Crouch Planing-Speed Estimate
The planing top-speed estimate and its diminishing return, the opposite regime from the displacement hull-speed wall.
Example
You enter
- Loaded displacement (lb) 6000
- Shaft / propeller horsepower (hp) 200
- Hull constant C (150 cruiser / 190 runabout / 210 race) 190
You get
- Planing speed 34.7 mph (30.1 kn)
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
ScopeCrouch's formula speed = C / sqrt(weight / hp), taken as miles per hour (Gerr's Propeller Handbook quotes knots for the same C), with the hull constant C about 150 average runabout / cruiser, 190 high-speed runabout, 210 race. A 6,000 lb runabout with 200 hp and C = 190 makes 34.7 mph; double the power to 400 hp and it reaches only 49.1 mph -- twice the horsepower buys sqrt(2) = 41% more speed, not double, because speed scales with the square root of the power-to-weight ratio. Assumes the boat is on plane (below the planing threshold use displacement hull speed). A planning estimate; the hull, propeller, and conditions govern.
Formula or tablespeed_mph = C / sqrt(weight_lb / hp), with the hull constant C ~150 average runabout-cruiser / ~190 high-speed runabout / ~210 race.
Source and editionCrouch's planing-speed formula (naval-architecture back-of-envelope for planing top speed), by name; the actual hull, propeller, and conditions govern.
Free accessCrouch's formula is a published naval-architecture estimate; the displacement, horsepower, and hull constant come from the boat and its class.
What governsEstimate. AHJ and licensed professional govern.
API field namesdisplacement_lb, shaft_hp, hull_constant, speed_mph
- Units the result is mph, not knots; do not compare directly to a displacement hull speed in knotsCrouch's formula convention
- Square-root return speed scales with sqrt(hp/weight), so doubling power gains about 41%Crouch's formula
- Hull constant C ~150 average runabout / cruiser, ~190 high-speed runabout, ~210 race; it dominates the estimatenaval-architecture practice