UNCLASSIFIED

AD NUMBER

AD915628

NEW LIMITATION CHANGE

TOApproved for public release, distributionunlimited

FROMDistribution authorized to U.S. Gov't.agencies only; Test and Evaluation; NOV1973. Other requests shall be referred toCommander, Army Armament Research andDevelopment Center, Attn: SMCAR-MSI.Dover, NJ 07801.

AUTHORITY

ARDEC ltr, 26 Jan 2010

THIS PAGE IS UNCLASSIFIED

COPY NO. ____

imr4 TECHNICAL REPORT 4588

SPIN-73

AN UPDATED VERSION OF THE SPINNER

COMPUTER PROGRAM

ROBERT H. WHYTE

NOVEMBER 1973

r

Distribution limited to U. S. Government agencies only (test and evaluation;November 1973). Other requests for this documcnt must be referred to PicatinnyArsenal, D'over, New jersey, Al 1N: .RF-Ib-T-S.

PICATINNY ARSENAL

DOVER, NEW JERSEY

The findings in tids report are not to be construedas an official Department of the Army position.

DISPOSITION

Destroy this report when no longer needed. Do notreturn to the o.rginator.

I a• • • "

Technical Report 4588

SPIN-73

AN UPDATFD VERSION OF THE SPINNERCOMPUTER PROGRAM

by

Robert H. Whyte

November 1973

AMCMS Code No. 554C.12.62000

Distribution limited to U.S. Covernment agencies only (testand evaluation; November 1973). Other requests for this document

must be referred to Picatinny Arsenal, Dover, New Jersey, ATTN:SARPA-TS-T-S.

Conducted for

Feltman Research LaboratoryPicatinny Arsenal

Dover, New Jersey 07801

I undei

Contract No. DAAA23-73-C-0033

by

Armament Systems Department

General Electric Co.Burlington, VT 05401

% -- --- ,

FOREWORD

Thi5 report documents tasks accomplished by the Armament Systems Department,

General Electric Company, Burlington, Vermont under United States Government

Contract No. DAAA21-73-C-0033 during the period from 14 August 1972 to 14 July

1973.

I P

ACKNOWLEDGEMENT

The author wishes to acknowledge the personnel of the Free Flight

Branch of the Ballistic Research Laboratories, Aberdeen Proving Grounds;

the Aeroballistic Branch of Picatinny Arsenal; and the Aeroballistics Branch

(Range G) Arnold Engineering Development Center for their cooperation in

the collection and interpretation of data used in this study.

2

-4W9

ABSTRACT

The SPINNER computer program has been updated to compute aerodynamic

coefficients for a wide variety of spin stabilized projectile shapes.

Improvements over the original program are substantial as ogive radius,

meplat diameter and rotating band diameter are accounted for instead of

assuming mean values. Test cases are shown comparing the 1969 SPINNER,

the 1973 SPINNER and experimental data. Input instructions and sample pro-

gram outputs are given along with the 1973 program listing.

3

4,

TABLE OF CONTENTS Pg

Foreword .. ...........................

Acknowledgement. ............................ 2

Abstract .. ...........................

List of :ables .. ........................

List of Figures. .......................... 6

Nomenclature .. .........................

Introduction .. ........................... 9

Procedure .. ........................... 11

Empirical Equations .. ...................... 13

Results and Discussion. .. .................... 19

Conclusions and Recommendations .. ................ 21

References. .. .......................... 22

Appendix A Curve Fit Technique .. .............. 71

Appendix B Input - Output - Description. .. ......... 75

Appendix C Program Listing SPIN-73. .. ........... 78

Distribution List.... .. .. . .... . . . .. . .. . . . . . 87

4.4

LIST OF TABLES

Page

I Coefficient Probable Errors 28

2 SPIN-73 Output 20MM M56A3 29

3 SPIN-73 Output 20MM 5 CAL ANSR 32

4 SPIN-73 Output 20MM 7 CAL ANSR 35

5 SPI-73 Output 20MM 9 CAL ANSR 38

6 SPIN-73 Output 20MM 10 CAL CONE CYL. 41

7 SPIN-73 Output 90MM M71 44

8 SPIN-73 Output 105MM MI 47

9 SPIN-73 Output 105MM XM380E5 50

10 SPIN-73 Output 5/38 NAVY 53

11 SPIN-73 Output 5/54 NAVY 56

12 SPIN-73 Output 155MM MI01/107 59

13 SPIN-73 Output 15IM M549 62

14 SPIN-73 Output 175MM M437 65

15 SPIN-73 Outpu- 175MM SRC 68

5

LIST OF FIGURES

Page

1 Projectile Parameter Model 27

2 Aerodynamic Data 20MM M56A3 30

3 Aerodynamic Data 20MM 5 CAL. ANSR 33

4 Aerodynamic Data 20MM 7 CAL. ANSR 36

5 Aerodynamic Data 20MM 9 CAL. ANSR 39

6 Aerodynamic Data 20MM 10 CAL. CONE CYL. 42

7 Aerodynamic Data 90MM M71 45

8 Aerodynamic Data 105MM Mi 48

9 Aerodynamic Data 105MM XM380E5 51

10 Aerodynamic Data 5/38 NAVY 54

11 Aerodynamic Data 5/54 NAVY 57

12 Aerodynamic Data 155M M101/107 60

13 Aerodynamic Data 155MM M549 63

14 Aerodynamic Data 175MM M437 66

15 Aerodynamic Data 175MM SRC 69

6

NOMENCLATURE

2A projectile cross-sectional area, ft'

Cp spin deceleration coefficient, Mp/qAd(2v)

Cm pitching moment coefficient, M /qAdm m

Cm damping moment coefficient, Mm /qAd(qd/2V)q q

C TImagnus moment coefficient, Mn /qd(pd/2V)

p pC N normal force coefficient, FN/qA

C yp magnus force coefficient, Fyp/qA(pd/2V)

C X axial force coefficient, Fx/qA

CG center of gravity, calibers from nose

I axial moment of inertia, slug-ft2

Iy transverse moment of inertia, slug-ft2

FN normal force, lbs.

F yp magnus force, lbs.

F axial force, lbs.x

M spin damping moment

pMm pitching moment about CG

M damping moment about CGmq

M magnus moment about CGnp

V total velocity, ft/sec.

d projectile diameter, ft.

g gravity, 32.174 ft/sec2

m projectile mass, slugs

projectile spin rate, radians/second

q projectile pitch rate, radians/second

[7

NOMENCLATURE (Continued)

2 2q dynamic pressure, 1/2p V , lb/ft

3total angle of attack, radians

P air density, slugs/ft3

Subscripts

(X Derivative with respect to sin a

2-2 Derivative with respect to sin

2 X

3-a 3 Derivative with respect to sin a

5 -cx5 Derivative with respect to sin a

8

e'." A

INTRODUCTION

The Armament Department of General Electric under contract to Picatinny

Arsenal has developed an empirical computerized model for predicting the

aerodynamic coefficients of spin stabilized ,rojectiles. The code name of

the new program is SPIN-73.

The starting point for the current study was the computer program

SPINNFR 70 which was developed at Picatinny Aasenal during the period from

September 1966 to October 1968. This program was modified by General Electric

in 196968 and 197071 to update the predictions of the drag coefficient and

also to perform a closed form dispersion analsis.

In general the method used during the development of the original

Spinner was as follows-

Basic projectile configurations were selected which were considered by

Whyte 68,70 to have well determined aerodynamic coefficients. Empirical equa-

tions and constants were developed, by a trial and error process, by which

the standard coefficierts could be adjusted for changes in total length, nose

length, boattail t.ngth and center of gravity.

The following limitations were and are present in the original program.

1., Nose length 1.8 to 4.0 calibers

2. Projectile length 3.6 to 9.0 calibers

3. Boattail length 0.0 to 1.0 calibers

4. Meplot diameter, 0.10 to 0.15 calibers

5. Nose radius, secant +100% to secant -30%

6. Rotating band diameter, 3.025 calibers

* References alphabetically listed starting on page 22.

9

However as most projectiles in service and under investigation during

the period from 1966 to 196q in general fell within the above bounds the

limitations of the program were not considered very serious.

Since 1970 several programs have been initiated by the Army and Navy

which are considering utilizing projectiles with nose lengths of up to 5.5

calibers and boattail lengths of up to 2.5 calibers.

Also payload and fuzing capabilities of several small arms projectiles

currently under development by the Air Force, Navy, and Army have dictated

blunter ogives (large meplats) and near tangent ogives.

Rotating band diameter are also of larger scale on small arms than

corresponding shapes of large calibers thereby complicating the prediction

process.

Because of these known limitations and future requirements the need for

a revised SPINNER was indicated. Thus this current study was initiated in

August 1972.

Sears6 0 of Eglin in 1972 published a computerized curve fit technique

for predicting the drag of projectile. His results indicated improvement

over the original SPINNER in the area of tangent ogives and meplat bluntness.

A similar method to that used by Sears was employed in updating SPINNER.

In discussing the computer programs the 1969 version of SPINNER will be

referred to as SPIN-69 and the 1973 version as SPIN-73.

10

21 -

PROCEDURE

The most difficult task in the analysis of data is determining a

constant accurate model which will adequately curve fit data under all cir-

cumstances, whereupon predictions of results under a different sets of

initial conditions do not result in completely useless answers.

An example of useless results is shown in figure 15 where the pre-

dicted axial force is negative in the SPIN-69 program. When terms of

higher order polynomials are employed to obtain good fits one must be very

cautious when using these polynomials to extrapolate or even interpolate

data. These cautions are pointed out because SPIN-73 does employ higher

order polynomials.

The equations used for fitting and probable) errors i.i1 be covered for

each coefficient individually.

In general the data utilized with very fei exceptions was obtained

from reports published by the Ballistic Resea:ch Laboratory (BRL) and

Arnold Engineering Development Center (AEDC). No wind tunnel data was used

at all in the data bank. Wind tunnel data aas used to determine trends

and comparisons were made with the trends resulting data fitting.

The references utilized to collect the experimental data are listed

starting on page 22. Unpublished data from BRL, Picatinny, AEDC and GE

were also used. The method used to curve fit the data is described briefly

in Appendix A.

Equations of the following general form were used for all coefficients.

Definitions of VL, VN, VB, VCG, BD, DM, OR, and BOOM are found in figure 1.

11

-

Cx =a1 + a2 (CVN) + a3 (CVN2)

+ a 3 (CXCL) + a4 i'CXCL )

+ a5 (CVN • CXCL)

+ a6 (CVB) + a7 (CBD)

+ a 8 (CMK) + a 9 (CMK )

" a10 (CVN - CMK) + a1 1 (CXCL CMK)

" a 11(CRAT) + --- etc.

where:

CVN = VN - 2.5

CXCL = VL - VN - VB - 1.5

CVB = VB

CBD = BD - 1.02

CMK = CMK - 1.05

CRAT = VN /OR - 0.40

The combinations, variations, and parameters which can be included in

19-28the fitting equation are nearly infinite. References such as Dickenson,

60 66 43Sears, Watt, and Murphy were used as guides for determining the most

effective way of deriving an empirical equation. By the trial and error pro-

cess equations of the above type were manipulated into a form which adequately

described the experimental data.

12

EMPIRICAL EQUATIONS

This section will describe individually for each coefficient the equations

contained in the computer program SPIN-73 as of June 1973.

Axial Force Coefficient

CXCL =V. - VN - VB - 1.5

CBD =DB - 1.02

CDM =(DM - 0.12) 2 CRAT =VN 2/OR -0.40

if 0 < VN < 3.0 set VNX = VN , DXN = 0.0

if 0 < CXCL < 1.5 set CXCLL = CXCL .DXCL =0.0

if 0.2 < VB < 0.65 set VBX = VB - 0.2 DXBT =0.0

If VN, CXCL, or VB are greater than the maximum

set VNX = 3.0 , DXN =(VN - 3.0) A 1 3

CXCLL = 1.5 ,DXCL = (CXCL - 1.5) 0.01

VBX =0.45 ,DXBT = (VB - 0.65) A 1 0

If VB is less than the minimum

VBX = 0.0 ,DXBT = 0.0

C X aII (VNX - 2.5) + a3(VNx -Ia2 a 2.5) 2

+a 4 (VNx - 2.5) 3 + a 5(CXCLL+a (rXCLL) 2

+ a 7(VBX) +a 8 (CRAT) + a 9(CRAT)

+ a 1 1 (CED) + a12 (0DM) -(BOOM/1.36, 20.01

-DXBT -DXN + DXCL

13

The "IF" statements are required to circumvent the need for higher order

polynomials in the equations. In this manner only linear extrapolation and

interpolations are allowed on the fringes of the program capabilities. This

should prevent completely erroneous estimates.

Normal Force Coefficient Derivative, Pitching Moment Coefficient Derivativeand Normal Force Center of Pressure

if 0 < VN < 3.0 set VNX = VN , DNX = 0.0

A Bif 0 < VB < 1.0 set VBNP = VB , VBMP = VB , VBX = VB

where: Subsonic A = 1.0, B = 0.8

Supersonic A = 1.5, B = 1.0

if VN or VB are greater than the maximum

set VNX = 3.0 , DNX = VN - 3.0

0.5 0.5VBX = 1.0 ,VBNP = VB VBMP VB

Now set

CVNN = VNX - 2.47

CXLL = VL - VN - VB - 2.15

CDKM = DM - 0,17

CBBD = BD - 1.04

CCRT = VN2/OR - 0.48

VBTI = CVL/4.7

CNAB = B1 + B, (CVNN) + B (CXLL) + B4 (CCRT) + B (CVNN)2 + B6 (CXLL)I I.3 456

CNBT =B 7 (VBNP) + B 8 (VBX CVNN) + B 9 (VBX .CXLL)

CNAT = CNAB + CNBT

14

*1i

AMOMSQ = CNAB [C1 + C2 (CVNN) + C3 (CVNN)2

3+ C4 (CVNN) + C5 (CXLL) + C6 (CXLL)

2

3+ C7 (CXLL) + C8 (CCRT) + C9 (CCRT)

2

+ C10 (CDNI4) + C1 1 (CCRT - CYNN) + C1 7 (DNX)]

AMOMBT = VBTT [C] 2 (VBMP) + C 1 3 (VBX - CVNN)

+ C1 4 (VBX • CXLL) + C1 5 (VBX • CCRT)

+ C1 6 (VBX • CCRT • CVNN)]

CPN = (AMOMSQ + &MOMBT)/CNAT

CN = CNATa

CM = (VCG - CPN) CN

Yaw Axial Force Coefficient

CXCL = VL - VN - VB - 1.5

CRAT = VN 2/OR - 0.40

CVB = VB

CX D1 + D2 (CXCL) + D3 (CRAT) + D4 (CVB) - CNU

The Yaw Drag coefficient may be computed by adding Cx and CN.

2

15

.... ... . -

Magnus Force Coefficient Derivative, Magnus Moment Coefficient Derivative,Magnus Force Center of Pressure

CVL = VL

CVB = VB

CXCL =VL - VN - VB - 1.5

CVN =VN - 2.5

CYPA =E 1 (CVL) -0.1 (CVB)

at a .0

CNPAN =-E 1 (CVL)j [IE2 + 0.55 (GXCL) + 0.80 (CVN)]

+ CVB (CVL/4.7)

CPF = -CNPAN/CYPA

C =Px CYPA

Cn PD (VCG -CPF () C Y

at a 2.00

CNPAN -E I(CVL) [E3+ 0.55 (CXCL) + 0.80 (CVN)]

+ CVB (CVL/4.7)

CPF (2 -CNPAN/CYPA

C p CYPA

n a()= (VCG -CPF () C p

at a =5.0'

CNPAN' -E]I (CVL) [E 4 + 0.55 (CXCL) + 0.80 (CVN) + CVB (CVL/4.7)

CPF (5) =-CNPAN/cYrA

16

N-T

C =CYPAYpa

C =(VCG- CPF Cnl (5) YpciPc( 5)

Damping Moment Coefficient

CLL = VL - 5.0

CCG = VCG - 3.0

CVB = VB

Cm = -5.093 [F1 + F2 (CLL) + F 3 (CLL ) + F 4 (CCG)

+ F5 (CCG) (CLL) + F6 (CCG) (CLL 2 ) + F 7 (CCG) (CVB)

+ F8 (CVB)]

Spin Deceleration Coefficient

C = GI (VL/5.51)1

Stability Analysis

The methods used for stability computations were extracted from references

44 and 45. They are identical to those contained in the original SPINNER.

Gyroscopic Stability Factor, sg

s = 2 2p2/7 C d 3 V2

g x Yp mn

Dynamic Stability Factor, sd

2 (CN -CX + (ki- 2 /2) C )

d (CN -Cx-(k 2-2/2)Cm + (k 1-2/2)C )ci q p

17

Nutation, Precession Frequencies u1,2

Px (il+ )

-l,2 21Y

Nutation. Precession Yaw Damping Rates, X1, 2

pA [1C (1 t 1) + (i + /2 U 1 C1,2 4m [N (1 ± +( 2 /2) (1 q n pak1 /q Pct

where

-2 2k1- = md2/I

k2- 2 = md2/Iy

Cy = 1i - i/7s

The dispersion (DISP) is the radius in mils of a circle which a projectile

will impact in a vertical plane when disturbed to a first maximum yaw angle of

5 degrees or less. The basis for this calculation is derived in Reference 71.

The time step (DELT) shown will provide 20 integrations per nutation

cycle. This is entirely adequate for a 4th Order Range Kutta integrator.

18

$ 'j

RESULTS AND DISCUSSIONS

The results of several test cases are presented in Figures 2 thru 15.

Plotted are experimental points, SPIN-69 and SPIN-73 results. Tabulated

outputs of SPIN-73 are shown as tables 2 thru 15.

The following ranges of parameters are demonstrated by the test cases.

Total length 3.8 thru 10.0 calibers

Nose length 1.6 thru 5.5 calibers

Boattail length 0.0 thru 1.0 calibers

Ogive radius tangent thru conical

Meplat diameter 0.0 thru 0.26 calibers

Band diameter 1.00 thru 1.05 calibers

In general the coz relations between SPIN-73 and the experimental data

is very good with noticeable improvements over SPIN-69. Most of the effort

during this current study has been directed at the Axial Force and Pitching

Moment correlations as these two coefficients are by far the most accurately

determined during the experimental process. Mach work still remains to be

done on these coefficients in terms of defining a more adequate empirical

model.

The most poorly determined coefficients remain the Magnus and damping.

It is this author's opinion that the SPIN-73 improvement in these the cal-

culations is negligible. While some new data has been published since 1968,

in general data was previously available on similar shapes. For example

the projectiles refered to as the XM380 and XM549 were experimentally

i9

-n 1,

investigated long ago as the T388 and T387. This data was available in 1967

and had been included in the original (SPIN-69) program.

The bulk of the data published by AEDC through calendar year 1972 is

suspect as far as the Magnus and damping coefficient are concerned because

the effect on lineai theory reductions of a slowly varying pd/2V was not taken

into account.

This author also found in several instances as did Sears that the

geometric description of the projectiles under test were not available

either in the data reports or the data files.

The probable errors to the experimental data of the SPIN-73 empirical

equations are shown in Table 1. The number of data points used to compute

the probable rror is shown in parenthesis.

20

CONCLUSIONS AND RECOMMENDATIONS

The SPIN-73 program has been shown through test cases to be more accurate

than the SPLN-69 program.

The updating rcf SPIN-73 should be continued as new data is accumulated.

Records should be kept of shortcomings and extremely poor predictions.

Data should be more carefully reported with respect to actual configura-

tion tested.

21

p,

~- ' - - - ~-,-.- , r--~.~

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3. Boyer, E. Comparison of the Aerodynamic Characteristics of the 20mm HEI,

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AD866b68.

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22

ALA,.-

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23

-| , i / ' A 1 i-. ..

32. General Electric Company, Advance Munitions Development Burlington, Vermont,Aerodynamic Data Files (Unpublished).

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38. Karpov, B.G. Aerodynamic Characteristic of the 175mm T203 Shell and the175mm Square Base Shell with Fuze M51A5. BRL MenLo Report 956, December 1955.

AD086528.

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AD021307.

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July 1963, AD442757.

45. Nicolaides, J.D. Free Flight Dynamics, Univ. of Notre Dame 1968.

46. Odem, C.T. A Revised Drag Coefficient, KD Based on the 8 Inch HowitzerShell, HE M106. BRL Memo Report 1065, April 1957, AD132170.

24

47. Odem, C.T. Drag Coefficient of HE Shell for the New Series of Field ArtilleryWeapons. BRL Memo Report 1013, July 1956. AD105611.

48. Picatinny Arsenal, Dover, New Jersey, Aeroballistics Branch Files.49. Piddington, M.J. Ihe Aerodynamic Properties of a Caliber .223 Remington

Bullet Used in the M16 (ARI5) Rifle. BRL Memo Report 1758, June 1966.AD489960.

50. Piddington, M.J. Comparitive Evaluation of the 20mm Developmental Ammunition- Exterior Ballistics. BRL Memo Report 2193, May 1972.

51. Piddington, M.H. Deformation Characteristic of One Lot (LC SP412) of 5.56mmM-193 Ammunition. BRL Memo Report 2016, October 1969. AD862966.

52. Piddington, M.H. Some Aerodynamic Properties of a Low Velocity Projectilewith a Hemispherical Nose and L/D of 4.3. BRL Memo Report 1639, April 1965.AD47237].

53. Piddington, M.H. Aerodynamic Properties of a 20mm HE-T Projectile for VRFWS.BRL Memo Report 2000, July 1969. AD859054.

54. Piddington, M.H. Aerodynamic Characteristic of the 7.62mm NATO AmmunitionM-59, M-80, M-61, M-62. BRL Memo Report 1833. March 1967. AD815788.

55. Roecker, E. Large Yaw Firings of the 20mm HEI, T282E1 Shell with Fuze T196at Mach Number 2.3. BRL Memo Report 888, April 1955. AD068718.

56. Roecker, E. Aerodynamic Characteristics of 30mm HEI Shell T306 ElO. BRLMemo Report 1098, August 1957. AD152952.

57. Roecker, E. The Aerodynamic Properties of the 105mm HE Shell, M1 in Subsonicand Transonic Flight. BRL Memo Report 929, September 1955. AD078604.

58. Roschke, E.J. The Effect Nose Truncation on the Aerodynamic Properties ofthe 9 Caliber AN Spinner Rocket Near Sonic Velocity. BRL Technical Note 902,May 1954. AD061551.

59. Roschke, E.J. The Drag and Stability Properties of the Hemispherical BaseShell, 75mm, T50E2. BRL Memo Report 927, September 1955. AD079488.

60. Sears, E.S. An Empirical Method for Predicting Aerodynamic Coefficients forProjectiles - Drag Coefficient, AFATL-TR-72-173, August 1972.

61. Schmidt, I.E. The Dynamic Properties of Pure Cone and Cone Cylinders. BRLMemo Report 759, January 1954. AD030249.

62. Schmidt, L.E. The Aerodynamic Properties of the 7-Caliber Army-Navy SpinnerRocket in Transonic Flight. BRL Memo Report 775, March 1954. AD035840.

63. Schmidt, L.E. Aerodynamic Properties of 4.9 Calibers Long, Square BasedShell at Transonic Speeds. BRL Memo Report 824, August 1954. AD047993.

25

- . .'~ -

64. Scott, W.E. The Effect of a Rotating Band upon Some Aerodynamic Coefficientof the Seven Caliber AN Spinner Rocket at M=l.8. BRL Memo Report 1302,September 1960. AD246223.

65. Scott, W.E. Some Aerodynamic Properties of a 105mm Model of the 155mm T-358Shell. BRL Memo Report 1369, September 1961. AD267268.

66. Watt, R.M. Free Flight Range Tests of Blunted 4, 4.5, and 5 Caliber Bodiesof Revolution with Secant-Ogive, Tangent-Ogive, and Conical Nose Shapes.AEDC-TR-71-166, December 1971.

67. Watt, R.M. Free Flight Range Tests of an Improved 20mm Shell. AEDC-TR-70-289,January 1971.

68. Whyce, R.H. Spinner - A Computer Program for Predicting the AerodynamicCoefficient for Spin Stabilized Projectiles. General Electric TIS 69 APB3,August 1969.

69. Whyte, R.H. Effects of Boattail Angle of Aerodynamic Characteristics of175mm M437 Projectile at Supersonic Mach Numbers. PATM 1646, September 1965.

70. Whyte, R.H. Spinner - A Computer Program for Emperically Predicting theAerodynamic Coefficients of Spin Stabilized Projectiles, Picatinny ArsenalESL IR 319, February 1967.

71. Whyte, R.H. Dispersion of Projectiles as a Function of Physical and Aerody-namic Properties. General Electric, Burlington, Vermont, Advance MunitionReport, January 1970.

72. Winchenbach, G.L. Free Flight Range Tests of Basic and Boattail Configurationsof 3 and 5 Caliber and Spinner Projectiles. AEDC-TR-70-12. March 1970.

73. Winchenbach, G.L. Free Flight Range Test of the 20mm M56A2 Shell with aModiiied M505E3 Fuze. AEDC-TR-67-108, June 1967.

74. Wincnenbach, G.L. Free Flight Range Tests of the 20mm M56A2 Shell with theM505E3 Fuze. AEDC-TR-65-258, January 1966.

75. Winchenbach, G.L. Free Flight Range Tests of a 25mm Shell with the M505A3Fuze. AEDC-TR-71-62, April 1971.

26

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APPENDIX A\

CURVE FIT TECHNIQUE

171

CURVE FIT TECHNIQUE

The method used to perform least squares fits to the experimental

data using the empirical equations was a GE Time Sharing computer program

code name LSQMM. This program was utilized with the GE415 computer at

the Armament Systems Department. The brief description starting or the

next page of this program was extracted from the following reference.

Numerical Analysis Routines #807231A

Information Service DepartmentGeneral Electric CompanyBethesda, Maryland

Issued August 1968 (Revised Feb. 1969)

7

72

LSQMM'Iii', i outint dt-terines the coefficients A Q,JI-I,2, .. N of the function

F (I), , fA ? 1,2 A Q I =1,2 .. M

which detormines the hi-,t .ippiotximation of the fun'-tion V (I) in either the weighted leastsquares sense or the muli-max sense.

UsageThe c..ling sequence for this coutine is:

CALL LSQMM(PI'i \,A,HW,M,N,NT,NS,AM,IDIMM,IDIMN)

where,

*PHI is the N(, imensionial array, PHI(MN, N),. of coordinate funcklons which are sup-pliedj 1)% thl( 'jL,. The kth column~j of PHI contains the kth coordinate function evalua-a* ed at each (f the data points (i.e., - PHI(I~k , I - 1, 2, . .~ ., M).

*Y is the one dimnisiondi array, Y(M), containing the dependent variables.*A i, the one diniersional irra%, A()The A array cwi A i's thit ( efficient s A(J) of the function F(I).

*RW is the nane, "4, an arra containting the residuails R(! Y(I)- F(!), the weilhts W(I),and temporal ;tora-e to Lave the vertical weia-hts %hile doing the horizontal itera-tioiis. It should cioitain at least 3 *M locations.

*M IS thet numb11er of data points.*N i,, the number of coefficients, i.e., number o1 coordinate functions.*NT is the maximumin number of vertical iterations. For least Squares fit, NT = 1.*For least Squares fit and when there is no division of the data points in min-max.,

NS(l) =M. Otherwise, NS is the array containing the index values of the ends of thesections when Lusint', mmn-max fit,

*AM is a t~o chniensional arrav. AM(N,N , used internally to contain the n'atrix ofthe s\ st err of I IT'ar equations.IDIMMN i,, th'- first dim ense 'n of Pill, i.e., PHI1 IDIYIN N)'.IDININ .. the first dimension of AI, i.e., AM(IDIMN,N).

DiscussionM 1

If the user wishes to, minimize 1.1w [Yiix F '1 w 0, miodif\, the PHI and Y arrays

as follows:

0w JH(1 j.........)wPH(1N

PHI V2

L M'PM Pil FII-). .. .. .. .. ..... w \IPHI(M,;;N)

AL 2IY (3)

73

Sample Problem

Find the ,,eeond ifr orn pelvyonjial F A3 ,2 A2 , A , which htst fits the lolinwig datain the least squares where M 9,. N 3, ',.T- 1.

X 4., -3. -2. -1, 0., 1., 2.:, 3., 4.

Y - 2., -3., - b -7.:, -6-, -3., 2., 9., 18.

Solutiov is F X - 2X-6,

Sample Solution

NEWNET FILE NAME--EXAMPLEREADY

10 COMMON PHI(9,3).X(9),A(3),Rh(27)20 COMMON AM(3,3)PY(9)*YA(9).NS 1)30 DATA M#N.NTNS/93*I.9/40 INPUT,(X(I)#I=I.M)50 INPUT, (Y( I), Ia1,M)60 CALL PHII(M*N)70 CALL LSOMM(PHIY.A.RW,M,NNTNS.AM,9,3)80 DO 40 I=IM90 YA(I)-0.0100 DO 30 JaIN110 30 YA(I)=YA(I)¢A(J)*PHI(IJ)120 40 CONTINUE130 PRINT 100140 1O0 FORMAI(" X F(X) Y-F(X) A(N)150 l ".)

170 DO 50 I=IN180 50 PRINT 60,X(1),YA(I)PRW(I).A(I)190 60 FORMAT(4EI3.4)200 K=N+1210 DO 70 I=KM

220 70 IRINT 80,X(I),YA(I)PRW(I)230 80 FORMAT(3E13.4)240 STOP250 END260 SUBROUTINE PHII(MN)270 COMMON PHI(9#3),X(9)280 "30 10 I=lM

290 1O PHI(I,1)=1.0300 IF(N-2) 40,15,15310 15 DO 30 Ii.M

320 DO 20 J=2,N3302 0 PHI(IJ)=x(I)**(J-1"

340 30 CONTINUE!'0 40 RETURN.e ENZ

RUN

EXA4PI F

4 - J. , ,-, , - ). , . ';,3.,#4.3. - ,-6 .. ;. - ,-3. ?,2 , 9.a•18.

X F(X) Y-F(X) A(N)-0, "0F*- ,+'r, +n 0. -0.6000E+01-f t.f+1 Ju,. .k-+ 0. 0.2000E+0l-U.2000e 'ci .60001 .01 0. 0. IO00E+01-0. EIOO 01 - , t, 0.0. -0, 6000E+0I 0.

0.IQOOE.O1 -O.3000E+Oi A.

03DOOE0i I q. 9000LOi 0.0.0 0, _'01 0. 0IROOE 2 0.

74

APPENDIX B

INPUT-OUTPUT DESCRIPTION

75

Z-. - -

INPUT-OUTPUT DESCRIPTION

PROGRAM NAME - SPIN-73

CODING DATE - July 1973

PURPOSE - Predict the aerodynamic coefficients of spin stabilized

projectiles at Mach numbers for 0.0 to 5.0.

Inputs to the program are the projectile physical dimensions,projectile mass properties, gun bore diame-er and twist, andthe local air temperature.

INPUTS

Card No. 1 (See Note D)

IBM CARD COL VARIABLE

1 - 7 VL Projectile length - calibers

8 - 14 VN Ogive length - calibers15 - 21 VB Boattail length - calibers22 - 28 VCG Center of gravity - calibers for nose29 - 35 DM Diameter Me'Plat - calibers36 - 42 BD B Rotating band diameter - calibers43 - 49 ORB Ogive radius - calibers

50 - 56 BOOM Boom length - caliber5

57 - 80 NTiTLE Descriptor

Card No. 2 (See Note C)

1 - 7 DIA Projectile diameter - inches

8 - 14 AX Axial inertia - inches lb-in2

15 - 21 TR Transverse inertia - inches lb-in2

22 - 28 WCT Prcjectile weight - lbs.29 - 35 TWIST Gun twist - cal/turn36 - 42 TFM1'P Air temperature - 'F

43 - 49 DGUN Gun bore diameter - inches50 - 56 NAUTO 0 Uses input dimensions

1 Automatic dimensions

A

BD set equal to 1.02 calibersDM set equal to 0.12 calibersOR set equal to 2 (-VN 2 ) (secant ogive)

BIf input as zero (0.0) these inputs are changed

BD set equal to 1.00 calibersOR set equal to secant ogiveDGUN set equal to DIA

CIt aero estimates are only requirementthis card should be left blank.rDRepeat cards I and 2 to stack cases

76

OUTPUTS

Line 1 - Organization designation

Linu 2 - Description of item being estimated

Line 3 - Title line - projectile dimensions

Line 4 - Projectile dimensions

Line 5 - Title line - projectile physical properties, gun properties

air temperature and density

Line 6 - Projectile physical properties, gun properties, air temperature

and density

Line 7 - 'Aerodynamic Coefficients'

Line 8 - Title line - Mach No., etc.

Line 9 - Cxo - Zero yaw axial force coefficient

CX2 - Yaw axial force coefficient per sin a

CNA - Normal force coefficient derivative per sin a

CMA - Pitching moment coefficient derivative per sin a

CPN - Normal force center of pressure - calibers for nose

CYP - Magnus force coefficient derivative per sin a

CNPA - Zero yaw Magnus moment coefficient derivative per Iin a

CNPA3 - Cubic Magnus moment coefficient derivative per sir, a5CNPA5 - Quintic Magnus moment coefficient derivative per sin a

CPF1 - Center of pressure of Magnus force at 10 yaw or less

calibers from nose

CPF5 - Center of pressure of Magnus force at 50 yaw, calibers

from nose

CNPA-5 - 50 - Secant slope of Magnus moment coefficientderivative (at 5" yaw) per sin a

Cmq - Damping moment coefficient

Clp - Spin deceleration coefficient

Line 10 'Stability Analysis'

GYRO Gyroscopic stability factor

SBAR Dynamic stability factor at 1° yaw

RECEP Dynamic reciprocal factor at 1' yaw

SBAR5 Dynamic stability factor at 5' yaw

RECIP5 Dynamic reciprocal factor at 5' yawSPIN Spin rate, radians/secondW1 Nutation frequency, radians/second

W2 Precession frequency, raaians/secondLI Nutation damping factor per foot @ 1' yaw

1,2 Precession damping factor per foot @ 1' yaw

LI-5 Nutation damping factor per foot @50 yaw-2-5 Precession damping factor per foot @ 5' yaw

DELT Integration tire step, seconds (20 per nutation)

DISP Dispersion factor per 50 first max yaw, mils

77

APPENDIX C

PROGRAN LISTING

SPIN-73

78

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" 45

DISTRIBUTION LIST

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Dr. E. Sharkoff 51-55Mr. S. Kravitz 56Mr. V. Lindner 57Mr. S. Wasserman 58Mr. J. Gregorits 59Mr. J. Dubin 60Mr. A. LoPresti 61Mr. .. Loeb 62Mr. D. -rtz 63-72Mr. R. Kline 73-77

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89

DOCUMENT CONTROL DATA -R & D(Se-.,,ty ,f rtle, bod) vt ab.1,4, I and indexing annotefion m.,,t b0e ntered wIhen the veI'roll report i. classified)

i oRj c,-A riN G AC 'VI TV (orporate alhot) Ide. REPORT SECURITY CLASSIFICATION

JNCLASSIFIEDArmament S;Y:stems Department 2bGRUGeneral etro.r 0

3 RF ORT TITLE

Spin-73 An Tipdated Vers-on of theSpinner Computer Progran

4 OESCAPTIVE NOTES (Type otrepor'andfiRlu.,-' date.)

5 AUTHORISI (Firer nAme, middle initial, lgat name)

Robert H. Whi te

6 REPORT OA'0 74. TOTAL NO OF PAGS = 17b NO OF REFS

NOVEMBER_1973 89___________75______

4CONTRAC -OR CkNN NO 94 ORIGINATOR'S REPORT NUWBER(S)

DA.!AA21-73 -C-,033b. PROJLCT NO Technical Report 4588

AM1CMS code No. 554C.l2.62000_____ _____________

C. 99 OTHER REPORT NOMS (Any othrrnumbere that may be assignedtis report)

10 I.SRIBTIO STTEMNTDistribution limited to U.S., Government agenAies only (test andevaluation, November 19?3) . Other requests f:)r this doeument must LE, referred toPicatinny Arsenal,~ Dover, N.J. . ATTN 9APPA-TS--T-r,.

it SUPPLEMENTARY NOTE:S 12 *PONSORING MILITARY ACTIVITY

Feitman Research LaboratoryPIctinny X rsenal

_____________ __________________ cver-, N.J, 0780113 ABSTRACT

The SPINNEI. corputer program has been updated to compute aerodynamiccoe-1ffcients tb'r a wide varict:, o-f spin stabil2zed projectile shapes.Improvemerts ovolt the original program are substantial as ogiveradius, met-iat. di:moe_r and rctating band diameter are account-' forinstead of assumru"q mear 'iia. Test cases are shown compar the1969 SPINNER, the _1973 .EPIN1,NER and experimental data. Input instruc-tions ard s-imple >rograim uuitputs are given along with the 1973 programnlisttnq.

3% 1% ~em 'S 01 96PLACIR. 00 I..I'. 147. I JAN4 64. WHICH IS

Security Clslfication

ONCLASS I FI EDSoicurity ClassificatIon

14 LINK A LINK 6 LINK CKEY WORD S

ROLE WT ROLE WT ROLE WT

Projectile

Spin StabilityComputer AnalysisDragPitching Moment

Magnus

Damping

SPINNER

i

UNCLASSI FIED.ewity claasifcation

DEPARTMENT OF THE ARMYUS ARMY RESEARCH. DEVELOPMENT AND ENGINEERING COMMANDARMAMENT RESEARCH, DEVELOPMENT AND ENGINEERING CENTER

PICATINNY. NEW JERSEY 07B06-5000

TECHNICAL REPORT DISTRIBUTION CHANGE

The distribution statement for the below technical paper is to be changed to I -

Approved for public release, unlimited.

Title: SPIN-73 an Updated Version of the SPINNER Computer Program

AD Number: AD0915628Report Date: November 01, 1973

(Signature) (date)

Robert E. Souders

Security SpecialistDPTMS 973-724-4058DSN 880-4058US Army Garrison, Picatinny Arsenal