Transcript ASE 167M Lecture Three - University of Texas at Austin

Lecture #2
Columbia…
7/18/2015
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ASE 167M Lecture 2
The Atmosphere
Computer #1
Created by
Eduardo Gildin
Lecture #2
Today’s Lecture
• Questions on Lecture #1 (Flight # 1)
–
–
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–
–
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Report # 1?
Flight Data # 1 ?
Theory ?
Curve Fitting ?
Etc ?
Auto-pilots?
• Atmosphere properties
• Atmosphere Toolbox (Matlab): Computer Project # 1
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Lecture #2
The Atmosphere
• Necessity for studying atmosphere conditions
– Performance of A/C completely dependent of the atmosphere conditions
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Lecture #2
The Atmosphere
• The atmosphere is the gaseous medium enveloping the
Earth
• The properties of the atmosphere are a function of time
and position (i.e. latitude, longitude, and altitude).
• These properties are nonlinear and deterministic but are
nonetheless unpredictable because of the scale and
interconnectivity of global meteorology (the Butterfly
effect).
– “The flapping of a butterfly's wings in China could cause tiny atmospheric
changes which over a period of time could effect weather patterns in New York.”
 This models the unpredictability of local weather patterns
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Lecture #2
The Atmosphere (2)
some information
•
•
•
•
50% of mass is within 5 km altitude
99% of mass is within 30 km altitude
Mass of atmosphere is 5x1015 tons
1
Mass of atmosphere 
total mass of
300
water
• 78% nitrogen, 21% oxygen,
0.93% argon, 0.031% CO2
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Lecture #2
The Atmosphere (3)
Layers of the atmosphere
• Troposphere - sea level to 28,000/55,000 ft
(11 Km ) (most airplane/jet airlines)
– Contains 75% of our atmosphere’s mass
– Height varies from poles to equator
~30000 ft at poles
~36000 ft at equator
 Tropopause: top layer of the Troposphere. It is the boundary
region between Troposphere and Stratosphere
• Stratosphere - up to approx. 50 miles
– Contains ozone layer
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Lecture #2
The Atmosphere (4)
• Mesosphere
– Middle Zone (out of 5) – “Upper Troposphere” regarding
temperature profile, but has a series of intense photochemical
reactions (dissociations and recombination)
• Ionosphere - up to approx. 650 miles
– solar radiation strips electrons from oxygen and nitrogen
molecules
– Important for communications
• Exosphere - out to “”
– Boundary region between the Earth’s atmosphere and the
interplanetary space
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Lecture #2
The Atmosphere (5)
more cool information
• Troposphere:
tropos  Greek for turning
• Stratosphere:
– Air moves only horizontally (jetstream)
• Ionosphere:
– Air particles are ionized by sun’s ultraviolet radiation
• Exosphere:
– outside
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Lecture #2
Temperature (T)
• What causes most of the planet’s thermal
effects?
Solar energy
Temperature Scales
Rankine: R = F + 459.68
Kelvin: K = C + 273.15
Celsius: C = 5/9 * ( F - 32 )
Fahrenheit: F = 9/5*C + 32
Celsius used freezing and boiling point of water
Fahrenheit ? (see http://www.straightdope.com/classics/a891215.html
http://www.futuresource.com/weather/cfcalc.asp
http://www.crh.noaa.gov/pub/temp2.htm )
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Lecture #2
Temperature (T)
• Temperature varies linearly
with altitude. The rate of this
variation is called the
Temperature lapse rate
– Dry adiabatic lapse rate = 10º C
per 1000 m (1 km)
– Wet adiabatic lapse rate = 6º C
per 1000 m (1 km)
– Difference is due to latent heat of
evaporation; due to
condensation, energy is
released which reheats the air
parcel to some extent  slower
cooling
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
h
(1000 ft)
315
250
1 km = 3281 ft
i= lapse rate
4
3
186
Isothermal Regions
130
2
82
65
36
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Tropopause
1
0
R
300
400
390
500
518
600
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Lecture #2
Pressure (P) and Density (r)
• Pressure is the effect felt from the weight of the
atmosphere (force/area) and is continually
changing due to air movement (sloshing) and
temperature changes.
– Recall that altitude is measured by a pressure
reading.
• Density is the mass of air particles per unit
volume and is a function of T, P, and humidity.
– It is the most important quantity in A/C Performance
(Engine Thrust, Airspeed Indicator, CD and CL, etc)
– Water vapor may account for as much as 5% of
density by volume.
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Lecture #2
The Standard Atmosphere
• It is impractical to consider all atmospheric
property variations for design and
performance of aircraft.
• The standard atmosphere is defined to
relate flight tests, wind tunnel tests,
general airplane design, and performance
to a common reference.
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Lecture #2
The Standard Atmosphere (2)
• This definition represents average conditions
derived from math models and experimental
data:
– Weather balloons
– Sounding rockets
• For design and analysis we want P(h), T(h), r(h),
and a(h)  Functions of altitude only!
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Lecture #2
Atmospheric Model Design
Considerations
• Many models available
– U.S. Standard Atmosphere (I & II)
– CIRA, MSIS, Harris-Priester, Jacchia-Roberts, …
• The atmospheric model is typically designed to
be representative of a certain operation point (i.e.
.78 M at 35,000 ft for an airliner).
• Designers must consider weather for
performance, flight planning, and hazard
assessment.
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Lecture #2
Derivation of Standard Atmosphere
• Recall equation of state for a perfect gas
(neglecting intermolecular forces)
P  rRT
– R is the specific gas constant. Value depends upon
the gas and system of units and is derived from
experimental data
• R= 287 m2/s2*K  for dry air
• R = 459.2 m2/s2*K  in the presence of water vapor
• R= 1716 ft*lb/(slug*R)
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Lecture #2
Derivation of Standard Atmosphere
• Method:
– Use the hydrostatic equation (the force
balance on a fluid at rest) to get a free body
diagram
– Develop differential equation of pressure
w.r.t. altitude
– Solve this DE for differing temperature
profiles of the layers of the atmosphere
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Lecture #2
The Hydrostatic Equation
W  rVg  r (dh) g
P+dP
Ftop   P  dP 11
Fbot   P 11
Fbot  Ftop  W
1
or
1
dh
W
P   P  dP  rdhg
dP   rgdh
P
dP g

dh
P RT
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•Solved by numerical integration
•Differing solutions for T(h)
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Lecture #2
Temperature Profile

h
(1000 ft)
315
250
1 km = 3281 ft
i= lapse rate
4

3
1
R

slope ft
186
Isothermal Regions
130
2
82
65
36
Tropopause
1
0
R
300
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400
390
500
518
600
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Lecture #2
Isothermal Solution to D.E.
dP g

dh
P RT
• Recall D.E.
• T(h) = T1
P
dP g h
 P  RT  dh
P
h
1
1
 P  g
ln   
h  h1   Ph  P1e
P1  RT
 g 
 
h h1 
RT
 1 
• Solve D.E.
• Use the equation of state to get density
P
rRT

 r h  r1e
P1 r1 RT1
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 g 
 
h h1 
RT
 1 
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Lecture #2
Varying Temperature Solution to D.E.
dP g

dh
P RT
• Recall D.E.
• Temperature varies as T(h) = T1+(h-h1)
dT
1
 const    dh  dT
dh

• Substitute T and dT into D.E.
P
dP g T dT
 P  R  T
P
T
1
1
 g 
T  R  
 P  g T 
ln   
ln    PT   P1  
P1  R T1 
T1 
g
R
P
rT T

  
P1 r1T1 T1 
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 g

  1
 R 
T
 rT   r1 
T1 
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Lecture #2
Initial Conditions for First Layer
• First layer is assumed to begin at sea level
–
–
–
–
P0 = 2116.2 lb/ft2
T0 = 518.69 0R (59 F)
r0 = 2.377x10-3 slug/ft3
Values repeated in lab manual
• We assume sea level conditions for our simulator
flights.
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Lecture #2
Speed of Sound and Viscosity
• Speed of the sound
a(T )  kRT
– k = 1.4 is the specific heat ratio for air
– Note that a(T) = a(T(h)) = a(h)
• Viscosity
 = 2.27 10 T
-8
3/2
(T + 198.6)
-1
– Note again that dependence on T implies
dependence on h.
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Lecture #2
Atmospheric properties variation
• Solutions of the
diff. equations for
the Standard
Atmosphere
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Lecture #2
Pressure, Density, and Temp. Altitudes
• We can define pressure, temperature, and
density altitudes since each property in the
standard atmosphere corresponds to a
given h.
– Note that you must keep track of layer
changes since there is not a one to one
mapping between h and T.
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Lecture #2
Pressure, Density, and Temp. Altitudes
• Behavior of aircraft depends on density
altitude.
• Altimeter depends on pressure altitude.
h
h(P 1)
h(P 1)
P1=const.
P2=const.
Same h reading in a/c
P3=const.
x
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Lecture #2
Computer Projects - Class
Administration
• Pick any programming language
– MATLAB
– Fortran, C, C++, Visual Basic, …
– Available at LRC
• Individual computer assignment
• There is no specific time for this “lab”
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Lecture #2
Computer Project 1 (1)
• 1) Write toolbox subroutine to calculate T(h),
P(h), r(h), a(h)
– Formula for this routine are in lab manual
– Make a function [Pres,Temp,dens,sos] = atmos(alt)
• Several if statements
• 2) Main Program – for test cases and problems
• Loop over altitude h in 1000 ft increments
– Call atmos(h,P,T,dens,sos)
• End loop
• Test cases from manual – COMPARE WITH TABLE
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Lecture #2
Computer Project 1 (2)
• Plot each property vs. h using your graphics
package of choice. Do NOT give reams of
numerical output or a single altitude reading per
sheet. A condensed table will suffice.
Altitude (h)
Properties
T,P,sos,dens
• Plot only region of interest (do not plot up to
2000000 ft) – You decide!!!!
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Lecture #2
Computer Project 1 (3)
• Answer questions 3 and 4
3) Calculate drag on an orbiter at 160 N.M.
circular orbit
–
–
–
–
–
 = 1.40765x1016 ft3/s2
rc = re + h,
re = 2.09257x107 ft
1 N.M. = 1852/0.3048 ft
S = 5200 sq. ft. and 400 sq. ft.
CD = 2.0
Vc 

rc
1
D  rV 2 SCD
2
4) Calculate the drag on an aircraft flying at 400
knots at 30,000 ft with CD = .05 and S = 600 sq.
ft.
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Lecture #2
Computer Project 1 (4)
• Reports:
– USE FORMAT FROM WEBPAGE…
– DUE IN TWO WEEKS
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Lecture #2
This Week
• Computer Program
• No Lab class
Next Week:
• Flight # 1 report due – during lecture
• Equations of motion / trim
• Flight # 2 Briefing
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