Airfoil Dynamic Stall and Rotorcraft Maneuverability

WILLIAM G. BOUSMAN

Army/NASA Rotorcraft Division

Aeroflightdynamics Directorate (AMRDEC)

US Army Aviation and Missile Command

Ames Research Center, Moffett Field, California

SUMMARY

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 effects such as the airfoil

section profile and Mach number, and appears to be independent of such parameters as Reynolds number, reduced

frequency, and blade sweep. For single-element airfoils there is little that can be done to improve rotorcraft

maneuverability except to provide good static cl

max characteristics and the chord or blade number that is required to provide

the necessary rotor thrust. However, multi-element airfoils or airfoils with variable geometry features can provide

augmented lift in some cases that exceeds that available from a single-element airfoil. The dynamic stall function is

shown to be a useful tool for the evaluation of both measured and calculated dynamic stall characteristics of singleelement, multi-element, and variable geometry airfoils.

NOMENCLATURE

ai, bi polynomial coefficients for cl

max , i =

0,1,2

as speed of sound, ft/sec

b number of blades

c blade chord, ft

cc section chord force coefficient

cd section drag coefficient

cdmax maximum drag coefficient in dynamic

stall, Fig. 6

cd0 section drag coefficient at zero lift

cl section lift coefficient

cl

max maximum lift coefficient in dynamic

stall, Fig. 6

cl static cl

max

cˆ

l corrected section lift coefficient, eq (10)

cm section moment coefficient

cmminminimum moment coefficient in

dynamic stall, Fig. 6

cn section normal force coefficient

C section chord force, lb

CL mean blade lift coefficient

CP0 profile power coefficient

CT thrust coefficient

e root cutout radius, ft

k reduced frequency

M Mach number; section moment, ft-lb/ft

Ma blade aerodynamic moment, ft-lb

Mc Mach number normal to leading edge

Msp fixed-system control moment, ft-lb

MT hover tip Mach number

M∞ free stream Mach number

q dynamic pressure, lb/ft2

r blade radial location, ft; correlation

coefficient

rsp swashplate moment radius, ft

R blade radius, ft

Re Reynolds number

T rotor thrust, lb
2

Tb blade thrust, lb

V(r,ψ) section velocity, ft/sec

VH maximum level flight speed, ft/sec

VT hover tip speed, ft/sec

α section angle of attack, deg

α0 mean angle of attack, eq (7), deg

α1 alternating angle of attack, eq (7), deg

∆cl Mach number correction for lift

coefficient, eq (11)

θ airfoil deformation angle, eq (21)

Λ sweep angle, deg

μ advance ratio

μv viscosity, lb-sec/ft2

ρ density, slugs/ft3

σ solidity; standard deviation

ψ azimuth angle, deg

ω oscillation frequency, 1/sec

Ω rotor speed, 1/sec

Superscript:

* limit condition

INTRODUCTION

The thrust capability of a helicopter rotor is

directly related to the lift capability of the blade airfoil

section. In forward flight the thrust of one blade can be

expressed as

T cV c r r

R

dr b T l e

R

( ) ( , )[ sin ] ψ ρ ψ μψ = + ∫ 1

2

2 2 (1)

and the thrust of the rotor must be summed over the b

blades. In hover, eq (1) can be simplified if a mean blade

lift coefficient, CL, is defined that is not dependent upon

the radius, r, or the blade azimuth, ψ

T cRV C b TL = 1

6

2 ρ (2)

The blade thrust can then be summed over the number of

blades and, in terms of the thrust coefficient, CT/σ, the

classical result is obtained

C C T

L

σ = 16 (3)

For a helicopter with MT = 0.65 and with CL defined at

0.75R, then for a modern airfoil such as the Sikorsky

SC1095, the maximum CL is about 1.1 (Ref. 1). In this

case, the maximum rotor thrust that can be expected is

CT/σ ~ 0.18.

In forward flight, the airfoil lift coefficient in eq

(1), cl (r,ψ), will be affected by the advance ratio and, if it

is assumed that roll moment balance must be maintained

at the rotor thrust limit (Ref. 2), then

C C T L

σ

μ μ

μ = − ++











 6

1 94

13 2

2 4

2

/

/ (4)

McHugh and his colleagues have measured the thrust

capability of a 10-foot diameter CH–47B model rotor in

the Boeing 20- by 20-foot V/STOL Wind Tunnel (Ref. 3,

4). These measurements are particularly useful as the

rotor was designed with sufficient structural strength that

the true aerodynamic thrust limit could be identified, that

is, the collective pitch angle where the rotor thrust reached

its maximum value. The rotor thrust limit from the

Boeing tests is shown in Fig. 1 and is compared to the

limit calculated from eq (4), assuming CL = 0.94.

The problem of relating rotor thrust capability to

airfoil section characteristics becomes more difficult than

suggested by eq (1) when it is recognized that the rotor

thrust limit is not dependent upon the maximum static

airfoil lift, but that there is an unsteady or dynamic

component that increases the thrust capability (Ref. 5).

Measurements of the rotor thrust of a full-scale H–21

rotor in the 40- by 80-Foot Wind Tunnel, by McCloud

and McCullough (Ref. 6), demonstrated that the rotor was

able to provide more thrust than would be calculated using

just the static airfoil lift coefficient (Ref. 5). This

additional lift, what is now referred to as dynamic stall,

has been the subject of extensive research over the past 40

years (Ref. 7, 8).

A fundamental problem for the rotor designer,

then, is to what degree does the airfoil design affect the

rotor’s thrust capability and, probably more important, the

increased pitching moment and power that accompanies

the augmented lift associated with dynamic stall. The

McCloud and McCullough experiments (Ref. 6) provided

a partial answer in that they demonstrated that a second

rotor, with improved static cl

max capabilities, also

improved the overall rotor thrust. Their measurements

showed that the increment in rotor thrust for the second

rotor was approximately proportional to the increase in

the static cl

max of the improved airfoil.

A great deal of fundamental information relating

to dynamic stall has been obtained since the first critical

experiments of Ref. 6, particularly from wind tunnel tests
3

of two-dimensional airfoil sections. Notable among these

tests are the experiments performed by McCroskey and his

colleagues (Refs. 9–11) wherein they examined the

dynamic stall characteristics of eight airfoils in a

comparative fashion in the 7- by 10-Foot Wind Tunnel at

NASA Ames Research Center. The purpose of the

present study is to use the Ames test data to better

understand the airfoil design characteristics that affect the

augmented lift in dynamic stall and the associated moment

and drag penalties. These data, as well as other test data,

will be used to understand what parameters most strongly

influence the dynamic stall loading. A comparison will

be drawn between dynamic stall loading as obtained from

two-dimensional wind tunnel data and from recent flight

tests of a UH–60A (Ref. 12). Based on the various test

data some general comments will be provided as concerns

design for rotorcraft maneuverability based on airfoil

dynamic stall characteristics on single-element airfoils.

The study will conclude with an examination of the

possibility of enhanced maneuverability using multielement airfoils or airfoils with variable geometry.

COMPARATIVE AIRFOIL TESTS

Ames Test Program

McCroskey and his colleagues (Refs. 9–11)

tested eight airfoils in the NASA-Ames 7- by 10-Foot

Wind Tunnel. Each airfoil was tested using the same

dynamic rig and, in general, the same range of test

conditions was covered. The eight profiles are shown in

Fig. 2.

The first of the eight profiles, the NACA 0012,

is representative of the first generation of airfoils used for

helicopters and has a symmetric section. With slight

modifications this section was used for Sikorsky Aircraft’s

H–34 family of helicopters, which first flew in 1954.

The AMES–01 airfoil was specifically designed

for use in helicopters and is representative of a second

generation of airfoils. It has not been used, however, in

an operational helicopter.

The Wortmann FX 69–H–098 airfoil is also a

second-generation airfoil and was designed for Bell

Helicopter Textron for use in some of their two-bladed

helicopters. For application to flight vehicles the airfoil

was modified to add camber near the trailing edge to shift

the section moment to zero and the modified airfoil is

different from the airfoil tested at NASA Ames. The

modified airfoil has been used in the 214 series of

helicopters (214A, 214B, 214C, and 214ST) and also the

AH–1T and AH–1W helicopters.

The Sikorsky-designed SC1095 airfoil is another

second-generation airfoil and is used on both their

UH–60A Black Hawk and the S–76. The airfoil is used

both inboard and outboard on the UH–60A with a

modified section, the SC1094 R8, used over the midportion of the blade. For the S–76, the SC1095 is used

only on the outer portion of the blade. Inboard the

SC1094 R8 is used for the mid-portion and transitions to

the SC1013 R8 near the blade root (Ref. 13). The

SC1095 airfoil as used on the S–76 includes a –3 deg

reflexed tab, to reduce the negative moment on this

section, and this is different from the airfoil tested at

Ames. The SC1095 on the UH–60A does not include a

tab and is identical to the airfoil evaluated in the Ames

program.

The Hughes Helicopters HH–02 profile was

tested with a –5 deg tab to balance out the pitching

moment from the camber of the airfoil. This secondgeneration airfoil is used on the AH–64A and AH–64D

helicopters.

The VR–7 profile was developed by Boeing

Vertol and was tested with a –3 deg tab in the Ames tests.

This airfoil is used on the current Boeing CH–47D, but

with a –6 deg tab. The VR–7 is also considered a secondgeneration airfoil.

The NLR–1 profile was designed specifically for

improved transonic performance and has been test flown

on an instrumented AH–1G helicopter (Ref. 14, 15).

Although it has good high Mach number performance its

low-speed characteristics are unsatisfactory and it has never

been used for a production helicopter.

The last profile, the NLR-7301, is representative

of a supercritical, fixed-wing section. Compared to the

other seven airfoils, it is characterized by a large leadingedge radius and large aft camber which results in large

negative pitching moments at all angles of attack. It is

not considered suitable for use in helicopter applications,

but was included in the test program to better understand

the dynamic stall characteristics of fixed-wing airfoil

sections with significantly different leading edge

geometries.

The airfoil chord for all of the eight profiles was

24 in. The airfoil was mounted vertically in the test

section of the 7- by 10-Foot Wind Tunnel such that the

airfoil spanned the shorter dimension. Thus the 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
4

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.

cc c

cc c

l c n

d c n

=− +

= +

sin cos

cos sin

α α

α α

(5)

The cd calculated in this manner does not include the

viscous drag, of course. The uncertainty in the section

forces and moment in deep stall has been estimated (Ref.

9) as

c

c

c

l

d

m

= ±

= ±

= ±

0 20

0 05

0 10

.

.

.

(6)

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

αω α α ω ( ) sin t t = +0 1 (7)

The lift, drag, and section moments for these conditions

were provided in Ref. 10 for each of the eight airfoils.

The number of test conditions, as defined by the mean

angle of attack, α0, the alternating angle of attack, α1, the

reduced frequency, k, and the Reynolds and Mach numbers

range from 49 for the Wortmann FX 69–H–098 to 121 for

the NACA 0012. Not all of these test points are included

here. For the NACA 0012 airfoil, a number of cases were

for quasi-static rather than dynamic stall conditions, that

is, the reduced frequency was approximately zero (k <

0.005), and these 21 conditions are not included. For the

NLR–1 airfoil, a set of test cases was run with α0 = –2

deg and α1 = 10 deg and, therefore, dynamic stall occurred

for negative lift conditions. These eight test cases have

also been excluded from the comparisons shown here.

Finally, 13 test conditions for the NLR–7301 are excluded

where α0 was set close to the static stall angle, and small

values of the alternating angle of attack, α1 = 2 deg, were

used to better understand this airfoil’s 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 cycle.

The Reynolds and Mach numbers for the test

conditions for the eight airfoils are shown in Fig. 3. The

maximum test section velocity is approximately M = 0.3

and this provides a Reynolds number of about four

million. As this tunnel operates with the stagnation

pressure vented to the atmosphere, the Reynolds number

is proportional to the Mach number as shown in the

figure. Reynolds number is also proportional to Mach

number for a helicopter in flight and this proportionality

is indicated in Fig. 3 for a number of the helicopters that

use the indicated airfoil sections. The Reynolds number

depends upon Mach number as

Re = ρ

μ

cas M

v

(8)

The helicopter characteristics shown in Fig. 3 are

calculated assuming flight at a pressure altitude of 3000

feet on a standard day. In this case ρ = 0.002175 slug/ft3,

as = 1105 ft/sec, and μ = 3.738 x 10-7 lb-sec/ft2.

The 24 in. chord used in the Ames tests provides

reasonably representative Reynolds numbers for these

airfoils over the Mach number test range. Note, however,

that these Mach numbers cover only the lower end of the

flight vehicle range where Mach numbers typically exceed

0.8 or 0.9 near the tip of the blade at high speed.

The mean and alternating angles of attack are

shown in Fig. 4 for the eight airfoils. Most of the test

points were for alternating angles of 5 and 10 deg, and

mean values of 5, 10, and 15 deg.

The reduced frequencies for the Ames tests are

shown as a function of Mach number in Fig. 5 for the

eight airfoils. For most of the airfoils the reduced

frequency ranged from about 0.025 to 0.20. For the

NACA 0012, the upper range of reduced frequency was

extended to values as high as 0.28.

Section force and moment time histories are

provided in Ref. 10 for each airfoil and each test case.

Figure 6 shows an example of the lift, drag, and moment

loops for a test condition for the NACA 0012 that

represents deep stall. Indicated on this figure are the

maximum lift point, the maximum drag point, and the

minimum moment point for 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 cycle.

The extrema from the Ames tests are shown in

Figs. 7 and 8 for all of the airfoils. Figure 7 shows the

maximum cl

 as a function of the minimum cm, and Fig. 8

shows the maximum cl as a function of the maximum cd.

The maximum lift, maximum drag, and minimum

moment are related by the dynamic stall vortex that is

shed from near the leading edge during deep stall.

However, these extrema do not occur simultaneously, and

the functional behavior shown in Figs. 7 and 8 represents

the envelope of loading rather than a simultaneous load.

Included in Fig. 7 are the measured static stall

characteristics at M = 0.3 from Ref. 9. Below stall there

is little variation in pitching moment with lift, as
5

expected. Most of the airfoils have very low steady

moments so as to avoid high loads in the control system.

The FX 69–H–098 and the SC1095 both show steady

moments as large as –0.03 or –0.04 but the other profiles

are closer to zero. The NLR–7301, however, shows a

significantly larger steady moment than the helicopter

sections, about –0.18. For a fixed-wing section, where

the moment is reacted by the tailplane, negative moments

of this size do not represent a serious problem. For

helicopters, however, where the moments must be reacted

by the control system, it is necessary to avoid large

aerodynamic moments.

In Fig. 8, the static drag measurements are

included in this figure as a dotted line and the drag

determined from wake measurements is shown by a solid

line. The latter measurements include viscous drag

effects. The steady drag measurements shown here were

obtained at M = 0.3.

The most obvious feature observed in Figs. 7 and

8 is that dynamic stall is characterized as a fairly uniform

or monotonic function. To a degree this result is expected

as most of the test points in these figures (cm < –0.15 and

cd > 0.4) are associated with one or more dynamic stall

vortices that are shed from near the airfoil leading edge.

The dynamic stall vortices, once formed, clearly dominate

the lift, the drag, and the moment and a universal

relationship is exhibited.

A second feature observed in Figs. 7 and 8 is that

as the dynamic moments and drag approach zero, the

dynamic lift approaches its static maximum value as well.

This characteristic is reasonably to be expected as at nearzero values of moment and drag, no vortex shedding is

associated with the unsteady airfoil motion and the

unsteady lift is not much greater than the static lift.

The data from Figs. 7 and 8 are repeated in Figs.

9 and 10 and are separated into cases with and without a

boundary layer trip. The untripped data are fitted with a

2nd-order polynomial as shown by the dashed lines. The

polynomials are defined as

c a ac ac

c b bc bc

l m m

l dd

=+ +

=+ +

01 2

2

01 2

2 (9)

The polynomials in eq (9) are referred to here as the

“dynamic stall functions.” The tripped boundary layer data

were excluded from the fit as it appears that these data

have a small but significant influence on the dynamic stall

function. The effect of the boundary layer trip is discussed

in greater detail in a subsequent section. The coefficients

of the fitting polynomials are shown in Tables 1 and 2

along with two measures of dispersion: the coefficient of

determination, r2, and the standard deviation, σ.

The polynomial fits obtained in Figs. 9 and 10

provide a fairly good representation of the dynamic stall

behavior with the exception, perhaps, of the fixed-wing

section, the NLR-7301, which shows more scatter than

the other airfoils.

The dynamic stall functions, based on cm and cd,

are compared for the seven helicopter sections in Fig. 11.

The polynomial fits are from Tables 1 and 2. At values

near zero cm or cd, the lift is close to the static cl

max. As

the section achieves higher cl in dynamic stall, the

moment becomes more negative and the drag more

positive. The NACA 0012 airfoil defines a rough lower

bound for the dynamic stall function over most of the

moment and drag values, and each of the second generation

airfoils shows improved capability with ∆cl of 0.2 to 0.5.

Some of the second-generation airfoils show an

improvement in the intercept, either a0 or b0, most

notably the VR–7 with the –3 deg tab. Other profiles,

however, show the biggest improvement at higher lift,

such as the AMES–01 and the HH–02. The NLR–1

shows good performance at moderate lift coefficients, but

near zero cm or cd, this airfoil shows reduced dynamic lift

and does not even match its static cl

max.

Another way to compare the dynamic stall

functions is separate out the static portion. This

comparison is shown for the seven helicopter sections in

Fig. 12 by plotting cl/a0 and cl/b0 as functions of cm and

cd. Except for the NLR–1, the dynamic stall functions for

these airfoils are very similar. Based on this comparison,

the AMES–01 and HH–02 airfoils appear to have the best

performance in the region with deep dynamic stall.

A comparison of the a0 and b0 intercepts in

Tables 1 and 2 shows that, in general, the intercepts for

each airfoil agree closely. This result is expected as the

dynamic stall behavior shown here, that is, the peak

loading that is seen in lift, moment, and drag are all the

result of the same unsteady aerodynamic phenomena.

There appears to be a rough correspondence

between the a0 and b0 intercepts from the dynamic stall

function and the measured static cl

max as shown in Fig.

13. A linear regression has been computed for the

relationship in Fig. 13 and the slopes relating the a0 and

b0 intercepts are 1.97 and 1.83, respectively, and the

intercepts are –1.28 and –1.13. However, the functional

relationship shown here is strongly affected by the poor

dynamic performance of the NLR–1 airfoil at near-zero

values of moment and drag and it is probably best to avoid

reading too much into the fitted line. It is sufficient to

conclude that an airfoil with a better static cl

max will also

provide better dynamic stall performance—a conclusion

reached by McCloud and McCullough over 40 years ago

(Ref. 6).
6

Table 1. – 2nd order polynomial fit of dynamic stall function, lift as a function of moment.

AIRFOIL a0 a1 a2 r2 σ

NACA 0012 1.439 -0.791 2.232 0.81 0.14

AMES–01 1.627 -0.361 4.210 0.85 0.13

FX 69–H–098 1.530 -0.107 3.519 0.84 0.12

SC1095 1.582 -0.532 2.869 0.95 0.07

HH–02 1.474 -0.643 4.054 0.95 0.08

VR–7 1.672 -0.229 3.773 0.84 0.14

NLR–1 1.184 -2.721 0.026 0.93 0.10

NLR–7301 1.618 -2.392 -0.973 0.53 0.15

Table 2. – 2nd order polynomial fit of dynamic stall function, lift as a function of drag.

AIRFOIL b0 b1 b2 r2 σ

NACA 0012 1.371 0.741 0.156 0.82 0.14

AMES–01 1.571 0.679 0.368 0.86 0.12

FX 69–H–098 1.516 0.238 0.649 0.85 0.12

SC1095 1.485 0.971 0.044 0.93 0.08

HH–02 1.373 0.997 0.129 0.93 0.09

VR–7 1.673 0.402 0.448 0.86 0.14

NLR–1 1.208 0.990 0.332 0.91 0.11

NLR–7301 1.769 1.010 -0.361 0.48 0.16

A review of the airfoil dynamic stall time

histories in Ref. 10 shows qualitative differences between

the various test conditions. These time histories have

been examined and a judgment has been made as to

whether, (1) a dynamic stall vortex is not evident in the

data, (2) a single dynamic stall vortex is evident and is

clearly shed from the airfoil, and (3) two dynamic stall

vortices are shed. In most cases these distinctions are

clear, but there are also situations where the time history

is ambiguous and the classification may not be

satisfactory. The dynamic stall data points, each assigned

to one of the three classifications, are shown in Figs. 14

and 15 and are compared with the polynomial fits of

Tables 1 and 2. This comparison shows that for the most

part, those conditions where dynamic lift is only slightly

higher than the airfoil maximum static lift coefficient are

generally characterized by light stall conditions where no

dynamic stall vortex is apparent. For more severe loading

conditions, a single dynamic vortex is observed, while for

the most severe loading, two dynamic stall vortices are

seen. The test points with two dynamics stall vortices

represent those conditions in the Ames tests that had the

greatest excursions in lift, moment, and drag.

Comparison of Ames Test Data with Other

Sources

An examination of dynamic stall data from the

eight airfoils tested in the Ames 7- by 10-Foot Wind

Tunnel (Refs. 9-11) shows that the loading in lift,

moment, and drag is very similar for the seven helicopter
7

airfoil sections over a wide range of parameters. It is

expected that these results should be supported by dynamic

stall test results from other facilities and comparisons are

shown in this section between the Ames data and a

number of other data sources for the NACA 0012,

SC1095, VR–7, and NLR–1 airfoils.

NACA 0012 dynamic stall test data were

obtained in the UTRC Main Wind Tunnel in an

investigation whose primary focus was to examine the

effects of blade sweep (Ref. 16). However, this

experiment also included unswept data as a baseline, and it

is these unswept data that are examined here. The effects

of sweep are discussed in a later section. Twelve pressure

transducers were installed on the upper surface of the

airfoil and eight on the lower surface, both in Gaussian

arrays. Lift, drag, and moment were obtained by

integrating the measured pressures and the cn and cc

coefficients were converted to wind tunnel axes using eq

(5). The test conditions and the maximum cl and cd, and

minimum cm are compared with the Ames tests results in

Fig. 16. The Ames test data are limited to those values

used to determined the polynomial fits in Tables 1 and 2.

Most of the UTRC data were obtained for M =

0.3, but a few values were also obtained at M = 0.1. The

range of alternating and mean amplitudes and the reduced

frequencies tested generally overlap the Ames test

conditions. The maximum cl and minimum cm values,

and the maximum cl and cd values obtained from the

UTRC dynamic stall loops compare quite well with the

polynomial fit obtained from the Ames data, generally

being within ±1σ of the Table 1 and 2 polynomials.

Three or four values at high lift are well outside the Ames

data scatter, however. These high lift points are the

values obtained at M = 0.1 and it is not clear whether the

low Mach number is a contributing influence.

Dynamic stall data have been obtained for the

SC1095 (and SC1094 R8) airfoil using the Ref. 16 test

rig in the UTRC Main Wind Tunnel, but these data have

not been published. However, a very limited number of cl

and cm loops have been shown by Gangwani (Ref. 17),

and these are compared with the Ames test data for the

SC1095 airfoil in Fig. 17.

The five UTRC test conditions were obtained for

M = 0.3 and generally fall within the range of the Ames

test conditions. The cl and cm extrema are slightly below

the Ames polynomial fit and two of the points are slightly

outside the ±1σ bounds.

Two sources of dynamic stall data have been

examined for the VR–7 airfoil. The first data set is from

the Centre D’Essais 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. 18. The second data set is from the

Ames water tunnel (Ref. 19). The CEAT data were

obtained in a conventional atmospheric wind tunnel using

a model with a 40-cm chord. Thirteen transducers were

installed on the airfoil to measure differential pressure 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 inches chord mounted

in the water tunnel’s 8.3- by 12-inch test section. The

lift, drag, and moment were measured by an external

balance with corrections for friction, but not for inertial

loads, which were considered negligible (Ref. 19). The

data from these two tests are compared with the Ames

data in Fig. 18.

The CEAT data were obtained at three Mach

numbers and show a Reynolds number about a third

lower than the Ames tests. The Mach number for the

water tunnel tests was, of course, zero and the Reynolds

number varied from 100,000 to 250,000. This range of

Mach and Reynolds numbers differs substantially from the

Ames tests. The range of mean and alternating angles of

attack for both the CEAT and water tunnel tests is

comparable to the Ames test. Similarly, the range of

reduced frequencies is also quite similar. For cl

 as a

function of minimum cm, most of the test points for the

CEAT and water tunnel tests are within the ±1σ bounds

of the Ames test. At large cm a few of the water tunnel

results show higher lift values, while at cm values nearer

zero, both the CEAT and Ames water tunnel tests show

some lift values that are low. No drag data are available

from the CEAT test, but the Ames water tunnel data

show good agreement with the Ames wind tunnel results,

with only a few low points at the lowest drag values.

Because the CEAT test used differential pressure

transducers, the integration of these pressures provides the

normal force coefficient, cn, rather than the lift coefficient,

cl. However, the differences between these two coefficients

tend to be small and, within the approximate nature of the

present analysis and the data scatter that is observed, it is

appropriate to include cn data when it is not possible to

compute cl. The difference between these two coefficients

is illustrated in Fig. 19, which shows both coefficients for

a dynamic stall loop for the NACA 0012 that was

obtained during the Ames tests.

An extensive set of unsteady airloads and

dynamic stall data have been obtained for the NLR–1

airfoil (Ref. 20, 21). The test data were obtained in the

Boeing Supersonic Wind Tunnel, using a two-
8

dimensional subsonic insert. This tunnel is located in

Seattle, WA. 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 deg.

Figure 20 compares the data from Ref. 20, 21

with the Ames tests. The Reynolds number in the

Boeing tests is about 25% higher than the Ames tests.

The range of mean and oscillating angles of attack is

similar to the Ames tests with the unstalled cases

removed. The range of reduced frequencies for the Boeing

tests extend 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 VR–7 airfoil, these data are for the normal

force coefficient rather than the lift coefficient.

PARAMETRIC EFFECTS ON THE

DYNAMIC STALL FUNCTION

Much of the focus of the two-dimensional

dynamic stall testing over the last 35 years has been to

understand the primary factors that influence dynamic stall

and its prediction. Thus, investigators have looked at the

influence of airfoil design, knowing that small changes in

airfoil design strongly affect the character of static stall;

that is, whether an airfoil shows leading-edge stall,

trailing-edge stall, or a mixed stall. Just as important has

been the effects of the angle of attack and its rate of

change in the stall environment, and experimentalists have

varied the mean angle of attack, α0, the alternating angle

of attack, α1, and the reduced frequency, k, to provide an

extensive range of parametric data to describe stall

behavior. This is well illustrated for the Ames tests

where the eight airfoils were tested over an extensive range

of angles of attack and frequencies, as has been shown in

Figs. 4 and 5. The dynamic stall function varies slightly,

depending upon airfoil section used, but little effect of

angle of attack and reduced frequency on the stall function

is observed. This is not to suggest that these parameters

are unimportant—the strength of the dynamic stall vortex

depends directly upon these parameters. But, once stall

occurs, the relationship between maximum lift, maximum

drag, and minimum moment is not influenced by these

parameters.

The comparisons that have been shown for the

VR–7 airfoil are surprising, perhaps, in that they indicate

that Reynolds number does not appear to have a major

effect on the dynamic stall function. Thus, data obtained

from the Ames water tunnel for Reynolds numbers of

100,000 to 250,000, agree quite well with data measured

in the wind tunnel with a Reynolds number of four

million.

However, there are a number of parameters that

may be important for characterization of the dynamic stall

function and these have not yet been examined. These

include (1) the boundary layer behavior, (2) variation in

Mach number, (3) blade sweep effects, (4) threedimensional effects (blade tip effects), and (5) the type of

testing methods used to obtain the dynamic stall

measurements. Four of these parametric effects will be

discussed in following sections.

Boundary Layer Transition Effects

Data were obtained in the Ames tests with a

boundary layer trip to examine effects of boundary layer

transition on dynamic stall. For some of the eight airfoils

it appeared that the boundary layer trip influenced the

dynamic stall function and, therefore, the tripped data were

not used in deriving the polynomial fits in Tables 1 and 2.

Figures 21 and 22 show the dynamic stall functions for

the eight airfoils and compare the untripped and tripped

data along with polynomial fits of these data. It appears

that the effect of the boundary layer trip for the NACA

0012, AMES–01, and NLR–1 airfoils is to reduce the lift

that is obtained in dynamic stall. However, for the FX

69–H–098, SC1095, and HH–02 airfoils the tripped

behavior appears to be within the scatter of the untripped

data. The VR–7 shows more scatter than the other

helicopter sections and it is also unclear whether there is a

clear difference between the tripped and untripped data.

The NLR–7301 airfoil shows a greater reduction in the

dynamic stall function because of the boundary layer trip

than is observed for any of the helicopter sections.

It appears from the comparisons of the airfoil

dynamic stall functions in Figs. 21 and 22 that boundary

layer transition influences the stall on some of these

airfoils. However, even when this effect is clearly

measurable, the overall influence of transition

characteristics is relatively small. The reasons why some

of these airfoils show more sensitivity to the boundary

layer transition than the other airfoils is not known.
9

Mach Number Effects

Most of the Ames test data were obtained for M

= 0.3, and it is not possible to determine the effects of

higher Mach number on the dynamic stall function using

these data. The dynamic stall data of Refs. 20 and 21 for

the NLR–1 airfoil were obtained for Mach numbers from

0.2 to 0.7 and this range of Mach numbers makes this

data set particularly useful. However, the NLR–1

dynamic stall characteristics differ somewhat from the

other helicopter sections and these differences decrease the

utility of this data set.

Figure 23 shows the maximum cn as a function

of the minimum cm for six Mach numbers and a separate

polynomial fit is used for each Mach number. As with

the previous comparisons, data are only shown when the

sum of the mean and oscillating angle of attack exceeds

12.4 deg. The dynamic stall functions appear similar for

all of the Mach numbers tested. As Mach number

increases, however, the extent of the augmented lift and

negative pitching moment is reduced.

The polynomial fits from Fig. 23 are compared

in Fig. 24. There is a general reduction in the dynamic

stall function as Mach number increases, although this

does not occur consistently at all pitching moments. The

maximum change in the normal force coefficient as Mach

number increases from M = 0.2 to 0.7 is about –0.3.

In the previous examination of the Ames test

data, it was shown that the a0 and b0 intercepts of the

dynamic stall function were related to the measured values

of static cl

max. In general, static clmax decreases with

increasing Mach number and it is of interest to determine

if the approximate decrease in the a0 intercept observed in

Fig. 24, is similar to changes in the static clmax

characteristics. Figure 25 compares the measured cnmax

from Ref. 20 with a best estimate of the intercepts of the

polynomials shown in Fig. 24. The dynamic stall

function a0 intercepts were estimated from Fig. 23, by

using the polynomials for M = 0.2 and 0.3 and then

adjusting this curve to best match the data in the figure.

The computed polynomial intercepts at the higher Mach

numbers were not used, as these polynomials show

excessive curvature. The comparison shown in Fig. 25

indicates that the cnmax and the best estimate of the

intercept show a similar trend, but the intercept estimate

is less affected by Mach number variation than the

measured cnmax.

The estimated intercepts from Fig. 25 can be

used to “correct” the cn and cm data by adjusting the steady

part of the data so that they are referenced to one Mach

number, that is,

cc c ˆ

nn n = −∆ (10)

where

∆c cM c nn n = − ( ) (.) 0 3 (11)

The cˆ

n is the corrected normal force coefficient, c Mn ( ) is

the static cnmax obtained from the best estimate in Fig. 25,

and cn (.) 0 3 is the static cnmax at M = 0.3. Figure 26

shows all of the dynamic stall data for the NLR–1 airfoil

with and without these corrections. Without corrections

the polynomial fit shown here provides a good fit of the

data with an r2 value of 0.82. The corrections to the data

do not improve the fit, and the r2 value shows a slight

decline.

The examination of Mach number effects shown

here suggests that there is a small influence of Mach

number on the dynamic stall function, but that within the

constraints of experimentally observed data scatter it may

not be possible to obtain corrections for these effects.

Effects of Blade Sweep

Unswept data for an NACA 0012 airfoil section

from Ref. 16 were compared with the Ames test data in a

previous section. This data set is also useful in that it

allows the direct comparison of swept and unswept test

data for dynamic stall. These data were obtained in Ref.

16 for two sweep angles, 0 deg (unswept) and 30 deg.

The onset Mach number, M∞, was varied depending upon

sweep angle so that the Mach number normal to the

leading edge, Mc was the same for all sweep conditions,

that is,

M M c = ∞ cosΛ (12)

where Λ is the sweep angle. The reduced frequency was

also selected based on the chordwise Mach number. The

pressure transducers were mounted in a chordwise array,

rather than a streamwise array for the swept conditions,

and the dimensional forces and moment were obtained for

this chordwise array. However, the coefficient forces and

moments were then calculated with the sweep effects

included, that is,

c t N t cq

c t Mt cq

c t C t cq

n

m

c

( ) ( ) / cos

( ) ( ) / cos

( ) ( ) / cos

=

=

=

2

2 2

2

Λ

Λ

Λ

 (13)

The final cl and cd coefficients were then resolved using eq

(5).

The dynamic stall functions of the NACA 0012

airfoil are compared for sweep angles of 0 and 30 deg. in

Fig. 27. The data include not only the unswept data
10

shown previously in Fig. 16, but also data obtained at a

chordwise Mach number of 0.4 for both sweep angles.

Polynomials have been fitted to both swept and unswept

data to assist the comparison. The two sets of data appear

to be in good agreement over the mid-range of cm and cd

values. However, at moment coefficients greater than

–0.35 or –0.40, the swept data show less lift, while at the

moments less than –0.10, the swept data appear to have

slightly greater lift.

Comparison of Oscillating and Ramp Tests

Dynamic stall data were obtained for the

Sikorsky SSC–A09 airfoil in the UTRC Large Subsonic

Wind Tunnel using two modes of dynamic stall testing

(Ref. 22). The first mode of testing was to oscillate the

airfoil around a mean angle of attack in the same manner

that was used in the Ames tests. In the second mode the

airfoil angle of attack was increased at a linear rate, that is,

a ramp function was used.

The SCC–A09 airfoil is a nine percent thick

airfoil with a relatively sharp leading edge radius. It was

designed to maintain the performance characteristics of

Sikorsky’s second-generation airfoils, such as the

SC1095, at lower Mach number but to increase the drag

divergence Mach number at zero lift (Ref. 23). In this

sense the SSC–A09 may be considered a third-generation

airfoil.

The model chord was 17.3 in. with 18 pressure

transducers installed on each surface. The pressures on the

airfoil were integrated to obtain the cn, cc, and cm

coefficients and these were converted to the cl and cd

coefficients in the wind tunnel axes using eq (5).

The measured extrema for lift, moment, and drag

are shown in Fig. 28 for both modes of testing.

Although the quantity of data are limited, particularly for

the oscillating tests, polynomial fits have been added to

the curves to better illustrate the differences. The basic

character of the dynamic stall function observed previously

for the second-generation airfoils is similar to that of this

airfoil. The ramp tests appear to show a slightly greater

lift augmentation during dynamic stall than is seen for the

oscillating tests, although this is less apparent for the liftdrag “polar” than for the maximum lift as a function of

minimum moment.

The SSC–A09, although a third-generation

airfoil, does not appear to be as good in dynamic stall as

the SC1095. Figure 29 compares the dynamic stall

characteristics of this airfoil from the oscillating airfoil

testing with the polynomial that was derived from the

Ames SC1095 test data. Although the number of test

points are limited, it appears that the SSC–A09 shows

0.1 to 0.3 less augmented lift than the SC1095 for the

same moment or drag conditions. This airfoil was

optimized for improved transonic performance (Ref. 23)

and this appears to have resulted in some additional

penalty in moment and drag under maneuver conditions.

COMPARISON WITH FLIGHT TEST

DATA

Reference 12 has examined dynamic stall on a

highly-instrumented UH–60A helicopter for three

conditions: a level flight case at high altitude, a diving

turn at high load factor, and the UTTAS pull-up

maneuver. This examination has 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 two-dimensional wind

tunnel testing. It is of considerable interest, therefore, to

see if this good qualitative agreement extends to the

dynamic stall function that has been defined here for the

two-dimensional test data.

The UTTAS pull-up maneuver from Ref. 12

(Counter 11029) has been re-examined to obtain

maximum cn and cm values from the flight data that

correspond with the extrema obtained from the twodimensional tests. The maneuver examined is basically a

symmetric pull-up that has been modified so that the entry

is made from level flight at VH. For the case here,

Counter 11029, 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. 30. In this figure each

symbol represents one revolution of the 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 cn–cm pairs.

A second reason for the selection of the UTTAS

pull-up is that the maneuver is representative of the load

limits for this aircraft. The peak oscillatory pitch-link

load measured during this maneuver is about 2860 lb.

The largest pitch-link loads that were obtained during airto-air combat testing on this aircraft were 2700 lbs and the

maximum loads encountered in the original flight loads

survey were 3040 lbs (Ref. 24).
11

An example of the integrated cn and cm

coefficients on the outer portion of the blade is shown in

Fig. 31. The data here extend from 0 deg to 360 deg and,

based on the nomenclature of Ref. 12, include the final

135 deg of Rev 13 and the first 225 deg of Rev 14. Under

unstalled conditions the cn can achieve relatively high

levels, but the cm are smooth and are seldom less than

about –0.10. The rapid variation seen in cm in Fig. 31 is

the best indicator of the shedding of a dynamic stall

vortex. For each potential stall event the lift and moment

time histories, as shown in Fig. 31, were examined. If

extrema in lift and moment showed behavior typical of the

shedding of a dynamic stall vortex, that is, the moment

minimum lagged the lift maximum, then both the peak cn

and cm coefficients were recorded as well as the associated

azimuth angles. The mean azimuth angle for a dynamic

stall point was used to compute the Mach and Reynolds

number based on the local velocity, that is,

Vr V r

R T ( , ) ( sin ψ μψ = + ) (14)

The reduced frequency was approximated depending upon

whether the stall cycle was the first, second, or third.

Referring to the sketch in Fig. 32, based on Rev 14, each

symbol represents the azimuth that is associated with a

stall event. The azimuthal spacing between stall cycles is

defined as ∆ψ12 and ∆ψ23. The oscillation frequency

associated with each cycle, is approximated

ω ψ

ω ψψ

ω ψ

1 12

2 12 23

3 23

360

0 5 360 360

360

≈

≈ +

≈

(/ )

. [( / ) ( / )]

(/ )

∆

∆ ∆

∆

(15)

and the reduced frequency is

k c

V r

i = ω

ψ

Ω

2 (, ) (16)

The frequencies associated with these stall cycles are a

consequence of the control system flexibility.

Measurements made of the control system stiffness for

this aircraft, Ref. 25, indicate that this frequency is about

4.2/rev. If the reduced frequency was defined based on the

fundamental rotor frequency, that is, 1/rev, then the

computed values would be a quarter of those that are

computed using eq (15).

Figure 33 compares the flight test data with the

Ames test data for the SC1095 airfoil. The cn and cm

coefficients for each stall event are categorized as either the

first, second, or third stall cycle, and different symbols are

used in Fig. 33 to indicate the cycle. The Reynolds and

Mach numbers are generally larger than those recorded in

the Ames tests, as expected for a full-scale flight vehicle.

The first cycle, which occurs on the retreating side of the

disk, occurs at a low Mach number and a number of these

cases overlap the Ames test data. The second cycle occurs

at moderate Mach number, while the third cycle stall

events occur at quite high Mach numbers. The reduced

frequencies in flight, based on eq (15), are considerably

higher that those used in the wind tunnel tests. However,

a good argument can be made that the reduced frequency

should be based on the rotor fundamental frequency at

1/rev, particularly for the first cycle. If this change is

made, the reduced frequencies in Fig. 33 are reduced by

roughly a factor of 4. The general hyperbolic character of

the reduced frequency with Mach number is the effect of

the local velocity term in the denominator of the reduced

frequency, see eq (16). The highest reduced frequencies are

associated with the lowest velocities, for instance, for

Cycle 1 at the more inboard radial stations.

The plot of the maximum normal force

coefficient as a function of the minimum moment

coefficient in Fig. 33 shows that the dynamic stall loading

in flight is roughly similar to the wind tunnel tests, but

the values of lift are less for moments approaching zero,

and higher for the deep dynamic stall conditions.

Moreover, the flight data exhibit considerable scatter in

comparison to the wind tunnel tests.

The flight data shown in Fig. 33 are for a full

range of Mach numbers and, based on the previous

examination of the NLR–1 data, it is expected that the

Mach number will affect the dynamic stall function

although it is not clear how to best correct for this effect.

The data shown in Fig. 33 are for not only the SC1095

airfoil (0.865R, 0.92R, 0.965R, and 0.99R) but also for

the SC1094 R8 airfoil (0.675R and 0.775R). An attempt

to “correct” these data has been made by using the

variation of static cl

max with Mach number obtained from

Ref. 1. The SC1095 data have been corrected to M = 0.3

using that airfoil’s cl

max variation and the SC1094 R8 data

have corrected to the same Mach number using that

airfoil’s cl

max variation. The corrected data are compared to

the Fig. 33 data in Fig. 34. A polynomial fit of both the

uncorrected and corrected data is shown in Fig. 34 along

with the polynomial fit for the SC1095 airfoil from Table

1 (based on cl, not cn). No improvement is seen in the

coefficient of determination, r2, for the corrected data, but

there is a reduction in the standard deviation of 19%. The

standard deviation for the flight data, about 0.25, is still

much greater than observed for the SC1095 airfoil tested

in the wind tunnel, where a value of 0.07 was obtained;

see Table 1.
12

DESIGN CONSIDERATIONS

Test data on airfoils oscillating in pitch show

that the airfoil’s lift is augmented dynamically beyond the

static stall angle although this additional lift is

accompanied by penalties in pitching moment and drag.

This is illustrated in Fig. 35 where the maximum lift and

drag, and minimum moment for the SC1095 airfoil

obtained from the Ames tests are shown. The dashed lines

represent the polynomial fits from Tables 1 and 2 for this

airfoil. Steady section data for the SC1095 are also

shown in this figure and the difference between the steady

lift and the dynamic stall function is an indication of the

augmented lift that is possible because of dynamic stall.

The steady section data were obtained at low speed in the

Glenn L. Martin Wind Tunnel at the University of

Maryland in the tests reported in Ref. 26 and are shown

for angles of attack from zero to 55 deg.

Crude boundaries have been added to Fig. 35 to

indicate limits on airfoil section moment and drag based

on pragmatic considerations. In the case of the section

pitching moments, variation at 1/rev or higher frequencies

will cause oscillating loads in both the rotating- and fixedcontrol systems that will cause fatigue damage if they are

excessive. Torsional loading typically increases with

forward speed and is greatest at the maximum forward

flight speed (Ref. 27). These torsion moments are largely

caused by unsteady aerodynamic loads that are not related

to blade stall. An examination of flight test data from the

UH–60A (Ref. 28) shows that the minimum section

moment recorded at the maximum level flight speed is

about –0.15, and that value has been used as the bound in

Fig. 35. Although there are numerous factors that affect

rotating and nonrotating system component endurance

limits, to a first approximation this boundary represents

operation that can be safely performed without

encountering fatigue damage.

The boundary for the section drag in Fig. 35 is

based on the ability of a helicopter to continuously

maneuver using available engine power, without having

to convert forward speed or altitude into power. In

estimating this boundary it is assumed that a helicopter is

maneuvering near its minimum power speed where the

greatest amount of excess power is available. The profile

power in this situation (Ref. 29) is

C

c

P

d

0

0

8

1 46 2 = +

σ

( .) μ (17)

It is assumed that induced and parasite power change only

slightly in a maneuver and that the excess power available

is used by the profile power. For these conditions the

power available is roughly twice the power required in

level flight or four times the profile power. For the

UH–60A in level flight, a nominal cd0 is about 0.0085.

If all the excess power is made equivalent to the cd0 term,

then this is equivalent to a profile drag of about 0.034.

However, the blade is not stalled over the entire disk, so

the estimated boundary is set at roughly three times this

value or a cd0 of roughly 0.1. The estimate of this

boundary is quite crude, but it does give a rough idea of

airfoil conditions where a helicopter can maneuver without

having to descend to maintain power to the rotor. At

higher speeds, the helicopter has the option to bleed off

airspeed to provide power to the rotor when there is

dynamic stall on the disk. In severe maneuvers a

helicopter will always require additional power to maintain

thrust, either by reducing airspeed or by descending.

Preliminary Design

Military and civilian designs differ in their need

for maneuver capability. A civilian helicopter does not

require that rotating and fixed-system controls be designed

for substantially more section moment capability than is

shown by the boundary in Fig. 35. A military helicopter

will, on occasion, require substantially more maneuver

capability than a civilian aircraft. The data from the

UH–60A shown in Fig. 34 show lift coefficients as high

as 3.5 with an associated section moment of –0.7.

However, this sort of maneuver requirement represents a

very small fraction of the military aircraft’s usage

spectrum. Civilian aircraft, although not requiring this

kind of maneuver capability, do need the ability to safely

encounter the loading that occurs in inadvertent

maneuvers, obstacle avoidance, or similar severe, but

infrequent conditions.

The prediction of the control loads caused by

dynamic stall in maneuvers is currently beyond the state

of the art. Thus, in a new design, or a modified aircraft, it

is necessary to scale the loads from previous flight test

data. However, in doing this scaling there are both

aerodynamic or performance aspects as well as structural

aspects that need to be taken into account. As an

example, consider the upgrade of an aircraft where the

gross weight is increased by 30% yet the aircraft is to

retain the same maneuver capability. For a limiting

maneuver, CT

*/σ, there is an associated limiting airfoil

section lift, cl

*, and moment, cm*. As

C T

bcRV

T

T

*

σ ρ = 2 (18)

then if the thrust, T, is increased by 1.3, then either b, c,

or R (or some combination) must also be increased by a

factor of 1.3. If the blade number, b, is increased from 4

to 5, then it is possible to avoid major changes in chord
13

or radius. Alternatively, the blade number and radius may

be held constant and the chord (and solidity) increased

instead. The dimensional aerodynamic moment on the

blade is

M cV r c a m = 1

2

2 ρ ψ (, ) * (19)

This moment is unchanged if the additional thrust is

obtained by increasing blade number and thus the rotating

controls loads will not be affected. However, if the chord

is increased by 1.3, then the aerodynamic moment will

also be increased by 1.3 and the rotating controls will

have to be resized.

The nonrotating control system is not dependent

upon the choice of b or c for obtaining the increased rotor

thrust. As an example the moment about the fixedsystem swashplate is

M br M sp sp a ∝ (20)

Thus, if the chord is increased the blade aerodynamic

moment will increase, while if blade number is increased,

the aerodynamic moment will stay the same but the fixedsystem controls will see the same increase.

Stall Prediction with Semi-empirical Models

Most comprehensive analyses now in use 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 that has been introduced in this

report provides a first check of these semi-empirical

models.

Gangwani (Ref. 17) has described a semiempirical stall model with multiple parameters that are

identified by fitting a select number of dynamic stall loops

from two-dimensional wind tunnel tests. In Ref. 17,

results are presented for both the NACA 0012 and

SC1095 airfoils. The predicted lift and moment extrema

using Gangwani’s model are compared with the data in

Fig. 36. It is unclear in Ref. 17 whether all of the data

used for the comparisons were also used in the fitting

process. Regardless, good agreement is observed between

the synthesized data and measurements for blade loading.

A workshop on dynamic stall was held at NASAAmes Research Center in 1992 to compare the predictions

of dynamic stall models with test data (Ref. 30). For this

purpose, data from tests on an oscillating wing with an

NACA 0015 profile were used as a baseline (Ref. 31).

The experimental test point selected for the calculations

was a 3-D case with the measurements obtained at the

47.5% span location of the wing. However, comparison

of the data at this span with two-dimensional test data

obtained during the same program shows that the

maximum lift and drag, and minimum moment are only

slightly affected by three-dimensional effects at this

inboard location. This case is interesting in that it

represents a “blind” test in that the collaborators who

made the calculations did not have access to these data

until the workshop.

The semi-empirical models used for the

workshop calculations included the Beddoes and Leishman

indicial models, a model for three-dimensional stall from

ONERA, a version of the Boeing stall model, and the

2GCHAS model. The Beddoes indicial model is an

evolution from an earlier indicial model (Ref. 32) and

includes three-dimensional effects (Refs. 33, 34). The

Leishman indicial model also derives from Ref. 32, but

was developed for Sikorsky Aircraft and is proprietary.

The ONERA model is based on potential flow theory and

is described in Ref. 35. It is not related to the well known

ONERA dynamic stall models developed by Tran and

Petot (Ref. 36). The 2GCHAS dynamic stall model is

also derived from Ref. 32 and was developed by Leishman.

Finally, the Johnson model is an implementation of the

Boeing dynamic stall model (Ref. 37) in the CAMRAD II

comprehensive analysis.

The data and the five semi-empirical models for

the workshop condition are compared in Fig. 37. It is

noted that the reference data point for the NACA 0015 test

is below the NACA 0012 fit based on the earlier Ames

tests. The predictions of most of the semi-empirical

models in Fig. 37 show good agreement with the lift, but

underpredict the moment and drag. Only the 2GCHAS

model provides a reasonably accurate prediction of each of

the three coefficients.

Currently, the comprehensive analysis

CAMRAD II includes five semi-empirical dynamic stall

models (Ref. 38). These include two of the older, simpler

models used by Boeing (Ref. 37) and Johnson (Ref. 39),

the Leishman-Beddoes model (Ref. 30), and two ONERA

models: the Edlin method developed by Tran and Petot

(Ref. 36), and Truong’s Hopf Bifurcation model (Ref. 40).

As each of the models is semi-empirical it is necessary to

adjust or identify the model parameters based on test data.

This has been done within CAMRAD II for the NACA
14

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 sections.

The predictions of the five models are compared

with single test points for the NACA 0012 and SC1095

sections in Fig. 38. The selected 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-tofair 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.

The three examples of predictions of the semiempirical models shown here provide mixed results.

Gangwani’s method is compared with the data over a range

of vortex strengths and shows good results. The other

methods, however, are evaluated for only one loading

condition and it is more difficult to judge them. In the

case of the NACA 0015 data, the 2GCHAS model

provides a good calculation for this single case, while the

other methods are less accurate. The wide variation in the

moment predictions that is observed here will likely result

in an inaccurate calculation of the torsional deformation of

the blade and the related angles of attack. Except for

Gangwani’s model, no suitable calculation of the loads in

stalled flight can be expected from these methods.

Stall Prediction By Direct Calculation

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, much as current

steady two-dimensional Navier-Stokes flow solvers are

used to develop coefficient tables for these analyses (Ref.

41).

One approach to direct calculation is to solve the

incompressible, unsteady, two-dimensional viscous flow

equations using vorticity as the primary variable and

solving the equations following a conformal mapping of

the physical domain to a circular region (Ref. 42). The

code used in this approach is called the ZETA code.

Calculations have been made using the ZETA code for

both the VR–7 airfoil (Ref. 43) and the VR–12 airfoil

(Ref. 44). The VR–12 airfoil, Fig. 39, is thinner than the

VR–7 and is designed for better performance at high Mach

numbers. Dynamic stall data for the VR–7 airfoil have

been discussed previously, including data from water

tunnel tests at NASA-Ames Research Center (Ref. 19).

The same facility has also been used to obtain dynamic

stall data on the VR–12 (Ref. 44). Figure 40 compares

the experimental measurements for these two airfoils with

the predictions for one condition using the ZETA code.

The single experimental case that is computed by the

ZETA code is indicated by the solid circles. The VR–7

polynomials from Tables 1 and 2 are used as a reference

for the VR–12 data and show fairly good agreement.

The reference test conditions in Fig. 40 represent

a moderate to severe dynamic stall case. For the VR–7,

the ZETA code overpredicts the moment and drag

(slightly), and significantly underpredicts the lift, missing

the experimental value by ∆cl

 = –0.3. For the VR–12,

the ZETA prediction falls directly on the VR–7 dynamic

stall function, but the dynamic stall vortex strength is

clearly too strong and lift, drag, and moment are

significantly overpredicted.

The AFDD workshop, mentioned previously,

included a blind comparison of semi-empirical models

with a test condition from an oscillating wing dynamic

stall test. This blind comparison also included

calculations using two Navier-Stokes flow solvers. The

first solver, Srinivasan’s TURNS code (Ref. 45), solves

the Reynolds averaged thin-layer Navier-Stokes equations

and uses the Baldwin-Lomax turbulence model. The

second solver (Ref. 46) has been developed at the Georgia

Institute of Technology (GIT) by Prof. Sankar and his

students. The predictions of these two codes are compared

with the light or moderate stall condition from the NACA

0015 experiment in Fig. 41. Both codes provide a good

prediction of the lift, but the moment and drag predictions

are unsatisfactory. The TURNS code shows little or no

effect of the stall cycle on moment and drag, while the

Georgia Tech code significantly overpredicts both moment

and drag. The comparison here is for the extreme values

only. An examination of the original comparison (Ref.

30) shows large errors in the phase of the loading in the

Georgia Tech code.

Rouzaud and Plop have reported the development

of a Reynolds-averaged, Navier-Stokes solver at ONERA

(Ref. 47). 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
15

Ames tests. These predictions, along with the Ames test

data, the reference point, and the polynomial fits from

Tables 1 and 2, are compared in Fig. 42. 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 in Ref. 47 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. 10) and the Navier-Stokes calculations

indicate only a single vortex.

The direct calculation results shown here are quite

mixed and, in general, are not accurate. The ONERA

results, in particular, indicate that the calculations are

sensitive to the turbulence modeling and this obviously

represents a serious challenge for these computations.

The great expense of these computations, unfortunately,

works against extensive testing of these methods. As a

minimum, however, it appears necessary that these

methods should be compared to at least each of the

dynamic stall cases from the Ames experiments that have

been shown to be qualitatively different, that is, stall cases

without a clear shed vortex, cases with a single vortex,

and cases with two vortices.

MULTI-ELEMENT AND

NONCONVENTIONAL AIRFOILS

As has been shown here, 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.

It may be possible, however, to enhance dynamic stall

performance using multi-element or variable geometry

airfoil designs. Two multi-element airfoils and an airfoil

that represents the limiting condition of a variablegeometry airfoil have been investigated in the Ames water

tunnel (Refs. 19, 44, and 48). In addition, ZETA code

calculations have been made for these configurations as

well as for an airfoil with blowing on the upper surface

(Ref. 43, 44). These measurements and calculations are

examined here.

A VR–7 airfoil has been tested in the Ames

water tunnel in both a baseline configuration and a

configuration with a leading edge slat. Data were obtained

over a range of reduced frequencies and Reynolds number

for a case with a mean angle of attack of 15 deg and an

alternating angle of 10 deg (Ref. 19). A single test point

from this data set has also been used as a basis for

calculations using the ZETA code. The airfoil and slat are

shown in Figure 43 along with comparisons of the

experimental data and the calculations. For these tests the

main airfoil is the VR–7 and it is identical to the airfoil

tested in the Ames wind tunnel tests. The baseline VR-7

and the main element shown in Fig. 43 are identical. The

slat is placed forward of the main airfoil and slightly

below the mean chord line.

The baseline VR–7 data show good agreement

with the VR-7 dynamic stall function and this was

discussed previously, see Fig. 18. The data measured for

the configuration with the slat show a substantial increase

in lift and, perhaps more important, a significantly reduced

penalty in terms of moment and drag. Two reference

points were selected for these two configurations and the

ZETA code was used to calculate the airfoil loading. For

the baseline airfoil the lift is underpredicted and the

moment overpredicted, as noted before in the discussion of

the ZETA code predictions; see Fig. 40. The prediction

for the slat configuration is substantially worse, with the

lift significantly underpredicted and the moment and drag

overpredicted. The calculations, in this case, do not show

the same improvement in dynamic stall performance as

shown by the data.

A similar test was performed on a baseline VR12 airfoil and a multi-element configuration (Ref. 44) and

calculations were again made with the ZETA code (Ref.

43, 44). In this case, however, rather than adding a

leading edge slat to the airfoil, an extendable leading edge

was designed, that when retracted, would fit inside the

profile of the unmodified VR–12. The VR–12 with the

extended leading edge, the experimental data, and the

calculations are shown in Fig. 44. As the VR–12 was

not one of the original eight airfoils tested in Ref. 9, there

is no polynomial fit based on experimental data, so the

VR–7 fit has been used instead. The data from the

baseline VR–12, as well as the modified airfoil, show

good agreement with the VR–7 polynomials. Unlike the

VR–7 configuration with a slat, however, no

improvement in dynamic stall performance is observed for

this airfoil with an extended leading edge. The ZETA

calculations in this case quite closely match the VR–7

dynamic stall function, but the lift and moment are

substantially overpredicted for both airfoils, and the drag is

overpredicted for the baseline airfoil.

The ZETA code has been used in Ref. 43 to

examine the potential of variable-geometry airfoil

configurations to provide augmented lift for

maneuverability, without the associated penalties in

moment and drag. Calculations were made for a VR–12
16

airfoil that was modified by rotating the first 25% of the

airfoil about the quarter chord point. Two configurations

were examined. In the first configuration, Case 2513, the

forward portion of the airfoil was rotated 13 deg nose

down and fixed at this location. In the second

configuration, the forward portion was moveable. In Ref.

43 this configuration was referred to as the variable-droop

leading-edge (VDLE) airfoil. Under normal circumstances,

the forward portion was fixed at zero deg, but when the

angle of attack exceeded 13 deg, the forward portion rotated

nose down proportional to angle of attack,

θ α= −13 (21)

where θ is the droop or rotation angle of the forward

portion. No experimental validation of the variablegeometry configuration has yet been obtained, but Case

2513, with the nose rotated down by 13 deg has been

evaluated in the Ames water tunnel (Ref. 48). The

experimental stall characteristics of the deformed airfoil are

compared with an unmodified VR–12 in Fig. 45. For

identical mean and alternating test conditions, there is a

general reduction in the strength of the dynamic stall

vortex for the Case 2513 tests, but this configuration

shows the same dynamic stall function as seen for the

unmodified airfoil. Thus, for the test conditions

examined, the Case 2513 airfoil provides no benefit. The

ZETA code was used to calculate a single test point to

compare with the experimental data. For the calculation

the lift is underpredicted, as are the moment and drag.

However, the calculated values agree well with the VR–7

polynomial fit.

The ZETA code was also used in Ref. 39 to

examine the effect of upper surface blowing on dynamic

stall performance. This was done by changing the normal

no-slip flow condition for a number of grid points on the

airfoil upper surface near the quarter chord. The normal

no-slip condition is referred to here as the zero blowing

case, and a boundary condition with the velocity set to

twice the free stream is called 2X blowing, and so forth.

The results of these calculations are shown in Fig. 46.

As these calculations were made for an NACA 0012

airfoil, the polynomial for this airfoil is used as a

reference line. In the case of zero blowing the ZETA code

shows the presence of a dynamic stall vortex, although the

lift is underpredicted. With blowing, the dynamic stall

vortex is eliminated and there is no lift augmentation for

this condition. The suppression of the dynamic stall

vortex in this case offers no advantage to the designer

seeking improved maneuverability characteristics.

CONCLUSIONS

The loading in lift, moment, and drag has been

examined for eight airfoils tested in the NASA-Ames 7-

by 10-Foot Wind Tunnel for an extensive range of test

conditions that result in the shedding of one or more

dynamic stall vortices from the leading edge of the airfoil.

The loading studied here is represented by the peak lift,

moment, and drag during a dynamic stall loop, as these are

the parameters that are related to maneuver limits for

helicopters in flight. That is, the peak lift coefficient is

related to the available thrust, the peak moment is related

to control system loads, and the peak drag is related to

power requirements. Based on this evaluation, the

following conclusions are made:

1. Each airfoil shows a characteristic relationship

between the peak lift, peak moment, and peak drag

over all test conditions for a wide range of airfoil

operating conditions. This characteristic, herein

referred to as the dynamic stall function, is a clear

indication of the importance of the loading caused by

the dynamic stall vortex as it forms on the airfoil,

convects along the upper surface, and finally leaves

the airfoil at its trailing edge.

2. The dynamic stall functions of the eight airfoils are

remarkably similar. However, the one fixed-wing

section included in the comparison, the NLR–7301,

shows somewhat different characteristics.

3. Polynomials fitted to the test data allow the estimate

of the lift coefficient for zero moment and zero drag

conditions, that is the intercept of the polynomial (a0,

b0). In general, the intercept values are observed to

be 0.1 to 0.2 higher than the static cl

max.

4. The polynomial intercepts, a0 and b0, provide a rough

approximation of an airfoil’s dynamic stall

performance, that is, how much lift an airfoil can

produce at a fixed penalty in moment and drag. These

intercepts appear proportional to the static cl

max and,

therefore, an airfoil with an improved cl

maxcan

reasonably be expected to have improved dynamic

stall performance.

Data obtained from five independent tests of four

of the eight airfoils in the Ames test series have been

compared to the Ames data and it is concluded that the

dynamic stall function of an airfoil is the same regardless

of the test facility or testing rig used. This includes tests

obtained in both wind tunnels and a water tunnel.
17

A number of parametric effects on the dynamic

stall function have been examined using either the Ames

test data or other data sets. It is concluded that

1. The amplitude and the frequency of the airfoil

oscillation do not influence the dynamic stall function

although they strongly effect the strength of the

dynamic stall vortex.

2. Reynolds number does not affect the dynamic stall

function.

3. Boundary layer behavior, as controlled by a trip on

the airfoil surface, has a small effect on the dynamic

stall function for some airfoils, but not for others.

For those airfoils influenced by a boundary layer trip,

the stall performance is reduced, that is, the lift is

reduced for a fixed moment or drag condition.

4. Mach number has a small but important effect on the

dynamic stall function. It appears that the shape of

the function is unchanged, but the intercept of the

dynamic stall function is reduced with Mach number

in a fashion similar to the reduction that is observed

in static clmax.

5. The sweep angle does not show a clear effect on the

dynamic stall function although a greater range of test

conditions is probably required to confirm this

conclusion.

Flight test data obtained on a UH–60A helicopter

in a limiting maneuver show a dynamic stall function

similar to that observed in two-dimensional wind tunnel

tests, although the scatter in the data is increased.

The problem of design for improved

maneuverability for a helicopter has been examined and it

is concluded that

1. Conventional airfoil design presently offers little

opportunity for increased helicopter maneuverability.

However, specific characteristics that provide

improved performance in unstalled flight may be

detrimental for stall performance.

2. If increased maneuverability is required for a

helicopter, then it is necessary to increase rotor

solidity. However, increases in rotor solidity will

also increase the loads in the rotating- or fixed-system

controls or both.

3. Based on the examination of the predictive capability

of a number of the semi-empirical models for

dynamic stall that are currently in use, it appears that

it is sometimes possible to obtain good results.

However, in the majority of cases, the present

methods show a wide variation in the predicted

loading and do not appear to be suitable for design.

4. An examination of a limited set of aerodynamic load

calculations using two-dimensional Navier-Stokes

flow solvers suggests that substantially more

progress is required for this difficult problem before

these methods can usefully support design.

Limited experimental and analytical efforts

looking at multi-element or variable-geometry airfoils

were examined in the context of the dynamic stall

function. Based on experiment, it appears that multielement airfoils may provide increased lift in some cases

without a severe moment or drag penalty, but this is not

obtained for all configurations. However, the calculations

used in these cases do not provide useful information

concerning the dynamic stall loading.

The dynamic stall function introduced in the

present study provides a useful means of evaluating the

accuracy of calculations for dynamic stall, and a means of

assessing experimental measurements of new or novel

airfoil sections.

ACKNOWLEDGMENTS

Leo Dadone of Boeing Helicopters in

Philadelphia is acknowledged for his discussion of the

helicopters sections used on aircraft made by Boeing.

Robert Flemming of Sikorsky Aircraft is acknowledged

for his comments on Sikorsky Aircraft airfoils and

testing. Frank Harris is acknowledged for his useful

comments on this manuscript. Prof. Gordon Leishman of

the University of Maryland is acknowledged for supplying

steady test data from the wind tunnel tests of the SC1095

and SC1094 R8 airfoils reported in Ref. 26. Jim

Narramore of Bell Helicopter Textron is acknowledged for

his discussion of the use of airfoil sections on aircraft

manufactured by Bell Helicopter. Roger Smith of Boeing

Helicopters in Mesa is acknowledged for his discussion on

the Apache rotor design and his useful comments on this

manuscript.

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19

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20

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21

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 = 0.05.

Figure 2. Eight airfoil profiles tested in the NASA Ames 7- by 10-foot wind tunnel (Refs. 9–11).
22

Figure 3. Reynolds and Mach number envelope for Ames dynamic stall tests. Reynolds and Mach number relation for

selected aircraft shown with dashed lines.
23

Figure 4. Alternating and steady angles of attack for Ames dynamic stall tests
24

Figure 5. Reduced frequency as a function of Mach number for the Ames dynamic stall tests.
25

Figure 6. Dynamic stall test point for NACA 0012 from Ames tests; Frame 9302.
26

Figure 7. Maximum lift coefficient as a function of minimum moment coefficient for Ames dynamic stall tests (Ref. 9–11).
27

Figure 8. Maximum lift coefficient as a function of maximum drag coefficient for Ames dynamic stall tests (Ref. 9–11).
28

Figure 9. Polynomial fit of maximum lift coefficient as a function of minimum moment coefficient for untripped data from

Ames dynamic stall tests (Refs. 9-11).
29

Figure 10. Polynomial fit of maximum lift coefficient as a function of maximum drag coefficient for untripped data from

Ames dynamic stall tests (Refs. 9-11).
30

Figure 11. Comparison of dynamic stall functions of seven helicopter airfoil sections.

Figure 12. Comparison of normalized dynamic stall functions of seven helicopter airfoil sections.
31

Figure 13. Comparison of polynomial intercepts of dynamic stall functions of seven helicopter airfoils.
32

Figure 14. Maximum lift coefficient as a function of minimum moment coefficient showing light dynamic stall, dynamic stall

with a single shed vortex, and dynamic stall with two shed vortices.
33

Figure 15. Maximum lift coefficient as a function of maximum drag coefficient showing light dynamic stall, dynamic stall

with a single shed vortex, and dynamic stall with two shed vortices.
34

Figure 16. Comparison of UTRC and Ames dynamic stall data for NACA 0012 airfoil.
35

Figure 17. Comparison of UTRC and Ames dynamic stall data for SC1095 airfoil.
36

Figure 18. Comparison of CEAT wind tunnel and Ames water tunnel data with Ames wind tunnel dynamic stall data for

VR–7 airfoil. CEAT measurements are of maximum normal force coefficient instead of lift coefficient.
37

Figure 19. Comparison of lift and normal force coefficients for dynamic stall loop for NACA 0012, Frame 9302..
38

Figure 20. Comparison of BSWT and Ames dynamic stall data for NLR–1 airfoil. BSWT measurements are of maximum

normal force coefficient instead of lift coefficient.
39

Figure 21. Maximum lift coefficient as a function of minimum moment coefficient showing effect of tripped boundary layer.
40

Figure 22. Maximum lift coefficient as a function of maximum drag coefficient showing effect of tripped boundary layer.
41

Figure 23. Maximum normal force coefficient as a function of minimum moment coefficient for NLR–1 airfoil at six Mach

numbers (Refs. 20, 21).
42

Figure 24. Comparison of polynomial fits for six Mach numbers for NLR–1 airfoil.

Figure 25. Comparison of best estimate of polynomial fit intercept with static normal force coefficient from wind tunnel

measurements (Ref. 20).
43

Figure 26. Comparison of uncorrected and corrected maximum normal force coefficient as a function of minimum moment

coefficient for NLR-1 airfoil.

Figure 27. Effect of blade sweep on dynamic stall function for NACA 0012 airfoil (Ref. 16).
44

Figure 28. Comparison of dynamic stall functions for SSC–A09 airfoil using oscillating and ramp forcing methods (Ref.

22).

Figure 29. Comparison of SSC-A09 and SC1095 airfoil dynamic stall functions.
45

Figure 30. UH–60A oscillatory pitch-link loads in the UTTAS pull-up (Ref. 12).
46

Figure 31. Normal force and moment coefficients on UH–60A rotor blade during UTTAS pull-up.
47

Figure 32. Schematic showing dynamic stall on UH-60A rotor for Rev 14.
48

Figure 33. Comparison of UH-60A flight test normal force and moment coefficients with Ames SC1095 test results.

Figure 34. Effect of Mach number corrections on dynamic stall function obtained in flight.
49

Figure 35. Dynamic and steady airfoil limits and design boundaries for the SC1095 airfoil.

Figure 36. Comparison of measured and synthesized data for maximum lift and minimum moment for two airfoils (Ref. 17).
50

Figure 37. Comparison of synthesized data for NACA 0015 wing with five semi-empirical models (Ref. 30)..

Figure 38. Comparison of synthesized data for NACA 0012 and SC1095 profiles using five semi-empirical models (Ref.

38).
51

Figure 39. VR-7 and VR-12 profiles.

Figure 40. Comparison of ZETA code predictions for VR-7 and VR-12 airfoils (Refs. 43, 44).
52

Figure 41. Comparison of Navier-Stokes predictions for NACA 0015 wing with experimental data (Ref. 30).

Figure 42. Comparison of Navier-Stokes predictions for NACA 0012 airfoil data using two turbulence models

(Ref. 47).
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Figure 43. Comparison of experimental measurements and calculations for a VR-7 with and without a leading-edge slat.

(Refs. 43, 44).
54

Figure 44. Comparison of experimental measurements and calculations for a VR-12 with and without a leading edge

extension (Ref. 44).
55

Figure 45. Comparison of experimental measurements and calculations for a VR-12 with a drooped leading section. (Ref.

48).
56

Figure 46. Calculated effects of blowing on an NACA 0012 airfoil. (Ref. 43).