A Method of Estimating Transient-cavity Diameters for Impact Craters Formed in Dry Sand

Introduction: Analyses of impact craters formed in laboratory experiments historically have been the source of many fundamental observations and interpretations of the impact-cratering process itself. Due to its ready availability, ease of handling, and lack of strength, dry sand of various types has been the target material of choice in the majority of such experiments. A consequence of its lack of intrinsic strength, however, is dry sand's inability to maintain slopes above its angle of repose. Evidence from field observations of simple terrestrial craters and laboratory craters formed in more cohesive granular media suggests that transient cavities are similar to paraboloids in shape. Cross-sections of craters formed in dry sand, however, are nearly conical with the wall slopes at or near the angle of repose, indicating that the original crater form has been modified by one or more processes, among which is simple slope failure. Because the dimensions and shape of the transient cavity reflect the detailed conditions of a given impact event, its characterization has long been a desired goal in experimentation. A means of estimating the position of the transient cavity's rim is suggested below, relying on determination of velocities of material ejected from the growing cavity. Approach: The method used here is founded on the observation that parabolic trajectories described by grains of sand ejected in laboratory-scale impacts in vacuo are, for the most part, relatively well-defined and orderly, even in cases involving very coarsegrained targets (Fig. 1). It is clear from the figure that fragments are ejected at decreasing speeds as the location of the final crater's rim crest is approached. Indeed, as the ejection speeds drop, the parabolic trajectories become smaller and smaller, with the result that the last, slowest piece of material to be ejected, describing the limiting case, would barely leave the cavity to be deposited on the top of the rim crest. Thus, by plotting the point at the a number of parabolic trajectories, the location of the transient cavity's rim crest should be approached as the elevations of the parabolic maxima approach the target surface. An example: This method can be illustrated by use of an existing dataset that describes seven impacts of 4.76-mm aluminum spheres into targets of blasting sand, with grain dimensions of 1-3-mm. The trajectory data for these impacts can be used to derive the x-y coordinates at which the of maxima of all the measured parabolic trajectories occur; the origin of the coordinate system is the impact point itself, and the xaxis lies along the pre-impact target surface. An example of the trend resulting from such measurements is given in Fig. 2