A Hybrid Supersonic/Subsonic Trajectory Model for Direct Fire Applications

Report No. ARL-TR-5574
Authors: Paul Weinacht
Date/Pages: June 2011; 40 pages
Abstract: A simple but accurate method of determining the trajectory of projectiles that traverse a flight regime that includes supersonic and subsonic flight is presented. Closed-form analytical solutions for the important trajectory parameters such as the time-offlight, velocity, gravity drop and wind drift are developed based on a power-law description of the drag variation with Mach number. The method demonstrates that the free-flight trajectory can be characterized in terms of five parameters; the muzzle velocity, muzzle retardation, a power-law exponent that describes the drag variation in supersonic flight, the transition Mach number where the flight transitions from supersonic to subsonic flight and the retardation at the transition velocity. The accuracy and simplicity of the method makes it very useful for preliminary design or performance assessment studies where rapid prediction of projectile trajectories is desired. Sample results are presented for the M855 projectile fired from the M16A2 rifle and a 9-mm pistol bullet fired from a handgun to demonstrate the viability of the method.
Distribution: Approved for public release
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Last Update / Reviewed: June 1, 2011