Analytic Hypersonic Aerodynamics for Conceptual Design of Entry ...

C l
0.5
0.4
0.3
0.2
0.1
0
−0.1
−0.2
−0.3
−0.4
−0.5
0 20
α, deg
40 60
C m,α
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
C m
1.4
1.2
1
0.8
0.6
0.4
0.2
−0.2
0 20 40 60
α, deg
V.B. Spherical Segment Family
0
0 20
α, deg
40 60
C n
0
−0.1
−0.2
−0.3
−0.4
−0.5
−0.6
−0.7
0 20
α, deg
40 60
Figure 7. Sharp Cone Moment Coefficient Validation, β = 20 o .
C n,β
0
−0.5
−1
−1.5
0 20 40 60
α, deg
Figure 8. Sharp Cone Stability Derivative Validation, β = 20 o .
δ c = 5 o
δ c = 15 o
δ c = 30 o
δ c = 5 o (CBA)
δ c = 15 o (CBA)
δ c = 30 o (CBA)
δ c = 5 o
δ c = 15 o
δ c = 30 o
δ c = 5 o (FD)
δ c = 15 o (FD)
δ c = 30 o (FD)
The blunting of entry vehicles to reduce aeroheating is often achieved through the addition of a spherical
segment as the nose of the vehicle. For common entry vehicles such as sphere-cones and blunted biconics,
the spherical segment family is parametrized by the nose radius, rn, and cone half-angle, δc (Figure 9). The
nose radius and cone half-angle determine the portion of the spherical segment used to blunt the vehicle
due to tangency conditions enforced between the spherical segment and conical frustum. The surface of the
spherical segment is parametrized by the distance from the origin along the x-axis, u = x, and revolution
angle, v = ω, as shown in Figure 9. The resulting position vector, r, is shown in Eq. (16).
r = [u r 2 n − u 2 cos(v) − r 2 n − u 2 sin(v)] T
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American Institute of Aeronautics and Astronautics
(16)