SPEED LENGTH RATIO & HULL SPEED CALCULATOR

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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.

 

SPEED in KNOTS

LENGTH in FEET

6

20.00

7

27.20

8

35.60

9

45.00

10

55.60

11

67.30

12

80.10

14

109.60

16

142.40

20

222.50

25

347.70

30

500.60

 

What happens in practice is that at the correct displacement speed a vessel is supported at bow and stern by crests, hence will ride level.  As speed rises the bow is still supported by an increased forward crest, but the stern is now in a hollow on a smaller (shorter) boat, hence the boat is traveling bows up trying to go uphill - which drains engine power - and is something the designer should avoid at all costs if a vessel is to be efficient.  The next thing to consider in the design process is: RESISTANCE and the POWER (HP) required to overcome the total DRAG.  

 

 
DISPLACEMENT HULL SPEED CALCULATOR
Boating calculators are provided by:  ANYBOAT.COM HOME PAGE

The calculator below will give the maximum speed attainable by a displacement vessel under ordinary conditions.  It uses a java script to find the speed of a given length vessel in knots.  The formula was provided in the text by Juan Baader, published by Norton & Co. in 1965.  The theory is based on repeated observations of the behavior of sailing yachts and the study of wave motion.  The formula holds true for displacement vessels!


Fill in the form line below with the water line length of the vessel.

(WORKS BEST WITH NETSCAPE NAVIGATOR - JAVASCRIPT ENABLED)

vessel length in feet

With our thanks to the many contributors to the resource and anyboat.com for hosting - copyright hereby acknowledged.

CONTACT:  nelson@solarnavigator.net  07905 147709 (UK)

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