Monday, November 14, 2016

Buoyant force in swimming and crew

My sister Becky is on both the swim team and the crew team at Franklin and Marshall, and it occurred to me that both of these sports utilize the principle of buoyancy. I wanted to compare the buoyant force acting on my sister when she swims to the buoyant force acting on the racing shell when she rows.

We can calculate the buoyant force on the swimmer if the density of pool water is 0.9927 g/ml, the swimmer’s mass is 61 kg, the volume she displaces is ~1/2 her total volume. Total volume for the average human of 64 kg is 4.4 L, which we can approximate to be her volume. Therefore the displaced volume is 2.2L. Her density can be calculated by:

Therefore we can use these values to calculate the buoyant force on her as she swims (floats):

Therefore, Becky feels 28.4N of buoyant force to keep her afloat.

To calculate the buoyant force on the shell she uses when she is rowing, we can use the same equations. Racing shells are typically made of carbon fiber reinforced polymer, which on average have a density of 1.55 g/cm3. The density of river water is 1.02 g/ml. We will approximate the volume displace by the shell to be 20 liters. An 8-person shell weighs 90 kg, in addition to the eight athletes, which we will approximate to be 61 kg each for a total mass of 578 kg.
Therefore, there is significantly greater buoyant force acting on the racing shell than acting on Becky when she swims.

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