For a boat hull, a simple way to think of theoretical boat speed is that a vessel is limited by the wave that boats hull creates. That is, because it is a displacement vessel it doesn’t climb its bow wave, as a planning vessel would, which limits the boats speed. 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. This is the limit to displacement boat speed

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 boats 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

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 reaching a higher boat speed.
David Gerr’s propeller handbook is an excellent reference with some extensions to this formula.

Crouch’s Planing Speed formula

This formula applied to planing boats only and only takes into account the displacement
of the hull, ignoring length. This may seem odd but as opposed to a displacement
hull, the most important factor in determining speed is displacement.
If you think of skipping stones as an analogy, 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.
See Planing Hull for details.

Displacement Hull Chart

This chart represents the speed a traditional
displacement hull can reasonably attain. Catamaran hull speed, trimaran
hull speed and light displacement hull speed may be higher. For these displacement
hull types it is recommended that you use David Gerr’s DL Ratio formula to
calculate a more accurate maximum SL Ratio.
Follow the steps in the boat speed calculator which includes Gerr’s DL ratio.

Hull Speed Calculator, Results

The results and the chart plot are based on an
SL Ratio of 1.34 this “magical” 1.34 is just a guide as to the
usual theoretical hull speed, beyond which the increasing amount of power required
to push a hull past a certain speed becomes impractical. 1.34 is typical but lighter
displacement boats may be allowed a higher number. Note that this number only applies
to displacement hulls. Hull speed, as
calculated here, is important as it is a building block to attaining figures like,
what power is required and ultimately calculating what propeller may be optimum
for a particular boat.

Hull Speed Chart

The chart displays speed at different percentages of theoretical hull speed. Typically
you will not try to push a displacement the vessel past 100% of hull speed but I
have shown the it at 125% so that in the next step it can be used to illustrate
how much power is required to push the hull past this speed.

Desired speed is populated from the hull speed or Gerr DL Ratio forms.
This is the maximum speed you require and should be less than the calculated hull speed.
For a displacement hull it is pointless to try go beyond hull speed. SeeSL Ratio
for more information on how hull speed is derived.

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.

Power Required Calculator, Planing Hull

Enter both values LWL and Desired speed. These are used in Wymans formula to calculate
estimated power required for the vessel.

This is the maximum speed 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.

Power Required Calculator, Results

HP quoted should be considered as SHP (shaft horsepower) i.e. the power available
at the shaft for the highest RPM's attainable. Most outboard manufacturers quote
HP as SHP. For inboards consult your manufacturer, as most are quoted in BHP (break
horsepower), SHP is typically 96% of BHP, depending on the number of bearings, gearboxes
and ancillaries. The results and the chart plot are based on an
SL Ratio of 1.34. this “magical” 1.34 is just a guide as to
the usual theoretical hull speed, beyond which the increasing amount of power required
to push a hull past a certain speed becomes impractical. 1.34 is typical but lighter
displacement boats may be allowed a higher number. Note that this number only applies
to displacement hulls.

Hull Speed Chart

The chart displays speed at different percentages of theoretical hull speed and
the SHP required to reach these speeds. Typically you will not try to push a displacement
the vessel past 100% of hull speed but I have shown the it at 125% to demonstrate
the increase of power required that makes going past hull speed impractical.

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.