A theory for the lateral response of airplanes to random atmospheric turbulence Page: 27 of 77
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NACA E 3954
Both theoretical methods (ref. 17) sand flight measurements (ref. 18)
have shown that the following expression approximates the spectrum of
lateral components of turbulence in the atmosphere over the frequency
range affecting the dynamic response of an airplane:
1H 1 + 3(k')2
xU [ + (k')2]2
Its horizontal counterpart has the spectrum
L 2
-W 1 + (k') 2
where k' _= and. L is the integral scale of turbulence. The
U
value 2sL may be considered an approximate measure of the average
eddy size in the turbulence. The data of reference 18 further indicate
that L is on the order of 1,000 to 2,000 feet, and probably closer
to 1,000 feet.
The foregoing expressions, having asymptotic logarithmic slopes
of -2 for values of k' -, , were first suggested in reference 19 on
the basis of wind-tunnel data and have since become generally accepted
as reasonable expressions for defining the power spectra of lateral and
longitudinal components of isotropic turbulence. Therefore, these
expressions normalized by the mean-square values are used herein as the
basis for calculations involving the components of atmospheric gusts as
sensed at the center of gravity (point spectra):
g =g g L 1 + 3(k')2
vg Wg T1 + k')2
4Ug L 2 (47)
ug 2 U1 (k')2
where
2 2 2
u = vg Wg
U
L as 1,000 feet25
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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/m1/27/: accessed March 28, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.