Hull speed, sometimes referred to as displacement speed, is the speed of a boat at which 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, with no noticeable inflection at hull speed. 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, 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 70%, even though they do not plane. Semi-displacement hulls are intermediate between these two extremes.
Hull speed can be calculated by the following formula:
where:
"LWL" is the length of the waterline in feet, and
"v" is the speed of the vessel in knots
The constant may be given as 1.34 to 1.51 knot·ft−½, or in metric units, 4.50 to 5.07 km·h–1·m-½ (where LWL is measured in metres and v is the speed in km/h)
Wave making resistance begins to increase dramatically in full-formed hulls at a Froude number of about 0.35, which corresponds to a speed-length ratio of slightly less than 1.20. This is due to a rapid increase of wave-making resistance due to the transverse wave train. At a Froude Number of 0.40 (speed-length ratio about 1.35) the wave-making resistance increases further due to the increase of the resistance caused by the divergent wave train which is added to the transverse wave train resistance. This rapid 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. On the other hand, these values change dramatically as the general proportions and shape of the hull are changed. Modern displacement designs that can easily exceed their 'hull speed' without planing include hulls with very fine ends, long hulls with relatively narrow beam and wave-piercing designs. These benefits are commonly realized by some canoes, competitive rowing boats, catamarans, fast ferries and other commercial, fishing and military vessels based on such concepts.
Since the wave amplitude increases the energy transferred to the wave for a given hull length the wave drag can be very sensitive to the vessel's weight.
A knot = 1 nautical mile per hour
1 knot = 1.8520 km/h
1 km/h = 0.540 knots
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