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Flat Plate Drag

Drag on flat plate is solely due to friction createdby laminar, transitional, and turbulent boundarylayers.

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Flat Plate Drag

Local friction coefficient

Laminar:

Turbulent:

Average friction coefficient

Laminar:

Turbulent:

For some cases, plate is long enough for turbulent flow,but not long enough to neglect laminar portion

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Effect of Roughness

Similar to MoodyChart for pipe flow

Laminar flow

unaffected byroughness

Turbulent flowsignificantly affected:Cf can increase by 7xfor a given Re

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Cylinder and Sphere Drag

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Cylinder and Sphere Drag

Flow is strong function ofRe.

Wake narrows forturbulent flow since TBL(turbulent boundary layer)is more resistant toseparation due toadverse pressure

gradient. sep,lam 80

sep,lam 140

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Effect of Surface Roughness

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Lift

Lift is the net force(due to pressure andviscous forces)perpendicular to flowdirection.

Lift coefficient

A=bc is the planformarea

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Computing Lift

Potential-flow approximation givesaccurate CL for angles of attack belowstall: boundary layer can be neglected.

Thin-foil theory: superposition of uniform

stream and vortices on mean camber line. Java-applet panel codes available online:

http://www.aa.nps.navy.mil/~jones/online_tools/panel2/

Kutta conditionrequired at trailing edge:

fixes stagnation pt at TE.

http://www.aa.nps.navy.mil/~jones/online_tools/panel2/http://www.aa.nps.navy.mil/~jones/online_tools/panel2/http://www.aa.nps.navy.mil/~jones/online_tools/panel2/http://www.aa.nps.navy.mil/~jones/online_tools/panel2/

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Effect of Angle of Attack

Thin-foil theory shows thatCL2 for < stall

Therefore, lift increases

linearly with

Objective for most

applications is to achievemaximum CL/CD ratio.

CDdetermined from wind-tunnel or CFD (BLE or NSE).

CL/CD increases (up to order100) until stall.

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Effect of Foil Shape

Thickness andcamber influencespressure distribution(and load distribution)and location of flowseparation.

Foil databasecompiled by Selig(UIUC)http://www.aae.uiuc.edu/m-selig/ads.html

http://www.aae.uiuc.edu/m-selig/ads.htmlhttp://www.aae.uiuc.edu/m-selig/ads.htmlhttp://www.aae.uiuc.edu/m-selig/ads.htmlhttp://www.aae.uiuc.edu/m-selig/ads.htmlhttp://www.aae.uiuc.edu/m-selig/ads.htmlhttp://www.aae.uiuc.edu/m-selig/ads.html

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Effect of Foil Shape

Figures from NPS airfoil javaapplet.

Color contours ofpressure field

Streamlines throughvelocity field

Plot of surface pressure Camber and thickness shown

to have large impact on flowfield.

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End Effects of Wing Tips

Tip vortex created byleakage of flow from high-pressure side to low-pressure side of wing.

Tip vortices from heavyaircraft persist fardownstream and posedanger to light aircraft.

Also sets takeoff andlanding separation atbusy airports.

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End Effects of Wing Tips

Tip effects can bereduced by attachingendplatesor winglets.

Trade-off betweenreducing induceddrag and increasingfriction drag.

Wing-tip feathers onsome birds serve thesame function.

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Lift Generated by Spinning

Superposition of Uniform stream + Doublet + Vortex

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Lift Generated by Spinning

CL strongly depends on rateof rotation.

The effect of rate of rotation

on CD is small. Baseball, golf, soccer,

tennis players utilize spin.

Lift generated by rotation iscalled The Magnus Effect.