Flight Stability of Spinning Projectiles at High Angles of Attack

The flight behavior of the spin-stabilized 105 mm M1 artillery projectile, when fired with high quadrant elevation, is studied using six-degrees-of-freedom trajectory simulations and theoretical methods of stability analysis. Trajectory simulation results confirm the known effect of overstabilization at the apogee, leading to high angles of attack (AoA), drift to the left, and base-forward descent. For quadrant elevations between nose-forward and base-forward descent, a previously unknown descent mode was discovered, with projectiles performing a low-frequency coning motion at high angles of attack of 73 and 104 deg, respectively. An exhaustive theoretical description of such high-AoA limit cycles is given that overcomes the limitation to small angles of attack prevalent in traditional concepts of projectile stability. Based on a formulation of the angular motion in spherical coordinates, conditions for the existence of limit cycles are identified and stability criteria are derived using Lyapunov's first method of linearization around equilibrium and eigenvalue analysis of the resulting Jacobian. The resulting criteria indicate that limit cycle flight is primarily governed by the Magnus moment coefficient. The method is applied to the 105 mm M1 projectile, and the coning motions observed in the trajectory simulations are accurately reproduced by the theory.