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Chapter 7Incompressible Flow About Wings of

Finite Span

Wing End Effects

Wing Tip Vortex Pressure / Lift Distribution

Lifting Line Theory(Vortex Structure)

Downwash and Induced Drag

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Elliptic Circulation (lift) Distribution

Circulation Distribution

Wing Planform

Downwash Distribution

Effect of AR on CL and CD (Experimental)

Spanwise Lift Distribution(Odd Fourier Terms)

Linear Model

Theory / Experimental Data(Straight Tapered Wing)

Lift Coefficient Distribution

Note: Peak lift coefficient is notat wing root

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Effect of Taper Ratio

Note: For a highly tapered wing the max. lift coefficient is at the tip.

Effect of Taper Ratio on Wing Stall

Rectangular, λ = 1.0

Tapered, λ = 0.4

Pointed, λ = 0.0

Panel Methods Modeling Method vs. Experimental

Λc/4 = 45o Λc/4 = - 45o

Vortex Lattice

Source Panel

Surface Potential

Elemental Panels and Vortices Single Element per Spanwise Position (Swept Tapered Wing)

Bound Vortex Location

Control Point Location

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Vortex / CP Location on Panel Induced Velocity at Point C

Horseshoe Vortex Elements

Sharp Leading Edges

• Flow separates at leading edge and reattaches further back

• This creates a low leading edge suction wing.

F-16

Leading edge flaps can be used to increase leading

edge suction.

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Delta Wings

Flow spills over the leading edge, separates and forms a strong vortex.

Delta Wings – Potential Flow Lift (Kp)

Delta Wings – Vortex Lift (Kv)

Delta Wings – Lift Coefficient

Note the high αααα values

Delta Wings – Drag (∆CD) XB-70At low subsonic speeds delta wings generate a nose-down

pitching moment.

The Valkyrie uses canards to generate a nose-up moment.

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Concord

Concord uses reflexed trailing edge for nose-up moment.

TU-144

Tupolev uses retractable canards

Leading Edge Extensions (LEX) Strake (LEX) VortexF-18 at α=20o

Vortex

Vortex Breakdown

Strake Implementation Effect of Strake on Lift