The longitudinal stability of a tethered rotary-winged aircraft

Abstract

A linearised mathematical representation of a tethered rctorcraft is developed in order to study the influence of various parameters on the machine’s longitudinal stability. The investigation is concerned principally with a vehicle having two side-by-side contrarotating rotors and a large tailplane. The first part of the thesis consists of a detailed development of the trim equations, and of linearised equations of longitudinal motion which are written in Earth-fixed axes. Aerodynamic derivatives are used to account for the perturbations to rotor and tailplane aerodynamic forces. Dcwnwash lag derivatives are developed using a hcrseshcevortex- plus-wake representation of the flew field of a rotor in forward flight. Because the analysis concentrates on the vehicle's dynamics, a simple quasi-static representation of the single tethering cable is adopted. This approach is adequate provided that the cable mass is a small fraction of the vehicle's mass. When the tether is straight and may be considered inelastic, the Routh-Hurwitz criteria predict that the machine can be made inherently stable in hcver by increasing the thrust tc weight ratio, provided that the cable length dees not exceed a certain small value. The tether must also be attached above the machine's centre of mass tc prevent an aperiodic "pendular" divergence. The same stability criteria show that the machine will be unstable in hcver when the tethering cable is long. When the tether is curved or elastic, simple analytic stability criteria cannot be obtained. Instead, in the second part of the thesis, the influence of various parameters on the vehicle's behaviour is examined by numerically solving particular characteristic equations. The numerical studies show that many vehicle ccnfigurations can be stable in wind, but most are unstable in hcver. The cable attachment point height remains a dominant parameter for hover flight, and in wind. Instability in hover often takes the form of a coupled pitch-translation oscillation similar to that observed in a conventional helicopter. Attaching the tether below the centre of mass can stabilise this oscillation, but results in an aperiodic divergent "pendular" mode. In wind, a tailplane of suitable size will impart asymptotic stability to the system. In strong winds a long tethering cable will be highly curved. The vehicle’s dynamic behaviour is then substantially unrelated to the cable profile. The natural modes shew little dependence on the machine’s geometry, and are strongly influenced by the horizontal tail surface.