JOURNAL OF THE AMERICAN HELICOPTER SOCIETY 55, 012004 (2010)
A Comparison of Coaxial and Conventional Rotor Performance
Hyo Won Kim
1
Richard E. Brown
∗
Postgraduate Research Student Mechan Chair of Engineering
Department of Aeronautics Department of Aerospace Engineering
Imperial College London University of Glasgow
London, UK Glasgow, UK
The performance of a coaxial rotor in hover, in steady forward flight, and in level, coordinated turns is contrasted with that
of an equivalent, conventional rotor with the same overall solidity, number of blades, and blade aerodynamic properties.
Brown’s vorticity transport model is used to calculate the profile, induced, and parasite contributions to the overall power
consumed by the two systems, and the highly resolved representation of the rotor wake that is produced by the model is
used to relate the observed differences in the performance of the two systems to the structures of their respective wakes.
In all flight conditions, all else being equal, the coaxial system requires less induced power than the conventional system. In
hover, the conventional rotor consumes increasingly more induced power than the coaxial rotor as thrust is increased. In
forward flight, the relative advantage of the coaxial configuration is particularly evident at pretransitional advance ratios.
In turning flight, the benefits of the coaxial rotor are seen at all load factors. The beneficial properties of the coaxial rotor in
forward flight and maneuver, as far as induced power is concerned, are a subtle effect of rotor–wake interaction and result
principally from differences between the two types of rotor in the character and strength of the localized interaction between
the developing supervortices and the highly loaded blade-tips at the lateral extremities of the rotor. In hover, the increased
axial convection rate of the tip vortices appears to result in a favorable redistribution of the loading slightly inboard of the
tip of the upper rotor of the coaxial system.
Nomenclature
C
D
sectional profile drag coefficient
C
L
sectional lift coefficient
C
P
rotor power coefficient
C
T
rotor thrust coefficient
N number of blades per rotor
n load factor
R rotor radius
r blade spanwise coordinate
v
i
induced velocity
z rotor axial coordinate
α section angle of attack
γ rotor bank angle/lateral shaft inclination
θ
0
collective pitch
θ
1s
longitudinal cyclic pitch
θ
1c
lateral cyclic pitch
∗
Corresponding author; email: r.brown@aero.gla.ac.uk.
Based on a paper presented at the American Helicopter Society 62nd Annual
Forum, Phoenix, AZ, May 9–11, 2006. Manuscript received June 2007; accepted
July 2009.
1
Currently a Postdoctoral Research Assistant, Department of Aerospace Engi-
neering, University of Glasgow, Glasgow, UK.
μ rotor advance ratio
σ rotor solidity
ψ wake age/blade azimuth
rotor rotational speed
Subscripts
i induced component
l lower rotor of coaxial system
p profile component
u upper rotor of coaxial system
Introduction
Recent developments in the rotorcraft world, led by Sikorsky Aircraft
Corporation’s announcement of their X2 demonstrator and the develop-
ment of several UAV prototypes, indicate a resurgence of interest in the
coaxial rotor configuration as a technological solution to operational re-
quirements for increased helicopter forward speed, maneuverability, and
load-carrying ability.
Note: Throughout this paper, the lower rotor of the coaxial system should be taken
to rotate anticlockwise and the upper rotor to rotate clockwise, when viewed from
above. In single rotor simulations, the rotor should be taken to rotate anticlockwise
when viewed from above.
DOI: 10.4050/JAHS.55.012004
C
2010 The American Helicopter Society012004-1
H. W. KIM JOURNAL OF THE AMERICAN HELICOPTER SOCIETY
The coaxial concept is not new, of course. Although Russia has his-
torically been the world’s largest developer and user of coaxial rotor
helicopters, and an extensive body of research has been produced in that
country, the United States, United Kingdom, Germany, and Japan have
also pursued research into the coaxial rotor configuration (Ref. 1). Some
highly innovative designs, such as Sikorsky’s S-69 Advancing Blade
Concept (also known as the XH-59A), and Kamov’s Ka-50 attack he-
licopter, have attempted to exploit the coaxial configuration to obtain
improved performance in parts of the flight envelope.
In several cases, however, the performance of practical coaxial con-
figurations fell short of expectations, and this led to a temporary hiatus
in the development of the concept. In many such cases, the shortcom-
ings in the practical implementation of the coaxial concept could be
traced back to deficiencies in modeling or understanding the specific
details of the interaction between the rotors and the effect of the wake
on the behavior of the system—especially under unsteady flight con-
ditions. In recent years, though, computational tools have developed to
the extent where the highly interactive and nonlinear wake flows gen-
erated by the two rotors of the coaxial configuration can be modeled
with a much greater degree of confidence than has been possible in the
past.
The aim of this paper is to quantify, through numerical simulation,
the differences in performance between coaxial and conventional rotor
systems in steady flight and during maneuvers, and, in particular, to
examine the effect of the differences in the structure and development
of their wakes on the performance of the two types of rotor system. The
aerodynamic environment of any of the blades of a conventional rotor
is strongly influenced by close interactions not only with its own wake
but also with the wakes that are generated by the other blades of the
rotor. The aerodynamic environment of the rotor blades in a coaxial rotor
configuration is further complicated by interactions with the wakes that
are generated by the blades on the opposing rotor of the system. Given the
relatively long-range nature of these interactions, the numerical modeling
of coaxial systems has always posed a significant challenge. This is
because adequate resolution of the loading on the blades, hence rotor
performance, requires the strength and geometry of the wake of the rotor
to be correctly captured and retained for the significant amount of time
during which it has an influence on the loading on the system. Adequate
resolution of the interrotor interactions that characterize the coaxial rotor
system still poses a significant challenge for most current numerical
methods because of the prohibitively large computational resources that
are required to prevent premature dissipation of the wake.
Computational Model
Calculations using the vorticity transport model (VTM), developed
by Brown (Ref. 2) and extended by Brown and Line (Ref. 3), are used
in this paper to expose some of the subtle differences between the wake
structures generated by conventional and coaxial rotor systems that lie
at the root of the differences in their performance. The VTM has shown
considerable success in both capturing and preserving the complex vortex
structures contained within the wakes of conventional helicopter rotors
(Refs. 2 and 3), and in Ref. 4 the ability of the method also to capture
convincingly the aerodynamics of coaxial rotor systems, both in hover
and in forward flight, was demonstrated.
The VTM is based on a time-dependent computational solution of
the vorticity–velocity form of the Navier–Stokes equations on a Carte-
sian grid that surrounds the rotorcraft. The problem of preserving the
vortical structures in the flow from the effects of numerical dissipation is
addressed very effectively by the convection algorithm that is used in the
VTM, resulting in a wake structure that remains intact for very large dis-
tances downstream of the rotor system. Hence long-range aerodynamic
interactions that are produced by wake effects generally tend to be well
represented. The VTM uses an adaptive grid system to follow the evolu-
tion of the wake. This is done by generating computational cells where
vorticity is present and destroying the cells once the vorticity moves
elsewhere. The computational domain is thus effectively boundary-free,
and s ignificant memory savings are achieved. Computational efficiency
is further enhanced by using a series of nested computational grids to
capture the wake. The cells within the outer grids are arranged to be
coarser than those closer to the rotor. This helps to reduce the overall
cell count during a computation while still maintaining a highly resolved
flow field near the rotor.
The rotor blades are assumed to be rigid, but the coupled flap–lag–
feather dynamics are fully represented through numerical reconstruction
of the nonlinear Lagrangian of the system to obtain the equations of mo-
tion of the blades. The inertial contributions arising from pitch and roll
rates, in the case of maneuvering flight, are accounted for by applying
the Lagrangian formulation in the inertial frame of reference. In the ver-
sion of the VTM used to generate the results presented in this paper, the
blade aerodynamics is modeled using an extension of the Weissinger-L
version of lifting line theory. Local blade stall is modeled using a vari-
ation on Kirchoff’s trailing edge separation model, where the length
of the stall cell is given as a prescribed function of local angle of
attack based on known airfoil characteristics. Since this aerodynamic
model is still essentially inviscid, the profile drag of the blade is cal-
culated as a separate function of local angle of attack and then added
to the local aerodynamic force that is calculated from the lifting line
model.
Throughout the simulations presented in this paper, the computational
domain is discretized such that one rotor radius is resolved over 40 grid
cells. The computational time step used to evolve the simulations is
chosen to be equivalent to 3 deg of the rotor azimuth.
Rotor Model
In Ref. 4, it was argued that the fairest fundamental comparison be-
tween the performance of conventional and coaxial systems would result
if the differences in the geometry of the two systems was confined to
those characteristics that fundamentally distinguish the two rotor con-
figurations, in other words the vertical separation between the blades
and their relative sense of rotation. Any differences in the performance
of the two types of rotor should then arise solely as a result of the dif-
ferences in the detailed interaction between the blades and their wakes
that arise within the two types of system. For this reason, in the present
work the aerodynamics of the coaxial rotor are compared to those of a
conventional, single rotor that has the same blade geometry and overall
number of blades. As in Ref. 4, this paper focuses on the characteristics
of the coaxial system referred to as “rotor 1” in Harrington’s widely
regarded experimental comparison of the performance of conventional
and coaxial rotors (Ref. 5). This system consisted of two, contrarotating,
two-bladed teetering rotors, separated by 0.19R along a shared rotational
axis, which were operated at a tip Reynolds number of about 1 × 10
6
.
The blades of Harrington’s rotors were untwisted, had linear taper, and
the blade sections were based on the symmetric NACA 4-digit profile.
For modeling purposes, the same spanwise variation in sectional lift and
drag coefficients along the span of the blades was assumed to hold for
both the conventional and coaxial rotor systems. In all cases the profile
drag of the blades was assumed to obey
C
D
(α) = max [0.0124, 0.49{1 − cos 2(α + 1.75
◦
)}](1)
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A COMPARISON OF COAXIAL AND CONVENTIONAL ROTOR PERFORMANCE 2010
where α is the local angle of attack of the blade section. This drag
model was extracted from the correlations of VTM predictions against
Harrington’s experimental data presented in Ref. 4 and is capable of
representing the drag rise that is associated with the onset of separation
and eventual blade stall. This drag model is used exclusively throughout
the simulations presented in this paper to avoid any variability in the
profile power from obscuring an argument that is essentially in terms of
induced power.
Hover
The power required by a rotorcraft for a given lifting capacity is
determined, in most cases, by the hover performance of its rotor system.
For a coaxial rotor, trim of the yawing moment is achieved by matching
the torque of the upper and lower rotors via differential collective pitch
input so that the net torque about the shared rotor axis is zero. It has
long been a point of contention whether or not this arrangement is more
efficient than the more conventional main rotor—tail rotor configuration,
where typically the tail rotor consumes an additional 5%–10% of the
main rotor power to maintain overall yaw moment equilibrium in steady
hover (Ref. 6).
In Fig. 1, VTM predictions of the performance of Harrington’s two-
bladed coaxial rotor are compared against predictions of the performance
of a four-bladed, conventional (i.e., planar, corotating) rotor configura-
tion. To ensure the strong geometric equivalence that was argued in Ref. 4
to be necessary for direct comparison of the performance of coaxial and
conventional systems, the conventional r otor has blades that have the
same geometry and aerodynamic properties as the blades of the coaxial
rotor. The geometric properties of the two types of rotors are contrasted
in Table 1. As a check on the validity of this approach, Fig. 2 shows the
similarity in the collective pitch required by the two rotors to trim to a
given thrust coefficient that would be expected between rotors that have
the same solidity and hence very similar lifting performance. Indeed, a
comparison of the performance of the two types of rotor when computed
using the same profile drag model, as shown in Fig. 1, reveals the coaxial
rotor to consume very similar, albeit consistently less, power than the
conventional rotor for the same thrust when this strong geometric and
aerodynamic equivalence between the two systems is enforced.
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006
C
T
C
P
Coaxial rotor
Equivalent rotor
Fig. 1. Power vs. thrust: comparison between rotors with identical
solidity and blade properties.
Table 1. Summary of rotor properties
Coaxial Rotor Equivalent Rotor
Rotor radius RR
Number of rotors 2 1
Blades per rotor 2 4
Rotor separation 0.190R n/a
Root cutout0.133R 0.133R
Overall solidity 0.054 0.054
Twis t NoneNone
Flap hinge offset 0 (teetering) 0.023R
Airfoil sections NACA-00xx series NACA-00xx series
Wake geometry in hover
This difference in performance must manifest itself in the geometry
of the wakes of the two types of rotor. In Fig. 3, VTM-generated contour
maps of vorticity magnitude on a vertical slice through the center of the
wake show the global differences between the geometry of the wake of
Harrington’s coaxial rotor and that of the equivalent four-bladed conven-
tional rotor. Near to the rotors, the images show the orderly downstream
procession of the tip vortices and their associated inner wake sheets,
the obvious difference between the two systems being the double-tube
structure formed by the tip vortices of the coaxial rotor. In both cases,
the orderly helicoidal structure of the wake is disrupted, roughly a rotor
radius below the rotor plane, as the individual tip vortices coalesce into
larger vortical structures. In the case of the coaxial rotor, the tip vortices
from both the upper and the lower rotors interact during this process to
form a single sequence of coalesced vortical structures. As originally ob-
served by Landgrebe (Ref. 7) in his study of the geometry of the wakes of
hovering rotors, the formation of these large structures effectively marks
the end of the contraction of the wake and, in fact, the beginning of an
expansion in the diameter of the wake as these structures continue to con-
vect downstream of the rotor. Eventually, these structures are themselves
torn apart, through their own mutual interaction, to form the extensive
field of highly disordered, low-level vorticity in the far-wake that is seen
in both images.
Figure 4 compares VTM calculations of the contraction and axial
convection rate of the tip vortices generated by Harrington’s coaxial rotor
system in hover with that of the equivalent, conventional rotor and thus
0
2
4
6
8
10
12
14
0 0.001 0.002 0.003 0.004 0.005 0.006
C
T
θ
0
(Deg)
Coaxial rotor (upper)
Coaxial rotor (lower)
Equivalent rotor
Fig. 2. Collective pitch required to trim to given thrust coefficient.
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H. W. KIM JOURNAL OF THE AMERICAN HELICOPTER SOCIETY
Fig. 3. Wake structure in hover (C
T
= 0.0025).
provides a somewhat more quantitative comparison of the differences in
wake structure between the two rotor systems. ψ is the wake age in terms
of relative blade azimuth since generation of the tip vortex. The finite
resolution of the flow domain yields an estimated error in the calculated
positions of the tip vortices of approximately 1/40 of the rotor radius.
Langrebe’s empirical correlations of wake geometry (Ref. 7) for isolated
rotors operating at the same thrust coefficient as the various individual
rotors of the conventional and coaxial systems are also plotted to allow
the differences between the wakes that are generated by the two systems
to be assessed more clearly.
The agreement between Landgrebe’s correlation and the VTM-
predicted tip–vortex trajectory for the equivalent rotor is extremely close,
Spatial positions of the tip vortex
-1
−0.8
−0.6
−0.4
−0.2
0
0.2
−1.2 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 1.2
z/R
Blade
Landgrebe
Equiv.
Upper
Lower
Equivalent rotor
0
0.5
1
0 180 360 540 720
ψ
ψ
(deg)
z/R
z/R
Upper rotor
0
0.5
1
Landgrebe (equiv. )
VTM (axial)
VTM (radial )
Lower rotor
0
0.5
1
0 180 360 540 720
(deg)
z/R
r/R
r/R
r/R
r/R
Landgrebe (single)
Landgrebe (equiv. )
VTM (axial)
VTM (radial )
Landgrebe (single)
Landgrebe (equiv. )
VTM (axial)
VTM (radial )
Fig. 4. Correlation of relative tip vortex trajectories against Landgrebe’s empirical model (Ref. 7) for the rotors in isolation (C
T
= 0.0048).
012004-4
A COMPARISON OF COAXIAL AND CONVENTIONAL ROTOR PERFORMANCE 2010
providing good faith in the quality of the numerical simulations. For the
coaxial system, it is immediately obvious that the axial convection rate
of the tip vortices that are generated by the upper rotor is greater, and,
conversely, for the lower rotor, is smaller, than the axial convection rate
of the tip vortices of the equivalent conventional rotor. This observation
is consistent with the expected effect of the interaction between the wake
structures that are generated by the two rotors of the coaxial system,
whereby the convection rate of the vortices from the upper rotor is en-
hanced by their passage through the region of downwash that is generated
by the wake of the lower rotor, and, vice versa, the convection rate of the
vortices from the lower rotor is reduced by virtue of their passage through
the region of retarded flow lying just outside the wake tube of the upper
rotor. Note though that the axial descent rate of the tip vortices of both
rotors of the coaxial system is increased compared to the rate at which
the vortices would convect if the rotors were to be operated in isolation,
as might be expected as a result of the increased overall thrust, and hence
the rate of transfer of momentum into the wake, of the combined rotor
system.
The rate of radial contraction of the tip vortices that are generated by
the upper rotor of the coaxial system is markedly increased compared
to that of both the same rotor if operated in isolation and the equiva-
lent conventional rotor. At first glance, the rate of contraction of the tip
vortices of the lower rotor, especially when measured in terms of wake
age, appears to be largely unaffected by the incorporation of the rotor
into the coaxial system. However, bearing in mind that the rate of axial
convection of the tip vortices from the lower rotor is higher than when
operated in isolation, the contraction of the wake tube that is generated
by this rotor is seen to be actually slightly less when incorporated into
the coaxial system than when operated in isolation. In this context, the
relative geometries of the resultant wake tubes of the coaxial and con-
ventional systems are more clearly visualized in the diagram at bottom
left in Fig. 4. Again, these changes in geometry are consistent with the
expected form of the mutual interaction between the vortex systems that
are generated by the two rotors of the coaxial system.
It should be noted that the VTM provides a fully unsteady computa-
tion even when only the trimmed state of the rotor is of interest. Figure 5
shows the unsteadiness of the aerodynamic environment that is experi-
enced by the blades of the rotors when in hover. The individual plots
show the radial distribution of inflow that is experienced by a single
blade, during a single rotor revolution, as a polar function of blade az-
imuth. A sharp peak in inflow on the lower rotor of the coaxial system,
induced by the nearby passage of the tip vortices from the upper rotor,
is clearly visible at a radius of approximately 0.75R. The very obvious
four-per-revolution character of this interrotor blade–vortex interaction
is a consequence of the 2N -per-revolution geometric periodicity of the
system. The upper rotor shows a far more benign variation of inflow along
the blade span because this interaction is absent. A weaker, secondary,
blade overpressure-type interaction results from the direct influence of
the bound vorticity of the blades of the upper rotor on those of the lower,
and vice versa, and is visible on both rotors as a ridge of slightly mod-
ified inflow over the entire span of the blade at 0, 90, 180, and 270 deg
azimuth (i.e., when the reference blade passes by one of the blades on
the adjacent rotor). In comparison, the bottom plot, for a blade on the
isolated, four-bladed equivalent rotor, shows none of these effects to be
present, and the resultant inflow distribution to be relatively steady except
near the tips of the blades, where the inflow is strongly influenced by the
proximity of the tip vortices that are trailed from the preceding blades of
the same rotor. The fluctuation in the inflow is associated with a small
variability in the trajectory of these vortices that seems to be induced
by the unsteadiness in the wake further downstream as the individual tip
vortices coalesce to form the larger, less coherent structures described
earlier. A similar, but much weaker, fluctuation in the inflow is predicted
Fig. 5. Spanwise inflow distribution experienced by a single blade
during one revolution when in hover (Harrington’s rotor, C
T
=
0.0048).
near the root of the blade where the effects of a similar unsteadiness in
the location of the root vortices is most strongly felt.
Hover performance
Figures 6–8 compare the computed distribution of blade loading (sec-
tional force normal to the blade chord normalized by rotor tip speed),
inflow, profile drag, and sectional power loading along the blades of the
upper and lower rotors of his coaxial system, one of the rotors of Harring-
ton’s system when operated in isolation, and the equivalent four-bladed
conventional system, to show in detail how aerodynamic interaction be-
tween the wake and the blades subtly modifies the performance of each
of the rotor systems. The error bars in the figures represent the variability
in the data over a single rotor revolution even when the rotor is ostensibly
in a trimmed flight condition.
Calculations are presented for a representative overall thrust coeffi-
cient of 0.005. At this operating condition, the lower rotor is required
to generate a thrust coefficient of 0.0022 and the upper rotor a thrust
coefficient of 0.0028 to satisfy a trim condition of zero overall torque
produced by the rotor system.
Figure 6 compares the upper and lower rotors of the coaxial config-
uration and exposes the effect of aerodynamic interactions between the
two rotors on the performance of the system. Figure 6(b) shows strong
distortion of the radial inflow variation along the lower rotor of the coax-
ial system compared to that along the upper rotor where the distribution
of inflow is qualitatively (and quantitatively) not very different from that
of one of the rotors of the coaxial configuration tested in isolation at
012004-5
