How to Calculate Altitude & Density

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Atmospheric pressure may be defined as the force the atmosphere exerts against the surface of a given area. It can be used to calculate the density of the air and can also determine altitude and other physical conditions. These calculations will use standard values, but atmospheric pressure can vary because of local conditions. These changes are important when studying the weather and climate.

Skill level:
Moderate

Things you need

• Calculator with scientific functions

Instructions

1. 1

Identify the physical constants of the Earth that we need for a calculation of altitude: The universal gas constant (R) holds throughout the universe and has a value of 8.31432 Newton meters/moles kelvin. The standard gravity (g) exerted by the Earth at sea level is 9.80665 meters per second squared (m/s^2). The molar mass (M) of the Earth's air is 0.0289644 kilograms per mole (kg/mol).

2. 2

Define the height zones to be used in the calculation of altitude. The minimum altitude of each zone is given in thousands of meters as follows: 0, 11, 20, 32, 47, 51 and 71.

3. 3

Define the standard temperature values. The standard temperatures (Tb) are based on the altitude zones given in step 2 and are given in kelvins as follows : 288.15, 216.65, 216.65, 228.65, 270.65, 270.65 and 214.65. The standard temperature lapse rate (Lb) is the rate at which the temperature is decreasing at a given altitude. The standard temperature lapse rates for the altitude zones in step 2 are given in kelvins per meter as follows: -.0065, 0, .001, .0028, 0 -.0028 and -.002.

4. 4

Provide the standard pressure (Pb) for each altitude zone in the desired units. The pressures for the seven altitude zones in pascals are as follows: 101,325, 22,632, 5474, 868, 110, 66 and 4.

5. 5

Use the following standard formula for calculating the pressure for a given height (h): P = Pb [Tb/(Tb + Lb (h -hb))]^(goM/RLb). Solving for h gives us the following: h = [Tb/(P/Pb)^(RLb/goM) - Tb]/Lb + hb. This equation will allow us to calculate the height (altitude) for a given pressure (P). Use the values for each altitude zone until you find a solution for h that lies within that altitude zone.

6. 6

Use the pressure to calculate the density of dry air. We can express the ideal gas law as d = p/RT where d is the density of the air, p is the pressure, R is the universal gas constant.

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