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Of the parameters that may be adjusted to give the helicopter freedom from ground resonance, that which is ignored most frequently is Λ3 (ratio of effective rotor mass to effective fuselage mass). This is because it is usually impractical to change it on an existing helicopter. However, if it is considered sufficiently early in the design of the fuselage, the ground resonance problem can be greatly reduced or even eliminated by the consideration of this parameter alone. The paper investigates the effects of fuselage dynamic properties on Λ3 and also gives results for the effect of Λ3 on the stability boundaries for some simple helicopter configurations.

A method is developed or drawing ground resonance stability boundaries in the (?1, ?) plane for arbitrary values of the parameters ??, A1 and Aa. The current values of ?1 and ? are expressed simply and directly in terms of the co‐ordinates (Y, Z) of points lying on a parabola whose equation involves ??, A1 and A3. The position of the intersections of this parabola with a certain unique curve in the (Y, Z) plane determines into which of three classes each stability boundary falls. All stability boundaries split up into two separate branches, and only in one class of boundaries do the branches align themselves in such a way as to permit the possibility of stability for all rotor speeds ?. A method is given showing how ??, A1 and A3 may be determined to achieve this effect.

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.

The equations of motion developed by R. P. Coleman have been evaluated for a particular helicopter configuration and a large number of different combinations of rotor and fuselage damping. These results are displayed graphically and reveal the dependence of the unstable range on rotor and fuselage damping. Some of the conclusions are in disagreement with those reached by Coleman. Both viscous and friction rotor dampers are considered.

SINCE in the context of this article it is the civil air transport application of rotorcraft which is of interest, only large passenger carrying rotorcraft are considered.

The basis and the extent of theoretical induced velocity calculations are reviewed. The theory is then applied to interference problems involving additional rotors, wings, and tails in the flow. For such cases, the interference effects can be calculated with acceptable accuracy. For hovering, superposition is used to introduce ground effect into the calculations. The resulting flow field offers a qualitative explanation of several previously observed phenomena. It is shown that, because of assumptions inherent in the analysis, the present induced‐flow theory cannot be used to predict the detailed aerodynamic loading on the rotor blades.