We’ve all seen movies or TV shows where a street vendor hands a child a huge bunch of balloons and up, up, up they go. Well, we were at a birthday party the other day, and they had a helium tank. So we started to wonder… how many balloons would it take to actually do that?
If anyone has any idea, I’d love to hear it. It’d also be fun to know how many you’d need for an adult as well as a child.
How many regular-sized helium-filled balloons would it take to lift someone? What is the equation to figure it out?
Here’s how you could figure it out…
If you have read the article How Helium Balloons Work, then you know that helium has a lifting force of 1 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 4/3pirrr. 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. Divide your 50,000 grams by the 14 grams per balloon and you find that you need 3,571.42 balloons to lift your weight. 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 of going to the amusement park, you go to an army surplus store and buy one 3-meter (about 10-foot) balloon. It can hold:
4/3 * pi * 150 * 150 * 150 = 14,137,000 cubic centimeters = 14,137 liters
It would only take four of those to give you the same lift.
One balloon that is 30 meters (about 100 feet) in diameter displaces 14,137,000 liters, so it can lift 14,000 kilograms (about 31,000 pounds) – this is roughly the size of a large blimp.