A theory for the lateral response of airplanes to random atmospheric turbulence Page: 4 of 77
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of the longitudinal response of airplanes to gusts and in reference 2
to the calculation of the lateral response to gusts. Because of the
method of accounting for the effect of the gusts, these analyses were
restricted to the consideration of the effects of isolated gusts of some
specified shape. Most early developments in the theory of response to
gusts were attempts to account for factors which were important in the
calculation of loads. For example, the calculation of loads due to
vertical gusts was extended in reference 3 to include the effects of
unsteady lift and of flexibility.
In the early methods of calculating gust response, the analysis did
not include such factors as the penetration effect (a result of the
penetration of a given gust at different times by different parts of the
airplane) and the variation of gust velocities along the fuselage and
spanwise directions. In recent years, some attempts have been made to
include these effects without changing te basic method of approach. In
reference 4 an approximate method was introduced for estimating the
penetration effect in the calculation of longitudinal response to gusts
by taking into account first-order effects of the time lag between the
penetration of the gust by the wing and ty he tail. The method used
was similar to that introduced in reference 5 for calculating the effect
of lag of downwash. A similar application of this concept to the calcu-
lation of lateral response to gusts was presented in reference 6.
A more realistic treatment of random disturbances in the atmosphere
was made possible with the introduction of a method of calculating the
statistical response of an airplane in terms of the statistical proper-
ties of atmospheric gust velocities. This method, known as statistical
dynamics, was first applied in reference 7 to the measurement of the
longitudinal response of an airplane to random vertical gusts and has
since been used extensively in langitudinal gust loads studies.
A theoretical analysis for the statistical lateral response of an
airplane to gusts was given in reference 8 where, in order to approximate
the effects of the. span, the turbulence was considered to be represented
by a combination of rolling gusts and side gusts having arbitrary distri-
butions along the flight path. With this representation of turbulence,
however, the question arose as to the relative magnitudes of the rolling
and side gusts which would satisfactorily represent atmospheric turbu-
lence. In reference 8 the assumption was made that an arbitrary gust
distribution across the span could be represented by a constant anti-
symmetric gradient which was assumed to be equal to the gradients existing
in the Corresponding distribution of side gusts. Experimental flight
measurements of reference 9 indicated, however, that the measured gradi-
ents of vertical gusts across the span di4 not agree with the theoretical
calculations of reference 8, and the assumption of nonisotropic atmos-
pheric turbulence was employed in order to fit the theory to the flight-
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Eggleston, John M. A theory for the lateral response of airplanes to random atmospheric turbulence, report, May 1957; (https://digital.library.unt.edu/ark:/67531/metadc56287/m1/4/: accessed April 22, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.