General heating distributions on the tumbling infinite cylinder

The Shuttle program plans to recover all flight hardware except the External Tank (ET). The ET reentry task requires the quaranteed safe disposal in a remote section and specific footprint of the Indian Ocean or the Antarctic Pacific. The ET is separated from the Orbiter at near orbital speeds and must reenter tumbling, to neutralize lift in an essentially ballistic trajectory. The aerothermodynamic heating becomes an intriguing, complex, and sophisticated series of flow field, boundary layer, and gas dynamic problems that is an important new technology in the reentering disposal task. The singular aspect given in this paper is the general heating distributions for all tumbling attitudes. The objective is to maintain simplicity in form but with variable coefficients to be analytically scaled to account for free molecule, convective laminar and turbulent flow, real gas dissociation or any Reynolds number or Mach number effects.