Atmosphere
SYST 460/560
Introduction to Air Transportation
System Engineering
Instructor: Lance Sherry (lsherry@gmu.edu)
1
Learning Objectives
• Properties of Atmosphere
– Temperature = f(altitude)
– Pressure = f(altitude)
– Density = f(altitude)
•
•
•
•
Atmosphere/Troposphere
Relationship between Properties
ISA
Delta ISA
2
Composition of Atmosphere
• Air is treated as a perfect dry gas
– 78% Nitrogen
– 22% Oxygen
– traces of other gases like Hydrogen, Carbon
dioxide, …
3
Composition of Atmosphere
Altitude
= Height
above
ground
Air particles
Less Dense
Gravity
More Dense
4
Properties of Atmosphere
• Density = f (Altitude)
– Density decreases as altitude increases
• Pressure = f (Altitude)
– Pressure decreases as altitude increases
• Temperature = f (Altitude)
– Temperature decreases as altitude increases
– drops 1 deg C for every 1000 ft increase in altitude
5
Basic Equations
• Boyles Law
PV=nRT
• n = number of moles
• R = universal gas constant
• D = m/V
– m = n * Molar Mass
• Thermodynamics
D = P/(R * T)
6
Basic Equations for Atmospheric
Properties
• The equation of state
• p = ρRT
– Where:
•
•
•
•
p: pressure
ρ: density
T:Temperature
R: gas constant.
• Variation of pressure
• dp/dh=-ρg,
– Where:
• g is the acceleration due
to gravity
• h is altitude
• p: pressure
• ρ: density
7
Equations for Atmospheric Properties
Linear T (i.e. atmosphere)
• T = To − Lh
• p/po = (T/To) (g/LR)
• ρ/ρo = (T/To) (g/LR)-1
• Constant T (i.e.
troposphere)
• T = To
• p/po = e(-g/RT)(h-ho)
• ρ/ρo = p/po
8
Atmosphere/Troposphere
Altitude = Height above
ground
36,089 feet
Density so low, no change in P, T
Troposphere (turbulent)
Atmosphere
Density enough, so change in P, T
9
Temperature
• Below 36,089 feet,
– Ambient Temperature (ºR) = -3.566º *
(Altitude/1000)
• Above 36,089 feet
– Ambient Temperature (ºR) = 389.988º
36,089
Altitude (ft)
Temp (ºR)
10
Pressure
• Pressure = Force/Area
• Below 36,089 feet
– Ambient Pressure (lb/ft2) = = (1 - : * 6.88 X 10-6 *
Altitude)5.26
• Above 36,089 feet
– Ambient Pressure (lb/ft2) = 0.223360 e ( (36.089 –
Altitude)/20.8057)
11
Density
• D = P/(R * T)
– T is constant, above 36,089 ft
– P decreases above/below 36,089 ft
12
International Standard Atmosphere
(ISA)
• Reference point at Sea Level at N45º32’ 40”
Parameter
Pressure
Density
Temperature
Symbol
Po
To
Value
2,116.22
0.002377
59⁰F = 15⁰C
Gravity
Gas Constant
Go
R
32.1741
53.35
o
Units
Lb/ft2
Slugs/ft3
Farenheit or
Celsius
ft/sec2
Ft/⁰R
13
ISA Ambient Ratios
• Temperature Ratio = Tambient / Tsea level = θ
• Pressure Ratio = Pambient / Psea level = δ
• Density Ratio = ambient / sea level = = δ/ θ
• from thermodynamics
14
Ambient Ratios
• Temperature Ratio = Tambient / Tsea level = θ = 1 – (6.8753 *
10-6) Pressure Altitude (pressure Altitude < 36,089 ft)
• Temperature Ratio = Tambient / Tsea level = θ = 0.7519
(pressure Altitude > 36,089 ft)
• Pressure Ratio = Pambient / Psea level = δ = 1 – (6.88 * 10-6 *
Pressure Altitude)5.26 (pressure Altitude < 36,089 ft)
• Pressure Ratio =P ambient / Psea level = δ = 0.22336
EXP((36,089 – Pressure Alt)/20,805.7) (pressure
Altitude > 36,089 ft)
• Density Ratio = ambient / sea level = = δ/ θ (from
thermodynamics)
15
Delta ISA
• Delta ISA is used to account for differences
between the standard ambient temperature and
the actual air temperature.
• Example: ISA temperature at 6000 ft is 3.3
degrees C. If it was 13 degrees at that altitude,
then ∆ISA = +10 (since 10 degrees warmer than
the ISA temperature)
• For example, you are scheduled to fly through an
airmass that is +40⁰ than standard temperature.
• Θ = (Tamb + ∆ISA) / (TSeaLevel + ∆ISA)
16
Homework
• Plot θ, δ, (x-axis) vs Altitude (y-axis from 1000 ft to 43,000 ft)
17