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!!!
2
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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