aircraft wing properties

7/28/2019 Aircraft Wing Properties

1/11

Wings

Wake Vorticies

Induced Drag

Lift Curve Slope

Swept Wings

Wing Flaps

MAE 2

Campbell, J.F., and Chambers, J.R., Patterns in the Sky, NASA SP-514, 1994.


2/11

2MAE 2

Wake Vorticies

A wake vortex is created by air leaking around the tips of a finite-length wing.

Pressure over the bottom surface is greater than that on the top surface.

Flow establishes a circular pattern downstream of the wing.

airflow

Right wing counter-clockwiserotation when viewed from behind

Left wing clockwise rotation whenviewed from behind


3/11

3MAE 2

Vortex Effects

The wingtip vortices cause a downward velocity component on the wing itself.

This downward flow is called downwash.

Downwash reduces the effective angle-of-attack at the airfoil.

Lift coefficient slope is reduced relative to angle-of-attack (will derive later).

Vortex downwash increases drag on the wing.

This source of drag is called induced drag or drag-due-to-lift.

There are many physical explanations for induced drag.

Every aerodynamicist has his/her favorite explanation.

V

V

w=downwash


4/11

4MAE 2

Induced Drag

Induced drag is estimated by tilting the lift vector by the angle-of-attack induced bydownwash acting on the wing.

The induced angle-of-attack at a given airfoil section depends on the lift distributionover the entire wing (and possibly other nearby aerodynamic surfaces).

b = wingspan

Lift Distribution

Downwash

Distribution


5/11

5MAE 2

Induced Angle-of-Attack

For an elliptical lift distribution, the downwash induced angle-of-attack isapproximated as:

i=

CL

AR

i=induced angle of attack

CL

=wing lift coefficient

AR=aspect ratiob=wingspan

S=wing reference area

AR=b2

S

A span efficiency factor (later related to Oswald's efficiency factor) is introduced toapproximate the induced angle of attack for non-elliptical lift distributions.

i=

CL

e ARe=efficiency factor

e1


6/11

6MAE 2

Induced Drag Coefficient

A new component of drag results when the lift force vector is tilted by the inducedangle of attack.

Di=L sin

iL

i

L=q S CL

i= CL

e AR

Di

q S=

CL2

e ARC

Di=

CL2

e AR

The induced drag coefficient is defined by normalizing this component of drag force.

CD

=cd

C

L2

e AR

The total wing drag coefficient (for subsonic speeds) is:

CD

=total drag coeff.

cd

=profile drag coeff.

Profile drag includes skin friction and pressure drag due to separation.


7/11

7MAE 2

Lift Curve Slope for Finite Wing

The left coefficient slope (with respect to angle-of-attack) is reduced in the presenceof downwash.

a= a0

1a0

e1

AR

CL

=a0

i=a

0 CL e1

AR

CL=a0

a0

CL

e1

ARC

L=a0

1a0

e1

AR

dCLd

a a=lift curve slope finite winga0

=lift curve slope infinite wing

e1

=efficiency factor


8/11

8MAE 2

Swept Wings : Subsonic

Sweeping the wings of a subsonic airplane moves drag divergence point to a higherMach number.

Mcr

airfoilMcr

swept wingM

crairfoil

cos

V

Vcos

Vsin

The airfoil responds only tothe velocity componentnormal to the leading edge.


9/11

9MAE 2

Swept Wings : Supersonic

Wave drag is reduced by sweeping the wing so that the leading edge is inside theMach cone.

M1 M1

Wing swept outside of Mach cone Wing swept inside of Mach cone

=sin1 1M =Mach angle

win

gLE

wing

LE


10/11

10MAE 2

Stall Speed

The stall speed is the slowest speed at which the aircraft can sustain level flight.

The lift force must balance weight to maintain steady, level flight.

Vstall=

2W

S CLmax

W=L=1

2V

2S C

L

The stall speed occurs when the airplane flies at its maximum lift coefficient.


11/11

11MAE 2

Flaps

A low value for stall speed leads to a safer airplane (slower landing speeds).

Stall speed is decreased by increasing the maximum lift coefficient.

L=0

=angle of attack

CL

L=0

(no flaps)

=0

=15 deg

=45deg

Trailing edge flap

aircraft wing properties

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