Recent empirical results that I have produced by dropping balls into sand indicate that the ellipticity of a crater- i.e. the ratio of major axis diameter to minor axis diameter - varies linearly with the angle of impact of an impactor (the angle between the impactor trajectory and the normal to the ground). I have also observed a linear relationship between Sin(impact angle) and the major axis diameter of the crater. I am struggling to find a derivation or explanation which might shed light on these results. Please help if you have any idea of why ellipticity and impact angle might be linearly related.
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