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16/08/2015 AE 6030 : Advanced Potential Flow, Class Notes

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AE 6030 : Advanced Potential Flow, Class NotesSection # 1

Basic Concepts and Results in Aerodynamics

Freestream Vector: Velocity of the fluid far ahead of the object in the flow, undisturbed by the

presence of the object.

Lift: Force perpendicular to the freestream, acting on the aircraft.

Lift = dynamic pressure X planform area X lift coefficient.

Drag: Force along the freestream, acting on the aircraft.

Drag = dynamic pressure X planform area X drag coefficient.

Dynamic Pressure:

or, ,

where is the undisturbed freestream density, is freestream speed , is the ratio of specific heats and is

the freestream Mach number.

Aspect Ratio:

where is the b is the span and is the S planform area of the wing. For a 2-D airfoil

Lift-Curve Slope of an airfoil:

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16/08/2015 AE 6030 : Advanced Potential Flow, Class Notes

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This is derived from "thin-airfoil theory" in low-speed flows where Mach number is close to 0.

In subsonic flow,

In supersonic flows,

Finite Wing Vortex system

Pressure difference between upper and lower surfaces must vanish at tips of the wing. There are twoeffects of this,

a ) Loss in lift, compared to 2-D airfoils.

b) Induced drag, i.e. drag induced by the force vector tilting backwards as a result of the induceddownwash..

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16/08/2015 AE 6030 : Advanced Potential Flow, Class Notes

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Important points1. Since induced drag is directly related to the lift it can be calculated by the same mathematicalformulation used to calculate lift.2. Does not require consideration of viscosity.3. No induced drag on 2-D airfoils under steady conditions.4. At finite Aspect ratios,

5. Ideal elliptic lift distribution implies minimum induced drag , i.e, efficiency e=1.

6. At low Mach numbers drag on well designed aircraft is primarily due to induced drag.

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