## Friday, March 5, 2010

### Sneeze Breeze

I often catch myself thinking about the great things that humanity could do if we all worked together.  And while it’s nice to think about things like stopping hunger or working for world peace, it’s more fun to think about sneezing.  If all of humanity faced the same direction and sneezed at once, how fast could we push a sailboat?

From physics we know that momentum has to be conserved.  As an upper bound, let’s assume all of the momentum from the sneezed air gets transferred to the boat.  Our lungs can hold about 500 cm3 of air and air has a density of 1.2 kg/m3, meaning that the total mass of a sneeze is given by,

mass = (density) · (volume)
= (1.2 kg/m3) · (500 cm3)
= 0.6 g.

According to Wikipedia, sneeze speeds lie between 75 km/hr and 1045 km/hr, so I’ll assume an average sneeze speed of 200 km/hr.  The world population is 6.7×109 people sneezing.  From this info, we can compute the total momentum of sneezed air,

momentum = (number of sneezes) · (mass per sneeze) · (speed)
= (6.7×109 sneezes) · (0.6 g) · (200 km/hr)
= 2.2×108 kg m/s.

We’ll assume that all this momentum is transferred to the ship.

For our model ship, we’ll consider the fully rigged tall ship Bounty II, which has been featured in numerous films including Mutiny on the Bounty, Treasure Island, and Pirates of the Caribbean.  It is listed at 412 tons = 3.7×105 kg.  From this we can estimate an upper bound for the total speed it would gain by the entire world sneezing on it,

speed = (momentum) / (mass)
= (2.2×108 kg m/s) / (3.7×105 kg)
= 600 m/s.

In contrast, the sound barrier is only 340 m/s, meaning the boat would be traveling at close to Mach 2 or twice the speed of sound..  Remember, however, that this is only an upper bound since a vast majority of the air’s momentum will not be transferred to the ship.

#### 1 comment:

1. This formula also does not take into account the magnitude of my neice's sneezes.