Atmospheric Pressure where
- = pressure at altitude
- = standard pressure at sea level (101325 Pa)
- = Temperature lapse rate (0.0065 K/m)
- = The altitude in question
- = standard temperature at sea level (288.15 K)
- = Earth surface gravitational acceleration (9.80665)
- = Molar mass of dry air (0.0289644 kg/mol)
- = Universal gas constant (8.31447 J/(mol•K))
Terminal Velocity where
- = velocity at the specified altitude
- = Mass of falling object
- = gravitational acceleration
- = projected area of the object
- = Coefficient of drag of the object
- = Density of the fluid through which the object is falling
Density of Air where
- = Absolute pressure
- = Specific gas constant for dry air (287.058 J/(kg·K))
- = Absolute temperature
Gravity at Altitude where
- = Gravity at elevation
- = Gravity at surface
- = Mean radius of the Earth
- = Elevation in question
Will need to combine these four functions over time and altitude (third order diff-eq?) to get the result.
Sources: