In Ref. (1) the dynamics of a rotor with high offset flapping hinges were considered, for twisted and tapered blades with ?3 coupling between flapping and feathering. In the present paper simple expressions are derived for the hub pitching and rolling moments of such a rotor, and it is shown that these moments must be balanced either externally (by aerodynamic surfaces for example) or internally by suitable inclination of the mechanical axis (Eqs. (7) and (8)). The relevant expression for total rotor moment is given in Eq. (17). In order to arrive at a solution, the vertical force acting on a single flapping pin was evaluated, and this is given by Eq. (5). This is particularly interesting, apart from stress calculations, in that it shows the mechanism whereby a blade which is out of track in the tip path plane can cause a first harmonic vertical vibration in forward flight. It is shown that a two‐bladed high offset rotor will always experience second harmonic hub vibration unless it is balanced out by inclination of the mechanical axis. In general, the mechanical axis position is seen to be an important parameter in both vibration and hub moments; a fact which has hitherto passed unrecognized except for some unpublished work at the Royal Aircraft Establishment by Mr P. Brotherhood. This does not necessarily imply that mechanical axis inclination is a panacea to cure all ills. By far its most useful effect lies in suppressing in‐plane vibration, to which vertical vibration is usually of second order importance. This is, of course, a separate subject.
Payne, P.R. (1955), "Hub Moments and Forces of a High Offset Rotor: Derivation of the Hub Pitching and Rolling Moments of a High Offset Rotor With Twisted and Tapered Blades", Aircraft Engineering and Aerospace Technology, Vol. 27 No. 1, pp. 14-15. https://doi.org/10.1108/eb032512Download as .RIS
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