A Direct-Fire Trajectory Model for Supersonic, Transonic, and Subsonic Projectile Flight

Abstract

This report presents a simple but accurate method of determining the trajectory of projectiles that traverse a flight regime that includes supersonic, transonic, and subsonic flight. Closed-form analytical solutions for the important trajectory parameters such as the time of flight, velocity, gravity drop, and wind drift are presented. The method makes use of individual power-law descriptions of the drag variation with Mach number within the supersonic, transonic, and subsonic regimes. The method demonstrates that the free-flight trajectory can be characterized with as few as six parameters: the muzzle velocity, muzzle retardation, a power-law exponent that describes the drag variation in supersonic flight, the transition Mach numbers between supersonic and transonic flight, the transition Mach number between transonic and subsonic flight, and the retardation at the subsonic transition Mach number. The accuracy and simplicity of the method make it very useful for preliminary design or performance assessment studies where rapid prediction of projectile trajectories is desired. Sample results are presented for a 9-mm pistol bullet that traverses supersonic, transonic, and subsonic flight to demonstrate the viability of the method.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 2014
Accession Number
ADA607593

Entities

People

  • Paul Weinacht

Organizations

  • United States Army Research Laboratory

Tags

Communities of Interest

  • Weapons Technologies

DTIC Thesaurus Topics

  • Ammunition
  • Angular Motion
  • Control Systems
  • Free Flight
  • Free Flight Trajectories
  • Mach Number
  • Munitions
  • Muzzle Velocity
  • Projectile Trajectories
  • Projectiles
  • Retardation
  • Small Arms Ammunition
  • Subsonic Flight
  • Supersonic Flight
  • Transitions
  • Transonic Flight
  • Weapons

Fields of Study

  • Physics

Readers

  • Aerodynamics/Aeronautics.
  • Control Systems Engineering.
  • Theoretical Analysis.

Technology Areas

  • Hypersonics