b c C m D d ' d d J I 1 L M M n N P N q Re R d S S t U x Y a a /3 7 Nomenclature wing span reference length , c = d f or bodies dC m /da;Ce f3 = dC e /d0 drag,coefficentC z> =Z)/(p 00 t/i/2)S sectional drag , coefficient c d = d ' I ( p «, U 2 , /2)c maximum diameter for body of revolution mean diameter, d=\ J 0 2 rd(x/£) bio wing momentum, coefficient body length forebody length forward of rotation center (Fig. 8) nose length = rolling moment, coefficient C, = £/ (p* U^ /2)Sb vortex wake wave length Mach number pitching moment, coefficient C m =M p /( Poo Ul/2)Sc yawing moment, coefficient C n =n/(p 00 U 2 00 /2)Sc = normal force, coefficient C N =N/ (p^ C/i/2)S = nose tip roll rate = pitch rate Reynolds number based on d max and freestream conditions; usually Re = R d Reynolds number, R d = U^d/vr eference area, S = ird 2 /4 reference area ( = projected wing area) time velocity axial body-fixed coordinate (distance from apex) side force, coefficient C Yangle rotation of plane of symmetry of forebody vortices (Fig. 8) cone half-angle 6 A = apex half-angle p = air density = roll angle <£' = coning angle (Fig. 8) > 5 = three-dimensional separation angle (Fig. 15) a' = total angle of inclination (Fig. 8) v -kinematic viscosity oj = angular rate Subscripts A = apex AM = effective apex angle A V = asymmetric vortices c = cone n = normal to body axis TV =nose P = port side s = separated flow S = starboard SV = symmetric vortices UV = unsteady vortices v = vortex W =wall oo = freestream conditions Introduction T HE continually increasing performance demands on present day aircraft and missiles have brought on intensive research aimed at providing the needed understanding of the vehicle aerodynamics at high angles of attack where separated flow vortices often have a dominating influence. Recently there has been a series of papers reviewing the state of the art for the prediction of these high-a aerodynamics. M Nielsen 1 ' 2 concentrated his attention on the existing capability of predicting the missile aerodynamics at high angles of attack where the effects of symmetric vortices Lars E. Ericsson has published more than 100 papers in his related fields. Pete Reding, an Associate Fellow of AIAA, has had roughly 22 years experience in the aerospace industry working generally in the field of unsteady aerodynamics. He was first mystified by body vortex effects during his two-and-a-half years at what was then Douglas Aircraft Company, where he worked immediately after graduation from the University of Michigan in 1958. Now at Lockheed Missiles and Space Co., Inc. (since 1961) he has wrestled with separated flows, booster aeroelastic stability, airfoil stall, the dynamics of bulbous based bodies, ablating bodies, shuttle vehicles, decelerators, dynamic support interference, and aeroacoustics. Not one to give up easily he has once again attacked the mysteries of body vortices. 98 L.E. ERICSSON AND J.P. REDING J. SPACECRAFTfrom the forebody and its canard surfaces on aft body and fins have demanded major new analytical/ex...