A simple defense conservative model for mass requirements of hypervelocity projectile impact shields for reentry vehicles

Simple analytical modeling of the physics of interaction of hypervelocity (50-100 km/s) projectiles with a bumper shield countermeasure is given. The interaction of projectile and bumper is discussed briefly. Expansion of bumper/projectile debris in the region between bumper and underlying vehicle and interaction of bumper/projectile debris cloud with a vehicle are examined. Expansion of debris is treated as an expansion superimposed upon a translation with partition derived from a simple inelastic collision model. The effect of nonunity aspect ratio of compressed debris is included. Debris colliding elastically with the vehicle will impart momentum equal to twice the incident normal component. A steady-state diffusion model is used to estimate the effect of stagnation radiative loss on collision elasticity. Impulse may be reduced up to a factor of 2 by stagnation radiative loss on collision elasticity. Impulse may be reduced up to a factor of 2 by stagnation radiative losses for small projectiles and large bumper/vehicle stand-off. Stagnation radiation loss is small for larger projectile and smaller stand-off. Impulse can be enhanced by vehicle ablation from radiative coupling, shock heating (inadequate stand-off), or liquid droplet microcratering (inadequate bumper thickness). Estimates of required bumper mass are given for a specific example