Longitudinal stability of a hovering, tethered rotorcraft

Linearized equations describing the perturbed longitudinal motion of a tethered rotorcraft are presented. The tethering cable is assumed to be straight and inextensible. This permits development of two degree-of-freedom equations which admit cable tension variations. Routh's criteria are applied to a simplified stability quartic for hovering flight in an analytic search for stable configurations. The cable length, equilibrium tension, and point of attachment strongly influence the stability of perturbed motion. If the cable is short, the machines considered may be inherently stable. This does not appear to be possible for hovering flight on very long cables. Numerical solutions to the complete stability quartic show good agreement with approximate Routh's-criteria predictions.