Wave-making resistance or wave resistance is a form of drag that affects any object moving on a surface of a fluid, such as boats and ships moving on the surface of water, and reflects the energy required to push the water out of the way of that body. For example, the hull of a moving watercraft creates waves (a wake) which carry energy away and resist the motion of the watercraft. Wave resistance is only one of the components of the total resistance or drag experienced by a body moving on a surface of a fluid, others being viscous drag and pressure drag.
Physics background
For small displacement hulls, such as sailboats or rowboats, wave-making resistance is the major source of the marine vessel drag. 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 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. 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 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. 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 wavelength. That wavelength is dependent upon the speed of the ship. From kinematics to design implications. Having established that the interference pattern is governed by speed relative to waterline length, we can articulate the corresponding design-oriented statement and how it guides practical reduction of wave-making drag: 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. In the ship wave system, a crest normally happens just after a high pressure point and trough happens just after a low pressure point in order to reduce the wave making resistance, the wave crest needs to be reduced and wave trough needs to be filled, so the general principles for reducing wave resistance involve reducing pressure just ahead of wave crest and increasing pressure just ahead of trough. Put differently, hull forms and appendages are arranged to manipulate the near-body pressure field so that the bow- and stern-generated waves are encouraged to interfere destructively rather than constructively over the operating range of speeds. Returning to an intuitive picture, this same dependence can be visualized as follows: 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 be large due to enhancement. The phase speed c {\displaystyle c} of waves is given by the following formula:
c = g 2 π l {\displaystyle c={\sqrt {{\frac {g}{2\pi }}l}}}
where l {\displaystyle l} is the length of the wave and g {\displaystyle g} the gravitational acceleration. Substituting in the appropriate value for g {\displaystyle g} yields the equation:
c in knots ≈ 1.341 × length in ft ≈ 4 3 × length in ft {\displaystyle {\mbox{c in knots}}\approx 1.341\times {\sqrt {\mbox{length in ft}}}\approx {\frac {4}{3}}\times {\sqrt {\mbox{length in ft}}}}
or, in metric units:
c in knots ≈ 2.429 × length in m ≈ 6 × length in m ≈ 2.5 × length in m {\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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