Roll period for large warships

This is based on a conversation I had yesterday with a prominent author and researcher on naval history topics. We had speculated over the last week or so about whether large metacentric heights were appropriate for large warships. The answer is that there are reasonable limits on metacentric height, due to its effect on roll period. The goal is have a roll period of less than 15 seconds for a large warship. Remember that the formula for roll period is

T=roll period in seconds
B=beam in feet
GM= metacentric height in feet
K= a constant that can vary in the range of 0.38 and 0.55

T=(B x K)/sqrt(GM)

It seems that SpringSharp is using a K of 0.42. Prof. Royce, at the Webb Institute told my friend that we should use a K of 0.4, unless there is some specific reason to use something else. If there is a great deal of mass at the sides of the ship, the K would be greater. If the mass was concentrated on the centerline, then the K could be slightly less than 0.4. It turns out that the Bismarck, Tirpitz, and H-Class design all had very large GM values, perhaps above 10.0. My friend speculated that they might have been snappy rollers.