- 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). 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). 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). 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). 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). 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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