An Analytic Ballistic Trajectory Model for Digital Fire Control.

This report develops a technique to represent the supersonic portion of a ballistic projectile's trajectory in analytic form. Particular emphasis is placed on the first two seconds of the trajectory as this region is of most importance in air-to-air combat applications where accurate computation of the projectile's position is required. Equations of motion are developed by treating the projectile as a translating mass particle in a plane parallel to the direction of gravity. Drag is the dominant forcing term in the direction opposite to the initial motion and gravity is dominant normal to the initial motion. Ignoring further perturbative effects of gravity and air density, these equations are solved in closed form.