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William G. Bousman
Army/NASA Rotorcraft Division
Aeroflightdynamics Directorate (AMRDEC)
US Army Aviation and Missile Command
Ames Research Center, Moffett Field, California
The loading of an airfoil during dynamic stall is
examined in terms of the augmented lift and the
associated penalties in pitching moment and drag. It is
shown that once stall occurs and a leading-edge vortex
is shed from the airfoil there is a unique relationship
between the augmented lift, the negative pitching
moment, and the increase in drag. This relationship,
referred to here as the dynamic stall function, shows
limited sensitivity to many parameters that influence
rotors in flight. For single-element airfoils it appears
that there is little that can be done to improve
rotorcraft maneuverability except to provide good
static clmax characteristics and the chord or blade
number that is required to provide the necessary rotor
thrust. The loading on a helicopter blade during a
severe maneuver is examined and it is shown that the
bladeÕs dynamic stall function is similar to that
obtained in two-dimensional wind tunnel testing. An
evaluation of three-dimensional effects for flight and
an oscillating wing in a wind tunnel suggests that the
two problems are not proper analogues. The utility of
the dynamic stall function is demonstrated by
evaluating sample theoretical predictions based on
semi-empirical stall models and CFD computations.
The approach is also shown to be useful in evaluating
multi-element airfoil data obtained from dynamic stall
section lift coefficient
maximum lift coefficient in dynamic
stall, Fig. 3
section moment coefficient
minimum moment coefficient in
dynamic stall, Fig. 3
section normal force coefficient
mean blade lift coefficient
thrust coefficient
reduced frequency, ωc 2V
Mach number
blade radial location, ft; correlation
blade radius, ft
velocity, ft/sec
maximum level flight speed, ft/sec
oscillating wing spanwise location,
oscillating wing span, in
section angle of attack, deg
mean angle of attack, eq (4), deg
alternating angle of attack, eq (4),
maximum drag coefficient in
dynamic stall, Fig. 3
ai, bi
polynomial coefficients for cl , i =
blade chord, ft
advance ratio
section chord force coefficient
solidity; standard deviation
section drag coefficient
oscillatory frequency, rad/sec
Presented at the 26th European Rotorcraft Forum, The Hague, Netherlands, September 26-29, 2000.
airfoil lift, but there is an unsteady or dynamic
component that increases the rotor thrust capability
(Ref. 4). Measurement of the rotor thrust of a fullscale HÐ21 rotor in the 40- by 80-Foot Wind Tunnel at
Ames Research Center in the 1950s, by McCloud and
McCullough (Ref. 5), demonstrated that the rotor was
able to provide more thrust than would be calculated
using just the airfoil static lift coefficient (Ref. 4).
This additional thrust, achieved by what is now
referred to as dynamic stall, has been the subject of
extensive research over the past 40 years (Ref. 6, 7).
A fundamental problem for the rotor designer,
then, is to what degree does the airfoil design affect
the rotorÕs thrust capability in maneuvers, and
probably more important, the increased pitching
moment and power that accompanies the augmented
lift associated with dynamic stall. The purpose of the
present paper is to examine two-dimensional wind
tunnel tests of a variety of helicopter airfoils and
assess their dynamic stall performance. Flight data on
a UHÐ60A in maneuvering flight will then be used to
relate the wind tunnel measured characteristics to
maneuver performance. A metric will be introduced,
herein called the dynamic stall function, and it will be
shown how this metric can be used to assess both
theoretical prediction methods and experimental
McHugh and his colleagues measured the steady
thrust of a 10-foot diameter CHÐ47B model rotor in
the Boeing 20- by 20-Foot V/STOL Wind Tunnel to
define the actual thrust limits of this rotor (Refs 1, 2).
Their measurements are particularly useful as the rotor
was designed with sufficient structural strength that
the true aerodynamic thrust limit was obtained, that is,
for any advance ratio and propulsive force, they
increased the collective pitch until the thrust reached
its maximum value and then reversed. The rotor thrust
limit as a function of advance ratio that was obtained
is shown in Fig. 1.
Figure 1. Comparison of measured and calculated
limit rotor thrust coefficient as a function of advance
ratio for a 10-foot diameter model rotor, X/qd 2s =
3.1 Ames Test Program
McCroskey and his colleagues tested eight
airfoils in the NASA-Ames 7- by 10-Foot Wind
Tunnel in the late 1970s and early 1980s (Refs. 8-10).
Each airfoil was tested on the same dynamic test rig
and, in general, the same range of test conditions was
covered. The eight profiles tested are shown in Fig. 2.
The NACA 0012 airfoil is representative of the
first generation of helicopter sections and has a
symmetric profile. The AMESÐ01, Wortmann FX
69ÐHÐ098, SC1095, HHÐ02, VRÐ7, and NLRÐ1 are
second generation airfoils and four of these are used in
current production aircraft. The eighth section, the
NLRÐ7301, is representative of a supercritical, fixedwing section. Compared to the other seven airfoils it
is characterized by a large leading-edge radius and
large aft camber which results in large negative
pitching moments at all angles of attack. The
NLRÐ7301 is not considered suitable for use in
helicopter applications, but was included in the test
Harris, in Ref. 3, has shown that the rotor thrust
limit in forward flight, assuming roll moment balance,
can be related to a mean blade airfoil lift coefficient as
CT CL  1 − µ 2 + 9 µ 4 / 4 
6  1 + 3µ 2 / 2 
At µ = 0, eq (1) becomes the expected
CT 1
= CL
Two-Dimensional Airfoil Tests
In Fig. 1, the mean value for CL has been set to 0.94,
and the Harris equation shows good agreement with
the McHugh thrust boundary.
The problem of relating rotor thrust capability to
airfoil section characteristics is more difficult than
suggested by eq (1) when it is recognized that the rotor
thrust limit is not dependent upon the maximum static
conditions, that is, the reduced frequency was
approximately zero (k < 0.005), and these 21
conditions are not included. For the NLRÐ1 airfoil, a
set of test cases were run with α0 = Ð2 deg and α1 = 10
deg and, therefore, dynamic stall occurred for negative
lift conditions. Therefore, these eight test cases have
also been excluded from the comparisons shown here.
Finally, 13 test conditions for the NLRÐ7301 are
excluded where α0 was set near the static stall angle,
and small values of the alternating angle of attack, α1
= 2 deg, were used to better understand this airfoilÕs
flutter characteristics. None of these conditions
indicated the shedding of a dynamic stall vortex and,
in some cases, the airfoil remained stalled for the full
Section force and moment time histories are
provided in Ref. 9 for each airfoil and each test
condition. Figure 3 shows an example of the lift, drag,
and moment loops for the NACA 0012 for a test
condition that represents deep stall. Indicated on this
figure are the maximum lift, the maximum drag, and
the minimum moment during the oscillation. These
extrema occur at slightly different angles of attack and
are, therefore, not coincident in time. However, they
are each related to the passage of the dynamic stall
vortex along the airfoil and are representative of the
maximum loading that occurs during a dynamic stall
The extrema from the dynamic stall loops for the
eight airfoils tested at Ames are shown in Figs. 4 and
5. Figure 4 shows the maximum lift as a function of
minimum moment, while Fig. 5 shows the maximum
lift as a function of maximum drag. Most of these data
were obtained without a boundary layer trip, but a
number of test conditions were obtained with a
boundary layer trip and are shown with a different
In general, each of the eight airfoils shows similar
characteristics. That is, as additional lift develops on
the airfoil in dynamic stall there is an associated
increase in both the negative pitching moment and the
pressure drag. For moments less than about Ð0.1, or
drag values greater than about 0.1, the test data show
that either one or two vortices are shed from the
vicinity of the airfoilÕs leading edge, and these vortices
are convected along the airfoilÕs upper surface and off
the trailing edge. A single vortex is generally seen for
moment values between Ð0.1 and Ð0.5, but at higher
lift, two shed vortices are observed, one following the
other. The relationship between lift, moment, and drag
that is seen in Figs. 4 and 5 is a consequence of the
convection of the dynamic stall vortices along the
airfoil. This loading characteristic is herein termed the
Figure 2. Eight airfoils tested in the NASA Ames 7- by
10-Foot Wind Tunnel (Refs. 8-10).
program to better understand the dynamic stall
characteristics of fixed-wing airfoil sections with
significantly different leading edge geometries.
The airfoil chord for each of the eight profiles was
24 in. The airfoils were mounted vertically in the test
section of the 7- by 10-Foot Wind Tunnel such that the
airfoils spanned the tunnelÕs shorter dimension. Thus
the effective height to chord ratio was 5.0, based on
the 10-foot width of the tunnel and the width to chord
ratio was 3.5. Fifteen pressure transducers were
mounted on the upper surface, ten were placed on the
lower surface, and a single transducer was installed at
the airfoil leading edge. The measured pressures were
integrated to obtain the section forces, cn and cc, and
the section moment, cm. The measured angle of attack
of the airfoil was used to convert these coefficients to
the wind tunnel axes.
cl = − cc sin α + cn cos α
cd = cc cos α + cn sin α
The cd calculated in this manner does not include the
viscous drag, of course.
Dynamic stall data were obtained in the Ames
tests by oscillating the airfoil in angle of attack around
a mean value. The airfoil motion was defined as
α (ωt ) = α 0 + α1 sin ωt
Typically, test data were obtained for mean angles of
10 and 15 deg and alternating angles of 5 and 10 deg.
Reduced frequencies varied from 0.02 to 0.20 and
most of the data were obtained for a Mach number of
0.3, but with some data taken for Mach numbers as
low as 0.04. The Reynolds number ranged from
400,000, at M = 0.04, to 4 million at M = 0.3. The
number of test conditions varied from 49 for the
Wortmann FX 69ÐHÐ098 to 121 for the NACA 0012.
Not all of these test points are included here. For the
NACA 0012 airfoil, a number of test points were
obtained for quasi-static rather than dynamic stall
Figures 4 and 5 also include static airfoil
characteristics for reference. As shown in Fig. 4 for
the helicopter sections, the moment is close to zero
over the normal range of airfoil lift and the moment
becomes negative only after the airfoil stalls. Figure 5
includes the static airfoil drag measured using a wake
survey (solid line) as well as the drag obtained from
integration of the measured pressures (dotted line).
Below stall, the drag values are very low, but once
stall occurs there is a substantial increase in drag.
A comparison of the dynamic and static lift, drag,
and moment in Figs. 4 and 5 indicates that as the zero
moment or zero drag axis is approached, the dynamic
stall function, as defined by these data, tends to
approach the measured airfoil static cl .
The dynamic stall function can be quantified by
fitting a 2nd-order polynomial to the data, and the
fitting polynomial is shown by dashed lines in Figs. 4
and 5. The fitting polynomials are defined as
cl = a0 + a1cm + a2 cm 2
cl = b0 + b1cd + b2 cd 2
The data obtained with a tripped boundary layer
were not used for the fit as in some cases these data
clearly show a dynamic stall function that differs from
the untripped data, see Ref. 11. The polynomial
coefficients defined by eq (5) are shown in Tables 1
and 2 along with two measures of dispersion: the
coefficient of determination, r2, and the standard
deviation, σ.
3.2 Oscillating Wing Test
Piziali (Ref. 12) tested an oscillating wing in the
same NASA-Ames 7- by 10-Foot Wind Tunnel as
used by McCroskey and his colleagues. Test data
were obtained for an NACA 0015 airfoil section in
both two- and three-dimensional configurations. The
wing had a span of 60 in and a chord of 12 in.
Differential and absolute pressure transducers were
installed at various span locations. For the twodimensional tests, data were obtained at four span
stations: three with differential pressure transducers
arrays and one with an absolute pressure transducer
array. The chordwise array of absolute pressure
transducers was located at a span of 0.500Y. At this
station ten pressure transducers were mounted on the
upper surface, eight were on the lower surface, and
one was placed at the leading edge. The pressures
were integrated to obtain the airfoil forces and these
forces were converted to the wind tunnel axis system
Figure 3. Dynamic stall test point for NACA 0012
from Ames tests; Frame 9302.
Òdynamic stall functionÓ and is used as a means of
characterizing the loads on an airfoil caused by
dynamic stall.
Figure 4. Maximum lift coefficient as a function of minimum moment coefficient for dynamic stall test data on eight
airfoils from Ames tests. Polynomial fit of untripped data.
Figure 5. Maximum lift coefficient as a function of maximum drag coefficient for dynamic stall test data on eight
airfoils from Ames tests. Polynomial fit of untripped data.
Table 1. 2nd order polynomial fit of dynamic stall function, lift as a function of moment.
NACA 0012
FX 69ÐHÐ098
NACA 0015
Table 2. 2nd order polynomial fit of dynamic stall function, lift as a function of drag.
NACA 0012
FX 69ÐHÐ098
NACA 0015
showed evidence of stalled flow over the entire range
of angles of attack.
The two-dimensional data for the NACA 0015
airfoil obtained from the span station with absolute
pressure transducers are shown in Fig. 6 with the
untripped and tripped data points indicated by different
symbols. The dynamic stall functions for these data
do not extend as far as was observed in the Ames tests
for the other airfoils and this indicates that the
dynamic stall vortex strength is somewhat reduced.
Polynomials have been fitted to these data and are
included in Tables 1 and 2 with the data from the
Ames tests.
using eq (3).
Test data were obtained for mean angles of attack
of 4, 9, 11, 13, 15, and 17 deg, and alternating angles
of 2, 4, and 5 deg. The reduced frequencies tested
ranged from 0.04 to 0.20. The Mach number was
approximately 0.3 and the Reynolds number about 2
million. Ninety-eight two-dimensional test points
were obtained and include both untripped and tripped
data. Forty-two of these points are excluded in the
present analysis as the maximum angle of attack was
less than the static stall angle of approximately 13.5
deg. An additional eight points obtained at angles of
17±2 deg are also excluded as these test conditions
Figure 6. Maximum lift coefficient as a function of minimum moment and maximum drag coefficients from test of
NACA 0015 airfoil. Polynomial fit of untripped data.
Ames tests, although the four points obtained at M =
0.1 lie outside the Ames 1σ boundary.
Two sources of dynamic stall data have been
examined for the VRÐ7 airfoil. The first data set is
from the Centre DÕEssais Aeronautique de Toulouse
(CEAT) wind tunnel in Toulouse, France, and was
obtained under the auspices of the U.S./France
Memorandum of Understanding for Cooperative
Research in Helicopter Aeromechanics. A general
description of the test procedures used with this wind
tunnel and test rig are provided in Ref. 14. The
second data set is from the Ames water tunnel (Ref.
15). The CEAT data were obtained in a conventional
atmospheric wind tunnel using a model with a 40-cm
chord. Thirteen differential pressure transducers were
installed on the airfoil and, hence, only normal force
and moment coefficients are available. The data from
the water tunnel tests were obtained on a model
airfoil of four in chord mounted in the water tunnelÕs
8.3- by 12-inch test section. The lift, drag, and
moment were measured with an external balance with
corrections for friction, but not for inertial loads,
which were considered negligible (Ref. 15). The
CEAT tests examined mean angles of attack of 10
and 15 deg, and alternating angles of 5 and 6 deg.
Reduced frequencies varied from about 0.02 to about
0.23. The Mach number ranged from about 0.12 to
0.3, and the Reynolds number varied from 1 million
to just under 3 million. The water tunnel tests
included mean angles of attack of 5, 10, and 15 deg,
and alternating angles of 10 deg. The reduced
frequencies varied from 0.025 to 0.20. The Mach
number was zero, of course, and the Reynolds
number ranged from 100,000 to 250,000. The data
3.3 Supporting Tests
Oscillating airfoil data are available from a
number of sources that can be compared with the
Ames test data in Figs. 4 and 5. These comparisons
are of value to confirm the general behavior of the
dynamic stall function and also to examine additional
test conditions beyond the range of parameters
examined in the Ames tests.
St. Hilaire et al. tested an NACA 0012 airfoil in
the Main Wind Tunnel at the United Technologies
Research Center (UTRC) and reported the results in
Ref. 13. The primary purpose of this test was to
examine the effects of sweep on blade stall, but the
data obtained for unswept conditions can be
compared directly with the Ames data. For these
tests, twelve absolute pressure transducers were
installed on the upper surface and eight were installed
on the lower surface. The section chord was 16 in.
Lift, drag, and moment were obtained by integrating
the measured pressures and the resulting forces were
converted to wind tunnel axes using eq (3). Mean
angles of attack ranged from 5 to 15 deg, and
alternating angles were either 5 or 10 deg. Reduced
frequencies varied over a range of 0.02 to 0.20. Data
were obtained for Mach numbers of 0.1, 0.3, and 0.4
(Reynolds numbers of 920,000, 2.8 million, and 3.7
million), but only data at M = 0.1 and 0.3 are shown
here, as this is the range of Mach numbers used in the
Ames tests. Figure 7 compares the UTRC
measurements with the polynomials based on the
Ames data from Tables 1 and 2. The scatter in the
Ames data is represented by ±1σ boundaries. The
UTRC data generally show good agreement with the
Figure 7. Comparison of dynamic stall extrema from UTRC tests of NACA 0012 airfoil with polynomial fits of Ames
test data.
Figure 8. Comparison of dynamic stall extrema from CEAT tests and from Ames water tunnel tests of VRÐ7 airfoil
with polynomial fits of Ames test data.
dominates the loading on the airfoil during dynamic
stall, is relatively insensitive to Reynolds number.
Dynamic stall data were obtained for the SC1095
(and SC1094 R8) airfoil in the UTRC facility using
the same procedures and test rig as for the NACA
0012 tests discussed above. Of these data, five liftmoment loops have been published by Gangwani
(Ref. 16). The remainder of these data remain
unpublished. Mean angles of attack of 9, 12, and 15
deg were tested with alternating angles of 8 deg. The
reduced frequencies ranged from 0.10 to 0.12, the
Mach number was 0.3, and the Reynolds number was
about 2.8 million. The five SC1095 test points are
compared with the Ames test data in Figure 9. The
UTRC data agree quite well with the Ames data, with
three of the points within the 1σ boundary and two
from these two tests are compared with the Ames data
in Fig. 8.
The data from both the CEAT wind tunnel tests
and the Ames water tunnel tests show good
agreement with the Ames wind tunnel data. Since the
CEAT data were obtained using differential pressure
transducers, only the normal force coefficient, cn, and
not the lift coefficient, cl, is computed. However,
there are only slight differences between these two
coefficients during dynamic stall (Ref. 11) and these
differences do not affect the comparison shown here.
The water tunnel test results show very good
agreement with the wind tunnel data despite the large
difference in Reynolds number. This interesting
result suggests that the dynamic stall vortex, that
Figure 9. Comparison of dynamic stall extrema from
UTRC tests of SC1095 airfoil with polynomial fits of
Ames test data.
Figure 10. Comparison of dynamic stall extrema from
BSWT tests of NLRÐ1 airfoil with polynomial fits of
Ames test data.
slightly outside. Very little scatter was observed in
the Ames test of this airfoil.
An extensive set of unsteady airloads and
dynamic stall data have been obtained for the NLRÐ1
airfoil (Ref. 17, 18). The test data were obtained in
the Boeing Supersonic Wind Tunnel, using a twodimensional subsonic insert. The airfoil chord was
6.38 in and, with the installed subsonic insert, the test
section was 36 in high and 12 in wide. Seventeen
differential transducers were installed on the model
and the pressures were integrated to provide cn and
cm. The data were obtained over a Mach number
range from 0.2 to 0.7 and for numerous combinations
of mean and alternating angles of attack, both stalled
and unstalled. For comparison with the Ames data,
only test points with M = 0.2 or 0.3 are used. In
addition, test conditions have been excluded in those
cases where the sum of the mean and alternating
amplitude is less than the static stall angle of 12.4
Figure 10 compares the data from Refs. 17, 18
with the Ames tests. The Reynolds number in the
Boeing tests is about 25% higher than the Ames tests.
The range of mean and alternating angles of attack is
similar to the Ames tests. The range of reduced
frequencies for the Boeing tests extends to 0.35, and
this is beyond the range tested at Ames. The
envelope of maximum cn and minimum cm for the
Boeing test is similar to that obtained at Ames and the
majority of test points fall within the ±1σ bounds of
the Ames data. Note again, as in the case of the
CEAT data for the VRÐ7 airfoil, these data are for the
normal force coefficient rather than the lift
Figure 11. Comparison of the measured NLRÐ1 static
maximum normal force coefficient and an estimate of
the a0 intercept from the dynamic stall data.
The dynamic stall data obtained on the NLRÐ1
section are of particular interest as they were obtained
over a large range of Mach numbers. The effects of
Mach number on the dynamic stall function have
been examined in Ref. 11. As Mach number
increases the dynamic stall function maintains
roughly the same shape as shown in Fig. 4, but is
reduced in extent. That is, at higher Mach numbers
the maximum cn and minimum cm obtained in the test
are reduced. In addition, there is a slight shift
downwards in the dynamic stall function with
increasing Mach number. This downward shift is
shown in Fig. 11, where an estimate of the
polynomial a0 coefficient (dynamic stall function
intercept) is shown as a function of Mach number.
Interestingly, the static cn measured on this airfoil
The dynamic stall functions of the nine airfoils
are compared in Fig. 13. Except for the NLRÐ1 and
NLRÐ7301, the form of the dynamic stall function for
these airfoils is similar. The poorest performance is
for the NACA 0015 profile, which is thicker than the
other helicopter sections. The thinner NACA 0012
profile shows better performance than the NACA
0015, and the second generation airfoils are, mostly,
substantially better than the symmetric NACA 0012.
The NLRÐ1 airfoil shows relatively good
performance in deep stall but, as noted previously, is
deficient in light stall conditions. The fixed-wing
section, the NLR-7301, starts with a higher a0 and b0
intercept than the other airfoils, but there is less of an
increase in lift as the stall becomes more severe.
(Ref. 17) shows a similar decrease with increasing
Mach number.
3.4 Airfoil Comparisons
The dynamic stall functions shown in Figs. 4Ð6
exhibit similar behavior and, as the function
approaches zero moment or zero drag, the lift
coefficient approaches the airfoil static cl . Figure
12 shows the dynamic stall function intercepts, that is
a0 and b0, as functions of the measured static cl of
the airfoils (Refs. 8, 12). As expected, the a0 and b0
intercepts are nearly the same for each airfoil and, for
most of the helicopter sections, the intercepts show a
lift increment over the static cl of 0.05 to 0.12.
The intercept values are largely defined by the
measurements for light stall conditions where no
dynamic stall vortex is shed and, in this sense, the
intercepts indicate the incremental lift that can be
obtained in unsteady motion without a moment or
drag penalty. The fixed-wing section, the
NLRÐ7301, has a considerably better cl than any
of the helicopter sections, but its dynamic stall
function shows an intercept well below the cl
which indicates that the airfoil will not obtain any lift
increment for unsteady motion. The NLRÐ1 airfoil,
which is a helicopter section designed for good
advancing blade transonic characteristics, does not
show good dynamic stall performance and the
intercept values are below the static cl .
Dynamic Stall in Maneuvering Flight
The dynamic stall function based on twodimensional wind tunnel data provides a useful means
of evaluating the dynamic stall performance of
various helicopter airfoil sections. A question of
interest, then, is to what extent can the dynamic stall
function be used to quantify the airfoil performance
during flight maneuvers. This section examines this
question, using flight data obtained on a UHÐ60A,
and also looks at three-dimensional effects.
4.1 UHÐ60A Flight Test Data
Reference 19 examined dynamic stall on a
highly-instrumented UHÐ60A helicopter for three
conditions: a level flight case at high altitude, a
diving turn at high load factor, and the UTTAS pullup maneuver. This examination demonstrated that
dynamic stall is remarkably similar for all of these
flight conditions and, in general, can be characterized
by the shedding of a vortex from near the leading
edge of the blade, just as has been observed in twodimensional wind tunnel testing.
The UTTAS pull-up maneuver from Ref. 19
(Counter 11029) was re-examined to obtain
maximum cn and cm values from the flight data that
correspond to the extrema obtained from the twodimensional tests. Data were examined at six radial
stations from 0.675R to 0.99R. The test maneuver is
basically a symmetric pull-up that has been modified
so that entry is made from level flight at VH. For the
case here, a load factor of 2.1g was obtained during
the pull-up. The measured oscillatory pitch-link
loads in this maneuver are shown in Fig. 14. In this
figure each symbol represents one revolution of the
Figure 12. Comparison of the a0 and b0 intercepts
from dynamic stall tests with the measured static
maximum lift coefficient from tests of nine airfoils.
Figure 13. Comparison of dynamic stall function for nine airfoils.
Figure 14. UHÐ60A oscillatory pitch-link loads in the
UTTAS pull-up (Ref. 19).
rotor. At the maneuver entry point, the oscillatory
loads are just under 1000 lb and, then, at about Rev
09, the loads rapidly increase until they reach a
plateau at about Rev 14. These loads are maintained
through Rev 22 for a duration of a little over two
seconds and then rapidly return to level flight values.
This maneuver is particularly useful for comparison
purposes as there are generally one to three cycles of
stall during each revolution from Rev 08 to Rev 25
and this provides many cnÐcm pairs to use in defining
the dynamic stall function.
Figure 15 provides a rotor disk map of the
dynamic stall events for Rev 14 during the pull-up
maneuver. The azimuth associated with each stall
event is defined as the mean of the azimuth at the cn
Figure 15. Rotor disk map showing dynamic stall
cycles on UHÐ60A rotor for Rev 14.
peak (lift stall) and the azimuth at the cm minimum
(moment stall). The first stall event occurs on the
retreating side of the rotor prior to 270 deg. The
dynamic stall for this first cycle initially occurs
inboard and then moves outboard towards the tip.
The second cycle occurs near the rear of the disk and,
except for the most outboard station, the stall occurs
simultaneously at all radial stations. The third cycle
occurs at about 45 deg in the first quadrant of the
the six radial stations are plotted separately and, for
each subplot, the individual data points represent
different revolutions during the flight maneuver. A
2nd-order polynomial based on the flight data is
shown in Fig. 17 and compared to the SC1095
polynomial from Table 1. Each figure also includes
the static stall characteristic measured in twodimensional tests (Ref. 8). At the two most inboard
stations, the flight data are 0.2 to 0.6 above the twodimensional characteristic. The airfoil at these
stations is the SC1094 R8, which is similar to the
SC1095 but has additional camber or droop at the
nose. No wind tunnel dynamic stall test data are
available for this airfoil so it is not known whether
the difference between the flight data and SC1095
dynamic stall function is because of the different
airfoil characteristics or for other reasons.
The flight data at 0.865R, which is about two
chords in from the tip, show good agreement with the
Ames test results. At 0.92R, about one and a quarter
chords in from the tip, the flight data show good
agreement with the Ames tests at the edge of the deep
stall region, but are somewhat lower in light stall. At
0.965R, a half chord from the tip, the flight data show
less lift in stall than would be predicted from the
Ames data and similar behavior is seen at 0.99R,
which is about 16% of a chord from the tip.
The primary effect of three-dimensional flow, as
observed for the first stall cycle during this maneuver,
appears to be a slight reduction in the dynamic stall
function for the radial stations within one chord of the
blade tip. An examination of the blade pressure data
(Ref. 19) shows that the dynamic stall vortex during
this first cycle is clearly in evidence at each of these
radial stations.
PizialiÕs oscillating wing data can be used to
examine three-dimensional effects in a manner
similar to the flight test data. Figure 18 shows data
from the Ref. 12 experiments where, as in the twodimensional tests, data are only included where the
combined steady and alternating angle of attack
exceeds the static stall angle. Data are shown at
seven spanwise stations and a polynomial fit is
included for the three-dimensional data as well as the
two-dimensional fit from Table 1. The static data
included in each figure are from three-dimensional,
quasi-static tests and therefore differ at each spanwise
Inboard on the wing, very good agreement is
observed between the two-dimensional and threedimensional characteristics. At 0.800Y, which is one
chord from the tip, the wing data follow the twodimensional characteristics, but it appears that a
rotor and, as with the second cycle, is simultaneous at
all radial stations.
All of the dynamic stall extrema for the UTTAS
pull-up are plotted on Fig. 16 and each of the three
cycles is indicated by a different symbol. Each
revolution (see Fig. 14) provides up to three extrema
for each radial station and there are approximately 17
revolution over the course of the maneuver which
results in 267 extrema. Included in Fig. 16 is the
SC1095 dynamic stall function from the Ames tests.
Although the trend of the flight test data is similar to
the dynamic stall function from two-dimensional
tests, the scatter is substantially increased. The
standard deviation of the flight data, relative to a
fitting polynomial, is about 0.31, where the standard
deviation for the wind tunnel test data is 0.07. Some
of this scatter is caused by the significant range of
Mach numbers in these data, from M = 0.2 to M =
0.8. In addition, the airfoil at the two inboard stations
is the SC1094 R8 and its stall characteristics may be
different from the SC1095. An approximate means of
correcting for Mach number effects has been
examined in Ref. 11. The correction was made based
on static cl and this reduced the standard deviation
to 0.25, but this scatter is still well above the twodimensional results.
Figure 16. Dynamic stall extrema during UTTAS
pull-up maneuver for UHÐ60A compared to SC1095
dynamic stall function.
4. 2 Three-Dimensional Effects
The lift and moment extrema that occur in the
first dynamic stall cycle of each revolution are
examined in Fig. 17 to see how the dynamic stall
behavior changes near the blade tip. As noted
previously, this first stall cycle occurs at the end of
the third quadrant at about 270 deg. Data for each of
Figure17. Dynamic stall extrema, for first stall cycle, measured at individual radial stations during UTTAS pull-up
compared with SC1095 dynamic stall function.
Figure18. Dynamic stall extrema measured on oscillating wing compared with NACA 0015 dynamic stall function.
number of the test points are unstalled, which
suggests that the vortex strength is reduced at this
station, compared to the two-dimensional case. At
0.900Y and 0.966Y, no dynamic stall occurs and there
is no indication in the pressure data that a dynamic
stall vortex is being shed at this location. The data at
0.966Y are 17% of chord inboard from the tip and are
comparable, therefore, with the data at 0.99R on the
UHÐ60A rotor. Further outboard on the wing, at
0.986Y and 0.995Y, the character of the lift and
moment data change and the unsteady data agree
quite closely with the data obtained for these
locations in quasi-static tests. The lift and moment
behavior at these outboard stations is a result of tip
vortex formation, not a shed dynamic stall vortex.
The comparison shown here, between dynamic
stall on a helicopter blade in flight and on an
oscillating wing in a wind tunnel, shows similarities
and differences. Inboard, both tests show that the
dynamic stall behavior is very similar to that
observed in two-dimensional tests. Within one or two
chords of the blade or wing tip, however, the two test
data sets differ. For the helicopter rotor blade, a shed
dynamic stall vortex is clearly observed for all of the
outer blade stations. Within a chord of the tip, the
flight data show a small reduction in the dynamic stall
function, while the basic character is similar to that
observed in two-dimensional tests. The oscillating
wing, on the other hand, indicates that a shed
dynamic stall vortex is no longer present within a
chord of the oscillating wing tip. The difference in
the three-dimensional behavior between the
helicopter and oscillating wing may be caused by
differences in the radial velocity distribution or
possibly other factors. The oscillating wing data
remain a valuable resource in the development and
testing of theoretical methods. However, as an
analogue for dynamic stall on a helicopter blade in
flight, the oscillating wing data do not appear
5.1 Semi-empirical Models
Most comprehensive analyses used in the
helicopter industry, government agencies, and
academia use some form of lifting-line theory to
calculate the aerodynamic loads on the rotor. In these
analyses the steady aerodynamic forces and moment
are based on tables or formulae from two-dimensional
wind tunnel tests. The steady data are then modified
to account for unsteady aerodynamics in the
calculation of the loading. For angles of attack
beyond the static stall angle, this approach
underpredicts the aerodynamic loads and some form
of semi-empirical dynamic stall model is used to
provide the lift, drag, and moment as a function of
angle of attack. The dynamic stall function can be
used to check these models and one example is shown
The comprehensive analysis CAMRAD II
includes five semi-empirical dynamic stall models
(Ref. 20). These include the models used by Boeing
(Ref. 21) and Johnson (Ref. 22), which are simpler
models with few parameters to fit; the LeishmanBeddoes model (Ref. 23); and two ONERA models:
the Edlin method developed by Tran and Petot (Ref.
24), and the Hopf Bifurcation model developed by
Truong (Ref. 25). As each of the models is semiempirical it is necessary to adjust or identify the
model parameters based on test data. This has been
done within CAMRAD II for the NACA 0012 airfoil,
but not for other airfoils. Thus, it is expected that
these models will provide a better prediction of the
NACA 0012 characteristics than for other airfoil
The predictions of the five models are compared
with single test points for the NACA 0012 and
SC1095 sections in Fig. 19. The two test points
represent moderate to fairly severe stalled conditions.
Most of the models provide a reasonable prediction of
the maximum lift, but are substantially less accurate
in predicting the minimum moment. In particular, the
Boeing and ONERA Edlin models show a significant
underprediction of the negative moment. The other
models show poor-to-fair agreement in moment.
Although it was anticipated that the predictions for
the NACA 0012 would be better than for the SC1095,
since the semi-empirical parameters in the models are
based on NACA 0012 test data, this is not the case.
Since only one stall condition was evaluated in
Ref. 20, an assessment of the semi-empirical models
is difficult. An appropriate evaluation should include
not only moderate stall conditions, as shown here, but
also a light stall case and a severe, deep stall case.
Dynamic Stall Function as a Metric
It has been shown here that the dynamic stall
function can be used to evaluate airfoil dynamic stall
performance from two-dimensional wind tunnel test
data and that these characteristics are related to the
measurements obtained on a helicopter during a
maneuver. The dynamic stall function can also be
used as a means of evaluating theoretical calculations
or experimental measurements of novel airfoil
Figure 19. Comparison of synthesized data for NACA 0012 and SC1095 profiles using five semi-empirical models
(Ref. 20).
in Ref. 26 shows that the extrema occur over a very
short range of time steps compared to the data and
there is an associated phase shift. In addition, the
experimental case used here included two shed
vortices (Ref. 9) and the Navier-Stokes calculations
indicate only a single vortex.
Simple changes to the boundary layer, as induced
by a boundary layer trip, for example (Ref. 11), do
not show a substantial effect on the dynamic stall
function for experimental measurements. The
ONERA calculations show a more significant
influence of the boundary layer in the example here
and this emphasizes the necessity of extensive
experimentation with computational models before
their utility can be demonstrated.
5.2 CFD Models
Numerous numerical methods have been
developed for the direct calculation of dynamic stall
on an oscillating airfoil and this approach remains an
exciting challenge for investigators interested in
classical fluid mechanics. These methods, presently,
are at a research or pilot stage and there has been no
anticipation of their use within the design process.
Eventually, however, it is envisioned that the best of
these methods will show some utility in the
development of semi-empirical models used within
the comprehensive analyses. One example of a
Navier-Stokes prediction for a case from the NACA
0012 data obtained at Ames is shown here.
Rouzaud and Plop have reported the
development of a Reynolds-averaged, Navier-Stokes
solver at ONERA (Ref. 26). They have examined the
effects of two turbulence models: those of Baldwin
and Lomax, and Launder and Sharma. They have
compared their analysis with a severe stall case for
the NACA 0012 from the Ames tests. These
predictions, along with the data point from the Ames
tests, and the polynomial fits from Tables 1 and 2, are
compared in Fig. 20. The calculations with the
Baldwin-Lomax model severely overpredict the
moment and the drag is also high. However, the
prediction using the Launder-Sharma model provides
good results. In this sense, the Launder-Sharma
model passes the necessary condition that there must
be a good prediction of the extrema. However, an
examination of the time behavior of the coefficients
5.3 Experimental Tests of Multi-element or
Variable Geometry Airfoils
As shown in this paper, conventional, singleelement airfoils show similar dynamic stall
characteristics. Although it is expected that small
gains in performance, in terms of dynamic stall, may
be obtained through careful design, substantial
improvements do not appear feasible. Improved
dynamic stall performance using multi-element or
variable geometry airfoil designs, however, may be
possible. Two multi-element airfoil designs have
been tested in the Ames water tunnel (Ref. 15, 27)
and their performance here is compared to the
dynamic stall function to illustrate the utility of this
approach as a means of evaluation.
Figure 20. Comparison of Navier-Stokes predictions for NACA 0012 airfoil data using two turbulence models (Ref.
Figure 21. Comparison of dynamic stall extrema for a basic VRÐ12 with an extendable leading-edge slat (Ref. 27).
Fig. 21. The airfoil profile with the slat extended is
also illustrated. No dynamic stall data are available
for the VRÐ12 from wind tunnel testing, so the
polynomials for the VRÐ7 airfoil from Tables 1 and 2
are used as an approximate representation of the
baseline airfoilÕs dynamic stall function. The water
tunnel data for the VRÐ12 airfoil show generally
good agreement with VRÐ7 polynomials based on the
Ames tests. The effect of the extendable slat on the
dynamic stall performance is negligible, as essentially
In Ref. 27, Plantin de Hugues et al. examined the
dynamic stall performance of a VRÐ12 airfoil with
and without an extendable leading edge slat. These
data were obtained in the identical fashion as
previously discussed for the VRÐ7 airfoil, Ref. 15.
The extendable slat was designed, so that when
retracted, the slat would fit inside the profile of the
unmodified VRÐ12. The experimental data obtained
in the water tunnel for both the basic VRÐ12 (slat
retracted) and with the slat extended are shown in
Figure 22. Comparison of dynamic stall extrema for a basic VRÐ7 airfoil and a VRÐ7 with a leading-edge slat (Ref.
the same dynamic stall function is obtained with or
without the leading-edge slat. For identical test
conditions, the extendable slat appears to reduce the
strength of the dynamic stall vortex, but this gives no
advantage in dynamic stall performance over a
conventional single-element airfoil.
A VRÐ7 airfoil was tested in the Ames water
tunnel in a configuration with a leading edge slat
(Ref. 15). The slat design was different from the
VRÐ12 configuration just discussed. Baseline data
for this configuration have already been shown in Fig.
9. The baseline data are repeated in Fig. 22, along
with the data obtained with the slat. The VRÐ7
dynamic stall function, from Tables 1 and 2, are also
included in the figure. As previously noted, the water
tunnel data for the basic VRÐ7 airfoil show good
agreement with the dynamic stall function based on
the Ames wind tunnel tests. Unlike the VRÐ12 with
an extendable leading edge, the dynamic stall
performance of the VRÐ7 with the leading-edge slat
is very different from the baseline airfoil. This multielement configuration shows a substantially
augmented lift capability with a reduced penalty in
terms of pitching moment and drag. In this sense,
this airfoil is clearly an improvement over a
conventional single-element airfoil.
Design Considerations
The dynamic stall function provides a useful
means of evaluating the experimental characteristics
of conventional airfoils as well as of novel designs, as
illustrated here for two multi-element airfoils. This
comparison also points out that it is not sufficient to
suppress the dynamic stall vortex or reduce its
strength, if the only result is that the lift, moment, and
drag are simply shifted to lower values. The reality
of a maneuver on a helicopter is the necessity of
achieving a maximum thrust capability. If a new
design simply shifts the location on the dynamic stall
function where dynamic stall occurs, this has no
utility, as the pilot will persist in moving the flight
controls until maximum thrust is achieved. A
comparison, therefore, of a novel design with a
current airfoil must be done on the basis of the
moment and drag penalties that occur at a constant lift
level. A comparison of two airfoils for the same α0,
α1, and k values is not sufficient if the same lift is not
Concluding Remarks
The loading on an airfoil, measured during twodimensional dynamic stall testing, was evaluated for
eight airfoils tested in the NASA-Ames 7- by 10-Foot
methods, and experimental tests of multi-element
airfoils. These comparisons have emphasized that in
evaluating new or improved airfoils, merely
suppressing the dynamic stall vortex has little utility.
Rather, a new design should have lower moment and
drag penalties for the same airfoil lift.
Wind Tunnel by McCroskey and his colleagues and
for a ninth airfoil tested subsequently by Piziali. The
loading, characterized by the peak airfoil lift and
drag, and minimum pitching moment, is shown to be
similar over a wide range of test conditions. The
loading characteristic is herein termed the dynamic
stall function and is a useful measure of airfoil
dynamic stall performance.
The dynamic stall function was characterized
using 2nd-order polynomials for maximum lift as a
function of minimum moment, and maximum lift as a
function of maximum drag. The steady polynomial
coefficients, a0 and b0, are shown to be closely related
to the airfoilÕs static cl . In general, the a0 and b0
values show an increment of 0.05 to 0.12 in lift over
the static cl . This indicates that an airfoil with an
improved cl will also show improved dynamic stall
The dynamic stall functions obtained from the
Ames tests were compared to other dynamic stall data
from a variety of test facilities and generally good
agreement was obtained.
The dynamic stall function appears to be
relatively insensitive to a number of operational
parameters and this was particularly noted in the case
of Reynolds number. Essentially identical results
were obtained for a water tunnel test with a Reynolds
number of 100,000 to 250,000 as for a wind tunnel
test with a Reynolds number of 4 million. This
insensitivity to Reynolds number is a clear indication
of the dominating effect on the loading of the
dynamic stall vortex.
The dynamic stall function measured in flight
during a severe maneuver was examined and,
although the scatter is greatly increased relative to
two-dimensional tests in the wind tunnel, similar
behavior is observed. An examination of the threedimensional characteristics for the flight case was
made. The dynamic stall vortex extends right to the
tip with little reduction in the augmented lift. These
three-dimensional effects are compared to dynamic
stall on an oscillating wing (obtained in a wind
tunnel) where the dynamic stall vortex disappears
within a blade chord of the tip. Although both tests
show some three-dimensional effects at the tip, these
are weak for the flight aircraft and strong for the
oscillating wing and, hence, the two test cases are
poor analogues. However, the highly twodimensional character of the flight data provides
encouragement that an accurate prediction of threedimensional effects is not important for the prediction
of dynamic stall on a flight vehicle.
The dynamic stall function was used to evaluate
the prediction of semi-empirical models, CFD
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American Helicopter Society 53rd Annual
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