# Displacement Hull Speed calculation

Discussion in 'Boat Design' started by Toby P, Jan 13, 2006.

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### Toby PJunior Member

For displacement vessels hull speed is usually given as:

p * LWL^0.5

where traditonally p = 1.34 has been used as it matches the bow wave length to LWL.

Realising that it is not a constant value, David Gerr has derived an empirical formula for calculating p based on the displacement/length ratio (his book is on its way from Amazon, thanks Skippy!), which presumably is a more accurate indication of true hull speed. Clearly, however, hull form also affects a boat's maximum hull speed.

My thinking is that a formula along the lines of the one below could be used to establish whether a hull is limited to a hull speed or whether it is able to break free and continue accelerating in displacement mode e.g. catamarans.

k = (D:L* tan(a))/(L/B)

D:L is the displacement:length ratio (non dimensional),
a is the bow angle of entry,
L is waterline length,
B is waterline max beam.
The waterplane coefficient, Cw, could be used in place of angle of entry of bow, ideally just Cw of forward half of hull would be used.

Some critical value of k splits those hulls that can readily progress through the normal p = 1.3 - 1.5 barrier e.g. cats, from those that can't. Some coefficients and indices need to be added to the terms in this equation to ensure that the influence of each factor is weighted properly.

For hulls that do not exceed the critical k value, factors other than bow wave formation dominate drag, so the concept of relating the hull's maximum speed to the square root of its length is of little practical importance. However, for hulls that do exceed the critical k value the hull speed coefficient, p, could be estimated on a revised Gerr formula that incorporates coefficients of form such as L/B, D:L and a. Has anyone done this? Does it sound like a stupid idea?

Alternatively you could take the opinion that there is no such thing as hull speed, hence trying to calculate it is pointless. Whilst this is technically correct (supply enough power and you WILL go faster) I believe that the notion of hull speed has proven it's worth over the years, so trying to establish it more accurately (without the need for CFD/VPP software) has to be a worth while exercise.

P.S. For the background to this thread see Humpless Planing in the Sailboat section of this forum.

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### kjellSenior Member

Juan Baader the writer of the book”Cruceros y Lanchas Veloces” introduced a very simple way of Displacement hull speed calculation.
He introduced the “R” Value. = similar to the Froude number but using V= Meter
L = LWL in meter. “R” = V/Square.root L . Speed Km/h.

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### Toby PJunior Member

I think that is just a metricised version of the 1.34 * LWL^0.5 equation - maybe we should all use Froude number to avoid confusion! The trouble with this formula is that it only considers length. Gerr realised that displacement also affects the top displacement speed. But hull shape also influences the speed, can anyone come up with a 'rule of thumb' formula which accounts for hull fineness as well?

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### kjellSenior Member

The displacement hull is a hull with narrow stern and the speed is limited to the waves the hull is producing. That is the reason for the “Hull speed”.If the hull has a wide stern it is a semi displacement hull or semi planning hull and the speed formulas are different.

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I tend to think it's probably impossible to come up with a single, simple equation that would be accurate enough for all hull forms and sizes.
The predictive value of such equation would tend to considerably diminish in extreme cases e.g. very small boats, very narrow hulls etc.
The problem seems to be that numerous factors affect R, and under different circumstances they don't always interact exactly in the same way with other factors.
A more useful approach could be to find for each boat category of general size and form an equation that best describes empirical findings, and therefore would have a good predictive value for design purposes.

Yoav

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### DavorNaval Arch.

If it would be that easy to calculate resistance what would be doing all these towing tanks and institutes.

Just to have ide of variety of calculations you can download my demo program:

http://www.sea-power.net

there you will find 22 methods to calculate resistance (only three awailable in demo), and there are much more.

rgds

Davor

7. ### Doug LordGuest

beam to length ratio

As I said in the other thread beam to length ratio is critical in understanding the changes related to when a boat will plane. Also the width of the transom is not, probably, an absolute determinant of planing characteristics. Examples include the IC and the Moth both of which have very narrow transoms and both of which plane.

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### Toby PJunior Member

Totally agree, Icetreader. A 'one size fits all' formula for everyting from dinghies to ships would be very difficult. I think it would have to be empirically based, ideally on a series of tank test results. Unfortunately there is no chance of me doing it. Any volunteers? Any ideas on what form the formula might take?

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### GuillermoIngeniero Naval

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### kjellSenior Member

Using the R-Value formula it is very easy to calculate boat speed for Displacement hulls.

R-Value S/L ratio
4.50 1.40
4.25 1.32
4.00 1.28
3.50 1.09
3.00 0.94

Boat speed Knots = (R* Sqr/Root L)/1.854

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### DavorNaval Arch.

Guillermo,

Davor

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### GuillermoIngeniero Naval

Oops! I was using a computer with Mozilla Firefox, instead of IE. I've done it from my laptop, which has IE.
Thanks.

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### APPJunior Member

Reference is made to TOBY P post at http://www.boatdesign.net/forums/bo...t-hull-speed-calculation-10098.html#post72497

Toby, Interesting formula. Do you have any values of k for specific boats? or otherwise said, how to interpret a k calculated for a specific boat?
Thanks
APP

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