Modeling the unsteady
aerodynamic forces of
a maneuvering rotor
Yihua Cao
Nomenclature
a
0
rotor coning angle
a
1
rotor rearward tilt angle
b
1
rotor lateral tilt angle
C
leu
unsteady airfoil section lift coef-
ficient
~
F force vector
~
F FxY FyY Fz
T
"
"
I
B
inertia matrix
m helicopter mass
~
M moment vector
~
M mxY MyY Mz
T
tY T time, sec
Tsbeu single blade unsteady thrust
V helicopter velocity
V
1
Y V
2
maneuver entry and exit veloci-
ties
~
V
B
helicopter velocity vector
~
V
B
#
x
Y#
y
Y#
z
T
X
E
YY
E
YZ
E
vehicle position in earth fixed
frame
Â
s
Y È
s
Y2
s
helicopter flight attitude angle
~
3
B
body rates
~
3
B
3
x
Y3
y
Y3
z
T
2
h
helicopter track angle
eu
unsteady airfoil angle of attack
helicopter sideslip angle
0
rotor collective pitch angle
c
rotor lateral cyclic pitch angle
s
rotor longitudinal cyclic pitch
angle
Introduction
It is well-known that the role of unsteady
aerodynamics is very important for maneu-
vering flight performance calculations in
both rotary and fixed-wing applications.
Although substantial progress has been made
recently in the modeling of unsteady aero-
dynamic characteristics of helicopter rotor
airfoils (Venkatesan and Friedmann, 1986;
Leishman, 1993), most applications in many
helicopter analyses have still concerned the
calculation of rotor vibratory loads, aeroelas-
tic stability and response calculations. As for
the flight dynamics analysis, only little papers
about the effects of unsteady aerodynamics on
flight performance in hover or forward flight
were recently published (He and Du Val,
1994; Turnour and Celi, 1997), while most
flight dynamics models use a quasi-steady
two-dimensional airfoil lifting theory to pre-
dict the blade loads.
In the past, flight dynamicists often used
the simple induced velocity distributions
The author
Yihua Cao is at the Institute of Aircraft Design, Beijing
University of Aeronautics and Astronautics, Beijing,
People's Republic of China.
Keywords
Aerodynamics, Rotors, Helicopters
Abstract
The details of predicting the aerodynamic forces of
maneuvering helicopter rotors are discussed in this paper.
A new approach to modeling the unsteady rotor
aerodynamic forces is presented based on the insight into
nonuniform induced velocity distribution, inflow dynamics
and unsteady airfoil behavior. For a specified maneuver,
the rotor control inputs and helicopter flight attitudes
during the maneuvering are first obtained using inverse
solution technique, and then the unsteady rotor forces are
numerically simulated by synthetically applying the vortex
theory, dynamic inflow theory and unsteady airfoil
aerodynamic models. Good results of the sample
calculations of lateral jink and pop-up maneuvers are
obtained.
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Contributed paper
444
Aircraft Engineering and Aerospace Technology:
An International Journal
Volume 71
.
Number 5
.
1999
.
pp. 444±450
# MCB University Press
.
ISSN 0002-2667