Definitions of Altitude
 Geometric Altitude (h)- Physical altitude above sea level
 Density Altitude (hd)- The geometric altitude on a standard
day at which the density would be equal to the density
experienced by the vehicle
Note: Aircraft performance (excluding engine power) depends
only on density altitude.
 Pressure altitude (hp)-The geometric altitude on a standard
day for which the pressure is equal to the existing
atmospheric pressure
These are related through the equation of state:
P=RT
 Absolute altitude (ha)- Distance from the center of the earth
Aircraft are in three places:
- Where they are supposed to be
- Where they think they are
- Where they really are
The Atmosphere
The challenge is to define the atmospheric properties as a
function of height so that this information will be readily
available analytically to guide both aircraft design and
operations
The equation of state of a perfect gas is:
P = RT
Where:
P = pressure in Newtons/square meter or Lb/square foot
 = density in Kg/M3 or Slugs/Ft3
T = Absolute temperature in degrees Kelvin (K) or degrees
Rankine ( R )
R = gas constant(287.05 n-m/kg K) (1718 ft-lb/slug R) for
air
Also important is the hydrostatic equation:
dP = -gdh
where:
g = the gravitational constant = 9.8 m/sec2 or 32.17 ft/sec2
at sea level
h = the altitude above sea level
dP = -gdh
Divide the hydrostatic equation by the equation of state
dP/P = -gdh/RT = -(g/RT)dh
First consider the isothermal region of the atmosphere:
h
 dP / P = -(g/RT)  dh
P
P1
h1
ln P/P1 = -(g/RT)(h-h1)
P/P1 = e-(g/RT)(h-h1)
Relate pressure and density through the equation of state:
P/P1 = T/1T1
Since the region is isothermal T = T1
 P/P1 = /1
and
/1 = e-(g/RT)(h-h1)
Now consider the case of gradient layers in which the
temperature varies linearly with height
Thus
T = T1 + a(h – h1), where a = dT/dh
T and h are the temperature and altitude at some point
in the gradient layer and T and h are the values at some
higher altitude point
a is called the lapse rate
dh = 1/a(dT)
Substituting for dh in dP/P = -gdh/RT gives
dP/P = -(g/aR)dT/T
P
T
P1
T1
 dP / P   g /( aR)  dT / T
ln P/P1 = -(g/aR)ln T/T1
Thus 
P/P1 = (T/T1) -(g/aR)
From the equation of state: P/P1 = (T/T1)(/1)
And 
 T/1T1 = (T/T1) -(g/aR)
Or
 /1 = (T/T1) -(g/aR+1)
Key Atmospheric Parameters
Lapse Rate a =-.0065 K per meter = -.00356 R per foot
At Sea Level
Ps = 1.01325 x 105 N/m2 = 2116.2 lb/ft2
s = 1.225 kg/m3 = .002377 slug/ft3
Ts = 288.16 K = 518.69 R
Summary
From the surface to the isothermal region;
For Temperature use: T = T1 + a(h – h1)
For Pressure use: P/P1 = (T/T1) -(g/aR)
For Density use:  /1 = (T/T1) -(g/aR+1)
Above 11,019 meters in the isothermal region
Temperature constant at 216.66 K to 25.1 Km
For Pressure use: P/P1 = e-(g/RT)(h-h1)
For Density use: /1 = e-(g/RT)(h-h1)
Isothermal Region
P/P1 = e-(g/RT)(h-h1)
/1 = e-(g/RT)(h-h1)
Temperature constant at 216.66 K to 25.1 Km
~ 11 Km
Gradient
Region
T = T1 + a(h – h1)
P/P1 = (T/T1) -(g/aR)
 /1 = (T/T1) -(g/aR+1)