I have seen lots and lots of references to the formula "X times
square root of waterline length" as defining hull speed with X
normally about 1.3 (speed in knots, length in Imperial feet.)
However, I have never seen an explanation of this.

Pictures of boats "trapped" between their bow and stern waves seem
to make sense. But they do not explain why a long wave would travel
faster than a short one.

Surely there is a book with the theory?


Thank you,
Sakari Aaltonen

It is not uncommon in nature for waves of different wavelength to have
different speeds. Light waves in transparent media have slightly different
wavelength dependent speeds, which leads to dispersion into the spectrum by
prisms.

The derivation of the dispersion relationship for gravitational surface
waves on fluids is somewhat complex and not obvious. It is found in many
fairly advanced mechanics texts. You will need to go to a college or
university library to find it. The result: wave speed is 1.3 times sq rt of
wavelength, where the 1.3 is a combination of the gravitational constant and
water density.

Brent
www.bensonsails.com

From: (Sakari Aaltonen)
Organization: Helsinki University of Technology
Newsgroups: rec.boats.building
Date: 16 Jul 2003 05:54:55 GMT
Subject: Hull speed theory?

I have seen lots and lots of references to the formula "X times
square root of waterline length" as defining hull speed with X
normally about 1.3 (speed in knots, length in Imperial feet.)
However, I have never seen an explanation of this.

Pictures of boats "trapped" between their bow and stern waves seem
to make sense. But they do not explain why a long wave would travel
faster than a short one.

Surely there is a book with the theory?


Thank you,
Sakari Aaltonen

On 16 Jul 2003 05:54:55 GMT, (Sakari Aaltonen)
wrote:

I have seen lots and lots of references to the formula "X times
square root of waterline length" as defining hull speed with X
normally about 1.3 (speed in knots, length in Imperial feet.)
However, I have never seen an explanation of this.

Pictures of boats "trapped" between their bow and stern waves seem
to make sense. But they do not explain why a long wave would travel
faster than a short one.

Surely there is a book with the theory?

Any fluid mechanics text is likely to derive the speed of a surface
wave in deep water. Books on naval architecture will more likely just
state the result.





Rodney Myrvaagnes J36 Gjo/a

"That idiot Leibniz, who wants to teach me about the infinitesimally small! Has he therefore forgotten that I am the wife of Frederick I? How can he imagine that I am unacquainted with my own husband?"

Sakari, there is a Usenet group that discusses hydrodynamics but I can't
remember the exact name.
The word "fluid" was part of it.

--
Jacques
http://www.bateau.com

"Sakari Aaltonen" wrote in message
...
In article ,
Brent Benson wrote:

The derivation of the dispersion relationship for gravitational surface
waves on fluids is somewhat complex and not obvious. It is found in many
fairly advanced mechanics texts. You will need to go to a college or
university library to find it.

No problem - I work at a university. Can you name one book?


Thank you,
Sakari Aaltonen

sci.engr.marine.hydrodynamics - but this is not very active.

However, you might find what you need by doing a Google search in the
"Groups" section for "hull speed". There was a large tread about hull speed
in rec.boats.builder a couple years back. You'll find more opinions than you
ever wanted...

Regards,

Don

Donald M. MacPherson
VP Technical Director
HydroComp, Inc.
email:
http://www.hydrocompinc.com
tel (603)868-3344
fax (603)868-3366





"Jacques Mertens" wrote in message
.. .
Sakari, there is a Usenet group that discusses hydrodynamics but I can't
remember the exact name.
The word "fluid" was part of it.

--
Jacques
http://www.bateau.com

In article ,
D MacPherson wrote:
sci.engr.marine.hydrodynamics - but this is not very active.

However, you might find what you need by doing a Google search in the
"Groups" section for "hull speed". There was a large tread about hull speed
in rec.boats.builder a couple years back. You'll find more opinions than you
ever wanted...

Thanks, but I'm not looking for _opinions_, really. I went to the
library today and found quite a number of books on fluid dynamics.
Some had sections on surface waves; the mathematical derivation
shows, indeed, that the propagation speed of such a wave is directly
proportional to the square root of the wavelength. I'll need some
time to work through that derivation...:-)


Sakari Aaltonen

Sakari Aaltonen ) writes:

Thanks, but I'm not looking for _opinions_, really. I went to the
library today and found quite a number of books on fluid dynamics.
Some had sections on surface waves; the mathematical derivation
shows, indeed, that the propagation speed of such a wave is directly
proportional to the square root of the wavelength. I'll need some
time to work through that derivation...:-)

well, you start with V = N x L where V = wave velocity, N = frequency of
vibration, and L = length of wave. that dosn't give you the square root of
wavelength, but something about the boat sitting down into the wave trough
gives an equation with boat length (water line length) as a factor but
darned if I remember how. I've seen it in one or two library books but
never wrote it down.

you'll have to post the derivation so its preserved in the newsgroup
archives for all time.

--
------------------------------------------------------------------------------
William R Watt National Capital FreeNet Ottawa's free community network
homepage: www.ncf.ca/~ag384/top.htm
warning: non-freenet email must have "notspam" in subject or its returned

"X times square root of waterline length" as defining hull speed with X
normally about 1.3 (speed in knots, length in Imperial feet.)
However, I have never seen an explanation of this.

What confuses me is the variability of the 1.3 value depending on the source.

How about the Pierre Gutelle book?
I have it in french but it is available in english, Wooden Boat sells it.
I found all the math theory about wave resistance with formulas in the 2nd
chapter then, it is applied in chapter 5.
He also shows a good bibliography listing many papers and books about wave
resistance.
Gutelle may give you all the answers you are looking for.
You'll see why that hull speed formula is very crude.
The French title is "Architecture du Voilier", volume 1 of 3.

--
Jacques
http://www.bateau.com

"Sakari Aaltonen" wrote in message
...
In article ,
D MacPherson wrote:
sci.engr.marine.hydrodynamics - but this is not very active.

However, you might find what you need by doing a Google search in the
"Groups" section for "hull speed". There was a large tread about hull
speed
in rec.boats.builder a couple years back. You'll find more opinions than
you
ever wanted...

Thanks, but I'm not looking for _opinions_, really. I went to the
library today and found quite a number of books on fluid dynamics.
Some had sections on surface waves; the mathematical derivation
shows, indeed, that the propagation speed of such a wave is directly
proportional to the square root of the wavelength. I'll need some
time to work through that derivation...:-)


Sakari Aaltonen

Here's a quote from a reputable source (which I won't name since they may not
like it) that explains it - sort of.

"THe energy associated with the transverse wave system travels at the "group
velocity" of the waves, which equals one-half of the phase velocity in deep
water. The propulsion system of the ship must therefore put additional energy
into the wave syste, to replace that which "falls behind". A nominal
relationship between ship speed and the length of the corresponding transverse
wave may be found by equating the ship velocity with the _celerity_ (phase
velocity) of a small-amplitude gravity wave in deep water,

Vship = Cwave = sqrt( g.Lw/(2.pi)) = 2.26 sqrt(Lw)

where Cwave = celerity or phase velocity of the wave in ft/sec
and Lw = length of the transverse wave in feet.

This can be converted into speeds in knots:

Vs = 1.34.sqrt(Lw) (sorry, no workings shown - trust me)

William Froude first pointed out the practical limiting speed for
surface-displacement ships whe he observed that "the speed with which wave
resistance is accumulating mosr rapidly, is the speed of an ocean wave the
length of which, from crest to crest, is about that of the ship from end to
end" (Froude 1955 p.280) This condition is found by substituting the length of
the ship for the length of the wave, giving a relationship commonly referred to
as the _hull speed_, or critical speed-length ratio:

Vs/sqrt(Ls) = 1.34

end quote

And there you have it.

Steve