Projectile Fire-Control Algorithm in a Spatially Varying Wind Field

Abstract

The fire-control solution is an important element of any modern weapon system, providing precise aiming of the gun to enable highly accurate projectile impact. To be practical, the fire-control solution must be computed rapidly and reliably while simultaneously including all pertinent physical effects that can alter the trajectory and impact point. Current fire-control solutions account for the effect of atmospheric wind in a rudimentary manner, typically assuming a constant crosswind that is estimated in the field or measured at the firing site. With the advent of advanced wind-measurement systems (light detection and ranging, for example), it is now possible to accurately measure three-dimensional wind velocities at numerous points approximately along the path of a direct-fire projectile. This article first shows the importance of wind knowledge along the line of fire for accuracy, particularly for long-range direct-fire shots. Then, a method to compute the fire-control solution of a projectile is defined, including the effect of exactly known spatially varying winds. By using a modified form of projectile linear theory that incorporates three-dimensional linearly varying atmospheric winds, a closed-form fire-control solution is obtained. Moreover, the solution can be rapidly computed. The key to the algorithm is partitioning the projectile linear-theory state-transition matrix in an input–output form that enables the aiming solution to be computed in terms of a desired impact point and measured atmospheric winds. The application of this algorithm is restricted to flat-fire trajectories where the angle of attack of the projectile remains low throughout because this is the key limitation of the projectile linear theory that must be maintained. The proposed algorithm is exercised on an example fire-control problem for such flat-fire trajectories with excellent results.