Consider a uniform flexible, wind-tunnel wing model. The wing span is = 2 m and the chord length is c = 0.2 m. The wing is clamped at y = 0, and at y = , it is constrained by a torsional spring of stiffness K.

The torsional rigidity of the wing is constant and it is GJ = 23 N.m2; the sectional lift-curve slope is also constant and it is a = 2 rad-1; the rigid angle of attack is r = 3 deg and is uniform along the wing; also, cm0 = 0. Assume that the shear center and the centre of gravity for all airfoil sections along the wing are located at 0.5c and 0.45c, respectively, from the leading edge. Take the mass per unit length of the wing as m = 5 kg/m.

1. Obtain a parametric expression for the spanwise distribution of the elastic twist, (y). Validate the expression of the elastic twist for the above-mentioned configuration against those for a clamped-free wing and a clamped-clamped wing. To do so, you need to suitably set the value of K.

2. Calculate the divergence dynamic pressure, qD, and the divergence speed at

the sea level for = K/GJ = 0.1, 1, 10, and 1000.

3. Plot the distribution of (in deg) as well as lift per unit length L (in N/m) along the span for values considered above, at one-third of their corresponding qD, i.e. q = qD/3. Discuss the results.