[American Institute of Aeronautics and Astronautics 18th Applied Aerodynamics Conference -...

(c)2000 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization.

AOO-39920AIAA-2000-4524

The Interactions Between a Canard and Thick BodiesPart III: Applications

Asher Sigal*

Department of Aerospace EngineeringSan Diego State UniversitySan Diego, CA 92182-1308

The longitudinal and control characteristics of four configurations that featurecanards and bodies having variable diameter were analyzed, and the results comparedwith experimental data. The basic analysis tool was the Missile Datcom code, which usescomponent buildup methodology. The interactions between the canard trailing vorticesand thickenings of the bodies and boattails were estimated using an approximate vortextracker and the Pitts, Nielsen and kaattary methodology. It was found that including thecontributions of the interactions in the analysis greatly improve the agreement betweencalculated results and test data.

Nomenclature Greek

cQ,CLotCmCmaCN

DeEfghh|nrRsS

side of square baselift coefficientLift curve slopepitching-moment coefficientpitching-moment curve slopenormal-force coefficientnormal-force curve slopeequivalent base diameterreference length, diameter of main bodyrelative error (Eqn. 10)root mean square error (Eqn. 1 1)lateral position of a trailing vortexlateral position of an image vortexvertical position of a trailing vortexvertical position of an image vortexnumber of testsbody radiusradial location of a trailing vortexsemispanreference area, (7t/4)D2

center of pressure location

* Visiting Professor; Associate Fellow, AIAA.E-mail: [email protected].

Copyright © 2000 by the American Institute of Aeronauticsand Astronautics, Inc. All rights reserved.

a angle of attack8 canard deflection

Subscript

1 thickening of main bodyc canardbt boattail

Designation of components and configurations

BCCUTTU

main bodycanardscanard unittailtail unit

Superscripts

ATD

analysistest data

Introduction

Part I of this work, Ref. 1, describes wind tunneltests of a modular model consisting of a canardunit, which is mounted on a thin forebody, and fiveinterchangeable main thick bodies. Part II, Ref. 2,identifies and analyses the interactions between thecanard vortex wake and the thickenings and the

894

(c)2000 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)1 Sponsoring Organization.

boattails of the main bodies. The analysis usesslender body theory to estimate the radialdisplacement of the free vortices, as they trail alongthe body. Then, the classic Pitts, Nielsen andKaattari3 (P-N-K) methodology is used to evaluatethe normal-force distribution, caused by the canardvortices. The analysis was verified by comparingcalculations of these interactions with the test dataofRef. 1.

The objectives of the present part of the work are:

1. Analyze configurations that feature canardswhich are mounted upstream of body sectionswith variable diameter, using a componentbuildup code (CBU). (Most or all CBU codesdo not consider the effects of trailing vorticeson bodies.)

2. Apply the present analysis of the effect ofvortex wake on bodies to these configurations,and add this effect as a correction to the resultsof the CBU code.

3. Compare the results, both plain and corrected,with available test data.

4. Evaluate the capability of the presentmethodology to improve the results of theCBU code in cases where the configurationsfeature a body with considerable diameterchanges downstream of the most forwardlifting surface.

Analysis

An approximate expression for the radial locationof the trailing vortices, at zero angle of attack, wasgiven in Ref. 2 as

R2-!-2 = Rc2-rc2 (a constant) (1)

where R,. is related to the exposed semi span of thecanard by

= rc+(7c/4)(s-r)c (2)

The horizontal positions of the trailing vortices, forcanards in the + and x orientations, are fc=R,; and£=(^2/2)^, respectively. The positions of theimage vortices are

The lift coefficient due to change hi the horizontaldistance between a free vortex and its image,following P-N-K3, is

= CLCA(f-g)/(f-g)c (4.a)a = CLaCA(f-g)/(f-g)c (4.b)

= CL5CA(f-g)/(f-g)c (4.c)

Eqns. (4) should be applied to all body segmentsthat feature a change of diameter.

The 1997 version of the Missile Datcom code (M-Datcom), Ref. 4, was used to obtain thelongitudinal characteristics of the selectedconfigurations and of their components. Then, thepertinent parts of Eqns. (4) were used to accountfor the direct interactions, which are not consideredby the code. The small differences between C^ andC^ were ignored. The M-Datcom code assumes,after Ref. 3, that the free vortices trail in thedirection of the free stream. The present analysisconsiders the lateral displacement of these vorticesas they trail along the body. A change in the lateralposition of the vortices affects the tail interferencefactor, which determines the contribution of the taildue to canard vortices. This creates an additional,indirect interaction, which was also taken intoaccount in the analysis. The modified results of theM-Datcom are entitled corrected.

The centers of pressure, at angle of attack and dueto canard deflection, were calculated using

= -Cma/CNo (5.a)(5.b)

Applications

g = (3.a)(3-b)

Canard-Body-Flare MissileSpearman and Robinson5 tested a canard-body-flaremissile model at Mach numbers of 2.01, 4.65 and6.8. A schematic of their research configuration isdepicted in Fig. 1. Test data covers angles of attackup to 20 deg., and canard deflections of up to 20deg. The M-Datcom computational model isslightly different from the actual geometry: Thenose of the computational model is a slightlyblunted tangent ogive. It maintains the bluntnessradius and the radius at mid root chord station ofthe actual model. The computational canard model

895


is trapezoidal, maintaining the same inclusive spanand exposed area as the actual planform. Theanalysis and the comparisons were done for Machnumbers up to 5.0, because part of the presentcorrection is based on incompressible slender bodytheory.

The lateral positions of the canard trailing andimage vortices, in body diameters, are given inTable 1. Note that the trailing edge of the canard islocated over the centerbody; thus it is expected thatthe canard vortices will affect mainly the flare.

The inclusive spans of both canard sets are smallerthan the diameter of the afterbody (subcaliber); thusit is expected that the effects of their vortex wakeon the thickening of the main body would benoticeable.

M-Datcom analysis of the body alone has twobranches. For M<1.2 the code uses slender bodytheory; while for M>1.2 it uses second order shockexpansion theory. A comparison betweencalculated and experimentally obtained stabilityderivatives of the body alone is shown in the two

Table 1 Lateral positions of the canard vorticesNASATMX-46

StationT.E. of canardBase of flare

f1.081.28

g0.230.57

(f-g)0.850.71

A(f-g)—

-0.14

A(f-g)/(f-g)c-

-0.165

Comparisons between M-Datcom analysis,corrected analysis and test data are presented inFigs. 2 and 3. The test data were obtained from Fig.7 of Ref. 5. The "saddle" in the calculated curves isattributed to the contribution of the canards, whichis obtained from a database. The correction, whichaccounts for the down load acting on the flare dueto canard vortices, decreases the normal-forcecurve slope by about 11% at M=2.0 to 7.4% atM=5.0. The reduction of the normal-force due tocanard deflection stability derivative is 16.5%, andis independent of Mach number. The correctedcomputational values are in better agreement withthe test data, except for the normal-force curveslope at M=4.65. The correction shifts the center ofpressures forward about 0.36D at M=2 to 0.18D atM=5. The corrected values are in very goodagreement with the data. The center of pressure dueto canard deflection, as calculated by the M-Datcom, is very close to that of the isolatedcanards. The correction shifts this center ofpressure forward between 0.5D at M=2.0 and 0.8Dat M=5.0, and improves the agreement with theexperimentally obtained data.

IMI Research ProjectilesThe body of these configurations, Ref. 6, consistsof a thin blunted forebody, an inflected thickening,and a cylindrical thick afterbody. The forebody isequipped with small canards as depicted in Fig. 4.

parts of Fig. 5. The jump in the analytical results atM=1.2, is attributed to the switch from one methodto the other. The gap between the calculated resultsand test data for the bodies alone is large, and isclose to the contribution of the canards units. Thus,it is expected that mis gap may mask the effect ofthe subject interactions in the case of canard-bodyconfigurations. In order to avoid this deficiency, itwas decided to isolate and study the contributionsof the canard units (canards and the mutualinteractions with the body on which they aremounted), rather than that of the wholeconfigurations. This was done by subtracting thestability derivatives of the body alone from those ofthe configurations.

CNa(CU) = CNa(B-C)-CNa(B) (6.a)Cmo(CU) = Craa(B-C)-Cma(B) (6.b)xcpCU/D = -Cm5(CU)/CN6(CU) (6.c)

This approach was applied to the output of the M-Datcom, to the corrected results, and to the testdata.

The lateral locations of the trailing vortices, inafterbody diameters, are given in Table 2. It isapparent from the table that the present analysisestimates that the canard-body interaction willdecrease the normal-force curve slope of canardunit C by 31%, and that of Cl by 32%.

896


Table 2 Lateral positions of the canard vorticesIMI research projectiles

StationI.E. of canard C

AfterbodyI.E. of canard Cl

Afterbody

f0.4060.5870.3970.584

g0.1720.4260.1680.428

(f-g)0.2340.1610.2290.156

A(f-g)—

-0.073--

-0.074

A(f-g)/(f-g)c

—

-0.31—

-0.32

Fig. 5 presents a comparison between analysis andtest data for the contribution of the canard units tolongitudinal stability derivatives. Note that thecharts contain results for both configurations: B-coccupies Mach numbers up to 1.6; while B-Clcovers higher Mach numbers. It is apparent thatcorrecting the results of the M-Datcom greatlyimproves the agreement between analysis and testdata. In particular, the interaction, which acts on thethickening of the body, shifts the center of pressureof the canard units forward. This effect iscorroborated by the test data, as can be seen in Fig.5.c.

Pavestorm IThe Pavestorm configuration features a canard unit,which is mounted on a thin forebody, a thick mainbody, a boattail and a tail. Smith7 tested thisconfiguration at transonic Mach numbers. Aschematic of the test model is shown in Fig. 7.Canard C3, which has the middle size, was selectedfor the present study.

The computational model contains three smalldeviations from the actual configuration: a) theactual nose (cone-cylinder-flare) was replaced by acone with fineness ratio of 2.44. This enables theuse of the first option of analysis, which uses adatabase. This option has the advantage of takinginto account the lift carry-over on the main body.

The selected fineness ration assures that the bodydiameter at the location of the center of the canardroot chord is equal to the actual diameter; b) theactual afterbody (boattail-box tail) was representedby a conical boattail. The computational modelbase diameter was calculated such that the normal-force curve slope of the equivalent base diameterwill equal that of the actual box tail, based onslender body theory. According to this theory, i. e.Nielsen,8 the normal-force curve slope of a squarebody is 2.47. Thus,

Tt/2 dbe2 = 2.47 c2

(7)

This gives d,,,, = 1.25c; c) the root chord of the tailis shifted outward, so that it matches thecomputational boattail. The inclusive span of thetail is maintained. A comparison between the actualbody and the computational model is depicted inFig. 8. The radial location of the canard vortices atselected body stations, in body diameters, are givenin Table 3.

The moment arms are l,/d=2.73 for the thickeningof the forebody and lbt/d=2.41 for the boattail. Thisgives the net effects

ACL =-0.043 CLC

ACm =-0.673 CLC

(8.a)(8.b)

Table 3 Lateral positions of the canard vorticesPavestorm I

StationT.E. of canard

Main bodyBase of boattail

f0.7410.8710.772

g0.0520.2860.113

(f-g)0.6890.5850.659

A(f-g)-

-0.1040.074

A(f-g)/(f-g)c-

-0.1510.108

897


The two configurations were analyzed with liftingsurfaces at both the + and x positions, and for non-deflected and 5.5 deg deflected canards. Body-tailconfiguration was also analyzed. The directcorrections use Eqns. (9), with calculated values forthe characteristics of the canard unit. Table 3 showsthat the radial location of the free vortices at the tailzone is slightly larger than that at their origin,namely at the canard trailing edge. Chart 7 of Ref.3 was used to estimate the effect of this change ofthe lateral position on the tail interference factor. Itwas found that the lateral shift increases theinterference factor by 3.4%, in absolute value. Thenormal-force curve slope of the tail unit, alone andin the presence of the canards, was obtained bysubtracting the normal-force curve slope of thebody alone from that of the body-tail and the body-canard-tail configurations. The difference betweenthe two cases is the contribution of the tail due tocanard vortices (downwash). The additionalcorrection was obtained by increasing thiscontribution by 3.4%, as mentioned above.

The experimentally obtained stability derivativeswere estimated by eye fitting straight lines to thegraphically presented data, at small angles ofattack. The pitching-moment curves of thecomplete configuration feature strong non-linearity,(sometimes called S curve) around zero angle ofattack. Thus, the experimentally obtained pitching-moment curve slope was not evaluated for thisconfiguration. Also, the net normal-forcecoefficient due to canard deflection is very smalland compares with the accuracy of the datareduction. Thus this coefficient, too, is not beingcompared.

Comparisons of calculated and experimentallyobtained longitudinal characteristics ofconfiguration B1-C3 are shown in Fig. 9. Test datawith undeflected canards are available for surfacesat the + position. It is apparent that the correctionimproves the agreement with test data, for bothstability derivatives. The normal-force andpitching-moment due to canard deflection of 5.5deg are presented hi Fig. 10. The calculated

normal-force coefficient is considerably larger thanthe test data. The present correction has the righttrend, but it is much smaller than the remaininggap. The matching pitching-moment curve withcanards in the + position is in very good agreementwith the data. In the x orientation, the agreement isgood at Mach number of 0.65, but a gap developsas Mach number increases.

The calculated and experimentally obtainednormal-force curve slopes of configuration B1-C3-Tl are presented in Fig. 11. In this case, the indirectcorrection adds to the direct one. For thisconfiguration, the M-Datcom results overestimatethe test data, while the corrected results are hi verygood agreement with it. Fig. 12 brings acomparison between calculated and experimentallyobtained data for the pitching-moment due tocanard deflection of 5.5 deg. In this case, theindirect correction offsets about 10% of the directcorrection. The findings are very similar to thosefound for configuration B1-C3, namely goodagreement with the test data for surfaces in the +orientation, and at M=0.65 also for the x position.At Mach numbers larger than 0.65 and x positionthere remains an unexplained gap between analysisand test data.

Error AnalysisIn order to quantify the improvement of theanalysis by including the present correction, erroranalysis was done. The relative errors and their rootmean squares were defined by

(9-a)(9.b)

(lO.b)

Similar relative errors were defined for thematching stability derivatives. The relative errorswere calculated for all the coefficients that wereanalyzed. The findings are summarized in thefollowing tables.

em = (CmA-Cm

ro)/CmTO

EN = V(SeN2)/n

898


Tables 4-7 Summary of error analysis

4) MASATMX-46

AnalysisM-DatcomCorrected

ENa0.0600.044

Ema6.221.87

EN80.3800.155

Em50.8900.369

5) HVO research projectiles (contributions of the canard units)


ENU0.7800.264

Ema0.5650.271

6) Pavestorm I, configuration B-C3


ENU0.1010.064

Emo0.3810.24

EN(5=S.5,+)0.2510.198

Em(6=5.5,+)0.2790.093

EN(8=5.5,x)0.4120.349

Em(8=5.5,x)0.4710.199

7) Pavestorm I, configuration B-C3-T


ENO0.0270.012

Em(S=5.5,+)0.1810.092

Em(8=5.5,x)0.2430.142

The large values of Ema in Table 4 are attributed tothe very small experimentally obtained pitching-moment curve slope. It is apparent that in all cases,the errors of the corrected analysis are smaller ormuch smaller than those of the uncorrectedanalysis.

Summary and Conclusions

The method for analyzing the effects of trailingvortices generated by canard units on thickeningsand boattails of bodies was applied to fourconfigurations. Three of them are canard-bodycombinations, and the fourth one is a canard-body-tail configuration.

Including these effects, as corrections to the resultsof the M-Datcom code, considerably improve theagreements between calculated results andexperimentally obtained data.

It is recommended to add to the M-Datcom code anoption to include the subject effects in the analysisof longitudinal and control characteristics.

Acknowledgments

The Missile Datcom code was obtained fromAFRL/Air Vehicle Directorate. I wish to thank Mr.William B. Blake and Mr. James Simon for theircontinues support and advice.

I am indebted to Israel Military Industries,Advanced Systems Division, for making then-unpublished wind tunnel data available for thisstudy.

A. S.

References

1. Sigal, A., and Victor, M., "The Interactionsbetween a Canard and Thick Bodies, Part I:Characteristics of the Components," AIAA-97-2249, June 1997.

2. Sigal, A., "The Interactions between a Canardand Thick Bodies, Part II: Analysis of theInteractions," AIAA-99-3146, June 1999.

3. Pitts, W. C., Nielsen, J. N., and Kaattari, G. E.,"Lift and Center of Pressure of Wing-Body-

899


Tail Combinations at Subsonic, Transonic, and 6.Supersonic Speeds," NACA report 1307, 1957.

4. Blake, W. B., "Missile Datcom User's Manual- 1997 Fortran 90 Revision," AFRL-VA-WP-1998-3009, Feb. 1998.

5. Spearman, M. L., and Robinson, R. B., 7."Longitudinal Stability and ControlCharacteristics at Mach Numbers 2.01, 4.65,and 6.8 of Two Hypersonic MissileConfigurations, One Having Low-Aspect-Ratio Cruciform Wings With Trailing-EdgeFlaps and One Having a Flared Afterbody and 8.All-Movable Controls," NASA TM X-46, Sep.1959.

Peleg, E., Tal, R., and Wetzler, M.,Unpublished wind tunnel results of canard-body research configurations, IMI, AdvancedSystems Division, Ramat Hasharon, Israel,Dec. 1999.Smith, D. K., "Effect of Several Canard Sizeson the Static Stability, Performance, and TrimCharacteristics of the Pavestorm I MunitionSystem at Transonic Speeds," ArnoldEngineering Development Center, Arnold AFStation, TN, AEDC-TR-72-67, May 1972.Nielsen, J. N., "Missile Aerodynamics"McGraw-Hill, Inc., New York, 1960.

- Hinge line

Fig. 1 Schematic of canard-body-flare configuration.After Spearman and Robinson, NASA TM X-46.

12

10

J •

6

4

a) 2

\^^ - - - Corrected ji-^^^^. o Test data j

^^^N"^-—— — —— ——— — — -o-_— -.

> 2.5 3 3.5 4 4.5 5M

QauX

b)

-3

-4

-5

-6

-7

-R

; •i 2.5 3 3.5 4 4.5 i

> i - - - Correctedj o Test data I

H— --„

i

Fig. 2 Comparison of longitudinal stability derivatives of canard-flare-body configuration: a)normal-force curve slope, and b) center of pressure location.

900


0a) 2 2.5 3.5

M

4.5 b)

Q

0X

-3

-4

-5

-6

-7

-R

2.5 3 3.5 4 4.5

: . } - -__._-_.____,_„._=__.ii ' '_..:: .i ——— M-Datcom1 - - -- Corrected1 [ o Test datai " "

Fig. 3 Comparison of control stability derivatives of canard-flare-body configuration: a) normal-force due to canard deflection, and b) center of pressure location.

Canard C

1.0

Canard Cl

0.4

Fig. 4 Schematic of IMI research projectiles.After Peleg, Tal and Wetzler.

mZ°

O

a)

O.*J

3

2.5

2

1.5

1

0.5

............ . . . . „---• — ----- --^___

......... . . .j ............. Q -

Of^

—— M-Datcom, M< 1.2— — — M-Datcom, M>1.2

o Testdata

0.8 1.2 1.6M

2.4 0.4

m

O

b)

4

3.5

9 ^i.O

2

1.5

... . . . . . . . . . . . . . . . . . . ...><F.r. ——————— .-.- , ——— -

0

• • • - • • ! ——— M-Datcom, M<i.2I — — - M-Datcom, M>1 .2I o Testdata [

0.8 1.2 1.6M

Fig. 5 Comparison of longitudinal stability derivatives of IMI body alone:a) normal-force curve slope, and b) pitching-moment curve slope.

2.4

901

(c)2000 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)1 Sponsoring Organization.

1.2

1aoa 0.8 -z

O0.6

0.4

0.2a) o

.._- .̂/ \

/,.~.,.̂_-—--"' A

4 0.8 1.2 ,, 1

— -

— - — - B-C, CorrectedA B-C, Test data

— — - B-C1, M-Datcom— - - — B-C1, Corrected

D B-C1, Test data

\^

^---DL.._

.6 2 2.

o

»t

3.5

3

2.5

2

1.5

10

-—^^ /'"•--../ '•*.

.......T.T"................. ....... .A....

A

4 0.8 1.2 1

———— B-C, M-Datcom

— - — - B-C, CorrectedA B-C, Test data

— — — B-C1, M-Datcom— - - — B-C1 , Corrected

D B-C1, Test data-TrT——-^^——— .-TTTT-nTTT-TTrJ

"••- .

^X^.......t^... ...............

•̂ .~--a* -

.6 2 2.

M

ao

3

2.5

2

1.5

1

n<i

\

\ - , . ...|...|................

\"". . . . ...... . . . . .

iI

I

"' —— - — ._._ -~'-~.A

......... ——— — _

— - — - BC, CorrectedA BC, Test data

— — — BC1, M-Datcom— -- — BC1, Corrected

O BC1, Test data

'•*•-.. -o--.__„. ........... .... .

0.4 0.8 1.2 1.6M

2.4

Fig. 6 Comparison of longitudinal stability derivatives of the canard units of IMI researchprojectiles: a) normal-force curve slope, b) pitching-moment curve slope, and c) center of pressure

location.

O.OI1 LCADim-

Fig. 7 Schematic of wind tunnel model of Pavestorm I.After Smith, AEDC-TR-71-67.

2.66^

Fig. 8 Comparison between the body and the computational model of Pavestorm I.

902


7

6

j 5

4

3

a) 20

0.5

0.4

<£ 0.3inIIiS0 0.2

0.1

0

15 ,-

14

13

11

10

9 ———————— ; ———————— , ———————— ; ————————

——— M-Datcom— — — Corrected

o Test data

-•——____••• ^— — tr-- — '" O

B-C3

.6 0.7 0.8 0.9M

Fig. 9 Comparison of the stabilitya) normal-force curve slope, and

B-C3 ^.'^.

+ j ——— M-Datcom, +— - - Corrected, +

| + Test data, +.. . . . . . . . . . . . . . . . ; — - — - M-Datcom, x . . . . . . . . . . . . . . . . . . . . . . . . .

j- - -- Corrected, x! x Test data, x

6 0.7 0.8 0.9M

;. 10 Comparison of the control loads due to 5a) normal-force, and b) pit

B-C3-T

_ -̂nO ^"~

o

.............. ___ Correctedo Test data

0.6 0.7 0.8 0.9 1

M

30

25

1 20U

15

10

51 0

derivativeb) pitchin

1.75

1.5

1.25

innS2Tj 0.75O

0.5

0.25

b) °

.5 deg canching-moi

3

2.5

_ 2

ujib 1 5

E1

0.5

00

——— M-Datcom- - - Corrected

o Test data ^^^^

~-^^:-"0 0 °

B-C3

6 0.7 0.8 0.9 1

Ms of configuration B1-C3:g-moment curve slope.

B-C3 _^.-"'

. . . . . . . . . . . . . . ——— M-Datcom, +- — — Corrected, +

+ Test data, +— - — - M-Datcom, x---- Corrected, x

x Test data, x

0.6 0.7 0.8 0.9 1

Mard deflection of configuration B1-C3:nent coefficients.

B-C3-T ^-''

— — —Corrected, ++ Test data, +

--_ -M-Datcom, x- - - -Corrected, x

x Test data, x

.6 0.7 0.8 0.9 1M

Fig. 11 Comparison of the normal-force curveslope of configuration B1-C3-T1.

Fig. 12 Comparison of the pitching-momentcoefficient due to 5.5 deg. canard deflection.

903

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