Power vs Hull Speed Calculator (Displacement Boats)
Horsepower to drive a displacement hull near its limit — Gerr's lb-per-hp curves turned into a planning tool, with the brutal last-knot price list.
Run it twice and see the wall: this 14,000-lb cruiser wants ~18 hp for 6.5 kt but ~33 hp for 7.3 (hull speed). Displacement power scales with SL cubed — the formula every repowering conversation should start with.
Formula
⚠️ For planning and education only — verify with your vessel's documentation, naval-architecture data and official sources. Not for navigation or stability decisions on real voyages without professional data.
Horsepower to drive a displacement hull near its limit — Gerr's lb-per-hp curves turned into a planning tool, with the brutal last-knot price list.
About Power vs Hull Speed Calculator (Displacement Boats)
“How big an engine does my boat need?” has a century-old answer for displacement hulls: Dave Gerr's curve relating pounds-per-horsepower to speed-length ratio, with power demand rising as the CUBE of relative speed. This calculator runs it for any displacement and waterline — returning the approximate shaft power for a target speed, the hull-speed context, and a verdict that flags when you've left the regime where more engine helps at all.
How to use Power vs Hull Speed Calculator (Displacement Boats)
- 1Enter — sensible defaults are pre-filled so you see a worked result immediately.
- 2Read the live results: .
- 3Check the "With your numbers" line to see the formula SL = V/√LWL; lb-per-hp = (10.665/SL)³ (Gerr/Crouch displacement relation); hp = Δ ÷ lb-per-hp substituted step by step.
- 4Adjust inputs (or flip the unit toggle) until the scenario matches yours, then copy or share the result.
Why use Power vs Hull Speed Calculator (Displacement Boats)?
- ✓Instant, free and private — every calculation runs in your browser, nothing is uploaded
- ✓Built on the published formula SL = V/√LWL; lb-per-hp = (10.665/SL)³ (Gerr/Crouch displacement relation); hp = Δ ÷ lb-per-hp with sources cited on the page
- ✓Run it twice and see the wall: this 14,000-lb cruiser wants ~18 hp for 6.5 kt but ~33 hp for 7.3 (hull speed). Displacement power scales with SL cubed — the formula every repowering conversation should start with.
- ✓Switch units, tweak any input and watch every result update live
Frequently asked questions
What is speed-length ratio and why does power follow its cube?+
SL = speed ÷ √waterline — the boat-world's Froude number in knots-and-feet clothing (hull speed is SL 1.34). Wave-making resistance grows roughly with the cube of speed in the displacement band, so the lb-per-hp a hull can carry collapses as (1/SL)³: SL 1.0 carries ~1,200 lb/hp, SL 1.3 only ~550. The cube is why the last knot costs double.
How much engine for a typical cruising sailboat's auxiliary?+
The traditional answer falls out of this math: 2–3 hp per ton (2,240 lb) of displacement reaches SL ≈ 1.1–1.2 in calm water — a 14,000-lb sloop motors fine on 18–25 hp. Bumping to 40 hp buys punching into chop and current (real value), not more flat-water speed (the wall doesn't negotiate). Modern boats over-spec for the chop case, sensibly.
Does the formula include propeller losses?+
Gerr's relation is calibrated to shaft horsepower with a decent propeller (50–55% propulsive efficiency baked into its empirical constants). A badly matched prop — wrong pitch, too small, fouled — can eat a third of the predicted performance, which is why repower disappointments are usually propeller stories. Our propeller-slip tool audits that half of the system.
Why does the verdict refuse speeds past SL 1.34?+
Because the empirical curve was fitted in the displacement regime — past hull speed, a true displacement hull squats, drags its stern wave and converts horsepower to wake almost dimensionlessly. Going meaningfully faster requires hull shape (flat run aft, chines) that develops dynamic lift: semi-displacement design. The tool flagging red isn't pessimism; it's telling you the question changed from engine to naval architect.
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