Air Density

The density of the atmosphere decreases with increasing altitude. As illustrated below, the density at an altitude of 24 km (15 mi, 79,000 ft) is only about 3% of its value at sea level!

Changes in atmospheric properties with altitude
Changes in atmospheric properties with altitude

This property of the atmosphere has three primary effects on an aircraft. Two are aerodynamic effects while the other relates to propulsion. The aerodynamic effects can be understood by reading a previous question regarding the lift equation. In that discussion, we introduced the following equation:

What this relationship tells us is that the lift (L) is directly proportional to the air density (ρ). Thus, the lift force decreases as the density decreases assuming all the other variables remain constant. A similar equation can be used to compute the drag on an airplane:

Again, the drag force (D) decreases as the air density decreases. However, less drag means that we can fly faster, assuming the aircraft engine delivers the same amount of thrust.

Indeed, we must fly faster in order to generate enough lift. The lift produced must equal the weight (W) of the aircraft in order to maintain level flight. Otherwise, the aircraft will descend to a lower altitude where conditions are such that L=W. Remember that in the above equation for lift, the lift force is also proportional to the square of the velocity (V). So to generate the same amount of lift as density decreases, either the velocity or the lift coefficient (CL) must increase (note that the wing area (Sref) is typically fixed). The lift coefficient is primarily a function of angle of attack, and we don't want to change the angle of attack too much because this also increases drag. Thus, increasing speed is the simple solution to maintaining the required lift.

This line of reasoning brings us to an interesting question. If drag keeps decreasing as density decreases and the aircraft can fly faster and faster, then why don't planes fly at even higher and higher altitudes until the density, and the drag, become zero? This issue leads us to the effect of density on propulsion. As you can read about in a previous question on jet engines, engines operate by compressing incoming air, mixing the compressed air with fuel, burning the mixture, and exhausting it to generate thrust. This process becomes more difficult as the air density decreases because the compression is less efficient. The air density eventually decreases so much that there is not sufficient compression to support combustion. When this occurs, the engine will "flame out" and the plane falls into a dive until density increases enough for the engine to be restarted.

Piston engines suffer from similar effects at high altitude for two reasons. First, the piston engine is also an internal combustion engine like the jet. If the air is too diffuse and cannot be adequately compressed for efficient combustion, the engine cannot generate sufficient power to turn the propeller at a high enough rate to generate the needed thrust. Second, the propeller itself generates thrust by accelerating air through the propeller disk. As density decreases, a smaller mass of air is accelerated reducing the thrust the propeller can produce.

In summation, the decrease in air density that occurs as an airplane climbs to higher altitudes has three effects: 1) reduces lift, 2) reduces drag, and 3) reduces thrust. The propulsion effect is the most significant, and it is in fact engine performance that limits the maximum altitude that an aircraft can reach. For practical purposes, we refer to an airplane's maximum altitude as the service ceiling, a value provided for many planes at The Aircraft Museum.
- answer by Jeff Scott, 30 September 2001

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