mae 331 lecture 4
TRANSCRIPT
Configuration Aerodynamics - 1Robert Stengel, Aircraft Flight Dynamics, MAE 331,
2010
• Configuration Variables
• Lift– Effects of shape, angle, and
Mach number
– Stall
• Parasitic Drag– Skin friction
– Base drag
Copyright 2010 by Robert Stengel. All rights reserved. For educational use only.http://www.princeton.edu/~stengel/MAE331.html
http://www.princeton.edu/~stengel/FlightDynamics.html
Description ofAircraft Configuration
A Few Definitions
Republic F-84F
Wing Planform Variables
• Aspect Ratio • Taper Ratio
! =ctip
croot
AR =b
crectangular wing
=b ! b
c ! b=b2
Sany wing
• Rectangular Wing • Delta Wing • Swept Trapezoidal Wing
Mean Aerodynamic Chordand Wing Center of Pressure
c =1
Sc
2y( )dy
!b 2
b 2
"
=2
3
#$%
&'(
1+ ) + )2
1+ )croot [for trapezoidal wing]
from Raymer
• Mean aerodynamic chord (m.a.c.) ~ mean geometric chord
• Axial location of the wing!s subsonic
aerodynamic center (a.c.)
– Determine spanwise location of m.a.c.
– Assume that aerodynamic center is at25% m.a.c.
from Sunderland
Trapezoidal Wing
Elliptical Wing
Mid-
chord
line
Medium to High Aspect Ratio Configurations
Cessna 337 DeLaurier Ornithopter Schweizer 2-32
• Typical for subsonic aircraft
Boeing 777-300
Low Aspect Ratio Configurations
North American A-5A Vigilante
• Typical for supersonic aircraft Lockheed F-104 Starfighter
Variable Aspect Ratio Configurations
General Dynamics F-111North American B-1
• Aerodynamic efficiency at sub- and supersonic speeds
Reconnaissance AircraftLockheed U-2 (ER-2) Lockheed SR-71 Trainer
• Subsonic, high-altitude flight • Supersonic, high-altitude flight
Uninhabited Air VehiclesNorthrop-Grumman/Ryan Global Hawk General Atomics Predator
Stealth and Small UAVsNorthrop-Grumman X-47B General Atomics Predator-C (Avenger)
InSitu/Boeing ScanEagle
Re-entry VehiclesNorthrop HL-10
Martin Marietta X-24A
Northrop M2-F2
Martin Marietta X-24B
JAXA ALFLEX NASA X-38
Biplane
• Compared to monoplane
– Structurally stiff (guy wires)
– Twice the wing area for the same
span
– Lower aspect ratio than a single
wing with same area and chord
– Mutual interference
– Lower maximum lift
– Higher drag (interference, wires)
• Interference effects of two wings
– Gap
– Aspect ratio
– Relative areas and spans
– Stagger
AerodynamicLift and Drag
Longitudinal Aerodynamic Forcesand Moment of the Airplane
Lift = CLq S
Drag = CDq S
Pitching Moment = Cmq Sc
• Non-dimensional forcecoefficients are dimensionalizedby
– dynamic pressure, q
– reference area, S
• Non-dimensional momentcoefficients alsodimensionalized by
– reference length, c
Typical subsonic lift, drag, and pitchingmoment variations with angle of attack
Circulation of Incompressible Air FlowAbout a 2-D Airfoil
• Bernoulli!s equation (inviscid, incompressible flow)
pstatic +1
2!V 2
= constant along streamline = pstagnation
• Vorticity Vupper (x) = V!+ "V (x) 2
Vlower (x) = V!# "V (x) 2
!2"D (x) =
#V (x)
#z(x)• Circulation
!2"D = #
2"D (x)dx
0
c
$ Lower pressure on upper surface
What Do We Mean by
2-Dimensional Aerodynamics?
• Finite-span wing –> finite aspect ratio
AR =b
crectangular wing
=b ! b
c ! b=b2
Sany wing
• Infinite-span wing –> infinite aspect ratio
What Do We Mean by 2-
Dimensional Aerodynamics?
Lift3!D = CL3!D
1
2"V 2
S = CL3!D
1
2"V 2
bc( ) [Rectangular wing]
# Lift3!D( ) = CL3!D
1
2"V 2
c#y
lim#y$0
# Lift3!D( ) = lim#y$0
CL3!D
1
2"V 2
c#y%&'
()*+ "2-D Lift" = CL2!D
1
2"V 2
c
• Assuming constant chord section, the “2-D Lift” is
the same at any y station of the infinite-span wing
For Small Angles, Lift isProportional to Angle of Attack
• Unswept wing, 2-D lift slope coefficient
– Inviscid, incompressible flow
– Referenced to chord length, c, rather than wing area
CL2!D
= CL"
( )2!D
" = 2#( )" [Lifting-line Theory]
• Swept wing, 2-D lift slope coefficient
– Inviscid, incompressible flow
CL2!D
= CL"
( )2!D
" = 2# cos$( )"
Classic Airfoil
Profiles• NACA 4-digit Profiles (e.g., NACA 2412)
– Maximum camber as percentage of chord (2)
– Distance of maximum camber from leadingedge, 10s of percent (4)
– Maximum thickness as percentage of chord (12)
– See NACA Report No. 460, 1935, for lift and dragcharacteristics of 78 airfoils
– Airfoils used on various aircraft:
NACA Airfoilshttp://en.wikipedia.org/wiki/NACA_airfoil
• Clark Y (1922): Flat lower surface, 11.7% thickness
– GA, WWII aircraft
– Reasonable L/D
– Benign computed stall characteristics, butexperimental result is more abrupt
The Incomplete Guide to Airfoil Usagehttp://www.ae.illinois.edu/m-selig/ads/aircraft.html
Fluent, Inc, 2007
Clark Y Airfoilhttp://en.wikipedia.org/wiki/Clark_Y
Relationship Between
Circulation and Lift
• 2-D Lift (inviscid, incompressible flow)
Lift( )2!D
= "#V# $( )2!D
!1
2"#V#
2c 2%&( ) thin, symmetric airfoil[ ] + "#V# $camber( )
2!D
!1
2"#V#
2c CL&( )
2!D& + "#V# $camber( )
2!D
Aerodynamic Strip Theory
• Airfoil section may vary from tip-to-tip
– Chord length
– Airfoil thickness
– Airfoil profile
– Airfoil twist
• Lift of a 3-D wing is found by integrating 2-D lift
coefficients of airfoil sections across the finite span
• Incremental liftAero L-39 Albatros
dL = CL2!D
y( )c y( )qdy
• 3-D wing lift
L3!D = CL2!D
y( )c y( )q dy!b /2
b /2
"
Effect of Aspect Ratio on WingLift Slope Coefficient(Incompressible Flow)
• Airfoil section lift
coefficients and
lift slopes near
wingtips are
lower than their
estimated 2-D
values
Effect of Aspect Ratio on3-Dimensional Wing Lift
Slope Coefficient(Incompressible Flow)
• High Aspect Ratio (> 5) Wing
CL!
=2"ARAR + 2
= 2"AR
AR + 2
#$%
&'(
• Low Aspect Ratio (< 2) Wing
CL!
="AR2
= 2"AR
4
#$%
&'(
All wings at M = 1
Bombardier
Dash 8Handley Page HP.115
For Small Angles, Lift isProportional to Angle of Attack
Lift = CL
1
2!V 2
S " CL0
+#CL
#$$%
&'()*1
2!V 2
S + CL0
+ CL$$%& ()1
2!V 2
S
where CL$= lift slope coefficient
• At higher angles,– flow separates
– wing loses lift
• Flow separationproduces stall
http://www.youtube.com/watch?v=RgUtFm93Jfo
Angle of
Attack
Maximum Lift ofRectangular Wings
Schlicting & Truckenbrodt, 1979
Aspect Ratio
Maximum
Lift
Coefficient
! : Sweep angle
" : Thickness ratio
Maximum Lift of Delta Wings with
Straight Trailing Edges
Schlicting & Truckenbrodt, 1979
! : Taper ratioAspect Ratio
Angle of
Attack
Maximum Lift
Coefficient
Aspect Ratio
Large Angle Variations in Subsonic
Lift Coefficient (0° < ! < 90°)
Lift = CL
1
2!V 2
S
• All lift coefficientshave at least onemaximum (stallcondition)
• All lift coefficientsare essentiallyNewtonian at high !
• Newtonian flow:TBD
Flap Effects onAerodynamic Lift
• Camber modification
• Trailing-edge flap deflectionshifts CL up and down
• Leading-edge flap (slat)deflection increases stall !
• Same effect applies forother control surfaces
– Elevator (horizontal tail)
– Ailerons (wing)
– Rudder (vertical tail)
Effect of Aspect Ratio on 3-D
Wing Lift Slope Coefficient(Incompressible Flow)
• All Aspect Ratios (Helmbold equation)
CL!
="AR
1+ 1+AR
2
#$%
&'(2)
*++
,
-..
Air Compressibility and Sweep Effects
on 3-D Wing Lift Slope Coefficient
• Subsonic 3-D wing, with sweep effect
CL!
="AR
1+ 1+AR
2cos#1 4
$
%&
'
()
2
1* M 2cos#
1 4( )+
,
---
.
/
000
!1 4
= sweep angle of quarter chord
Air Compressibility Effects on
3-D Wing Lift Slope Coefficient
• Supersonic delta (triangular) wing
CL!
=4
M2"1
Supersonic leading edge
CL!
=2"
2cot#
" + $( )
where $ = m 0.38 + 2.26m % 0.86m2( )
m = cot#LEcot&
Subsonic leading edge
!LE = sweep angle of leading edge
Wing-Fuselage Interference Effects• Wing lift induces
– Upwash in front of the wing
– Downwash behind the wing, having major effect on the tail
– Local angles of attack over canard and tail surface are modified,affecting net lift and pitching moment
• Flow around fuselage induces upwash on the wing, canard,and tail
from Etkin
Aerodynamic Drag
Drag = CD
1
2!V 2
S " CD0
+ #CL
2( )1
2!V 2
S
" CD0
+ # CLo+ CL$
$( )2%
&'()*1
2!V 2
S
Parasitic
Drag
• Pressure differential,viscous shear stress,and separation
Parasitic Drag = CD0
1
2!V 2
S
Reynolds Number andBoundary Layer
Reynolds Number = Re =!Vl
µ=Vl
"
where
! = air density
V = true airspeed
l = characteristic length
µ = absolute (dynamic) viscosity
" = kinematic viscosity
Reynolds Number,
Skin Friction, and
Boundary Layer
• Skin friction coefficient for a flat plate
Cf =Friction Drag
qSwet
where Swet = wetted area
Cf ! 1.33Re"1/2
laminar flow[ ]
! 0.46 log10 Re( )"2.58
turbulent flow[ ]
Typical Effect of ReynoldsNumber on Parasitic Drag
from Werle*
* See Van Dyke, M., An Album of Fluid Motion,Parabolic Press, Stanford, 1982
• Flow may stay attachedfarther at high Re,reducing the drag
Effect of Streamlining on Parasitic Drag
Next Time:Configuration
Aerodynamics - 2