Hull speed calculator
A displacement hull makes a wave as long as itself. Going faster means climbing its own bow wave, which takes disproportionate power.
kt
kW
Hull speed
7.281kt
- Hull speed
- 13.49 km/h
- Speed to length ratio at your speed
- 1.1042
- Above hull speed
- 0
- Displacement to length ratio
- 172.0
- Rough power for that speed
- 90.87 kW
- Speed that power might reach
- 3.62 kt
Show the working
- Waterline length = 9
- Displacement = 4500
- Speed to evaluate = 6
- Engine power = 20
- lwl_ft = 9 * 3.280839895013123 = 29.5276
- Hull speed = 1.34 * sqrt(29.5276) = 7.281 46
- Hull speed = 7.281 46 * 1.852 = 13.4853
- Speed to length ratio at your speed = 29.5276 > 0 ? 6 / sqrt(29.5276) : 0 = 1.104 17
- Displacement to length ratio = 29.5276 > 0 ? (4500 / 1016.0469088) / (0.01 * 29.5276)^3 : 0 = 172.035
- Above hull speed = 6 > 7.281 46 ? 1 : 0 = 0
- Rough power for that speed = 4500 > 0 ? 4500/1000 * 1.104 17^3 * 15 : 0 = 90.8691
- Speed that power might reach = 4500 > 0 ? (20 / (4500/1000 * 15))^(1/3) * sqrt(29.5276) : 0 = 3.622 62
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- hull speed in knots = 1.34 x sqrt(waterline length in feet)
- the constant comes from the deep-water wave speed relation
Hull speed is a soft limit, not a wall. Light, slender hulls exceed it; heavy ones struggle to reach it.
Power required rises roughly with the cube of the speed-length ratio, which is why the last knot is so expensive.