HS
Theoretical hull speed
V (knots) ≈ 1.34 * sqrt(LWL_ft) ≈ 2.43 * sqrt(LWL_m)
Hull speed (knots) ≈ 1.34 × √LWL (feet), or ≈ 2.43 × √LWL (metres). That is the wave-trap speed for a displacement monohull: not a hard wall, but the point where wave-making resistance climbs steeply. Use waterline length LWL from the yard sheet - never badge LOA. Plan passages at about 80-85% of that number under power.
Formula
V (knots) ≈ 1.34 * sqrt(LWL_ft) ≈ 2.43 * sqrt(LWL_m)
Imperial: LWL in feet, result in knots. Metric: LWL in metres multiplied by 2.43 yields knots (or by 4.50 for km/h). Use strictly waterline length LWL, not LOA.
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Rule of thumb
Practical passage planning rule: set cruising passage speed at 80-85% of theoretical hull speed (ratio 1.05-1.15 instead of 1.34). The engine operates in its fuel sweet spot, consuming 40-50% less diesel than at wide-open throttle. Substituting badge LOA for waterline length overstates a 24-hour run by 15-20 nautical miles.
Limits
Applies strictly to displacement monohulls. Narrow multihull amas create little transverse wave resistance and exceed 1.34 easily without planing. Modern cruising hulls with wide, flat aft sections and hard chines break free from the displacement hollow, surfing at 9-12 knots down Baltic swells under spinnaker.
Boat examples
- Hallberg-Rassy 36
Displacement cruiser: LWL 9.35 m gives 7.42 knots theoretical speed. Economical motoring target sits at 6.0-6.2 knots; attempting 7.4 knots doubles hourly fuel consumption.
- Linjett 40
LWL 11.00 m yields 8.05 knots. Longer waterline raises cruising averages significantly across open Baltic stretches.
- Beneteau First 31.7
LWL 8.80 m calculates to 7.20 knots, yet the lighter hull with wide transom regularly surfs at 9-10 knots on broad reaches in 20 knots of breeze.
History
Rooted in William Froude 1870s towing tank experiments at Torquay. Deep-water transverse wavelength matches vessel waterline at Froude number Fn ≈ 0.40. The bow rides its bow wave crest while the stern sinks into the wave hollow. Climbing out requires huge power or dynamic lift.
FAQ
- What is the hull speed formula?
- V (knots) ≈ 1.34 × √LWL in feet, or ≈ 2.43 × √LWL in metres. Example: LWL 9 m → √9 = 3 → 3 × 2.43 = 7.29 knots.
- Why 1.34?
- It represents deep-water wave mechanics converted to imperial units: sqrt(g / (2*pi)) in feet per second converted into nautical knots gives 1.341.
- Is hull speed a hard speed limit?
- No. It marks where displacement resistance climbs steeply. Multihulls, planing hulls, and modern wide-transom cruisers surfing downwind regularly exceed the number.
- Do I use LOA or LWL?
- Only LWL (waterline). Badge LOA with overhangs overstates the 24-hour run by 15-20 nautical miles if you plug it into 1.34 × √length.
- Does hull speed apply under power?
- Yes. Displacement wave-making resistance governs motoring just as under sail. Excess engine power near Fn 0.40 merely builds a tall stern wave rather than pushing the boat forward.