A Test of Maxwell’s Z Model Using Inverse Modeling

Introduction: In modeling impact craters a small region of energy and momentum deposition, commonly called a “point source” [1,2], is often assumed. This assumption implies that an impact is the same as an explosion at some depth below the surface. Maxwell’s Z Model [3,4], an empirical point-source model derived from explosion cratering, has previously been compared with numerical impact craters with vertical incidence angles, leading to two main inferences. First, the flowfield center of the Z Model must be placed below the target surface in order to replicate numerical impact craters [5]. Second, for vertical impacts, the flow-field center cannot be stationary if the value of Z is held constant; rather, the flow-field center migrates downward as the crater grows [6]. The work presented here evaluates the utility of the Z Model for reproducing both vertical and oblique experimental impact data obtained at the NASA Ames Vertical Gun Range (AVGR). Specifically, ejection angle data obtained through Three-Dimensional Particle Image Velocimetry (3D PIV) [7,8] are used to constrain the parameters of Maxwell’s Z Model, including the value of Z and the depth and position of the flow-field center via inverse modeling.