There is an important aeroelastic effect on roll control by ailerons that is significant on most conventional airplanes at both subsonic and supersonic speeds. This results from the elastic distortion of the wing structure associated with the aerodynamic load increment produced by the control. As illustrated in Fig. 2.23, the incremental load caused by deflecting a control flap at subsonic speeds has a centroid somewhere near the middle of the wing chord. At supersonic speeds the control load acts mainly on the deflected surface itself, and hence has its centroid even farther to the rear. If this load centroid is behind the elastic axis of the wing structure, then a nose-down twist of the main wing surface results. The reduction of angle of attack corresponding to 8a > 0 causes a reduction in lift on the surface as compared with the rigid case, and a consequent reduction in the control effectiveness. The form of the variation of C, s with pV2 for example can be seen by considering an idealized model of the phenomenon. Let the aerodynamic torsional moment resulting from equal deflection of the two ailerons be T(y) hpV28a and let T(y) be antisymmetric, T(y) = — T(—y). The
twist distribution corresponding to T(y) is в(у), also antisymmetric, such that (Xy) is proportional to T at any reference station, and hence proportional to pV28a. Finally, the antisymmetric twist causes an antisymmetric increment in the lift distribution, giving a proportional rolling moment increment AC, = kpV28a. The total rolling moment due to aileron deflection is then
ДС; = (C4)ng, A + kpV28a (3.13,1)
and the control effectiveness is
ClSa = (QJrigid + kPV2 (3.13,2)
As noted above, (C, So)rigid is negative, and к is positive if the centroid of the aileron- induced lift is aft of the wing elastic axis, the common case. Hence C, S j diminishes with increasing speed, and vanishes at some speed VR, the aileron reversal speed. Hence
0 = (QJrigid + kpV2R
k = -(clSaigiAPv2
Substitution of (3.13,3) into (3.13,2) yields
This result, of course, applies strictly only if the basic aerodynamics are not Mach – number dependent, i. e. so long as VR is at a value of M appreciably below 1.0. Otherwise к and (C/s )rigid are both functions of M, and the equation corresponding to
(3.13,4) is "
C/«„(M) — (C;5a)rigid(M) — ^ (C/5u)ngid(MK)
where Мл is the reversal Mach number.
It is evident from (3.13,4) that the torsional stiffness of the wing has to be great enough to keep VR appreciably higher than the maximum flight speed if unacceptable loss of aileron control is to be avoided.