Equivalent Blade Chords and Weighted Solidity

For blades that are nonrectangular in planform the local solidity cr(r) varies along the blade span. In this case, to find the thrust coefficient we must use

(3.140)

where the local solidity of the blade appears inside the integral sign. Because the chord varies along the blade span, then the rotor solidity must be written as

(3.141)

As discussed by Gessow & Myers (1952), the purpose of weighted solidities is to help compare the performance of several rotors that may have different blade planforms, for example, rotors with different amounts of taper. The main idea is to generate an equivalent rectangular rotor blade that takes into account the fundamental aerodynamic effects of varying blade chord. The concept, however, is not applicable strictly when applied to other than simple planform shapes. The weighted solidity concept is similar to the mean geometric and aerodynamic chords used in fixed-wing analysis, where an equivalent rectangular wing is derived. In helicopter analyses, two forms of weighted solidities may be used, namely, thrust weighted solidity and power (or torque) weighted solidity. Before defining these quantities, it is instructive to recall the concepts of mean chords used in fixed-wing analyses.