What if you could stand where airliners fly?

Look up! Sometimes you can see a tiny airplane, far up in the sky.

What if you could stand up there? Would it be warm or cold? Is there air to breathe?

A NASA page says airliners fly above about 30,000 feet, close to 10 kilometers up. What is the air like out there, outside their windows?

You might think that higher up, closer to the Sun, it should be warmer. In this lab you can climb from the ground to airliner height in a model of the atmosphere and read off the temperature, the air pressure and how much air you would get in each breath.

UCAR describes the troposphere as the lowest layer of the atmosphere, extending to about 10 km, where air pressure drops and temperatures get colder as you climb. Commercial passenger jets fly near its top or in the lower stratosphere.

This lab uses the International Standard Atmosphere, an averaged model, to quantify those changes. What are the temperature, pressure and density at 11 km, and where does the cooling stop?

On the ground, the air is thick. There is lots of air to breathe.

In the model, it is a mild 15 degrees at the seaside.

Start at sea level. The model's standard air is 15 °C, with a pressure of 101.3 kilopascals: that is the weight of all the air above pressing down on every surface. Water boils at 100 °C here.

This standard atmosphere is an average. NASA explains that scientists built it from many measurements of the atmosphere, averaged and fitted with equations, so that engineers have a typical day to design aircraft for.

At sea level the ISA sets T₀ = 288.15 K (15 °C), p₀ = 101.325 kPa and ρ₀ = 1.225 kg/m³. NASA Glenn's version of the model gives T = 15.04 − 0.00649 h (°C, h in meters) through the troposphere, with pressure following a power law of temperature.

NASA notes that such models are developed from averaged atmospheric measurements, with separate standard, hot, cold and tropical days. The lab treats every day as that average day; real air changes with the weather.

Now Olly floats up, up, up to where airplanes fly.

Brr! It is very, very cold. And the air is very thin. Each breath would hold much less air.

Now slide the height to 11 kilometers, about where many airliners cruise. The model's air is now about −56 °C. The pressure has fallen to 22.6 kilopascals, less than a quarter of sea level.

Each breath would hold only about 30 percent as much air as on the ground, and water would boil at about 62 °C. Try other heights: in the model the air pressure halves by about 5.5 kilometers, and at Mount Everest's height, 8.8 kilometers up, the air is about −42 °C.

At 11 km the model gives T = 288.15 − 6.5 × 11 = 216.65 K (−56.5 °C), p = 22.6 kPa (22.3 percent of sea level), ρ = 0.364 kg/m³ (30 percent of ρ₀), a boiling point of 61.7 °C, and a stretchy balloon 3.4 times its launch volume.

Pressure halves near 5.5 km (50.5 kPa). Above 11 km the model's temperature stays at −56.5 °C while pressure keeps falling exponentially, to 5.5 kPa at 20 km.

Air is pulled down by gravity. So most air stays near the ground.

High up, there is less air. And it is colder, far from the warm ground.

Air has weight. Gravity pulls it down, so the air near the ground is squeezed by all the air above it. Climb higher and there is less air above you pressing down, so the pressure drops and the air spreads thinner.

The Sun mostly warms the ground, and the ground warms the air near it. NASA's energy budget explains that the atmosphere is generally warmer near the surface and colder higher up. In the standard atmosphere, the air cools by about 6.5 °C for every kilometer you climb, until about 11 kilometers.

Pressure at any height is the weight of the air column above. With hydrostatic balance and the ideal gas law, a linear temperature profile gives p = p₀(T/T₀)^(g₀/RL), with exponent 5.256; above 11 km, at constant temperature, pressure decays exponentially.

NASA's energy budget notes that most solar heating happens at the surface and that the atmosphere is generally warmer near the ground and colder aloft. The model's limits: dry air, mid-latitude averages, no weather, and a ceiling of 20 km; UCAR notes that in the stratosphere the air warms with height, because ozone absorbs ultraviolet light; the model keeps a constant temperature from 11 to 20 km.

Airplanes fly high because thin air lets them go fast.

Their cabins are pressurized. Outside, it is freezing!

A NASA page explains that speed is the main reason airliners fly above about 30,000 feet, close to 10 kilometers. The air is much thinner up there, so a plane can go faster for the same push. NASA adds that the main reason airliners have pressurized cabins is to let them fly that high.

UCAR says commercial passenger jets fly in the lower stratosphere, partly because it has fewer bumpy updrafts and gives a smoother ride. Most clouds, and 99 percent of the air's water vapor, are in the layer below.

A NASA Goddard educational page (Stargaze) attributes cruise altitudes above 30,000 ft (about 10 km) mainly to speed: thinner air allows higher speed for the same lift and drag, and pressurized cabins exist chiefly to allow this. UCAR places commercial jets in the lower stratosphere, where temperature rises with height and the air lacks the turbulence and updrafts of the troposphere; it puts the jet stream near the boundary between the two layers.

UCAR puts 99 percent of atmospheric water vapor in the troposphere, which is why most clouds are below cruising aircraft. UCAR gives about 10 km for the top of the troposphere; the ISA uses a standard 11 km.