Atmospheric Flight

Buoyancy

The pressure in the atmosphere slowly decreases as one rises in altitude. If the pressure on top of a ball could be carefully measured, one would find that the air pressure is slightly less there than at the bottom of the ball. The greater pressure acting on the bottom of the ball results in a small lift force pushing up on the ball.

The amount of lift force depends on the pressure difference between the top and the bottom, and also on the amount of surface area that the pressure acts on. It turns out that a certain object has the same buoyant force no matter what orientation it has in the atmosphere. As an example, imagine a long, slender object like a hot dog. If the hot dog is held horizontally, then there is not very much difference in altitude from the bottom to the top side of the hot dog. But, there is a lot of area along the whole length of the hot dog on which the pressure acts.

Horizontal hot dog has small pressure difference but large area.

If the hot dog is stood up vertically, then the difference in height between the top end and the bottom end is greater, but the amount of area at the end is less. The effect of increasing the pressure difference and decreasing the area cancel out, and the buoyancy is the same if the hot dog were horizontal.

Vertical hotdog has big pressure difference but small aera.

Realizing that the buoyancy comes from both the height and the surface area of the ends, one might guess correctly that the buoyancy depends on the volume of the object. (An advanced mathematical explanation.)

Buoyancy also depends on the density of the fluid. Fluid can be defined as a liquid or gas. Water has enough density that the buoyancy on a hot dog in water is enough to make it float. Of course, in the atmosphere, the air density is much less - about 0.001 times the density of water, so a hot dog would not be buoyant enough to float in the atmosphere.

The Greek mathematician and engineer, Archimedes, described the amount of buoyancy force on an object as equal to the weight of the fluid that it displaces.

The weight of the fluid displaced is this displaced volume times the fluid density.

Since the buoyancy force on an object in the atmosphere is so small, an object must be very large and very light to get enough buoyant lift to be useful.

Hot air balloons use the buoyancy force for lift. In order for a hot air balloon

to carry two people of average weight it would need to be almost 55 feet in diameter. This balloon would then displace about 6,200 pounds of air, but the hot air inside the balloon would weigh about 5,200 pounds, thus making the useful lift only 1,000 pounds. If the balloon envelope, basket, fuel tanks, and burner weigh about 600 pounds, that would leave about 400 pounds of lift to pick up two people.

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Compare Balloons on Earth and Mars

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