newtonian mechanics - The Relationship Between Crater Diameter and the Velocity of an Object

I'm doing a design lab, where I have to "investigate the nature of craters formed on sand." I've done some research and figured out that the cube of the diameter ($d$) of the crater formed by an object is proportional to Kinetic Energy, i.e. $d^3$ is proportional to $\frac12mv^2$ (I got this information from this website, under the "Crater Size (Level Two)" heading).

I was wondering what would have to be added to this relationship (adding/subtracting numbers or adding in coefficients to either side) to turn this relationship into an equation. If all I have is the relationship and then I find a value for $m$ using this relationship and not any equation, will this value mean anything?