Page 569 - Aircraft Stuctures for Engineering Student
P. 569
550 Elementary aeroelasticity
Substituting for T in Eq. (13.26) from torsion theory (7‘ = GJd8/dz) and rearranging
we have
-+ e=- ;pv2c2 [ acl PZ acl - *f,cz)(] (13.27)
d28 ;pv2ec‘acl/aa
e- - - e-fa(z)C
dz2 GJ GJ aa v at aC
Writing
we obtain
It may be shown that the solution of Eq. (13.28), satisfying the boundary conditions
8=0 atz=O and dO/dz=O atz=s
is
sin X(s - sl)
]
x [fa(z){ 1 - cos X(z - SI)} - cos xr sinXz 5 (13.29)
where
cos X(z - sl) = 0 when z < s1
The spanwise variation of total local wing lift coefficient is given by strip theory as
(13.30)
where 8 is known from Eq. (13.29) and a is the steady flight wing incidence.
The aileron effectiveness is often measured in terms of the wing-tip helix angle
(ps/ V) per unit aileron displacement during a steady roll. In this condition the rolling
moments due to a given aileron deflection, [, wing twist and aerodynamic damping
are in equilibrium so that from Fig. 13.6(a) and Eq. (13.23) and noting that ailerons
on opposite wings both contribute to the rolling, we have
(13.31)
from which
(13.32)
