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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»

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.


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