_ / Magnus moment \ V */2PSlVpd / = axial and transverse moments of inertia = amplitudes of the two yaw model arms for a symmetric missile = trim angle magnification factor = reference length = mass -XYZ components of the missile's angular velocity = reference area = dynamic stability factor = 2c0/d0o gyroscopic stability factor = (op) /4C^ = time = magnitude of the missile velocity = missile-fixed axes, the X axis along the longitudinal axis of the missile, positive forward = nonspinning aeroballistic axes = angles of attack and sideslip in the missilefixed system = circular limit motion radius = polar angle of £ = K j / K j ( j = l , 2 ) = value of \j for a linear Magnus moment = the complex angle of attack in the missile-fixed system = 0 4ict = be i9

Symmetric Missile Dynamic Instabilities

Ballistic Re-entry Vehicle Flight Dynamics

Fluid dynamics of unsteady separated flow. Part I. Bodies of revolution

A 1000-ft hypervelocity range was used to obtain the free-flight static and dynamic stability and drag data presented for a 10° semiangle cone. Measurements indicate that the damping-in-pitch derivatives for the cone increase appreciably with increasing Mach number between M = 8 and 16 at a Reynolds number (based on model length and freestream conditions) of about 0.4 X 10 6. Further, Cma for the cone decreases significantly as the noseradius to base-radius ratio of the cone is increased up to 0.1 for amplitudes greater than about 5°. Comparisons of the range stability data with wind-tunnel data (involving sting-supported models) obtained in different test facilities indicate that appreciable differences in Cma and (C,mq + Cma) exist in some cases.

Free-flight investigation of the aerodynamic characteristics of a cone at high Mach numbers

A previously developed analytic theory for the unsteady aerodynamics of moderately blunt slender cones has been extended to include the effects of large nose bluntness, nonzero angles of attack, and finite oscillation amplitudes. It is shown that the developed theory agrees well with available experimental data and correctly predicts the opposite effects of nose bluntness on static and dynamic stability including the highly nonlinear characteristics at angles of attack and oscillation amplitudes up to cone half-angle magnitudes. A universal scaling law has been derived that gives the nose-bluntness effects on static and dynamic characteristics for the above angle-of-attack and amplitude ranges with sufficient accuracy for preliminary design of conical re-entry vehicles flying ballistic or lifting re-entry trajectories.

Effects of nose bluntness, angle of attack, and oscillation amplitude on hypersonic unsteady aerodynamics of slender cones

T effect of nose shape asymmetries on the aerodynamics of a 10° cone (d= 5 in) was studied in ARL's 20-in.-hypersonic wind tunnel (M^ = 14.2, pt = 1500 psi, Tt = 2000°R, Re^d = 2.3 x 10, TJTt = 0.3, y = 1.4). Surface pressures were measured at various angles of attack and sideslip. Schlieren pictures were taken with a special nose model at several roll attitudes. Stability derivatives were measured by the free oscillation technique at the reduced frequency cod/IV^ « 0.003. The results are summarized and some conclusions relating to flight dynamics are drawn. Figure 1 shows a sketch of model A and the pressure distribution over the afterbody. The asymmetry of the nose tip is the result of a planar cut 40° off the x-z plane. The projected frontal area of the cut is approximately ^% of the base area. The schlieren picture on the left-hand side of Fig. 2 shows the shock contour in the x-y plane near the nose of model A. The plot below is a cross section of model and shock at the axial station l/L = 0.2. In the neighborhood of $ = 270°, the observed shock nearly coincides with the sharp cone shock, as given by the expression

Aerodynamics of a Slender Cone with Asymmetric Nose Bluntness at Mach 14

Pressure correlation for blunted slender cones.

Hypersonic stability derivatives of blunted slender cones

: The report describes experiments on the stability of an STA standard 10 degree cone. The free oscillation experiments on a sting mounted, open base model used an Optron tracker to register the model's oscillation about zero angle of attack. Values of the static and dynamic pitching moment stability derivatives are given for independent combinations of nine initial oscillation amplitudes (between 1/2 degrees and 5 degrees), five reduced frequencies (omega d/2V between .0025 and .007), two pivot axis locations (x sub cg/l = 55% and 60%), and two nominal Mach numbers (M = 12 and 14).

http://www.dtic.mil/cgi-bin/GetTRDoc?AD=AD0657027&Location=U2&doc=GetTRDoc.pdf

Hypersonic stability derivatives for a standard 10 degree cone

: A 10-deg. circular cone with various spherical and conical (45 degrees) nose bluntnesses of 1.7%, 10% and 25% was investigated in ARL's Mach-14 wind tunnel. Test results confirm that the static and dynamic stability coefficients are not equal in pitch and in yaw for nonzero angles of attack if the pitching moment becomes a nonlinear function of angle of attack due to nose flunting. The inequality of the in plane and out of plane stability derivatives was found at small angles of attack which are only fractions of the cone half angle. (Author)

Otto Walchner

Papers

Aerodynamics of a Slender Cone with Asymmetric Nose Bluntness at Mach 14

Pressure correlation for blunted slender cones.

Hypersonic stability derivatives of blunted slender cones

Hypersonic stability derivatives for a standard 10 degree cone

'In-Plane' and 'Out of Plane' Stability Derivatives of Slender Cones at Mach 14,