# Hull speed

Hull speed or displacement speed is the speed at which the wavelength of a vessel's bow wave is equal to the waterline length of the vessel. 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 exceeded, a vessel in displacement mode will appear to be climbing up the back of its 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 knot·ft−½) because of the rapid increase of resistance from the transverse wave train. When the Froude Number grows to ~0.40 (speed-length ratio ~1.35), the wave-making resistance increases further from the divergent wave train. This trend of increase in wave-making resistance continues up to a Froude Number of ~0.45 (speed-length ratio ~1.50), and peaks at a Froude number of ~0.50 (speed-length ratio ~1.70).

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

## Empirical calculation and speed-length ratio

Hull speed can be calculated by the following formula:

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

where:

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

If the length of waterline is given in metres and desired hull speed in knots, the coefficient is 2.43. 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−½ in metric units.

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

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.

## References

• A simple explanation of hull speed as it relates to heavy and light displacement hulls
• Hull speed chart for use with rowed boats
• On the subject of high speed monohulls, Daniel Savitsky, Professor Emeritus, Davidson Laboratory, Stevens Institute of Technology
• Low Drag Racing Shells