Data obtained by Westland Helicopters from a simulation of a teetered tail rotor shows instability at sufficiently high forward velocity of the aircraft, and also indicates a rotor natural frequency at nearly three times the rotor rotation frequency. The Study Group was asked to provide an explanation of these observations. Using a linear model for the teetering motion and the umbrella `flap' mode of the tail rotor blades, the Study Group showed that parametric terms, containing the forward velocity, provide excitation at frequencies which are once and twice the blade rotation frequency. Taking the classical damped Mathieu equation as a `toy' model of the system, and observing the near 3:2 ratio between the natural rotor frequency and the second excitation frequency, suggested that the observed instability arises as the forward velocity passes into the 3:2 resonance tongue of the stability map of the Mathieu equation. The current `snapshot' eigenvalue method, in use at Westland Helicopters, does not capture this instability. The Study Group recommended instead that Floquet theory be applied to a time-dependent linearised model.

Problem presented by
Alan Irwin, Westland Helicopters

Study Group contributors
Andre Aigner (University of Exeter)
Sasha Balanov (University of Lancaster)
Alan Champneys (University of Bristol)
Rich Eyres (University of Bristol)
Mike Friswell (University of Bristol)
Jens Gravesen (Technical University of Denmark)
Chris Halse (University of Bristol)
Poul Hjorth (Technical University of Denmark)
Natalia Janson (University of Lancaster)
David Lloyd (University of Bristol)
John Ockendon (University of Oxford)
Sasha Silchenko (University of Lancaster)
David Wagg (University of Bristol)
Charles Wang (University of Lancaster)
Dave Wood (University of Warwick)
Jenny Wright (University of Bath)
Xu Xu (University of Aberdeen)