Was it physically possible for the Balloon Boy to fly away? A mathematical explanation
Last week, news organizations erupted with the story that a six-year-old boy, Falcon Heene, climbed into a helium-filled Mylar balloon in Colorado and floated away from his parents. The story turned out to be a hoax, but could it have been physically possible?
Last week, news organizations erupted with the story that a six-year-old boy, Falcon Heene, climbed into a helium-filled Mylar balloon in Colorado and floated away from his parents.
When the balloon landed, the boy wasn't on board, terrifying locals who searched for him and captivating a nation.
The story turned out to be a hoax (the boy was hiding in the family's attic) and publicity for a reality television show.
But was it actually physically possible for that balloon to carry away a child of his size?
Adam Weiner at Popular Sciencetook a stab at the math to find out if a helium-filled balloon would have sufficient buoyancy to actually lift the boy.
Buoyancy is a result of a difference in pressure between the top and bottom of a submerged object. Invoking Archimedes' Principle -- which says that the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object -- Weiner writes that, "in order to lift off of the ground, the upward buoyant force must be greater than the downward force of gravity acting on the contents of the balloon, including the helium, the balloon material, any attached components, and any small boys that publicity, obsessed parents may claim to be on board."
Under the assumption that the boy weighed 40 lbs. and using an approximation of the volume of the balloon based on captured video of the incident, Weiner attests that yes, the boy could have been lifted off the ground "if the balloon material and any attached components weighed less than about 9 pounds."