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From: (no name) (no email)
Date: Thu Oct 26 2006 - 08:45:37 EDT
In a message dated 10/26/06 12:01:10 AM,
writes:
> >
> > I have applied Keith's Formula to an excell SS. Any thoughts on the
> > validity of Keith's to a powercat? Coefficients?
>
> I am unfamiliar with this formula, and I generally suspect that catamaran
> hulls are different enough from monohulls that great modifications would
> need to be made to it to get realistic predictions.
>
>
Keith's formula for relating speed, power, length, and displacement 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 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 its
tail.
What the scaling constant in Keith's formula does is correct for difference
in hull shape (prismatic coefficient, etc), hull condition (squeaky 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 requirement with speed for
a
hull of given length 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.
Keith's formula makes no provision for the beam or shape of a hull. That is
all handled by appropriate changes to the scaling constant. I assume that the
formula would be applicable for catamarans or trimarans at displacement speeds
with the right scaling constant but that would have to be determined by
experiment.
You can't accept any of the maritime formulas on blind faith but Keith's
formula seems to be one of the more reliable ones for approximating power
required
to move a displacement hull. It considers LWL, displacement, speed, and
power. Inherent in the calculations are assumptions made about propeller
efficiency, specific hull configuration, units of measurement, and sea
conditions. These
are included in the scaling constant. Generally the mathematical formulas
give results which are in error by no more than 10% when compared with actual
in-water trials. Nothing beats actual tank tests or full scale prototypes,
but
using a computer is a lot cheaper.
Larry Z
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