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.     

Counterweapon Aiming for Defense of a Moving Target

Previous correspondence [1, 2] considered the problem of defending moving target by means of a counterweapon launched from the target to intercept the attacker, deriving relations between attacker-target ranges at counterweapon launch and at intercept of the attacker, and the speed capabilities of the counterweapon. The present correspondence derives the location of the intercept point in target-centered coordinates (the counterweapon aimpoint), analyzes the complicated behavior of range and bearing settings with attack geometry, and formulates the relations for determining whether any given attack can be countered under restrictions on speed or angle at which the counterweapon may be fired. Exhaustive analysis is not attempted. A simplified treatment portrays kinematic conditions which must exist if the target is to counter the attack before the target is impacted by the attacking vehicle, through the use of examples.