Horsepower for a Target Planing 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.

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.

Crouch's formula is a published naval-architecture estimate; the displacement, target speed, and hull constant come from the boat and its class.

Estimate. AHJ and licensed professional govern.

Field names used by the API: target_speed_mph, displacement_lb, hull_constant, required_hp

• Square-law power horsepower scales with the square of the target speed, since speed scales with sqrt(hp/weight)Crouch's formula
• Units the target speed is mph, not knots; do not enter a displacement hull speed in knotsCrouch's formula convention
• Hull constant C ~150 heavy cruiser, ~190 runabout, ~210 race; it dominates the estimatenaval-architecture practice