Nose Cone Tip Thermal Analysis

This article will describe:

1. The thermal considerations in designing a nose cone tip
2. A mathematical model to describe how hot the nose cone tip is expected to get
3. The numerical method used to determine the temperature profile of the tip
4. The final design choice made for Hermes II

Nose cone tip thermal consideration

Hermes II is expected to reach high speeds in low atmosphere: approx Mach 3.5 at just 10,000 ft when burn out occurs. At these high speeds, the stagnation point temperature of the air is extremely high:

$//<![CDATA[ \begin{array}{l}T_{stag} = T \left(1 + \frac{\gamma - 1 }{2} M^2 \right) = 268 \left( 1 + \frac{1.4 - 1 }{2} 3.5^2 \right) = 924 K\end{array} //]]>$

The service temperature of aluminium is on the order of 580K, for steel it is 1200K. 

Does that mean that a steel nose cone is sufficient to withstand the flight? Not necessarily. 

We need to understand how the