A Method for Studying the Transient Blade-Flapping Behavior of Lifting Rotors at Extreme Operating Conditions Page: 3 of 28
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NACA TN 3366
It is the object of this paper to develop equations and to present
a method for determining the stability of blade flapping motion which
avoids the no-stall and incompressibility assumptions, as well as some
other restrictive aerodynamic assumptions that are normally employed in
rotor analyses, and which properly accounts for the reversed-velocity
region. The method, which is applicable to numerical solution by automatic
computing machines, can also be used to account for the effects of stall,
compressibility, and high rotor angle-of-attack operation on the steady-
state flapping motion at more conventional helicopter tip-speed ratios
and to compute the transient blade-flapping response arising from arbitrary
control inputs. No specific terms are included in the equations, however,
to account for blade torsional or bending flexibility. The method is
illustrated by examples of blade-stability calculations of free-to-cone
and seesaw rotors at tip-speed ratios equal to or greater than 1.0 and of
the transient flapping response of a free-to-cone rotor to arbitrary con-
trol inputs at a tip-speed ratio equal to 0.3.
A ,B coefficients.of -cos * and -sin $, respectively, in
expression for e; therefore, lateral and longitudinal
cyclic-pitch angles, respectively, deg
B tip-loss factor (assumed equal to 0.97 herein); blade ele-
ments outboard of radius BR are assumed to have profile
drag but no lift
c blade section chord, ft
Cdo section profile drag coefficient
Ce equivalent blade chord (on thrust-moment basis),
cr3d r dr, ft
CI section lift coefficient
dD drag force on blade element, ib
dFC centrifugal force on blade element, lb
dFI inertia force on blade element, lb
lift force on blade element, lb
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Gessow, Alfred & Crim, Almer D. A Method for Studying the Transient Blade-Flapping Behavior of Lifting Rotors at Extreme Operating Conditions, report, January 1955; (https://digital.library.unt.edu/ark:/67531/metadc56061/m1/3/: accessed March 20, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.