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.

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.

A variational procedure is developed, in the form of an extension of the Rayleigh‐Ritz method, leading to a rapid estimation of the flapwise vibration modes and frequencies of a helicopter rotor blade. The initial data required are the blade mass and stiffness distribution and the angular velocity of the rotor blade. The normal modes and frequencies are subsequently used to determine blade shapes in flight. The aerodynamic forces only enter at a late stage of the analysis, and the effect of differing flight conditions is readily assessed. The method makes extensive use of matrix formulation and particularly lends itself to electronic computation techniques. A numerical example is given for the special case of constant spanwise blade mass distribution, although the method may readily be extended to cover this restriction. The bending moment distribution is also worked out, and flexible and rigid blades are compared.

The following series of articles presents a new geometrical system of determining the lateral stability of aeroplanes. The method is intended to appeal particularly to engineers on account of two advantages: it is simple and rapid in operation, and gives a clear insight into the several factors governing the stability. Thus, whereas in the classical method stability calculations entail the drawing and analysis of quartic curves, the results are here obtained, and with greater generality, merely by the use of curves of the second degree. Furthermore, the effects of typical changes in design characteristics may easily be assessed with the minimum of effort. The fundamental analysis is essentially mathematical and follows the treatment first laid down by G. H. Bryan in 1911 and since developed by Bairstow, Glauert, Jones and Bryant. Physical explanations are included where possible to amplify the underlying principles.

IT is readily understood that no instrument or measuring device can be entirely free from errors duo to physical imperfections of manufacture. Gyroscopes in particular are affected in this way, requiring, as they do, complete absence of bearing friction if use is to be made of their property of preserving fixity in space of the direction of their spin axis when free from external forces. The impossibility of achieving this ideal condition results in a small degree of drift of the gyro‐axis, and detracts from the value of a gyroscope as a direction indicating device. In spite of this deficiency, in cases where steadiness of pointer reading is of prime importance, standard gyroscopic directional instruments serve a very useful purpose, provided the necessity of applying corrections at appropriate time intervals is recognized and observed. Latterly, development along the lines of automatic compensation has overcome this defect, and has led to the advent of the ‘monitored’ gyroscopic compass.