Horsepower for a Target Planing Speed
The shaft horsepower Crouch's formula says a planing hull needs to hit a target speed.
Example
You enter
- Target planing speed (mph) 34.7
- Loaded displacement (lb) 6000
- Hull constant C (150 cruiser / 190 runabout / 210 race) 190
You get
- Required shaft horsepower 200 hp
No published worked example is on file for this calculation. It is checked against a hand-worked derivation of its method and an independent reference test.
Details, formula, and sources
Scopehp = weight x (speed / C)^2 (speed taken as mph; Gerr quotes knots for the same C; C about 150 average runabout / cruiser, 190 high-speed 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 or tablehp = weight_lb x (speed_mph / C)^2, with the hull constant C ~150 average runabout-cruiser / ~190 high-speed runabout / ~210 race; the inverse of speed_mph = C / sqrt(weight / hp).
Source and editionCrouch's planing-speed formula (naval-architecture back-of-envelope) solved for the power, by name; the actual hull, propeller, and conditions govern.
Free accessCrouch's formula is a published naval-architecture estimate; the displacement, target speed, and hull constant come from the boat and its class.
What governsEstimate. AHJ and licensed professional govern.
API field namestarget_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 average runabout / cruiser, ~190 high-speed runabout, ~210 race; it dominates the estimatenaval-architecture practice