A Coning Theory of Bullet Motions

TL;DR

Coning Theory provides a comprehensive explanation of spin-stabilized bullet motion, including aerodynamic jump, yaw of repose, and spin-drift, by modeling the coning motion as synchronized gyroscopic precession and orbital center-of-gravity motion.

Contribution

It introduces a new unified model of bullet coning motion, integrating gyroscopic precession with orbital CG motion, supported by new equations and synchronization principles.

Findings

Explains aerodynamic jump and spin-drift phenomena.

Develops equations for orbital CG motion driven by aerodynamic forces.

Shows synchronization of precession and orbital motions as fundamental to bullet behavior.

Abstract

Each observable ballistic phenomenon of a spin-stabilized rifle bullet can be explained in terms of the acceleration of gravity and the total aerodynamic force acting on that bullet. In addition to the coning motion itself, Coning Theory explains the spinning bullet's aerodynamic jump and its steadily increasing yaw of repose together with its resulting spin-drift. The total aerodynamic force on the bullet comprises its drag and lift rectangular components and produces an associated overturning moment acting upon the rigid bullet. The coning motion of the bullet includes two distinct but synchronized aspects: 1) the well-known gyroscopic precession of the spin-axis of the bullet, and 2) the previously little-known orbiting of the center of gravity of the bullet around its mean trajectory with the nose of the bullet angled inward toward that trajectory. New equations are developed governing the orbital motion of the CG as a circular, isotropic harmonic oscillation driven by the lift and drag forces as they revolve together at the gyroscopic precession rate. Standard Tri-Cyclic Theory governs the uniform circular precession of the spin-axis driven by the overturning moment acting on the spinning bullet as a free-flying gyroscope. The synchronization of these two motions is the defining principle of Coning Theory.