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Subject: TWL: Re: Keith's formula
LRZeitlin@XXX.XXX
Date: Mon Nov 04 2002 - 10:31:58 EST
In a message dated 11/4/02 5:03:26 AM,
trawler-world-list-request@XXX.XXX writes:
<< it would
be useful to the list if each of you would publish references to your
sources, or describe your computations in detail so that the rest of us can
make our own assessment of the results. >>
Peter,
Keith's formula is described on p. 105 of "Skene's Elements of Yacht Design,
8th ed." revised by Francis S. Kinney. It is published by Dodd, Mead & Co.,
New York, ISBN: 0-396-06582-1. The book also has a number of other techniques
for calculating the power requirements of boats and is a compendium of other
material useful to yacht designers.
I use the following formula: KTS = (LWL)^.5 x C x ((HP x 1000)/D)^.333
This is essentially Keith's formula restated for easy computer calculation.
LWL is measured in feet.
D is measured in lbs.
C is a scaling constant which varies between 1.1 and 1.5 and must be
determined by observation or experimentation with a specific type of boat. I
use a constant of 1.18 for a typical displacement trawler hull. This is based
on experience, not on theory. Lower values of the constant imply a more
pessimistic outlook and prescribe more power for a given speed. Values above
1.2 tend to be too optimistic.
The presence of arbitrary constants in an equation are a serious fudge
factor. I was once told by a professor of mathematics that if you have two
arbitrary constants in an equation, you can make the resulting curve look
like a puppy dog, and if you throw in a third arbitrary constant, you can
make it wag it's tail.
What the scaling constant in Keith's formula does is correct for difference
in hull shape (prismatic ratio, etc), hull condition (squeeky clean or
barnacle covered), sea state (mill pond or "real world"), measurement units
(statute miles, knots, kilometers, lbs., kilograms, tons, etc.), and
propeller efficiency (usually assumed to be about 50%). All the basic formula
does is provide the shape of the curve of increasing power requirements for a
hull of given length with speed and displacement. The scaling constant
changes the axes of the graph to meaningful units.
The best way to use Keith's formula, or any similar formula, is to make exact
measurements of a boat's power requirements at a specific speed and
displacement. Then calculate the proper constant. Using this constant, power
requirements (and fuel consumption) can then be estimated for that same hull
for a range of speeds and displacements. You can generalize to other boats of
the same general type with less accurate results. It would not do, however,
to use Keith's formula to compare displacement, semi-displacement, and
planing boats.
Where Nordhavn went wrong in its original estimate of the fuel consumption of
the N40, was to accept conclusions based on towing tests of model hulls then
extrapolate to full sized dimensions. The actual hull was loaded far heavier
than the load estimated for the model, and the actual propeller efficiency
apparently was lower than that estimated for the model. And of course the we
ather was worse than that experienced in the towing tank.
Larry Z
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