Standard Atmosphere :

• The pressure at zero altitude is p_o = 1013.25mb
• The temperature at zero altitude is T_o = 283.15K = 15C
• The temperature lapse rate is constant





where .

• It satisfies ideal gas equation





where R_d is the gas constant for dry air (= 287.04 J kg^-1 K^-1)

• It satisfies hydrostatic equation





where g is the acceleration due to gravity (= 9.801 m s^-2) and is a constant if z is the geopotential height.

Pressure Altitude :

the pressure altitude is the altitude in the standard atmosphere at which a given pressure (p_stn) will be observed.

For standard atmosphere, the height-pressure relationship is (derivation using hydrostatic equation can be found at http://hurri.kean.edu/~yoh/calculations/standatm/StdAtm.html ),

Density Altitude :

• the density altitude is the altitude in the standard atmosphere where air density is the equivalent to that at the airport.  The effect of water vapor is not considered here.


For standard atmosphere, the height-density relationship is (derivation using hydrostatic equation can be found at http://hurri.kean.edu/~yoh/calculations/standatm/StdAtm.html ),





and

Altimeter Setting :

the pressure value to which an aircraft altimeter scale is set, so it will indicate the altitude above mean sea level of the aircraft on the ground at the location for which the pressure was determined.

The altimeter setting is the pressure "reduced" to sea level using the temperature profile of the "standard" atmosphere without regard to water vapor.

For standard atmosphere, the height-pressure relationship is (derivation using hydrostatic equation can be found at http://hurri.kean.edu/~yoh/calculations/standatm/StdAtm.html ),

where p_o is 1013.25mb and T_o is 288.15 K.

This equation of height-pressure relationship is modified if the aircraft altimeter scale is set at p_as (altimeter setting) instead of standard pressure p_o :

where T_as is the corresponding temperature reading when the altimeter scale is set at  p_as.  Since altimeter is calibrated according to the standard atmosphere, we also have that T_as and  p_as must be related by :

In order to show the height of the plane above the runway, it is important to choose the altimeter setting (p_as) such that the altimeter should indicate station/runway elevation (z_stn) at observed station pressure (p_stn).  According to the modified height-pressure relationship,

Eliminating T_as from the two equations above, we get

The stations elevation (z_stn) usually is about 0.3 m above the official station elevation since there is the typical location of the altimeter of the plane.