The Atmosphere
Abbreviations
 SL = sea level
 SA = standard atmosphere
Static and Dynamic Pressure
Total Pressure
Static Pressure P
29.92” Hg at SL in SA
Dynamic Pressure q
q =  V2 / 2
Dynamic pressure q =  V2 / 2
 is also called Ram Air Pressure
 is a major cause of parasite drag
 (lower case rho) = air density in slugs/ft3; V = true airspeed (TAS) in ft/sec;
q = ram air pressure in #/ft2
We are unconcerned with units in the dynamic pressure equation. However,
every pilot should know the implications of the equation q =  V2 / 2: Ram air
pressure q is
 directly proportional to air density
 directly proportional to TAS squared
Standard Atmosphere
 “Average” static pressure, absolute temperature, and density (among
other parameters) in the atmosphere from SL upward
 Compiled from scientific observations at many locations around the
earth over a extended period of time
 A theoretical concept: no air mass precisely replicates the SA
 To compare the performance of two aircraft operating in different air
masses, must determine their density altitudes in a SA
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Standard Atmosphere Table—a table listing atmospheric properties in a SA
Use ONLY this SA Table in quiz and test calculations!!!
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Pressure Ratio  (small delta) in SA
 = P / P0
 P is static pressure at your altitude
 P0 is static pressure at SL in SA (29.92” Hg)
Lapse rate of P in a standard atmosphere is 1” Hg / 1000’ (this “rule of thumb
is an accurate approximation in the lower atmosphere ONLY)
Altitude (ft)
1000
5000
10000
20000
29920
Calculated  Using Rule of Thumb
28.92 / 29/92 = 0.96658
24.92 / 29.92 = 0.83287
19.92 / 29.92 = 0.66576
9.92 / 29.92 = 0.33155
0 / 29.92 = 0.00000
Actual 
0.96439
0.83205
0.68770
0.45954
0.29690
Temperature Ratio  (theta) in SA
 = T / T0
 T is absolute temperature at your altitude
 T0 is absolute temperature at SL in SA (288O Kelvin or 519O Rankine)
 KO = Co + 273O (e.g. 15O C + 273O C = 288O K)
 RO = FO + 460O ( e.g. 59O F + 460O F = 519O R)
Lapse Rate of temperature in SA is about 2O C (3.6O F) /1000’ from SL to the
tropopause. This approximation is highly accurate.
Altitude (ft)
10000
20000
30000
Calculated  Using 2O /1000’ Lapse Rate
(-5+273) / (15+273) = 0.93056
(-25+273) / (15+273) = 0.86111
(-45+273) / (15+273) = 0.79167
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Actual 
0.93125
0.86249
0.79374
Suppose the temperature ratio at your altitude is 0.86249. Find the
temperature in degrees F at this altitude in SA.
T = T0  = (59 + 460)O R (0.86249) = 447.632O R
T = 447.63O R – 460O = -12.367O F
Density Ratio  (small sigma)
 =  / 0
  is air density at your altitude
 0 is air density at SL in SA
No rule of thumb exists for the lapse rate of air density in SA.
Relationship between Pressure, Temperature, and Density in SA
=/
Example: FL350 / FL350 = 0.23530 / 0.75936 = 0.30987 = FL350
( is a mathematical symbol that means “is proportional to”)
=/=
𝑷⁄𝑷𝟎
𝑻 ⁄𝑻 𝟎
∝ 𝑷⁄𝑻
Important: The equations  =  /  reflects the fact that air density is
 Directly proportional to static air pressure
 Inversely proportional to absolute air temperature
SMOE (Standard Means of Evaluation)
 SMOE = 1 / 
 Some SA tables have a column for 
 Some SA tables have a column for SMOE
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Speed of Sound in Air a
 depends on air temperature T only (counterintuitive?)
 a = a0  where a0 = 661.74 nm/hr, the speed of sound at SL in SA
Example: if  = 0.79374, then a = a0  = 661.74 0.79374 = 589.56 nm/hr
Mach Number M
 ratio of TAS to the speed of sound at cruise altitude
 M = TAS / a = TAS / (a0 )
Math Review: Linear vs. Non-Linear and Direct vs. Inverse Functions
 y = f(x)—a mapping from a domain x to a range y
 Linear : y changes at a constant rate with respect to x—results in a
straight line plot
 Non-linear: y changes at a varying rate with respect to x—results in a
curved line plot
 Direct (x, y; x, y))
 Inverse (x, y; x, y)
Examples:
Linear, Direct: y = x
Linear, Inverse: y = -x
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Non-Linear: y = x2
Direct in1st Quadrant
Inverse in 2nd Quadrant
Variation of SA Parameters with Altitude
 , ,  are all inverse
 ,  are both non-linear;  is linear (and has a discontinuity)
 a is linear inverse (and has a discontinuity)
 SMOE = 1 /  is non-linear direct
 0.0 < , ,  ≤ 1.0 in SA at SL and above
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Altitude Measurement
Indicated Altitude (IA)—read on the altimeter. To find altimeter error:
 Set field elevation on altimeter
 Read Kollsman window value
 Compare Kollsman value to reported altimeter setting
 Example:
o Altimeter setting = 3.12 with field elevation set
o Kollsman window reading = 3.15
o Altimeter error = 3.15 – 3.12 = + 0.03
o Set Kollsman window to next reported altimeter setting + 0.03
Pressure Altitude (PA)—IA corrected for non-standard static pressure P
 E6B / Flight Computer or use 1” Hg /1000’ rule of thumb
 Since P decreases as altitude increases (inverse function)
o Non-standard high static pressure  PA lower than IA
o Non-standard low static pressure  PA higher than IA
o  is a mathematical symbol that means “implies”
 Example 1:
o IA = 35’ (field elevation); Altimeter setting = 30.14
o 30.14 – 29.92 = 0.22: corresponds to 0.22 (1000) = 220’
o PA = 35’ – 220’ = -185’ (subtract because pressure is nonstandard high, implying PA < IA)
 Example 2:
o IA = 35’ (field elevation); Altimeter setting = 28.40
o 29.92 – 28.40 = 1.52: corresponds to 1.52 (1000) = 1520’
o PA = 35’ + 1520’ = 1555’ (add because pressure is non-standard
low, implying PA > IA
Density Altitude (DA) – PA corrected for non-standard temperature T
 Use an aviation computer or chart to make this correction
 Note: Since   P/T, correcting IA for non-standard P and PA for nonstandard T is equivalent to correcting IA for non-standard density
 Thus, DA = IA corrected for non-standard air density
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Use the chart below to find DA by correcting PA for temperature T
 Locate T on bottom horizontal scale
 Proceed vertically to intersect the curved PA line
 At the intersection, proceed horizontally to read
o DA on left vertical scale
o SMOE on right vertical scale
 Note: each small block on the left vertical-axis = 250’ of altitude
T = -15o C; PA = 6000’ (non-standard low temperature)
DA = 5000 – (4.5*250) = 3875’; SMOE = 1.05
Required Accuracy: ± 250’ DA, ± 0.01 SMOE
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