Higher Harmonic Control

In forward flight with a rotor operating under first-order cyclic control, a considerable proportion of the lifting capacity of the blades has been sacrificed, as we have seen in Chapter 4, in order to balance out the roll tendency. The lift carried in the advancing sector is reduced to very low level, while the main load is taken in the fore and aft sectors but at blade incidences (and hence lift coefficients) well below the stall. This can be seen explicitly in a typical figure-of-eight diagram, for example that in Figure 6.1c. Little can be done to change the situation in the advancing sector, but in the fore and aft sectors, where the loading has only a minor effect on the roll problem, the prospect exists of producing more lift without exceeding stalling limits in the retreating sector. In principle the result can be achieved by introducing second and possibly other harmonics into the cyclic control law. The concept is not new: Stewart [17] in 1952 proposed the use of second – harmonic pitch control, predicting an increase of at least 0.1 in available advance ratio. Until the 1980s, however, the potential of higher harmonic control has not received general development. Overall the problem is not a simple one, as it involves the fields of control systems and rotor dynamics at least as extensively as that of aerodynamics. Moreover, the benefits could until now be obtained by less complicated means, such as increasing tip speed or blade area. As these other methods reach a stage of diminishing returns, the attraction of higher harmonic control is enhanced by comparison. Also, modern numerical methods allow the rotor performance to be related to details of the flow and realistic blade aerodynamic limitations, so that the prediction of performance benefits is much more secure than it was.

A calculation provided by Westland Helicopters illustrates the aerodynamic situation. The investigation consisted in comparing thrust performances of two rotors with and without second-harmonic control, of quite small amplitude – about 1.5° of blade incidence. Local lift conditions near the tip were monitored round the azimuth and related to the CL-M boundary of the blade section. The results shown in Figure 6.38 indicate that second-harmonic control gave an advantage of at least 0.2 in lift coefficient in the middle Mach number region appropriate to the disc fore and aft sectors.

Figure 6.38 Use of second-harmonic control: calculated example

This translated into a 28.4% increase in thrust available for the same retreating-blade boundary. A further advantage was that the rotor with second-harmonic control required a 22% smaller blade area than the data rotor, which, whether exploited as a reduction say from six blades to five or as a weight saving at equal blade numbers, would represent a considerable benefit in terms of component size and mission effectiveness.

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