Math: The Diving Edition

Everyone enjoys playing volleyball with bowling balls at Haigh, so I thought it would be fun to find something like that but soft to play with in the pool.  The trouble is, finding something that will be negatively buoyant, but not too negative, so when I came across a small 10lb. medicine ball on clearance at Dick’s, I wondered if it would fit the bill.

Lift Bag by Sheryl

In chapter one of the open water manual, we all learned that things are neutrally buoyant if they displace an amount of water that equals the weight of the object.  So if I figure out the volume of the ball, I would be able to find out if it will sink and the degree of negativity.

I measured the circumference: 23in. 

Volume Sphere =  π *diameter³ ÷ 6    

Diameter = circumference ÷ π, so 23in. ÷ 3.14= 7.32 in. diameter.  

THEN,   π*7.32³/6=205.6 in³ is the volume of my medicine ball. 

Converting to ft³=205.6/1728= 0.12ft³

A cubic ft. of freshwater weighs 62.4lbs. 

So: 62.4lbs./1ft³ =  X/0.12ft³ = 7.49lbs. displaced. 

Then, 10lbs.(weight of ball)-7.49lbs.(weight of water it displaces) = 2.51lb negative buoyancy for my ball.

Now, I know that I could have just put it in the water to see if it floated, but this was a good exercise.  When doing underwater recovery, or just a job in which we need to move a heavy object underwater, knowing how to calculate displacement saves a bunch of trial and error.  It also helps when you want to sink something.  You need to figure out how much positive buoyancy the object has in order to know how much weight to add.  It is kind of like what I go through with new divers to estimate the amount of lead they will need to sink.

So now you have an idea what I am doing in the off season!