Aircraft Performance Thrust Required Curves Dr. … Performance Thrust Required Curves Dr. Aamer...
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Aircraft Performance Thrust Required Curves Dr. Aamer Haque http://math.iit.edu/~ahaque6 [email protected] Illinois Institute of Technology 2009
Transcript of Aircraft Performance Thrust Required Curves Dr. … Performance Thrust Required Curves Dr. Aamer...
Aircraft Performance
Thrust Required Curves
Dr. Aamer Haque
http://math.iit.edu/[email protected]
Illinois Institute of Technology
2009
Model Assumptions
Steady Level Flight Constant Altitude Constant Airspeed No turns
Parabolic Drag Polar Relates Drag and Lift Coefficients
Constant Configuration No flaps
Constant Weight Boeing 777 “Data” used as an Example
Level Flight - Equilibrium of Forces
Image from: http://img258.imageshack.us/img258/7016/boeing777200deltaairlinra1.png
Not an endorsement of DELTA or any other airline!
L
W
T D
Thrust = Drag Lift = Weight
Wing Geometry
AR=b2
S
c
b
Chord
Wing Span
Wing Area
Aspect Ratio Some Boeing 777 data can be found at:http://www.aerospaceweb.org/aircraft/jetliner/b777/
b
c
S
Sweep Angle measured at quarter chord location
Aerodynamics of Airfoils
q=12V 2
L=C Lq S
D=C Dq S
DynamicPressure
Lift
Drag
lb/ft2
lb
lb
Image from: http://www.imaph.tu-bs.de/lehre/99/irro/conformi_e.html
Lift Slope
C L= f ,M ,Re
Parabolic Drag Polar
CD=CD0K C L2
CD0=0.017 K=0.0386
Components of Drag
B= KW2
12S
Parasitic Drag Lift=Weight
Induced Drag
Total Drag D V =D p V Di V =AV 2 BV 2
A=12S C D0
Di V =K C L2 q S
D p V =AV2
Di V =BV 2
D p V =CD0 q S
L=W⇒C L=WqS
Minimum Drag Airspeed
Minimum DragAirspeed
Maximum L/D
V min= BA1/4
= KCD0 1/4
12 WS
LD max= 12K C D0
The Minimum Drag Airspeed is the airspeed for maximum endurancebut not the airspeed for maximum range
Thrust Required = Drag
D p V =AV2 , Di V = B
V 2 , V min occurs when Di=D p
D V =D p V Di V
Stall – Low Speed Limit
V stall= 2C Lmax WS
Image from: http://quest.arc.nasa.gov/aero/virtual/demo/aeronautics/tutorial/wings.html
Cannot fly below stall speed
C L= f ,M ,Re
M=0.75
Shock Waves – High Speed Limit
Image from: http://www.centennialofflight.gov/essay/Theories_of_Flight/Transonic_Flow/TH19.htm
Supercritical Airfoil
http://www.aerospaceweb.org/question/airfoils/q0127b.shtml http://en.wikipedia.org/wiki/Supercritical_airfoil
Supercritical airfoils have a larger drag divergence Mach number
M DR=V DR
c
Thrust Required - Limits
V stall
V DR
M DR=0.85
Lift to Drag Ratio
L /Dmax=19.5 occurs at V min
Atmospheric Changes with Altitude
=SL
Temperature becomes constantat the Tropopause (36,000 ft)
Thrust Required – Altitude Effects
