How a hot air balloon actually rises
Hot air is thinner than cold air, and that is the entire mechanism. The interesting part is how little difference it takes, and how much fabric you need to make it useful.
A hot air balloon floats for the same reason a cork floats: it displaces more weight of the surrounding fluid than it weighs itself. The fluid here happens to be air, and the trick for making the balloon lighter than the air it displaces is simply to heat the air inside it.
The numbers are smaller than you think
Air at 20 °C weighs about 1.2 kg per cubic metre. Heat it to 100 °C and it weighs about 0.95 kg per cubic metre, because the same pressure now has to be held up by faster-moving molecules and there are fewer of them in the same space.
The difference is roughly a quarter of a kilogram per cubic metre. That is all the lift a hot air balloon ever gets.
A quarter of a kilo per cubic metre is not much, which is why balloons are enormous. A common sport balloon holds around 2,800 m³ — a sphere about 17 m across — and produces something like 700 kg of gross lift. Take away the envelope, the basket, the burner and a load of propane, and what is left is two or three people.
Because the fabric will not have it. Nylon envelopes are run at up to about 120 °C, and the material's limit is not far above that. Going from 100 °C to 120 °C buys only a few more kilograms of lift per hundred cubic metres, so balloons are built large rather than hot.
What changes in the air changes the balloon
Because lift depends on the difference between inside and outside, the same balloon behaves differently in different air.
- Cold days lift better. Colder outside air is denser, so the same inside temperature gives a bigger difference. Winter mornings are strong; hot summer afternoons are weak.
- Altitude weakens it. Higher up the air is thinner, so a quarter of a kilogram per cubic metre becomes a fifth, then a sixth. Every balloon has a ceiling where the burner cannot make up the difference.
- Weight matters enormously. Fuel is heavy, and a balloon gets lighter and livelier through a flight as it burns it.
Why it is never steady
The envelope is a big, slow thermal mass full of air that is constantly losing heat through the fabric and out of the open mouth at the bottom. Left alone, a balloon cools, sinks, and keeps sinking.
So a pilot is always doing one of two things: adding heat, or waiting to see what the last burn did. And what the last burn did arrives late — several seconds to warm the air, more for the whole envelope to respond, more still for several tonnes of balloon to change its vertical speed.
That lag is why ballooning feels like it does. You are not steering a vehicle so much as making suggestions to one, ten or twenty seconds before you need them to take effect.