Question

Find the induced velocity in the direction normal to the camber line a point on where the slope is 0.087. Given the angle of attack is 5° and free-stream velocity is 20 units. Use thin airfoil approximation.

(a) 0

(b) 101.74 units

(c) 98.26 units

(d) 3.48 units

This question was posed to me by my school principal while I was bunking the class.

The query is from The Symmetric Airfoil topic in chapter Incompressible Flow over Airfoils of Aerodynamics

Answer 1

The correct answer is (a) 0

To explain I would say: For a thin airfoil, the sum of free stream velocity component (V∞) and the induced velocity normal to the camber line is zero. And for small angles, V∞n ≈ V∞(α-\(\frac {dz}{dx}\)) where α is the angle of attack in radians and \(\frac {dz}{dx}\) is the slope at that point. Solving, V∞n ≈ 20(0.087-0.087), this is equal to the induced velocity.