Depth of Immersion of a Cylinder

I have no idea what an integral is or what the Riemann integral refers too. But dividing a "segment" up like that would get you very close to the area of the segment using basic math. You would draw it out on paper or something, to the dimensions of your cylinders. You would draw a bunch of vertical lines, say an inch apart. Wherever the vertical lines go through the arc are the opposing corners of the light blue rectangles. For each vertical space, you would find the area of the dark blue rectangle. Then find the area of the light blue rectangle above it. Since the arc bisects them from corner to corner in pretty much a straight line, divide that amount by 2 and add that to the sum of the dark blue rectangle below it. Do that for all of them, add them all together and that's pretty close to the area of the segment. The two on the right are obviously different, you could guestimate the areas there, like 1/3 or 60% or whatever looks close. If you drew more vertical lines in those areas and divided it into smaller rectangles, it would become more accurate.

Once you get that number then you figure volume, displacement, etc.

Of course, if you can score a planimeter you don't have to bother with any of this.

http://en.wikipedia.org/wiki/Planimeter

There's probably a program on the web that will do it all easier than anything.


Edit: The red chart would be done basically the same as the blue, except you would be figuring out the area of the (white) right triangles and adding them to the red bars. I guess that would work for the blue chart as well.

 

It's a fairly basic engineering problem.

You didn't quite provide enough information to solve the problem, so I made some assumptions. Presumably, there are two pontoons, and they are connected by some sort of framing, which has a deck of some sort on top?

I put together a quick and dirty worksheet which calculates the draft of a pontoon boat or pontoon float, both unloaded, and with people on board.

To get your beer, you will need to know the weight of the framing and platform on top of the pontoons, and you should be able to use my worksheet as a guide to work out your own calcs.

I assumed that the framing and platform weighed 500 pounds, which came out to a draft of a little over 8 inches.

 

Thank you everyone for their help and input! I think I’ve calculated where the finished dock will sit once in the water.

The finished dock is 48’ long by 8’6” wide with 27” steel tubes weighing 54.07#/ft. The steel pontoons weigh 5,190 lbs.; the substructure weighs 1,000 lbs. and the decking is 1,747 lbs. for a total of weight of 8,584 lbs.

I’ve calculated the dock, alone, will have a draft of 10.53 inches. Under load as per the “recommended maximum gross load” calculation from Transport Canada (as a reference point); the dock’s maximum gross load is 7,613 lbs. which will put the draft of the dock at 17.54 inches.

Baring I did everything correctly, I’m confident with those numbers; and if any of you find yourself up in Georgian Bay you are all welcome to come by, see how she floats and the beers are on me!!

Nick

 

According to the above, you've exceeded your gross allowable weight... But if you're happy, I'm happy.

Are you near Honey Harbour?

 

Tom,

Are you referring to the gross allowable weight not exceeding 50% of the carrying capacity of the pontoons or I made an error in the TC gross load calculation? We have a place just north of Parry Sound.. do you know the area?

Nick

 

Nick,

You either added your vessel weight incorrectly, or forgot to tell us about some of the weights.

By my count, 5,190 + 1000 + 1747 = 7,937 pounds.

Assuming that your 8,584 value is correct, the drafts look correct.

I have attached a revised worksheet, showing the Gross load calcs, and the 7,937 weight of the vessel.

Good luck.

 

I know Honey Harbour to Parry Sound but mostly around HH. I spent my summers there as a kid.

 

Thanks Matt, I had made a simple weight calculation!