# The Science Guys

### July 2000

I am 12 years old and weigh about 100 pounds. How many helium balloons would it take to lift me?

About 250 B.C. King Hieron of Greece asked Archimedes to determine whether his crown was made of pure gold or an alloy. The task had to be performed without destroying the crown. Legend has it that Archimedes figured out a solution while taking a bath. He observed that his arms did not appear to weigh as much when they were in the water. This gave him the idea for what is now known as Archimedes Principle. Legend further states that Archimedes was so excited at his discovery, he leaped from his bath and ran naked down the street shouting "Eureka" which is Greek for "I found it."

Archimedes’ principle gives us the answer to our question today. The principle states, "any body in a fluid is buoyed up by a force equal to the weight of the fluid displaced." In the case of a person in water, they are ’buoyed up’ with a force equal to the weight of the water their body displaces or pushes out of the way. In the case of a balloon, the fluid is the surrounding air. Most people do not think of air as having weight but it does, specifically 0.0807 pounds per cubic foot.

When a less dense (lighter) fluid is placed in a more dense (heavier) fluid, the lighter one floats on top. This lighter fluid is ’held up’ by a buoyant force. That buoyant force is equal to the weight of the heavier displaced fluid. Since the displaced fluid is heavier, the buoyant force is greater that the weight of the lighter fluid so the lighter fluid floats on the heavier fluid.

Helium is less dense than air. Helium has 0.0114 pounds per cubic foot. For a one cubic foot helium filled balloon , gravity pulls the down on the helium with a force of 0.0114 pounds while the air pushes up with a force equal to the weight of the air the helium displaced, or 0.0807 pounds. The difference in the up and down force is 0.069 pounds. Therefore each cubic foot of helium could lift 0.069 pounds. In order to lift 100 pounds (which would include the weight of your load, the balloon, and the helium) you would need 1449 cubic feet of helium. This would require a balloon with about a 15.5 foot diameter. If instead you used small spherical (one foot diameter) balloons (which holds about 0.526 cubic feet of gas), it would take over 2754 of them to lift the 100 pounds.

Therefore a handful of small balloons will not lift you off the ground. It is possible however to lift a person as evidenced by the following story that appeared in the newspaper in 1997. A California man wanted to recline in a lawn chair about 30 feet above his back yard, buoyed up by weather balloons. When he wanted to return to the ground he planned to pop balloons one by one with a pellet gun.

The poor fellow attached 45 large weather balloons to a lawn chair and inflated them with helium. He climbed into the lawn chair and released the anchor rope. The buoyant force rocketed him into the blue and he came to equilibrium at about 11,000 feet! Too afraid to pop a balloon, he eventually strayed into the air approach corridor of Los Angeles International Airport where he was spotted by a passing jetliner. After being rescued by a helicopter, he was arrested for violating the air space of LA International! If only he had taken the time to apply physics to the situation, perhaps he could have avoided the ordeal.