# How do hot air balloons work?

One of the most surprising things about air that may not be intuitive is that it is a fluid and like any other fluids exerts a pressure on objects.

Standing on earth with layers of air above us, we are constantly being ‘weighed down’ by a pressure of ~1atm at all times.

All objects in air are also assisted by a buoyant force that is caused from the pressure difference between the top and bottom surfaces.

Let’s now consider the hot-air balloon in particular. A force diagram is probably the best way to start:

Therefore we see that in order for the hot air balloon to float, we need to have the buoyant force compensate for the net weight from the balloon, the load on it and the air inside it:

$F_B > w_{envelope} + w_{load} + w_{hot-air}$

Say you built a modest hot-air balloon that just barely managed to get off the ground. How would you make it go higher ?

You don’t want to play around with $w_{load}$ because you don’t want to throw out any of your passengers or your supplies. You can’t really play around with $w_{envelope}$ without re-making the balloon again.

BUT you can reduce the weight of the hot air inside the balloon ( $w_{hot-air} = m_{hot-air} g = (\rho_{hot-air} V_{hot-air}) g$) ! How ?

Recall the ideal gas law $P = \rho R T$. Assuming that the pressure and the volume of the hot-air balloon does not change we note that:

$\rho_{hot-air} \propto 1/T_{hot-air}$

meaning that if we want to reduce the density of air, we just need to crank up the temperature.

And with a spectacular burner onboard our hot air balloon, we can easily increase the temperature of the air inside the balloon!

That’s pretty much how hot-air balloons work! You increase the temperature of the air inside the balloon to go up, decrease the temperature to go down and skillfully adjust the temperature to hover.

Questions to ponder:

• When you increase the temperature of air, its density decreases. What do you think happens to all the molecules that were previously inside ? Do they exit the balloon ?
• Different shaped hot-air balloons is a common sight. Do you think that the Buoyant force changes for each shape? (Review the formula for Buoyant force discussed in the previous post)
• How do you think Helium balloons work ?

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