AERODYNAMIC TRANSFER FUNCTIONS
Finally, it should be remarked that there is no need to accept the small inaccuracy associated with the use of unsteady derivatives such as CL&, etc. In Sec. 5.11 it was shown how the use of aerodynamic transfer functions could avoid this difficulty entirely, and equations (5.14,1 to 3) were presented for this purpose. To obtain a transfer function from the indicial response, (5.11,6) can be applied. Thus if the step-function response of Fig. 7.17 is designated AL(t(t), then
®Za(S) — 6v^Za(‘S)
and similarly for all other transfer functions that appear in (5.14,1 to 3).
When the information available is in the form of a frequency-response analysis or measurement, then the transfer function can be obtained from it directly. From (3.4,25) we have the general relation for frequency response of a linear system in terms of the transfer function. Thus, let Gav(s) be the transfer function relating any aerodynamic coefficient Ca to any state variable v and Gav(ik) be the frequency-response vector giving Ga for periodic v. G(s) is obtained from G(ilc) by replacing ik by s, or к by —is.