U = w = p = q = p = q = r = Qc = 0 Thus the equations of motion reduce to

0 = Xu. и + Xw. w – mgQ cos Qe + XBl. Bl

0 = Zu. и + Zw. w – mgQ sin Qe + ZBl. Bl 0 = Mu. и + Mw. w + MBi. Bi

If it is assumed that the trimmed pitch attitude is small, such that cos Qe = 1 and sin Qe = Qe, then:

0 = Xu. и + Xw. w – mg Q + XBi. Bl 0 = Zu. и + Zw. w – mgQQe + ZBi. Bl 0 = Mu. и + Mw. w + MBi. Bi Thus:

w=–M – im„ .и+MBl. b ]

Mw

and assuming that the pitch attitude change is small:

0 = Zu. и + Zw. w – mgQQe + ZBl. Bl

Z

= Zu. и – M [Mu. и + MBi. Bl ] + ZBi. Bl

M w

0 = Mw Zu. и – Zw Mu. и – Zw MBl . Bi + Mw ZBl . Bi

= u[mw Zu – Zw Mu ] – Bi [Zw MBl – Mw ZBl ]

Bi = [Mw Zu – Zw Mu ]

U [ZW MBl – Mw ZBl ]

Since there is little change in vertical force with changes in longitudinal cyclic:

dB = Mw Zu – Zw Mu

du Zw MBi

this equation will only be valid if the pitch attitude required to hold the off-trim speed is not large when compared with the trim speed. Once again it should be appreciated that the presence of MBi (longitudinal cyclic control power) in the above equation means that the test cannot be used to evaluate the magnitude of the static stability (Mu) since the amount of stick deflection required is dependent on the control power. In addition it should be noted that the above equation contains a contribution from Mw. Only small excursions from the trim speed can, therefore, be tested since if large rates of descent or climb are experienced the results will be corrupted by Mw effects.

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