As this is for a game does it have to be realistic?
If not you can make the equation to suit your needs. I.e if r = radius and m = mass then You can then decide the factor k yourself.
Is this what you had in mind?
Hi. I'm doing a small video game project. Would there be a very simple, generic formula I could use for modeling the blast radius of an explosion? I.e., a general relationship between yield (or perhaps mass) and blast radius? I'm not creating a detailed simulation of explosion effects or anything... I just need to detonate virtual bombs and have the blast circle for each bomb seem appropriately sized for the various yields (or masses) used.
It has to be realistic in the sense of "models reality" but not in the sense of "models all aspects of reality". The user will be inputting the explosion yields (or masses). Therefore, my formula cannot be pure fiction because there is the possibility that the user might know something about the general relationship between blast radius and explosion yield, and thus might expect certain adjustments in the yield to result in appropriate adjustments to the blast radius. This is significant because the coverage of the blast will affect the user's score.
On the other hand, this model can be simplified somewhat because I don't need to know the differences in force or pressure at various points along the radius. I just need to calculate some effective "edge".
(Thinking out loud...)
Wouldn't it be something along the lines of
where Y is the yield (mass, whatever) and K is the constant?
My thinking: say we translate the value of Y directly into a number of lines (rays) emanating from a single point of origin (the center of the explosion). We could say these are traveling particles from the explosion. In any (very) idealized explosion, these particles would move out in all directions in (3D) space, in an equidistant manner. So, if we wanted to calculate the strength (S) of the explosion at any point of distance from the origin, maybe we could divide the yield by the area of a sphere formed at that radius:
or
So, if I make S a constant (some lower strength value defining the effective edge of the explosion), then for my purposes the formula can be stated as:
or
Thoughts...? Obviously not taking account factors like the ground surface, or gravity pulling particles down. But these are not factors in my game project, either.