Altitude of Stabilization for Slowly Tumbling Re-Entry Vehicles

Abstract

Abstract : An analysis is made to identify the parameters which determine the altitude of stabilization defined as the altitude at which the angle of attack rate first vanishes for slowly tumbling re-entry vehicles. The analysis is limited to small tumble rates and angles of attack which allow the assumptions of Cm = Cm and Cm = constant respectively. An expression is derived which implicitly relates the altitude of stabilization to (1) the initial descent velocity, VE sin , (2) the atmospheric scale height, (3) a vehicle stability parameter, Cm Al/I, and (4) the quantity ( o/ o). The important result is the fact that the initial angle of attack and initial tumble rate, i.e., o and o respectively, appear only as a ratio, o/ o, the remaining parametric quantities being properties of the vehicle, the atmosphere, and the trajectory.