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Hull speed ordisplacement speed is the speed at which the wavelength of a vessel'sbow wave is equal to thewaterline length of the vessel. As boat speed increases from rest, the wavelength of the bow wave increases, and usually itscrest-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.Ship drag for a displacement hull increases smoothly 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 modernnaval architecture, where considerations of speed/length ratio orFroude number are considered more helpful.

As a ship moves in the water, it createsstanding waves thatoppose its movement. This effect increases dramatically in full-formed hulls at aFroude 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.

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 infeet, and

${\displaystyle v_{hull}}$ is the hull speed of the vessel inknots

Note that the 1.34 is not a dimensionless constant.

If the length of waterline is given inmetres and desired hull speed in knots, the coefficient is 2.43 kn·m^−½. 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, or 1.25 to 1.41 m·s⁻¹·m^−½ in SI 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.

Because the hull speed is related to the length of the boat and the wavelength of the wave it produces as it moves through water, there is another formula that arrives at the same values for hull speed based on the waterline length.

${\displaystyle v_{hull}=\sqrt{\frac{L_{WL}\cdot g}{2\pi }}}$

where

${\displaystyle L_{WL}}$ is the length of the waterline in meters,

${\displaystyle v_{hull}}$ is the hull speed of the vessel in meters per second, and

${\displaystyle g}$ is the acceleration due to gravity in meters per second squared.

This equation is the same as theequation used to calculate the speed of surface water waves in deep water. It dramatically simplifies the units on the constant before the radical in the empirical equation, while giving a deeper understanding of the principles at play.

Wave-making resistance depends on the proportions and shape of the hull: many modern displacement designs can exceed their hull speed even withoutplaning. These include hulls with very fine ends, long hulls with relatively narrowbeam andwave-piercing designs. Such hull forms are commonly used bycanoes,competitive rowing boats,catamarans, andfast ferries. For example, racing kayaks can exceed hull speed by more than 100% even though they do not plane.

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

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

Semi-displacement hulls are usually intermediate between these two extremes.

• Ship resistance and propulsion – Forces in naval architechture
• Wave-making resistance – Energy of moving water away from a hull

• 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

Wikimedia Commons has media related toHull speed.

• Converter: knots > km/h & km/h > knots

• Marine propulsion
• Fluid dynamics
• Water waves

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