Question 11.5: Using the Space Shuttle vehicle data and entry conditions in...
Using the Space Shuttle vehicle data and entry conditions in Example 11.2, determine the critical altitude and velocity for peak aerodynamic heating rate for an equilibrium glide.
We determined the Shuttle’s ballistic coefficient in Example 11.2:
C_{B}=\frac{m}{S C_{D}}=410 \mathrm{~kg} / \mathrm{m}^{2}
Equation (11.89) is used to determine the critical altitude for peak heating rate on an equilibrium glide:
h_{\mathrm{crit}}=\frac{-1}{\beta} \ln \left[\frac{4 C_{B}}{r_{0} \rho_{0}(L / D) \cos \phi}\right]
Using \beta=0.1378 \mathrm{~km}^{-1}, r_{0}=6,375,416 \mathrm{~m}, \rho_{0}=1.225 \mathrm{~kg} / \mathrm{m}^{3}, L / D=1.1, and bank angle \phi=50^{\circ}, we obtain
h_{\text {crit }}=58.94 \mathrm{~km}
We use Eq. (11.90) to determine the critical velocity for peak heating during the glide:
\nu_{\text {crit }}=\sqrt{\frac{g_{0} r_{0}}{3}}=4.565 \mathrm{~km} / \mathrm{s}
where we have used g_{0}=9.80665 \mathrm{~m} / \mathrm{s}^{2} as the Earth’s standard gravitational acceleration.