# wave generation

Discussion in 'Powerboats' started by Zekamaboy, Jan 18, 2010.

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### ZekamaboyNew Member

Hi there

For any given power boat, I'm interested in the size of the wave(s) generated by the boat a) just below planing speed, and b) just above planing speed.

This is from an environmental viewpoint.

I wondered whether the wave size (height, length, speed) was greater at sub-planing speed. I read elsewhwhere that once a boat is on the plane, the faster it goes the lower the wave height generated. Since wave velocity is proportional to wave height (I think!) then would this imply that planing waves have less impact on the shore than displacement waves?

Any anecdotal and mathematical input on this issue would be much appreciated, thanks.

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### tom28571Senior Member

A primary anecdotal observation is that almost all boats generate the highest waves in the lower end of the transition range between displacement and planing. In this range the boat is still down on (or nearly on) its static displacement lines and pushing the most water which generates the waves.

After reaching full planing speed, far less of the boat hull is submerged and thus less wave height is formed. The force required to maintain the boat in equilibrium is the same regardless of the speed, whether the force is from buoyancy (displacement) or dynamic (planing) source. The vertical component of this lifting force is always equal to the weight of the boat. When planing, the work or energy required to hold the boat in equilibrium is spread over a greater distance and while the total energy put into the waves is nearly the same per unit of time, the incremental wave height is lower.

I said the total energy put into the waves is "nearly" the same because the trim angle of the hull changes with speed. A higher trim angle results in more energy directed forward which adds to wave height. At higher speed, lesser trim angle is needed to support the boat and thus less energy is wasted in generating waves.

No math here, just a thought experiment resulting from observation. I'm sure those steeped in theory can find some fault with these ideas, but it does fit the observable situation.

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### matt H.Junior Member

lately I have been studying shore lines and possibly a better way of naturally cleaning lakes just from subtle wakes that boats create
its interesting and almost as though the natural lake almost gives its own remedy

different style hulls and how the boats weight is distributed makes a difference in wakes

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### jehardimanSenior Member

No. FWIW, wave energy per ft of wave face is proportional to wave length*height squared, and wave length is proportional to period squared, and wave speed is proportional to period. This means that as a vessel speeds up, wake wave length increases and wake height decreases even though the energy in the wake is increasing approximately with the square of the speed.

It is important to remember that wave height has very little to due with either beach erosion or wake energy. Rather it is wave energy proportional to wave period leading to longer time above the minimum Keuleganâ€“Carpenter numbers on the grain size that effect erosion. See Oceanographical Engineering by Robert Wiegel and the wiki on Sediment Transport. There were also some recent (last 2 or 3 years) papers in SNAME Transactions and Marine Technology on wakes and erosion. There are also some studies not to use (such as the WDOT one on high speed ferries in Rich Passage), as they have had significant technical comment.

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### CDKretired engineer

The impact on the shore is different, not necessarily less. The energy stored in a small wave traveling at say 40 mph may cause more damage than a high wave going much slower.
I used to think that planing would bother nearby boat owners less, but that is just because of the distance between me and the guy who was hit by a fast moving wave.

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### matt H.Junior Member

I would suspect that since sound travels through water that there
is some sort of scale
cleanliness /temp / altitude .
then going into speed that the wake is made as sound and could possibly reinforce the wake in a harmonic disposition
ultimately its all quite interesting really, the theory one could displace or posibly
even cancel a under water shock wave would be of great interest
to many

Im guessing with math and physics one could gather some rough data just from this picture

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### Leo LazauskasSenior Member

"Macfarlane Renilson wave wake"
then try,
"Doctors Day wave generation"
then try,
"Molland Wash Wave"
and finally
"transverse diverging wave decay"

That should give you a few different models for wave decay of displacement vessels.

Have fun!
Leo.

Last edited: Jan 19, 2010
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### BitoJunior Member

Some Math

Wave generation by a planing hull is related to the pressure drag, which can be approximated for most planing boats with straight sections as follows:

Wave Drag = Pressure Drag = Displacement x Tangent(Trim Angle)

See "Hydrodynamic Design of Planing Hulls," by D. Savitsky, in the 1964 issue of Marine Technology, for more information on trim and drag.

Trim angle reaches a maximum at, "hump speed," which is just before the boat gets on plane. Using the methods in Savitsky, 1964, you can estimate the trim and the pressure drag. You may be able to find a program for free to do the calculations. Use of displacement*tan(trim) could help you relate wakes between different boats, if you know some baseline boat.

There is a recent paper in the January, 2010 issue of Marine Technology, by D. Savitsky and M. Morabito, that deals with "The Surface Wave Contours Associated with the Forebody Wake of Stepped Planing Hulls." This paper discusses the trough made directly behind a planing hull. There are references to a number of studies done at the Davidson Laboratory, Stevens Institute of Technology, on wake measurements behind planing boats. These measurements were typically done within 6 beams aft of the boat and a few beams on either side. These equations will not be applicable far from the boat.

The paper has some equations for the dimensions of the trough just behind the boat. Essentially, the trough gets bigger as trim and wetted length (and hence displacement) increases. There are some analytical solutions mentioned in the paper, dating back to the 1930s and 1940s, but these are not yet ready for use.

Essentially, displacement * tan(trim) is what drives the size of the hole behind the boat, which drives the wave pattern far away. I haven't seen any research on the connection between the hole behind the boat and the wave pattern far away, although it may not be too difficult to determine. You are essentially a moving pressure patch, a subject that has been treated by people like Sir. Thomas Havelock and Larry Doctors.

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### Leo LazauskasSenior Member

If the original poster just wants the wave pattern behind moving pressure distributions then there are some equations and plots in:

There are also some whacky distributions with very small wave
resistance in:
but there are no wave patterns in that paper.

Leo.

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### ZekamaboyNew Member

Hi all

I'm not sure whether this comment is in the right place (inexperienced in forum usage), but I would like to thank you all for your contributions to my query, they have pointed me in a much more accurate direction than I was originally going.

Cheers

Zekamaboy

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