Question

Which of the following is the correct solution of the transformed fundamental equation of aerodynamics for a symmetrical airfoil?

(a) γ(θ)=2αV∞\(\frac {sin⁡\theta }{1+cos\theta }\)

(b) γ(θ)=2αV∞\(\frac {1+cos\theta }{sin⁡\theta }\)

(c) γ(θ)=2αV∞\(\frac {1-cos⁡\theta }{sin\theta }\)

(d) γ(θ)=2αV∞\(\frac {cos\theta }{sin\theta }\)

The question was posed to me during an internship interview.

This is a very interesting question from The Symmetric Airfoil topic in section Incompressible Flow over Airfoils of Aerodynamics

Answer 1

Right choice is (b) γ(θ)=2αV∞\(\frac {1+cos\theta }{sin⁡\theta }\)

The explanation is: The solution of the fundamental equation of thin airfoil theory is obtained using the transformation of coordinates. We have α and V∞ and using the standard integrals we can find a solution for γ(x) as γ(θ)=2αV∞\(\frac {1+cos\theta }{sin⁡\theta }\) where 0≤θ≤π for 0≤x≤c.