A mechanism for ablation-induced spin-up.
A spin-change mechanisms that have been suggested in the past require a mass asymmetry, e.g. offset, in combination with an aerodynamic lifting force, generated either by a nonzero angle of attack on a symmetric vehicle" or by an ablation-induced nose asymmetry. For thermally expanding surfaces a spin change can occur without any (initial) e.g. offset, but a nonzero angle of attack is required. The present Note describes a mechanism for spin-up at zero angle of attack on a symmetric perfectly balanced vehicle (without e.g. offset or inertia-axes-misalignments). It has been argued by the present authors in an earlier paper that ablation-induced grooving or cross-hatching, or both, on a re-entering missile cannot cause any spin-up, but will work the opposite way for the following reason: The ablation-induced pattern on the vehicle surface will follow the local flow direction existing at the time of pattern production. That is, if the spin rate is p0, local body radius r, and vehicle velocity U,% the bias of the pattern flow angle is de(tQ) = P0r/U0. When l/o has decreased an amount A£7 during re-entry, the angular bias of the surface flow at a later time during the re-entry would be p0r/(U0 — AC/), if the spin rate remained constant. That is, the angular bias of the pattern "frozen" at time t0 will at a later time, t0 + t, be such that it causes a spin-down to a new equilibrium rate set by the inviscid net bias angle A6e. -CV] (1) SURFACE STREAMLINE (LAMINAR FLOW) VORTEX PATH