Understanding Hot Air Balloon Physics

Rwanda has cultivated itself as a country of interesting surprises by keeping it as a destination of interest for media, researchers, first-time visitors and various fans.

From aligning with Arsenal football club, Paris Saint-Germain football club to introducing drones to facilitate the country’s healthcare sector and many more, this week Rwanda has introduced hot air balloons in Akagera National Park tourism offers.

“We are delighted to partner with Royal Balloon Rwanda to add another exciting product to adventure tourism experiences in Rwanda,” said Clare Akamanzi, CEO of Rwanda Development Board.

For most Rwandans and other visitors, hot air ballooning can raise many questions about how they can truly embrace it when visiting Akagera National Park.

Hot air balloon physics

Simply put, a hot air balloon is a lighter-than-air aircraft consisting of a bag, called an envelope, which contains heated air. The heated air inside the envelope makes it buoyant, as it has a lower density than the cooler air outside the envelope. Like all aircraft, hot air balloons cannot fly beyond the atmosphere.

The principle of hot air balloon physics is the Archimedes’ principle which states that the buoyancy force on a submerged object is equal to the weight of the fluid displaced by the object.

For a hot air balloon, the upward buoyant force acting on it is equal to the weight of the air displaced. The air density is 1.2 kg per cubic meter; so to lift a balloon you will have to move a large volume of air so that its weight exceeds the weight of the envelope, plus the weight of the passengers, and that the upward force is greater than the downward force of gravity.

Additionally, an object floating in water stays buoyant using the same principle as a hot air balloon.

As shown in the figure above, the center of buoyancy acts through the point VS, which is the center of gravity of the volume V of the object. This volume is equal to the displaced volume of the fluid. The upward buoyancy force FB is equal to the weight of the volume of fluid displaced V.

In order for the object to remain in an unconditionally stable orientation (i.e. it does not rotate), the center of mass of the object g must be directly under the point VS.

This means that if the object were to be rotated in any way, it will automatically return to the original position where the point g is directly below the point VS. This is what is meant by unconditional stability.

For a hot air balloon, the upward buoyant force acting on it is equal to the weight (or mass) of the cooler surrounding air displaced by the hot air balloon.

Since the air inside the envelope is heated, it is less dense than the surrounding air, which means that the buoyant force due to the cooler ambient air is greater than the weight of the heated air inside the envelope.

And for lift to be generated, this Archimedean thrust must be greater than the weight of the heated air, plus the weight of the envelope, plus the weight of the nacelle, plus the weight of the passengers and the equipment on board.

As a result, the hot air balloon will experience enough buoyancy force to take off completely from the ground.

As shown in the figure below, the weight of the hot air balloon is more concentrated near the bottom of the balloon (at the location of passengers and equipment), so the center of mass g balloon is always below the center of buoyancy VS.

Therefore, the balloon is always stable during flight (i.e. it will always stay upright).

Hot Air Balloon Physics – How It Works

If the balloon operator wishes to lower the balloon, he can either stop lighting the burner, which causes the hot air in the envelope to cool (decreasing the buoyancy force), or he opens a small vent at the top of the balloon envelope (via a line of control).

This releases some of the hot air, which decreases the buoyancy force, which also causes the balloon to sink.

To maintain a constant altitude, the balloon operator intermittently fires and turns off the burner once he reaches the approximate altitude he desires. This makes the ball go up and down (respectively).

This is the only way for him to maintain an approximately constant altitude, since maintaining a strictly constant altitude while maintaining zero net buoyancy (on the balloon) is virtually impossible.

If the balloon operator wishes to move the balloon laterally (in a horizontal direction), he must know in advance the direction of the wind, which varies with altitude. So he simply raises or lowers the hot air balloon to the altitude corresponding to the wind direction he wants, which is the direction he wants the hot air balloon to go.

The balloon remains inflated because the heated air inside the envelope creates a higher pressure than the surrounding air.

However, since the shroud has an opening at the bottom (above the burner location), the expanding hot air can escape, preventing a large pressure differential from developing.

This means that the pressure of the heated air inside the balloon ends up being only slightly higher than the pressure of the cooler surrounding air.

An efficient hot air balloon is one that minimizes the weight of hot air balloon components, such as the envelope, and onboard equipment (such as the burner and propane tanks).

This in turn minimizes the required temperature of the air inside the envelope necessary to generate sufficient buoyant force to generate lift. Minimizing the required air temperature means that you minimize the energy needed by the burner, thus reducing fuel consumption.

Hot Air Balloon Physics – Analysis

Let’s examine the physics of a hot air balloon using an example calculation.

The heated air inside the envelope is at approximately the same pressure as the outside air. With this in mind, we can calculate the density of air heated to a given temperature, using the ideal gas law, as follows:

P = ρRJ

Or:

P is the absolute pressure of the gas, in Pa

ρ is the density of the gas, in kg/m3

R is the gas constant, in Joules/kg.K

J is the absolute temperature of the gas, in Kelvins (K)

Now,

Normal atmospheric pressure is about 101,300 Pa

The gas constant for dry air is 287 Joules/kg.K

The air inside the envelope is usually heated to an average temperature of around 100 degrees Celsius, or 373 K

Substituting the above three values ​​into the ideal gas law equation and solving for ρ we have ρ = 0.946 kg/m3. It is the density of the heated air inside the envelope. Compare this to normal (ambient) air density which is about 1.2 kg/m3.

Then, for a medium-sized balloon with an envelope volume of 2800 m3 we wish to determine the net upward buoyancy force generated by the envelope.

Net buoyancy is defined here as the difference in density between ambient air and heated air, multiplied by the volume of the envelope. Thereby,

FB, clear = (1.2−0.946)×2800 = 711 kg (1565 lbs)

This is the net buoyant force pushing the heated air upwards inside the envelope. The hot air balloon components (such as the envelope, basket, burner, fuel tanks and passengers) can weigh a maximum of 711 kg so that the buoyancy force can completely lift the hot air balloon off the ground.

compiled by Taarifa

Royal Balloon launches Rwanda’s first hot air balloon