Under the condition that a warship escapes along a linear direction, the analytic solution of the torpedo tracing trajectory is obtained by solving the corresponding differential equation using the coordinates rotation transformation.

Proposed Mathematical Model

Under the modeled condition, torpedo Pursuit Range S can be calculate by the following formular:


  • k denotes the speed of the torpedo is k (k > 1 ) times than the speed of the enemy ship,
  • The launch location of the torpedo is exactly a nautical miles due west of the enemy ship.
  • The enemy ship escape with a constant speed v knots/min along a straight path.
  • The escape direction of the enemy ship is at an angle of θ with the x-axis.


Full paper (in Simplified Chinese): click here


author={Shi-Wei Yu, Cheng Jin},
journal={Studies in College Mathematics},
title={Torpedo Tracing of Warship Escaping Along a Linear Direction},
number={29-31, 43},