# Displacement Calculation

Discussion in 'Sailboats' started by Soloman1970, Nov 8, 2013.

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### Soloman1970New Member

I have read dozens of post about hull displacement and unless you have a simple shape or a square hull it seems like there is no agreed formula on how to calculate the displacement of a sailboat hull. I have designed a boat that I intend to build but I am worried that the DWL will be way off. The boat is a 50' fiberglass/plywood over frame sloop with 16'6" max beam (13'10" at WL). The hull itself has a 2' 2" draft and the keel extends an additional 4' 4" below that, making total draft 6'6". The boat is relatively light, 21k lbs with an additional 7 to 9k lbs in lead ballast, depending on DWL. Can anyone help me calculate the DWL? Please and Thankyou... K

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### Soloman1970New Member

Also it is a full keel with a skeg hung rudder, very old school.

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### TANSLSenior Member

You need to have the body lines, or offsets table, of your ship. There are approximate formulas (by comparison with similar vessels) but what you're interested to know is the displacement, as accurate as posible, of your boat. If you have some drawings of it, and you send them to me, I'll see if I can help.

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### TANSLSenior Member

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Er...i take it from your comment you're not a naval architect nor are you a student of naval architecture. There is one very simple and accurate formula. Any text book will show you...or does that mean you have to explore text books?

What you have described is that you have drawn a boat, not designed it.

I assume that is a "guess draft"..?...or is that actually how she sits in the water?

The displacement must equal its weight i.e. Archimedes principal.

If you have a Lines plan, then it is a simple matter of creating a set of hydrostatics. From the calculated hydrostatics and an accurate weight calculation, you can determine what draft she will sit at.

If all this is beyond you, then I suggest you seek advice locally from someone how can show you, with pen, paper and a calculator. It is not difficult, but not easy to explain using line by line replies (of endless Qs why this and that) in a web blog. It is a "hands on" requirement, if you wish to learn and understand.

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### TANSLSenior Member

You are quite right but we are used to people, in this fórum, saying that they have designed a ship when all they have done is a nice drawing. Many 3D models, renderings, show up as a result of design work when it is just a decorative object.
Now, with the computer, everyone thinks that he can design ships.

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### Richard WoodsWoods Designs

Don't forget its not just the displacement that's important. It has to float level, so your CofG must be in the right place. And the hull shape itself determines whether a boat is successful or not.

As an extreme a boat could weigh what you want, but trim badly bow or stern. Even if it floated level, you could have an unbalanced hull - so it doesn't sail straight, the wrong Cp - so its slow and cranky, and many other factors

At the very least I'd make a scale model to sail first before spending several years building

if you don't have time for that then posting a drawing of your proposal would be sensible

Richard Woods of Woods Designs

www.sailingcatamarans.com

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### PARYacht Designer/Builder

Welcome to the forum.

You can roughly calculate you displacement by multiplying your water plane by it's hull only midship draft and employing a qualifier. Of course, this only tells you what you've drawn, not the boat's actually displacement.

Displacement is a fairly simple (if tedious by hand) calculation using Simpson's or trapezoidal rules, but again, this only tells you what you've drawn, not the actual displacement. To get a real displacement you need a center of masses calculation, so you know how much hull you'll need so she floats where you'd like her to float.

Post a picture or sketch of your proposed hull (all three views).

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### TANSLSenior Member

In this phase of the project, for what you now want to know, you DON'T NEED, absolutely NOT, have made any calculation of center of mass. All you need is to have cross sections and longitudinal profile of the vessel (could also be done with the water lines but it is normal, at this stage, not have them). No need either to have the three views of the ship, why?. You need, though, to know the draft at which you want to calculate the displacement. The water plane, at this stage of the project, is always taken parallel to the baseline that you have defined to draw the shapes of the boat.
Later, when studying the loading conditions, you will need to know the position of the center of gravity of the boat at each loading condition. But this is a much later stage of the project.

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### gonzoSenior Member

Actually displacement is one of the easiest parts of the design to calculate. All it takes is the addition of the weight of everything that goes in the boat. Displacement=total weight.

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### PARYacht Designer/Builder

Which assumes a weight study.

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### TANSLSenior Member

Gonzo and PAR , all I'm going to say next, is already known by you. I do not want to lecture anyone but to explain why I say, categorically, that it is not necessary a weight's study.
In the early stages of a project is impossible to know the weight of the boat because you know neither the scantlings nor equipment that is going to take the boat and therefore weight is unknown. At first we can estimate a depth and hydrostatic values ​​are calculated (one of them is the volume ) to that depth or different drafts. So I say that you do not need any mass study to calculate the displacement. There is or not a need of mass study? , the reality is that, in that momento, it is impossible to do. Later, with the most advanced project , calculate the actual weight and check whether the resulting draft resembles estimated or whether to change some feature of the vessel. That is the " spiral of project" and so you must proceed with this and many other project variables.
I hope this helps Soloman1970.

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### Richard WoodsWoods Designs

I agree, and why it is a design spiral.

And also why no designer will say, as the OP has done "I have designed a boat" because you cannot say that until the spiral has run full circle

Training, experience and previous existing designs will allow a established designer to have a feel for, say, the weight of a 50ft full keel monohull without doing a weight estimate. Something a first time designer doesn't have.

So its very much harder when starting from scratch. As the displacement and weight must match, it's very much a chicken and egg situation

Richard Woods of Woods Designs

www.sailingcatamarans.com

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### TANSLSenior Member

It is clear that when the OP said "I have designed a boat" has expressed incorrectly the situation, so point out Ad Hoc.
That's another definción of the "spiral of the project".

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### PARYacht Designer/Builder

Agreed, at this stage of the design spiral, an accurate weight estimate is a way off, around the spiral, but after a GA sketch, you do need to have some idea of how much boat you need, otherwise you'll be around the spiral a lot more then you'd like, just playing catch up with the weights. I think it's very unlikely the OP has any idea what the spiral is.

I'm assuming this person is designing by hand, simply because if they where using a software package, the basic premise of their question would be already answered. Since the poster is asking for appropriate displacements, he hasn't the basic hydro capabilities, that we take for granted, hence my assumption.

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