Page 568 - Aircraft Stuctures for Engineering Student

13.2 Control effectiveness and reversal 549

t’

X
>
Lines

z’
A’ T

az
cc;y, +-!!I
dz
( b)
Fig. 13.6 Aileron effectiveness and reversal speed (finite wing).

effects we consider the antisymmetric lift and pitching moment produced by aileron
deflection. Thus, in Fig. 13.6(b), the forces and moments are changes from the level
flight condition.
The lift AL on the strip shown in Fig. 13.6(b) is given by

(13.23)

where dcl /aa has been previously defined and ac, /a< is the rate of change of local
wing lift coefficient with aileron angle. The function fa(.) represents aileron forces
and moments along the span; for 0 < z < sl,fa(z) = 0 and for s1 < z < S,fa(Z) = 1.
The pitching moment AMo on the elemental strip is given by

AM0 = 1 TpV2?6z-fa(z)E o ( 1 3.24)
acm
a<
in which acm,/a< is the rate of change of local pitching moment coefficient with
aileron angle.
Considering the moment equilibrium of the elemental strip of Fig. 13.6(b) we
obtain, neglecting wing weight

c ~ + ALec + AMo = 0 (13.25)
z
dz
or substituting for AL and AMo from Eqs (13.23) and (13.24)