"Bart Senior" .@. wrote
What is the formula for the hull speed of a typical multihull?


It's the same, just use a higher multiple (ie speed-length
ratio).


Bart Senior wrote:
Here is another more specific question.

What speed could you expect to do in a multihull with
a 56' waterline?


How is it rigged & how heavily is it loaded? Who is sailing
it? How hard is the wind blowing? Is the water choppy?

The usual hull speed formula is SQR RT(1.34*LWL)
in words, multiply the waterline length by 1.34 and then
take the square root of the resulting number, which is the
hull speed in knots. The multiplier "1.34" is the
'speed-length ratio' mentioned earlier, most modern boats
will beat that pretty easily. For an average fin-keel
racer-cruiser, 1.5 is a better number to use (doesn't sound
like much difference, but try it). Multihulls can hit
speed-length ratios of 1.8 or higher.

A hull that is very narrow, like a Navy destroyer or a Hobie
cat, will not suffer as much drag from making waves. The
cut-off point seems to be a length/beam ratio of about 8:1
so a really fast 56 foot catamaran will have hulls narrower
than 7 feet (this sound wide, but think how many big cats
have athwartship berths in the hulls).

So your 56' cat might have a realistic sailing speed of 10
to 13.5 knots without doing anything exceptional, you could
plan on passagemaking speeds in this range!

For cats with good performance, the speed-length ratio might
be 1.9 or higher. A better way to approximate the speed
potential is a formula that includes displacement & sail
area: take the hull speed formula & multiply it by the ratio
of sail area's cube root to the displacement's fourth root

{(SLR*LWL)^0.5}*{(SA^0.333)/(DISP^0.25)}

It's interesting to play with these numbers and see the huge
difference between conventional racer-cruisers and modern
hi-tech sportsboats & multihulls.

Fresh Breezes- Doug King