Ejecta velocity distribution of impact craters formed on quartz sand: Effect of projectile density on crater scaling law

In order to clarify the effects of projectile density on ejecta velocity distributions for a granular target, impact cratering experiments on a quartz sand target were conducted by using eight types of projectiles with different densities ranging from 11 g cm−3 to 1.1 g cm−3, which were launched at about 200 m s−1 from a vertical gas gun at Kobe University. The scaling law of crater size, the ejection angle of ejecta grains, and the angle of the ejecta curtain were also investigated. The ejecta velocity distribution obtained from each projectile was well described by the π-scaling theory of v0gR=k2x0R-1μ, where v0, g, R and x0 are the ejection velocity, gravitational acceleration, crater radius and ejection position, respectively, and k2 and μ are constants mostly depending on target material properties (Housen, K.R., Holsapple, K.A. [2011]. Icarus 211, 856-875). The value of k2 was found to be almost constant at 0.7 for all projectiles except for the nylon projectile, while μ increased with the projectile density, from 0.43 for the low-density projectile to 0.6-0.7 for the high-density projectile. On the other hand, the π-scaling theory for crater size gave a μ value of 0.57, which was close to the average of the μ values obtained from ejecta velocity distributions. The ejection angle, θ, of each grain decreased slightly with distance, from higher than 45° near the impact point to 30-40° at 0.6 R. The ejecta curtain angle is controlled by the two elementary processes of ejecta velocity distribution and ejection angle; it gradually increased from 52° to 63° with the increase of the projectile density. The comparison of our experimental results with the theoretical model of the crater excavation flow known as the Z-model revealed that the relationship between μ and θ obtained by our experiments could not be described by the Z-model (Maxwell, D.E. [1977]. In: Roddy, D.J., Pepin, R.O., Merrill, R.B. (Eds.), Impact and Explosion Cratering. Pergamon, NY, pp. 1003-1008). Therefore, we used the extended Z-model by Croft (Croft, S.K. [1980]. Proc. Lunar Sci. Conf. 11, 2347-2378), which could be applied to the crater excavation process when the point source was buried at the depth of d under the target surface, and then all the experimental results of μ and θ were reasonably explained by suitable Z and d values of the extended Z-model.