Defending a Moving Target Against Missile or Torpedo Attack

Problems involving kinematics of a counterweapon intercepting an attacking missile are well known. However, when the attacker's target, the counterweapon's launch platform, is moving, the problem generally becomes amenable only to trajectory simulation. Such may be the case in defense against torpedo attack against a ship and other situations involving the use of antimissile missiles. This paper derives the kinematic relations among the three bodies (missile, target, and counterweapon) in closed form under the asymptotic approximation of constant-bearing trajectories (collision courses). It is shown that the defending target, even if moving, can still determine the optimum course for its counterweapon when range and speed of the attacking vehicle are unknown. A simple relation is derived for the ratio between the attacker-target range (and time to impact) at counterweapon launch and the range at interception of the attacker by the counterweapon. Normalized curves are presented for some representative cases of defense by a counterweapon of known speed against a torpedo or missile attack on a moving target. The equations are shown to reduce to the familiar form for a stationary target.