THE FINITE AIRPLANE
The finite extent of the airplane is seen to be important when significant variations of gust velocity can occur between one point and other—e. g. between right and left wing tips, or between wing and tail. An example of these effects for a wing is seen in the experimental results of Nettleton (ref. 13.14), a sample of which is shown in Fig. 13.8. This is a rather extreme case in that the scale of the turbulence L is about equal to the wing chord. The aspect ratio is effectively infinite. Here w is the upwash measured a short
distance in front of the wing, L is the lift measured on a small strip of wing, Ay is the spanwise separation of two lift strips, or of one strip and the upwash probe, and t* is the time delay for which JtwIi(Ay, r) is a maximum. A relatively small correlation length for w is seen to lead to a larger correlation length for (w, L) and a still larger one for (L, L).
To allow for such effects, i. e. to remove altogether or in part the limitations we found above on wave number, naturally entails some cost in additional complexity of analysis or experiment. We outline below the principles of five methods of doing this that seem adequately to span the spectrum of possible approaches, although they are not all-inclusive. In all the analysis methods the approximation is made that the airplane has no significant z dimension, i. e. that variations of the gust field with z are negligible. The turbulence is then characterized by a two-dimensional spectrum function TXQj, Q2) or its associated correlation function. Each of the methods has advantages and limitations, and the choice for any particular study will reflect the problem itself, the kind and extent of aerodynamic information and computing machinery available, and the tastes of the analyst.