Hull Speed Formula
Calculate the theoretical maximum speed of a displacement hull from its waterline length.
Used in sailboat and powerboat design and performance estimation.
The Formula
V_hull (knots) = 2.43 × √LWL(m)
Hull speed is the theoretical maximum speed at which a displacement hull (a boat that travels through water rather than over it) can efficiently travel. At this speed, the boat sits precisely in the trough between the bow wave and the stern wave it generates. Exceeding hull speed requires a disproportionate increase in power as the hull tries to climb its own bow wave — an energetically unfavourable state for displacement vessels.
Variables
| Symbol | Meaning | Unit |
|---|---|---|
| V_hull | Theoretical maximum hull speed | knots |
| LWL | Length at the Waterline (not total boat length) | feet or metres |
| 1.34 | Empirical constant (LWL in feet) | — |
| 2.43 | Empirical constant (LWL in metres) | — |
Example 1
A 30-foot sailboat has a waterline length of 25 feet. What is its hull speed?
V_hull = 1.34 × √25
V_hull = 1.34 × 5
Hull speed ≈ 6.7 knots
Example 2
A cruising yacht has a waterline length of 9 metres. What is its hull speed?
V_hull = 2.43 × √9
V_hull = 2.43 × 3
Hull speed ≈ 7.3 knots
When to Use It
- Setting realistic passage-planning speed estimates for a displacement sailboat or cruiser
- Comparing performance potential between two boats of different waterline lengths
- Understanding why longer boats are generally faster under sail
- Evaluating whether a motorboat is being driven at an efficient speed
Important exceptions: Planing hulls (powerboats, dinghies, some performance sailboats) can exceed hull speed by riding on top of the water. Semi-displacement hulls operate efficiently slightly above hull speed. Very light racing sailboats with wave-piercing bows can also exceed this theoretical limit. The formula applies most accurately to traditional displacement cruising yachts and ships.
Note that LWL (waterline length) is typically shorter than the boat's overall length (LOA), especially on boats with overhanging bows and sterns. LWL changes slightly with loading — a heavier load sinks the boat slightly, increasing LWL and therefore hull speed marginally.