Collective pitch derivatives

When the collective pitch, 0c, is increased, each blade experiences an increase in lift and the total rotor thrust is increased. The pitch increase also leads to an increase in flapback of the disk in forward flight and a subsequent nose-up pitching moment. This helps to explain the derivatives:

(1) Forward force due to collective (X0c). The forward force due to collective is usually negligibly small.

(2) Vertical force due to collective (Z0c). An increase in collective always produces
an increase in thrust ( — ve Z) so is always negative. It is known as the collective control power derivative, or the heave control power.

(3) Pitching moment due to collective (M0c). As outlined above, the increased flapback and thrust combine to produce a nose-up pitching moment in forward flight so the derivative is positive. As the disk does not flapback in the hover, M0c is zero in this flight regime, provided the horizontal stabilizer is unloaded and the tail rotor is conventional (not canted). Cyclic pitch derivatives

Remembering that only fore/aft cyclic are being considered, any such pitch change will result in a change in the disk tilt, also fore/aft, and of the thrust vector. Hence, a pitching moment will be generated, nose-down for forward stick deflection and nose – up for rearward stick. The corresponding cyclic derivatives are:

(1) Forward force due to longitudinal cyclic (XBl). The forward force due to longi­tudinal cyclic is usually negligible.

(2) Vertical force due to longitudinal cyclic (ZBl). The vertical force due to longi­tudinal cyclic is negligible.

(3) Pitching moment due to longitudinal cyclic (MBl). Pitching moments are generated as described above, and MBl is known as the pitch control power derivative, or the ‘longitudinal cyclic control power’.

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