Approximation of Buoyancy Force of Hot Air Balloons

For this example problem we will calculate the buoyancy force of a hot air balloon made out of tissue paper and birthday candles. The dimensions of the balloon are approximately 40 cm×40 cm×60 cm, giving a total volume of 9600 cm^3 (or 0.096 m^3).

The density of air is given as 1.29 kg/m^3 at sea level and 0ºC (9). Density is calculated by the equation:

Dfuid = M/V                                                           (3)

The mass of the air displaced by the balloon can be calculated by multiplying the volume of the balloon by the density:

Dfuid × V = M

1.29 kg/m^3 × 0.096 m^3 = 0.12384 kg

The calculated value of M can be plugged into equation 2:

B = M g                                                              (2)

0.12384 kg × 9.8 m/s^2 = 1.21 N

The approximated buoyancy force for the hot air balloon is 1.21 N. The weight of the balloon its self is ~ 52g (0.052 kg). This is the weight of the tissue paper, balsa wood, and birthday candles used to construct a functional balloon. The force needed to lift it is only 0.51 N (the mass of the balloon times g, the acceleration of gravity). This means that the balloon has ~0.7 N more buoyancy force than is needed to lift it. This extra force could hypothetically be used to lift a payload, that payload, by these calculation could weigh no more than 70g (that's the same weight as approximately 12 U.S. quarters).

http://www.ushotairballoon.com/redtrans1.gif

Created by John Rowley 2005.