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National Advisory Committee for Aeronautics, Technical Notes - A Method for the Calculation of the Lateral Response of Airplanes to Random Turbulence

A relatively short method of calculating the lateral motions of an
airplane due to random.atmospheric turbulence is presented. The gust
velocities are represented as eguivalent rigid—body rotations of the
airplanes; namely, rolling gusts, yawing gusts, and side gusts. Random
distributions of gust velocities across the span are taken into account
in defining the rolling and yawing gusts. Complex stability derivatives
are used to account for the random distribution of side gusts along the
fuselage and vertical tail and the lag effect incurred as the airplane
penetrates the gusts. The suggested gust spectrum is based on a simple
analytical expression which fits available measurements of atmospheric
turbulence. A A5—step sample calculation procedure for obtaining the
response of the airplane in each degree of freedom is presented in
tabular form.

Most calculations of the response of airplanes to gusts have been
made on the assumption that the effect of the gust on the airplane is
approximately equivalent to the effect of a rigid-body motion of the
airplane producing a distribution of angle of attack similar to that
caused by the gust. 0n the basis of this assumption, disturbances in
the form of rolling gusts, yawing gusts, and side gusts have been employed
in calculating lateral response to gust disturbances. This approach is
convenient because the standard aerodynamic stability derivatives which
are used in airplane stability calculations may also be used to determine
moments caused.by the gust velocities. This approach as usually applied
neglects effects due to lag in penetration of the gusts by different parts
of the airplane and, because linear gradients of the gust velocity along
the span are assumed, it cannot account for the random spanwise distribu-
tion of gust velocities encountered in flight through atmospheric turbu—
lence. Furthermore, the relations between the magnitudes of the rolling,
yawing, and side gusts required to produce effects similar to actual
atmospheric turbulence are not known beforehand.

In reference 1, a theoretical method for calculating the lateral
response of an airplane to atmospheric turbulence has been proposed
which accounts in a rather complete manner for the effects neglected or
approximated in previous methods. This method uses an approach somewhat
different from that described in the preceding paragraph in that the
forces and moments applied to the airplane by gusts are determined in
power-spectral form in terms of the horizontal, vertical, and side com—
ponents of gust velocity.