Page 563 - Aircraft Stuctures for Engineering Student

544 Elementary aeroelasticity

where T is the applied torque at any spanwise section z and AL and AMo are the lift
and pitching moment on the elemental strip acting at its aerodynamic centre. As Sz
approaches zero, Eq. (13.4) becomes
dT dL dMo
-+ ec-+- = 0 (13.5)
dz dzdz
In Eq. (13.4)
AL = -pV2cSz-(a OCl + e)
1
2 Sa
where dcl /acu is the local two-dimensional lift curve slope and

in which c,,~ is the local pitching moment coefficient about the aerodynamic centre.
Also from torsion theory (see Chapter 3) T = GJ dO/dz. Substituting for L, Mo and T
in Eq. (13.5) gives
-+ - (13.6)
d28 4 pV2ec2 (acl /&)e - - $ p V2e? (del /da)a - i pV2c2c,,o
dz2 GJ GJ GJ
Equation (13.6) is a second-order differential equation in 0 having a solution of the
standard form
(13.7)

where

and A and B are unknown constants that are obtained from the boundary conditions;
namely, 6 = 0 when z = 0 at the wing root and de/& = 0 at z = s since the torque is
zero at the wing tip. From the first of these

and from the second

Hence
6 = [ e(zTaa) I (13.8)
+a (tanhsinAz+cosXz- 1)

or rearranging

(13.9)