Question 11.4: Using the Vostok vehicle and entry data from Example 11.1, d...
Using the Vostok vehicle and entry data from Example 11.1, determine the critical altitude and velocity for peak heating rate during a ballistic entry.
Recall from Example 11.1 that the Vostok’s ballistic coefficient is
C_{B}=\frac{m}{S C_{D}}=296.05 \mathrm{~kg} / \mathrm{m}^{2}
and the dimensionless coefficient is
B=\frac{\rho_{0}}{2 \beta C_{B} \sin \gamma_{\mathrm{EI}}}=-268.9650
We use Eq. (11.85) to determine the critical altitude for peak heating rate:
h_{\text {crit }}=\frac{\ln (-3 B)}{\beta}=48.572 \mathrm{~km}
Referring back to Example 11.1, we see that the altitude for peak heating rate is about 2.94 \mathrm{~km} above the altitude for peak deceleration as expected.
We use Eq. (11.87) to compute the critical velocity for peak heating rate:
\nu_{\mathrm{crit}}=\frac{\nu_{\mathrm{EI}}}{e^{1 / 3}}=0.7165 \nu_{\mathrm{EI}}=5.546 \mathrm{~km} / \mathrm{s}
Recall that the critical velocity for peak deceleration is 4.694 \mathrm{~km} / \mathrm{s} (see Example 11.1). Therefore, this result also shows that peak heating rate occurs before peak deceleration.