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.
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'.
Hull speed can be calculated by the following formula:
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