# Hull displacement calculation

Discussion in 'Stability' started by orang laut, Nov 14, 2006.

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### orang lautJunior Member

Guillermo, thank you for the reply. I still have a couple of other questions concerning this, but felt that it was not suitable content under the topic of Propulsion > Diesel engines.

For the benefit (hopefully) of others, I paste here the initial spark of this issue:

Quote:
Originally Posted by orang laut
One small question: how is the hull displacement calculated?

You need to know waterline length, waterline beam, and body draught amidships (just body, not total draught under the keel). Then you need the "Block coefficient" which may vary a lot depending on hull forms. But for a rough estimative on a sail boat it should be not far away from 0.4
So if you multiply Lwl*Bwl*Hd*0.4 you get (roughly) the underwater volume of the hull. Now multiplying this by the weight density of water (If salt then it's around 1.025 tonnes/m3 or 64 lbs/ft3 depending on units chosen) you get the displacement weight in tonnes (if you chose measurements in metres) or pounds (if you did it in feet).
As said, this is a rough figure just to get a first idea. Being accurate takes quite a bit of more time and knowledge.

Cheers.
__________________
Guillermo Gefaell
Motorsailers & Motorsailing
Banjer 37 Motorsailer Club

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### orang lautJunior Member

Thanks Guillermo..

When you said that the block coefficient depends on the hull form, am I correct to assume that this 0.4 for most sailboats refers to a semi-displacement hull?

Just to check if I got the basic idea right: the more 'flat' & 'fat' the hull is, the higher the block coefficient value? So block coefficient of 1 is for a floating box?

By the way, block coefficient is a big mouthful (& fingerful), is there an abbreviation/ short form of this?

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### GuillermoIngeniero Naval

The simplification of using a block coeffcient (Cb) of 0.4 is just to try to get a rough idea of the displacement of an average sailing boat, knowing its Lwl, Bwl and Td, not to generalize. This coefficient is hardly used when designing a sailing boat, but rather the prismatic one. And yes, you're right about the flat&fat idea.
I strongly recommend you the reading of Dave Gerr's book "The Nature of Boats". It's not a book for yatch designing but, quoting Gerr: "..was written as a browser's reference to understanding how boats tick: how you can judge and evaluate different hulls....or even start doodling up a new design from scratch. It's written in plain english, not highfalutin technical jargon and there's little math included here that's more difficult than adding up your grocery bill. Rules of thumb and simple charts make everything from estimating hull thickness to specifying a sailboats rig to proportioning engineroom vents to selecting propellers and more...."

(I earn no commissions at all on the selling of Dave's books! )

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### orang lautJunior Member

Hehe...

I wouldn't mind even if you did earn something out of it. Thanks for the infos

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### 101Junior Member

I've got a question and have been looking for an answer, perhaps someone can help. I am looking at two boats. Boat #1 is reported to have a displacement of X and boat #2 is reported to weigh Y. I know these are different measurements but always thought they really ment the same thing. If I am looking for the lighter of the two boats, how do I use the information?

Thanks

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### TrevlynsSenior Citizen/Member

Block coefficient is normally used in shipping terms. Yachts use the prismatic coefficient (PC) and this basically refers to the “fullness” of the ends compared to the area of the midsection. The box would be 1, but a fine ended catamaran hull for example could be .66 or even higher. This indicates it would be quite buoyant in the ends to reduce pitching.

The usual calculation for displacement is determined by the areas of underwater sections (normally divided into 10 equal sections along the waterline length.) These numbers are punched into a formula called Simpsons Rule (just google it) which has long been the method for displacement calculation.

Displacement can be either weight (unladen) or volume displacement. Volume displacement is the normally used figure which is the total weight of the craft with all its gear and stores etc. as designed to sit on the LWL.

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### Crag CaySenior Member

If I read this right, I think it might need a little clarification:

Displacement is the boat's weight. Since circa 220BC, they have been recognised as being one and the same thing. The symbol is 'delta' and the units are pounds, Kgs or Ton(ne)s

Displacement volume (V) is, (as the name suggests) the volume of water displaced by a floating vessel of a given displacement weight. Its units are cubic feet or metres, but is rarely seen in any publicity information about boats. It is further complicated as for any given displacement weight, a vessel's displacement volume will vary depending on whether it's floating in sea water (with the Med and Atlantic even being different) or fresh water.

Now the complication comes when appraising boats as to which 'diplacement weight' is being talked about. It will obviously vary with the amount of equipment, stores and people that are aboard. Some definitions have been standardised, especially when required for ISO stability tests or racing handicapping.

However 'brochure displacement' is not governed by any standards, and as there are many benefits in quoting the minimum when marketing certain types of boats (including cruising sailing boats to boost their ballast ratio), the weight of the boat before being anti-fouled and without even dew on the decks, is liberally rounded down to the next lowest, easy to print figure.

This contrasts with 'live aboard displacement after 2 years' where the water line has to be moved half way up the top sides.

None of these should be confused with 'fiscal displacement' which is the amount of money displaced from your bank account once you become a boat owner. This is often plotted against 'Marital Righting Moment' (RMm) which attempts to predict the likelihood of you getting up of the floor, once your wive discovers the size of your boat's 'fiscal displacement'.

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### DGreenwoodSenior Member

None of these should be confused with 'fiscal displacement' which is the amount of money displaced from your bank account once you become a boat owner. This is often plotted against 'Marital Righting Moment' (RMm) which attempts to predict the likelihood of you getting up of the floor, once your wive discovers the size of your boat's 'fiscal displacement'.

OK that made me laugh...in a very uncomfortable sort of way!?!?

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### 101Junior Member

Thanks, but my wife has already provided me the correct information for fiscal displacement as well as the range of positive stability! ;-)

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### singlepropJunior Member

I just love the last 2 quotes, but that does not change the fact that quality of life does not depend on money, available or not (meaning that living on a boat cannot be compared to living in a trailor or a villa for that sake). There is so much more live-ability and quality of life to the "ocean way".

regards singleprop

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