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

bye-bye.

this subject has been tossed around far too many times on the net and always
always always always those who read it somewhere *insist* it is a Law of
Physics.

it ain't.

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?"

"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.

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

In article ,
Stephen Baker wrote:

"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)

Yes, this is the formula. But what I'm interested in is the theory
it's based on - the general theory of waves in fluids, of which
small-amplitude deep-water surface waves are one particular case.



Thank you,
Sakari Aaltonen

Sakari says:

Yes, this is the formula. But what I'm interested in is the theory
it's based on - the general theory of waves in fluids, of which
small-amplitude deep-water surface waves are one particular case.


What you need is not a discussion on the hull-speed theory, but a degree in
fluid dynamics.

;-)

Seriously, however, this is what you need to read, although you may need more
background first.

http://www.amazon.com/exec/obidos/tg...=1058555603/sr
=1-6/ref=sr_1_6/002-5456679-7453635?v=glance&s=books

Steve "application not theory" Baker

Stephen C. Baker - Yacht Designer
http://members.aol.com/SailDesign/pr...cbweb/home.htm

In article ,
Stephen Baker wrote:

Seriously, however, this is what you need to read, although you may need more
background first.

http://www.amazon.com/exec/obidos/tg...=1058555603/sr
=1-6/ref=sr_1_6/002-5456679-7453635?v=glance&s=books

Lighthill, James: "Waves in fluids"? Yes, our library has several
copies. However, I happened to pick up "Mathematical theory of wave
motion" by G.R. Baldock and T. Bridgeman; it might be just enough.

But I'm leaving for a three-week sailing vacation on Sunday, and
shall, for some time, be concentrating on real waves instead of
theoretical ones.


Sakari Aaltonen

it ain't any theory whatsoever. It was merely a "scientific" explanation given
to 19th century British naval brass to "help" them understand why putting 2x
the power in a boat didn't make the boat go 2x the speed.

The "theory" sounded scientific and it had numbers in it and it was called a
theory so the brass accepted it.

most sailboats built in the last several decades will easily exceed
"theoretical" hull speed. in fact, a deep vee hullled Hobie cat (displacement
hull by any standard) at 18 feet will under many points of of sail easily pass
a 45 foot sailboat (also a displacement hull for most every 45 sailboat out
there).

but please use the term, for it lends credibility and pananche when talking to
young lovelies at the yacht club bar.