General explicit expressions are derived for the harmonic forces produced at the hub by an n-bladed unbalanced helicopter rotor. Imbal¬ances due to property differences, among the blades and to nonuniform spacing between the blades are considered. It is shown mathematically that these two types of imbalances have equivalent effects. Forces applied to the hub both in and normal to the plane of rotation of the blades are analyzed. The additional first harmonic forces transmitted to the hub in the plane of rotation by an asymmetric rotor-blade system may be especially appreciable due to the influence of the high static centrifugal forces exerted by each blade. Simple expressions are derived for the amplitudes of these forces. The effect of small simultaneous property and spacing imbalances can be obtained by superposition of the separate effects of each imbalance. Numerical examples are given throughout to illustrate the order of magnitude of the results obtained herein. For convenient reference, an analysis of the forces transmitted to the hub by a balanced rotor of n blades is given.
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