On Turning Ships

Along time ago, in a galaxy far far away I wrote a paper [1]  on the relationship between ship tactical diameter size and speed. In that paper I used a hand waving argument based on geometric similarity and hydrodynamic forces scaling with the square of speed to conclude that the tactical diameter should be independent of speed and proportional to length.

Here I just want to observe that this result can be deduced from dimensional analysis. The variables of interest are D the tactical diameter (we could use turn rate but when converted back into tactical diameter we would get the same result), L the ship length (or the cube root of displacement, since we are considering a geometrically similar family of vessels these scale in the same way) and speed v. The only dimensionless quantity that can be formed from these is D/L (ignoring powers of this ratio which will give the same result in the end). Thus the only dimensionally correct relation between the variables is essentially of the form D/L=k a constant. Thus we get that the tactical diameter is independent of speed and proportional to length.

The more-or-less independence of speed is supported by the data presented in [1], though the length dependence is rather poorly supported. presumably because the ships considered are not geometrically similar.

References
1. Larham R. “On Turning Ships”, Summer 1983, Battlefleet (Journal of the Naval Wargames Soc.)
https://www.researchgate.net/publication/312472208_On_Turning_Ships