A DIRECT-FIRE TRAJECTORY MODEL FOR SUPERSONIC THROUGH SUBSONIC PROJECTILE FLIGHT

摘要

A simple but accurate method of determining the direct-fire trajectory of projectiles thattraverse a flight regime that includes supersonic, transonic 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 presented. The method makes use ofindividual power-law descriptions of the drag variation with Mach number within thesupersonic, transonic and subsonic regimes. The method demonstrates that the free-flighttrajectory can be characterized with as few as six parameters; the muzzle velocity, muzzleretardation, a power-law exponent that describes the drag variation in supersonic flight, thetransition Mach numbers between supersonic and transonic flight, the transition Machnumber between transonic and subsonic flight and the retardation at the subsonic transitionMach number. The accuracy and simplicity of the method makes it very useful forpreliminary design or performance assessment studies where rapid prediction of projectiletrajectories is desired. Sample results are presented for a 9mm pistol bullet that traversessupersonic, transonic and subsonic flight to demonstrate the viability of the method.