Could someone explain Holsapple's simple scaling law?
Furthermore, is Holsapple simple scaling law able to be used on Earth in the context of dropping an object and measuring the impact crater size?
Lastly, I’ve seen this equation, but I’m not sure if it’s a correct simplification of the law
$\displaystyle D=A \left( \frac {mgh} {\rho} \right)^{\frac 1 3}$
Where $A$ is a dimensionless constant.
I've also seen the form $\pi D= D( \frac {\rho}{M_i} )^{\frac 1 3}$
I’ve been trying to derive an equation to link the following variables, material density, height of drop and crater radius when I stumbled upon this, but I’m unsure whether it could be used on such a small scale (i.e. ball drop into sand).
If it can, could someone explain how/what variables must be changed in order for its possibility? (if applicable)
