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

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Aerodynamics - 2