A simple way to think of theoretical hull speed is that a vessel is limited by the
wave it creates. That is, because it is a displacement vessel it doesn’t climb
its bow wave as a planning vessel would. Going faster than the theoretical hull
speed is possible but the wave moves under the transom so the boat has to plow through
the water at an angle, bow up which then requires exponentially more power to move
the vessel once theoretical hull speed is reached.

So a displacement boats theoretical hull speed is when the wave length is equal
to the waterline length. The important thing here is the length of the wave is relative
to the length of the boat.

The SL Ratio is a simple formula for calculating displacement hull speed which is
typically 1.34

Velocity = (g * Length / 2 pi) ^ ½

g = acceleration of gravity (32.15 ft/sec ^2)

Convert ft./sec. to Knots and the result is 1.34 * L^½

Metric V(m/s) = 1.25* LWL^1/2

But of course, not all hulls are the same; depending on other factors like displacement
and beam the boat may create a larger or smaller bow wave in proportion to its length.
Heavier displacement vessels will have difficulty getting over 1.1 times the theoretical
hull speed whereas vessels with lighter displacement and slimmer hulls like catamarans
will have less trouble.
David Gerr’s propeller handbook is an excellent reference with some extensions
to this formula.

This is the maximum speed that you require. Note, there are other factors, such
as safety, not covered by this calculation that would limit desired speed. Contact
the designer manufacturer to find out what the vessels maximum
SL Ratio is.

Power Required Results

The results show the estimated required power at the shaft. Note that engines are
rated differently for inboard diesels. For example SHP is approximately 95% of BHP
due to losses in the transmission, to ancillaries etc.

Power Required Chart

This shows the SHP required for a % of hull speed.

Select your preferred form of measurement, feet or meters and enter your boats LWL.

Length at waterline, LWL

Sometimes referred to as, waterline length or LWL. This is the length of the vessels
hull, from center fore to center aft at the level of the water. This is usually
given by the manufacturer and is the primary factor in determining hull speed. There
may be a large variations between the vessels overall length LOA and the waterline
length due to overhang i.e. the LWL may well be quite a bit less than the LOA. For
example older sail boats had traditionally larger overhangs at the bow.

Skipping stones gives us a first good look at a planing hull. First off a good skipping
stone should be flat so that it can skim (plan) over the water at high speed, secondly
it’s got to be small/light enough so that you can throw it fast enough to
allow it to skim. If that stone isn’t the right shape or don’t throw
it right I’ll break the surface and slow down rapidly. These two characteristics
apply to the planing hull. The shape of the hull’s run needs to be flat to
be conducive to planing (skimming) and the power to weight ratio needs to be sufficient
to get it up on plan. For the usual planing and
Semi-Displacement Hull. , determining the quarter beam buttock angle is
a way to estimate the speed the hull can attain relative to its length. The quarter
as measured from the center of the transom a quarter of the beam.

See David Gerr's propeller handbook for an illustration and details on how to measure
this.

The maximum SL Ratio ,provided by David
Gerr in his propeller handbook, as determined by quarter beam buttock angle: Planing
boats SL Ratio of 2.5 or higher, Buttock angle of 2 degrees or less Semi-Displacement
boats SL Ratio of 1.5 to 2.5, Buttock angle of 3 to 6 degrees. Displacement boats
SL Ratio of 1.5 or less, Buttock angle of 7 degrees or more.