Why should it use square of the radius? If it isn't just going to use radius, it should use cube of radius since ships are three dimensional objects? 
It's not so much about realism as balance. If you add up all the radiuses of ships in a cap, you tend to get much lower totals for low-cap ships than for high-cap ships. So it's much harder to boost the attacks of a cap of high-cap ships. If you instead look at the squares of ships' radiuses, the total per cap is approximately independent of cap size. (There's great variation between ship types, but those are the trends.) This is the point I was ineloquently trying to make in
this post a while ago. The graphs show that a cap of high-cap ships
should be just as easy to boost as a cap of low-cap ships (on average), but this contradicts players' experience.
Anyway, when I get some time I'll try and set up a little experiment with carefully chosen starting bonus ships against 1/1 Turtles, and try to confirm my hunch. (Or anyone's welcome to beat me to it!)
