2-D Inviscid, Linearized, Thin Airfoil Theories

14.4.1.1 Incompressible Flow (M0 = 0)

Thickness Effect

In Thin Airfoil theory, what type of singularity distribution is used to represent thickness?

Which forces and moment coefficients are not zero in the symmetric problem associated with thickness, Ci, Cm, o, and Cd?

Is the pressure coefficient Cp affected by thickness? Explain.

Camber Effect

The Selig 1223 has a mean camber line which is parabolic to a good approximation, and a relative camber dm = d/c = 0.086.

Write the expressions of C; and Cm, o in terms of a and dm (Use results derived in class).

Find the angle of zero lift, (a)Cl=0.

What are the values of the following coefficients in the linear expressions of the lift and moment curves:

dCl _ dCm, o „

~j 5 Cl07 5 Cm, o0

da da

Sketch the flow past the mean camber line at a = 0. Explain.

Equilibrium About an Axis

If a hinge is placed at the nose of the Selig 1223 and the profile is allowed to rotate freely about it, what would the equilibrium angle be in deg (neglect weight)?

Is the equilibrium stable? Why?

Where is the center of pressure at equilibrium?

Sketch the free-body diagram of the profile at equilibrium, including the reaction, Cr of the hinge.

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