In one of my periods of wishful thinking about what was possible for powering ships, I conceived of a 38-knot light battlecruiser. The designed displacement was 29,000 tons and the armament was 4-13.5in/45 guns. The powerplant would generate 180,000 SHP. The speed-length ratio (V/sqrt(L)) was 1.3034. The dimensions were 850ft x 95ft x some draft. Let us assume a Cp=0.54 and a Cm=0.92. That would mean that the mean draft was 25.3ft. Two years later, I estimated it would take 209,235 SHP to reach 38 knots. Right now, I would not believe that 38 knots would be reachable under any circumstances.
The look of the ship was not that dissimular to the Courageous, except that the bow was raked. I gave her two funnels, with the fore funnel raised. There was no conning tower. The bridgework just rose at the start of the deckhouse. There was a tripod mast with a lower director top and then the main top centered on the mast. There was a light pole topmast with yards. There was also a mainmast that was sufficent to have a derrick. There was the usual distinctive top, with the triangular web pieces and then the pole topmast with a yard. The forecastle was very long, with a step foreward of the after turret. I didn't include any secondary armament, but there should have been at least some 4in guns for anti-torpedo work.
I had the mistaken idea, thirty years ago, that you could extrapolate a speed-length curve, based on SHP/ton of displacement. The problem is that "kind of works" for the residuary resistent (wavemaking), but it ignores the frictional resistence.
Frank Fox had seen my fantasy ship that had hoped to reach 45 knots, and gently demonstrated that it couldn't be done. The fastest that was feasible was about 33 knots (as I recall). The problem was that the length was too short (770ft). If you want speed, you must have length with enough displacement to carry a large power plant.
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