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An empirical model for transient crater growth in granular targets based on direct observations |
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| Authors: | Satoru Yamamoto Olivier S Barnouin-Jha Seiji Sugita |
| Institution: | a Center for Global Environmental Research, National Institute for Environmental Studies, Tsukuba 305-8506, Japan b The Johns Hopkins University, Applied Physics Laboratory, Laurel, MD 20723, USA c Institute of Physical Education, Keio University, Yokohama, 223-8521, Japan d Graduate School of Frontier Sciences, University of Tokyo, Chiba, 277-8561, Japan e Planetary Exploration Research Center, Chiba Institute of Technology, Chiba, 275-0016, Japan |
| Abstract: | The present paper describes observations of crater growth up to the time of transient crater formation and presents a new empirical model for transient crater growth as a function of time. Polycarbonate projectiles were impacted vertically into soda-lime glass sphere targets using a single-stage light-gas gun. Using a new technique with a laser sheet illuminating the target Barnouin-Jha, O.S., Yamamoto, S., Toriumi, T., Sugita, S., Matsui, T., 2007. Non-intrusive measurements of the crater growth. Icarus, 188, 506-521], we measured the temporal change in diameter of crater cavities (diameter growth). The rate of increase in diameter at early times follows a power law relation, but the data at later times (before the end of transient crater formation) deviates from the power law relation. In addition, the power law exponent at early times and the degree of deviation from a power law at later times depend on the target. In order to interpret these features, we proposed to modify Maxwell’s Z-model under the assumption that the strength of the excavation flow field decreases exponentially with time. We also derived a diameter growth model as: d(t)∝1-exp(-βt)]γ, where d(t) is the apparent diameter of the crater cavity at time t after impact, and β and γ are constants. We demonstrated that the diameter growth model could represent well the experimental data for various targets with different target material properties, such as porosity or angle of repose. We also investigated the diameter growth for a dry sand target, which has been used to formulate previous scaling relations. The obtained results showed that the dry sand target has larger degree of deviation from a power law, indicating that the target material properties of the dry sand target have a significant effect on diameter growth, especially at later times. This may suggest that the previously reported scaling relations should be reexamined in order to account for the late-stage behavior with the effect of target material properties. |
| Keywords: | Impact processes Cratering Collisional physics |
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