Staying Power Models and Naval Wargames

First let me define what I mean by staying power in the context of warship survivability. Staying Power is the ability of a ship to absorb hits and continue operating effectively (or sometimes just surviving). Thus we may measure staying power as the mean number of hits of some standard weapon needed to render the ship mission killed or more drastically sunk.

In many sets of naval wargame rules at least some aspect of staying power increases linearly with displacement. The question that I want to discuss here is how well is this assumption supported by historical data?

One of the main sponsors of the analysis of staying power on the basis of historical data is Captain Wayne Hughes of the Naval Postgraduate School at Monterey. His book [1] contains a summary of some of the results of investigations of historical data on staying power. These results may be summarised as: Staying power is proportional to the cube root of displacement. I have spent some time investigating the assumptions behind these results [2] and find them at least partially flawed, but even with the flaws corrected staying power still appears to vary as the 2/3rd power of displacement (at least for a number of significant forms of attack). There are limitations on the reliability of this modelling but the broad conclusion that staying power grows more slowly than displacement appears to be robust, and we are left with the conclusion that a force of two 20,000 ton ships has greater staying power than a force comprised of a single 40,000 ton ship, even when allowance is made for greater protection that may be built into the larger vessel.

References
1. Hughes W.P., Fleet Tactics and Coastal Combat, Naval Inst Press, 2000.
2. Larham R., Historical Data in Modelling Warship Battle Damage Survival Probability, 2nd IMA Conference on Mathematics in Defence, October 2011, link to copy on Academia.edu