Dynamic Stability Analysis of Spin-Stabilized Projectile

An aerodynamically unstable projectile can be made gyroscopically stable by imparting spinning motion along its longitudinal axis. However, gyroscopic stability alone is insufficient for the projectile flight stability; rather, the projectile flight must be both gyroscopically and dynamically stable during the entire duration to be called stable flight. The dynamic stability of the projectile can be examined by analyzing its epicyclic motion modes called precession and nutation. The present study presents mathematical expressions to calculate these epicyclic motion modes and projectile dynamic stability conditions derived from a linearized epicyclic motion differential equation. These expressions are used to calculate the gyroscopic and dynamic stability parameters of the subject 105-mm artillery projectile during the entire duration of its flight. When launched at a higher elevation angle, the 105-mm projectile has the maximum chance of becoming unstable at flight apogee. Therefore, this analysis is performed considering a higher elevation angle to investigate projectile stability at the most likely region of instability. The values of the precession and nutation mode's damping and frequency are calculated along entire trajectory. Also, the gyroscopic vs. dynamic stability is provided on the ballistics diagram to investigate the stability of the flight. Finally, the results of epicyclic motion modes are discussed along with the six-DOF non-linear dynamic trajectory model results for comparison.