SpaceX Starship
In June 2024, the upper stage of SpaceX's experimental Starship rocket successfully performed a controlled re-entry into the earth's atmosphere for the first time during a test flight. This is a significant milestone, as Starship is intended to be the world's first fully reusable rocket, and successfully recovering the upper stage is an essential part of this. At a mass of 85 tonnes, the Starship upper stage is one of the largest and heaviest man-made objects ever to re-enter the atmosphere.
Figure 3: Left: Plasma build-up on Starship during re-entry, as captured by an onboard camera. The black silica tiles for the thermal protection system are visible on the bottom right of the spacecraft. Credit: SpaceX Right: A computer rendering of starship entering the atmosphere. The direction of travel is down and to the right. Credit: SpaceX.
Due to the extremely high speeds involved, the vehicle experiences extreme heating effects during its re-entry, which must be appropriately managed to prevent destruction of the vehicle. For this reason, the forwards-facing side of Starship is covered in a thermal protection system comprised of thousands of hexagonal silica tiles.
(a) Before entering the atmosphere, Starship is on a sub-orbital trajectory which reaches a maximum altitude above the Earth's surface of 213 km. Since the test is designed to simulate re-entering from orbit, at this point Starship is travelling at $94\%$ of the circular orbit velocity for that height --- just slow enough to re-enter the atmosphere instead of orbiting the Earth. Determine the total energy of Starship at this point.
(b) Starship is decelerated by atmospheric drag forces until it reaches negligible speed and altitude. Determine the work done by the atmosphere during re-entry.
Starship is 50 m tall, has a diameter of 9 m, and the nose cone takes up the top 14 m. Its outer skin is made of 4 mm thick stainless steel, which has a specific heat capacity of $500$ J kg$^{-1}$ K$^{-1}$, a density of $8000$ kg m$^{-3}$ and a maximum operational temperature of $900^{\circ}$C. To maximise the amount it is slowed down by atmospheric forces, Starship travels through the atmosphere pointing perpendicular to its direction of travel, as shown in Figure 3.
(c) Given that it initially has a temperature of approximately $0^{\circ}$C, calculate the maximum thermal energy which can be safely transferred to the steel during re-entry. Assume all heating occurs uniformly on the forwards facing side of the spacecraft body, and that conduction to the rest of the spacecraft is negligible.
(d) Show that this means the thermal protection system has to be good enough that $<1\%$ of the thermal energy generated by the deceleration of the Starship by the atmosphere is transferred to the steel body of the spacecraft.
