## Thursday, March 25, 2010

### Best. Goalie. Ever.

Never mistake a “hockey league for people who have never played hockey before” for a “hockey league for people who have never skated before.”  Concussions ensue.  During my ill-advised attempt at athleticism, I was struck by one question in particular: If we padded up a morbidly obese fat guy and shoved him in the goal, could he block every shot?  How fat would a hockey goalie need to be to completely block the goal?

Consider a cylindrical goalie.1  Since an official NHL hockey goal is 4 ft tall and 6 ft wide, a 6.0 ft tall goalie would be more than tall enough to cover the top of the goal.  To span the width, he must have a minimum radius of 3.0 ft.  Using the formula for the volume of a cylinder, we can estimate his total volume,

volume =  π · (radius)2 · (height)
=  3.14159 · (3.0 ft)2 · (6.0 ft)
= 4.8 m3 (~170 ft3).

Some people can float in water while others sink2, so our bodies must have a density close to that of water, roughly 1.0 g/cm3.  From this, we can compute his total mass,

mass = (density) · (volume)
= (1.0 g/cm3) · (4.8 m3)
= 4,800 kg.

At over 5 tons, our heavyweight would need to weigh about eight times more than the world’s largest man.

[2] This guy would probably float.