RE: [Paddlewise] FATNESS ratio

Robert Livingston <bearboat2_at_comcast.net> asked:

>>>>>John Winters refers to a flatness ratio as the
displacement (as a volume)/(.01*Length)^3
This is closely related to the concept of displacement length ratio
differing only by a constant multiplier.
Does anyone know if this is just an invention of John's or is the fatness
ratio actually an accepted nautical measurement term.<<<<<

I think the constant multiplier is .1 (rather than the .01 you used) which
after being cubed in the divisor becomes a multiplier of 1000. Therefore the
"Fatness ratio" could be defined as 1000 times the "Volumetric Coefficient"
(which is a non-dimensional version of the displacement-length ratio). I
think John probably made up the term "Fatness Ratio". Multiplying the
"Volumetric Coefficient" by 1000 makes it a number without several zeros
after a decimal point (which makes it easier to think about). The Volumetric
Coefficient is a very important ratio in regards the drag performance of a
hull. It is one of the most major ones we take into account in determining
the drag calculations for Sea Kayaker.
If you take the total displacement (the weight of the boat and its contents)
and convert it into volume by dividing that weight by the weight of the
volume of sea water in a cubic unit (that you are measuring length in) and
then divide that by the waterline length cubed you get the Volumetric
Coefficient. (It will be the same what ever units you choose to measure in.)
For instance, using feet as the unit we know that a cubic foot of sea water
weighs 64 pounds so by dividing the total weight of the boat in pounds (its
displacement) by 64 we get its volume in cubic feet. Dividing that volume by
the waterline length in feet to the 3rd power (making it into a big cube of
the same units) we get the volumetric coefficient (which is the ratio
between the volumes of those respective cubes). Multiplied by 1000 and
kayaks will likely fall into a range of .9 to 3.0 with a few extreme
exceptions. Most fall between 1.0 and 2.0. Of the first 82 kayaks measured
by Sea Kayaker magazine (with 250 pounds of paddler and gear weight added)
the average "Fatness ratio" was 1.42, the median was 1.32, and the highest
was 4.27 (Dawn Trakker--small rec. kayak) and the lowest was .77 (Futura
II--surfski).

Matt Broze
www.marinerkayaks.com
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