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.