Pond Boss Forums INTRO Questions & Observations Floating Math Problem?

Okay you math wizzes, I need your help. Also you dock builders who have had experience building a floating dock.
I just acquired a large piece of foam ( 3 feet by 7 feet by 12 inches thick. I also have two plastic 55 gallon drums. If used all this to build a floating platform to add to my dock, how much weight could it hold.?

Answer: One Fatty McButterpant.

You must have used your slide rule to derive that answer, but it's cool, I like it hope Mc does.

I'll take a swing at it, heybud.

Each 55 gallon drum will displace 55 gallons of water, times 8 lbs/gallon for 440 pounds each (minus the weight of the drum). Now I just went outside and picked up a steel 55 gallon drum; I will therefore guess that 25 lbs is a fair estimate for drum weight. This means the 2 drums will displace about 2x(440lbs - 25 lbs) or 830 lbs.

Now for the foam. Water weighs about 62 lbs per cubic foot. The volume of your foam is 3'x7'x1', or 21 cubic feet. This means it will displace about 21x62 or about 1300 lbs, minus the weight of the foam. You can weigh or estimate that yourself (since it would vary with the type of foam, and since I don't have a clue off the top of my head how much ANY kind of foam weighs :rolleyes: ), but for discussion purposes, let's say the foam weighs 100 lbs (which sounds high to me). That means the foam will displace about 1200 lbs of water.

Therefore the total water displacement of your bouyant materials is roughly 830 + 1200, or about a ton. Don't forget to subtract the weight of the lumber or whatever you use for structure and deck on the dock, and note that you will only be able to hold up a ton IF the barrels and the foam are completely submerged (how deep dosen't matter, but they have to be all wet).

I would hazard to guess that you can have a dock which will hold up SEVERAL Fatty McBs.

Theo's got if figured. Take note regarding what he said about the drums and foam needing to be totally submerged to hold a ton of weight. If you assume that you only want the drums and foam to be half sugmerged then since both are regular symmetric shapes the easy answer is don't let the structure and expected load to go over 1/2 ton. If you want the drums to ride up either lower or higher in the water the calculation is more complicated since you have to figure out how much water is displaced by however much drum you want submerged. Also make sure to somehow put the foam in a symmetric location with respect to the drums otherwise the platform will float crooked. It is much easier to use either all drums or all foam. But if you do something like cut the foam in half and put one piece centered along two edges with the drums centered in the middle or centered on the other two edges. Think of keeping it balanced. This will of course only work if you build the structure symmetric as well. Can't have the structure heavier on one end then the other.

Almost. I would use about half (or less) of that since you don't want your floats completely submerged. 1000# still would hold a couple of big guys with no problem and still be quite stable.

Minor point. It does matter how much you are sumerged. The resistance or upward force is 62.4lbs per foot of submergance. So at 2', it would be 124.8lbs of pressure per sq. ft. This is a linear function, and can be used to calculate the pressure or force on the face of a dam, etc.

ROFL. How do I get to be a unit of measure? I should have picked a better nickname.

Sorry Bad Boy, but the upward force is 62.4 pounds per cubic foot of water displaced, not per foot of depth. If you push a 55 gallon drum half way into the water the bouyancy is roughly half the volume times 62.4 or 55/2x62.4=1716 pounds minus the weight of the barrel and whatever is on top of the barrel. This is an easy calculation because at half submerged the volume of barrel under water is half the barrel. It doesn't matter that the barrel is only 12 inches into the water it is how much water it displaces. If you try to push a 10 foot boat down into the water 12 inches it takes way less than pushing a 20 foot boat the same distance down, right? And it is not linear since the barrel is round not square. It would be linear for a square/rectangular object sumberged into the water but not a round object. If the barrel is submerged less than half into the water it is a more complicated calculation because you have to figure out how much a small section of round barrel is displacing and since the equation for a circle is by definition not linear the bouyancy is not linear either. Just remember, an object's bouyancy is equal to the weight of the water it displaces when submerged minus it's own weight. That's why hollow things filled with air float better than solid objects unless the solid object is very light like foam. That's also why a steel ship can float if it's hollow.

Sort of bz. First your units are not consistant. Water weighs 62.4 lbs per cubic foot, or 8.3 lbs/gallon. You would need to use 8.3 times 55 divided by two to get the weight of the water displaced.

Bouyancy is the summation of all the upward forces, minus all of the downward forces created by the liquids pressure. The forces on an object exerted by a liquid are normal (90 degrees) to that surface. Inclined surfaces have a vertical and horizontal component. In an object not moving, the horizontal components cancil out and are not of concern. Pressure is a linear function of depth. In other words, for every foot of depth, your pressure increases by 62.4lbs per cubic foot (you can do the unit conversions to get pounds per square inch). You are correct in that the bouyancy is equalivant to the weight of the water it displaces, less any other downward forces such as the weight of the drum. My point was that it does matter how much you push the drum into the water (depth dependant) until the drum or what ever is fully submerged. At which point the summation of upward forces less the downward forces all created by pressure is a constant.

Oops, you are correct Bad Boy. I got my units mixed but the theory is still correct and you corrected the math. If you do my math using 8.3 pound per gallon it will come out correct. The answer is that 228 pounds minus the barrel weight will push the barrel half way down into the water. I typed this during lunch hour and haste makes waste. I thought the number sounded large. Seems like we both agree that as you submerge a barrel more and more the bouyancy is not linear because of its shape until it is fully submerged at which point the bouyancy is constant no matter what depth. And yes pressure is linear but it has little to do with bouyancy unless the barrel collapses under the pressure at which point its displacement has changed. That's not what we're dealing with however when building a floating dock. My point is simply that all you need to do is calculate how much water is displaced by whatever portion of the barrel is in the water and your bouyancy is the weight of that water minus the weight of everything including the barrel.

bz and Bad Boy,

Great discussion! Just another one of a million reasons I love this forum.