained in each multiple fit are designatedin the left hand column of Table 3.

The major coefficients will be discussed individually. Emphasis has been placed onthe multiple fit results. Only minimal effort was expended in attempts to determine non-linearities from single fits.

1. Axial Force Coefficient

The zero-yaw axial force coefficient (also CDo) is plotted versus Mach number in Fig-ure 2. The single and mutiple fit are separately graphed. Little difference, if any, is notedwhen comparisons to Reference 2 are made. The error in the axial force coefficient at zeroyaw is estimated to be less than 0.004. The yaw-axial force (Cx2) is shown for each mul-tiple fit. When the average yaw levels were under 5 degrees, this coefficient was estimatedand held constant during the analysis. Reference 2 provided estimated values for C.X-2 asthe average yaw levels were large for the M483A1 and similiar XM795.

"4

2. Normal Force Coefficient

The normal force coefficient determination is dependant on the magnitude of projectileyaw. Assuming a typical gun launch, with a first maximum yaw of 3 degrees, the size ofthe slow arm KS will be 1.U degrees For the M483A1, this will result in the radius ofthe swerve vector equal to 0.015 meters. This is approximately 5 times the demonstratedrange accuracy and results in a CN,, error of about 7%.

Most projectiles fired supersonically had swerve arm.3 of less than 0.01 meters andexpected coefficient errors approach 15%.

The multiple fit results are plotted in Figure 3. The cubic term was estimated onmany projectiles and held constant. These estimates were based on Reference 1 and sev-eral sets of wind tunnel data. The accuracy of the zero yaw CN,, as represented by thefaired line is approximately 5% subsoni'c/transonic and 10% supersonic.

3. Magnus Force Coefficient

The Magnus force coefficient's effect on the motion of the center of gravity is nearlyan order of magnitude smaller than the normal force coefficient. However, on those multi-ple fit groups where the maximum yaw observed exceeded 10 degrees, this coefficient wassolved for and determined. The determined value ranged from about -1.0 to -1.6. On allother groups the Cyp,, was estimated at -1.0 and held constant. See Table 3 for details.This magnitude of Cys,, is similiar to the values determined on other projectile test pro-grams with large enough yaw (Reference 6).

4. Pitching Moment Coefficient

The pitching moment coefficient derivative, C,,,,, is very non-linear with increasingMach number as shown in Figure 3. This same trend was first observed in Ref. 1 andlater detailed in Ref. 2. The 1987-1989 firings added substantially to the definition of Cmckabove M=0.96. The Cmo peaks near M=0.90 at a value of 4.85. The C,, then drops to alow value of 4.45 at M=0.96 and rapidly clirabs to 4.63 near M=1.0. The supersonic peakis near M=1.5 with Cma equal to 4.88. A downward trend then begins with Cm, falling to4.51 near M=2.3. Tabulated Cm, are given in Table 3 for the multiple fits. The estimatedaccuracy of the zero yaw Cm,, is about 2%.

The cubic pitching moment is very weak with a value of about -7 subsonically andless than -3 supersonically. Estimated values were utilized in many of the multiple fits.The values were obtained from Ref 2. and are consistant with other experimental data.The error in the cubic pitching moment coefficient is about +/- 3.

5

5. Pitch Damping Coefficient

The pitch damping coefficient, Cmq, can only be determined on spin stabilized projec-tiles when the Magnus moment coefficient is well modeled with respect to non-linearities.Linear Theory reductions produce large coefficient scatter for Cm.. q when Magnus non-linearities are present. Linear Theory values for Cmq varied from +47 to -30 below M=1.The 6DOF multiple fit analysis reduced this variance to a range of -4 to -17. Some of theremaining variance is due to Mach number trends, however, it is estimated that ti mnd linedrawn in Figure 4 has an estimated error of magnitude 3.

No attempt was made to determine higher order terms of pitch damping as simulatedtest cases have shown minimal influence on the resultant motion.

6. Spin Damping Coefficient

The spin damping coefficient, Cip, was estimated based on yawsonde data containedin Reference 1. This estimate is plotted in Figure 4.

7. Magnus Moment Coefficient

The Magnus moment coefficient, C,,p of the M483A1 is very non-linear with angle ofattack and Mach number. When the maximum yaw angle in the data set to be analyzedis greater than 5 degrees, the use of higher order terms must be closely reviewed foradequacy. Reference 2 discusses the use of an estimated Magnus table (C,,p, vs. a). Theinterpolated derivative is then form factored by using only linear and cubic terms to evolvethe appropriate non-linear behavior with angle of attack.

For the multiple fit analysis of test data below M=1.1, a table of C,,p vs a vs Machnumber was estimated and input in a data file. As described in the Data Analysis Sectionabove, the values of C,,p were interpolated and then form factored into a contour whichminimized the probable error of fit. This process was iterative in that the input table wasadjusted several times to ensure realistic modeling over the entire range of angle of attackand Mach number.

The final coefficients are given in Table 4. This is the actual data utilized for the finalmultiple fit reductions.

Table 3 (Multiple Fits) shows values for C,,p,, above M=1.1. Below M=1.1, the ap-proach described above was utilized and the expansion terms are not cubic/quintic. Figures5 thru 16 present plots of C,,p vs a and C7,•p• vs. a 2 at Mach numbers from 0.65 to 2.0.

In general, below M=0.98, C,,,, is very negative (about -5) near zero yaw, crosses 0.0at about 4 degrees and increases to a maximum of 1.0/1.25 at 6 degrees yaw. This trend issimiliar to that reported in Ref. 2. However, the goodness of the C,,,, trend with yaw levelpresented in Figures 5 to 16 is much better than Reference 2. The large quantity of data

S~6

from M= 0.85 to M=!.C greatly improved the quality of and confidence in the results. Theprobable errors of fit were very low (most less than 0.1 degrees) considering that 4 and 5projectiles with maximum yaw levels exceeding 12 degrees were being simulataneosly fit.

8. Stability Considerations

Tile gyroscopic and dynamic stability of the M483A1 has been computed for muzzleexit conditions at ambient conditions. The equations given below are discussed in Reference4.

Gyroscopic Stability Factor

21,2p 2 _S'g = rp4,Cmad 3 V2

Ballistic Factor

0 1=

Fast - Slow Vector Magnitude (Initial Conditions)

IF = 2-mnz.

Ks =-Elm-,•2

Mean Squared Yaw

S2 = T,- 2 2

Fast Mode Damping Factor

AF = I,)CN- - ( ,.)(1 + ) )C.q -

Slow Mode Damping Factor

As = [,A[(1 + ,)CN. - (-,)(1 -+ (!2)(!)C.4m 0)1, 21 (-Z- 0,)c 1,

The gyroscopic stability factor of the M483A1 was computed for muzzle exit conditions(1/20 twist) and both a standard (15C) and cold (-40C) day. These values are presented

,' 7

in Table 5.

The fast and slow nmode damping factors in the above equations were set equal tozero, the equations re-arranged, and solved for the two limit values of C,•,,. The slopescomputed have been plotted in Figures 5 thru 16.

The point at which C,,p is crossed by the negative slope is the magnitude of the slowmode (arm) limit cycle. The projectile will cone at this yaw angle (3.5 degrees at M= 0.87- Figure 8) at steady state conditions.

If the C,,p is crossed by the positive slope, the projectile has a fast mode dynamicinstabilty. Using Figure 8 (Mach 0.87) as an example, a slight dynamic instability causedby a positive C,,p exists from about 5 thru 9 degrees yaw. Above 9 degrees, the Cnp fallsbelow the boundary and the projectile is stable in both fast and slow modes.

The same answers can be achieved using the Cnp, versus mean squared yaw presen-tations. This trend was noted in Reference 2.

The consequences of this highly non-linear dynamic stability situation does not readilylend itself to closed form prediction. A series of 6DOF trajectory simulations with initialconditions (pitch-yaw rate) being varied for purposes of computing the effect on rangeprecision should be done. Cold, ambient, and hot atmospheres should be included alongwith the effect on temperature on the muzzle velocity.

IV. Conclusions

The aerodynamic coefficients of the M483A1 projectile have been computed based onspark-range tests conducted in 1975,1987,1988, and 1989.

The multiple fits showed that there were essentially no aerodynamic differences be-tween the projectiles manufactured in the mid 1970's and late 1980's.

The probable errors of the multiple fits were very low and support a high confidencelevel in the determined coefficients. Overall, the quality of the Transonic Range data fromthe 1988 tests is the best, within the experience of the author. This indicates that boththe calibration of the facility, and the film reading process have improved in recent years.

The coefficients presented in this report should be incorporated into an aerodynamicdata package for the M483A1. This package should be made available to all governmentand private industry parties involved in the development/evaluation of projectiles withshapes similiar to the M483A1.

"8

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I4 .-, Co 8 8 0 8 00 00 e e @C0 o @ 0 0

cc P.I 0 o 0 C. 00 @1 eO ec e@ . ec C.e 1@8 8

;80I 00 00 08 88N08 ON 00 80 00 00 00 00

0J mam em e.08 40 M48 cc0. 00 .40 cc 0 00

"I .0 .40 .48 .40 @c 100 00 88 0 @0 @0 a @00 00 00 00 00

0.omm m ~ M O .M 8.4 00 1 00 00 0 0 00 cc 0.41=0 10 1=0 1=0 wM OM 0 M w' qo o M 0q' q ;

0 00 0 80 00 a8 @0 @0 0 a 0 00 0 00 00

00 00 00 @0 @0 @8 08 @ @8 0 00 @0 01 1 0 00 00

I .u 1 141 8ýa 0 0 N0 9 -08 04 a 0 0 00 N4 a 0 L 0 a* 0C4 4 4 IOu u .0 9%0 .00 .0 0 P8 a 0 a 0 at .0 a0 . 0

7 UV N 0 0 0ý 00 .4 .4 .4 0 1! 0 .4

IU-t .48 10 00- -- @ NO NO, NO NO NO cc 0 00 N00 O, 100 Ccfl0 .00

.0i 00 Iwe 0o MO* 10Cc 4400 MO MO 80* 100 NO 1 me 10 1 0 0 NO 0

00 1=0 we we we C.. ma me0 (4 0 :0 C0 00 10 e 0 0 w

I0 0 P4 a 0 N0 P40 f0 m 0 04 a0f 0 V 0 0 (0 M0

N : M : : a: : W: 00 0 00 00 ona 0 00 00 00 o0

a f" 0 f" a0r"00@ a@m 00 00 0-0 00 00I n ai *i o aL

UUI .0 In0 .0 - .4-W0 .4 0 0 a 0 .0 .40 - .0 . 40 cc 0 .40 .40 If 40

4.. fn ?4 Cfl 1

I ~ ~ ~ ý g4 NO NO NO NO N O N O O .0 .0 MO N O N

"4 IN 0 NO we $4 Co to we we mo Ff. MO MO NO MOgO o

I 4M MOMAO M O M O M O M O M O M

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u Id- 00 0000 00

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41 ~ 'A 0 0 0 M 00InC

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E loo C, M0 : 0m a n ao

A : *in *0 0 *a0 0 % .0 in

In : .4. 04 10 .4 . 0 w

'89 NN 0

~ I 80 '0 -o ma0in .4 in ft

ma 10 no 13

0@ I

,n co cc 00 00 800= @90 .4; qnO ' 0' c0

00 cc0.0 00 0 9 00 c0o0 00 co0 00 00

.4 d

go* 4 0 0 @ 0 00 0 000 00 00. .00 00 O 00u

c .00 1. 00 00 . l00 0M 0 08 @00 0 00 00 a0u oo 00 02a aaa am0 00 00 a0 @0 0 0 00P 0

14 1 0 00 00 00 00 00 00 00 0 00 0

u . .4

m in : n n. M o 10 n n n

ccIJ 00 00 a a0 mN fn 010 0.4140 010 000 ON 00 M

@00 000 000 000 000 000 @00 000 .' .. 040

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1! 1 IiI C!C I * ; 9 a -

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lu l O MO %=0 U=C 1== =0 400 00 100 140 M O

a~ uI * en .. fn *. .. in .4 4..i

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in "4000 0 0 m .40 @0 0 00 0 10 004

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MU 1 1 It C

0 Iq

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14 14 14 14 H1414 14 14 141p 14 14 1414H 64

: 41 I 11 1: "

14 IH 000 .n4.1H 4 0 o .40 .4 1.14 g 40 .404 1

I I 15

M4483 1 CG a 3.64 CALIBERS F"ON ROSE

MAGMUS MOMENT VS. ANGLE OF ATTACK VS. MACH N4U"BNER

MACH UNUMER0.50 0.75 '0.87 0.90 0.93 0.96 1.00 1.25 1.50 3.00

AOA0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.00.5 -0.026 -0.026 -0.038 -0.065 -0.070 -0.050 -0.012 0.0046 0.0079 0.00791.0 -0.050 -0.050 -0.074 -0.120 -0.130 -0.100 -0.023 0.0092 0.0157 0.01572.0 -0.074 -0.074 -0.107 -0.160 -0.170 -0.140 -0.039 0.0185 0.0314 0.03143.0 -0.037 -0.037 -0.070 -0.100 -0.110 -0.090 -0.034 0.0277 0.0471 0.04714.0 0.015 0.015 0.007 0.005 -0.002 -0.010 -0.001 0.0370 0.0623 0.06285.0 0.057 0.057 0.090 0.085 0.085 0.035 0.040 0.0462 0.0784 0.07846.0 0.086 0.086 0.130 0.130 0.135 0.070 0.060 0.0554 0.0941 0.09417.0 0.105 0.105 0.140 0.155 0.165 0.090 0.070 0.0646 0.1097 0.10978.0 0.116 0.116 0.150 0.170 0.180 0.110 0.079 0.0738 0.1253 0.1253

10.0 0.132 0.132 0.150 0.160 0.180 0.120 0.097 0.0920 0.1563 0.156312.5 0.150 0.150 0.140 0.145 0.150 0.110 0.115 0.1147 0.1948 0.194815.0 0.160 0.160 0.120 0.120 0.120 0.105 0.135 0.1372 0.2329 0.2329

Table 4. Magnus Moment Cv, vs Angle of Attack vs Mach Number

Mach No. C,,, S, 15C S,-40C0.65 4.20 2.06 1.690.75 4.52 1.91 1.570.85 4.75 1.82 1.490.87 4.80 1.80 1.480.90 4.85 1.78 1.460.93 4.60 1.88 1.540.96 4.45 1.94 1.591.00 4.63 1.87 1.531.25 4.77 1.81 1.481.50 4.88 1.77 1.452.30 4.53 1.91 1.57

Table 5. Muzzle Gyroscopic Stability Factor

16

Lci

't o

In

0049

4.)

0 0

in0A

00

In I

170

M483A1

6 DOF Reduction - Coefficient Output0.5-

MultipleFit Results

0.4-

0.3-

C 0.2-X0

0.1-

0.0-0.5 1.0 1.5 2.0 2.5

Mach Number

0.5

SingleFit Results

0.4-

0.3-

C 0.2-X0

0.1-

0.0-0.5 1.0 1.5 2.0 2.5

Mach NumberFigure 2. Axial Force Coefficient vs Mach Number

18

M483A1

6 DOF Reduction - Coefficient Output4

MultipleFit Results

3-0

CNa

1-

O- ,-i,, -- , '!- -m 11

0.5 1.0 1.5 2.0 2.5

Mach Number

6.0-Multiple

Fit Results

5.5

5.0"

41.5-

Cma 4.0 -

3.5-

3 .0- 1.. .. .. .

0.5 1.0 1.5 2.0 2.5

Mach NumberFigure 3. Normal Force and Pitching Moment Coefficients vs Mach Number

19

M483A16 DOF Reduction - Coefficient Output

20,

MultipleFit Results

0-

q 0-40-

-0-20- , . . .. .. . ' ..

0.5 1.0 1.5 2.0 2.5Mach Number

EstimatedData

-0.01-

-0.02-"C -0.03-

1

P-0.04-

-0.05- . . . . . , ,,. , . ..

0.5 1.0 1.5 2.0 2.5

Mach Number

Figure 4. Pitch Damping and Spin Damping Coefficients vs Mach Number20

M483A1 MACH NO. 0.650ALPHA VS. CNP

N ........ ....P ./....C............................

.7Z,.. _ de BOUI.d ________

-0.1- -

0344010 12 14

ALPHA

M483AI MACH NO. 0.650DBAR-SQ VS. CNPA

2--

... . Fait Mode Boundary

.74. ....0- ~ .../ ..... •........................ .... ..... ....................• Slow Mode Boundary

CNP -2-

A~

-4-_____ ____ _

nT~-r r rr -r- rr Inn -rrr. -- Imrm -rr7 r,

DELBAR SQFigure 5. Magnus Moment Coefficients vs Angle of Attack at Mach No. 0.65

21

M483A1 MACH NO. 0.750ALPHA VS, CNP

N .. . .. . , .... . ..... ... . .. o t s 7

N ............... .......P "•• J ........ Slow Mode Boundary

-**- * I I I 1_ I_ _

S4 E 12 14

ALPHA

M483A1 MACH NO. 0.750',AR-SQ VS. UNPA

2-

Fast Mode Boundary

0 - -- --..... .............................. 1...................-/ ------..-. ..............Slow Mode Boundary

CNPA /

-4-

0 25 50 75 100 12.5 150 175

DELBAR SQFigure 6. Magnus Moment Coefficients'vs Angle of Attack at Mach No. 0.75

22


_ •.- '- •°'3 °O'

CN

..... .......... .....S low Mode Boundary

10 12 14

ALPHAM483A1 MACH NO. 0.850

2- DBAR-SQ VS. CNPA

Fast Mode Boundary......................... ....................

0-

"Slow Mode Boundary

CNp -2-A

-4-

0 25 50 75 100 125 150 175DELBAR SQ

Figure 7. Magnus Moment Coefficients vs Angle of Attack at Mach No. 0.85

23


C

NP ** S -- __ __ I __ _ _ _ _ _ _ _ _ _

"N. .. . .

04 14


______ ______ DBAR-SQ VS. CNPAA II

N 0- 1 -1..:

Slow Mode Boundary

CNP -2-A

0 25 30 73 100 125 130 175

BA-DELBAR SQFigure 8. Magnus Moment Coefficients vs Angle of Attack at Mach No. 0.87

24


o,=so

tA

N .. .. . . . .. . . . .. ... .. .. ... ......SMoe ndy

-0. 1-

0244810 13 14

ALPHA

M483A1 MACH NO. 0.900DBAR-SQ VS, CNPA

2 I I I I

Fast Mode Boundary

0-......... ...Slow Mode Boundary

CNP -2-A

-4-

'7~~ ~ C .,%I I0 2:.5 50 &W'""''•:• d

DELBAR SQ


25

M483A1 MACH NO. 0.930

________ALPHA VS. CNP0.3

$ I

-\

N - \

N ............ .

0 Slow Mode Boundary

ALPHA

M483A1 MACH NO. 0.930DBAR-SQ VS. CNPA

2 t I

Fast Mode Boundary..... .. •.,• ="€=' ..-"'r e...• o . .. .. .......... q.......... t....

° ...... •............... ................................. J.......... l....Slow Mode Boundary

CNp -2- ,

A

-4--

0 25 50 75 100 125 150 175

DELBAR SQ


26


0,]&

C/

N° ..... ....... • • "-- - -

N .Q-\ .. ,...... -- A...............

'Slow Made Boundary

0 _ _ _ _ _ _

-- - --

0 210 1


2 DBAR-SQ VS. CNPAa Md B a

Fast Mode Boundary

S/Slow Mode Boundary

CNP -2

A

-4 -

S" 2C 73 100 12, 150 17I


27


O0 . 3

PN S- . .. ..........._ Slow ModeBoundary

-0.1-

-0.2-- I r - I I

0 4 10 12 14

ALPHA

M483A1 MACH NO. 1.000DBAR-SQ VS. CNPA

1 1 1 Fast Mode Boundary

Slow Mode Boundary

C/

NP -2-A

-4-

0 25 50 75 100 125 150 175


28

M483A1 MACH NO. 1.100AI PHA VS. CNP

I II - °

0.2-0

C

N .......... ........ ..........

P Slow Mode Boundary

• I

-4.3B

-Slow Mode Boundary .1A

0 5 55 10125 150 175

LRAR-SQ VS. CNPA

o - ..j ......... ................ ""''.......... '',; . . .. .. ... .

CN

p -22A

--4-

o 25 50 75 100 125 150 175

DELBAR SQFigure 18. Magnus Moment Coeffcients vs Angle of Attack at Mach No. 1.1029

M483A1 MACH NO. 1.250ALPHA VS. CNP,

0.)i

o.I . I '"1

N . . . . .. . . . . . . . . .F -

p Slow Mode Boundary

-0.2-

04 0.* 1,2 ,14


2' DRAR-SQ VS. CNPA

- - - - - - - -- - - - -- -- -

Slow Mode Bounilry

CNP -2-A

-4-- -

0 25 50 75 100 125 150 175

/ DELBAR SQFigure 14. Magnus Moment Coefficients vs Angle of Attack at Mach No. 1.25

30

M483A1 MACH NO. 1.500ALPHA VS. CNPR ~ I '

:.- ... ;;

C .*N '.--r. . . .• ".......... .......... . . . . .N - Slow Mode Boundary

ALPHA

M483A1 MACH NO. 1.500_______ ______ DSAR-SQ VS. CNPA____

2

_ -) I I i i i

O-......... ........... -- ... ............................... ....Slow Mode Boundary

CNP -2--A

-4-

0 25 50 75 100 125 150 175


31

M483A1 MACH NO. 2.000___ALPHA VS. CNP

0ON

Ito

N. - .........

N to

Slow Mode Boundary


2- __DBAR-SQ VS. CNPA

Slow Mode Boundary

CNP -2-A

-4-

-- 1--i7-,=-,-r -r-i- = 1TT Ti-T- -ri-i7T- -F1TT-r i-FT-r

0 25 50 75 100 ,25 150 175


32

References

1. Craver, G.A., Hathaway, W.H. and Whyte, R.H.., "Yaw Sonde and TransonicRange Data Reduction on the 155mm XM483 and other Projectiles," PA-TR-4872, Pi-catinny Arsenal, Dover, NJ, November 1975.

2. Whyte, R.H., Hathaway, W.H. and Friedman, E.M., "Analysis of Free FlightTransonic Range Data of the M483A1, and XM795 Projectiles," ARLCD-CR-79016, AR-RADCOM, Dover, NJ, August 1979.

3. Rogers, W., "The Transonic Free Flight Range," BRL-TR-1044, Ballistic ResearchLaboratory, June 1958. (AD 200177)

4. Murphy, C.H., "Free Flight Mot-on of Symmetric Missiles," BRL-R-1216, BallisticResearch Laboratory, July 1963. (AD 442757)

5. Hathaway, W.H., and Whyte, R.H., "Aeroballistic Research Facility Free FlightData Analysis Using the Maximum Likelihooh Method," AFATL-TR-79-98, Eglin AirForce Base, FL, December 1979.

6. Whyte, R.H., Burnett,J.R., Hathaway, W.H., Brown, E.F., "Analysig of Free FlightAerodynamic Range Data of the 155mm M549 Projectile," ARLCD-CR-80023, ARRAD-COM, Dover, NJ, October 1980.

33


34

List of Symbols

A 7rd 2/4, reference area

SCx !axial forcel /[(1/2)pAV 2 ]

Cyp. +[Magnus; forcel/[(1/2)pAV 2(pd/2V))]

CN ±- Inormal force I /['(1 /2)pAV2]

CPN center of pressure of the normal force (calibers from the nose)

Cte, ± Iroll damping momentl /[(1/2)pAdV 2 (pd/(2V))]

C,)%4- ±Magnus momentl /[(1/2)pAdV 2 (pd/(2V))]

CmIq ± (damping moment sumf /[(1/2)pAdV 2(qd/2V))]

Cm, ± -static momentl /[(1/2)pAdV 2]

d reference length: the projectile diameter

.I, II the projectile's axial and transverse moments of inertia

m projectile mass

M Mach number

p, q, r components of the projectile's angular velocity

S9 The gyroscopic stability factor, gyroscopic instabilityoccurring when 0 < Sg < 1

t time

u, v, w projectile velocity components

V projectile velocity

X, Y, Z range coordinates, a right-handed system with X positive down-rangeY positive left and Z positive upward.

Xc f V dt, arclength along the trajectory

& the total angle of attack, arccos (u/V)

35

6- mean-squared yaw: _> K2 + K2

AF, As damping rates of the yaw fast and Clow arms

p air density

"36

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aerodynamic coefficients of the m483a1 determined … · april 1991 final, jan 90 -jan 91. 4. title...

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