Mean Wing Chords

For a fixed (nonrotating) wing, the lift L on the wing of area S and total lift coefficient Ci is given by

(3.142)

where Ci is the local section lift coefficient, c is the local chord, and s is the semi-span – see Houghton & Carpenter (1993). We note that the wing area can be written as
where c is known as the standard mean chord or the geometric mean chord. Using this definition then

(3.144)

If an ideal, elliptically loaded wing with elliptical chord is assumed, then Q is constant along the wing, and so Q = Cl. This gives

(3.145)

which is the usual definition of mean chord used for fixed wings.

3.4.1 Thrust Weighted Solidity

Now consider the rotor case. The rotor-thrust coefficient can be written as

(3.146)

Assuming constant Q, as in the case of the fixed wing, gives

(3.147)

Therefore, based on this assumption the equivalent thrust weighted solidity is

(3.149)

This parameter takes into account the primary aerodynamic effect of varying planform, weighting the effects at the tip more heavily than stations further inboard. McVeigh & McHugh (1982) suggest a modification to the weighted solidity definition to take account of tip sweep. In this case, Eq. 3.148 is modified to read

(3.150)

where cr is now measured perpendicular to the local 1/4-chord line and A is the local s weep angle of the 1/4-chord from the blade reference axis. The proper validity of this latter expression, however, has not been confirmed.