at which the intercepting projectile is fired at the target for example if the velocity v is 150 m s mach 0 5 and the distance x is 50 m then the characteristic time is about u2153 of a second at the time t d a number of radial arms airscrew unfold hinged aft these arms are airfoil shaped in their cross section they act as a windmill deriving torque from the axial flow the axial flow velocity is the speed of the intercepting projectile thus the transient effect of unfolding the radial arms is to reduce the linear momentum of the projectile slow it down and increase its angular momentum spin it up the end of the transient is then when there is no exchange of momentum i e when the airscrew is essentially an anemometer of course overall aerodynamic drag will cause both linear and angular momentum to decrease in time but on a longer time scale the intercepting projectile may be spinning from being fired from a rifled barrel in fact the initial rotational spinning velocity is a design parameter of the problem this rotational velocity must however be such that there is a windmilling effect after deployment there is the spin up and linear velocity slowdown phase which is shown in fig1 as the slope becoming more vertical after the deployment and linear velocity slowdown and spin up phase comes the intercept phase during the time before the intercept phase begins two events must.