Consider a straight wing that is flexible only in torsion. The wing root is embedded in the wall of a wind tunnel, the other end free. The torsional stiffness is GJ = 4 Nm2, the span is 1 m and the chord is 0.25 m. Assume the aerodynamic center at ¼ of the chord and the elastic axis at half the chord. Assume any data or condition not provided, justify your choice. 1. Determine the expression and value of the dynamic divergence pressure. 2. For dynamic pressures less than divergence, determine and plot the evolution of the lift distribution (along the span) with increasing dynamic pressure. Analyze and justify the results. The. For dynamic pressure equal to half the divergence dynamic pressure, determine the percentage change in lift (relative to the rigid case) caused by aeroelastic effect. 3. Calculate and graph the evolution of wing shape with increasing dynamic pressure from zero velocity to divergence dynamic pressure. Analyze and justify the results.

def lift_dist(q, GJ, c, L, x, c_a=0.25, c_e=0.5):
    # q = dynamic pressure
    # GJ = torsional stiffness
    # c = chord 
    # L = span
    # x = distance from the root
    # c_a = aerodynamic center
    # c_e = elastic axis
    
    q_c = (4*L**2*GJ)/(numpy.pi*c**2) #dynamic divergence pressure
    
    #parameters
    epsilon_t = (q*c*c_a)/(GJ*c_e)
    epsilon_c = (4*q*L**2)/(numpy.pi*c**2*GJ)
    theta_t = (numpy.pi*x)/(2*L)
    
    #lift distribution
    cl_dist = (1/2)*(1-numpy.cos(theta_t))*epsilon_c*(1+2*ep