The Avoidance of Ground Resonance: Exact Stability Criteria for Helicopters on Isotropic Supports

An examination is made of the way in which the ground resonance properties of a helicopter depend on the fuselage damping, blade damping, drag hinge offset, inter‐blade spring stiffness, blade mass and angular velocity of the rotor as specified by the parameters λƒ, λβ, Λ1, Λ2, Λ3 and Ω respectively. A direct method of drawing stability boundaries in the (Ω, λβ) plane is developed, and the geometry of these boundaries as the remaining parameters vary is studied theoretically at length. Arising out of the geometry, the validity of Coleman's criterion for stability is examined, and it is shown that the requirement that the product λƒ,λβ should have a certain minimum value is not itself sufficient to ensure stability for all Ω. The condition can be made sufficient by a proper and unique choice of the individual values of ?f and ??, and these values are found in terms of Λ1, Λ2, and Λ3. All other cases of stability require a larger value of the product λƒ, λβ. An alternative criterion for stability is developed which gives the minimum value of λƒ capable of ensuring stability for all Ω. This, and the preceding criterion, are mathematically exact, and follow from Coleman's equations of motion as applied to the case of a helicopter on isotropic supports. A brief account is also given of the case of a rotor having inter‐blade friction damping as against the viscous damping previously assumed.