# More questions (Priogue) and math.

Discussion in 'Boatbuilding' started by jdarling, Jul 1, 2009.

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### jdarlingJunior Member

Ok, so I have a question posed to me by my son while we were working out the basic plans for his boat project. Given the attached picture how do you calculate the angle (red ???) and distance (blue ???) for the centerline of the boat?

My gut reaction was to say that we couldn't until we actually built the boat, but then that defeats the purpose of this being a learning project that incorporates the math of angles. So, I'm hoping that anyone can answer how to find that angle and distance and explain the process to me so I can explain it to him .

Any help, great thanks. Heck I'd love to see a link that told me how to calculate all sorts of things related to boats (displacement for example) so I can explain them to him .

Thanks again,
- Jeremy

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### rwatsonSenior Member

Careful- this boat design thing can be addictive

Panel Shape
Your plan is not how it will turn out using angled sides on straight edged side panels.

Get yourself some stiff cardboard and cut two "sides". Tape the ends together and make a boat shape. Notice how the sides are vertical.

Now, when you 'tilt' the sides of the boat at an angle (use a 'frame' in the centre of the boat to force an angle). The two ends will become higher than the centre of the boat.(you get 'rocker' ) This is a good thing, as the boat will turn easier. Too much rocker, and you wont be able to steer in a straight line.

You can do the 'math' on some big cardboard boxes, using packing tape to do a really big model, till you get the hang of it.

May I suggest it will be a lot easier to spend a little more on some proper marine plywood that will be much easier to bend, and wont be that much more expensive in the end.

If you search the net, you will see a lot of these types of boat plans, and that will give you a much better 'vision'

=================================================
Displacement

... is easier if you use Metric.
eg
1 cubic metre = 1000 litres (volume).
1 litre (volume) of water = 1 kilo (weight)

A square box .5 metre x .25 metre x 2 metres = .25 cubic metres

.25 x 1000 = 250 litres (volume)
it will therefore support
250 kilos of weight (including the weight of the box) in water.

Most simple boats are a square box (from stern to centre), and a triangle (from centre to bow)

so continuing the example above

a) 1 box :- 1 metre (length from stern to centre) x .25 metres (depth) x .5 metres (width)

b) 1 triangle :- (half base x height) = 1 metre (from bow to centre) x .25 metre (half width) x .25 metre (depth)

add the answer of A to the answer of B = how many cubic metres of displacement for a simple boat.

Beats cubic feet, gallons etc.

The illustration below comes from http://www.selway-fisher.com/Dinghies.htm

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### PARYacht Designer/Builder

You could use angle "call outs" to specify the sectional shapes, but it would be more difficult then just using a direct "half breadth" measurement, as is traditionally done.

On simple, hard chine shapes like this you generally don't need many measurements. Typically, the "heights" and half breadths are recorded on evenly spaced intervals (stations).

The heights on a flat bottom boat would be two measurements at each station, the keel or bottom and the sheer. These would be measured from a base line or the LWL. If from the LWL, then + numbers indicate those above it, - those below.

Half breadths on this type of hull would be two measurements at each station, the sheer and the chine, both measured horizontally from the boat's centerline.

As you can see there's no need for angles, though I do understand your desires for their use with your son.

The "rake" of the stem and stern do typically have an angle indicated, which is often in relation to the base line, LWL or the bottom, depending on which is clearer or designers fancy.

As far as how to draw in this new style, I'm not sure I can help here in this format. You could use a drawing program or CAD to "flesh" out the design, picking up the angles as you find necessary. It would be a more error prone method of building, but it's an exercise in math right.

There's no "easy" way to get the volumetric calculations preformed. By hand (the way I learned) many can be painfully tedious. With computers, much of this has been absorbed in the functions of software.

Attached is an approximation of you little boat with the measurements necessary to get it built. The heights are measured from the bottom of the boat so a keel dimension isn't needed. The breadths are from the centerline to the outside of the planking. With drawing software or CAD, you can generate this in 5 minutes. The presentation of the information is done many ways. This one for example doesn't have a "body" or sectional plan shown. This is because the drawing provides enough information so you can build station molds.

May I recommend you add some "rocker" to the bottom of the hull, you've drawn to make the boat maneuverable. With the dead flat bottom she'll be fighting attempts to turn her.

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### neroSenior Member

If your CAD package is 3D, then extrude the bottom panel up and get the volume to the design water line. In metric this will be the displacement ... which is the amount of weight (including the weight of the boat) that the boat will support when immersed to that line.

Make some scale models first. It will help tie together what you see on the screen and reality. Don't be surprised if your son understands faster than you.

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### lewisboatsObsessed Member

Stick a protractor on your drawing then do a cardboard model to see if it works. It is called the empirical method...also something that should be learned.

Steve

PS: I think there is a bit too much angle to the sides...you will induce too much rocker at a guess.

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### jdarlingJunior Member

WOW, thanks for all of the answers and details so far everyone.

We are going to build several "prototypes" before building the actual boat itself. I was thinking of using some leftover plastic signs that I have lying around to make these from. That way they should last a bit longer.

The drawing was done in MS Paint (I know, not good, but quick for an idea). I've looked at several boat modeling packages (FreeShip - the one from sourceforge, hulls, and some others that I can't remember) but in the end Paint gave him a pretty picture he could quickly grasp . Later I'll worry about teaching him how to use a CAD package to actually build something more advanced.

I figured that the stems (not pictured) would force the actual angle of the sides outward angle, but had yet to figure out their proper angles (that was the models purpose).

For measurements, guess that's another good lesson in math to add to the list. How to convert from standard to metric. Then use that to calculate his ideal displacement.

The link to download freeship+ (http://freeship-plus.hotmail.ru/FreeShip3_04 update.rar) seems to be broken. When I try it I get a not found response will have to see if the one from SF can do the same thing.

Final reply, on the subject of wood. Eventually, I plan on getting the marine ply for the final build. The order right now is planned out as prototypes, 1/8" door ply and ducktape (I have lots of this lying around), then final design from marine with proper fiberglassing.

One nice thing about a project like this, it takes time and he has to work on patience on top of everything else .

Thanks again everyone, and any more advice keep posting as I make sure to check and read as much as I can.

- Jeremy

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### jdarlingJunior Member

How the heck did I miss that link. I actually did read the thread... Must have got lost in the chatter

10. ### apex1Guest

Jaja, our drivel queens...................... might have destroyed a joung mans brilliant future........ well, or so....................

.

drivel

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