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'''Hull speed''', sometimes referred to as '''displacement speed''', can be thought of as 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, the size of the bow wave increases, and therefore so does its wavelength.  When '''hull speed''' is reached, a boat in pure displacement mode will appear trapped in a trough behind its very large bow wave.
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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 [[Ship resistance and propulsion|drag]] for a displacement hull increases smoothly and at an increasing rate with speed as hull speed is approached and exceeded, with no noticeable inflection at hull speed. However a normal design displacement boat that is not light in weight will begin to climb its own bow wave as its hull speed approaches and it will not be able to climb out of the trough created and so will never reach its hull speed.<ref>http://www.antrimdesign.com/content/heavy-boats-light-boats-and-hull-speed</ref>
 
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 wave]]s that [[Wave making resistance|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 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: 
 
<math>v_{hull} \approx 1.34 \times \sqrt{L_{WL}}</math>
 
where:
:"<math>L_{WL}</math>" is the length of the waterline in [[foot (unit)|feet]], and
:"<math>v_{hull}</math>" is the hull speed of the vessel in [[knot (unit)|knots]]
 
The constant may be given as 1.34 to 1.51 knot·ft <sup>−½</sup> in imperial units (depending on the source), or 4.50 to 5.07&nbsp;km·h<sup>−1</sup>·m<sup>-½</sup> in metric units.
 
The ratio of speed to <math>\sqrt{L_{WL}}</math> 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: modern displacement designs that can easily exceed their 'hull speed' without [[Planing (sailing)|planing]] include hulls with very fine ends, long hulls with relatively narrow beam and [[wave-piercing]] designs. These benefits are commonly realised by some [[canoe]]s, [[Rowing (sport)|competitive rowing boats]], [[catamaran]]s, [[High-speed craft|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 (sailing)|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, the unfavorable amplification of wave height due to constructive interference diminishes as speed increases above hull speed. For example, world-class racing kayaks can exceed hull speed by more than 100%,<ref>[[List of world records in canoeing]]</ref> even though they do not plane.  Semi-displacement hulls are usually intermediate between these two extremes.
 
==See also==
* [[Ship resistance and propulsion]]
* [[Wave making resistance]]
 
==References==
*[http://www.antrimdesign.com/content/heavy-boats-light-boats-and-hull-speed A simple explanation of hull speed as it relates to heavy and light displacement hulls]
*[http://www.frontrower.com/hullspeed.htm Hull speed chart for use with rowed boats]
*[http://legacy.sname.org/newsletter/Savitskyreport.pdf On the subject of high speed monohulls], Daniel Savitsky, Professor Emeritus, Davidson Laboratory, [[Stevens Institute of Technology]]
*[http://www.cyberiad.net/library/rowing/misbond/misbond.htm Low Drag Racing Shells]
<references/>
 
==External links==
* [http://pmyers.pcug.org.au/Freeware/Knotes2KmPerHr.html Converter: knots&nbsp;> km/h  &  km/h&nbsp;> knots]
 
==Useful==
* [http://www.sonar-equipment.com/useful_conversion_factors_table1_p00.htm Conversion Factors and Tables]
 
[[Category:Marine propulsion]]
[[Category:Fluid dynamics]]
[[Category:Water waves]]

Latest revision as of 16:43, 23 November 2014

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