A comparison of piecewise cubic Hermite interpolating polynomials, cubic splines and piecewise linear functions for the approximation of projectile aerodynamics

Modelling and simulation of projectile flight is at the core of ballistic computer software and is essential to the study of performance of rifles and projectiles in various engagement conditions. An effective and representative numerical model of projectile flight requires a relatively good approximation of the aerodynamics. The aerodynamic coefficients of the projectile model should be described as a series of piecewise polynomial functions of the Mach number that ideally meet the following conditions: they are continuous, differentiable at least once, and have a relatively low degree. The paper provides the steps needed to generate such piecewise polynomial functions using readily available tools, and then compares Piecewise Cubic Hermite Interpolating Polynomial (PCHIP), cubic splines, and piecewise linear functions, and their variant, as potential curve fitting methods to approximate the aerodynamics of a generic small arms projectile. A key contribution of the paper is the application of PCHIP to the approximation of projectile aerodynamics, and its evaluation against a set of criteria. Finally, the paper provides a baseline assessment of the impact of the polynomial functions on flight trajectory predictions obtained with 6-degree-of-freedom simulations of a generic projectile.