This
is a handy rule whereby boat speed in knots (V) is compared to
hull waterline length in feet (L) where V divided by the square
root of L = the speed/length ratio or S/LR.
By
way of example a boat 30 feet on the waterline at 6 knots has a
S/LR of: 6 / 5.48 = 1.095. At 10 knots her S/LR (10/5.48)
= 1.82. Whereas, a 400 foot ferry at 15 knots has a S/LR
(15 / 20) = .75.
This
rule allows us to categorise hull lengths which will suit a
particular speed for a displacement vessel. For our
purposes there are 3 categories to consider:

LOW
SPEED  up to a S/LR of around 1.5

MEDIUM
SPEED  with a S/LR between 1.5 to 3.0

HIGH
SPEED  having a S/LR above 3.0
It
will be seen that a 30 foot motor boat on the waterline at 20
knots has a S/LR of 3.6 (high speed) but that a 300 footer at
the same 20 knot speed with a S/LR of 1.15 is classed as a low
speed vessel. For the 300 footer to be considered high
speed she would have to be traveling (work formula backwards) V
= 3 x 17.3 = 52 knots or more.
WAVE
MAKING & DISPLACEMENT SPEED
Why
does the above S/LR work? Well, as a boat moves through
the sea it pushes water aside  in doing so making waves  that
much is obvious. If we investigate further and look at the
pattern a hull generates as it moves through calm water you
might identify 3 distinct wave patterns. The first set of
pressure waves runs diagonally out from the bow. A fine
angle of entry reduces the bow wave considerably. The
second wave runs out less visibly from the stern. However
a third more important set, runs along the vessel's side which,
depending on the speed of travel, produces a crest of water at
the bow lifting the boat, followed by a trough into and then
another crest, etc. The faster a boat moves, the bigger
the crest lifting the bow out of the water.
On
a big boat there may be several crests at the bow ending at the
stern. It takes power to move so much water to produce a
wave. The heavier a craft, the more water will have to be
moved to pass through, in terms of simple drag: the wetted area
or pipe resistance (as in water in a hose pipe). The
distance between wave crests is governed by boat speed.
Any type of boat from canoe to supertanker makes the same length
of wave at the same speed. Only the wave size alters in
line with the vessels weight and form. On high speed
vessels that rise out of the water, or plane, the above may to
some extent be overcome.
