# Flat Bottom Boat Stability

Discussion in 'Stability' started by Jeep8499, Dec 5, 2013.

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### Jeep8499New Member

Hello,

I am an engineering student studying in the mechanical concentration. As part of a project, I am trying to design a small aluminum flat bottom boat (roughly 14' long by 5' wide).

I would like to perform some calculations on my design with regard to stability. I have had no experience in this area, however, I'm more than willing to read and learn. Specifically, what I'd like to calculate is how much the boat will tip if a person inside the boat shifts from the center of the boat to the very edge of the side of the boat. I'd then like to know how this relates to the width of the boat.

Can anyone tell me what type of calculations I need to do or point me in the right direction? I've done some reading with regard to stability, but haven't found any clear-cut relationships for this type of calculation. Is this just far more involved that what I'm expecting?

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Hi Jeep8499

Welcome to the forum.

What your asking whilst is easy enough for a naval architect is a bit beyond you at this stage since there is a lot of background reading required first, and you would be asking more Qs with each reply. However, I can recommend a very good book with shall assist you:

"Introduction to Naval Architecture" by EC Tupper.

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### SaqaSenior Member

Hey mate, check out the freeware called hulls. Allows you to enter different weights and angles for heel calculations and righting moments

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### philSweetSenior Member

If you just need an estimate, or if you are just trying to get a handle on the important variables, that can be done quite easily. It quickly gets complicated if you allow the boat six degrees of freedom and start shifting loads. It is easier still if you assume small angles of heel, but better not to, at least for the first few calcs.

If you make the assumption that the boat is only going to roll about it's fore-aft axis, things are a lot more manageable and the problem can be worked out on graph paper in an evening. The info below makes this assumption and several others.

I would recommend that you look at the mindship cross-section on paper and get the method sorted in your head. Then switch to excel and repeat the calculations at each of ten stations along the boat. Then combine these.

You need the weight of the empty boat and it's center of gravity.
You need the weight of the occupant and their center of gravity.
Locate the fore-aft position of the occupant and get the boat floating level such that the longitudinal center of buoyancy (CoB) of the boat is in line with the total center of gravity (CoG).

Now you can roll the midship at constant displacement and calculate the righting moment for several angles of heel. It is well worth the effort at some point to write a spreadsheet that does this. It is a bit time consuming though if you have, say, fifty beam offsets from keel to chine at each fore-aft station. You have to accurately match the displacement each time.

The usual way to look at the problem is to figure the heeling torque that the load induces, and calculate the angle that produces the required righting moment. If the heeling torque depends on the angle of heel, like it would in a small boat, then an iteration may be required. Work it all out as algebra first for a simple block so you can see the dependency on weights and dimensions. Numerically, for a spread sheet implementation, the surveyors' method of area and moment calcs works well. If the occupant is assumed to be standing, you need an expression that relates the CG of the occupant to the CG of the boat as a function of beam, draft, and angle of heel. Basically, a standing person's weight allways passes vertically though their feet, so this simplifies things a bit.

When you have a first cut, check to see if the longitudinal CoB has changed as a result of the boat healing. You may have to make a small correction for that and reiterate. This can all be done grapically by counting squares inside a large picture of the section shapes of the boats as well.

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### Mr EfficiencySenior Member

The simplest way would be assume the boat is an open rectangular box, and work from the standpoint that the centre of gravity is on the same vertical line as the centre of buoyancy, at equilibrium. Better still, start by heeling the boat just enough so that one side just leaves the water, you'll be left with a nice triangle it is easy to find the geometric centre of !

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### PetrosSenior Member

welcome to the forum Jeep,

there is lots of free ware boat design software that would do this calculation for you but I think it would be more impressive if you do the calculation by hand or with an Excel spread sheet that you write yourself.

All you need to determine from your description is the static angle of heel when the passenger is off to one side in one axis. this is a simple equation if you assume the hull is a simple rectangle, you are summing the moments around some point, like the center line. the weight of the volume of the water displaced, times the distance to the centroid is your righting moment, and the weight of the passenger times the distance to the center line must equal. A few trial error attempts to balance the forces should yield you the heel angle.

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