Comparison of traditional agility metrics to Beck performance and agility metrics using linear error theory

Abstract

Previous investigations have studied the robustness of agility metrics to variations in initial conditions and uncertainties in physical characteristics and coefficients. In each of these investigations, the selected agility metrics were evaluated in a Cartesian coordinate system. It is known that values of calculated parameters can be sensitive to the particular form of the equation used, which in turn results from the choice of coordinate system. Although simple and intuitive for quantifying agility, Cartesian coordinates are not necessarily the best coordinate system for studying agility. Best is defined here as the form of agility equation, resulting from choice of coordinate system, which is most robust to variations in initial conditions and uncertainties in physical characteristics and coefficients. This paper seeks to establish the relationship between form of agility equations, choice of coordinate system, and the measured agility of high performance aircraft. Cartesian based agility metrics consisting of time to roll through bank angle metric, average pitch rate metric, and power onset/loss parameter metric, are compared to the Beck metrics which are based in the Frenet coordinate system. Each group of metrics is evaluated with initial condition errors and parametric uncertainties of physical constants using linear error theory to validate the use of linear approximations to propagate the errors, l^. is shown that the Beck metrics are less sensitive to initial condition errors and parametric uncertainties for the longitudinal and axial axes. The time to roll through bank angle metric is less sensitive to these variations than the Beck metrics for evaluating agility in the lateral axis.