About Hull Speed Calculator (1.34·√LWL, S/L Ratio & Crouch)
The hull speed calculator estimates how fast a boat can go from its waterline length using the classic Froude-derived displacement rule V = 1.34·√LWL: when the speed-length ratio reaches about 1.34, the bow wave the hull generates is as long as the waterline itself, the boat sits in the trough of its own wave, and pushing faster demands disproportionately more power. A 25 ft waterline gives 1.34 × 5 = 6.7 knots (7.7 mph). Hull speed is a soft guidance limit, not a wall — light, easily driven hulls exceed it, and heavy ones struggle to reach it.
Two companion cards put that number in context. The speed-length ratio card computes S/L = V/√LWL for any speed and bands it into displacement (below 1.34), semi-displacement (1.34 up to 2.9), or planing (2.9 and above) operation, following the regime framing in Dave Gerr's Propeller Handbook. The Crouch card estimates the top speed of a planing powerboat from displacement and shaft horsepower with Crouch's empirical formula V = C/√(Δ/SHP) — in knots, as Gerr formulates it — using his published constants: C = 150 for average runabouts and cruisers, 190 for high-speed runabouts, and 210 for race boats.
How It Works
- Enter the waterline length LWL in feet (not the length overall — LWL is the length actually in the water at rest). The hull speed card returns 1.34·√LWL in knots and statute mph, and the chart shows how hull speed grows with the square root of waterline length, with your boat marked on the curve.
- Enter a boat speed in knots to check the speed-length ratio S/L = V/√LWL for the same waterline. The regime badge classifies the ratio: below 1.34 the hull runs in displacement mode, from 1.34 to just under 2.9 it is in the semi-displacement transition, and at 2.9 or above it is planing. The bands are guidance — real hulls transition gradually and the exact edges vary by hull form.
- For a planing powerboat, enter the loaded displacement in pounds and the shaft horsepower, then pick a Crouch constant: the presets are Gerr's 150 (average runabouts, cruisers, passenger vessels), 190 (high-speed runabouts, very light high-speed cruisers), and 210 (race boat types), or enter a custom C between 100 and 250 for a hull you have trial data on.
- The Crouch result is in knots — Gerr's formulation — with a statute-mph twin readout (1 kt = 1.15078 mph). Because speed scales with √(SHP/Δ), doubling horsepower multiplies the estimate by only √2 ≈ 1.41, and adding weight costs speed the same way.
Worked Example
A runabout displaces 3,000 lb loaded and carries 100 shaft horsepower. With the average-runabout constant C = 150, Crouch's formula gives V = 150/√(3000/100) = 150/√30 = 27.39 knots, or 31.52 mph. For comparison, a displacement cruiser with a 25 ft waterline has a hull speed of 1.34 × √25 = 6.7 knots (7.71 mph), and running that hull at 10 knots would mean a speed-length ratio of 10/√25 = 2.000 — deep in the semi-displacement band, far past the 1.34 hull-speed point but short of the 2.9 planing edge.
Formulas
- Displacement hull speed (classic Froude-derived rule)
V_hull = 1.34 * sqrt(LWL)- Speed-length ratio and regime bands
S/L = V / sqrt(LWL); displacement < 1.34 <= semi-displacement < 2.9 <= planing- Crouch's planing speed formula (Gerr's formulation)
V = C / sqrt(Δ / SHP)
Standards & References
- Dave Gerr, Propeller Handbook (International Marine), pp. 15-17 — Crouch's formula in knots and the C constants by hull type
- Dave Gerr, Propeller Handbook ch. 2 — speed-length-ratio regimes; true planing above an S/L of about 2.9
- Classic Froude-derived displacement hull speed relationship V = 1.34·√LWL
Frequently Asked Questions
Is hull speed a hard limit on how fast my boat can go?
No — it is a soft guidance point, not a wall. At S/L ≈ 1.34 the bow wave is as long as the waterline and drag climbs steeply, so pushing a heavy displacement hull past it takes enormous power for little gain. But light, slender hulls (multihulls, rowing shells, light cruisers) routinely exceed 1.34, and semi-displacement and planing hulls are designed to climb past it. Treat 1.34·√LWL as the economical cruise ceiling for a conventional displacement hull.
Does Crouch's formula give knots or mph?
As formulated in Dave Gerr's Propeller Handbook (pp. 15-17), V = C/√(Δ/SHP) with C = 150/190/210 gives KNOTS, and that is what this calculator encodes, with a statute-mph twin readout at 1.15078 mph per knot. Some older texts print the same formula with constants intended for mph, which is a common source of confusion — if you calibrate a custom C from trial data, be consistent about the unit you measured.
Which Crouch constant C should I use?
Gerr's published values: C = 150 for average runabouts, cruisers, and passenger vessels; 190 for high-speed runabouts and very light high-speed cruisers; and 210 for race boat types. The vast majority of ordinary planing craft are at or just above 150 — reaching 190+ requires a narrow, efficient, lightly loaded hull. If you have measured trial data for a sister hull, back-calculate C = V·√(Δ/SHP) and use it as a custom constant.
What is the speed-length ratio and what do the regime bands mean?
S/L = V(knots)/√LWL(ft) normalizes speed by waterline length so hulls of different sizes can be compared. Below about 1.34 the hull runs in displacement mode, fully supported by buoyancy. From 1.34 to about 2.9 it is semi-displacement: partly wave-bound, partly lifted, with rapidly rising power demand. At about 2.9 and above the hull is planing, supported mostly by dynamic lift. The edges are guidance, not physics constants — published sources place the planing transition anywhere from 2.5 to 3.0 depending on hull form.
Why does my boat need so much more power for a few more knots?
Resistance grows non-linearly with speed. Near hull speed, wave-making drag rises steeply because the hull is climbing its own bow wave — the last knot before S/L 1.34 can cost more power than all the previous ones. Once planing, Crouch's formula shows speed scales with √(SHP/Δ): to double a planing boat's speed you need four times the power-to-weight ratio, which is why weight reduction is as valuable as horsepower.
Should I use waterline length or length overall?
Waterline length (LWL) — the length of the hull actually in the water at rest. Bow overhangs and swim platforms add length overall (LOA) but do not lengthen the wave system the hull generates at displacement speeds. On many sailboats LWL is 10-20% shorter than LOA, and overhangs immerse as the boat heels or squats, which is one reason real boats can slightly beat the nominal 1.34·√LWL figure.