The standard atmospheric model is an idealized representation of the Earth's atmosphere. It divides the atmosphere into five distinct layers based on temperature: troposphere, stratosphere, mesosphere, thermosphere, and exosphere.
1. Temperature at 38,969 meters altitude:
The altitude of 38,969 meters falls within the second layer of the atmosphere called the stratosphere, which begins at around 18,000 meters and ends at about 50,000 meters (18 to 50 km). In this layer, the temperature generally increases with altitude.
According to the U.S. Standard Atmosphere 1976 model, the temperature in the stratosphere can be calculated using the following formula:
T = T₀ + a(H - H₀)
where
T is the temperature at the given altitude (in Kelvin),
T₀ is the reference temperature at the beginning of the layer, H₀ is the reference altitude at the beginning of the layer, H is the given altitude, and a is the temperature lapse rate.
For the stratosphere (H₀ = 20000 m, T₀ = 216.65 K, a = 0.001 K/m):
T = 216.65 + 0.001*(38969-20000) = 216.65 + 0.001*18969 = 216.65 + 18.969 = 235.619 K
So the temperature at 38,969 meters altitude is approximately 235.619 K.
2. Air pressure at 38,969 meters altitude:
To calculate the air pressure at 38,969 meters altitude, we can use the following equation from the U.S. Standard Atmosphere 1976 model:
P = P₀ * (1 + a*(H-H₀)/T₀)^(-g*M/(R*a))
where
P is the air pressure at the given altitude (in Pascal),
P₀ is the reference air pressure at the beginning of the layer, g is the acceleration due to gravity (9.80665 m/s²), M is the molar mass of the air (0.028964 kg/mol), R is the ideal gas constant (8.31432 J/mol*K), and other terms are as defined before.
For the stratosphere (P₀ = 5.4749 x 10⁴ Pa):
P = 5.4749 x 10⁴ * (1 + 0.001*(38969-20000)/216.65)^(-9.80665*0.028964/(8.31432*0.001)) ≈ 3022.57 Pa
So the air pressure at 38,969 meters altitude is approximately 3022.57 Pa.
3. Air density at 38,969 meters altitude:
To calculate the air density at 38,969 meters altitude, we can use the equation:
ρ = P*M/(R*T)
where
ρ is the air density at the given altitude (in kg/m³) and other terms are as defined before.
For the stratosphere:
ρ = 3022.57*0.028964/(8.31432*235.619) ≈ 0.03526 kg/m³
So the air density at 38,969 meters altitude is approximately 0.03526 kg/m³.
As encouraged to do by Prof. kstra, the following exercises investigate what the atmospheric properties were like at the altitude Mr. Baumgartner went to (38,969 m).
Whilst practising, the following picture of the standard temperature profile may be of help.
What is, according to the standard atmosphere, the temperature (in Kelvin) at 38,969 metres altitude?
What is, according to the standard atmosphere, the air pressure (in Pascal) at 38,969 metres altitude?
What is, according to the standard atmosphere, the air density (in kilograms per cubic metre) at 38,969 metres altitude?
1 answer