492:, is often used on large power vessels to reduce wave-making drag. The bulb alters the waves generated by the hull, by changing the pressure distribution ahead of the bow. Because of the nature of its destructive interference with the bow wave, there is a limited range of vessel speeds over which it is effective. A bulbous bow must be properly designed to mitigate the wave-making resistance of a particular hull over a particular range of speeds. A bulb that works for one vessel's hull shape and one range of speeds could be detrimental to a different hull shape or a different speed range. Proper design and knowledge of a ship's intended operating speeds and conditions is therefore necessary when designing a bulbous bow.
420:, the hull actually settles slightly in the water as it is now only supported by two wave peaks. As the vessel exceeds a speed-length ratio of 1.34, the wavelength is now longer than the hull, and the stern is no longer supported by the wake, causing the stern to squat, and the bow to rise. The hull is now starting to climb its own bow wave, and resistance begins to increase at a very high rate. While it is possible to drive a displacement hull faster than a speed-length ratio of 1.34, it is prohibitively expensive to do so. Most large vessels operate at speed-length ratios well below that level, at speed-length ratios of under 1.0.
91:
speaking, these two wave systems, i.e., bow and stern waves, interact with each other, and the resulting waves are responsible for the resistance. If the resulting wave is large, it carries much energy away from the ship, delivering it to the shore or wherever else the wave ends up or just dissipating it in the water, and that energy must be supplied by the ship's propulsion (or momentum), so that the ship experiences it as drag. Conversely, if the resulting wave is small, the drag experienced is small.
95:
between the bow wave and stern wave is proportional to the length of the ship at the waterline. For example, if the ship takes three seconds to travel its own length, then at some point the ship passes, a stern wave is initiated three seconds after a bow wave, which implies a specific phase difference between those two waves. Thus, the waterline length of the ship directly affects the magnitude of the wave-making resistance.
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it resonates with a wave that has a trough under it. If it has about twice the length it will therefore have only square root (2) or 1.4 times the speed. In practice most planing hulls usually move much faster than that. At four times hull speed the wavelength is already 16 times longer than the hull.
529:
A qualitative interpretation of the wave resistance plot is that a displacement hull resonates with a wave that has a crest near its bow and a trough near its stern, because the water is pushed away at the bow and pulled back at the stern. A planing hull simply pushed down on the water under it, so
473:
design. The total amount of water to be displaced by a moving hull, and thus causing wave making drag, is the cross sectional area of the hull times distance the hull travels, and will not remain the same when prismatic coefficient is increased for the same lwl and same displacement and same speed.
109:
A simple way of considering wave-making resistance is to look at the hull in relation to bow and stern waves. If the length of a ship is half the length of the waves generated, the resulting wave will be very small due to cancellation, and if the length is the same as the wavelength, the wave will
94:
The amount and direction (additive or subtractive) of the interference depends upon the phase difference between the bow and stern waves (which have the same wavelength and phase speed), and that is a function of the length of the ship at the waterline. For a given ship speed, the phase difference
90:
A salient property of water waves is dispersiveness; i.e., the greater the wavelength, the faster it moves. Waves generated by a ship are affected by her geometry and speed, and most of the energy given by the ship for making waves is transferred to water through the bow and stern parts. Simply
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Since semi-displacement and planing hulls generate a significant amount of lift in operation, they are capable of breaking the barrier of the wave propagation speed and operating in realms of much lower drag, but to do this they must be capable of first pushing past that speed, which requires
309:
98:
For a given waterline length, the phase difference depends upon the phase speed and wavelength of the waves, and those depend directly upon the speed of the ship. For a deepwater wave, the phase speed is the same as the propagation speed and is proportional to the square root of the
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barrier and transition into a realm where drag increases at a much lower rate. The disadvantage of this is that planing is only practical on smaller vessels, with high power-to-weight ratios, such as motorboats. It is not a practical solution for a large vessel such as a
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of the bow wave, the rate of increase of the wave drag will start to reduce significantly. The planing hull will rise up clearing its stern off the water and its trim will be high. Underwater part of the planing hull will be small during the planing regime.
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then it is possible to refine the hull shape along its length to reduce wave resistance at one speed. This is practical only where the block coefficient of the hull is not a significant issue.
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Reducing the displacement of the craft, by eliminating excess weight, is the most straightforward way to reduce the wave making drag. Another way is to shape the hull so as to generate
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that affects surface watercraft, such as boats and ships, and reflects the energy required to push the water out of the way of the hull. This energy goes into creating the wave.
392:{\displaystyle {\mbox{c in knots}}\approx 2.429\times {\sqrt {\mbox{length in m}}}\approx {\sqrt {6\times {\mbox{length in m}}}}\approx 2.5\times {\sqrt {\mbox{length in m}}}}
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bow, with a sharper angle that pushes the water out of the way more gradually, the amount of energy required to displace the water will be less. A modern variation is the
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Since wave-making resistance is based on the energy required to push the water out of the way of the hull, there are a number of ways that this can be minimized.
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Sukas, Omer Faruk; Kinaci, Omer Kemal; Cakici, Ferdi; Gokce, Metin Kemal (2017-04-01). "Hydrodynamic assessment of planing hulls using overset grids".
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significant power. This stage is called the transition stage and at this stage the rate of wave-making resistance is the highest. Once the hull gets
304:{\displaystyle {\mbox{c in knots}}\approx 1.341\times {\sqrt {\mbox{length in ft}}}\approx {\frac {4}{3}}\times {\sqrt {\mbox{length in ft}}}}
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Thus, the magnitude of the wave-making resistance is a function of the speed of the ship in relation to its length at the waterline.
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A graph showing resistance–weight ratio as a function of speed–length ratio for displacement, semi-displacement, and planing hulls
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rule of thumb used to compare potential speeds of displacement hulls, and this relationship is also fundamental to the
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416:" (speed in knots divided by square root of length in feet) of 0.94, it starts to outrun most of its
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A hull with a blunt bow has to push the water away very quickly to pass through, and this high
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Proceedings of the Royal
Society of London. Series A, Mathematical and Physical Sciences
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83:, such as sailboats or rowboats, wave-making resistance is the major source of the
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Squire, H. B (1957). "The Motion of a Simple Wedge along the Water
Surface".
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the gravitational acceleration. Substituting in the appropriate value for
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If the hull is designed to operate at speeds substantially lower than
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Graph of power versus speed for a displacement hull, with a mark at a
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These values, 1.34, 2.5 and very easy 6, are often used in the
103:. That wavelength is dependent upon the speed of the ship.
656:, Daniel Savitsky, Professor Emeritus, Davidson Laboratory,
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as it moves through the water. Semi-displacement hulls and
409:, used in the comparison of different scales of watercraft.
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hulls do this, and they are able to break through the
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173:{\displaystyle c={\sqrt {{\frac {g}{2\pi }}l}}}
465:requires large amounts of energy. By using a
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133:of waves is given by the following formula:
27:For wave drag on supersonic aircraft due to
48:creating waves in calm water at low speed.
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424:Ways of reducing wave-making resistance
38:Energy of moving water away from a hull
654:On the subject of high speed monohulls
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508:Semi-displacement and planing hulls
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545:Hull (watercraft)#Categorisation
488:A special type of bow, called a
658:Stevens Institute of Technology
540:Ship resistance and propulsion
202:is the length of the wave and
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110:be large due to enhancement.
412:When the vessel exceeds a "
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634:10.1016/j.apor.2017.03.015
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622:Applied Ocean Research
591:10.1098/rspa.1957.0202
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53:Wave-making resistance
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432:Reduced displacement
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414:speed–length ratio
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235:{\displaystyle g}
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126:{\displaystyle c}
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296:length in ft
271:length in ft
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678:Water waves
490:bulbous bow
484:bulbous bow
478:Bulbous bow
451:supertanker
384:length in m
365:length in m
346:length in m
29:shock waves
667:Categories
556:References
550:Hull speed
502:hull speed
457:Fine entry
446:hull speed
403:hull speed
329:c in knots
254:c in knots
101:wavelength
79:For small
642:0141-1187
628:: 35–46.
607:121875606
378:×
372:≈
360:×
352:≈
340:×
334:≈
290:×
277:≈
265:×
259:≈
160:π
33:wave drag
534:See also
418:bow wave
579:Bibcode
442:planing
317:units:
313:or, in
75:of 1.34
63:Physics
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605:
599:100279
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315:metric
182:where
31:, see
603:S2CID
595:JSTOR
337:2.429
262:1.341
638:ISSN
467:fine
438:lift
57:drag
630:doi
587:doi
575:243
375:2.5
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285:3
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230:g
210:g
190:l
166:l
157:2
153:g
146:=
143:c
121:c
35:.
20:)
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