How many regular sized helium filled balloons would lift someone? What is the equation to figure it out?

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Question

How many regular sized helium filled balloons would lift someone? What is the equation to figure it out?

Answer

Here's how you could figure it out...

If you have read the HSW article entitled How Helium Balloons Work then you know that helium has a lifting force of one gram per liter. So if you have a balloon that contains 5 liters of helium, the balloon can lift 5 grams.

A normal balloon at an amusement park might be 30 centimeters (about 1 foot) in diameter. To determine how many liters of helium a sphere can hold, the equation is 4/3*pi*r*r*r. The radius of a 30 centimeter diameter balloon is 15 centimeters, so:

4/3*pi*15*15*15 = 14,137 cubic centimeters = 14 liters So a normal amusement park balloon can lift about 14 grams assuming that the weight of the balloon itself and the string is negligible.

If you weigh 50 kilograms (about 110 pounds), then you weigh 50,000 grams. 50,000 grams / 14 grams per balloon = 3571.42 balloons to match your weight. So you might want to add 500 more if you actually would like to rise at a reasonable rate. So you need roughly 4,000 balloons to lift yourself if you weigh 50 kilograms, and you can adjust that number according to your weight.

Let's say that instead you go to an army surplus store and you buy one 3 meter (about 10 feet) balloon. It can hold:

4/3*pi*150*150*150 = 14,137,000 cubic centimeters = 14,137 liters It would only take 4 of those to give you the same lift. If you bought one balloon 30 meters (about 100 feet) in diameter, it displaces 14,137,000 liters. So it can lift 14,000 kilograms, or about 31,000 pounds. This is roughly the size of a large blimp, and that is why blimps have to be so big.

See How Helium Balloons Work for more details on helium and hot air balloons.

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