Ballast Required for a Buoy

by Mike Mills

Submitted : Spring 2013

The approach taken to solve the problem has two main parts. First, find the volume of ballast and the volume of water displaced. Then use this data to calculate the height of the ballast inside of the buoy. Archimedes’ Principle is used to find the volumes. Setting up this equation will give two unknowns; which are the two previously specified volumes. The volume of water displaced is found by using the Trapezoidal Rule with the height and radius of the buoy. From here, plug the value of water displaced into Archimedes’ Principle equation and solve for the volume of ballast. Now, the height of the ballast in the buoy can be found with the following and applying linear interpolation: the volume of ballast, the volume of the buoy and the given height values. The height of the ballast is 6.18 cm which is reasonable since the buoy is curved making it a non-uniformly distributed object.

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