Spark range data reduction using a Gauss collocation method

Abstract

A new method is proposed for reducing spark range data using a Gauss pseudospectral collocation. Existing methods use numerical integration to propagate the differential equation model and its sensitivities forward in time. Here, a collocation method is used to transcribe the differential equations into algebraic ones that are easily solved. Realizing that the auxiliary equations used to find model sensitivities are linear, a second transcription renders a set of linear algebraic equations that solve exactly for the needed sensitivities without iteration. Thus, measurement sensitivities with respect to initial conditions and aerodynamic parameters are easily found through solution of a set of linear algebraic equations. The method is demonstrated on a set of actual data from the M898 155-mm projectile. For models using fixed-plane coordinates, and only the 10 most influential aerodynamic coefficients, the new method produces results that rival established commercial codes in accuracy.