Floatable Weight

How do I determine how much weight a hull of defined measurements will carry. For example, if I built a rectangular box hull measuring 8.5’ x 24’ x 3’, how much weight would it float 1) if open, or 2) sealed closed?

 

1 cubic foot will displace 62.4 lbs of fresh water. So 8.5 X 24 X 3 = 612. 612 X 62.4 = 38, 188.8 lbs But that is the weight that will bring the water up to the top of your box. If it's open, water would flow in and it would sink. If its sealed with that load on top it would probably roll over and dump it's load. Load capacity is less than that. On outboard recreational boats it's 1/5 of that. On inboard boats its 1/7 of that . If it's for carrying cargo or passengers for hire then load capacity is based on stability. Loads are placed at a specified distance from the centerline and the heel is measured. That is used to determine how much weight it would take to cause the boat to roll over, and the safe load is a percentage of that.

I forgot to subtract the weight of the boat. so if your boat weighs 3,000 lbs then the capacity would be 35,188.8.

 

Welcome to the Forum Luke.
Ike has covered it very well above.
Can you tell us a bit more about this boat please?
Are you intending to build something like this rectangular box, or are you simply using it as an illustration for calculating the volume / displacement?
If you did want to put this box in to service afloat, I think that to be on the safe side you probably would not want to load it past a draft of say 12".
At this draft the displacement would be 12,730 lbs; if the hull weight is 3,000 lbs, then the maximum load would 9,730 lbs (or 4,423 kg).
This is still a lot of weight, and it's ability to carry this amount is determined by the stability as Ike says.
You would not have to worry about the stability if the cargo is (for example) 4 tonnes of lead ingots stowed on the hull bottom inside the barge.
But if you are carrying (for example) some machinery on deck, then the centre of gravity of the cargo will be much higher, and the stability will be much less.

 

Ike, thanks for your answer. Could you please explain why the capacity is so dramatically reduced for outboard and inboard propulsion?

 

These are the formulas used in the US Coast Guard regulations for monohull, non-inflatable motor boats under 20 feet in length. For boats with 2 HP or smaller outboards, or for rowboats the formula is 3/15 of the difference between the fully submerged displacement minus the weight of the boat. These formulas were developed in the early 1970's and were based on numerous factors, some technical. The USCG does not have a formula for boats over 20 feet in length not used to carry more than 6 passengers for hire. Also no USCG formulas for canoes, kayaks, multihulls, inflatable boats, sailboats, paddleboards or sailboards not used to carry more than 6 passengers for hire.

Other countries have their own formulas.

 

Based on research done in the 50's and 60's mainly by the British it was determined that each of theses types of boats need a safety factor. It is not the maximum capacity because that would sink the boat or make it unstable. One of the tests used to determine compliance with the rule is a stability test. A percentage of the weight for persons is placed to one side of the boat and it is not allowed to heel more than 30 degrees. Why 30 degrees? Because research and practical experience has shown that if the heel reaches 30 degrees or more the boat has a tendency to keep on going, and capsize. So a safety factor is use to limit the load thereby limiting it's tendency to heel excessively and capsize. As you start to increase the amount of weight in the boat, it becomes less and less stable. (that is a generalization and there are many other factors such as length, breadth, depth, CG, and so on) It is different for outboards and inboards because of the greater weight of inboard propulsion. On larger boats or ships the amount of load is based on a stability test called an inclining. Known weights are placed at a known distance from the centerline and the heel angle is measured. From that the safe load can be calculated. Ever notice those lines on a ships hull usually at the bow near the waterline. Those are called plimsole lines (also called a load line) and they are there to show how heavily loaded the ship is. Its the same idea. Even a big ship cannot carry a load that would fill up the inside of the ship. It would capsize.

So a safety factor is used for small boats so they don't get overloaded and capsize.

 

However, for most of these there are accepted industry standards, which are laws in some countries, such as Canada and the EU. These standards are published by ABYC (American Boat And Yacht Council) and ISO.

 

Thanks again to you all for willingly explaining unknowns to a landlubber! I guess more info is warranted. I would like to think I can build my own houseboat, but know nothing of the science, laws or regulations affecting my project. This site I stumbled on by chance and thought I’d expose my ignorance! Looks like it worked. So , width does more to affect carrying capacity than length, is that right?

 

Not necessarily . Capacity is a combination of length, width, depth of the hull, and somewhat the shape of the hull. Increasing the width will increase stability and will increase resistance to roll but may make the boat so stiff it becomes uncomfortable and has a harsh ride. When it comes to boat design everything is a compromise. All the important dimensions have to work in harmony. Change one and it affects all the others. Besides why build your own houseboat. There are thousands of perfectly good used ones on the market at bargain prices, that probably need a little fixing up, but are far cheaper than building one. see Houseboat Magazine forums. https://www.houseboatmagazine.com/forum/

 

And following on from Ike's post above, if you are still REALLY keen on building your own houseboat, it would be well worthwhile buying a set of plans 'off the shelf' rather than trying to design it yourself.
Even rectangular floating boxes are quite complicated to 'get right' re their design.

Here are a range of houseboats on the Glen-L site -
Houseboats-boatdesign https://www.boatdesigns.com/Houseboats/departments/7/

Some more here
BoatPlans.com http://www.boatplans.com/cgi-local/shop.pl?type=categ&categ=010&cart_id=

Here is one that is a bit more 'boat shaped' than a rectangular box -
Lingcod 27 https://devlinboat.com/lingcod-27/
And still with Devlin, but back to the box - this one is only 20', but she also has a 28' big sister.
Millie Hill 20 https://devlinboat.com/millie-hill-20/