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Aerodynamics II: Drag

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Viscous Drag

Reynolds number is a dimensionless parameter

important in determining the viscous drag on a body.

The units of viscosity are kg/m s

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The Boundary Layer

Increasing Reynolds number

The turbulent boundary layer has higher velocities, and is

rougher, but it also has more energy than the laminarboundary layer.

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Viscous Drag, cont.

Viscous drag is made up of skin friction drag and

pressure drag.

Skin friction is the frictional force associated with theair rubbing against the surface of the vehicle.

Generally, the skin friction component of the viscous

drag becomes larger at higher Reynolds number.This is because the turbulent boundary layer has

higher velocity and causes more vigorous rubbing

of the air on the surface.

Other contributors to high skin friction drag are:

Rough surface

Large surface area

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Viscous Drag, cont.

Pressure drag occurs when the pressures betweenthe fore and aft facing surfaces do not balance:

Generally, the pressure drag decreases as the

Reynolds number increases. This is because theturbulent boundary layer has more energy and can

remain attached to the body surface more easily than

the laminar boundary layer. Streamlining helps to reduce pressure drag.

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Pressure Drag vs Skin Friction Drag

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Aside: Separation

When a wing is at a high enough angle, the boundary layer cannot

hold on to the top surface any longer. When separation occurs,the wing is said to have stalled. A turbulent boundary layer can

remain attached more easily than a laminar one. Thus higher

Reynolds number leads to higher stall angle and, therefore, higher

maximum lift coefficient.

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Induced Drag

Net Aerodynamic ForceLift

Induced Drag

The action by the wing is actually down and slightly

forward, creating a reaction that is up (Lift) and

slightly rearward (Induced Drag). The amount of

induced drag depends on the amount of lift

generated.

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Estimating Induced Drag

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Exercise - Total Incompressible Drag

The Embraer Brasilia is flying at the conditions given

in the previous exercise. What is the total drag of theaircraft?

b = 19.78 m m = 11,000 kg S= 39.4 m2

= 0.771 kg/m3 CDP= .022

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Major Concepts

Incompressible Drag Parasite drag from viscous effects

Induced drag dependent on lift

Parasite Drag Skin friction (increases with Reynolds Number)

Pressure drag (decreases with Reynolds Number)

Reynolds Number is a dimensionless quantity

Low Reynolds number (< 500,000) laminar boundarylayer; high Reynolds number (>500,000) turbulentboundary layer

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Major Concepts, cont.

Wing terminology

AR = b2/S= Aspect Ratio

Induced Drag depends on amount of lift produced

Definition of drag coefficient: