Question

?(?) = ??(? − 1)(? − ?) 

where k > 0 and b > 0. Depending on the choice of b, this equation can represent a reflex aerofoil in which the mean camber line curves upward toward the trailing edge. To check whether the aerofoil is reflex, one checks to see whether the above curve has both a maximum and minimum (with the maximum occurring ahead of the minimum). 

(i) Obtain the value of x where corresponding to maximum camber, and if appropriate the value of x corresponding to minimum camber. 

(ii) Evaluate the coefficients A0, A1, and A2 as defined in thin aerofoil theory.

(iii) Hence determine, the lift coefficient, CL, the pitching moment coefficient about the aerodynamic centre, CmAC, and the centre of pressure of the aerofoil. 

The values of k, b and incidence α are given by k= 0.15 b= 0.7 a=3

Hint: The following information will be useful in carrying out the integrations: 

???2? = 1 /2 (1 + ???2?)            ???????2? = 1/2 (???? + ???3?) 

where θ is related to x by:

 ? = ?/2 (1 − ??? ?)