# Hull speed

Hull speed or displacement speed is the speed at which the wavelength of the boat's bow wave (in displacement mode) is equal to the boat length. As boat speed increases from rest, the wavelength of the bow wave increases, and usually its crest to trough dimension (height) increases as well. When hull speed is reached, a boat in pure displacement mode will appear trapped in a trough behind its very large bow wave.

From a technical perspective, at hull speed the bow and stern waves interfere constructively, creating relatively large waves, and thus a relatively large value of wave drag. Though the term "hull speed" seems to suggest that it is some sort of "speed limit" for a boat, in fact drag for a displacement hull increases smoothly and at an increasing rate with speed as hull speed is approached and exceeded, often with no noticeable inflection at hull speed.

The concept of hull speed is not used in modern naval architecture, where considerations of speed-length ratio or Froude number are considered more helpful.

## Background

As a ship moves in the water, it creates standing waves that oppose its movement. This effect increases dramatically in full-formed hulls at a Froude number of about 0.35, which corresponds to a speed-length ratio (see below for definition) of slightly less than 1.20 (this is due to a rapid increase of resistance due to the transverse wave train). When the Froude Number grows to ~0.40 (speed-length ratio about 1.35), the wave-making resistance increases further due to the divergent wave train. This trend of increase in wave-making resistance continues up to a Froude Number of about 0.45 (speed-length ratio about 1.50) and does not reach its maximum until a Froude number of about 0.50 (speed-length ratio about 1.70).

This very sharp rise in resistance at around a speed-length ratio of 1.3 to 1.5 probably seemed insurmountable in early sailing ships and so became an apparent barrier. This leads to the concept of 'hull speed'.

## Empirical calculation and speed-length ratio

Hull speed can be calculated by the following formula:

$v_{hull} \approx 1.34 \times \sqrt{L_{WL}}$

where:

"$L_{WL}$" is the length of the waterline in feet, and
"$v_{hull}$" is the hull speed of the vessel in knots

The constant may be given as 1.34 to 1.51 knot·ft −½ in imperial units (depending on the source), or 4.50 to 5.07 km·h−1·m in metric units.

The ratio of speed to $\sqrt{L_{WL}}$ is often called the "speed-length ratio", even though it's a ratio of speed to the square root of length.

## Hull design implications

Wave making resistance depends dramatically on the general proportions and shape of the hull: many modern displacement designs can easily exceed their 'hull speed' without planing.

These include hulls with very fine ends, long hulls with relatively narrow beam and wave-piercing designs. Such hull forms are commonly realised by some canoes, competitive rowing boats, catamarans, fast ferries and other commercial, fishing and military vessels based on such concepts.

Vessel weight is also a critical consideration: it affects wave amplitude, and therefore the energy transferred to the wave for a given hull length.

Heavy boats with hulls designed for planing generally cannot exceed hull speed without planing.

Light, narrow boats with hulls not designed for planing can easily exceed hull speed without planing; indeed, once above hull speed, the unfavorable amplification of wave height due to constructive interference diminishes as speed increases. For example, world-class racing kayaks can exceed hull speed by more than 100%,[1] even though they do not plane. Semi-displacement hulls are usually intermediate between these two extremes.

Ultra light displacement boats are designed to plane and thereby circumvent the limitations of hull speed.