Aerodynamic Characteristics of Tandem-control and Rolling ... · used for the analysis. Results presented include highcontrolled missile models with fixed and free-rolling tail angle

AIAA 2002-4511Prediction of the NonlinearAerodynamic Characteristics ofTandem-control and Rolling-tail Missiles

D. Lesieutre, J. Love, and M. DilleniusNielsen Engineering & Research, Inc.Mountain View, CA

AIAA Atmospheric Flight MechanicsConference

5-8 August 2002 / Monterey, CAFor permission to copy or republish, contact the copyright owner named on the first page.

For AIAA-held copyright, write to AIAA Permissions Department,1801 Alexander Bell Drive, Suite 500, Reston, VA, 20191-4344.

Copyright å2002 by Nielsen Engineering & Research, Inc.

Published by the American Institute of Aeronautics and Astronautics, Inc. with permission.

1American Institute of Aeronautics and Astronautics

AIAA 2002-4511

PREDICTION OF THE NONLINEAR AERODYNAMIC CHARACTERISTICSOF TANDEM-CONTROL AND ROLLING-TAIL MISSILES

Daniel J. Lesieutre , John F. Love , Marnix F. E. Dillenius* † ‡

Nielsen Engineering and Research, Inc.Mountain View, CA 94043

ABSTRACT fin deflection angle, deg

Predicted nonlinear aerodynamic characteristics of- roll angle, degseveral canard-body-tail missile models are presented- fin set roll angle with respect to body-fixedand compared to wind tunnel data. Configurations with vertical axis, positive right wing down, degboth fin sets deflectable (tandem-control) are analyzedto investigate the effectiveness of canard-only, tail-only, INTRODUCTIONand combined tandem-control effectiveness for bothvertical translation and pitch attitude changes. Recently, experimental data obtained by NASAConfigurations with canard control fins and free-rollingpersonnel has become available for tandem-controltail fin sections are investigated for their ability to missile configurations. These data exhibit manyminimize vortex-induced lateral forces and moments nonlinear characteristics associated with vorticalassociated with canard control. Engineering- and interaction between fin sets. In addition, there areintermediate-level aerodynamic prediction codes are several sets of experimental data taken for canard-used for the analysis. Results presented include highcontrolled missile models with fixed and free-rolling tailangle of attack aerodynamics, induced lateral forces, sections. These data also exhibit nonlinearitiestandem-control fin deflections, estimates of free rotating associated with strong canard-tail vortical interferencefin section performance, and rotational dampingincluding induced lateral forces and moments. An initialestimates. Good agreement with experimental data is investigation of the ability of an engineering-levelobtained for a variety of nonlinear and asymmetric flightaerodynamic prediction code to predict theconditions. characteristics of these configurations has been

LIST OF SYMBOLS configurations in more detail, using both engineering-a body radius at fin mid-rootchord level and intermediate-level aerodynamic predictionAR aspect ratio (two fins joined at root) codes.C body crossflow drag coefficientdc

C rolling moment/q S l TECHNICAL APPROACHl ∞ R R

C roll-damping coefficient; ∂C /∂(pl /2V )lp l R ∞C pitching moment/q S l ; positive nose up This section summarizes the experimental data and them ∞ R R

C normal force/q S prediction methodology employed in this investigation.N ∞ R

C fin normal force/q S The estimation of rolling-tail section properties is alsoNF ∞ R

C body dC /d� at �=0 presented.N� N

D body diameter, maximumL body length DESCRIPTION OF MISL3l ,L reference lengthR REF

p,q,r rotational rates, rads/sec The engineering-level missile aerodynamic predictions exposed fin spans fin semispan measured from body centerlinem

S reference areaR

x center of pressureCP

x moment centerMC

� included angle of attack, degc

_____________________Senior Research Engineer, Senior Member AIAA*

Research Engineer†

President, Associate Fellow AIAA‡

� fin taper ratio

F2

1,2

3,4

presented. This paper is aimed at investigating these2

code MISL3 has been developed for aerodynamic2

performance prediction and for preliminary design ofconventional missiles. The method uses the Triservicesystematic fin-on-body force and moment data base4,5

The prediction methodology employed covers a Machnumber range from 0.5 to 5.0, fin aspect ratios from0.25 to 10.0, angles of attack to ±90°, arbitrary rollangles, and deflection angles from -40° to 40°. Themethod uses the equivalent angle of attack concept

Step 1ForebodyStep 2

Fin Set 1

Step 3Afterbody

Step 4Fin Set 2

Fin Panels

InterferenceShells


AIAA 2002-4511

which includes the effects of vorticity and geometricscaling. The current version of the MISL3 program has configurations with unconventional fin shapes. A recentbeen developed by extending the methodology to modelextension of the code enabled the modeling of theconical changes in body diameter (flares, boattails) and subsonic Penguin missile with canards on the nose andto allow arbitrary interdigitation angles between fin sets.This, in combination with the roll rate capability of thecode, allows estimation of the performance ofconfigurations with rolling fin sets. Reference 2provides more details regarding the methodologyemployed by MISL3 and presents comparisons toexperimental data for a wide variety of configurations.ROLLING-TAIL CHARACTERISTICS

DESCRIPTION OF MISDL Estimation of the aerodynamic characteristics of the

The intermediate-level aerodynamic prediction code The roll equation of motion for the tail section as aMISDL is based on panel methods and other function of time t is:6,7

singularity methods enhanced with models for nonlinearvortical effects. The body of the missile is modeled byeither subsonic or supersonic sources/sinks and doubletsfor volume and angle of attack effects, respectively.The fin sections are modeled by a horseshoe-vortexpanel method for subsonic flow and by first-orderconstant pressure panels for supersonic flow. Up tothree fin sections can be modeled and nonlinear fin andbody vortices are modeled. The body vorticity ismodeled using the VTXCHN vortex-cloud methoddescribed in Refs. 6-8. The overall calculation proceedsas follows: 1) the VTXCHN module is used to computethe forebody loads including vortex shedding andtracking, 2) loads within the fin set are calculatedincluding the effects of forebody vorticity, 3) thevorticity shed from the forebody and the forward fin setis included as an initial condition in VTXCHN modulewhich tracks and models additional vortices shed fromthe afterbody, and 4) if second or third fin sets arepresent, steps 2 and 3 are repeated. A schematic of thecalculation procedure and paneling layouts is shown inthe following sketch.

The range of parameters of the MISDL code include:Mach numbers from 0.0 to 3.0 with a modified shock-expansion capability to higher supersonic speeds, anglesof attack up to 20 degrees, arbitrary roll angles,rotational rate effects, and nonuniform flow effects.

MISDL can model noncircular body configurations and

deployed and folded wings. A version of MISDL6

employing an optimizer was used to designunconventional fin planforms for several designobjectives including minimization of fin hinge momentsand maximization of normal force.9

rolling tail section including tail section roll rate follows.

T = T (t) + T (t) + T (t) = I (dp/dt) (1)AF AD BF X

where T is torque and I is the moment of inertia in rollX

of the tail section. The subscript designations are:AF - aerodynamic forcing,AD - aerodynamic damping, andBF - bearing friction (or brake force).

The time-dependent aerodynamic forcing torque on thetail fins, T (t), is caused by the aerodynamic fin forcesAF

which are dependent on the angle of attack and the finsection roll angle, - . The aerodynamic dampingF2

torque, T (t), is dependent on the tail section roll rateAD

and the angle of attack. The third torque, T , can beBF

used to model bearing friction and/or braking torque.

In this paper, the rolling tail characteristics are estimatedbased on static characteristics and calculated rolldamping characteristics. The analysis of Falanga is10

followed. For steady-state conditions (constant roll rate,no variance with - ), the sum of the moments must beF2

zero.

$moments = M + M + M = 0 (2)AF AD BF

Substituting M = C q S l andAF ∞ R Rl

M = C (pl /2V )q S lAD R ∞ ∞ R Rlp

into Eqn. (2) and solving for the roll rate p, yields:

(3)

For cases where the bearing torque is much smaller thanthe aerodynamic torque, the roll rate can be estimated asfollows:


AIAA 2002-4511

(4)

For a high quality bearing, this assumption is valid.Eqn. (4) is used to estimate the tail fin roll rate withpredictions of C and C . Conversely, Eqn. (4) is usedl lp

to estimate the experimental tail section roll damping,C , from the measurements of C and p. Eqn. (3) canlp l

be used to compare to rolling tail results with a brake-force applied.

RESULTS

This section presents longitudinal and lateral-directionalaerodynamic predictions for several tandem-controlconfigurations, and for configurations with canard-controlled fixed and free-to-roll tail sections. Predictedresults obtained with engineering- and intermediate-levelprediction codes are shown. Nonlinear aerodynamiccharacteristics associated with high angle-of-attack andasymmetric flow conditions are illustrated. Comparisonsof predictions to the Tandem-Control Model data baseare presented. The effects of interdigitation between finsets is analyzed along with the estimation of tail finsection roll rate for a canard-tail configuration with afree-rolling tail section.

TANDEM CONTROL

Tandem-Control Model Experiment. Tandem-Controldata presented in this section were obtained from testsconducted in the NASA/LaRC Unitary Plan WindTunnel at free-stream Mach numbers from 1.75to 2.86. The test objective was to provide an1,2

aerodynamic database to study and evaluate tandemcontrol effectiveness. The model consists of a 3-caliberogive nose followed by a 12-caliber cylinder withcruciform inline canards and aft tail fins. Tests wereperformed on two models. Both models had the samecanard fins, AR = 1.6 and � = 0.625. The first modelshown in Figure 1 had larger span tail fins, AR = 2.33and � = 0.625, and the second model tail fins identicalto the canard fins, Figure 3. Model aerodynamic forcesand moments were measured with an internally mountedsix-component strain-gage balance. To assure turbulentflow over the model all tests were performed withboundary-layer transition strips located on the modelnose and near the leading edges of the canard and tailfins. The test Reynolds number based on body diameterwas 4.33x10 .5

Tandem-Control Model Predictions. Figures 1 and 2show measured and predicted results for the Tandem-1

Control Model with larger span tail fins described

above. For M = 1.75 and - = 0°, MISL3 predictions∞

are shown in Figure 1, and MISDL predictions are inFigure 2. Results are shown for four sets of horizontalfin deflections:

1) = 0°, = 0°CANARD TAIL

2) = 10°, = 5°CANARD TAIL

3) = 10°, = 10°CANARD TAIL

4) = 5°, = -5°CANARD TAIL

The zero deflection case is the reference. Cases 2) and3) are deflections for vertical translation, and Case 4) isdeflection for rotation in pitch. The normal force,pitching moment, center of pressure, and axial force asa function of � are all predicted very well by MISL3,c

Figure 1. The nonlinear characteristics of the pitchingmoment are predicted especially well by MISL3, and thecenter of pressure predicted is within a body radius ofthe measured values. The axial force characteristics arealso predicted well. The MISDL predictions, Figure 2,are also predicted well with the largest errors occurringabove 20° angles of attack.

The results in Figure 3 are for the Tandem-Controlconfiguration with identical canard and tail finsdescribed above. Figure 3 depicts the configuration andpresents MISL3 results for canard pitch control forM = 1.75 and - = 45°. This case is shown because of∞the nonlinearities in the pitching moment which arise inthe “X” orientation from canard vortices affecting thetail fins. MISL3 predicts the nonlinear pitching momentcharacteristics well, and predicts the overall center ofpressure to within a body radius for this configuration.

TWO-FIN SET CONFIGURATION WITHFREE-ROLLING TAIL SECTION

Figures 4 through 10 present results for a similar canard-tail missile model. The model has a 3-caliber3

tangent-ogive nose and an overall body length of 15diameters. The test Reynolds number based on bodydiameter was 4.17x10 Results for three test5

configurations are presented. For all configurations, thecanards are in the - = 0° orientation (“+” orientation,F1

designated C+). Three tail section orientations weretested:

1) - = 0° (“+” orientation, designated T+),F2

2) - = 45° (“x” orientation, designated Tx), andF2

3) tail section free to rotate (designated T-free).

The C+Tx and C+T+ configurations are depicted inFigures 4 and 8, respectively. Results are presented forcanard roll control and canard yaw control deflections.


AIAA 2002-4511

The purpose of comparing to this experimental data was roll effect seen on canard-controlled missiles. For theseto investigate the predictive capabilities of the MISL3and MISDL codes and to gain insight into theaerodynamic characteristics of configurations withrolling tail sections. In this investigation, the codeswere used to 1) estimate the static roll characteristics ofthe tail section under the influence of asymmetric canardvortices arising from roll and yaw control deflections, 2)estimate the roll damping characteristics of the tailsection as a function of angle of attack, and 3) estimatethe roll rate of the free-to-rotate tail section as afunction of angle of attack.

Canard Roll Control. Figure 4 compares measured3

and predicted pitch plane aerodynamic characteristics fora Mach number of 1.7 with the horizontal canardsdeflected for roll control, = -5° ( = ( -ROLL ROLL C2

)/2). Measured and predicted results are shown forC4

the C+T+ and C+Tx configurations. In addition, themeasured data for the C+T-free configuration are alsoshown. The normal-force coefficient is predicted wellfor the C+T+ configuration. MISL3 and MISDLsomewhat underpredict the characteristics of the C+Txconfiguration. The C+T+ pitching moment is in goodagreement. The C+Tx pitching moment isoverpredicted. For MISL3, the center of pressure ispredicted within one body radius for both configurationsexcept for small load conditions near � = 0°. MISDLc

predicts the center of pressure to within one body radiusfor C+Tx and within eight-tenths of a diameter forC+T+. The axial force is predicted well. The measuredcharacteristics of the C+T-free configuration fallbetween the C+T+ and C+Tx characteristics.

Figure 5 compares measured and predicted rollingmoment characteristics for the C+T+ and C+Txconfigurations with canard roll control, = -5°. InROLL

addition, the direct canard rolling moments predicted byMISL3 and MISDL are compared to the C+T-freemeasured results. The free-to-rotate tails do not pass arolling moment to the main balance, except throughbearing friction forces which are very small. It is seenin Figure 5 that the predicted direct roll control is invery good agreement with the measured C+T-freerolling moment. MISDL slightly overpredicts the canardrolling moment. The MISL3 predicted rolling momentsfor the C+T+ and C+Tx configurations agree well withdata up to 4° angle of attack and have the correct trendsabove 4°. MISDL predicts the rolling moments for theC+T+ and C+Tx configurations very well in magnitudeand trend.

This rolling moment is difficult to predict because it isdominated by the canard and body shed vorticesinfluencing the tail fins. This is the classical induced

configurations, the induced tail fin rolling momentopposes the direct canards control and actually causesthe overall rolling moment to oppose the intent of thecanard deflection.

Figure 6 shows the MISL3 predicted crossflow velocityfields at the leading edge of the tail fin section forangles of attack of 0, 4, 8, and 12°. For � = 0°, Figurec

6(a), it is seen that the canard vortices produce acounterclockwise swirling flow (looking forward) whichproduces the negative induced rolling moment on thetail fin section as seen in Figure 5. For � = 4°, Figurec

6(b), the effects of the vortex shed from the right canardvortex is not apparent because it is lightly loaded(� + = -1°). There is a stronger vortex on the leftc C2

side corresponding to � + = +9°. The flow field isc C4

asymmetric and results in a negative induced tail finsection rolling moment. The results for � = 8°,c

Figure 6(c), show a large vortex from the left canard anda weaker one from the right canard. The higher angleof attack results in the vortices tracking further abovethe body. There is still an asymmetric flow field whichproduces a negative tail section rolling moment for boththe C+T+ and C+Tx configurations. Figure 6(c) alsoindicates the beginning of the body shed vorticitymodeled by MISL3.

When � = 12°, Figure 6(d), the canard vortices havec

tracked to positions above the tail fin region, andsignificant body shed vorticity is present. The inducedrolling moment on the tail fin section is small for thisangle of attack for both the C+T+ and C+Txconfigurations, but it has a positive slope as seen inFigure 5. Above 12° angle of attack, the predictedinduced rolling moment from the tail fins is positive. The experimental data show this behavior to a lesserextent. In the prediction, this arises from theasymmetric body vorticity (produced due to asymmetriccanard vorticity). The left-side body vorticity is weakerthan the right-side; the result is an induced positive rollon the tail fins for both the C+T+ and C+Txconfigurations. This is similar, but opposite, to theresults at lower angles of attack with asymmetric canardvortices. Further insight is gained from these crossflowvelocity predictions when the variation of tail sectionrolling moment as a function of interdigitation angle isdiscussed next in connection with Figure 7(a).

For the canards deflected *5° for right-wing-down rollcontrol ( Figure 7(a) shows the predicted staticROLL),

rolling-moment coefficient of the tail fin section as afunction of tail fin set roll angle - . Results are shownF2

for angles of attack of 0, 4, 8, and 12°. The tail finrolling moment is negative (right fin up) for angles of


AIAA 2002-4511

attack below 8°. This is apparent in the flow field =-5° ( = ( + )/2). Figures 8 and 9predictions shown in Figures 6(a)-6(c) which show compare measured and predicted rolling momentpartially counterclockwise flow fields for � = 0 and 4°.c

Above 4° angle of attack, a significant cyclic variationin C develops, Figure 7(a). For 12°, the rolling momentl

variation is cyclical and changes sign. The slope of Cl

with respect to - (positive clockwise) at the zeroF2

crossings is such that the tail section “locks-in” to azero roll rate when it is near the “X” orientation,- = 45, 135°.F2

To estimate the tail fin roll rate using Eqn. (4), C andl

C must be estimated. C is estimated as the mean Clp l l

with respect to - (see Figure 7(a)). The roll dampingF2

coefficient, C , is estimated by running MISL3 andlp

MISDL with a nonzero roll rate (tail fins only) andcomputing C . It was found that C is constant for thelp lp

range of roll rates under investigation (that is, C isl

linear with respect to p). However, there is adependence on angle of attack as shown in Figure 7(b).The experiment did not measure the roll damping, butit was estimated using Eqn. (4) as follows:

(5)

where the rolling moment coefficients are given by theexperimental values and the roll rate is the experimentalvalue in radians per second.

For the predictions, tail fin roll rate is estimated as -C /C (Eqn. (4), and converted to rpm) and is shown inl lp

Figure 7(c). The magnitude of the roll rate isunderpredicted by MISL3 and overpredicted by MISDL.For both codes, the trends are predicted well. Thecharacteristics of the rolling moment predicted withrespect to - are such that the tail fins “lock-in” to aF2

zero roll rate around 12°. The experimental resultsindicate that this happens at 14° as does MISDL. Thepredicted results are dependent on the prediction of Cl

and C for the tail section. These quantities are difficultlp

to predict accurately, especially when they areinfluenced by upstream asymmetric vorticity.

Both MISL3 and MISDL provide reasonable estimates ofthe roll rate characteristics of a free-to-roll tail sectionunder the influence of the asymmetric flow fieldassociated with canard roll control as a function of angleof attack.

Canard Yaw Control. Figure 8, 9, and 10 comparemeasured and predicted rolling moment aerodynamic3

characteristics for canards deflected for yaw control,

YAW YAW C1 C3

characteristics for the C+T+ and C+Tx configurations,respectively. In addition, the canard-only rollingmoments predicted by MISL3 and MISDL are comparedto the C+T-free measured results. Figure 10 comparespredicted and measured tail section roll rate andestimated tail section roll damping.

The C+T-free results shown in Figure 8 or 9 show therolling moment associated with the canards deflected foryaw. Near zero angle of attack, the rolling moment iszero. As the angle of attack is increased, a rollingmoment develops due to top to bottom asymmetries inthe nose flow field due to the presence of the body bowshock and to the flow expansion over the upper surfaceof the nose. The expansion over the upper surface ofthe nose results in a reduction in dynamic pressure inthe region of the upper canard fin. This “shading” of theupper fin results in a net positive rolling moment for thecanards alone. This effect is not predicted adequatelyby engineering-level and intermediate-level aerodynamicpredictions code.

For the C+T+ and C+Tx configurations MISL3 andMISDL predict the rolling moment behavior well as seenin Figures 8 and 9. It is difficult to predict the nonlinearrolling moment because it is due to induced vorticalinterference of the canard vortices on the tail fins. Foryaw control, the results are dependent on the path of thelower canard vortex past the tail fins. MISL3 predictsthe correct trend but underestimates the peak magnitude.MISDL predicts the low angle of attack characteristicswell and tends to overestimate the rolling moment athigher angles. Overall, both MISL3 and MISDL estimaterolling characteristics good enough for preliminarydesign estimates.

For the canards deflected -5° for nose-to-left yawcontrol ( ), Figure 10(a) shows the predicted staticYAW

rolling-moment coefficient of the tail fin section as afunction of tail fin set roll angle - . Results are shownF2

for angles of attack of 0, 4, 8, and 12°. It is seen thatthe tail fin rolling moment has no zero crossings forangles of attack below 8°. Like the roll control resultsin Figure 7(a), above 4° angle of attack, a significantcyclic variation in C develops. For 12°, the rollingl

moment variation is cyclical and changes sign. Theslope of C with respect to - (positive clockwise) atl F2

the zero crossings is such that the tail section “locks-in”to a zero roll rate when it is near the “X” orientation,- = 45, 135°.F2

To estimate the tail fin roll rate using Eqn. (4), C andl

C must be estimated. C is estimated as the mean Clp l l


AIAA 2002-4511

with respect to - (see Figure 10(a)). The roll damping ACKNOWLEDGMENTSF2

coefficient, C , shown in Figure 10(b) is estimated bylp

running MISL3 and MISDL with a nonzero roll rate (tailfins only) and by using Eqn. (5) to estimate theexperimental value. The Mach number variation of theroll damping coefficient, C , is predicted well bylp

MISL3. MISDL underestimates C for M = 2.16lp ∞and 2.86.

The tail fin roll rate is estimated as -C /C (Eqn. (4),l lp

and converted to rpm) and is shown in Figure 10(c).The roll rate p is inversely proportional to C and islp

very sensitive to its estimation. For MISDL, theunderestimation of C for M = 2.16 and 2.86 results inlp ∞

an overprediction of roll rate. Neither MISL3 norMISDL predict the correct roll rate trend as a functionof Mach number. The experiment indicates that the rollrate decreases with increasing Mach number whichimplies that C decreases faster than C with increasingl lp

Mach number. A detailed study is required to furtherassess these effects. The predicted results are dependenton the prediction of mean C and C for the tail section.l lp

These quantities are difficult to predict accurately,especially when they are influenced by upstreamasymmetric vorticity.

Note that the characteristics of the rolling momentpredicted with respect to - , Figure 10(a), are such thatF2

the tail fins “lock-in” to a zero roll rate around or above12°. The experimental results indicate that this happensat 14°. The roll equation of motion given by Eqn. (1)would need to be integrated within MISL3 and MISDLto determine when “lock-in” actually is predicted.

CONCLUSIONS

This paper describes the prediction of the nonlinearaerodynamic characteristics of missile configurationswith tandem-controls and free-rolling tail sections. Theextensive comparisons to experimental aerodynamic datainclude longitudinal and lateral aerodynamiccharacteristics including nonlinear vortex-inducedeffects. In general, the predicted aerodynamiccharacteristics are in good to excellent agreement withthe experimental data and provide insight intounderstanding the nonlinear characteristics of missileswith free-to-rotate tail sections.

NEAR would like to thank Mr. A. B. Blair, Jr., (retired)and Mr. Jerry M. Allen of NASA/LaRC for theirassistance in obtaining the Tandem-Control wind tunneldata.

REFERENCES

1. The Tandem-Control Data taken by A. B. Blair, Jr.,NASA Langley Research Center.

2. Lesieutre, D. J., Love, J. F., Dillenius, M. F. E., andBlair, A. B., Jr., “Recent Applications and Im-provements to the Engineering-Level AerodynamicPrediction Software MISL3,” AIAA 2002-0275,Jan. 2002.

3. Blair, A. B., Jr., “Wind-Tunnel Investigation atSupersonic Speeds of a Remote-Controlled CanardMissile With a Free-Rolling-Tail Brake TorqueSystem,” NASA TP 2401, Mar. 1985.

4. Blair, A. B., Jr., “Supersonic AerodynamicCharacteristics of a Maneuvering Canard-ControlledMissile with Fixed and Free-Rolling Tail Fins,”SAE Paper 901993, Oct. 1990.

5. Allen, J. M., Shaw, D. S., and Sawyer, W. C.,“Analysis of Selected Data From The TriserviceMissile Data Base,” AIAA 89-0478, Jan. 1989.

6. Lesieutre, D. J., Dillenius, M. F. E., and Gjestvang,J., “Application of MISDL/KDA AerodynamicsPrediction Method to Penguin Missile,” AIAA2002-0277, Jan. 2002.

7. Dillenius, M. F. E., Lesieutre, D. J., Hegedus, M.C., Perkins, S. C., Jr., Love, J. F., and Lesieutre,T. O., “Engineering-, Intermediate- and High-LevelAerodynamic Prediction Methods andApplications,” Journal of Spacecraft and Rockets,Vol. 36, No. 5, Sep.-Oct. 1999, pp. 609-620.

8. Hegedus, M. C., Dillenius, M. F. E., Perkins, S. C.,Jr., and Mendenhall, M. R., “Improved Version ofthe VTXCHN Code,” NEAR TR 498, Aug. 1995.

9. Lesieutre, D. J., Dillenius, M. F. E., and Lesieutre,T. O, “Multidisciplinary Design Optimization ofMissile Configurations and Fin Planforms forImproved Performance,” AIAA 98-4890, Sep. 1998.

10. Falanga, R. A., “Supersonic Investigation of aSpinning and Nonspinning Model of a Cajun (orApache) Rocket Vehicle With Roll-Control Tabs,”NASA TN D-2576, Jan. 1965.

αc

(xC

P-

x MC)/

D

0 10 20 30

-20

-10

0

10

20

αc

(xC

P-

x MC)/

D

0 10 20 30

-20

-10

0

10

20

Figure1.- Comparison of measured and MISL3predicted aerodynamic characteristics fora tandem-control missile;M∞ = 1.75, φ = 0°, Ref. 1.

Figure2.- Comparison of measured and MISDLpredicted aerodynamic characteristics fora tandem-control missile;M∞ = 1.75, φ = 0°, Ref. 1.

7American Instituteof Aeronautics and Astronautics

αc

CN

0 10 20 30

0

5

10

15

20Exp. δc = 0, δt = 0Exp. δc = 10, δt = 5Exp. δc = 10, δt = 10Exp. δc = 5, δt = -5MISL3 δc = 0, δt = 0MISL3 δc = 10, δt = 5MISL3 δc = 10, δt = 10MISL3 δc = 5, δt = -5

M∞ = 1.75SREF = SBASE

αc

Cm

0 10 20 30

-20

-15

-10

-5

0

5

10

LREF = DBASE

xMC/L = 0.49

-2

-1

0

1

2

Enlarged viewof results, α > 8°

αc

CN

0 10 20 30

0

5

10

15

20Exp. δc = 0, δt = 0Exp. δc = 10, δt = 5Exp. δc = 10, δt = 10Exp. δc = 5, δt = -5MISDL δc = 0, δt = 0MISDL δc = 10, δt = 5MISDL δc = 10, δt = 10MISDL δc = 5, δt = -5

M∞ = 1.75SREF = SBASE

αc

Cm

0 10 20 30

-20

-15

-10

-5

0

5

10

LREF = DBASE

xMC/L = 0.49

-2

-1

0

1

2

Enlarged viewof results, α > 8°

αc

CA

0 10 20 30

0.5

1

1.5

2ReD = 4.33x105

αc

CA

0 10 20 30

0.5

1

1.5

2ReD = 4.33x105


αc

CN

0 10 20 30

0

5

10

15Experiment δCpitch = 0°Experiment δCpitch = 5°Experiment δCpitch = 10°MISL3 δCpitch = 0°MISL3 δCpitch = 5°MISL3 δCpitch = 10°

M∞ = 1.75φ = 45°

SREF = SBASE

αc

Cm

0 10 20 30

-5

0

5

10

15LREF = DBASE

xMC/L = 0.49

αc

(xC

P-

x MC)/

D

0 10 20 30-20

-15

-10

-5

0

5

Figure3.- Comparison of measured and MISL3predicted aerodynamic characteristics,canard pitch control for φ = 45°,M∞ = 1.75, Ref. 1.

δC4 = +5°

δC2 = -5°

Figure4.- Comparison of predicted and measuredpitch-planeaerodynamic characteristicsof acanard-tail configuration (Ref. 3) with:1) tails inlinewith canards (C+T+),2) tails interdigitated 45° (C+Tx), and3) tails free to rotate (C+T-free).

αc

V∞

φF1 = 0° (C+) φF2 = 45° (Tx)

FS1 FS2

αc

CN

0 10 20-4

-2

0

2

4

6

8

Exp. C+T+Exp. C+TxExp. C+T-freeMISL3 C+T+MISL3 C+TxMISDL C+T+MISDL C+Tx

M∞ = 1.7δROLL =-5°

SREF = SBASE

(a) Normal-Force Coefficient

αc

Cm

0 10 20-6

-4

-2

0

2

SREF = SBASE

lREF = DBASE

xMC/L = 0.6

(b) Pitching-Moment Coefficient

αc

(xC

P-

x MC)/

D

0 10 20-1

0

1

2

SREF = SBASE

lREF = DBASE

xMC/L = 0.6

(c) Center of Pressure

αc

CA

0 10 20 300

0.5

1

1.5

2

ReD = 4.33x105

αc

CA

0 10 200

0.2

0.4

0.6

0.8

1

SREF = SBASE

(d) Axial-Force Coefficient

ReD = 4.17x105

Figure6.- Predicted crossflow velocity fields at theleading edgeof the tail fin section,

M∞ = 1.7, δC2 = -5°, δC4 = +5°.

φF1 = 0° (C+) φF2 = 45° (Tx)

FS1 FS2

δC4 = +5°

δC2 = -5°

V∞

(b) αc = 4°

Tail Fin Span

V∞

(d) αc = 12°

V∞

(c) αc = 8°

Body ShedVorticity

Tail Fin Span V∞

(a) αc = 0°

Figure 5.- Comparison of predicted and measuredrolling-moment aerodynamic characteristicsof acanard-tail configuration (Ref. 3) with:1) tails inlinewith canards (C+T+),2) tails interdigitated 45° (C+Tx), and3) tails free to rotate (C+T-free).


αc

Cl

0 10 20

-0.2

0

0.2

0.4

0.6 Exp. C+TxExp. C+T-freeMISL3 C+TxMISL3 canard onlyMISDL C+TxMISDL canard only

(b) Rolling-MomentCoefficient: C+Tx

Vortex-InducedRoll (Tail)

αc

Cl

0 10 20

-0.2

0

0.2

0.4

0.6 Exp. C+T+Exp. C+T-freeMISL3 C+T+MISL3 canard onlyMISDL C+T+MISDL canard only

(a) Rolling-MomentCoefficient: C+T+

Vortex-InducedRoll (Tail)

φF1 = 0° (C+) φF2 = 0° (T+)

FS1 FS2

δC4 = +5°

δC2 = -5°


αc

Cl

0 5 10 15

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Exp. C+T+Exp. C+T-freeMISL3 C+T+MISL3 canard onlyMISDL C+T+ M∞ = 1.70MISDL canard only M∞ = 1.70

M∞ = 1.70

Figure 8.- Comparison of predicted and measuredrolling-moment aerodynamic characteristicsof acanard-tail configuration (Ref. 3) withcanard yaw control: C+T+ and C+T-free.δYAW = -5°, M∞ = 1.70, 2.16, 2.86.

αc

Cl

0 5 10 15

-0.2

-0.1

0

0.1

0.2

0.3

0.4


M∞ = 2.16

αc

Cl

0 5 10 15

-0.2

-0.1

0

0.1

0.2

0.3

0.4


M∞ = 2.86

αc

p(ta

ilse

ctio

n)(r

pm)

0 5 10 15 20

-1000

-500

0 ExperimentMISL3MISDL

(c) Tail Fin Section Roll Rate (rpm)

αc

Clp

(tai

lsec

tion)

-5 0 5 10-60

-50

-40

-30

-20

-10

0

Exp. M∞ = 1.70MISL3 M∞ = 1.70MISDL M∞ = 1.70

(b) Tail Fin Section Roll Damping - Clp

φF2

Cl(t

ails

ectio

n)

0 60 120 180-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

αc = 0° C+T(φF2)αc = 4° C+T(φF2)αc = 8° C+T(φF2)αc =12° C+T(φF2)

(a) Tail Fin Section Cl vs. φF2

Stable Roll Positions ⇒ "roll lock"

α = 12°

Figure7.- Comparison of predicted and measuredtail section aerodynamic characteristics,M∞ = 1.7, φ = 0°, δC2 = -5°, δC4 = +5,tail free to rotate, Ref. 3.

φF1 = 0° (C+) φF2 = 45° (Tx)

FS1 FS2

δC1 = +5°

δC3 = +5°

φF1 = 0° (C+) φF2 = 45° (Tx)

FS1 FS2

αc

Cl

0 5 10 15

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Exp. C+TxExp. C+T-freeMISL3 C+TxMISL3 canard onlyMISDL C+Tx M∞ = 1.70MISDL canard only M∞ = 1.70

M∞ = 1.70

αc

Cl

0 5 10 15

-0.2

-0.1

0

0.1

0.2

0.3

0.4


M∞ = 2.16

αc

Cl

0 5 10 15

-0.2

-0.1

0

0.1

0.2

0.3

0.4


M∞ = 2.86

Figure 9.- Comparison of predicted and measuredrolling-moment aerodynamic characteristicsof acanard-tail configuration (Ref. 3) withcanard yaw control: C+Tx and C+T-free.δYAW = -5°, M∞ = 1.70, 2.16, 2.86.

Figure10.- Comparison of predicted and measuredtail section aerodynamic characteristics,M∞ = 1.70, 2.16, 2.86, φ = 0°, δYAW = -5°,tail free to rotate, Ref. 3.


φF2

Cl

0 50 100 150-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

α = -4° C+T(φF2)α = 4° C+T(φF2)α = 8° C+T(φF2)α = 14° C+T(φF2)

M∞ = 1.70

Stable Roll Positions⇒ "roll lock"

(a) Tail Fin Section Cl vs. φF2

δC1 = +5°

δC3 = +5°

αc

Clp

-5 0 5 10

-50

-25

0

Exp. M∞ = 1.70Exp. M∞ = 2.16Exp. M∞ = 2.86MISL3 M∞ = 1.70MISL3 M∞ = 2.16MISL3 M∞ = 2.86MISDL M∞ = 1.70MISDL M∞ = 2.16MISDL M∞ = 2.86

(b) Tail Fin SectionRoll Damping - Clp

αc

p(r

pm)

-5 0 5 10 15

-600

-400

-200

0

200

400

600

800

1000

Exp. M∞ = 1.70Exp. M∞ = 2.16Exp. M∞ = 2.86MISL3 M∞ = 1.70MISL3 M∞ = 2.16MISL3 M∞ = 2.86MISDL M∞ = 1.70MISDL M∞ = 2.16MISDL M∞ = 2.86

(c) Tail Fin Section Roll Rate (rpm)

Documents

Aerodynamic Characteristics of Tandem-control and Rolling ... · used for the analysis. Results presented include highcontrolled missile models with fixed and free-rolling tail angle