Effect of Structural Flexibility

Many vehicles when flying near their maximum speed are subject to important aero – elastic phenomena. Broadly speaking, we may define these as the feedback effects upop the aerodynamic forces of changes in the shape of the airframe caused by the aerodynamic forces. No real structure is ideally rigid, and aircraft are no exception. Indeed the structures of flight vehicles are very flexible when compared with bridges, buildings, and earthbound machines. This flexibility is an inevitable characteristic of structures designed to be as light as possible. The aeroelastic phenomena which result may be subdivided under the headings static and dynamic. The static cases are those in which we have steady-state distortions associated with steady loads. Examples are aileron reversal, wing divergence, and the reduction of longitudinal stability. Dy­namic cases include buffeting and flutter. In these the time dependence is an essential element. From the practical design point of view, the elastic behavior of the airplane affects all three of its basic characteristics: namely performance, stability, and struc-

tural integrity. This subject occupies a well-established position as a separate branch of aeronautical engineering. For further information the reader is referred to one of the books devoted to it (Bisplinghoff, 1962; Dowell, 1994).

In this section we take up by way of example a relatively simple aeroelastic ef­fect; namely, the influence of fuselage flexibility on longitudinal stiffness and con­trol. Assume that the tail load L, bends the fuselage so that the tail rotates through the angle Да, = – kL, (Fig. 3.9) while the wing angle of attack remains unaltered. The net angle of attack of the tail will then be

a, = awb – e – i, ~ kL, and the tail lift coefficient at 8(, = 0 will be

C/„ = а, a, = a,(aKh – є – і, – kL,)
But L, = CLihpV2S„ from which
CL, = a,(awb -€~i,- kClJzpV2Sl)	(3.5,1)
Solving for CLi, we get
Cl,
CL, p wb ^ if)	(3.5,2)

1 + ka, S,~V2 2

Comparison of (3.5,2) with (2.3,13) shows that the tail effectiveness has been re­duced by the factor 1/[1 + ka,(p/2)V2S,]. The main variable in this expression is V, and it is seen that the reduction is greatest at high speeds. From (2.3,23) we find that the reduction in tail effectiveness causes the neutral point to move forward. The shift is given by

Да, _ / де

д h„ =—- VH 1 – — (3.5,3)

a da

where

The elevator effectiveness is also reduced by the bending of the fuselage. For, if we consider the case when 8e is different from zero, then (3.5,1) becomes

Cu = a,(awb – є-i, – kC[ppV2Sl) + ae8e

and (3.5,2) becomes

c = at(<xWb – e – it) + ae8e L’ 1 + ka, hpV2St

Thus the same factor 1/(1 + ka, p/2V2S,) that operates on the tail lift slope a, also mul­tiplies the elevator effectiveness ae.