Sounding rocket fin design to mitigate roll lock-in

Roll lock-in is a persistent high angle of attack, nonlinear coning motion sometimes observed in the flight of reentry vehicles and sounding rockets. For example, it has occurred during Aerobee sounding rocket and Sidewinder missile flights prior to the introduction of rollerons. This paper focuses on how fin design effects the probability of lock-in. The high angle of attack response is driven by misalignment and/or offset thrust and drag forces, amplified by during pitch-roll resonance. High angles of attack engender nonlinear roll moments which cause the roll rate to follow the pitch natural frequency. It is well known that such roll moments can arise when the center of mass is offset from the vehicle symmetry axis. However, this paper explores another source of nonlinear high angle of attack roll moments, interaction between vorticity shed from a fore body and tail fins. Both kinds of roll moment have similar magnitudes. However, lock-in due to center of mass offset is, apart from static margin, not affected by fin design. The location and strength of the shed vortex pair are found from wind tunnel data. Roll moments are estimated from strip theory assuming incompressible cross flow. Conditions for steady state roll lock-in, and its probability of occurrence, are derived from the rigid body moment equations. A technique for significantly reducing the probability of roll lock-in by adjusting the fin exposed semispan and static margin is presented, and used to show that, for a typical university sounding rocket, static margins larger than the classical two caliber heuristic rule can mitigate this problem. Fin taper ratio was studied, and found to have a relatively minor effect. Little difference between three and four fins was found. But, more than four fins, at fixed static margin, can significantly reduce the incidence of roll lock-in. Six fins are much better than four, and eight are better still.