To fly a hot air balloon takes a lot of teamwork, air, and heat, to get off the ground.  A team of individuals are needed to lay the enormous balloon made of reinforced nylon, a light but strong material, flat on the ground.  The balloon is also referred to as an “envelope.”   They then use a small gas fan to fill up this envelope.  The balloon may look full with this air, but it is still lying on the ground.  In order to make it stand tall, and eventually fly, a propane burner is ignited to heat up the air already inside the balloon.
 You may have noticed that hot air rises already if you have been in a really warm place, like a sauna, then went to a really cold place, like the snow.  If you did this, you would notice steam coming off your body and going up into the air.  

Another way you may have noticed warm air rises is on a hot day if you live, or have been in a house with two levels.  In a house like this, without air conditioning, you may notice as you walk from the bottom level to the top, it feels hotter, and if you walk from the top floor to the bottom floor, then it gets cooler. 

The reason why the hot air balloon rises is because hot air rises.  The inside air that has been heated rises due to the difference of density between the hot and cold air particles.  The heated air, the air that is inside the balloon, is less dense than the cool air, the air outside of the balloon.  And objects that are less dense rise.  

Volume = How much space something takes up  
Mass = How much there is of something 
Density = Mass / Volume 


The reason we know that the hot air is less dense than cool air is due to the Ideal Gas Law.  The Ideal Gas Law states that the Pressure times the Volume is equal to the number of molecules times the gas constant ( R ) times the Temperature.  Sometimes if you think of it in this equation it is a little easier to understand.
PV = nRT
To figure out why hot air is denser, we are going to examine 2 variables, or letters, in this equation; the Volume and the Temperature.  As we increase the Temperature with the propane burner, the Volume will also increase.

Since we know that the Volume is getting bigger, we can use this knowledge and see how it will affect the density, and since we know the equation for density is

Density = Mass / Volume

You can see that the bigger the volume gets, the smaller the density is.

For example.    If you heat the air, your temperature increases, then your volume will increase.  Let’s say the volume will increase from 600 to 1000.   The mass is 10.  Therefor when we plug these numbers into the equation to find density we get

Original air density =  10 / 600  which = 1/6

Heated air’s density  = 10 / 1000 which = 1/ 10

And we know that one-tenth is less than one-sixth   1/10 < 1/6
Therefor the air that is heated is less dense, and an object that is less dense will rise

In addition to all this fun information about density,
you also need to consider the force of the air pushing
on the hot air balloon that gives it a lift.
This force is called the Boyant Force.
You can also think of the Boyant Force
as the pressure water has to hold a boat up,
like the water helps the boat float, the air helps the hot air balloon float.


This is why when the balloon will fly.

Are you interested in hands on activities concerning hot air balloons?
For more fun facts about hot air balloons.
See a diagram of the parts of a balloon
This page was created November 1999 by Amanda Renchin
I am an elementary education major, mathematics minor at Concordia College in Moorhead, MN
If you have an questions or comments send an e-mail my way at