Horsepower for a Target Planing Speed
The inverse of the crouch-planing-speed tile: the shaft horsepower Crouch's formula says a planing hull needs to hit a target speed, hp = weight x (speed / C)^2 (speed in MILES PER HOUR, not knots; C about 150 cruiser, 190 runabout, 210 race). A 6,000 lb runabout targeting 34.7 mph at C = 190 needs 200 hp; to reach 49.1 mph it needs about 400 hp -- horsepower rises with the SQUARE of the target speed, so 40% more speed roughly doubles the power. Assumes the boat is on plane. A planning estimate; the hull, propeller, and conditions govern.
Formula and source
hp = weight_lb x (speed_mph / C)^2, with the hull constant C ~150 heavy cruiser / ~190 runabout / ~210 race; the inverse of speed_mph = C / sqrt(weight / hp).
Crouch's planing-speed formula (naval-architecture back-of-envelope) solved for the power, by name; the actual hull, propeller, and conditions govern.
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