What is the formula for working out the top speed of a displacement vessel?

Question

I believe the answer to be the length of the boat at the waterline multiplied by a given coefficient. If this is correct what is the coefficient and if it's wrong how do you work out the maximum speed?

Answer 1

An easy basic formula is the "waveform" way of square root of twice the waterline length in feet gives you max hull speed in knots.  This relates to when the bow wave rises again at the waterline stern so to go any faster you end up dragging the stern down and ahead into the trough of the waveform so the boat adopts a bow up attitude and then needs to climb up the bow wave.  You can get a bit more top speed through sheer power applied but you really begin to drink the fuel in doing so.  On power boats with stern trim tabs you can get a bit of stern lift from them to help but unless you can power up the bow wave and "plane" then you are at max hull speed.

So applying this to a boat with a 30 ft waterline length, square root of 60 is 7.7 knots, compared to 6.3 knots if your waterline length is only 20 feet.

Answer 2

FORMULA FOR ESTIMATING THE SPEED OF A MOTOR BOAT

M= C∛L×P

B

[ Divide by B ] : 'Answers' hasn't yet woken up to underlines, formulae and notation - Divide main line of equation by 'B'. And notice: that's a cube root.

M = Speed of vessel in statute mph

L = Length of vessel, (W/L) (feet)

B = extreme beam (feet)

P = brake horse power of engine

C = constant = 9.5 moderate speed type [displacement]

   8.5 high speed type [plane]

Old, but it still works - if I can find my modern references, I will modify! (ie: S.I.)

Answer 3

The simple formula is:

Hull speed = the square root of waterline length times 1.34

http://home.golden.net/~capone1/wsc/calc...

Answer 4

1.34 times the square root of the waterline length (in ft) gives a very close figure for the hull speed. If you want to go faster than this buy a massive engine or a longer boat