A theory for the lateral response of airplanes to random atmospheric turbulence Page: 3 of 77
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NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
TECHNICAL NOTE 3954
A ~EORY FOR THE LATERAL RESPONSE OF AIRPlANES
TO RANDOM ATMb1SPK RIC TURBUI E
By John M. Eggleston
The lateral motions of an airplane flying through continuous random
isotropic turbulence have been derived in terms of (1) the transfer
functions relating the motion in the various degrees of freedom to the
yawing moment, rolling moment, and side force, (2) the statistical forces
and moments at the center of gravity due to gust velocities acting on the
lifting surfaces of the airplane, and (3) the power spectra of the three
orthogonal components of gust velocity acting on the airplane along the
flight path. The method takes into account the random variations of
gust velocity across the span and along the fuselage. Solutions are
given in the form of equations relating the power spectra of the angular
motions of the airplane to the power spectra of the gust velocities.
Three airplanes of different size are used to demonstrate the method,
illustrate characteristic trends, and exhibit some simplifications pos-
sible in the calculations. For these airplanes the effects of horizontal
gusts (that is, gusts parallel to the flight path) and side forces due
to gusts on the airplanes were found to be negligible.
By using one of the example airplanes, a comparison is drawn between
the present theory and several less comprehensive theories for calcu-
lating the effect of gusts on wings of finite span and the effect of
gusts on the motions of the complete airplane.
The classical theory of stability and control of airplanes has been
applied to the calculation of response to controls and response to gusts.
In the calculation of response to gusts, however, the angle-of-attack
distributions which produced the forces and moments applied to the air-
plane by the gust have customarily been assumed to be equivalent to those
resulting from a rigid-body motion of the airplane. This method was
applied in NACA Report 1 and other early reports (ref. 1) in the study
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Eggleston, John M. A theory for the lateral response of airplanes to random atmospheric turbulence, report, May 1957; (digital.library.unt.edu/ark:/67531/metadc56287/m1/3/: accessed September 25, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.