Configuration Aerodynamics Lecture4-5

7/30/2019 Configuration Aerodynamics Lecture4-5

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Configuration AerodynamicsRobert Stengel, Aircraft Flight Dynamics

MAE 331, 2008

Configuration variables

Longitudinal aerodynamicforce and momentcoefficients Effects of configuration

variables

Angle of Attack

Mach number

Copyright 2008 by Robert Stengel. All rights reserved. For education al use only.http://www.princeton.edu/~stengel/MAE331.html

http://www.princeton.edu/~stengel/FlightDynamics.html

Reference Characteristics

Configuration

Variables

c =1

Sc 2dy

"b 2

b 2

#

=2

3

$

%

&'

(

)1+ *+ *

2

1+ *c

root

Aspect Ratio

Taper Ratio

Mean Aerodynamic Chord

"=c

tip

croot

AR =b

c rectangular wing

=

b"b

c "b=

b2

Sany wing

from Raymer

Medium to High Aspect Ratio Configurations

Cessna 337 DeLaurier Ornithopter Schweizer 2-32

Typical for subsonic aircraft

Boeing 777-300


2/13

Low Aspect Ratio Configurations

A-5A Vigilante

Typical for supersonic aircraft F-104 Starfighter

Variable Aspect Ratio ConfigurationsF-111 B-1

Aerodynamic efficiency at high and low speeds

Reconnaissance AircraftU-2 (ER-2) SR-71

Subsonic, high-altitude flight

Supersonic, high-altitude flight

Biplane

Compared to monoplane

Structurally stiff (guy wires)

Twice the wing area for the samespan

Lower aspect ratio than a singlewing 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


3/13

Longitudinal Aerodynamic

Forces and Moment

Lift= CLq S

Drag = CDq S

Pitching Moment=Cmq Sc

Non-dimensional forcecoefficients aredimensionalized by dynamic

pressure and reference area Non-dimensional moment

coefficients aredimensionalized by dynamicpressure, reference area, andreference length

Typical subsonic lift, drag, and pitching

moment variations with angle of attack

Circulation and Lift

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

"(x) =#V(x)

#z(x)

Circulation

" = #(x)dx0

c

$

2-D Lift (inviscid, incompressible flow)

Lift= "#

V#$

=

1

2"#

V#

2c 2%&( ) thin, symmetric airfoil[ ]

+ "#

V#$cambe

For Small Angles, Lift is

Proportional to Angle of Attack

Lift= CL

1

2"V2S# CL

0

+

$CL

$%%

&

'()

*+1

2"V2S, CL

0

+ CL%%[ ]

1

2"V2S

where CL% = lift slope coefficient

2-D lift slope coefficient: inviscid,incompressible flow, unswept wing(referenced to chord length rather thanwing area)

CL

"

= 2#

2-D lift slope coefficient: inviscid,incompressible flow, swept wing

CL"= 2#cos$

Effect of Aspect

Ratio on Wing Lift

Slope Coefficient

High Aspect Ratio (> 5) Wing

CL

"

=

2#AR

AR+ 2

Low Aspect Ratio (< 2) Wing

CL

"

=

#AR

2

All Aspect Ratios (Helmboldequation)

CL

"

=

#AR

1+ 1+AR

2

$

%&

'

()2*

+

,,

-

.

//

All wings at M = 1


4/13

Air Compressibility Effects on

Wing Lift Slope Coefficient

Subsonic, 3-D wing, with sweep effect

CL"

=

#AR

1+ 1+AR

2cos$1 4

%

&''

(

)**

2

1+ M2 cos$1 4( )

,

-

.

.

/

0

11

Supersonic delta (triangular) wing

CL

"

=

4

M2#1

Supersonic leading edge

CL"

=

2#2cot$

#+ %( )

where %= m 0.38+ 2.26m & 0.86m2( )

m = cot$LE

cot'

Subsonic leading edge

"1 4

= sweep angle of quarter chord

"LE = sweep angle of leading edge

Flow Separation Produces Stall

Decreased lift

Increased drag

Large Angle Variations in Subsonic

Lift Coefficient (0 < < 90)

Lift=CL1

2"V2S

All lift coefficientshave at least onemaximum (stallcondition)

All lift coefficientsare essentiallyNewtonian at high

Newtonian flow:TBD

Flap Effects on

Aerodynamic Lift

Camber modification

Trailing-edge flap deflectionshifts CL up and down

Leading-edge flap deflectionincreases stall

Same effect applies forother control surfaces Elevator (horizontal tail)

Ailerons (wing)

Rudder (vertical tail)


5/13

Wing-Fuselage Interference Effects

Wing lift induces Upwash in front of the wing

Downwash behind the wing

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 = CD1

2"V

2S# CD

0

+ $CL2[ ]1

2"V

2S

Parasitic Drag

Parasitic Drag =CD0

1

2"V

2S

Pressure differential,

viscous shear stress,and separation

Reynolds Number, Skin Friction,

and Boundary Layer

Reynolds Number =Re ="Vl

=

Vl

#

where

"= air density

V = true airspeed

l = characteristic length

= absolute (dynamic) viscosity

#= kinematic viscosity

Skin friction coefficient

Cf =Friction Drag

q Swet

where Swet = wetted area

Cf "1.33Re#1/2 laminar flow[ ]

" 0.46 log10

Re( )#2.58

turbulent flow[ ]


6/13

Typical Effect of Reynolds Number

on Drag

Flow may stay attachedfarther at high Re, reducingthe drag

from Werle*

* See Van Dyke, M., An Album of Fluid Motion,Parabolic Press, Stanford, 1982

Effect of Streamlining on Drag

Induced Drag

Lift produces downwash (angle proportional to lift) Downwash rotates velocity vector

Lift is perpendicular to velocity vector

Axial component of lift induces drag

CDi = CLi sin"i # CL0 + CL""( )sin"i # CL0 + CL""( )"i $ %CL2

$C

L

2

&eAR=

CL

21+'( )

&AR

where

e = Oswald efficiency factor

'= departure from ideal elliptical lift distribution

Spitfire

Spanwise Lift Distribution

of 3-D Wings

Wing does not have to have an elliptical planform

to have a nearly elliptical lift distribution

Straight Wings (@ 1/4 chord)(McCormick)

Straight and Swept Wings

(NASA SP-367)

TR = taper ratio,


7/13

Oswald Efficiency and

Induced Drag Factors Approximation for e

(Pamadi, p. 390)

e "1.1C

L#

RCL#

+ (1$ R)%AR

where

R = 0.0004&3+$0.008&

2+ 0.05&+ 0.86

&=AR '

cos(LE

Graph for(McCormick, p. 172)

Higher AR

CD

i

=

CL

2

"eAR

CD

i

=

CL

21+ "( )

#AR

P-51 Mustang

http://en.wikipedia.org/wiki/P-51_Mustang

Wing Span = 37 ft(9.83 m)

Wing Area = 235 ft(21.83 m2)

Loaded Weight= 9,200 lb (3,465 kg)

Maximum Power =1,720 hp (1,282 kW)

CDo = 0.0163

AR = 5.83

"= 0.5

P-51 Mustang Example

CL"

=

#AR

1+ 1+AR

2

$

%&

'

()

2*

+

,,

-

.

//

= 4.49 per rad(wing only)

e = 0.947

0= 0.0557

1= 0.0576

CD

i

= "CL

2

=

CL

2

#eAR=

CL

21+$( )

#AR

Drag Due to

Pressure Differential

Blunt base pressure drag

CDbase

= Cpressurebase Sbase

S " 0.29Sbase

Cfriction

Swet

M


8/13

Air Compressibility Effect

Subsonic

Supersonic

Transonic

Incompressible

Shock Waves inSupersonic Flow

Drag rises due to pressureincrease across a shock wave

Subsonic flow Local airspeed is less than sonic

(i.e., speed of sound)everywhere

Transonic flow Airspeed is less than sonic at

some points, greater than sonicelsewhere

Supersonic flow

Local airspeed is greater thansonic virtually everywhere

Drag Coefficient

vs. Mach

Number

Critical Mach number Mach number at which local flow

first becomes sonic

Onset of drag-divergence

Mcrit~ 0.7 to 0.85

Sweep Angle

Effect on Wing Drag

Mcritswept =Mcritunswept

cos"

Transonic Drag Rise and the Area Rule

Richard Whitcomb (NASA Langley) and Wallace Hayes (Princeton)

YF-102A (left) could not break the speed of sound in level flight;

F-102A (right) could

Supercritical

Wing

Thinner chord sections lead to higher Mcrit Richard Whitcomb!s supercritical airfoil

Wing upper surface flattened to increaseMcrit Wing thickness can be restored

Important for structural efficiency, fuel storage,etc.

Pressure distribution

on Supercritical Airfoil

()

(+)


9/13

Large Angle Variations in Subsonic

Drag Coefficient (0 < < 90)

All drag coefficients converge to Newtonian-likevalues at high angle of attack

Low-ARwing has less drag than high-ARwing

Newtonian Flow

No circulation

Cookie-cutter flow

Equal pressure acrossbottom of the flat plate

Normal Force =Mass flow rate

Unit area

"

#$

%

&'Change in velocity( ) Projected Area( ) Angle between plate and velocity( )

N= "V( ) V( ) Ssin#( ) sin#( )

= "V2( ) Ssin2#( )

= 2sin2#( )

1

2"V

2$

%&

'

()S

* CN

1

2"V

2$

%&

'

()S=CNq S

Lift= Ncos"

CL =

2sin2"( )cos"

Drag = Nsin"

CD = 2sin3"

Application of Newtonian Flow

Hypersonic flow (M ~> 5) Shock wave close to surface

(thin shock layer), merging with

the boundary layer Flow is ~ parallel to the surface

Separated upper surface flow

Space Shuttle inSupersonic Flow

High-Angle-of-AttackResearch Vehicle (F-18)

All Mach numbers athigh angle of attack Separated flow on upper

(leeward) surfaces

Lift vs. Drag for Large Variation in

Angle-of-Attack (0 < < 90)

Subsonic Lift-Drag Polar

Low-ARwing has less drag than high-ARwing,but less lift as well

High-ARwing has the best overall L/D


10/13

Lift/Drag vs. Angle of Attack L/D is an important performance metric for aircraft

L

D=

CLq S

CD

q S=

CL

CD

Low-ARwing has best L/D at intermediateangle of attack

Stagger Effect on Biplane

CL

vs. CD

and CL

vs. L/D

NACA TN-70

Biplane wing with no stagger has the best L/D

Pitching Moment

Body " Axis Pitching Moment= MB = " #pz + #sz( )xdxdysurface

$$ + #px + #sx( )#pxzdydzsurface

$$

Pressure and shear stress differentials times moment armsintegrate over the surface to produce a net pitching moment

Center of mass establishes the moment arm center

Pitching Moment

MB " # Zix1 +

i=1

I

$ Xiz1 + Interference Effects+ Pure Couplesi=1

I

$

Distributed effects canbe aggregated to localcenters of pressure


11/13

Pure Couple

Net force = 0

Net moment " 0

Rockets Cambered Lifting Surface

Fuselage

Net Center of Pressure

and Static Margin Local centers of pressure can be aggregated at a net center of

pressure (or neutral point)

xcpnet =x

cpC

n( )wing + xcpCn( )fuselage + xcpCn( )tail + ...[ ]CNtotal

Static Margin = SM=100 xcm " xcpnet( )

c,%

#100 hcm " hcpnet( )%

Static margin reflects the distance between the center of massand the net center of pressure

Effect of Static Margin on

Pitching Moment

MB =

Cmq Sc " Cmo #CN$ hcm # hcpnet( )$[ ]q Sc " Cmo #CL$ hcm # hcpnet( )$[ ]q Sc

" Cmo +%C

m

%$$

&

'(

)

*+q Sc = Cmo + Cm$$( )q Sc

= 0 in trimmed (equilibrium) flight

For small angle of attack and no control deflection

Typically, static margin is positive and !Cm/! is negative forstatic pitch stability

Pitch-Moment Coefficient

Sensitivity to Angle of Attack

MB= C

mq Sc " Cmo + Cm

#

#( )q Sc For small angle of attack and no control deflection

Cm"

# $CN"net

hcm $ hcpnet( ) # $CL"net hcm $ hcpnet( ) = $CL"netx

cm$ x

cpnet

c

%

&'

(

)*

= $CL"wing

xcm $ xcpwing

c

%

&'

(

)*$CL

"ht

xcm $ xcpht

c

%

&'

(

)*= $CL

"wing

lwing

c

%

&'

(

)*$CL

"ht

lht

c

%

&'

(

)*

=Cm

"wing

+ Cm

"ht referenced to wing area, S


12/13

Horizontal Tail Lift Sensitivity

to Angle of Attack

CL"ht( )aircraft =Vtail

VN

#

$

%&

'

(

2

1)*+

*"

#

$

%&

'

(,elasSht

S

#

$

%&

'

(CL"ht( )ht= Wing downwash angle at

the tailVTail= Airspeed at vertical tail;

scrubbing lowers VTail,propeller slipstreamincreases VTail elas= Aeroelastic correction

factor

Effects of Static Margin and Elevator

Deflection on Pitching Coefficient

Zero crossingdetermines trim angleof attack

Negative sloperequired for staticstability

Slope, !Cm/! , varieswith static margin

Control deflectionaffects Cmo and trimangle of attack

MB = Cmo + Cm""+ Cm#E#E( )q Sc

Subsonic Pitching Coefficient

vs. Angle of Attack (0 < < 90)Pitch Up and Deep Stall

Possibility of 2 stableequilibrium (trim) points withsame control setting Low

High

High-angle trim is calleddeep stall Low lift

High drag

Large control momentrequired to regain low-angletrim


13/13

Documents

Configuration Aerodynamics Lecture4-5