Non-intrusive Measurements of Crater Growth

A new experimental technique to measure crater growth is presented whereby a high speed video captures profiles of a crater forming after impact obtained using a vertical laser sheet centered on the impact point. Unlike previous so called “quarter-space experiments”, where projectiles were launched along a transparent Plexiglas sheet so that growth of half a crater could be viewed, the use of the laser sheet permits viewing changes in crater shape without any physical interference with the cratering process. This technique is used to investigate the evolution of craters formed following the vertical impact of polycarbonate projectiles launched at velocities <300m/s into a target of uniform-sized 220μ glass beads. Results show changes in crater shape as a function of time during excavation that seem to be at odd with some of the scaling rule assumptions [1, 2, 3] typically used to assess cratering on the asteroid and planets. They also provide detail views into the factors controlling crater modification at least in the laboratory and possibly at planetary scales. Figure 1. Schematic illustrating the experimental setup Experimental setup: The experiments are undertaken at the University of Tokyo Vertical Gun Range. During each experiment a vertical laser-sheet is used to illuminate a line across the target at the point of impact. The frames of a high-speed video camera that is placed above the crater captures changes in this line or profile as the crater grows after impact (Figure 1). These data provide the temporal changes in crater depth, diameter and wall slope. The projectile were launched using a single-stage lightgas gun vertically at velocities ranging from 85 to 280m/s. In all but one case, the projectiles were polycarbonate rounded-tipped cylinders with a mass of 0.49g and a length and diameter of 0.90 and 1.0 cm respectively. The target was made up of soda-lime glass spheres. Each sphere possessed a density of 2.5gcm-3 and a mean diameter of 220μm. The bulk density of the target was 1.59gcm-3, implying a target porosity of 36%. The effective static angle of repose of this material is small at around 25. This value is low and indicates that this target is essentially cohesionless; its strength is derived nearly entirely from its friction angle which is ~22 for smooth spheres [4]. All the experiments were conducted at vacuum conditions with atmospheric pressures below 50Pa. Imaging processing: In order to obtain the real dimensions of the craters profiles observed in each individual video frame, we had to convert pixel dimensions to centimeters. We achieve this by filming prior to each experiment a 2 by 2cm-gridded calibration target that is placed in the plane of the laser sheet at the impact location. A conversion approach is then used, whereby we rectify the pixel dimensions (xp, yp) of the tilted CCD within the high speed video camera onto points (xl, yl) in the plane of the laser sheet. The calibration target provides the tie points to make the projection from (xp, yp) to (xl, yl) possible. This technique is commonly used to project one tilted image plane onto another [5]. We tested our image processing technique, by comparing the final depth and diameter of several crater obtained from our images, with measurements obtained using a profilometer that was set in the laser plane after impact. Our imaging technique reproduces on average the profilometer measurements for final crater diameter to ~2%, and crater depth ~4% relative to the pre-impact surface. In general, both the diameters and depths obtained from the images are well within the accuracy of the profilometer measurements. Results: Once the pixel dimensions are converted to cms, (e.g. Figure 2), crater depth, diameter and wall slope can all be measured as a function of time. From these data, we obtain information on the transient crater shape at the end of excavation, final crater shape ofter modification Lunar and Planetary Science XXXVII (2006) 1243.pdf