Wake Study – Wavemaking

[Halcyon]

I’m currently doing a wake study and could do with a little help. The study is for a displacement monohull traveling below hull speed. The boat could be of any Lwl, any displacement and any speed < hull speed.

The two areas I need assistance with are:

• The angle of Bow and Stern waves (from the longitudinal centerline)
• Wave height (trough to crest)

Wave angle

Wave angle must be proportional to speed, ie the faster a boat the more acute the angle.

Is speed the only factor (as with wavelength) or does resistance (displacement, Cp, etc.) have an effect?

Are there any formulas or empirical data that can help predict the angle?

Wave Height

With wave height I’m working from the assumption that displacement is the major factor governing wave height with a relationship with speed. I am assuming that none-optimized Cp, entry angle and CoB have an impact but it is marginal.

Length/Beam ratio also appears to have an impact, with slimmer hulls (cat sponsons of 11 to 12 :1 ratios) creating lower wave heights (even when not accounting for interference, one wave canceling or amplifying another).

As with the wave angle, are there any formulas or empirical data that can help predict the wave height?

Could it be that the sum of resistance related to the speed creates the height? Is there a formular?

Your help would be greatly appreciated.

[Leo Lazauskas]

Originally Posted by Halcyon

I’m currently doing a wake study and could do with a little help. The study is for a displacement monohull traveling below hull speed. The boat could be of any Lwl, any displacement and any speed < hull speed.

The two areas I need assistance with are:

• The angle of Bow and Stern waves (from the longitudinal centerline)
• Wave height (trough to crest)

Wave angle

Wave angle must be proportional to speed, ie the faster a boat the more acute the angle.

Is speed the only factor (as with wavelength) or does resistance (displacement, Cp, etc.) have an effect?

Are there any formulas or empirical data that can help predict the angle?

Wave Height

With wave height I’m working from the assumption that displacement is the major factor governing wave height with a relationship with speed. I am assuming that none-optimized Cp, entry angle and CoB have an impact but it is marginal.

Length/Beam ratio also appears to have an impact, with slimmer hulls (cat sponsons of 11 to 12 :1 ratios) creating lower wave heights (even when not accounting for interference, one wave canceling or amplifying another).

As with the wave angle, are there any formulas or empirical data that can help predict the wave height?

Could it be that the sum of resistance related to the speed creates the height? Is there a formular?

Your help would be greatly appreciated.

I don't understand where you got your ideas about wave angles.

The best two references are:

Marine Hydrodynamics - J. N. Newman: A good graduate text.

Surface Waves - Wehausen and Laitone: The great "encyclopedia" of water waves is available online.

Best of luck!
Leo.

[Halcyon]

Leo

Thanks for the reply.

I got my ideas from intuition, not always the best source of information.

Matt

[PI Design]

I have it in my mind that Lord Kelvin (he of the temperature scale) showed that stern waves are always at 19 degrees. Can't find my notes though.

[Leo Lazauskas]

Originally Posted by PI Design

I have it in my mind that Lord Kelvin (he of the temperature scale) showed that stern waves are always at 19 degrees. Can't find my notes though.

The Kelvin angle in infinitely deep water is precisely arctan(1/sqrt(8)). That's about 19.5 degrees.

Newman's book gives an excellent derivation.

Cheers,
Leo.

[Leo Lazauskas]

Originally Posted by Halcyon

Leo

Thanks for the reply.

I got my ideas from intuition, not always the best source of information.

Matt

Save the intuition for betting on horses and picking football winners!

For some examples of wave patterns have a look at:

http://www.cyberiad.net/wakeimages.htm

There are significant differences in finite depth water and finite width channels.

All the best,
Leo.

[Halcyon]

Leo many thanks for your help, it has been invaluable.

I bought Newman as suggested and fortunately my wife went back to the UK and was able to pick up my old math’s books from storage. I haven't done calculus since my engineering degree. Been too busy getting my hands dirty.

In terms of the angle of the wake I was way out, but heck, what are forums for? Thanks to Kelvin, interesting to know he did more than just undercut Celsius.

Perhaps I used the word intuition out of context, by the way I have always broken even at the racetrack (I wouldn’t put too much weight on that though as the data sample is too small, I’ve only been twice) and I hate football, rugby has fewer ponces and better songs.

I also read the papers on your web site.

Some questions on your software and restricted channels for application on environmental impact surveys:

1. Is it possible to modify parameters for the reflective surfaces to emulate, for example, a sandy beach or an angled concrete wall?
2. Could the tool model waves in a channel with a defined shape and profile taked from CAD?

I also found your responses, and others, to a similar post sent on this forum in May last year.

http://boatdesign.net/forums/showthread.php?t=9971

There was an interesting tangent on the nature of the fairer sex on this thread, makes for interesting reading. Gosh this forum is better than "neighbors", who needs soap operas?

Matt

[Leo Lazauskas]

Originally Posted by Halcyon

Leo many thanks for your help, it has been invaluable.
Some questions on your software and restricted channels for application on environmental impact surveys:

1. Is it possible to modify parameters for the reflective surfaces to emulate, for example, a sandy beach or an angled concrete wall?
2. Could the tool model waves in a channel with a defined shape and profile taked from CAD?

No, Michlet is not yet able to predict the effect of beaches or variable seabed geometry. They are very tough problems that I started on but haven't
yet got around to finishing. Among other problems I have is that I have no idea of how beach materials (e.g. sandy, muddy, reedy etc) can be modelled.

A very recent paper on this topic (and some others mentioned in their biblio)
that you might like to look at is:

"Numerical and Experimental Study on Ship Wash Including Wave-Breaking on Shore", Chun-Beom Hong and Yasuaki Doi, JOURNAL OF WATERWAY, PORT, COASTAL, AND OCEAN ENGINEERING, ASCE / SEPTEMBER/OCTOBER 2006.

Good luck,
Leo.