It seems almost magical: a basket carrying a dozen people, held aloft by nothing more than a bag of warm air. No wings, no engine, no moving parts. Just a flame, a fabric envelope, and the invisible hand of physics. So what exactly is going on? Why does heating air make something as heavy as a hot air balloon — which can weigh well over 300 kilograms even without passengers — rise gracefully into the sky?
The answer lies in a principle that Archimedes described more than two thousand years ago, refined by Charles's Law from the eighteenth century. Together, these ideas explain not just why balloons fly, but why they can be controlled with such precision. Let us break it down.
The Core Principle: Buoyancy
You already understand buoyancy intuitively, even if you have never thought about it in scientific terms. Drop a beach ball into a swimming pool and it pops straight back to the surface. Pour oil into water and it floats on top. A cork bobs on the waves. In every case, the lighter substance rises above the heavier one.
Archimedes' principle states this formally: an object immersed in a fluid experiences an upward force (buoyancy) equal to the weight of the fluid it displaces. If the object is lighter than the fluid it displaces, it rises. If it is heavier, it sinks.
Now here is the key insight for ballooning: air is a fluid. It behaves according to the same principles as water, just at much lower densities. A hot air balloon is essentially a very large, very light object immersed in the fluid of the atmosphere. If the air inside the balloon's envelope can be made lighter (less dense) than the air outside, the balloon experiences an upward buoyant force — and it rises.
Hot Air Is Less Dense Than Cool Air
At sea level on a typical day (around 20 degrees Celsius), air has a density of approximately 1.2 kilograms per cubic metre. That might not sound like much, but when you consider that a balloon envelope contains around 2,800 cubic metres of air, the total mass of air inside is substantial — roughly 3,360 kilograms at ambient temperature.
When the pilot fires the burner and heats the air inside the envelope, something important happens. The air molecules gain energy and move faster, spreading apart from one another. The same number of molecules now occupies a larger volume — or, put another way, fewer molecules remain in the same volume as some are pushed out through the open mouth at the bottom of the envelope.
At 100 degrees Celsius, air density drops to approximately 0.95 kilograms per cubic metre. That is a reduction of about 21 per cent compared to the ambient air outside.
This density difference is the entire basis of balloon flight. The air inside the envelope is lighter than the air outside, so the balloon experiences a net upward force — just like a beach ball pushed underwater experiences a net upward force from the denser water around it.
Charles's Law: The Mathematics of Expansion
The relationship between temperature and gas volume was formalised by French physicist Jacques Charles in the 1780s — coincidentally, around the same time that the Montgolfier brothers were conducting the first balloon flights. Charles's Law states:
At constant pressure, the volume of a gas is directly proportional to its absolute temperature.
In mathematical terms: V/T = constant (where T is measured in Kelvin).
What this means in practice is straightforward. If you heat a gas from 293 K (20 degrees Celsius) to 373 K (100 degrees Celsius), its volume increases by a factor of 373/293 = 1.27. The gas expands by 27 per cent.
In a balloon envelope, this expansion pushes air out through the open bottom. The envelope does not get bigger — it is already fully inflated. Instead, the heated air that remains inside is simply less dense, because some of it has been displaced. Fewer kilograms of air now occupy the same 2,800 cubic metres of space.
It is worth noting that Jacques Charles was himself a balloon pioneer. He launched the first hydrogen gas balloon in 1783, just months after the Montgolfiers' hot air flights. The history of ballooning is deeply intertwined with the history of physics itself.
Calculating the Lift
Let us work through the numbers for a typical commercial balloon to see how much lifting force is generated.
The Envelope
A standard commercial balloon has an envelope volume of approximately 2,800 cubic metres (about 100,000 cubic feet). This is the volume of air that the balloon displaces in the atmosphere.
Density Difference
- Ambient air density (at 20°C): approximately 1.20 kg/m³
- Heated air density (at 100°C): approximately 0.95 kg/m³
- Density difference: 0.25 kg/m³
Gross Lift
The gross lift is the density difference multiplied by the envelope volume:
0.25 kg/m³ × 2,800 m³ = 700 kg
This means the buoyant force on the balloon is equivalent to supporting a mass of roughly 700 kilograms. That is the total upward force available before we account for the weight of the balloon system itself.
Net Lift (What Can Actually Fly)
Now we subtract the weight of everything that is not payload:
- Envelope fabric: approximately 120-150 kg
- Basket: approximately 70-80 kg
- Burner system: approximately 35-45 kg
- Fuel (propane tanks): approximately 80-100 kg (full)
- Rigging, instruments, lines: approximately 15-25 kg
Total balloon system weight: approximately 300-400 kg
Net lift available for passengers and pilot: 300-400 kg
This is why a typical commercial balloon can carry a pilot plus 8 to 16 passengers, depending on the specific balloon size and the weight of the individuals. Larger balloons with envelopes of 4,000 to 6,000 cubic metres can carry proportionally more.
If you are curious about the full mechanical system — burners, fuel tanks, envelope construction — our guide on how hot air balloons work goes into comprehensive detail.
Why the Balloon Stops Rising
If hot air rises, why does the balloon not simply keep going up until it leaves the atmosphere? This is a question that reveals an elegant piece of atmospheric physics.
As the balloon ascends, the surrounding air becomes less dense. Remember, the atmosphere is not uniform — it gets thinner with altitude. At sea level, air density is 1.2 kg/m³. At 1,000 metres, it drops to about 1.1 kg/m³. At 3,000 metres, it is around 0.9 kg/m³.
The balloon's lift depends on the difference in density between the air inside the envelope and the air outside. As the balloon climbs into thinner air, this difference shrinks. The buoyant force decreases. At some point, the upward force exactly equals the downward force of gravity on the balloon system, and the balloon reaches equilibrium — it stops rising and floats at a constant altitude.
If the pilot wants to go higher, they fire the burner again, heating the air further and restoring the density differential. If they want to descend, they open the parachute valve at the top of the envelope to release some hot air, allowing cooler ambient air to enter and increasing the density inside. This is how pilots control altitude with remarkable precision.
This self-regulating behaviour is one of the things that makes hot air balloons inherently stable. A balloon at equilibrium will tend to stay at that altitude unless the pilot actively changes something. There is no stalling, no loss of lift, no sudden drops. The physics of buoyancy act as a constant, gentle support.
Simple Analogies That Make It Click
If the density calculations feel abstract, here are some everyday analogies that capture the same principle.
The Beach Ball in a Pool
Push a beach ball underwater and release it. It rockets to the surface because it is far less dense than the water around it. A hot air balloon is a beach ball in a pool of air — less dense than its surroundings, so it rises.
Oil and Water
Pour cooking oil into a glass of water. The oil rises to the top and floats because it is less dense. Hot air inside a balloon envelope is like the oil — it floats upward through the denser cool air.
A Bubble Rising in a Pint
Watch a bubble rise through a glass of beer. The bubble is a pocket of gas (carbon dioxide) that is less dense than the liquid around it. A hot air balloon is essentially a very large, controlled bubble rising through the atmosphere.
A Lava Lamp
The coloured blobs in a lava lamp heat up at the bottom, expand, become less dense, and rise. At the top they cool, become denser, and sink back down. A hot air balloon operates on exactly this principle — the pilot just has the ability to control the heating and cooling cycle.
The Role of Temperature Control
One of the most remarkable aspects of balloon flight is how precisely the pilot can control altitude simply by adjusting the air temperature inside the envelope.
A short burst from the burner — perhaps two to three seconds — adds enough heat to lift the balloon by 15 to 30 metres. A longer burn of five to ten seconds might produce a climb of 50 to 100 metres. The response is not instantaneous; there is a lag of 15 to 30 seconds as the heat distributes through the air mass inside the envelope. Experienced pilots learn to anticipate this delay and fire the burner before they need the lift, rather than reacting to altitude changes after they happen.
To descend, the pilot opens the parachute valve — a panel of fabric at the very top of the envelope that can be pulled open by a cord. Hot air escapes, cooler air enters from below, the average temperature inside drops, density increases, lift decreases, and the balloon descends. Close the valve and fire the burner, and the descent stops.
This delicate dance between burner and valve is what allows a skilled pilot to hold the balloon at a specific altitude, skim just metres above treetops, or climb smoothly to several hundred metres — all using nothing more than the principle of buoyancy. For more on the safety aspects of these manoeuvres, see our balloon safety guide.
Why Hot Air and Not Another Gas?
You might wonder why balloons use heated air rather than a lighter gas like helium or hydrogen. The answer involves practicality, cost, and safety.
Helium is lighter than air even at ambient temperature, so a helium balloon does not need a burner — it naturally floats. But helium is expensive, non-renewable, and once released it cannot be recovered. A single flight would cost thousands of pounds in helium alone. Our article on whether hot air balloons use helium explores this comparison in full.
Hydrogen is even lighter than helium and was used in early balloon flights, but it is highly flammable — a characteristic that led to several disasters in ballooning history and ultimately to the Hindenburg tragedy in airship aviation.
Heated air, by contrast, is free, endlessly renewable, and controllable. The pilot can increase lift by adding heat and decrease it by releasing heat. This controllability is what makes hot air balloons so practical for commercial passenger flights. The only cost is the propane fuel, which is inexpensive and widely available.
How This Science Becomes an Experience
Understanding why a balloon rises is intellectually satisfying, but nothing prepares you for how it feels. The mathematics of buoyancy and Charles's Law translate into an experience of extraordinary gentleness. There is no lurch, no acceleration, no vibration. The ground simply falls away beneath you as though the earth is sinking and you are staying still.
Many passengers describe the sensation as dreamlike. The silence after the burner shuts off, the slow rotation of the landscape below, the vast expanse of sky in every direction — these are the experiential consequences of floating on a cushion of warm air, held aloft by nothing more than a temperature difference of eighty degrees.
If you have any concerns about how the experience feels — particularly if you are nervous about heights — our guide on overcoming the fear of heights on a balloon ride may be helpful.
Ready to Experience Buoyancy for Yourself?
Every sunrise over the Palmerie, the science of Archimedes and Charles transforms into one of the most beautiful experiences Morocco has to offer. A hot air balloon ride over Marrakech lets you float peacefully above the palm groves and farmland, the Atlas Mountains glowing in the morning light, while 2,800 cubic metres of warm air hold you gently in the sky.
Check our price guide to find the right flight for you, or read our first-time flyer tips to know exactly what to expect. The science is fascinating — but the experience is unforgettable.