A Math Question: Buoyency

Here’s an interesting question that I hope someone can help me with. I’m looking to make a floating light system, but the only batteries I have access to are FIRST batteries. They’re a bit big.

So here’s exactly what I’m looking for, and I’m hoping to learn some math along the way. I have exactly 15 pounds of electronics and batteries, and I need to know the volume of the container that I’d need in order to make this float. I’d rather do the math for this first, so I can build the container out of Lexan, rather than doing the guess and check type experiment. It would be floating in standard pool water (chlorinated fresh water), with not too much water disturbance.

So how might one go about finding this out?

You just need to calculate the average density of the whole container to it’s weight… If the density is less than 1 Kg/L, it floats.

So, you could calculate the volume of some random boxes to guess and check, or you can work backwards knowing you need to offset 15 lbs.

easy enough.

A cubic foot of water is about 64 lbs. A battery is about 15 lbs.

Rough order of magnitude math cause I’m too lazy to do it right:

Lets say a battery weighs about the same as a fourth cubic foot of water.

Therefore if the battery is larger than a fourth cubic foot, it floats, if less than a fourth cubic foot, it sinks.

Archimedes principle.

Thanks Archy

This is why I like the metric system. For as much as your float masses, it will need to displace an equal or greater mass of water. 1 Kg of float = 1 Kg of water = 1 Liter = 1000 cubic centimeters. I don’t even have to waste the brain power on remembering how many pounds a cubic foot of water weighs.

Find out how much volume a pound of water takes up (Google, perhaps?), then build a container to the shape you want with 20 times the volume of a pound of water.


A one gallon engine is the Buick 231 cubic inch (3.8 liter) V6. This I can remember.

And a pint is a pound, the world 'round. This I can also remember

so you need to displace two gallons of water (462 cubic inches, which happens to be a 1960s Lincoln engine) to make a battery float (8 pints in a gallon, two gallons = 2 x 8 lbs/gal = 16 lbs), and you need to displace more than that for the rest of the weight of your system.

you do understand about cubic inches, I trust…just multiply the height times the width times the length (assuming a rectangular box) and you get the volume in cubic inches of your box.

You are a CAD master. Use it. Draw the ‘boat’ without making the air and parts inside of it. Just don’t hollow it. That way you don’t have to solve for the volume of the boat. You just draw it and set the density for water. Check the weight, make sure it is more then the weight of the battery and equipment.

This is the way of the true CAD master, young mathawan.:wink:

Woah, you all rock! Thanks a ton, I’ve now got my dimensions all done for a lexan box I’ll be making to float in my pool with some sweet lights (FRC green cathodes). The box will measure 14" long by 5" tall by 10" wide. This should be slightly less than twice the buoyancy that I need, which should also give me plenty of room to put in all the electronics. I’ll probably upload some pictures once I finish building the thing.

Thanks for the help!

You are a veritable plethora of information. It never dawned on me until now that this particular Lincoln engine was twice the size of the Buick and was a gallon versus 2. we’ve got our selves a regular click and clack contender.

I just did a little punching in the calc and did the volume of 8 cylinders of 4 in bore and 4 in stroke and got 400 cu. I just had to try that out. back in the day the 4x4 happened frequently enough, like in a John Deere Model 40.

Don’t forget to add for “freeboard” in case there are any waves. Don’t want to swamp your electrics.