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Frequency Response Functions and Human Pilot Modelling

In the treatment of the response of aircraft to gust by power spectral techniques, the frequency response function
plays a central role. For gust encounter, the frequency response function is defined as the response (amplitude and
phase) of the variable of concern, such as acceleration, bending moment, or stress, due to a unit sinusoidal gust en-
counter. Through means of the frequency response function and an input spectrum, two basic structural response
quantities A and No are derived, which are of key significance in load response studies.
The question has been raised, “What is the state of the art of calculating the frequency response functions and,
in turn, the basic A and N0 values?” The question should be rephrased, however. At present it appears that we
can determine a specific frequency response function with fair accuracy. An airplane, however, has many different
flight conditions, due to variations in weight, speed, and altitude and, thus, a given airplane has many different
frequency response functions, even for a given response variable. The problem, therefore, is not only that of how
well we can establish a specific frequency response function, but also how well we can isolate and determine the
appropriate frequency response function, or more generally, how well we can combine the various frequency response
functions so as to obtain a realistic overall or composite description of the response. The purpose of this paper
is thus to discuss these problems.
These quantities are noted to be associated with the area and radius of gyration of the area under the output spectrum.
The upper limit we in expressions (3) and (4) represents one of the problems that is encountered in evaluating A
and No . The means for establishing we , as recommended in reference 1, is shown in figure 2. In some cases the
No variation with we is fairly flat after a certain we is reached, curve a, and in this case no difficulty is encountered
in establishing N0 . In other cases N0 seems to increase monotonically with increasing we , curve b; in this case
N0 is taken at the we representing the top of the knee of the A curve, as suggested in reference I.