How do you figure out the weight lifting ability of a hot air balloon? — BK, Meraux, LA
The air surrounding an object pushes upward on it with a force equal to the weight of the air the object displaces. The observation is called Archimedes’ principle. If the object weighs less than the air it displaces, the object will experience a net upward force and will float upward. Since hot air is less dense and weighs less than cold air, a balloon filled with hot air can weigh less than the air it displaces. To determine the net upward force on the balloon, you subtract the total weight of the balloon (including the air inside it) from the weight of the air it displaces.
At room temperature, air weighs about 12.2 newtons per cubic meter (0.078 pounds per cubic foot). But air’s density and weight are proportional to its temperature on an absolute temperature scale (in which absolute zero is the zero of temperature). At 200° F, air weighs about 20% less than at room temperature, or about 9.7 newtons per cubic meter (0.062 pounds per cubic foot). Thus each cubic meter of 200° F air inside the balloon makes the balloon 2.5 newtons lighter than the air it displaces (or each cubic foot of that hot air makes it 0.016 pounds lighter). If the balloon’s envelope, basket, and occupants weigh 4000 newtons (900 pounds), then the balloon will have to contain about 1600 cubic meters (56,000 cubic feet) of hot air in order to float upward.