AD-A258 753

NSWCDD/TR-92/509

IMPROVED EMPIRICAL MODEL FOR BASE DRAGPREDICTION ON MISSILE CONFIGURATIONSBASED ON NEW WIND TUNNEL DATA

BY FRANK G. MOORE TOM HYMERWEAPONS SYSTEMS DEPARTMENT

FLOYD J. WILCOX, JR.

NASA LANGLEY RESEARCH CENTER I..HAMPTON. VA 23681-0001 DTIC ,:*

ELECTEDEC2 91992

OCTOBER 1992 AApproved for public rleaIse; distribution is unlimited,

4

V . NAVAL SURFACE WARFARE CENTERDAHLGREN DIVISION ..Dahlgren, Virginia 22448-5000

92-3289592 1 21 0 70

NSWCDD/TR-92/509

"O IMPROVED EMPIRICAL MODEL FOR BASE DRAGPREDICTION ON MISSILE CONFIGURATIONS

BASED ON NEW WIND TUNNEL DATA

BY FRANK G. MOORE TOM HYMERSTRATEGIC SYSTEMS DEPARTMENT

FLOYD J. WILCOX, JR.NASA LANGLEY RESEARCH CENTER

HAMPTON, VA 23681-0001

OCTOBER 1992

Approved for public release; distribution Is unlimited,

NAVAL SURFACE WARFARE CENTER

DAHLGREN DIVISION

Dahigren, Virginia 22448-5000

NSWCDD/TR-92/509

FOREWORD

The effort described in this report is one part of the theoretical developmentnecessary to make the last version of the Naval Surface Warfare Center DahigrenDivision (NSWCDD) Aeroprediction Code, published in 1981, more applicable topresent and future weapon concepts. The particular theoretical developmentincluded in this report addresses the improvements needed for base drag predictionon missile configurations ýhat may have combined effects of angle of attack and fincontrol deflection, fin location, and fin thickness.

Appreciation is expressed to NASA Langley Research Center (NASA/LRC) forits support in designing, building, and testing the wind tunnel model used forobtaining additional wind tunnel data. Acknowledgements are also given to JimBible and Sam Hardy of the Aeromechanics Branch, who provided isome of the earlierwind tunnel model design ideas and wind tunnel test consultation.

The empirical base drag methodology developed in this report, along withpartial cost of the wind tunnel model, was provided through the Office of NavalResearch (Dave Siegel) and, more specifically, the Surface-launched WeaponsTechnology Block Program managed at NSWCDD by Robin Staton. Appreciation isexpressed to these individuals for their support in this work.

Approved by:

DAVID S, MALYIVACDeputy Department HeadWeapons Systems Department

Acceiion ForNTIS WCRA&i .&

DTIC MA~Unaniinoun~ed

Ju~stificatiton .

ByJ ......... n.........................Distributlon !

Avi i OIsty Code.j;

-) l c~ I r[

NSWCDD/TR-92/509

ABSTRACT

New wind tunnel data have been taken, and a new empirical model has beendeveloped for predicting base drag on missile configurations. The new wind tunneldata were taken at NASA/LaRC in the Unitary Plan Wind Tunnel at Mach numbersfrom 2.0 to 4,5, angles of attack to 160, fin control deflections up to 200, fin thickness-to- chord (t/c) ratio of 0.05 to 0.15, and fin locations flush with the base to two chordlengths upstream of the base,

The newly developed empirical model uses these data along with previous windtunnel data. It estimates base drag as a function of all the above variables along withboattail and power-on or power-off effects. In comparing the new empirical model tothat used in the former aeroprediction code, the new model gives improved accuracycompared to wind tunnel data, The new model also is more robust due to inclusion ofadditional variables, On the other hand, additional wind tunnel data are needed tovalidate or modify the current empirical model in areas where data are not available.

ii

NSWCDD/TR-92/509

CONTENTS

Section

1 INTRODU CTION .............................................. 1

2 EXPERIMENTAL TESTS ..................................... 52.1 MODEL DESCRIPTION .............. .. .. .. ....... ....... 52,2 WIND TU14NEL TESTS . ..... ............... ............. 82.3 MEASUREMENTS AND DATA ................................... 9

3 EMPIRICAL MODEL FOR BASE DRAG PREDICTION ........... 143,1 BODY-ALONE CONFIGURATION ................................ 143.2 BODY-TAIL CONFIGURATION ................................. 16

4 COMPARISON OF BASE DRAG EMPIRICAL MODELSTO WIND TUNNEL DATA ..................................... 234.1 BODY-ALONE ANGLE-OF-ATTACK EFFECTS ...................... 234,2 BODY-TAIL CONFIGURATIONS ................................. 24

5 SUMMARY AND RECOMMENDATIONS ....................... 35

6 REFERENCES ............................................... 36

7 SYMBOLS AND DEFINITIONS ................................. 38

DISTRIBUTION ............................ .................. (1)

iii

NSWCDD/TR-92/509

ILL'J TRATIONS

Figure Page

1 MEAN BODY-ALONE BASE PRESSURE COEFFICIENT USED INOAP AND IAP ............... .................................. 2

2 BASE PRESSURE COEFFICIENT CHANGE DUE TO t/c WITH FINSLOCATED FLUSH WITH BASE USED IN OAP ........................... 3

3 DISTANCE FROM BASE WHERE FINS DO NOT AFFECT BASE PRESSURECOEFFICIENT AS USED IN OAP ...................................... 3

4 MISSILE BASE PRESSURE MODEL DESCRIPTION ....................... 5

5a PERCENT INCREASE IN BODY-ALONE BASE PRESSURE COEFFICIENTDUE TO ANGLE OF ATTACK (M.;2! 2) .................................. 15

5b PERCENT INCREASE IN BODY-ALONE BASE PRESSURE COEFFICIENTDUE TO ANGLE OF ATTACK (M. < 2) .......... ........ ..... 15

6 EFFECTS OF ANGLE OF ATTACK AND CONTROL DEFLECTION ON BASEPRESSURE COEFFICIENT (M,. = 2, x/c = 0) ....... II........................ 17

7 PERCENT INCREASE IN BASE PRESSURE COEFFICIENT DUE TO COMBINED

EFFECTS OF ANGLE OF ATTACK AND CONTROL DEFLECTION (tic -0) ..... 18

8a EFFECTS OF FIN t/c RATIO ON BASE PRESSURE COEFFICIENT (x/c = a = 8 = 0) 19

8b EFFECTS OF FIN t/d RATIO ON BASE PRESSURE COEFFICIENT (x/c = a = 8 = 0) 19

9 PERCENT INCREASE IN BASE PRESSURE COEFFICIENT DUE TO FINTHICKNESS AT VARIOUS VALUES OF I a + 81 .......................... 21

10a PERCENT INCREASE IN BASE PRESSURE COEFFICIENT DUE TO FINLOCATION (IEa+ NU = NE, ME=2I0) .. D.................. T FN........... 21

10b PERCENT INCREASE IN BASE PRESSURE COEFFICIENT DUE TO FINLOC ATION (ja+81 =5,0,M =v2.0) ............................................. 22

10c PERCENT INCREASE IN BASE PRESSURE COEFFICIENT DUE TO FINLOCATION (I a + 81 = 10,0°, M . =2.0) .......... .............. ................... 22

iv

NSWCDD/TR-92/509

ILLUSTRATIONS (CONTINUED)

Figure Page

Ila COMPARISON OF BODY-ALONE BASE PRESSURE PREDICTED BY THEOAP AND IAP AS A FUNCTION OF ANGLE OF ATTACK (M. = 0,6, 1.0) ........ 25

1 lb COMPARISON OF BODY-ALONE BASE PRESSURE PREDICTED BY THEOAP AND IAP AS A FUNCTION OF ANGLE OF ATTACK (M. = 1.5,2.5) ........ 26

tic COMPARISON OF BODY-ALONE BASE PRESSURE PREDICTED BY THEOAP AND IAP AS A FUNCTION OF ANGLE OF ATTACK (M = 3.5, 4.5) ......... 26

12a COMPARISON OF BODY-TAIL BASE PRESSURE PREDICTED BY THYOAP AND IAP AS A FUNCTION OF CONTROL DEFLECTION(t/c =0.05, M== 20, 2.5, 4.,5;x/c =O .0 - .. .. . .............. . .. 27

12b COMPARISON OF BODY-TAIL BASE PRESSURE PREDICTED BY THEOAP AND IAP AS A FUNCTION OF CONTROL DEFLECTION(t./c= 0,05, M,==06, 1,0,1.5; x/c=0) . ............ .. ... .. . 27

12c COMPARISON OF BOPY-TAIL BASE PRESSURE PREDICTED BY THEOAP AND IAP AS A FUNCTION OF CONTROL DEFLECTION(t/c= 0,10, M.= 2.0,2,5,4,5; :e-=-O) ... ... ....... .. . . . . . . . 28

12d COMPARISON OF BODY-TAIL BASE PRESSURE PREDICTED BY THEOAP AND IAP AS A FUNCTION OF CONTROL DEFLECTION(tic= O0, 10, M,==0, 6, 1,0, 1 ,5; x/c =0) . ... II .... I...... .. . 28

12e COMPARISON OF BODYTAIL BASE PRESSURE PREDICTED BY THEOAP AND IAP AS A FUNCTION OF CONTROL DEFLECTION(tic =0 .15,M .==2.0, 2,5, 4,5; x/c= 0) . ..... I... . .. I . I... . I.. .. 29

12f COMPARISON OF BODY-TAIL BASE PRESSURE PREDICTED BY THEOAP AND IAP AS A FUNCTION OF CONTROL DEFLECTION(te= 0.15, M .==0.6, 1,0, 1,5; x/C =0) ... . ......... I.... . . . .. 29

13a COMPARISON OF BODY-TAIL BASE PRESSURE PREDICTED BY THEOAP AND IAP AS A FUNCTION OF FIN THICKNESS (a = 8 = 0;x/,,= 0; M w= 3.0,1 4 5) .................................. ......... 30

V

NSWCDD/TR-92/509

ILLUSTRATIONS (CONTINUED)

Figure Page

13b COMPARISON OF 13ODY-TAIL BASE PRESSURE PREDICTED BY THEOAP AND IAP AS A FUNCTION OF FIN THICKNESS (a= 80;x/c=0;M.=1.5,2,0) ................................... I............. 30

13c COMPARISON OF BODY-TAIL BASE PRESSURE PREDICTED BY THEOAP AND YAP AS A FUNCTION OF FIN THICKNESS (a = 6=0;x/c=O;M.=0.6, 10) *. ..... 4 ..... I.................... 31

13d COMPARISON OF BODY-TAIL BASE PRESSURE PREDICTED BY THEOAP AND YAP AS A FUNCTION OF FIN THICKNESS (a = 8 0;xjc=I.0;1Mi=3.,'l. 5) .............. 1.1.1....I................-.......31

13e COMPARISON OF BODY-TAIL BASE PRESSURE PREDICTED BY THEOAP AND YAP AS A FUNCTION OF FIN THICKNESS (a=68=0;,xc = 1.0; M. =1.5,2,0 . . 0. 6 . .. . .. I .... ....... I............ 32

13f COMPARISON OF BODY-TAIL BASE PRESSURE PREDICTED BY THEOAP AND YAP AS A FUNCTION OF FIN THICKNESS (a = 8 = 0;xlc=l1.0; M.= 06,6)1.0)..... I...........11.......II...............k......32

13g COMPARISON OF BODY-TAIL BASE PRESSURE PREDICTED BY THEOAP AND WAPAS A FUNCTION OF FIN THICKNESS (a =68=0;x/c=2.0;M.=3.0,4.5).. ........... I...... .... I...... .6,........ I.....33

13h COMPARISON OF BODY-TAIL BASE PRESSURE PREDICTED BY THEGAP AND YAP AS A FUNCTION OF FIN THICKNESS (a = 8 = 0;x/c =2. 0; M,=1.5,10) . . ................. ...................... 33

13i COMPARISON OF BODY-TAIL BASE PRESSURE PREDICTED BY THEOAP AND lAP AS A FUNCTION OF FIN THICKNESS (a= 8 =0;

x/c=2.0;MX=0.6, 1.0)............. ............ I.... t...I. .. I......, 34

14 COMPARISON OF BODY-TAIL BASE PRESSURE PREDICTED BY THEOAP AND TAP AS A FUNCTION OF CONTROL DEFLECTION ANDANGLE OF ATTACK (tlc=0,15,x/c=1.0, M.=2,0) ....................... 34

vi

NSWCDD/TR-92/509

1. INTRODUCTION

For the past 20 years, the Naval Surface Warfare Center Dahlgren Division hasbeen involved in developing codes to calculate aerodynamics on tactical weapons,These codes have attempted to meet the changing need3 of the Tactical WeaponsCommunity and keep pace with aerodynamic requirements. A recent effortl wasundertaken to look at where we have been, where we are, and where we need to go inthe future with respect to aerodynamic codes. One of the primary needs identified inReference 1 was an upgrade of the NSWCDD aeroprediction code to allow Machnumbers up to 20 (including the effects of real gases), improved lift prediction withparticular emphasis on low aspect ratio lifting surfaces, and improved base dragprediction. All three of these efforts were undertaken. This report deals with thethird of these objectives, providing improved base drag prediction capability formissile configurations.

The latest version of the aeroprediction code2-4 (hereinafter referred to as OldAeroprediction Code or OAP) calculates base drag empirically, It estimates the body-alone, zero angle-of-attack, power-off base drag using an average of wind tunnel datapresented in several references.5 -13 These data assume a long cylindrical afterbodywith a fully developed turbulent boundary layer ahead of the base. Figure 1 showsthe base pressure coefficient currently used in the OAP as a function of Machnumber, iieviations to this curve are expected due to Reynolds number, temperature,boattail or flare, angle of attack, fin thickness-to-chord (t/c) ratio, fin location, findeflection, low body fineness ratio, or power on,. [ Note that Figure 1 also shows thoImproved Aeroprediction Code (IAP) body-alone base pressure coefficient based onthe present wind tunnel results, which will be discussed later, ]

The methodology of References 2 through 4 neglects the effects of Reynoldsnumber by assuming a Reynolds number combined with body roughness that is highenough to ensure fully developed turbulent flow at the base. Surface temperatureeffects are also neglected. The body is assumed to be at least 5 to 6 calibers long sothat body fineness ratio effects are minimal. Also fin deflection effects were notaccounted for due to lack of data, The body-alone, angle-of-attack base pressurecoefficient change was estimated from Reference 7 and given in the OAP as

Ac ) = (Cr8 ) - = - (0.012 0.0036M.) a;a S 150 (1)

NSWCDD/TR-92/509

0.25 .-.-. .- _

- -~~ lAP -

0,2 . . • .... ... ... ........ ....A . . .

0 A s s u m p tio n s . .... . .Body Length > 6 Calibers

o Turbulent B,L. at Base0.05 o Cylindrical Afterbody

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5Mach Number

FIGURE 1, MEAN BODY-ALONE BASE PRESSURECOEFFICIENT USED IN OAP AND IAP

The base pressure was allowed to change up to an angle of attack of 150 and was heldconstant for angles of attack greater than this, The effects due to fin t/c ratio and finlocation were estimated using the meager amount of data from References 14 through16. Below M=--1,5, the effects were extrapolated to M®=0 based on judgment andsome test data on configurations where the effects of fins could not clearly beseparated from other effects. Figure 2 shows the change in the base pressurecoefficient for various values oft/c ratio and Mach number that are in use in the OAP.

The effect of the location of the fins on base pressure was also estimated by useof the data in Reference 15, These data were interpolated in a linear sense (seeFigure 3) as a function of fin t/c ratio according to

x- 0ot/c (2)

where x is the distance from the base to the tail trailing edge (8 = 0°) where the fin hasno effect on base pressure. As an example, Equation (2) would indicate that the finneeds to be located one chord ahead of the base for a t/c = 0.1 fin to have no effect onbase pressure, The fin effect on base pressure would therefore vary linearly from amaximum at x/c = 0 to zero for x/c • 1.0.

2

"NSWCDD/TR-92/509

EXPERIMENT

"a REF 15A REF 16

- - -- EXTRAPOLATED

S-.6, t/1

/14p

II •

0,. 1.0 1S 2.0 2.5 3.0

MACH NUMBER (M.)

FIGURE 2, BASE PRESSURE COEFFICIENT CHANGE DUE TO t/cWITH FINS LOCATED FLUSH WITH BASE USED IN OAP

1,2 00- S

- ------ EXP(REF1S)--------------------------------EXTRAPOLATED

x = DISTANCE FROM BASE TO TAIL0,4 TRAILING EDGE (8= 00) WHERE

V A FIN OF GIVEN THICKNESS HASNO AFFECT ON BASE PRESSURE

0~ 1 " ' 10 .04 .08 .12 .16 .20

t/c

FIGURE 3, DISTANCE FROM BASE WHERE FINS DO NOT AFFECTBASE PRESSURE COEFFICIENT AS USED IN OAP

3

NSWCDD/TR-92/509

Finally, power-on effects were estimated by modifying the methodology ofBrazze117, 18 for higher values of mass flow at the nozzle exit, Also, boattail effectswere estimated by the empirical data of Stoneyl 2 to give

c A b c,,B( d) ) (3)

Here, CpB includes all the effects just otated. For the details of the methodology andequations used, the interested reader is referred to References 19 and 20.

There are several problems with the methodology used in the OAP, All of thesestem from the limited wind tunnel data available to estimate the change in basepressure as a function of the key parameters of interest, For most tactical missiles, itis believed that the neglect of Reynolds number, surface temperature, and bodylength-to-diameter ratio effects are acceptable so long as one remembers theconstraints upon which these assumptions are made, Also, it is believed that themethodology in the OAP for inclusion of boattail and power-on effects are acceptableat present, However, estimates of the change in base pressure due to angle of attack,fin thickness, fin deflection, and fin location need to be improved upon or accountedfor.

More specifically, the data for angle-of-attack effects were limited to smallangles of attack (5100) and Mach number. The data for fin location and t/c ratio werelimited to 1.5 r MG S 2.4; 0 S t/c 5 0.10; 0 : x/c s'5 2.0, It is well known that asMach number gets high, base drag goes to zero, Hence, it is desirable to have basepressure measurements for Mc < 5.0; a S 300; t/c : 0.15; x/c Z 2.0; and 8 S 200,Also, data where a combination of these variables is investigated simultaneously isneeded. Using these data, a more extensive and comprehensive empirical model toestimate base drag on missile configurations can be developed. While the data areneeded for an improved base drag prediction model, they could also be very useful invalidating Navier Stokes codes and in selecting appropriate turbulence models,

As a result of the need for additional wind tunnel test data, a request was niadeto NASA Langley Research Center (NASA/L, RC) to assist in providing such data,The data taken to date are for 2.0 :5 Mw S 4.5, a 5 1.6, 8 5 200, t/c S 0,15, and x/c S2.0. While these data are not as extensive as desired, they are by far the most exten-sive base drag database to date and will help in refining the empirical base dragprediction model of References 19 and 20. Hopefully, additional data at lower Machnumbers and higher angles of attack will be obtained in the future for additionalrefinements.

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NSWCDD/TR-92/509

2. EXPERIMENTAL TESTS

2.1 MODEL DESCRIPTION

A photograph and drawing of the missile base pressure model are shown inFigure 4. The missile body was an ogive-cylinder 36 in. long and 5.0 in, in diameter.Four cruciform aft tail fins could be attached to the missile body in a plus orientationat three longitudinal locations. At each longitudinal location, the fin incidence couldbe set at 0", 10*, and 20*. Three sets of fins were tested that had the same planformbut varied in thickness. The base was instrumented with 89 pressure orifices thatwere arranged along radial lines at 22.50 increments and 7 constant radiuses fromthe center of the base.

a. MODEL MOUNTED IN WIND TU L4NEL

FIGURE 4, MISSILE BASE PRESSURE MODEL DESCRIPTION

5

NSWCDD/TR-92/509

Instrumantallonleads passage 2

Tangent point

h. BODY AND SUPPORT STRUT DETAILS

4,00

Pivot pointx 2L

0 04,00 iCo0:00 2 0

cLONGITUDINAL FIN LOCATIONS

FIGURE 4. MISSILE BASE PRESSURE MODEL DESCRIPTION(CONTINUED)

NSWCDD/TR-92/509

z

Ole ON 0

OR Oh . 4

.12

*WW

7

NSWC DD/TR-92/509

The model was attached to a vertical strut near the mi ldle of the mrissile bodyon the upper surface (leeward side of model as a increases). The strut had a diamondcross section and was swept 150, The strut leading edge wedge half-angle was 12° andwas sufficiently small to maintain an attached shock on the leading edge at thelowest Mach number tested and at small angles of attack, At larger angles of attack,the strut was on the leeward side of the missile. body and would have minimalinfluence on the missile base pressure. The top, of the strut was sufficiently far fromthe model centerline (19,25 in,) so that a Mach line emanating from the top leadingedge of the strut would not intersect a tail fin on the mri.el and would intersect themodel centerline at least 1.5 body diameters downstrcaiýA of the model base at thelowest Mach number tested, The strut was attached to the tunnel model supportsystem through a 90°-offset sting holder that allowed the vertical position of themodel to be varied in the test section. The model nose was typically slightly belowthe tunnel centerline to increase the maximum attainable angle of attack andprovide clearance at the tunnel ceiling to ensure that the strut was outside of thetunnel wall boundary layer to minimize possible boundary layer separation andtunnel flow breakdown.

2.2 WIND TUNNEL TESTS

The wind tunnel tests were conducted in the NASA/LaRC Unitary Plan WindTunnel (UPWT), which is a continuous flow, variable pressure supersonic windtunnel with a Mach number range of 1.5 to 4.6. The tunnel has two test sections, eachof which covers only part of the Mach number range; the low Mach number testsection has a range of 1.5 to 2.9, and the high Mach number test section has a re.'age of2.4 to 4.6. The test sections are approximately 4 ft square by 7 ft long, The nozzleahead of each test section consists of an asymmetric sliding block that allows acontinuous variation of Mach number while the tunnel is in operation. A completedescription of the tunnel and test section calibration Information is presented in aNASA report.21

The tests were conducted at the following conditions:

mo Po T0 q

( / ft) (Cl / f't2 ) (OF) (11 / ft2)

2,0 2 x 106 1253 125 449

2,5 2 x 106 1600 125 410

3,0 2 x 10 6 2216 150 380

3,5 2 x 106 2882 150 324

4.0 2 x 106 3698 150 273

4,5 2 x 106 4666 150 229

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NSWCDD/TR-92/509

The dew point in the tunnel was maintained sufficiently low at all testconditions to ensure negligible water condensation effects. The model angle of attackwas varied from 0' to approximately 160 for tests conducted in the high Mach numbertest section (M, at 2.5) and from 00 to approximately 100 for tests conducted in the lowMach number test section (Mo = 2.0).

The tunnel flow angularity was determined by measuring the pressuredifference between two orifices located 180' apart in a vertical plane on the missilenose as the model was run through a small angle of attack range. These pressuredifferences were plotted against the model attitude which was referenced to thehorizontal, A least-squares fit was applied to the data and the tunnel flow angularityat a given Mach number was the angle at which the pressure difference was zero,This procedure was performed at all Mach numbers and all the data were correctedfor tunnel flow angularity,

To ensure a turbulent boundary layer over the model, transition grit wasapplied to the missile nose and to the leading edge of each fin, The transition stripswere located 1,8 in. from the model nose measured along the model surface and 0,6 in,from the fin leading edges measured streamwise, For M. ; 2.5, the transition stripsconsisted of #35 sand grit (0,0215±0.0018 in,) individually spaced 0,09 in. apart onthe model nose and 0,12 in, apart measured parallel to the fin leading edges, ForMw =-2.0, the transition strips consisted of #45 sand grit (0,0152 ± 0,0013 in.) sparselysprinkled in a lacquer film, The size and location of the transition grit wasdetermined from documented procedures 22 except that a critical roughness Reynoldsnumber of 1800 was used instead of the recommended value of 600. The increase incritical roughness Reynolds number above the recommended value was due to theeffects of high Mach number and was determined using guidance from a NASApublication 23 and unpublished data obtained in the UPWT,

2,3 MEASUREMENTS AND DATA

The pressures on the model were measured with two electronically scannedpressure modules that were located inside the model. The modules had a full-scalerange of ±5 psid, All 89 pressure orifices on the model base were measuredsimultaneously for each data point. The model angle of attack was measured with anaccelerometer that was mounted inside the missile body,

The missile base drag coefficient was calculated using an area weightedaverage of the base pressure coefficients as shown in the following equation.

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NSWCDD/TR-92/509

Ax An 17 A-DB + + i=1O -I(

D A,)+ I-A)4 I AAI

PA( i= AI + I cPi()I I c,(,) (4)

+ ~ , I-~~ I PI A - ,()j

where

CpI = pressure coefficient corresponding to orifice ii = orifice number

A = base areaA1 , A2 ,,.,, A8 = area used as weighting factor

Tests were conducted both with and without tail fins. Data were obtained atdiscrete a for cases with tail fins and over a range of a for cases without tail fins. Acomplete description of all the configurations that were tested is contained in Table 1,Table 2 contains a list of the base drag data,

Two problems arose during this test that affected the uncertainty of themeasured pressure data using the electronically scanned pressure modules. The firstproblem was model vibrations, which were possibly caused by either normal tunnelvibrations being transmitted through the long-cantilevered sting/strut oraerodynamic flow unsteadiness which caused the model and sting/strut to vibrate,The model was not instrumented to determine the exact cause of the vibrations. Thesecond problem was temperature variations inside the model that were primarilycaused by the variation of tunnel stagnation temperature as the tunnel was broughtonline to the desired test conditions. Because no data were specifically obtained todetermine the experimental data uncertainty caused by model vibrations andtemperature variations, the pressure data uncertainty was estimated from dataobtained during routine checks of the pressure instrumentation to ensure datasystem integrity, The checks consisted of either applying a known pressure to themodules on all the pressure ports and comparing the module reading to a standardpressure gauge or calibrating the module on-line 24 and comparing data points takenbefore and after the calibration. Using the data from these checks, the base dragcoefficients are estimated to have an uncertainty of approximately ±5 percent of thecalculated values.

10

NSWCDD/TR-92/509

TABLE 1. CONFIGURATION INDEX

Configuration Fine 05 10 o.15 .5 1.0 1.6 2.0 2.5 0 s 10 15 20M.,,=2.0)(M..k2.5

1 sweep sweep

2 xX xX 0,5,10 0

3x x x 0.5,10 0

4 X X x 0,5,10 0

5 x X X 015,10 0

x X XX 0,5,10 0

7 X X 0,5,10 0

a X X X 0.6.10 0

9 X XX 0.5,10 0

10 X x x 0,5,10 0-I1I x x x 0.5,10 012 X X __ x 0,5,10 0

13 X X X 015,10 0

14 x X X 0,5110 c;

15 x X x 0,6,10 0

18 x 7xý -x 0,5,10 ndt

NSWCDD/TR.92/509

TABLE 2, BASE PRESSURE COEFFICIENT DATA

Configuration Moo _ _, CDB Configuration Me* a CDB

1 2.0 0.0 0.138 1 4.5 0.0 0.053

1 2,0 2.0 0,151 1 4.5 2.0 0.056

. 2.0 4.0 0.172 1 4.5 4,0 0,058

2 2,0 6,0 0,192 1 4,5 6,0 0.u61

. 2.0 8.0 0.207 1 4.5 8.0 0.060

1 2.0 10.0 0.218 1. 4.5 10.0 0,059

1 2,0 12.3 0,231 1 4.5 12.0 0.0591 4.5 14.0 0.059

1 2.5 0,0 0,106 1 4.5 15,0 0,058

1 2.5 2.0 0,11.9 1 4.5 16,0 0,057

1 2.5 4.0 0,1361 2.5 6.0 0,148 2 2,0 0,0 0,167

2 2.5 8,0 0,157 2 2,0 5.0 0,190

1 2,5 20.0 0,165 2 2,0 10.0 0,210

1 2,5 12.0 0.160 2 2.5 0.0 0,136

1 2,5 14,0 0,156 2 3,0 0.0 0,114

1 2,5 15.0 0.154 2 3,5 0,0 0.092

1 2.5 15.8 0,149 2 4.0 0.0 0,0732 4,5 0,0 0.058

1 3,0 0.0 0.0901 3.0 2,0 0.099 3 2.0 0,0 0.194

1 3,0 4.0 0,109 3 2,0 5.0 0,204

1 3,0 6,0 0,127 3 2,0 10,0 0,219

1 3,0 8,0 0.123 3 2,5 0,0 0.1501 3,0 10.0 0.129 3 3,0 0,0 0.1181 3.0 12.0 0.119 3 3.5 0,0 0.094

1 3,0 14.0 0,118 3 4,0 0,0 0,075

1 3,0 15.0 0.118 3 4,5 0,0 0,061

1 3.0 16.2 0,1214 2.0 0A0 0.224

2 3,5 0.0 0,080 4 2.0 5,0 0.223

1 3.5 2.0 0.086 4 2,0 20.0 0,227

1 3.5 4.0 0,091 4 2.5 0.0 0,161

1 3.5 6.0 0,096 4 3,0 0,0 0,122

1 3,5 8,0 0,099 4 3.5 0,0 0,095

1 3.5 10.0 0.096 4 4,0 0.0 0,075

1 3.5 12,0 0,094 4 4,5 0.0 0,061

1 3.5 14,0 0.0951 3,5 15.0 0,094 5 2.0 0,0 0,158

2 3.5 15.6 0,094 5 2,0 5,0 0,1845 2,0 1.00 0,208

1 4.0 0,0 0.065 5 2.5 0.0 0.12'/

2 4.0 2,0 0,068 5 3.0 0.0 0.208

1 4.0 4,0 0,073 5 3.5 0.0 0,089

1 4.0 6.,0 0,076 5 4.0 0,0 0,071

1 4.0 8,0 0,077 5 4.5 0,0 0.05B

1 4.0 10,0 0.074

1 4.o 12,0 0,074 6 2.0 0,0 0.180

I1 4,o 14.0 0,0114 6 2,0 5,0 0,197

2 4.u 15.0 0.074 6 2.0 10,0 0,213

2 4.0 16.1. 0.074 6 2.5 0.n 0.146

6 3,0 0.0 0,111'

6 3.5 Q o (. 0.0946 4.0 0,0 0,07/06 4,5 0.0 0,061.

12

NSWCDD/TR-92/509

TABLE 2. BASE PRESSURE COEFFICIENT DATA (CONTINUED)

Oonfiguratlon M.. a_, CDB Configuration Ma a CDB

7 .--10 0.0 0.21,9 13 2.0 0.0 0.1417 2.0 5.0 0,221 13 2.0 5.0 0.1607 2,0 10,0 0.226 13 2.0 10.0 0.1887 2.5 0,0 0.160 13 2.5 0.0 0.1217 3.0 0.0 0,121 13 3.0 0.0 0.1037 3.5 0.0 0.09S 13 3,5 0.0 0.0877 4.0 0,0 0,074 13 4.0 0.0 0.0687 4.5 0.0 0,059 13 4.5 0,0 0.055

8 2.0 0.0 0,148 14 210 0.0 0,1438 2,0 5.0 0.174 14 2,0 5,0 0,1728 2.0 10.0 0,204 14 2.0 10.0 0,2078 2.5 0,0 0,116 14 2,5 0,0 0,116a 3,0 0.0 0.100 14 3,0 0.0 0,100a 3.5 0,0 0.084 14 3.5 0,0 0.0848 4.0 0.0 0,067 14 4.0 0.0 0,068a 4.5 0,0 0.054 14 4,5 0,0 0,055

9 2.0 0,0 0,185 15 2,0 0,0 0,1419 2.0 5,0 0,193 15 2,0 5.0 0,1719 2.0 10.0 0,210 15 2.0 10.0 012089 2,5 0.0 0.141 15 2.5 0,0 0,1129 3.u 0.0 0.113 I5 3,0 0,0 0,0959 3.5 0.0 0.091 i1 3,5 0,0 0,0829 4.0 0.0 0,072 15 4,0 0,0 0.0669 4,5 0.0 0.058 15 4,5 0,0 0,054

10 2.0 0.0 0.216 16 2,0 0.0 0,13910 2.0 5,0 0.217 16 2.0 5.0 0,16810 2.0 .0,0 0.225 16 2.0 10.0 0,20710 2,5 0.0 0.15510 3,0 0,0 0.12010 3,5 0,0 0.09310 4,0 0,0 0.07310 4,5 0.0 0.057

11 2.0 0.0 0.13811 2,0 5,0 0.15b.1 2.0 10.0 0.192

11 2,5 0.0 0.10911 3,0 0.0 0.09011 3,5 0,0 0.07911 4.0 0.0 0.0o411 4,5 0.0 0o052

12 2.0 0,0 0,1.3912 2.0 5.0 0,15812 2.0 10.0 0,19012 2.5 0.0 0,11312 3.0 0.0 0.09612 3,5 0.0 0,08312 4,0 0.0 0.06712 4.5 0.0 0.054

13

NSWCDD/TR-92/509

3. EMPIRICAL MODEL FOR BASE DRAG PREDICTION

3.1 BODY-ALONE CONFIGURATION

Using the wind tunnel data of Tables 1 and 2, the percent change in the body-alone base pressure coefficient was calculated as a function of angle of attack, andthese results are given in Figure 5a for Mach numbers 2.0 < Mo : 4.5. Note that nodata are available above M.= 4.5, so a linear extrapolation indicates no change inbase pressure with angle of attack above Mo= 5,5. Also, no data could be taken forangles of attack greater than about 15' because the model support strut would havehit the tunnel ceiling, For higher angles of attack, the data for M, ; 2.5 show anangle of attack where the base pressure increase is a maximum and then a gradualdecline with further increases in a. This general trend was assumed for all results inboth Figures 5a and b until additional high angle-of-attack data are made available,The large NASA Tri Service Data Base 25 was investigated for inclusion of highangle-of-attack pressure effects, However, the emphasis in those tests was on liftingproperties, and the axial force was of secondary concern. Hence, while axial force andbase pressure information is available, the accuracy of the base pressure informationis not believed to be as good as desired for use here.

For Mach numbers below 2, the data of Reference 26 were used to obtain thechange in base pressure due to angle of attack, These results are given in Figure 5b,In contrast to Reference 25, this test did concentrate on axial force information, TheReynolds number of the transonic portion of the test was also high enough to ensure aturbulent boundary layer at tho base for Mach numbers less than 1,5, However, onlythree base pressure taps were mounted on the base of the model, and a sting was alsoin place. Hence, the data are probably not of the same quality as that of the morerecent data in this report where numerous pressure taps were available to get a moreaccurate average of base pressure,

It should be pointed out that both Figures 5a and 5b are given in percent changein the body-alone base pressure coefficient as a function of angle of attack, Thesecurves were obtained using data from Table 2 and Figure 1 for 2,0 5 M, ,.5 4,5 andReference 26 for 0,6 : Mw : 1,5. The quantity F1 was calculated by subtracting thebody-alone value of C 1) at a= 0 (from Table 2 or Reference 26) from the body-alonevalue of Cp, at some a (from Table 2 or Reference 26) and dividing this quantity bythe body-alone value of CpB1 at a=0' from Figure 1. This method ofnondimensionalizing the change in C R of the present experimental data with the Cpjat a=O0 from Figure 1 compensates for the slight difference between the body-alonevalue of CpLj at a=00 from Figure 1 and Table 2 of Reference 26, It should beemphasized that throughout this section describing the derivation of the empiricalbase drag prediction model, the body-alone value of C p, at a = 0° (ptj))rN'.o. ) used tonondlmensionalize the changes in the present experimental data was obtained fromFigure 1,

14

NSWCDD/TR.92/509

I Pi1/11tLni

'04

ICvIO4N(1)

doopI

- I- I

0 0I

~ - N: ~I

,~ 11Al

doI

/~I 6'

SAl8

m m

o ot -0 D0 i N ( ld ,) ) - S ' N S )

15

NSWCDD/TR-92/509

In viewing Figures 5a and b, it is evident that angle of attack has a strong effecton base pressure and hence base drag, It is also evident that additional wind tunneldata are needed for angles of attack greater than 150 at M. : 4.5.

The base pressure coefficient and drag of the body-alone configuration is thenestimated as

(CPI)NF, -(cpB)N, - i + 0,01 F1 (5)

and

CAB (P)d )3 (Sa)

where (CPB)NF ,.o comes from the LAP results of Figure I and F1 from Figures 5a andb. Note that the recent data of this report and the Reference 26 data allowed slightrevisions of the OAP results for (CP•HNF, u.- o as seen in Figure 1,

If the engine is in a power-on mode, the base pressure coefficient at a= 0 will bemodified according to References 16 and 17 as currently done in the OAP.

3.2 BODY-TAIL CONFIGURATION

There are three significant base pressure effects that need to be accounted for onmisciles having tail surfaces located nuar the base, These include fin deflection, finthickness, and fin location, Fin planform shape and aspect ratio also are designparameters of interest. However, they will not be modeled in the present empiricalmethodology. As seen in the Section 2 discussion on the wind tunnel test, a doublewedge airfoil section was used for all tests. The fin planforms had a constant aspectratio of 1,82 and the fin trailing edges were sharp. The planform shape chosen wasthus fairly typical of missile tail fin planforms both in aspect ratio and airfoil section,

The first effect to consider is control deflection, Initially, it was hoped that bodyangle of attack and fin control deflection could be separated and modeled separately.However, it became clear that this was not possible for two reasons: (1) more datawere needed than %ere acquired in the test and (2) based on the limited amount ofdata available, it appeared that angle of attack and control deflection were closelycoupled, As a result, when fins were present, the empirical model arrived at a curvethat gave the percent increase in base pressure coefficient as a function of theabsolute value of a+ 8 based on the limited amount of data available. To arrive atthis curve, it was first necessary to determine the increase in base pressure due to findeflection for zero thickness fins. This was done by taking the data for the threevalues of t/c available and extrapolating to t/c =0. An example of this is shown inFigure 6 for M =2 at x/c= 0. At this Mach number, both angle of attack and controldeflection data were available for each value of t/c from 0,05 to 0,15. For other Mach

16

- -•:-• , - . ... • -• .. . . . "u, --r- :-no:, • IU ll I ! 1 ! 1 •

NSWCDD/TR-92/509

numbers, only control deflection data were available at x/c = 0. As seen in Figure 6,the change in base pressure due to fin deflection or body angle of attack varies nearlylinearly with fin t/c ratio making it easy to pick off the value of ACp5 due to findeflectibn or body angle of attack at t/c = 0, Figure 7 presents the entire data set ofincrease in base pressure at tUc = 0 as a function of I a + 8 1. Here, the figure has beennondimensionalized by the value of the body-alone base pressure coefficient (obtainedfrdm Figure 1) and given as a percentage increase. A linear extrapolation of the dataabove M. = 4.5 indicates that there is no increase at M= 5.5. However, no accuratedata are known to be available for M, <2, so the curve for M. =2 is assumed to holdbelow Mw= 2. It should be pointed out that this is one reason that the empiricalmodel was derived in terms of percent increase in base pressure coefficient relative tothe body-alone base pressure coefficient at a= 0. This way, even though no data forcontrol deflection effects are available below Moo= 2, we still know (CPB)NF -Ofairlyaccurately for the body alone; hence, it is believed that the assumption ot using thecurve in Figure 7 to represent the percent increase in base pressure due to findeflection is better than trying to derive a model based on the value of ACpB due to findeflection The only assumption in Figure 7 is therefore the shape of the curve atM= 2 is assumed to apply below M= 2.

O Maiosolo.u0lO0."* euO0.hSnlO- ghsI0.SIn

", 10 4 eu+6|

- .04o-.02

-04

0 AD AD .ii ,10

t/€

FIGURE 6. EFFECTS OF ANGLE OF ATTACK AND CONTROLDEFLECTION ON BASE PRESSURE COEFFICIENT

(M. = 2, x/c= 0)

17

NSWCDD/TR-92/509

It is apparent in viewing Figure 7 that additional wind tunnel data are neededfor control deflection and body angle of att'.tck below Mo=2 as well as combinedvalues of I a+6 I at Mw>2 in order to have a more accurate estimate of percentincrease in base pressure coefficient due to control deflection. However, untiladditional data become available, Figure 7 will be the model used in the IAP.

S0 M 00=

I00

c o ---------...................

II ... . .. .....

01 0 I s 20 i s D o 3

I/ + 6I (dg)

FIGURE 7, PERCENT INCREASE IN BASE PRESSURE COEFFICIENTDUE TO COMBINED EFFECTS OF ANGLE OF ATTACK

AND CONTROL DEFLECTION (t/e -0)

The next parameter of interest is fin thickness effects on base pressure, Mostreferences (see for example 14 and 16), including the OAP model, estimate thechange in base pressure as a function of fin t/c ratio. However, in plotting data fromseveral sources, see Figure 8a, it appeared that t/c may not be the most appropriateparameter, Fin thickness-to-body diameter (t/d) was also investigated (see Figure 8b)and this appeared to be a much more appropriate way to approximate fin thicknesssince the data of Figure 8a was coellesed in a much smoother curve in Figure 8b. Asa result, the empirical model of fin thickness effects on base pressure will be derivedon the basis of t/d versus t/c.

NSWCDD/TR-92/509

- 0.8 - 0 WILCOX DATAEl SPAHR& DICKEY (REF 15)

C, HILL & ALPHER (REF 27)

II U [z -0.46

0

II~1It

-0,2- 00

0 0 0

0 1 2 3 4 5

FIGURE 8a. EFFECTS OF FIN tic RATIO ONBASE PRESSURE COEFFICIENT (x/c a 8= 0)

ol -0.6IIU

U-3

-0.4u•U -0,4

0

II -0., oH o

11IIU o

0 0

00m

1 2 Ma 3 4 5

FIGURE 8b, EFFECTS OF FIN t/d RATIO ONBASE PRESSURE COEFFICIENT (x/c a =8 0)

19

NSWCDD/TR-92/509

In analyzing the data of the present report, it also became clear that fin thick-ness was an important parameter at low angle of attack and control deflection butbecame less important at larger values of I a + 8 I. That is, given the increase of CpBdue to I a+8 I from Figure 7, the additional increase in CPB due to fin thicknessdecreased with increasing I a+ 8 I. These results are shown in Figure 9, which givesthe additional percent increase in base pressure due to fin t/d ratio as a function ofMach number and I a+ 8 I. Once again, additional data are needed, in particular forMach numbers less than 2. For I a+ 5 = 0, the data of Reference 27 supplements thepresent data down to Mo = 1. Until additional data are available, the trend of F 3below Mo = 1 is assumed to be similar to that of the base pressure coefficient curve ofFigure 1, Also, for values of I a+ 8 300, fin thickness effects on base pressure areassumed to be zero.

The total body base pressure coefficient for fins located flush with the base isthen

(CPB ) 8,a, 8, /C. fC0=1 + 0.01 F 2)(CPB )NP, u=0 + 0.01 F3(t/d) (6)

where (CPB) F, •.o, F2, and F3 come from the LAP curve of Figure 1 and Figures 7 and9, respectively.

The final parameter to model is fin location effects relative to the body base.Figure 10 shows the percent change in base pressure coefficient for various angles ofattack and t/d values as a function of x/c for M. = 2. This figure was based on the newwind tunnel data of Tables 1 and 2. Note that at a= 0, Figure 1Oa, (taken here tobe I a+ 81 ), &Cp, goes close to zero about a caliber or so ahead of the base. Also notethat the ACp, of Figure 10 is the change in base pressure at a given angle of attackdue to the presence of the fins.

On the other hand, examining Figures 1Ob and c, it is seen that as a or I a+6 Ibecomes appreciable, the fins need to be located about 2.5 calibers ahead of the basebefore the fin effects are minimal and the body angle-of-attack effect is the dominantfactor.

Also, it is noted that the percent change in base pressure coefficient in Figure 10for a=5 and 100 initially has a negative slope similar to the a=0 case but thenreverses and approaches no change at x/c = 2.5. As a result, a numerical interpolationis used to compute the percent change in 6CPB as a function of x/c, I a+ 8 I, and t/d,This same percent change is assumed to occur at all Mach numbers since no data areavailable other than at Mo-= 2.

20

NSWCDD/TR-92/509

DATA SOURCES

-60 0 SPAHR & DICKEY(REF 15)o HILL & ALPHER (REF 27)

(FREE FLIGHT)-*,A,00 WILCOX

S-SO

-20 0a 0 I I 'I ' "

02 3 4

me

FIGURE 9, PERCENT INCREASE IN BASE PRESSURE COEFFICIENTDUE TO FIN THICKNESS AT VARIOUS VALUES OF a + 81I

200-20 0-I.. .. . .

-..... 0Sritd -. 08 I

-10

.' I • -- .......

A -15-'

-20.0 0.2 0.4 0.6 0.8 1 t,2 1:,4 1.6 1,8 2

"5COEFFICIENT DUE TO FIN LOCATION ( -I a+ =0*, M. = 2,0)

21

NSWCDD/TR-92/509

20- - - - - - - - -

t/d-,04

d 10- t/d.-.----- -

U.

I,LA

'IQ e

-200 0.2 0,4 0.6 0.8 1 1.2 1.4 1:6 1.8 2

X/C

FIGURE 10b. PERCENT INCREASE IN BASE PRESSURECOEFFICIENT DUE TO FIN LOCATION (I a + I = 5.0, M. = 2.0)

20 -.... . .. ............

15s- --t/d-,04

.. tldm..O

t/d.,ll

U.o

aQ U

+

-20F -4-0 0.2 0.4 0.6 0.8 1 1.2 1.4 1,6 1.8 2

x/c

FIGURE 10c. PERCENT INCREASE IN BASE PRESSURECOEFFICIENT DUE TO FIN LOCATION (I a + 86 = 10,00, M, = 2.0)

22

NSWCDD/TR-92/509

Once the percent change in CPB has been determined from Figure 10, the totalCpB is then

(cP) ,, x - (Cp) + 0.01(ACPB)a,8,t/cX1c (7)

Here (CpB,) is the body-alone base pressure at a given angle of attack and &CpB is the"change due to the effect of fins from Figure 10. Note that (CPB)NFP ( is calculated byEquation (5). As a result, the effect due to fins and body angle of attack will changefrom that due to fins in presence of the body when the fins are flush with the base tothat of the body alone at angle of attack when the fins are far enough upstream.

Power-on and boattail effects will modify this base pressure coefficient the sameas previously discussed.

To summarize the fin location effects, if x/c is close to zero, Equation (6) is usedto compute the fin effect on base pressure, If x/c # 0, a numerical interpolation isused based on Figure 10 where the variables are x/c, t/d, and I .+8 1, The body-aloneangle of attack effect is computed by Equation (5). The fin effects on base pressurevary from the values of Equation (6) where x/c = 0 to those of the body-alone Equation(5) upstream of the base, The total power-off base pressure coefficient is then givenby Equation (7). The base pressure coefficient is modified for power-on effects ascurrently done in the OAP, The base drag including boattail effects is then

C A B ) a ,V ,x c ( d r (8 )

4. COMPARISON OF BASE DRAG EMPIRICAL MODELSTO WIND TUNNEL DATA

This section compares the improved empirical base drag prediction model (TAP)with the older version currently in use in the 1981 version of the aeroprediction code(OAP) to wind tunnel data. The data used will be that of the present tests plus thoseof Reference 26 for low Mach number body-alone angle-of-attack effects,

4.1 BODY-ALONE ANGLE-OF-ATTACK EFFECTS

Figures 11a, b, and c show the results of the IAP and OAP prediction results forbody-alone angle-of-attack base pressure for several Mach numbers. The IAP resultsshow improvement over the OAP prediction at all Mach numbers. However, the OAPmodel, even though it was based on a very sparse amount of data, exhibits the correcttrends and is reasonably accurate, The maximum error on Cp,, compared to the data

23

NSWCDD/TR-92/509

for the OAP was about 20 percerft, The IAP model of course duplicates the windtunnel results just as it was designed to do.

Figures lla, b, and c further illustrate the fact that the empirical models of theOAP and IAP basically guess as to the behavior of base pressure above a= 15' due tolack of a reliable database, This guess is believed good at Mw ;? 3.5 but questionablefor lower Mach numbers. On the other hand, it is certainly better than assuming nochange in base pressure with angle of attack, which is what many engineering codesassume.

4,2 BODY-TAIL CONFIGURATIONS

As already discussed, when there is a tail located in the vicinity of the base, thebase pressure is affected due to several parameters. Figure 12 shows the IAP resultsfor Cp5 as a function of 8 compared to the results of the present test data of Wilcox.Also shown are the OAP results, which are straight lines because the OAP empiricalmodel does not include 8 as one of its parameters, Figures 12a and b are for t/c=0.05,Figures 12c and d are for t/c-=0.10, and Figures 12e and fare for t/c=0,15. All figuresare for x/ca=0 and w given for several Mach numbers, For Mach numbers of 2and greater, the present data are used to compare the OAP and IAP models to. ForMw0 < 2, no known good quality data are available so only models are shown, Notethat at all Mach numbers (other than M® = 2), the IAP represents the available datareasonably well, At Mo '= 2, the empirical model intentionally is slightly higher thanthe current experimental data for two reasons, First, to use the data of the currenttests would cause the IAP curve of Figure 1 to be unsmooth. Second, it is suspectedthat the values of the present test may be slightly on the low side compared to theOAP curve of Figure 1, which represents a compilation of experimental data fromother sources.

Figure 13 compares the base pressure coefficient of the OAP and IAP as a func-tion oft/c for x/c-=0, 1.0, and 2.0 and at several Mach numbers, Data of Tables I and2 are shown where available, In examining Figure 13, it is clear that the IAP issuperior to the OAP when compared to the Table 1 and 2 data for values of the vari-ous parameters that are available. For Mach numbers where data are lacking, it issuspected that the present model is also superior, However additional data arerequired to substantiate this.

The final case considered is one in which several v&'riables are considered simul-taneously. This is generally the situation in actual flight environments, The caseconsidered is for t/c =0.15, x/c= 1, and Mach number 2. Base pressure coefficient ver.,sus control deflection is given in Figure 14 for the OAP, IAP, and the data of Tables 1and 2 at 8=0. Note that tho OAP gives only a constant value for Cp,, independent of aand 8 when fins are present whereas the IAP shows a variation according to the newempirical model for a=0 and 5°. However, for a= 100, no variation is shown becauseno data are available for x/c>0 where a and 8 are both increased, Hence, the

24

NSWCDD/TR-92/509

empirical model changes only up to jct+ 81 -=100 when x/c .> 0. 1. Above Jac4-81 = 10',no additional change is assumed to oceur, Also, note that the main differencebetween the wind tunnel data and the TAP results is the slight difference in the(CPB)NF, .0 body-alnne values. The empirical model appears to represent the changein CpB with combined angle-of-attack and x/c values reasonably well.

-0.35

0.

0 5 10 15 20 25 soAngle of Attack (dog)

FIGURE Ila. COMPARISON OF BODY-ALONE BASE PRESSURE PREDICTEDBY THE OAP AND 1AP AS A FUNCTION OF ANGLE OF ATTACK

(MOD=0. 6, 1.0)

25

NSWCDD/TR-92/509

-0.35-

-0.3. -0 . ....... ...... . . . .. .. . .. . .. . .... ...... . .'.• -.-.. .........: ':. .-. -... .. ..-.. . - -..-.. ... ...-.. .... ...

.. .. • --.. .. ....

• .... WILCOX)-O ,O S ........................... ....... ...... ...... . ... .........

-0.1 -OA-

BUTLER

0.0 5 10 15 20 25 00

Angle of Attack (dog)

FIGURE 111, COMPARISON OF BODY.ALONE BASE PRESSURE PREDICTEDBY THE OAP AND 1AP AS A FUNCTION OF ANGLE OF ATTACK

(M,= 1,5, 2, 5)

....-- ....

.0.25 OAP ............ "-

- O , 3 .. ... . . ... .... .. . ......... . ... .. . ..

o.. .~ ~ ~ .... ......... ... ... .................. 1................... .........1 .... ..............

-0.1 .....

.0 .0 5 ........... ........ U

04--4-- - ---- --0 5 10 15 20 25 80

Angle of Attack (dog)

FIGURE Ile, COMPARISON OF BODY-ALONE BASE P11ESSURE PREDICTEDBY THE OAP AND IAP AS A FUNCTION OF ANGLE OF ATTACK

(M.=3,5, 4,5)

26

NSWCDD/TR-92/509

-0.32 - -- ____________

-0.28- IWN.JIDA M,: r2.0

-0.24. [--0.2 -........... .......... ..... ..... .......... .....' ......... ..................... ................

i -0.16

.. . . ............ ................................ ....... ..............

-0.04 S.... M~=4.5

0 -- --_________________________"___'"'""__0 0 4 2 8 10 12 14 l6 18 208(deg)

FIGURE 12a, COMPARISON 0F BODY-TAIL BASE PRESSURE PREDICTEDBY THE OAP AND IAP AS A FUNCTION OF CONTROL DEFLECTION

(t/u- =O0.05; Mw = 2,0, 2,5, 4,5•; x/u = 0)

-0.32 M = 1.0 - .- -

-0.28

� . ... . ... ... ..........................................

-0.12"

-0.08- MP=I.6

-0.04- h-

0 2 4 a 8 10 12 14 16 18 208 (dog)

FIGURE 12h, COMPARISON OF BODY-TAIL BASE PRESSURE PREDICTEDBY THE OAP AND IAP AS A FUNCTION OF CONTROL DEFLECTION

(t/ = 0,05; M =_- 0,0, 1.0, 1,5; x/ = O)

27

NSWCDDTR-92/509

-0.28.

-0.2.-M=.0 2 ,.............o ..................................... ..........

.0.16m-0-12 1 ........... .... ........... ..................... 4............... ........................ . ......... ................. ....;• •

.0.08M

• 0.04 .

00 2 4 a 1 '0 12 '4 t6 1' 206 (dog)

FIGURE l2c, COMPARISON OF BODY.TAIL BASE PRESSURE PREDICTEDBY THE OAP AND IAP AS A FUNCTION OF CONTROL DEFLECTION(Wo = 0.10 ; Mo = 2,0, 2,6, 4,5; xtc - 0)

"- 0 .3 2 t e m o o -1 0

-0 .2 8 ....... ........ ::: ......... ....................... .. ...... ._. • ..................... ... .. .-... ....,.... &..........................-0.24 - .... - - - • - " M oo = 1.5

-0.2....... ....... ... .. ........ ..... ..-.........5-0.16- .. . ...... M . 6 . ý ...

.0.12

-0.08-

0,041

0 2 4 0 a 10 12 14 is 18 206 (dog)

FIGURE 12d, COMPARISON OF BODY-TAIL BASE PRESSURE PREI)ICTEDBY THE OAP AND IAP AS A FUNCTION OF CONTROL DEFLECTION

(t/c=0.10; M,- 0,6, 1.0, 1,5; x/(!= 0)

28

NSWCDD/TR-92/509

-0.32

0.24 M®= 2.0•

(d042

•-0,16 • -- I---- .....

"0.12 M®=2.5"•''•

o.lu.lealomQel•i.hwweQeouDb6emt| quo0e•vevoeee.4bmI.eeeQQ•ebel•elmamom.m•.lmmP mev.ml|HlleQ.e ImoQ•me.I iioeooelO.veBml

-0.08'S.... " -°w

"0.04 '• M® = 4.5

O0 4 0 6 1'0 1'2 1'4 1• '(• le 20

8(dog)

FIGURE 12., COMPARISON OF BODY-TAIL BASE PRESSURE PREDICTEDBY THE GAP AND lAP AS A FUNCTION OF CONTROL DEFLECTION

(t/c= 0,15; M= = 2,0, 2,5, 4,5; x/c= O)

10.32 ::::::::•••

"0.2 ", ...... . ........ , ........ ......... • o• -•, ,m•...'.;• i, ,.,,,, ............................

$ -0.16. M= .6'•

-0.12' •

-0.08

-0.04

0 4 O 6 10 12 14 16 18 205 (deg)

FIGURE 12t', COMPARISON OF BODY.TAIL BASE PRESSURE PREDICTEDBY THE OAP AND IAP AS A FUNCTION OF CONTROL DEFLECTION

(t/c=0,15; M•=0,6) 1,0, 1.5; x/c=0)

29

NSWCDD/TR-92/509

0.32-

0.285 Yw

0.24--- *0*-A-

0.-" .-

o ~ o ............... ..... ...........0 ,...............1..-...................8... .... ... ............

00,

0 0.04 0.08 0.12 0.10 0,2t/c

FIGURE 13a. COMPARISON OF BODY-TAIL BASE PRESSURE PREDICTEDBY THE OAP AND IAP AS A FUNCTION OF FIN THICKNESS (a = 8 =0;

,c/C 0; M. =3,O, 4, 5)

0.32-

0.2 85 ..... . -wim . ..... ..... a '

... ......... ........

L..............

00 0,04 0.08 0.12 0.18 0.2t/c

FIGURE 13b, COMPARISON OF BODY-TAIL BASE PRESSURE PREDICTEDBY THE OAP AND IAP AS A FUNCTION OF FIN THICKNESS (a = 8 =0;

xlc=0; M.= 1.5,2.0)

30

NSWC DD/TR-92/509

-0.32-

-0.24 ..... ... .....

-0.2........

NM-=.6___

-00

0 0.04 0108 0.12 0.16 0.2tic

FIGURE 13c, COMPARISON OF BODY-TAIL BASE PRESSURE PREDICTEDBY THE OAP AND IAP AS A FUNCTION OF FIN THICKNESS (a 6 0;

X/o=0; M. =0.6, 1.0)

-0.32-

~-0-16-M. 3 0 ....

-0.12 -

-0.084

0 0.04 0.08 0.12 0.18 0.2t/c

FIGURE 13d, COMPARISON OF BODY-TAIL, BASE PRESSURE PREDICTEDBY THE OAP AND IAP AS A FUNCTION OF FIN THICKNESS (a = 8 = 0;

x/c m 1. 0; M. . 3.0,4.5)

NSWCDD/TR-92/509

-0.32.

ICAPI.o.=4~ ~ ~ ~ ~~~1 ..... • ........................................ ....................0. 6 -.. . ............ .....

-0.16 ....................... ... " -' ." _ ..

"-0.12 04U

00 0.04 0.05 0.12 0.16 0.2

t/c

FIGURE 13e. COMPARISON OF BODY-TAIL BASE PRESSURE PREDICTEDBY THE OAP AND IAP AS A FUNCTION OF FIN THICKNESS (a = 6 0;

x/c= 1,0; M.= 1,5, 2,0)

"-0.32-

"O . 2 4M 4 = 1 .............................. .. .:. • ' • ........ .........I............ . ... ....... ..........

-0AP ..... 24 .. .. ~. 0 ........-0 . 4 O , ........ ::,:: . .................,.., ... .... .... .......... ....... ............ ..... ......... ....................

;;- .. . . .. ....... ;. .

-0.2 --- .... 2. - -" .......

S- . 6 . .... ... ........ ..... ... ... .. ... ...................... .......... .............. ...... ..... ....... .. .. .................. I ......... .... ... .... ..... .... ....... ......... ...... ......... . ........ ......

"Om 2 .......................... Ii :::I•?•I:,I II::,D• ,•..................

M.=. 6/"- 0 ,0 8 - .......... ....... .... ................. ......... ..... .. ... ....... ... . ..................... .................... ........ ..... .............. ........... ............ ................. ..................... ...... .

"-0.04 16...........................

0 0.04 0.08 0,12 0,116 0.2t/c

FIGURE 13f, COMPARISON OF BODY-TAIL BASE PRESSURE PREDICTEDBY THE OAP AND IAP AS A FUNCTION OF FIN THICKNESS (a = 8 = 0;

x/c= 1.0; M. 0=.6, 1.0)

32

NSWCDD/TR-92/509

-0.328-

-0 .2 4 -.. ...... .... . . .. ...... ................

-0. 12 - -...

-0 .0 8 . ... ... ............ . . . . . . . ...... . . . .-0 .8 .................................................... .......... ......... ... .....................

o 4--_0 0.04 0.08 0.12 0.18 0,2

t/c

FIGURE 13g. COMPARISON OF BODY-TAIL BASE PRESSURE PREDICTEDBY THE OAP AND lAP AS A FUNCTION OF FIN THICKNESS (Q = 6 0;

x/c= 2.0; M.=3,0, 4,5)

-0.32 _ __

-0.28-

IA M.=1.5".

-0 2 .... ... ... ,-:............. -............ - .- ........ ..... ... ........ ....

* -0.12. -- - .* - .... - * --.

Mw=2.0/-0 .0 8 ........................ ...... .... ..... .. ...

-0 .0 4 . . ..- . . . .. . .... ......-. -.. ... .

00 0,04 0,08 0.12 0.16 0.2

t/c

FIGURE 13h. COMPARISON OF BODY-TAIL BASE PRESSURE PREDICTEDBY THE CAP AND IAP AS A FUNCTION OF FIN THICKNESS (a'= 8 = 0;

x/c = 2,0; M.:-- 1,5, 2.0)

33

NSWCDD/TR-92/509

-0.324

-0.28 ..........~~ ~~..... O .. .... . . ... . . ........................... ................ ....

.0.2

u~-0.16

.0.12 ~----- - - ' _ _ _

S-0 .0 8 .1....-...... ........... .. .

-0.04

0 0.04 0.08 0.12 0.16 0.2t/c

FIGURE 13i. COMPARISON OF BODY-TAIL BASE PRESSURE PREDICTEDBY THE OAP AND IAP AS A FUNCTION OF FIN THICKNESS,(o = 8 = 0;

x/c= 2.0; M®.=0,6, 1.0)

-0.32,

-0.28ALPHA = 10.0

-0.24.

402,.............. . ..... ........ ........1111IJ•

-0.16

-0.12 = -

OALP A0. ALPHA 5.-0.04 LLtJ

0 2 4 6 8 W0 12 14 10 18 20Delia (dog)

FIGURE 14. COMPARISON OF BODY-TAIL BASE PRESSURE PREDICTEDBY THE OAP AND IAP AS A FUNCTION OF CONTROL DEFLECTION

AND ANGLE OF ATTACK (tic =0.15, x/c= 1.0, M® =2.0)

34

NSWCDD/TR-92/509

5. SUMMARY AND RECOMMENDATIONS

To summarize, new wind tunnel data have been generated to aid in basepressure prediction as a function of body angle of attack, Mach number, fin controldeflection, fin thickness, and fin location. Data were taken over a Mach numberrange of 2 to 4.5, angle of attack of 00 to 160, fin t/c ratio of 0,05 to 0,15, fin location offlush with the base to two chord-lengths ahead of the base, and control deflection of 00to 200, At Mach 2, some data were taken with a combination of several of the abovevariables present whereas at other Mach numbers, only one parameter was changedfor a given tunnel condition,

Based on these new data, more recent data from other wind tunnel tests con-ducted since the empirical base drag model for the OAP was developed in the mid-1970's, and the data from which the empirical model was originally developed, a newand improved empirical base drag prediction model has been developed. This newmodel is a function of Mach number, angle of attack, fin control deflection, fin thick-ness, and fin location, In comparison with thc OAP and the new wind tunnel data set,it is seen that the IAP reduces the errors of the OAP substantially. Furthermore, theOAP did not account for fin deflection or even angleu. ...' -'I effects if tail fins werepresent,

While the new model estimates angle-of-attack effects to 30', control deflectionup to 300, and fin thickness effects for all Mach numbers, in many cases these esti-mates are based on extrapolations and engineering judgment, As a result, additionalwind tunnel data are needed to validate or modify the current model as appropriate.In particular, it is recommended that data be taken for base pressure for the followingconditions:

1. body alone: 15 : a !5 300; 0 S Mw s 4,5

2. body tail: fins flush with base; 150 a :!' 300; Mw -5 4.5

3, body tail: fins flush with base; a=0; 0.05 : t/c 5 0,15, 0 S Mo < 2.0

4. body tail: fins upstream of base; several values of a and 8; one value oft/c; three Mach numbers

5. body tail: more cases where combinations of several parameters aretested simultaneously for use in an empirical model validation

All data taken in future tests should be taken witn the same rigor as with the presenttests where enough pressure taps are used to get a good average of base pressure foruse in base drag computations,

35

NSWCDD/TR.92/509

8. REFERENCES

1. Moore, F. G., Computational Aerodynamics at NA VSWC: Past, Present, andFuture, NAVSWC TR 90-569, October 1990.

2, Devan, L., Aerodynamics of Tactical Weapons to Mach Number 8 and Angle ofAttack 1800. Part I, Theory and Application, NSWC TR 80-346, October 1980,

3. Devan, L,; and Mason, L., Aerodynamics of Tactical Weapons to Mach Number 8and Angle of Attack 180°' Part II, Computer Program and Users Guide, NSWCTR 81-358, September 1981.

4. Devan, L.; Mason, L,; and Moore, F. G.' "Aerodynamics of Tactical Weapons toMach Number 8 and Angle of Attack 180°,'P AIAA Paper No. 82-0250, 20thAerospace Sciences Meeting, Orlando, FL.

5. Love, E. S., Base Pressure at Supersonic Speeds on Two-Dimensional Airfoils andon Bodies of Revolution with and without Turbulent Boundary Layers, NACA TN3819, 1957,

6. Chapman, D. R., An Analysis of Base Pressure at Supersonic Velocities and Com-parison with Experiment, NACA TR 1051, 1951.

7. Bureau of Naval Weapons, Handbook of Supersonic Aerodynamics, NAVWEPSReport 1488, Vol. 3,1961.

8. Reller, J. 0., Jr,; and Hamaker, F. M., An Experimental Investigation of the BasePressure Characteristics of Nonlifting Bodies of Revolution at Mach Numbersfrom 2.73 to 4.98, NACA TN 3393, 1955.

9. Peck, R. F., Flight Measurements of Base Pressure on Bodies of Revolution withand without Simulated Rocket Chambers, NACA TN 3372, 1955.

10. Fraenkel, L. E., A Note on the Estimation of the Base Pressure on Bodies of Rev-olution at Supersonic Speeds, Royal Aircraft Establishment TN No. AERO 2203,1952.

11. U. S. Army Missile Command, Engineering Design Handbook: Design of Aero.dynamically Stabilized Free Rockets, AMCP 706-280, 1968.

12. Stoney, W. E., Jr., Collection of Zero-Lift Data on Bodies of Revolution from Free-Flight Investigations, NASA TR R-100, 1961.

36

NSWCDD/TR-92/509

13. Kurzweg, H. H,, "New Experimental Investigations on Base Pressure in theNOL Supersonic Wind Tunnels at Mach Numbers 1.2 to 4.24," NOL Memo10113,1950.

14. Heyser, A.; Maurer, F.; and Oberdorffer, E., "Experimental Investigation oil theEffect of Tail Surfaces and Angle-of-Attack on Base Pressure in SupersonicFlow," Conference Proceedings: The Fluid Dynamic Aspects of Ballistics,AGARD-CP-10, pp, 263-290, 1966,

15. Spahr, J. R.; and Dickey, R, R., Effect of Tail Surfaces on the Base Drag of a Bodyof Revolution at Mach Numbers of 1.5 and 2.0, NACA TN-2360, 1951.

16. Hill, Freeman K.; and Alpher, Ralph A,, "Base Pressures at Supersonic Veloci-ties," Journal of Aeronautical Sciences, Vol. 16, No , pp. 153-160, March 1949.

17. Brazzel, Charles E.; and Henderson, James H., "An Empirical Technique forEstimating Power-On Base Drag of Bodies-of-Revolution with a Singe JetExhaust," Proceedings, Specialists Meeting Sponsored by the AGARD FluidDyuamics Panel, held in Mulhouse, France, 5-8 September 1966.

18. Johnson, L. H,, "Approximate Engine-On Base Pressure Computations forAerodynamic Computer Codes," NSWC K21 Tech. Memo 82-11, March 1982.

19. Moore, F. G., Body Alone Aerodynamics of Guided and Unguided Projectiles atSubsonic, Transonic, and Supersonic Mach Numbers, NWL TR-2796, November1972.

20, Moore, F. G., Aerodynamics of Guided and Unguided Weapons: Part I-Theoryand Application, NWL TR-3018, December 1973.

21. Jakckson, Charlie M,, Jr.; Corlett, William A.; and Monta, William J., Descriptionand Calibration of the Langley Unitary Plan Wind Tunnel, NASA TP 1905, 1981.

22. Braslow, Albert L,; and Knox, Eugene C., Simplified Method /br Determination ofCritical Height of Distributed Roughness Particles for Boundary-LayerTransition at Mach Numbers from 0 to 5, NACA TN 4363,1958.

23. Braslow, Albert L,; Hicks, Raymond M,; and Harris, Roy V., Jr., Use of Grit-TypeBoundary-Layer-Transition Strips on Wind-Tunnel Models, NASA TN D-3579,1966.

24. Juanarena, Douglas B., "A Multiport Sensor and Measurement System forAerospace Pressure Measurements," Proceedings of the 25th InternationalInstrumentation Symposium, 1979.

37

NSWCDD/TR-92/509

25. NASA Langley Research Center Tri-Service Missile Database, Transmitted fromNASA/LaRC Jerry M. Allen to NAVSWC on 5 November 1991 (formal NASAdocumentation in process).

26. Butler, C; Sears, E.; and Pellas, S., Aerodynamic Characteristics of 2-, 3-, and 4-caliber Tangent-Ogive Cylinders with Nose Bluffness Ratios of 0.00, 0.25, 0.50,and 0.75 at Mach Numbers from 0.6 to 4.0., AFATL-TR-77-8, January 1977,

27, Hill, Freeman K.; and Alpher, Ralph A., Base Pressure at Supersonic Velocities,Johns Hopkins University, Bumblebee Report 106, November 1949.

7. SYMBOLS AND DEFINITIONS

A base area, in.2

A1, A2, A3,...A 8 area sections used for weighted base drag coefficientcalculations in.2 (see Equation 4)

c fin root chord, in.

CAB axial force coefficient due to base pressure

CDB base drag coefficient = (CAU),ýo

CPB base pressure coefficient

CpI pressure coefficient, (pi - p) / q

d body diameter at the body base

drer reference diameter

Fi, F2, F3 symbols defining parameters used in semiempirical model

MW. freestream Mach number

p freestream static pressure, lb/ft2

Pi measured static pressure, lb/ft2

P0 stagnation pressure, lb/ft2

38

NSWCDD/TR-92/509

freestream dynamic pressure, lb/ft2

radius, in,

't radius of base, 2.5 in,

SRn freestream unit Reynolds number per foot

t fin thickness at root chord, in,

trip fin thickness at tip, in.

t/C fin thickness.to.chord ratio

t/d fin thickness-to-body reference diameter ratio

To stagnation temperature, 'F

x distance frdm body base to fin trailing edge (for 6 = 00)

X/c distance from body base to fin trailing edge (for 6=0*) in tailroot chord lengths

a body angle of attack (dog) (positive nose up)

8 fin control deflection (positive leading edge up)

Subscripts on Cp B

NF CPH of body alone with no fins

t/c CM of body with fins of a given thickness-to-chord ratio

X/c Cp, of body with fins located a given distance from the bodybase in fin root chord lengths

a Cps of body at a given angle of attack

S8 Cp of body with fins at a given deflection angle

39

NSWCDD/TR-92/509

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REPOT DOUMETATIN PAE I Form ApprovedREPO T D CUMETATON P GEQMS No. 0704-0188

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1. AGENCY USE ONLY (Leave blank 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED

October 1992 Final4, TITLE AND SUBTITLE S. FUNDING NUMBERS

Improved Empirical Model for Base Drag Prediction onMissile Configurations Based on Now Wind Tunnel Data

6. AUTHOR(S)Frank G, Moore Floyd Wilcox (NASA/LaRO) Tom Hymer

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATIONREPORT NUMBER

Naval Surface Warfare Center NSWCDD/,TR-02/509Dahigren DivisionDahigren, VA 22448-50000. SPONSORINGIMONITU.RING AGENCY NAME(S) AND 10. SPONS RIV G.MONITORING

AGENCY. REPORT NUMB ER

Surface-lauriched Weapons Technology Block ProgramOffilce of Naval Research

11. SUPPLEMENTARY NOTES

12a. DISTRIBUTION1AVAILABILITY 12b. DISTRIBUTION CODE

Approved for public release; distribution is unlimited.

13. AISTRACT (Maximum 400 words)

New wind tunnel data have been taken, and a new empirical model has been developed foi pred icti ng basedrag on missile configurations. The new wind tunnel data were taken at NASA[LaltC in the Unitary PlanWind Tunnel at Mach numbers from 2.0 to 4.5, angles of attack to 180, fin control deflections up to 20', finthickness-to- chord (t/c) ratio of 0.05 to 0.15, and fin locations flush with the base to two chord lengthsupstream of the base.

The newly developed empirical. model uses these data along with previous wind tunnel data, It estimatesbase drag as a function of all the above variables along with boattail and power-on or power-otf effects, Incomparing the new empirical model to that used in the former aeroprodiction code, the now model gives im-proved accuracy over wind tunnel data, The now model also is more robust due to inclusion of additionalvariables. On the other hand, additional wind tunnel data are needed to validate or modify the currentempirical model in areas where data are not available.

14. SUBJECT TERMS 15. NUMBER OF PAGES

empirical model missile configuration wind tunnel - RCECD

base drag prediction 16. RCECD

17. SECURITYCAIFAIO 16. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION 20. LIMITATION OF AI35TRACTOFREPOI4T OF THIS PAGE OF ABSTRACT

UNCLASSIPIED UNCLASSIFIED UNCLASSIFIED UL

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