Scale size effect in momentum enhancement

When an impactor strikes a body at hypervelocities the momentum transferred to the impacted body is greater than the initial impactor momentum. This effect is due to the crater ejecta, and when the impacted body's mass provides some of the momentum change, the effect is referred to as momentum enhancement. The small amount of data on this question implies that there is a scale effect - that is, as the projectile size increases there is an increase in the imparted momentum beyond that anticipated due to the increase in projectile size. Recently, experimental data was gathered on the increase in momentum caused by crater ejecta when 4.45-cm diameter aluminum spheres struck granite targets. The amount of momentum enhancement (characterized by the ratio β) was greater than 2 for 2 km/s impacts. Compared with other data at much smaller scale, these tests imply an impactor scale and an impactor density effect for hypervelocity strikes into rock. The implied impactor size scale effect is surprisingly large - to a 0.4 power - and extrapolation indicates that a 1-meter aluminum sphere striking a consolidated rock surface at 10 km/s could have a β exceeding 40, supposing the scale size effect does not saturate on the order of 10 cm. Such a large momentum enhancement shows that kinetic impactors can be very efficient at deflecting asteroids.