Hot Air Balloons
The basic principle behind hot air balloon physics is the use of hot air to create buoyancy, which generates lift. A hot air balloon consists of a large bag, called an envelope, with a gondola or wicker basket suspended underneath. A burner (with power typically of several megawatts) sits in the basket and is used to heat the air inside the envelope through an opening. This heated air generates lift by way of a buoyant force.
The hot air inside the envelope is less dense than the surrounding (cooler) air. This difference in density causes the hot air balloon to be lifted off the ground due to the buoyant force created by the surrounding air. The principle behind this lift is called Archimedes' principle, which states that any object suspended in a fluid, is acted upon by an upward buoyant force equal to the weight of the fluid displaced by the object. So an object floating in water stays buoyant using the same principle as a hot air balloon. The figure below illustrates Archimedes' principle for an object completely submerged in a fluid (such as water, or air).
As shown above, the center of buoyancy acts through point C, which is the centroid of the volume V of the object. This volume is equal to the displaced volume of the fluid. The upward buoyant force FB is equal to the weight of the displaced volume of fluid V.
For a hot air balloon, the upward buoyant force acting on it is equal to the weight 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 surrounding air is greater than the weight of the heated air inside the envelope. And for lift to be generated, this buoyant force must exceed the weight of the heated air, plus the weight of the envelope, plus the weight of the gondola, plus the weight of passengers and equipment on board. As a result, the hot air balloon will experience sufficient buoyant force to completely lift off the ground.
As shown above, 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 of the hot air balloon is always below the center of buoyancy C. Therefore, the balloon is always stable during flight.
Physics of Balloon: Operation
To maintain a steady altitude, the balloon operator intermittently fires and turns off the burner once he reaches the approximate altitude he wants. This causes the balloon to ascend and descend (respectively). This is the only way he can maintain an approximately constant altitude, since maintaining a strictly constant altitude by way of maintaining a net zero buoyant force (on the balloon) is practically impossible.
The balloon stays inflated because the heated air inside the envelope creates a pressure greater than the surrounding air. However, since the envelope has an opening at the bottom (above the location of the burner), the expanding hot air is allowed to 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 greater than the cooler surrounding air pressure.
An efficient hot air balloon is one that minimizes the weight of the balloon components, such as the envelope, and on board equipment (such as the burner and propane fuel tanks). This in turn minimizes the required temperature of the air inside the envelope needed to generate sufficient buoyant force to generate lift. Minimizing the required air temperature means that you minimize the burner energy needed, thereby reducing fuel use.
Physics of Balloon: Analysis
The heated air inside the envelope is at roughly the same pressure as the outside air. With this in mind we can calculate the density of the heated air at a given temperature, using the Ideal gas law, as follows:
P = ρRT
Where:
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
T is the absolute temperature of the gas, in Kelvins (K)
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