formula for finding waterline?

I have traditionally built from other peoples' plans and would like to give a try at building my own design without spending years in marine school. I understand some of the formulas for determining hull speed, but how do I find the waterline?
I am a CAD designer and use Solidworks and/or Unigraphics in the aerospace industry, so I am familure with finding center of gravity (CG), balance, mass properties, ect. My question is how can I determine the hull displacement and waterline from a CAD model?
I have drawn up some great hull designs, but I would like to know if they are practical or even realistic.

 

Fresh water weighs 62.4 pounds per cubic foot.
Salt water weighs 64 pounds per cubic foot.

So each cubic foot displaced can support those weights, in those water conditions.

If you know the total weight of the boat and its contents you can then determine how many cubic feet will be submerged. Since the shape of the boat's volume from the waterline down is a complex shape, you would have to have a way of calculating where the line would be to fit the given required submerged volume. It should be an easy job for a computer!

 

I am glad I use SI
One cubic meter of water is (praktically) 1000kg or a ton.
One cubic decimeter (or one litre) is one kg.
In SolidWorks or other standard cad programs you have to guess I think, try with the waterline you think look right, slice the model and compute the volume and lcb of the underwater body, compare that with your (estimated) total weight and cg.

 

Start by computing main section area,multiply by waterline length and then by desired or estimated prismatic coefficent. This will give rough displacment of your hull in that trim.
Once you have your design "close" you can use simpsons rule to complete detailed calculations.

Tactic

 

I'm not sure how to do it in CAD. But here's what I do in Rhino. Maybe you can do something similar.

I create the hull and then create a horizontal plane that's larger than the hull. I place the plane at my targeted waterline and trim off the hull above that plane. I then do a volume inquiry of the remaining portion and calulate the weight of the water it'll dispace. Make adjustments to hull shape to get my desired displacement at my desired waterline.

 

The way I do this in solid works is that i create my hull upon a filled body then I shell the body to the exact thickness off the hull, this is then used for further detailing.

The interesting thing is that when you completely finish your design and if you have entered the correct density of the materials u have been using even put in some real people + some extra weight you get a realistic weight=>displacement of your design.

Then it comes: as I said, I designed the hull as a solid. Solidworks can do weight, area, volume and... calculations. Knowing the weight -> displacement -> volume that it corresponds to, you can now cut of pieces of the top of the solid hull until you get the desired volume of your solid to match the displacement volume. I even think you could put this in an equation so it would do this automaticly(thinking this right now so I am not shure) ( it's a bit like JEM's method here above)

The more tricky part of this will be? How is the boat sitting in the water I have not been looking into this problem for the moment. As the hull is not a uniform shape(cubic, cylindric,...) but has a deadrise and more surface area aft than forward and a CG point not necc in the center of the boat. Maybe someone could give an answer to that?

greetz,

 

Forgot to mention the point about hull thickness. Good point Daniel. My designs are mostly canoes and kayak and only 1/4" (6 mm) plywood at most. So I don't have to worry to much about actual hull weight. Simple guesses are accurate enough since I can change things simply and quickly. Not the case for a larger design.

For a bigger boat, you have to take the hull weight into higher consideration. The way I do it may not be the best approach because you'll have to go back and forth between calculating hull weight and adjust the shape and waterline to make everything fit together.

 

Danielsan,

You're approach is sound I guess. When you find the volume of water, it also represents a cg etc. When your predictions, watertank, fuel and people weight are calculated right in your material properties in SW, you should check if those two cg's correspond. Otherwise adjust your hullshape or move some stuff.
anyone has a beter idea?

 

Waterline

Not shure about what you mean by comparing the 2 cg's. The thing a did not fid out for so far is how the boat lays in the water. It must be a relation between wetted surface(s), CG, displacement,...?

If anyone has a exact rule for this, it will be more than welcom!!

greetz,

 

Thanks JEM,
I like this idea, it a very easy process in CAD. I will give it a try.

 

WOW!
Thanks for all the information.
This gives me a good place get started. :idea:

This is a great forum with a huge knowledge base.

 

Daniel, your " 2 CGs" are the CG of your boat (the center of all its weights, hull ballast, equipment, rig, ...) and the CB / Center of buoyancy which is the center of the displaced volume of water.

These 2 points, CG and CB have to be at the vertical. usually the CG is above the CB. Actually the boat will always settle in a stable position where they are vertical to each other, so assuming your boat has a symetric hull, the CG is on the centerline and you have to distribute and trim your weights symetrically and your hull will float upright. If you move a weight out of center, the buat will lean over. If you heel the hull, the CB with it's upward force moves out of the vertical alignment and will push that side up until the CB is again vertical with the CG.This force, the righting moment, is calculated from the displacment and the traverse distance between the CB and the CG. (there is of course another stable but less desirable condition, with the capsized boat upside down, and CB and CG inverted but also vertical.)

As to the fore and aft position, assume that the CB is just aft of the center of the WL, and you have to place you weights the same way to have the CG above in the fore&aft sense.

Baldur:
This means also that you do not design the hull the way it will but the way it should float, given a certain displacement, and shaped according to the desired parameters, type of propulsion, targeted speed... and then see that building, scantling, equipment and charge will fit in at the right places and produce a) a displacement that will sink the hull in exactly to the DWL and b) give you a perfect vertical alignement of the CB and CG in such a way that the boat is floating even.

The thing to keep in mind is that you can not design a hull and then look where the waterline might be, and which position will she float. You have to define the displacemment first plus a couple of vital parameters, and then design around that.

Very useful for first decisions is the prismatic coefficient, as Tactic already mentioned: Multiply the estimated aread of the largest section by the lentgth of the waterline, that gives you an imagined hull with parallel lines, with blunt edges fore and aft, or 100 %. (similar to a floating cylnder) the prismatic coeff is the percentage of this imagined volume that the real hull occupies. Most sailing boats will have a prismatic around 50 to 55 % these days. So, if you decide the WL length, the hull draft and scetch out the master section, multiply one with the other you get a 100 % volume, and if you take 55 % of its weight (in sea water) you have a first realistic calculation of your future displacement. The result is good enough to start, even if at that point you have not yet defined the hull lines, entries, appendices etc. this will be the target displacement that you will have to fit with all that you built and charge into your boat.

A good way to rough out a design is to have a look at boats of similar type, construction and material and pick the main parameters: length and width at the waterline, displacement, depth of the hull (without appendices) and the postion of the largest section, and copy these as a starting point to your own project. You will find that boats that may look radically different actually often have the almost exact same basic numbers... and you should be worried if your own design will turn out radically different numbers, because it means that either you have just re-invented yacht design and won'
t know what to do with all the money or it's complete nonsense and you have to start all over ;-)

Around this, you can now design your topsides, cabin, rig and interior arrangements, assuming that you will have an identical ballast at the same place to start with. Then you calculate the total weight from all the bits and pieces and compare it to the displacment to see if it fits.

Estimate as detailed as possible all your weights. Calculate your CG for the entire boat including ballast, equipment and rig. If you are roughly above the largest section and just above or below the waterline you have something you could work on with.

After that you really have to go more into detail with coefficiants and parameters. Half the work is calculating them for your hull and comparing them to other boats and to known safe, optimized values, making educating choices, refining your criteria and start over again and again. For that your really have to read some books. There are the good old classics, like Skene's Elements of yacht design, or a quick primer like Ted Brewer, Understanding Boat Design. Brewer also has quite a good introduction on his website at http://www.tedbrewer.com/yachtdesign.html.

My personal favorite for general intro is Dave Gerr, The Nature of Boats, because it not only gives you the formulas and ways to calculate and judge but also tons of additional facts, opinions and anecdotes and it's a great read.

Enjoy ;-)

Gerd

 

Yes, and along the same lines:
- "volumecentroid" gives you the CB
also:
Select the hull and superstructure (separately, to take in account the fact that the deck usally is built lighter) and
- "area" to guesstimate the weigths, knowing the material
- "areacentroid" to find the Center of Gravity (will work for example for an entire assembly of deck, cabin, cockpit etc assuming it is of roughly the same weight throughout) and then calculate the combinened CG for the entire hull-shell
Adjust for structure, or design it and as surfaces and do the same
Good enough for first calcs.

--... plus of course "hydrostatics" in Rhino



Gerd