Question

The equation \(\frac {1}{2\pi } \int_0^c \frac {\gamma(\xi)d\xi}{x-\xi}\)=V∞α is called the fundamental equation of thin airfoil theory for______

(a) Cambered airfoils only

(b) Symmetric airfoils only

(c) All thin airfoils

(d) Symmetric and positively cambered airfoils

I got this question by my college director while I was bunking the class.

I need to ask this question from The Cambered Airfoil in portion Incompressible Flow over Airfoils of Aerodynamics

Answer 1

Correct choice is (b) Symmetric airfoils only

To elaborate: The original fundamental equation of thin airfoil theory is \(\frac {1}{2\pi } \int_0^c \frac {\gamma(\xi)d\xi}{x-\xi}\)=V∞(α-\(\frac {dz}{dx}\)). For the symmetric airfoils, \(\frac {dz}{dx}\)=0 and so \(\frac {1}{2\pi } \int_0^c \frac {\gamma(\xi)d\xi}{x-\xi}\)=V∞α is valid. While for the cambered airfoils \(\frac {dz}{dx}\) is non-zero.