Reformulation of the acceleration rate vector from Frenet's formulas using body axis velocities and accelerators

Abstract

It has been theorized that fighter aircraft agility can be described by the acceleration rate vector of the aircraft as represented within the Frenet's formulas of differential equations. Frenet's formulas describe a curve (or in this case the aircraft's flight path) as a function of curvature and torsion. Many attempts have been made to understand the effects of curvature, torsion, and acceleration rate on fighter aircraft agility, but the acceleration rate vector and its components have been shown to be elusive terms to measure and quantify. The purpose of this paper was to reformulate Frenet's formulas with measurable terms, i.e. aircraft velocities and accelerations. Once the equations were presented in more tangible terms, it was found that in addition to the body axis acceleration rate terms, the other dominant terms are body axis forward and vertical velocity and acceleration. It was also shown that in certain maneuvers the body axis acceleration rates may be decoupled so that each component of Frenet's equations for the acceleration rate vector may be described solely by the body axis acceleration rate.