Arbitrary Motion of a Thin Wing

For elliptically loaded thin wings it is possible to determine the indicial admittance functions like Wagner and Kussner functions for arbitrary motions of wing. Accordingly for the sudden angle of attack change from 0 to ao we have the Wagner function to give the lift creation

cL (s) = 2nao/(s) (4.59)

and, similarly for the effect of the gust with magnitude wo on the lift change as the Kussner function

Wr-,

cLg(s) = 2paa—v(s) (4.60)

Here, s is the reduced time based on the root half chord. The Jones approach for the Wagner and Kussner functions are given in exponential form which has coefficients and exponents given in Table 4.1 and their plots are provided for a wing with an aspect ratio of 6 (Fig. 4.5).

Table 4.1 The Wagner and the Kussner functions variations with respect to aspect ratio

AR bo b1 b2 b3 b1 b2 b3

= bo – bie_bi°s – b2e~bs – Ьзє-Ьs