Page 561 - Aircraft Stuctures for Engineering Student

542 Elementary aeroelasticity

L
t

AC

Fig. 13.2 Determination of wing divergence speed (two-dimensional case).

two-dimensional flow, as shown in Fig. 13.2. The torsional stiffness of the wing, which
we shall represent by a spring of stiffness K, resists the moment of the lift vector, L,
and the wing pitching moment Mo, acting at the aerodynamic centre of the wing
section. For moment equilibrium of the wing section about the aerodynamic centre
we have
Mo + Lec = KO (13.1)
where ec is the distance of the aerodynamic centre forward of the flexural centre
expressed in terms of the wing chord, c, and 8 is the elastic twist of the wing. From
aerodynamic theory
MO = ~~v’sccM,~, L = 4pv2scL

Substituting in Eq. (13.1) yields
$~V~S(CCM,O + ecCL) = KO

or, since

in which (Y is the initial wing incidence or, in other words, the incidence corresponding
to given flight conditions assuming that the wing is rigid and CL.o is the wing lift
coefficient at zero incidence, then

(a + e) = Ke
-pv2s CCM,~ + eCL:, + ec- acL aa 1
l
2 [
where aCL/aa is the wing lift curve slope. Rearranging gives

or

(13.2)