If you have watched the Pixar movie “Up” (2009), then you have probably wondered how many balloons it takes to lift a person. In order to figure this out, we first need to know that helium has a lifting force of 1 gram per liter (also known as 9.8 Newtons of lift). So if you have a balloon that contains 5 liters of helium, the balloon can lift 5 grams.
(1) Balloon lifting force
Assume a normal balloon at an amusement park might be 30 centimeters (about 1 foot) in diameter.
(2a) Balloon size
(2b) Balloon size
To determine how many liters of helium a sphere can hold, the equation is
(3) . The radius of a 30-centimeter-diameter balloon is 15 centimeters, so:
(4) cubic centimeters = 14.1 liters
(5) From (1) and (4), we can assume that one normal balloon can lift can lift 14 grams (0.014 kg), assuming the mass of the balloon and the string are negligible.
For simplicity sake, assume that in the movie “Up” the mass of Mr. Carl Fredricksen is 50 kilograms (about 110 pounds).
(6) Mass of subject = 50,000 grams
Next we divide the 50,000 grams by the 14 grams per balloon and find it takes 3,571.42 balloons to lift your 50 kg.
(7) Number of balloons per 50 kg person = 3,571
Aerospace Cubicle Engineer recommends a safety margin of 10%, plus extra balloons to allow a reasonable climb rate. The recommended number of balloons for a 50 kg subject would be 4,000.
Part b of the question would be, “How many balloons would it take to lift a house?” The rule of thumb in construction is that there are 200 pounds per square foot for a single-level home, 275 for two levels and 350 for three levels. Let us assume Mr. Fredricksen’s home was a two-story, 2,000-square foot home.
Therefore, we just need to use (4) and (8) to determine the number of balloons to lift Mr. Fredericksen’s home.