Analysis and Test of a Staggered Multiple Tail

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(c)l999 American Institute of Aeronautics & Astronautics

A99-16394

AIAA-99-0513Analysis and Test of a StaggeredMultiple-Tail

Y. Elimelech and A. SigalTechnion - Israel Institute of TechnologyHaifa, Israel

37th AIAA Aerospace SciencesMeeting and ExhibitJanuary 11-14, 1999 / Reno, NVFor permission to copy or republish, contact the American Institute of Aeronautics and Astronautics1801 Alexander Bell Drive, Suite 500, Reston, VA 20191


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derivatives of the body alone from those of theconfigurations.G&-WV = C,,JC) + C,(B) (3)Cma(WV = GJC>v + Cm,Wv

The contributions of the body alone wereobtained from the British ESDU4 database.Then, the normal-force and thepitching-moment curve slopes of theconfigurations were calculated by adding thecontributions of the body alone to those of thetail units. A correction, which accounts for themasking effect of the body boundary layer onthe fins, was included, as described in Ref. 3.CP.,JC)~ = G,(Wdb + 1 GJWC,a(C)H = G,(Wdb + rl Gn,UU>xcp d = -Gnu /Crq,

(4)

ResultsThe baseline generic configuration that wasselected for this study is depicted in Fig. 2. Itfeatures a tangent ogive cylinder body having afineness-ratio of 12.5. The six-fin tail has aninclusive span of 1013 body diameters and aroot chord of 713 diameters . The aspect ratio is4/3, the taper ratio is 0.5, and the leading edgeis swept 45 deg. The thickness of the fins isabout 0.07 diameters, and the leading edgesand the trailing edges are beveled a t aninclusive angle of 10 deg. Four staggeredconfigurations were obtained by shifting threealternate fins forward 0.5, 1 O, 1.5, and 2.0 rootchords. The designations of theseconfigurations are also given in Fig. 2. Thereference length and area are center bodydiameter and cross-sectional area, respectively.The reference point for moments is the centerof the body, namely 6.25 diameters from thetip.In the vicinity of Mach number of 1.4 theVorlax code fails, because the leading-edgesweep is close to the Mach angle. Fairing ofthe normal-force curve slope through thisregion was done with the normal-force curveslope of a plane wing, composed of a pair oftail fins, as a guideline.The results of the analysis are presented in thetwo parts of Fig. 3. The subsonic branchesinclude tail correction factor of q=O.96, whichcorresponds to the test conditions that will bediscussed in the next chapter. At the subsonicregion, stagger Pl increases the normal-forcecurve s lope by 4.5%, while P2 to P4 increase itby1 1%. The analytical results in the supersonicrange do not show a~monotonous trend, but

cross each other. The width of the bandcontaining the normal-force curve slopes of thestaggered configurations is about 2.8 units, andthe average increase, relative to that of thebaseline configuration is 12% to 9%.The Experimental Investigation

The Wind Tunnel ModelsThe model consists of a comm on main bodyand five interchangeable modular tail units.Sleeves were used to complete the shape of theafterbodies to perfect cylinders. Each tail unitwas machined as an integral part. For details,see the general assembly of the baselineconfiguration, which is depicted in Fig. 3.Wind-Tunnel and Test ConditionsThe tests were-carried out in the transonic windtunnel of the Faculty of Aerospace Engineeringat the Technion. This is a closed cycle, ejectordriven facility. The test section is 60 cm wideby 80 cm high. The floor and the ceiling areperforated. Each model was tested in the Rlroll orientation at Mach numbers of 0.75 and1.11 and at a Mach sweep at a nominal angleof attack of 3.0 deg. Configurations PO and P3were tested also in the R2 position. Reynoldsnumber, based on body diameter, was about0.45 106. A six-component sting balance wasused to measure the loads. Pressure probesmeasured the base pressures, enabling theevaluation of the base drag coefficient.The Longitudinal CharacteristicsFig. 5 shows the longitudinal characteristics ofthe five configurations at Mach number of0.75. It is apparent that the stagger increasesboth the normal-force curve slope and thenon-linearity of the curves. The normal-forcecoefficient curves of configurations P2 to P4coincide. Increase of stagger result lessnegative pitching-moment curve slopes,indicating the expected forward shift of thecenter of pressure. Results of tests in the R2roll position practically coincide withcorresponding results in the Rl position.The stability derivatives were obtained byfitting straight lines to the linear sections of thenormal-force coefficient vs. angle of attack andthe pitching-moment vs. normal-forcecoefficients. The results are compared with theanalytical predictions in Figs. 3 and 4. AtM=0.75, the experimentally obtainednormal-force curve slope is lower than thatcalculated by 15% for the baselineconfiguration to 5% for configuration P4.Nevertheless, the test results show theexpected trend due to staggering - an increase

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of 20% in the normal-force curve slopes ofconfigurations P2 to P4. The agreement incenter of pressure location is very good. Theexperimentally obtained results at M=l .I 1show an even larger effect of staggering - a25% increase in the normal-force curve slope.The Axial-ForceFig. 7 shows the dependence of the axial-forcecoefficient (base contribution excluded) uponMach number for the body alone, and thebaseline configuration with 3 and 6 fins. In thesubsonic region, the contribution of 6 finsamounts to 3-4 times that of 3 fins. Dragdivergence Mach numbers (defined bydCx/dM=0.2) with 3 and 6 fins are 0.88 and0.84, respectively. Fig. 8 shows the effect ofstagger on the axial-force coefficient. It isapparent that in the subsonic range staggeringdecreases the axial-force coefficient, relative tothat of the baseline configuration, by about12%. It also increases the drag divergenceMach number from 0.84 to 0.88 and 0.89 forconfigurations Pl and P2, respectively.Staggering strongly decreases the axial-forcecoefficient in the transonic range.

Summary and ConclusionsThe longitudinal aerodynamic characteristicsof a generic configuration with a six-fin tailwere analyzed using a hybrid method. Theresults show that adding stagger to the tail unitincreases the normal-force curve slope.

Wind tunnel tests at Mach numbers o f 0.75 and1.11 verify the analytical prediction and showthat staggering also has favorable effects onthe axial-force coefficient, especially in thetransonic range.References

Nielsen, J. N., Missile Aerodynamics,NEAR, Inc., Mountain View, CA, 1988.Sigal, A., A Hybrid Method fo r theAnalysis of Multiple-Tail Configurations,AIAA-93-3655, Aug. 1993.Miranda, L. R., Elliot R. D., and Baker W .M., A Generalized Vortex LatticeMethod for Subsonic and SupersonicFlow, NASA CR 2865, 1977.Anon., Computer Program forCalculations of Normal Force and PitchingMoment of Forebody-cylinderCombinations at Angle of Attack up to 90degrees and Mach Numbers up to 5,ESDU Data Item No. 90034, ESDUInternational Plc., London, UK, 1983.

2.5- ak=0.61

-I2 4 6 6 10

n

Fig. 1 The dependence of the normal-force curve slope of a slender tail uniton the number of fins.

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a)

b)


RI

74.7400 7/3D

I2.5D

L-4XST

3lf.2_I) _ 032DRZ

0.4 0.8 1.2 1.6 2M

Fig. 2 Schematic of the configurations: a) the baseline, andb) the staggered arrangements. ~

-baseline--- stagger PI. . . . . . stagger P2-.-. stagger P3-..- stagger P4

0 test, M=0.75I O test, M=l .I 1

?

t

0 : -------f -.-___.fj -3 -.. .._.. -0-----W.-i-.---- - _____ ._.-..--_0-t -.:.- _....._._. . ._.__...x m----o. 04 ____----:. . ..-- g+-.r~.::---

-5 -..-..--i--------;..----.-~---.---.b, -6

M-

Fig. 3 The stability derivatives of the staggered configurations: a) normal-forcecurve slope, and b) center of pressure location.4


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0.80

0.60

0 0.40

0.20

0.000.40 0.60 0.80 1.00 -120

M

Fig. 7 The axial-force coefficient of the baseline configuration.

0.80

0.60

G 0.40

0.20

0.00

o baseline I: :

0.40 0.60 0.80 1.00 ,I~.20M

Fig. 8 The axial-force coefficient of the staggered configurations.

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Analysis and Test of a Staggered Multiple Tail