Greeting Larry! I was streaming through this months threads and came
across yours about fuel consumption. Quite interesting to say the least.
I always wondered why/how you could save so much by just slowing down a
knot or two. Going slow was something that I had to understand before
moving up to a trawler from my go fast boat. Going from 12 to 10 or 10
to 8 is no problem because we're in no hurry!! Thanks for info!!
Tom Nolin
Here is a long answer for a short question. In general the power
required to move a displacement boat through the water rises as the
cube of the speed. It takes very little power to achieve very slow
speeds. One mule could pull a 30 ton barge along the Erie Canal at
about one knot. So dropping the speed slightly means a large saving in
power and hence of fuel. Example: Moving a boat at 10 kt. takes almost
twice the power as moving it at 8 kt.
In my former professional work we used Keith's formula as a first
approximation of the power required to achieve a given speed. You can
do all the calculations on a pocket calculator but in my day we used a
slide rule. It is usually accurate to within 10%.
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 it's tail.
What the scaling constant in Keith's formula does is correct for
difference in hull shape (prismatic coefficient, 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 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.
The Nordhavn 40, in its circumnavigation, used 35% more fuel than
anticipated. The original published estimate of fuel consumption was
seriously flawed. Where Nordhavn went wrong 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 Pacific
ocean weather was worse than that experienced in the towing tank.
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. Nothing beats actual tank tests or
full scale prototypes, but using a computer is a lot cheaper.
Larry Z