Wednesday, June 13, 2007

Buoyancy for your Swimmy Thang!

Our friend and co-conspirator Dan Atwell has taken time out of his busy life to create a great article for Swimmy Thang! on how to determine how much buoyancy your bot will need. Thank you Dan!!! Your contribution is greatly appreciated!

Here is a little basic video to get you up to speed for Dans experiments!



Buoy•an•cy noun, Pronunciation [boi-uh n-see, boo-yuh n-see]

1. The power to float or rise in a fluid; relative lightness.
2. The power of supporting an object so that it floats; caused by upward pressure exerted by the fluid in which an object is immersed.

The majority of ROV’s, are heavier than water, and most of the time buoyancy is achieved through trial and error. Hopefully we will have changed this method to a more positive way of calculating the buoyancy for ROV’s.

Example to test ROV buoyancy

First weigh your ROV on a scale. As an example in our trial we used a 5lb weight (M1). We tied our weight to a cord to and let it sink to the bottom. This was submerged in a 5 gal tub of water filled to the top. We pulled the weight out of the water by the cord. Let the weight drain over the tub until all the water drains off weight. Now carefully measure the water you put back into the tub to fill it up to the top and that is the displacement weight of the water lets say as an example it comes to 7 oz of water (M2). A little less than a cup of water. Now subtract that M2 from M1 and that gives you the true weight (TM).

To test your ROV, you will need to find a container large enough to follow the steps above. Not to large so that you can not measure the displaced water.

M2 – M1 = TM or 7oz - 5lb = 4.9lb TM

The weight of freshwater is 62.4lb per cubic ft.
The weight of saltwater is 64lb per cubic ft.

For our purpose of our test we used salt water to calculate the rest of the formula. Now divide true weight (TM) by 64.

4.9lb / 64 = .07 cubic ft of air

By the way a cubic ft of air weighs .08lb. A cubic ft is 12 inches x 12 inches x 12 inches, and that equals 1728 cubic inches. Now back to the equation, we need .07 cubic ft of air to make our weight become neutral buoyancy. Multiple 1728 cubic inches by .07 cubic ft of air and that equals 120.96 cubic inches of air needed.

.07 x 1728 cubic inches =120.96

Now we need a container that has 120.96 cubic inches of air in it. If we use a cylinder (cylinder weight was included in the weight with cap removed). Using a cylinder, with a 3 inch inside diameter, we will need to calculate the length of the cylinder to accommodate the 120.96 cubic inches of air we will need to float the 5lb weight.

The formula for a cylinder, Volume = pi (3.14159) x ratios squared x height.

V = pi r2 h

120.96 = 3.14159 x 2.25” x 17.11”

How was the formula calculated, multiply 3.14159 (pi) times 2.25 (r x r) equals 7.0685775. Now divide 120.96 sq in of air by 7.0685775 equals 17.11. So the cylinder will be 17.11 inches long.

Now we should think about were to place the cylinder to balance the weight of the 5lb’s and make it float level in the water. You will have to determine the center of the 5lb’s and attach the cylinder (float).
Interesting Note
It is named after Archimedes of Syracuse, who first discovered this law. Vitruvius (De architectura IX.9–12) recounts the famous story of Archimedes making this discovery while in the bath (for which see eureka) but the actual record of Archimedes' discoveries appears in his two-volume work, On Floating Bodies. The ancient Chinese child prodigy Cao Chong also applied the principle of buoyancy in order to measure the accurate weight of an elephant, as described in the Sanguo Zhi.
If there are any question, E-mail Dan Atwell at jdatwell@sbcglobal.net

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