Analytic/numeric methods of various levels of complexity are used to predict the response of spacecraft to hypervelocity debris impacts. Analytic methods developed to aid spacecraft designers in the design of protective shields are the least complex. These include (1) "ballistic limit" equations (Cour-Palais, 1986; Herrman and Wilbeck, 1986; Reimerdes et al., 1993), which calculate the size of a particle stopped by a particular shield as a function of impact speed, impact angle, and impactor density; and (2) shield sizing equations (Christiansen, 1993), which provide estimates of shield thicknesses and spacings required to protect against particles of given sizes, velocities, densities, and impact angles. Shield sizing equations may incorporate ballistic limit equations to determine the effects of impact on the individual walls that make up the shield.
Analytic methods available to spacecraft designers for predicting the damage caused by impacts, and the effects of that damage, are slightly more complex. These include (1) impact damage and effects equations derived from physical principles (Watts et al., 1993, Watts et al., in press) and (2) semiempirical impact cratering, perforation, and spallation equations (e.g., Cour-Palais, 1979; Carey et al., 1984; Hörz et al., 1994). Other analytic models that are useful for providing a qualitative understanding of impact damage include the Grady model (Grady, 1987; Grady and Passman, 1990), the Tate model (Tate, 1967, 1969), and the Ravid and Bonder model (Ravid and Bonder, 1983; O'Donoghue et al., 1989).
There are, however, currently no standardized risk assessment models to determine the probability of component degradation or failure due to orbital debris impacts. Performance degradation models are also not standardized and currently exist for only a few component types. Because of this, spacecraft degradation due to debris impact is currently modeled by combining basic engineering model predictions of the expected environment with empirical scaling models for damage prediction. These empirical scaling laws, though, must often be applied via unproven extrapolations to materials and velocities that were not included in the original data sets on which the empirical models were based. After predicting damage, simple performance degradation "rules" relating degradation to damage area can be applied to determine whether performance will remain within specifications.
Empirical equations based on ballistic limit curves or other experimental data are often used to predict the performance of debris shields. These equations can produce good results if experimental data have been generated for similar particle configurations and velocities (Christiansen,