AIAA 99–1020 Subsonic Static and Dynamic Aerodynamics of Blunt Entry Vehicles Robert A. Mitcheltree , Charles M. Fremaux, NASA Langley Research Center, Hampton, Virginia Leslie A. Yates, AerospaceComputing, Los Altos, California 37th Aerospace Sciences Meeting and Exhibit January 11–14, 1999/Reno, Nevada Forpermissiontocopyorrepublish,contacttheAmericanInstituteofAeronauticsandAstronautics 1801AlexanderBellDrive,Suite500,Reston,VA22091 Subsonic Static and Dynamic Aerodynamics of Blunt Entry Vehicles (cid:3) y Robert A. Mitcheltree , Charles M. Fremaux, NASA Langley Research Center, Hampton, Virginia z Leslie A. Yates, AerospaceComputing, Los Altos, California The incompressible subsonic aerodynamicsof four entry-vehicle shapes with variable c.g. locations are examined in the Langley 20-Foot Vertical Spin Tunnel. The shapes examined are spherically-blunted cones with half-cone angles of 30, 45, and 60 deg. The nosebluntnessvariesbetween0.25and0.5timesthebasediameter. TheReynoldsnumber based on model diameter for these tests is near 500,000. Quantitative data on attitude and location are collected using a video-based data acquisition system and reduced with a six deg-of-freedom inverse method. All of the shapes examined su(cid:11)ered from strong dynamic instabilities which could produced limit cycles with su(cid:14)cient amplitudes to overcomestaticstabilityofthecon(cid:12)guration. Increasingconehalf-angleornosebluntness increases drag but decreases static and dynamicstability. Nomenclature (cid:27) =ratioof air density at altitude to that at sea level 2 2 A1;A2;A3 = coe(cid:14)cients in velocity (cid:12)t (Eq. 5) (cid:23) = kinematic viscosity at altitude, m =2s 2 (cid:23)0 = kinematic viscosity at sea level, m =s CD = drag force coe(cid:14)cient CD;0;CD(cid:11)2 = drag force coe(cid:14)cient terms (Eq. 1) (cid:21) = radius of gyration Ix=M, m p CL = Lift force coe(cid:14)cient CL0;CL(cid:11);CL(cid:11)3 = lift coe(cid:14)cient terms (Eq. 2) Introduction Cm = moment coe(cid:14)cient referenced to c.g. Selection of the aeroshell shape for an entry vehi- Cm0;Cm(cid:11);Cm(cid:11)3 = moment coe(cid:14)cient terms (Eq. 3) cleis usuallydrivenbytheneed forhigh aerodynamic Cmq = dynamic damping derivative drag, low aerothermal heating, and su(cid:14)cient aerody- Cmq;0;Cmq;(cid:11)2 = damping derivative terms (Eq. 4) (cid:3) namic stability. Fortunately, shapes such as blunted, Cmq =simpli(cid:12)eddynamicstabilityparameter(Eq. 6) large-angle cones which have high drag also minimize D = maximum body diameter, m 2 the aerothermal heating environment. Blunted large Ix = moment of inertia about the x-axis, kg(cid:0)m 2 anglecones,however,cansu(cid:11)eraerodynamicstability Iy = moment of inertia about the y-axis, kg(cid:0)m 2 problems if the packagingof the vehicle’s payload can Iz = moment of inertia about the z-axis, kg(cid:0)m not position the center-of-gravity (c.g.) close to the M = model mass, kg vehicle’s nose. N = model to vehicle length scale factor The aerodynamic stability of a blunted, large-angle ReD = Reynolds number based on diameter cone varies across the speed regimes. At hypersonic Rn = model nose radius, m continuumconditions,bluntshapesexhibitacceptable t = time, sec stability even for a c.g. position behind the maxi- V = free stream velocity, m=s mum diameter location of the aeroshell. At transonic x;y;z = coordinate directions, m speeds, such a c.g. position is accompanied by a zc:g: = distance center-of-gravityis aft of nose, m 1;2 bounded dynamic instability which will induce os- (cid:11) - total angle of attack, deg: cillatory motions. At subsonic speeds, the strength of (cid:2) = Pitch angle, deg: thedynamicinstabilitycanovercomethestaticstabil- (cid:9) = Yaw angle, deg ity causing the vehicle’s oscillations to diverge into a 3 tumbling motion. Therefore,the c.g. requirementfor (cid:3) Aerospace Engineer, Aerothermodynamics Branch, Aero- an entry vehicle whose entry pro(cid:12)le includes subsonic and Gas Dynamics Division, NASA Langley Research Center, SeniorMemberAIAA. (cid:13)ightisdrivenbythesubsonicdynamicstabilityofthe y Aerospace Engineer, Vehicle DynamicsBranch, Flight Dy- aeroshell. namicsand Control Division,NASALangley Research Center, The low-speed dynamics of blunt entry vehicle SeniormemberAIAA. z shapes were studied in the late 1960’s and early Vice President Aerospace Computing, Los Altos, CA., Se- niormemberAIAA 1970’s as the planetary entry probes for Mars-Viking, Copyright(cid:13)c1999bytheAmericanInstituteofAeronautics Pioneer-Venus, and Galileo-Jupiter were designed. and Astronautics, Inc. No copyright is asserted in the United These studies included tests in the NASA Lang- States under Title 17, U.S. Code. The U.S. Government has 4(cid:0)6 ley 20-Foot Vertical Spin Tunnel , horizontal wind a royalty-free license to exercise all rights under the copyright 7;8 9;10 11 claimedherein for governmental purposes. Allother rights are tunnels ,droptests ,and(cid:13)ighttests . Astheer- reservedbythe copyrightowner. raticdynamicbehaviorofhigh-dragbodiesinsubsonic 1of9 AmericanInstitute ofAeronauticsandAstronauticsPaper99{1020 Table1 Model Geometry,Mass andc.g. Location Table 2 Model Mass Inertias 2 2 2 Case Cone (deg) Rn=D M, kg zc:g:=D Case Ix (kg-m ) Iy (kg-m ) Iz (kg-m ) 3050a 30 0.50 1.378 0.357 3050a 0.0113 0.0108 0.0159 3050b 30 0.50 1.377 0.329 3050b 0.0108 0.0103 0.0159 4525b 45 0.25 1.373 0.354 4525b 0.0104 0.0101 0.0152 4525c 45 0.25 1.355 0.324 4525c 0.0109 0.0103 0.0137 4550b 45 0.50 1.355 0.250 4050b 0.0104 0.0099 0.0152 4550c 45 0.50 1.370 0.266 4550c 0.0104 0.0099 0.0152 6025a 60 0.25 1.552 0.230 6025a 0.0105 0.0099 0.0182 6025b 60 0.25 1.481 0.246 6025b 0.0105 0.0098 0.0176 (and transonic) (cid:13)ows was revealed, entry systems de- signers sometimes chose to avoid these (cid:13)ight regimes Table 3 Dynamic Scaling Relationships by deploying parachutes at supersonic speeds. These Parameter Scale Factor earlier studies also revealed the necessity of dynamic Linear Dimension N testing to determine the stability of blunt shapes in Relative Density 1 transonic and subsonic (cid:13)ows. A vehicle whose static Froude Number 1 stabilityappearsacceptablefromstatic-stingmounted 3 Mass N =(cid:27) wind tunnel tests may possess dynamic instabilities 5 Moment of Inertia N =(cid:27) which ca3n lead to unacceptable or divergent behavior Linear Velocity N1=2 in (cid:13)ight . Linear Acceleration 1 The objective of the present workis to examine the 1=2 Angular Velocity 1=N incompressiblesubsonicdynamicsoffourentry-vehicle 1=2 Time N shapes with variable c.g. locations in the Langley 20- 3=2 Reynolds Number N (cid:23)=(cid:23)0 Foot Vertical Spin Tunnel. The shapes examined are spherically-blunted cones with half-cone angles of 30, 45,and60deg. Thenosebluntnessvariesbetween0.25 Inertiaswere adjusted by the addition of weightsto and 0.5 times the base diameter. Quantitative data represent scaled (cid:13)ight values of designs with centrally on model attitude and position are collected using a positioned payloads. Free (cid:13)ying models tested in the video-baseddataacquisitionsystemandreducedwith Spin Tunnel can be dynamically scaled using the dy- a six deg-of-freedom (6DOF) inverse method. Repre- namic scaling parameters in Table 3. The dimensions sentativedataat twoc.g. locationsforeachshape are ofmass, length, andtimearescaledsothatthemodel presented as well as the results of the data reduction resultsmaybeapplieddirectlytopredictthebehavior calculations. ofafull-scalevehicle. Inthisprocess,timeisscaledon the basis of equal Froude number, length on the basis Geometries and Dynamically-Scaled of similar geometry, and mass properties by assuming equalrelativedensity, (i.e.,theratioofvehicledensity Models to air density at the desired altitude). Full scale val- The four geometries examined are the spherically uesareobtainedbydividingmodelvaluesbythelisted blunted cones presented in Fig.1. Two di(cid:11)erent c.g. scalefactors. Adetaileddiscussionofdynamicscaling locations are examined for each geometry. The c.g. may be found in Ref. 12. locationsselected areon the geometricsymmetryaxis TheReynoldsnumbersbasedonmodeldiameterfor and positioned just forward of the neutral dynamic the present tests were 440,000 to 526,000. The back- stability point. C.g. locations are measured from the wardsfacingstepafterbodywaschosentoanchor(cid:13)ow actual nose of the model. The eight cases for which seperationpoints in anattempt tominimize Reynolds data collection and reduction areperformed are listed number e(cid:11)ects. in Table 1. The (cid:12)rst entry in the table is the case designator. Table 2 presents the associated moments Vertical Spin Tunnel and Data of inertia. The models were constructed of high density foam Acquisition and(cid:12)berglassintwosections. All modelsusedacom- The Langley 20-Foot Vertical Spin Tunnel is an at- monafterbodysectionwhichincludedthemechanism mospheric, annular return, vertical wind tunnel. The tovarythemodel’sc.g. location. Themaximumdiam- test section is 20 feet across and 25 feet in length. A eterofallmodelswas0.355mandeachhadashoulder 400hpelectricmotor(1300hpforshortperiods)turns radius (between forebody and afterbody) of 0.009m. a 3-bladed, (cid:12)xed pitch fan to produce speeds of up to 2of9 AmericanInstitute ofAeronauticsandAstronauticsPaper99{1020 27 m/s, with a maximum acceleration and decelera- Data Reduction 2 2 tion capability of 4.6 m/s and 7.6m/s , respectively. The MSPS position and attitude data for each case The present tests were run at speeds between 18 and were analyzed using a 6 degree-of-freedom parameter 15 22 m/s. Figure 2 presents a schematic of the facility. identi(cid:12)cation routine, CADRA2 . For the present A complete description may be found in Ref. 13. application,CADRA2 identi(cid:12)esparametersinexpres- For the tests, a lightweight tether system was used sionsfortheaerodynamiccoe(cid:14)cientsutilizingthenon- to reduce model damage from impact with the tun- linear approach outlined in Ref. 16. The expressions nel walls. A smooth metal ring was suspended in the fortheaerodynamiccoe(cid:14)cientsforthisaxisymmetric, center of the test section using guy wires. The tether low speed study are: wasattachedto therearfaceoftheafterbody, routed 2 through the metal ring, and attached to the tunnel CD =CD0 +CD(cid:11)2sin (cid:11) (1) wall. At the beginning of a test, the model was sus- 3 pended on the tether with the tunnel fan stopped. As CL =CL0 +CL(cid:11)sin(cid:11)+CL(cid:11)3sin (cid:11) (2) thetunnelwasbroughtuptospeed,thetetherbecame 3 Cm =Cm0 +Cm(cid:11)sin(cid:11)+Cm(cid:11)3sin (cid:11) (3) slack when model drag equaled the model weight (see 2 Fig. 2). The tether appeared to have little in(cid:13)uence Cmq =Cmq;0 +Cmq;(cid:11)2sin (cid:11) (4) on the model motions. where the usual Mach number terms, used in bal- Standard videotapes are made to document each listics range studies, have been omitted. The absence test and aid in qualitative analysis. However, pri- oftime-varyingvelocityinformation in thedataintro- mary data for tests of free-(cid:13)ying models are 6 degree- duced di(cid:14)culties in the identi(cid:12)cation of the nonlinear of-freedom (6DOF) motion time histories, obtained terms. Consequently, the data were also reduced as- via the Spin Tunnel Model Space Positioning Sys- suming linear aerodynamics by neglecting the higher tem (MSPS). The MSPS is a non-intrusive, computer order terms in the above expressions. workstation-basedsystem that uses two video camera In an attempt to discernthe velocityvariationsand views of retro-re(cid:13)ective targets attached to known lo- reveal the nonlinear aerodynamics, the velocity was cations on a model to generate post-test estimates of modeled as model attitude and position at a sample rate of 60 Hz. The angles of oscillations are pitch and yaw con- V =V0+ dz +A1t+A2t2+A3t3 (5) sistent with aircraft de(cid:12)nitions where the nose of the dt equivalent aircraft is at the nose of the capsule. The withthecoe(cid:14)cientsofthisexpressionaddedtothelist accuracy of angles reported by MSPS is within plus of parametersto be identi(cid:12)ed by CADRA2. or minus one deg of the actual values. However, due Due to the uncertaintyin velocityvariationsduring to the small size of the models (diameter of 0.355 m), the test, the estimated errors for the coe(cid:14)cients pre- the accuracy of the system was degraded. No error dicted are 10% for drag, 5% for moment coe(cid:14)cient, analysis for the current tests was performed, but it is and plus or minus 0.01 for the damping coe(cid:14)cients. believed that the angle values reported in this docu- ment are to within plus or minus two deg. Stability, Limit Cycles, and Divergence Data acquisition using the MSPS system begins at Stability can be de(cid:12)ned in various ways, however, a time speci(cid:12)ed by the operator during a test run. de(cid:12)ning the acceptable stability fornonlinear systems As such,the beginningofthe plots(t=0)containedin such as oscillating aeroshells is di(cid:14)cult. Typically, thisreportcorrespondstoanarbitrarypointinthetest whenthec.g. locationofanaeroshell(likethoseshown butoftenfollowedanintentionalperturbationofmodel in Fig. 1) is very closetoits nose, the vehicledisplays attitude. Forthepresenttests,lossoftracksometimes stablesubsonicbehavior. Anyperturbationinattitude occurredwhenthemodelwasrolledorpitchedtosuch is decayed until it vanishes. As the c.g. is moved aft a large angle that the targets were no longer visible. fromthenose,amarginallystablebehavioremergesin Visual review of the corresponding test videotape is which a limit cycle oscillation exists. In addition, the used to supplement the data provided by MSPS for stabilityofmostbluntaeroshellswillbifurcateintobi- this purpose. Reference14providesfurtherdiscussion stability: capableofstable(cid:13)ightinbothaforwardand of the MSPS system. backwardsorientation. Atthispoint,theamplitudeof Test section velocity is not recorded by the video- aperturbationfromwhichthevehiclecansuccessfully based MSPS system. It can be obtained using pitot- return to a forwardfacing attitude becomes bounded. static pressure probes as well as a temperature probe As the c.g. location is moved further aft, the ampli- protruding from the tunnel walls. The calculated air- tudeofthelimitcycleincreasesandtheamplitudeofa speedisusedtodeterminetheaverageequilibriumsink allowableperturbationwhichreturnstoaforwardori- rateof the free-(cid:13)ying model. Velocity is varied during entation decreases. As the c.g. is moved even further the test to maintain the model in the test section. aft, an initially forward orientation will divergeinto a 3of9 AmericanInstitute ofAeronauticsandAstronauticsPaper99{1020 tumbling motion which, depending on the afterbody predictionfortheneutrallydynamicstabilityforac.g. shape, may or may not seek a backwardsorientation. locationat0.387diametersbackfromthenoseforthis The oscillatory motion of a blunt entry vehicle in 30-deghalf-anglegeometry. Thelocationofmaximum subsonic terminal descent is analogous to that of a diameter is 0.373diameters back from the nose. nonlinear mass-spring-damper system. In this anal- Figures 5 and 6 present the oscillations associated ogy, static stability correspondsto the spring sti(cid:11)ness with the 45 deg half-angle cone model whose nose and dynamic stability corresponds to the damper’s radius is 0.25 times the base diameter. The oscilla- characteristics. The dynamic damping of an aeroshell tions in Fig. 5 show no indication of decay. This is highly nonlinear and can be destabilizing at small geometry and c.g. combination is either unstable or angle-of-attack and stable for larger angles which (if seekingalimitcyclewhoseamplitudeisslightlylarger statically stable) leads to limit cycle behavior. The than the amplitudeoftheobservedoscillations: afact (cid:3) amplitude of the limit cycle and the amplitude of a con(cid:12)rmed by the slightly positive value for Cm;q in perturbation which does not result in a tumbling mo- Table 4. The amplitude of the (cid:12)nal limit cycle this tion is a function of the dynamic stability, the static c.g. location will produce for this geometry is esti- stability, and the mass properties of the vehicle. mated at 20 - 25 deg. Both of these cases appear to have large velocity variations during the test pe- Results and Observations riod. Since the velocity was not recorded as part of The pitch, (cid:2), and yaw, (cid:9), angles measured in the the data, the 6DOF data reduction is unable to dis- eight cases examined are presented in Figs. 3-10. In tinguish nonlinearaerodynamiccoe(cid:14)cientvariations. mostcases,themodelwasperturbedpriortot=0and A prediction of the neutral dynamic stability point themotionpresentedisthedecayofthatperturbation. is for a c.g. location of 0.346. This extrapolation Forclarity,the60-Hzdiscretedataispresentedinline compares favorably with a qualitative observation of form. Gaps during data collection produce the inter- the c.g. location behind which divergence occurs. In spersed linear segments in Figs 5,6,7, and 10. particular, for c.g. locations at 0.325 diameters, all Figures3and4presenttheoscillationsobservedfor perturbations were damped. For c.g. locations at two di(cid:11)erent c.g. locations for the 30-deg half angle 0.345to0.358diameters,smallperturbationsdamped cone with nose radius equal to half of the base diam- while large variations diverged. When the c.g. posi- eter (con(cid:12)guration 3050). The large amplitude of the tion was positioned at 0.391 diameters back from the oscillations in (cid:12)gure 3 is an indication of the size of nose, the model diverged without perturbation. The the initial perturbationpriorto data collection. Com- locationofmaximumdiameteris0.407diametersback parison of the frequency of oscillation between Fig. 3 from the nose. andFig. 4indicatesthatboth c.g. locationsarestati- Figures 7 and 8 present the oscillation for the 45 callystablewithFig. 4indicatingthehigherfrequency deg half angle cone with nose radius equal to half (cid:3) (larger negative Cm;(cid:11)). of the base diameter. The values predicted for Cm;q Despite the aparent growth in (cid:9) in Fig. 4, the in Table 4 are both negative, and the observation of amplitutde of the total angle-of-attack oscillation is the motions during the test indicate that these were decayinginFig. 3and4. Thisdecayindicatesdynam- both non-divergent con(cid:12)gurations (i.e. bounded limit ically stable con(cid:12)gurations. Reducing this data with cycles). The trend of dynamic damping with c.g. lo- linear and nonlinear aerodynamic coe(cid:14)cients and (cid:12)ts cation for con(cid:12)guration 4550 in Table 4, however, is tothevelocityvariationsproducedminimaldi(cid:11)erences incorrect. Thisreversalisduetotheuncertaintyinthe in the predicted aerodynamics. The data do not indi- data reduction for this parameter. It is not possible cate the vehicle is in a limit cycle. The amplitude of to extrapolate these quantitative values to determine thelimitcycle,ifoneexists,issmallerthantheangles theneutraldynamicstabilityc.g. location. Additional measured during the test. Table 4 presents a predic- variationofthemodel’sc.g. locationtofurtheraftpo- tion of the aerodynamic coe(cid:14)cients assuming linear sitions (i.e. test cases not listed in Table 1) revealed coe(cid:14)cients and no velocity variation. Table 5 present that for c.g. locations at 0.274 and .278 diameters the predictions when the velocity model of Eq. 5 is back from the nose, the vehicle assumed a limit cycle used. The value presented as damping is the term: aftersmallperturbationsbut coulddivergeafter large 2 perturbations. For a c.g. location of 0.288, the model (cid:3) (cid:21) Cm;q =Cm;q(cid:0) CL;(cid:11) (6) diverged without perturbation. The location of the (cid:18)D(cid:19) maximum diameter is 0.303 diameters back from the (cid:3) Cm;q is a simpli(cid:12)ed form of the dynamic stability pa- nose. 19 rameter for terminal descent. If it is negative the Figures 9 and 10 present the 60 deg half-angle cone oscillations are damped and decaying. The values for cases. For both c.g. locations examined, the mod- (cid:3) Cm;q given in Tables 4 and 5 are average values for els appear to be at or near limit cycle behavior with (cid:3) the current state of the oscillations. Assuming a lin- amplitude 25-30 deg. Again the trend in Cm;q is re- (cid:3) ear variation in Cm;q with c.g. location results in a versedmakingitimpossibletopredictthec.g. location 4of9 AmericanInstitute ofAeronauticsandAstronauticsPaper99{1020 nonlinear terms from Eqs. 1-4 did little to improve Table4 AerodynamicCoe(cid:14)cients: :Linearresults the (cid:12)ts to the data. In addition, with the large am- without velocity variations plitudemotionsexhibitedbymanyofthetests, higher (cid:3) order terms may be required in Eqs 1-4 Case zc:g:=D CD;0 Cm;(cid:11) Cm;q 3050a 0.357 0.5011 -0.0984 -0.015 Conclusions 3050b 0.329 0.5083 -0.1122 -0.029 The incompressible subsonic aerodynamics of four 4525b 0.354 0.6218 -0.0791 +0.005 entry-vehicle shapes with variable c.g. locations were 4525c 0.324 0.5973 -0.0923 -0.013 examined in the Langley 20-Foot Vertical Spin Tun- 4550b 0.250 0.6820 -0.1459 -0.005 nel. Quantitative data on attitude and position are 4550c 0.266 0.6606 -0.1295 -0.010 collected using a video-based data acquisition system 6025a 0.230 0.7537 -0.1187 +0.003 andreducedwithasixdeg-of-freedom(6DOF)inverse 6025b 0.246 0.7150 -0.1068 +0.002 method. Subsonic drag increases with increasing cone half- angle and nose bluntness. The drag coe(cid:14)cient of a 45 degree half-angle cone is 33 percent higher than Table5 AerodynamicCoe(cid:14)cients: :Linearresults with velocity variation a 30 degree half-angle cone when both have a nose radiusequaltohalftheirbasediameter. A60degcone (cid:3) Case zc:g:=D CD;0 Cm;(cid:11) Cm;q exhibits 20 percent higher drag than a 45-deg cone 3050a 0.357 0.5069 -0.0984 -0.018 whenbothhaveanoseradiusequalto0.25timestheir 3050b 0.329 0.4809 -0.1098 -0.027 basediameter. Fora45deghalf-anglecone,increasing 4525b 0.354 0.6251 -0.0794 +0.004 the nose radius from 0.25 to 0.50 times the diameter 4525c 0.324 0.5988 -0.0924 -0.016 increases the drag 10 percent. 4550b 0.250 0.6681 -0.1434 -0.004 Staticstability,asmeasuredbythemagnitudeofthe 4550c 0.266 0.6512 -0.1276 -0.009 moment coe(cid:14)cient slope, decreases with movement of 6025a 0.230 0.7554 -0.1187 +0.003 thec.g. awayfromthenose. Thisdecreaseinstability 6025b 0.246 0.7072 -0.1060 +0.002 occurs more rapidly when the cone half-angle or the degree of nose bluntness is increased. Theabilityofastaticallystablebluntshapetodecay for neutral dynamic stability. Variation in c.g. loca- perturbations (its dynamic stability) decreases with tionfromadditionaltestingindicateaneutralstability movement of the c.g. away from the nose. Decreased point near 0.260 diameters back from the nose. This dynamic stability isaccompanied by the emergenceof valueissmallerthanthe0.29valuedeterminedinRef. limit cycle oscillations. The amplitude of these oscil- 3 for a geometry with the same forebody shape but lations increase with movement of the c.g. away from larger afterbody shell. (The radius of gyration nor- the nose. In addition, the magnitude of a perturba- malized by diameter ((cid:21)=D) for the present model was tionwhichdoesnotresultindivergencedecreaseswith 0.230 compared to the larger value of 0.252 examined movement of the c.g. away from the nose. All of the inRef. 3.) Thelocationofmaximumdiameterforthis shapes examined su(cid:11)ered from strong dynamic insta- geometry is 0.265 diameters back from the nose. bilities which (if the c.g. was moved su(cid:14)ciently back A static wind tunnel test of the 60-deg half angle from the nose) could produce limit cycles with suf- 6 cone in Ref. 18, at ReD = 1(cid:2)10 , predicted a zero (cid:12)cient amplitudes to overcome static stability of the angle drag coe(cid:14)cient of 0.81 which is higher than the con(cid:12)guration. In particular, the onset of uncontrolled present prediction of 0.70 { 0.75. tumbling motion was caused by dynamic instabilities The e(cid:11)ect of cone half angle and nose bluntness on even while the models possessed static stability. drag is presented in Fig. 11. Figure 12 compares The use of a parameter identi(cid:12)cation routine to the static stability of the eight cases examined as a extract non-linear aerodynamic coe(cid:14)cients from free function of c.g. location. In this (cid:12)gure, the two c.g. (cid:13)ightmotion historiesfromaverticalwind tunnel, re- locationsforeachmodelareconnectedwithalineand quiressimultaneousmeasurementofthevelocityvaria- labeled with the geometry identi(cid:12)er from Table 1. A tions. Inaddition,theexpressionsfortheaerodynamic similar comparison for the dynamic damping parame- coe(cid:14)cients mayrequirehigh orderterms than consid- ter is presented in Fig. 13. When comparing stability ered in the present work. of two di(cid:11)erent shapes, it should be remembered that thelengthfromnosetomaximumdiameterisdi(cid:11)erent References 1 for each shape. Uselton, B. L.; Shadow, T. O.; and Mans(cid:12)eld, A. Attempts to extract nonlinear aerodynamic coe(cid:14)- C.: \DampinginPitchDerivativesof120and140Deg cients from the data were suspect as a result of the Blunted Cones at Mach Numbers 0.6 through 3.0," interaction with velocity variation. The inclusion of AEDC TR-70-49,1970. 5of9 AmericanInstitute ofAeronauticsandAstronauticsPaper99{1020 2 17 Marko, W. J.:\TransonicDynamic and Static Sta- Chapman,G.T.,Yates,L.A.,\DynamicsofPlan- bility Characteristics of Three Blunt-Cone Planetary etary Probes: Design and Testing Issues," AIAA 98- Entry Shapes," NASA CR-107405, JPL TR 32-1357, 0797, Jan. 1998. 18 Sept., 1969. Mitcheltree,R.A.,StardustAeroDatabasepaper 3 Mitcheltree,R.A.,andFremaux,C.M.,\Subsonic DynamicsofStardustSampleReturnCapsule,"NASA TM 110329,March, 1997. 4 Bendura,R.J.:\LowSubsonicStaticandDynamic 0 StabilityCharacteristicsofTwoBlunt120 ConeCon- (cid:12)gurations," NASA TN D-3853, Feb., 1967. 5 Costigan, P. J.:\Dynamic-Model Study of Planetary-Entry Con(cid:12)gurations in the Langley Spin Tunnel," NASA TN D-3499, July, 1966. 6 Cahen, G. L.: \E(cid:11)ects of Shape and Mass Prop- erties on Subsonic Dynamics of Planetary Probes," Journal of Spacecraft and Rockets, Vol. 12, No. 8, Aug., 1975. 7 Marte, J. E.; and Weaver, R. W.:\Low Subsonic Dynamic-Stability Investigation of Several Planetary- EntryCon(cid:12)gurationsinaVerticalWindTunnel(Part I)," JPL TR 32-743, May, 1965. 8 Ja(cid:11)e, P.:\Terminal Dynamics of Atmospheric En- try Capsules," AIAA Journal, Vol. 7, No. 6, June, 1969. 9 Cassanto, J. 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B.; and Fremaux,C.M.:\RecentExperienceswithImplement- ingaVideoBasedSixDegreeofFreedomMeasurement System for Airplane Models in a 20-Foot Diameter VerticalSpinTunnel,"ProceedingsoftheSPIEVideo- metrics Conference, Vol. 1820, 1992, pp. 158-180. 15 Yates, L. A., and Chapman, G. T., \A Compre- hensive Automated Aerodynamic Reduction System for Ballistic Ranges," WL-TR-96-7059, Wright Labo- ratory, Armament Directorate, Oct. 1996. 16 Chapman, G. T., Kirk,D. B., \A Method for Ex- tracting Aerodynamic Coe(cid:14)cients From Free-Flight Data," AIAA J., Vol 8, No 4, pp 753-758, April 1970. 6of9 AmericanInstitute ofAeronauticsandAstronauticsPaper99{1020 4550 50 6025 Q 40 y 30 20 z g 10 4525 de 3050 y , 0 x Y , -10 Q -20 -30 -40 -50 0 2 4 6 8 10 t,s Fig.1 Fourgeometriesexaminedandtheirnomen- clature (cone half angle/nose bluntness ratio). Fig. 4 Pitch and Yaw from test for case 3050b 50 Q 40 y 30 20 g 10 e d , 0 Y , -10 Q -20 -30 -40 -50 0 2 4 6 8 10 t,s Fig. 5 Pitch and Yaw from test for case 4525b Fig. 2 Schematic of 20-Foot Vertical Spin Tunnel 50 50 Q Q 40 y 40 y 30 30 20 20 ,deg 100 ,deg 100 Y, -10 Y, -10 Q Q -20 -20 -30 -30 -40 -40 -500 2 4 t,s 6 8 10 -500 2 4 t,s 6 8 10 Fig. 3 Pitch and Yaw from test for case 3050a Fig. 6 Pitch and Yaw from test for case 4525c 7of9 AmericanInstitute ofAeronauticsandAstronauticsPaper99{1020 50 50 Q Q 40 y 40 y 30 30 20 20 g 10 g 10 e e d d , 0 , 0 Y Y , -10 , -10 Q Q -20 -20 -30 -30 -40 -40 -50 -50 0 2 4 6 8 10 0 2 4 6 8 10 t,s t,s Fig. 7 Pitch and Yaw from test for case 4550b Fig. 10 Pitch and Yaw from test for case 6025b 50 Q 0.9 40 y 30 0.8 20 6025 g 10 0.7 e C d D,0 4550 , 0 Y, -10 0.6 4525 Q -20 0.5 3050 -30 without velocity variation with velocity variation -40 0.4 30 45 60 -500 2 4 6 8 10 Cone Half-Angle, deg t,s Fig. 11 Variation in drag coe(cid:14)cient with cone Fig. 8 Pitch and Yaw from test for case 4550c half-angle 6025a 50 0.00 Q 40 y 30 20 -0.05 g 10 C de m,a 4525 , 0 Y, -10 -0.10 6025 Q 3050 -20 -30 4550 -0.15 -40 0.20 0.25 0.30 0.35 0.40 -50 z /D 0 2 4 6 8 10 c.g. t,s Fig.12 Variationinmomentcoe(cid:14)cientslopewith Fig. 9 Pitch and Yaw from test for case 6025a center-of-gravity for each model 8of9 AmericanInstitute ofAeronauticsandAstronauticsPaper99{1020 0.030 0.020 0.010 C * 6025 Oscillations m,q Growing 0.000 Decaying 4525 -0.010 4550 -0.020 3050 -0.030 0.20 0.25 0.30 0.35 0.40 z /D c.g. Fig. 13 Variation in damping parameter with center-of-gravity for each model 9of9 AmericanInstitute ofAeronauticsandAstronauticsPaper99{1020