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8.6 Gust loads 253

from arbitrary assumptions of gust shapes and sizes. It is assumed that kast velocity is
a random variable which may be regarded for analysis as consisting of a large number
of sinusoidal components whose amplitudes vary with frequency. The power spectrum
of such a function is then defined as the distribution of energy over the frequency
range. This may then be related to gust velocity. To establish appropriate amplitude
and frequency distributions for a particular random gust profile requires a large
amount of experimental data. The collection of such data has been previously referred
to in Section 8.2.
Calculations of the complete response of an aircraft and detailed assessments of the
‘discrete’ gust and power spectral methods of analysis are outside the scope of this
book. More information may be found in Refs 1,2,3 and 4 at the end of the chapter.
Our present analysis is confined to the ‘discrete’ gust approach, in which we consider
the ‘sharp-edged’ gust and the equivalent ‘sharp-edged’ gust derived from the ‘graded’
gust.

The simplifying assumptions introduced in the determination of gust loads resulting
from the ‘sharp-edged’ gust, have been discussed in the earlier part of this section. In
Fig. 8.14 the aircraft is flying at a speed V with wing incidence olo in still air. After
entering the gust of upward velocity u, the incidence increases by an amount
tan-’ u/ V, or since u is usually small compared with V, u/ V. This is accompanied
by an increase in aircraft speed from V to ( V2 + u2$, but again this increase is
neglected since u is small. The increase in wing lift AL is then given by
(8.22)

where dCL/da is the wing lift-curve slope. Neglecting the change of lift on the
tailplane as a first approximation, the gust load factor An produced by this change

U
Still air
‘ I

Fig. 8.14 Increase in wing incidence due to a sharp-edged gust.