Question

Given the component of free-stream velocity in the direction perpendicular to the camber line is 15 units and the velocity induced by the vortex sheet is 4 units at a point. The angle of attack for the thin airfoil is α. Then which of the following condition is true in case of thin airfoil theory?

(a) 15sinα+4=0

(b) 15+4=0

(c) 15cosα+4=0

(d) 15tanα-4=0

The question was posed to me in an online interview.

My doubt is from The Symmetric Airfoil in chapter Incompressible Flow over Airfoils of Aerodynamics

Answer 1

Right answer is (b) 15+4=0

To explain: In thin airfoil theory, the camber line has to be a streamline. Thus, the component of velocity in the normal direction to the camber line is zero at any given point. This means the sum of velocity components by the free stream velocity and the induced velocity is zero.