Question

The correct formula for the Fourier sine series appearing in the solution of thin airfoil theory is_____

(a) An=\(\frac {2}{\pi }\int_0^{\pi }\frac {dz}{dx}\) cos⁡n∅ d∅

(b) An=\(\frac {1}{\pi }\int_0^{\pi }\frac {dz}{dx}\) cos⁡n∅ d∅

(c) An=\(\frac {2}{\pi }\int_0^{2\pi }\frac {dz}{dx}\) cos⁡n∅ d∅

(d) An=α-\(\frac {1}{\pi }\int_0^{\pi }\frac {dz}{dx}\) cos⁡n∅ d∅

I had been asked this question in my homework.

Query is from The Cambered Airfoil in section Incompressible Flow over Airfoils of Aerodynamics

Answer 1

The correct answer is (a) An=\(\frac {2}{\pi }\int_0^{\pi }\frac {dz}{dx}\) cos⁡n∅ d∅

The explanation is: From the general solution of thin airfoil theory we have An=\(\frac {2}{\pi }\int_0^{\pi }\frac {dz}{dx}\) cos⁡n∅ d∅ and A0=α-\(\frac {1}{\pi }\int_0^{\pi }\frac {dz}{dx}\) cos⁡n∅ d∅ where the limits are 0≤∅≤π.