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.A-
NASA TECHNICAl.
MEMORANDUM
NASA TM X-72843
!
X
,ecZ
EFFECTS OF THICKNESS ON THE
AERODYNAMIC CHARACTERISTICS OF AN
INITIAL LOW-SPEED FAMILY OF AIRFOILS
FOR GENERAL AVIATION APPLICATIONS
By Robert J. McGhee and William D. Beasley
(NASA-TM-X-728_3) EFFECTS OF THICKNESS ON
THE AERODYNAMIC CHARACTERISTICS OF AN
INITIAL LOW-S_ED FAMILY OF AIRFOILS FO_
GENERAL AVIATION APPLICATIONS (NASA) 51 p
HC AO4/MF A01 CSCi 01A G3/02
N79-13000
Unclas
]234 2
a.
_w
REPRODUCEDBYNATIONAL TECHNICAL
INFORMATION SERVICEU. S. DEPARTMENT OF COMMERCE
SPRINGFIELD. VA. 22161
NATIONALAERONAUTICSANDSPACEADMINISTRATION
LANGLEYRESEARCHCENTER,.HAMTON,VIRGINIA23665 ....
https://ntrs.nasa.gov/search.jsp?R=19790004829 2020-04-22T02:57:17+00:00Z
I:l
"IT
-_lr'--
4
P
1. Report No. ] 2. Government Acclmon No.
!NASA TM X-7_84_4 Title and Subtitle
Effects of Thickness on the Aerodynamic Character-istics of an Initial Low-Speed Family of Airfoilsfor General Aviation Applications
7. Author(s)
Robert J. McGhee and William D. Beasley
12.
Performing Orpni_tion Name and Adam
NASA Langley Research CenterHampton, VA 23665
S_mtiori_ AglmCy _mt and Addrm
National Aeronautics and Space Administration
Washington, DC 20546
3. Recilm_nt's Cat_log _W}.
5. Relict Date
June ] g766. Puforming Orpnizatioo Code
8. Plrforming Orgmnizaticm Report No.
10. Work Unit No.
505-06-31-02
11. Contract or Grant No.
13. Type of Rq)ort and Period Covered
Technical Memorandum14. Sponsoring Agency Code
15. _o_tarv Not_
Special technicalat a later date.
information release, planned for formal NASA publication
16. AbClTa_
Wind-tunnel tests have been conducted to determine the effects of airfoil
thickness-ratio on the low-speed aerodynamic characteristics of an initial
family of airfoils.; The family of airfoils are designated as NASA LS(1)-0413,
0417, and 0421 airfoils. The results were compared with theoretical predictions I
obtained from a subsonic viscous method. The tests were conducted over a Mach
number range from O.lO to 0.28. Chord Reynolds numbers varied from about
2.0 x lO6 to 9.0 x lO6.
17. Key W_ (Sug_sted by Author(t) ) (STAR _tegor y underli
General Aviation AircraftLow-Speed Airfoil SectionsReynolds Number EffectsThickness Ratio EffectsExperimental-Theoretical Comparisdn
tg. Secmitv Oauif. (of this report)
Unclassified
_. Secmitv C,kmf. (of this laMP)
Unclassified
"Available from t The Nali°_l Technical Inf°rmati°n S_rvica' Springfield'
21. NO. of Plges ] 22. Price-
Virginia 22151 __ --
,i,
J_
EFFECTS OF THICKNESS ON THE
AERODYNAMIC CHARACTERISTICS OF AN
INITIAL LOW-SPEED FAMILY OF AIRFOILS
FOR GENERAL AVIATION APPLICATIONS
By Robert J. McGhee and William D. Beasley
Langley Research Center
SUMMARY
An investigation was conducted in the Langley low-turbulence pressure
tunnel to determine the effects of airfoil thickness ratio on the aerodynamic
characteristics of an initial family of airfoils. The results are compared
with theoretical predictions obtained from a subsonic viscous method. The
tests were conducted over a Mach number range from about 0.I0 to 0.28 and a
Reynolds number range from about 2.0 x 106 to 9.0 x 106 . The geometric angle
of attack varied from about -I0 ° to 22 o .
The results of the investigation indicate that the 13-percent airfoil
provided the best performance for this thickness family of airfoils. At a
Reynolds number of 4.0 x 106 with fixed transition near the leading edge, the
maximum lift-drag ratios were about I00, 80, and 60 for the 13, 17, and 21-
percent airfoils. Increasing the airfoil thickness ratio resulted in an average
increase in drag coefficient of about three counts (0.0003) for each percent
increase in thickness ratio at the design lift coefficient with fixed transi-
tion near the leading edge. Maximum lift coefficients at a Mach number of
0.15 and a Reynolds number of 6.0 x 106 decreased from about 2.0 to 1.8 as
the airfoil thickness ratio increased from 0.13 to 0.21. Stall character-
istics were of the trailing-edge type for the airfoil family. Maximum lift
coefficient was generally insensitive to roughness, just sufficient to trip
f
the boundary-layer, for the 13-percent airfoil but was progressively more
sensitive with increasing thickness ratio. Maximum lift coefficients for this
thickness family were substantially greater than the older NACA airfoils of
comparable thickness ratios. Comparisons of experimental section data with
the theoretical viscous method of NASA CR-2523 were good for the 13- and 17-
percent airfoils, but were poor for the 21-percent airfoil.
INTRODUCTION
Research on advanced technology airfoils has received considerable
attention over the last several years at the Langley Research Center. Refer-
ences 1 and 2 report the results of 17- and 13-percent-thick airfoils designed
for light General Aviation airplanes. References 3 and 4 report the results
of a Fowler flap system and spoiler effectiveness for the 17-percent-thick
airfoil. This report presents the basic low-speed aerodynamic characteristics
of a 21-percent-thick airfoil derived from the 17-percent-thick airfoil of
reference I. In addition, this report discusses the effects of varying airfoil
thickness ratio for this initial family and indicates some of the limitations
in present analytical performance prediction methods.
The investigation was performed in the Langley low-turbulence pressure
tunnel over a Mach number range from 0.I0 to 0.28. The chord Reynolds number
varied from about 2.0 x 106 to 9.0 x 106 . The geometrical angle of attack
varied from about -I0 ° to 22 o .
SYMBOLS
Values are given in both SI and U.S. Customary Units.
and calculations were made in the U.S. Customary Units.
The measurements
2
Cp
C
Cc
c d
c' d
CI
C
Cm
Cn
h
I/d
M
P
q
R
t
X
Z
Z c
z t
pressure coefficient, PL - P_
%
airfoil chord, centimeters (inches)
section chord-force coefficient, SCp d(_)
section profile-drag coefficient, ._'d d(_)wake
point drag coefficient
section lift coefficient, c n cos _ - c c sin
lift'curve slope per degree
section pitching-moment coefficient about quarter-chord point,
section normal-force coefficient, -/Cp d(_)
vertical distance in wake profile, centimeters (inches)
section lift-drag ratio, cl/c d
free-stream Mach number
static pressure, N/m 2 (Ib/ft 2)
dynamic pressure, N/m 2 (Ib/ft 2)
Reynolds number based on free-stream conditions and airfoil chord
airfoil thickness, centimeters (inches)
airfoil abscissa, centimeters (inches)
airfoil ordinate, centimeters (inches)
mean line ordinate, centimeters (inches)
mean thickness, centimeters (inches)
geometric angle of attack, degrees
3
Subscripts:
L
max
0
Oo
local point on airfoil
maximum
conditions at _ = 0°
free-stream conditions
AIRFOIL DESIGN AND DESIGNATION
This airfoil family was obtained by linearly scaling the mean thickness
distribution of the 17-percent-computer-designed airfoil of reference I. Thus,
all three airfoils have the same camber distribution and the design lift
coefficient is 0.40. This method of obtaining the airfoil family was selected
for two reasons: to determine the performance of a scaled family of airfoils
and to validate the subsonic viscous method of reference 5 for a range of
thickness ratios for aft cambered airfoils. The airfoil section shapes are
shown in figure l, and figure 2 shows the mean camber line and mean thickness
distributions. Tables I, II, and III present the airfoil coordinates.
This initial family of airfoils are designated in the form LS(1)-XXXX.
LS(1) indicates low-speed (Ist series), the next two digits are equal to the
airfoil design lift coefficient in tenths, and the last two digits are equal
to the airfoil thickness in percent chord. Thus the GA(W)-I airfoil (ref. l)
becomes LS(1)-0417 and the GA(W)-2 airfoil (ref. 2) becomes LS(1)-0413. The
21-percent-thick airfoil of this family is designated as LS(1)-0421.
MODELS, APPARATUS, AND PROCEDURE
Models
The airfoil models were constructed utilizing a metal core around which
plastic fill and two thin layers of fiberglass were used to form the contour
4
of the airfoils. The models had chords of 61 cm (24 in.) and spans of
91.44 cm (36 in.). The models were equipped with both upper and lower surface
orifices located 5.08 cm (2 in.) off themdspan. The airfoil surface was
sanded in the chordwise direction with number 400 dry silicon carbide paper
to provide a smooth aerodynamic finish. The model contour accuracy was generally
within +.lO mm (.004 in.).
Wind Tunnel
The Langley low-turbulence pressure tunnel (ref. 6) is a closed-throat,
single-return tunnel which can be operated at stagnation pressures from l to
lO atmospheres with tunnel-empty test section Mach numbers up to 0.42 and 0.22,
respectively. The maximum unit Reynolds number is about 49 x lO6 per meter
(15 x lO6 per foot) at a Mach number of about 0.22. The tunnel test section
is 91.44 cm (3 ft) wide by 228.6 (7.5 ft) high.
Hydraulically actuated circular plates provided positioning and attach-
ment for the two-dimensional model. The plates are lOl.60 cm (40 in.) in
diameter, rotate with the airfoil, and are flush with the tunnel wall. The
airfoil ends were attached to rectangular model attachment plates (fig. 3) and
the airfoil was mounted so that the center of rotation of the circular plates
was at 0.25c on the model reference line. The air gaps at the tunnel walls
between the rectangular plates and the circular plates were sealed with flex-
ible sliding metal seals, shown in figure 3.
Wake Survey Rake
A fixed wake survey rake (fig. 4) at the model midspan was cantilever
mounted from the tunnel sidewall and located one chord length behind the
trailing edge of the airfoil. The wake rake utilized total-pressure tubes,
5
0.1524 cm (0.060 in.) in diameter, and static-pressure tubes, 0.3175 cm
(0.125 in.) in diameter. The total-pressure tubes were flattened to O.lOl6 cm
(0.040 in.) for 0.6096 cm (0.24 in.) from the tip of the tube. The static-
pressure tubes each had four flush orifices drilled 900 apart and located 8
tube diameters from the tip of the tube and in the measurement plane of the
total-pressure tubes.
Instrumentation
Measurements of the static pressures on the airfoil surfaces and the wake
rake pressures were made by an automatic pressure-scanning system utilizing
variable-capacitance-type precision transducers. Basic tunnel pressures were
measured with precision quartz manometers. Angle of attack was measured with
a calibrated digital shaft encoder operated by a pinion gear and rack attached
to the circular model attachment plates. Data were obtained by a high-speed
acquisition system and recorded on magnetic tape.
TESTS AND METHODS
The 0421 airfoil was tested at Mach numbers from O.lO to 0.28 over an
angle-of-attack range from about -lO° to 220 . Reynolds number based on the
airfoil chord was varied from about 2.0 x lO6 to 9.0 x lO6. The airfoil was
tested both smooth (natural transition) and with roughness located on both
upper and lower surfaces at 0.075c. The roughness was sized for each Reynolds
number according to reference 7. The roughness consisted of granular-type
strips 0.127 cm (0.05 in.) wide, sparely distributed, and attached to the
airfoil surface with clear lacquer.
The static-pressure measurements at the airfoil surface were reduced to
standard pressure coefficients and machine integrated to obtain-section normal-
force and chord-force coefficients and section pitching-mement coefficients
6
about the quarter chord. Section profile-drag coefficient was computed from
the wake-rake total and static pressures by the method reported in reference 8.
An estimate of the standard low-speed wind-tunnel boundary corrections
(ref. 9) amounted to a maximum of about 2 percent of the measured coefficients
and these corrections have not been applied to the data.
Testing of airfoil 0421 utilized high precision lower-range transducers
to measure the wake-rake total pressures compared to the earlier testing of
airfoils 0417 (ref. l) and 0413 (ref. 2). These new transducers indicated a
small difference in total pressure outside of the wake compared to the tunnel
total pressure. Accounting for this pressure difference resulted in a minor
change in the drag data reported in references l and 2. This drag adjustment
has been applied to the most pertinent data of references l and 2 and included
in this report.
PRESENTATION OF DATA
Figure
Section characteristics for LS(1)-0413 airfoil ............ 5
Section characteristics for LS(1)-0417 airfoil ............ 6
Effect of Reynolds number on section characteristics for
LS(1)-0421 airfoil ......................... 7
Effect of Mach number on section characteristics for
LS(1)-0421 airfoil ......................... 8
Effect of Reynolds number on the chordwise pressure
distributions for LS(1)-0421 airfoil ................ 9
Comparison of chordwise pressure distributions for
LS(1) thickness family of airfoils ................. lO
7
Figure
Effect of thickness ratio on section characteristics for
LS(1) thickness family of airfoils ................. II
Variation of maximum lift coefficient with Reynolds number
for LS(1) thickness family of airfoils ............... 12
Variation of maximum lift coefficient with Mach number for
LS(1) thickness family of airfoils ................. 13
Variation of drag coefficient with Reynolds number for
LS(1) thickness family of airfoils ................. 14
Variation of lift-drag ratio with lift coefficient for
LS(1) thickness family of airfoils ................. 15
Comparison of maximum lift coefficient for present LS(1)
thickness family with HACA airfoils ................ 16
Comparison of experimental and theoretical section
characteristics for LS(1) thickness family of airfoils ....... 17
DISCUSSION
Lift.- The effects of thickness ratio on the lift characteristics are
summarized in figure II for H = 0.15, R = 4.0 x lO6, and transition fixed at
x/c = 0.075. The thickness ratio appears to have little effect on ci,o and
the angle of zero lift for thickness ratios up to 0.17. However, for a
thickness ratio of 0.21 the angle of zero lift increases by about 0.40o . The
angle of zero lift is largely determined by the airfoil camber, and this
increase is attributed to viscous decambering for the thick airfoil. Figure 7
shows a decrease in the angle of zero lift at the higher Reynolds numbers, a
result of the thinner turbulent boundary-layers, which supports the viscous
8
decambering effect that occurred at low Reynolds numbers. The chordwise
pressure data for _ = 0° and R = 4.0 x lO6 (fig. lO (a)) clearly illustrate
the decrease in lift coefficient that occurred for the 21-percent airfoil.
The pressure data also indicate large adverse viscous effects with increasing
angle of attack for the 21-percent airfoil. Figure II indicates a modest
decrease in lift-curve-slope for the 21-percent airfoil.
The variation of maximum lift coefficient with thickness ratio
(R = 4.0 x I06; fig. ll) shows a decrease in Cl,ma x for about 1.95 to 1.48
for an increase in thickness from 13- to 21-percent with transition fixed at
x/c = 0.075. The effects of Reynolds number on Cl,ma x for the thickness
family both smooth and rough are shown in figure 12. Increases in Reynolds
number has a large, favorable effect on Cl,ma x. The 13-percent airfoil dis-
plays the largest values of Cl,ma x for the Reynolds numbers shown. Application
of roughness at x/c = 0.075 resulted in small effects on Cl,ma x for the 13-
percent airfoil; however, large decreases occurred for the thicker airfoils.
For example, for the 21-percent airfoil at R = 6.0 x lO6, roughness decreased
Cl,ma x by about 0.14.
Comparison of the maximum lift coefficients for this thickness family
with the older NACA airfoils are shown in figure 16 at a Reynolds number of
6.0 x lO6 for the airfoils smooth. The values of cl,max vary from about 2.0
to 1.80 for increases in thickness ratio from 0.13 to 0.21, for the present
family. The largest values of Cl,ma x for the older NACA airfoils were obtained
for the 230 airfoil series, and varied from about 1.74 to 1.28 for increases
in thickness ratio from 0.12 to 0.24. The new airfoil family represents a
substantial improvement in Cl,ma x compared to the older NACA airfoils. This
result is important because it offers the possibility for improving the
9
performance of light general aviation airplanes by reducing the wing area and
increasing the wing loading.
The effects of Mach number on c for this airfoil family are shownl,max
in figure 13 at a Reynolds number of 6.0 x lO6. Increasing the Mach number
results in similar decreases in Cl,ma x for all three airfoils up to about
M = 0.28. The large reduction in Cl,ma x for the 13-percent airfoil at M = 0.35
is attributed to supercritical flow occurring near the leading edge on the
upper surface of the thinner airfoil. The pressure data of figure lO(c) for
= 12° and M = 0.15 illustrate the larger pressure peaks for the 13-percent
airfoil compared to the thicker airfoils. Large pressure peaks and local
supersonic velocities usually result in a decrease in Cl,ma x with increasing
Mach numbers.
The stall characteristics of this airfoil family are of the trailing-
edge type. References l and 2 reported this result for the 17- and 13-percent
airfoils and the pressure data of figure 9 show this result for the 21-percent
airfoil.
Comparison of the experimental lift data with the viscous flow theory
of reference 5 for a Reynolds number of 4.0 x lO6 with transition fixed at
x/c = 0.075 are shown in figure 17. As previously reported (ref. l and 2)
the theoretical method satisfactorily predicts the lift data for angles of
attack where no significant boundary-layer flow separation is present for
both the 13- and 17-percent airfoils. However, figure 17(c) indicates poor
agreement between experiment and theory for the 21-percent airfoil. This
result is not surprising because of the extensive turbulent boundary-layer
thickening and separation which occurred on the aft upper surface of the
21-percent airfoil at low Reynolds numbers. Examination of the pressure data
of figure 9 indicate separated-flow type pressure recovery on the aft upper
surface of the airfoil at low angles of attack. Reference 5 indicates that
for airfoils of thickness ratios of 0.18 or greater the theory generally over-
predicts the lift. Theoretical calculations madeat higher Reynolds numbers
generally resulted in the samepoor agreement.
Pitching-moment.- The variation of the quarter-chord pitching-moment
coefficient at zero angle of attack with thickness ratio is presented in
figure II for R = 4.0 x lO6 with transition fixed at x/c = 0.075. No effect
of thickness ratio is shown for the 13- and 17-percent airfoils; however, a
less negative value of Cm,o (positive increment) is shown for the 21-percent
airfoil. This result is attributed to the viscous decambering that occurred
for the 21-percent airfoil at low Reynolds numbers (see discussion under lift).
Comparison of the section data of figure 7(a) R = 2.0 x lO6) with 7(e)
(R = 9.0 x lO6) illustrate the more negative values of Cm, o resulting from
the effective increase in camber for the thinner turbulent boundary layers
at the higher Reynolds number. Comparisons of the experimental cm data with
the theory of" reference 5 (fig. 17(c)) illustrate the poor agreement obtained
for the 21-percent airfoil.
Drag and lift-drag ratio.- In practical general aviation application
boundary-layer transition usually occurs near the leading-edge of the airfoils,
a result of aerodynamic roughness caused by fabrication methods, dirt, paint
erosion, or insect remains gathered in flight. Thus the discussion of the
drag data is limited to fixed transition at x/c = 0.075. The effects of
thickness ratio on cd are consistent (increasing cd with increasing thickness
ratio) with the results reported in reference lO for the NACA airfoils. At
the design lift coefficient of 0.40 and R = 4.0 x lO6, figure II shows that
li
increasing thickness ratio results in about an average increase in cd of three
drag counts (0.0003) for each percent increase in thickness ratio. The varia-
tion of cd with Reynolds number for the thickness family is shown in figure 14
for cI = 0.40 and cI = l.O. The scale effects at cI = 0.40 (fig. 14(a)) are
generally consistent with flat-plate drag variations. At cI = l.O (fig. 14(b)),
the increments in drag are about the same for the Reynolds number range for the
13- and 17-percent airfoils. However, large increases in cd are shown for the
21-percent airfoil, particularly at the low Reynolds numbers. This result is
attributed to extensive turbulent boundary-layer separation on the aft upper
surface of the airfoil as illustrated by the pressure data of figure 9.
Figure 15 shows the variation of lift-drag ratio with cI for the thickness
family. As expected, increasing the airfoil thickness decreases the lift-drag
ratio, while increases in Reynolds number has a favorable effect on lift-drag
ratio. At a Reynolds number of 4.0 x lO6 the maximum lift-drag ratios were
lO0, 80, and 60 for the 13, 17, and 21-percent airfoils. Also, the lift
coefficients for high lift-drag ratios were increased as the airfoil-thickness
ratio was decreased.
Comparison of the experimental drag data with the theory of reference 5
(fig. 17) indicate surprisingly good agreement for the entire thickness
family at lift coefficients where attached flow was present.
SUMMARY OF RESULTS
Low-speed wind-tunnel tests have been conducted in the Langley low-
turbulence pressure tunnel to determine the effects of airfoil thickness ratio
on the aerodynamic characteristics of an initial family of airfoils. The
12
results have been compared with theoretical predictions obtained from a
subsonic viscous method. The tests were conducted over a Mach number range
from about O.lO to 0.28 and a Reynolds number range from about 2.0 x lO6 to
9.0 x lO6. The following results were determined from this investigation"
I. The 13-percent airfoil provided the best performance for
this thickness family of airfoils.
2. At a Reynolds number of 4.0 x lO6 with fixed transi-
tion near the leading edge, the maximum lift-drag
ratios were about lO0, 80, and 60 for the 13-, 17-,
and 21-percent airfoils.
3. Increasing the airfoil thickness ratio resulted in an
average increase in drag coefficient of about three
counts (0.0003) for each percent increase in thickness
ratio at the design-lift coefficient with fixed transi-
tion near the leading edge.
4. Maximum lift coefficients at a Mach number of 0.15
and a Reynolds number of 6.0 x lO6 decreased from
about 2.0 to 1.8 as the airfoil thickness ratio in-
creased from 0.13 to 0.21. Stall characteristics
were of the trailing-edge type for this airfoil
family.
5. Maximum lift coefficient was insensitive to roughness,
just sufficient to trip the boundary layer, for the
13-percent airfoil but was progressively more sensitive
with increasing thickness ratio.
13
1
o
Maximum lift coefficients for this thickness family
were substantially greater than the older NACA a_r-
foils of comparable thickness ratios.
Comparisons of experimental section data with the
theoretical viscous method of NASA CR-2523 were good
for attached boundary-layers for the 13- and 17-
percent airfoils, but were poor for the 21-percent
airfoil.
REFERENCES
I. McGhee, Robert J.; and Beasley, William D.: Low-Speed Aerodynamic Char-
acteristics of a 17-Percent-Thick Airfoil Section Designed for General
Aviation Applications. NASA TN D-7428, 1973.
2. McGhee, Robert J.; Beasiey, William D.; and Somers, Dan M.: Low-Speed
Aerodynamic Characteristics of a 13-Percent-Thick Airfoil Section
Designed for General Aviation Applications. NASA TM X-72697, 1975.
3. Wentz, W. H., Jr.; and Seetharam, H. C.: Development of a Fowler Flap
System for a High Performance General Aviation Airfoil. NASA CR-2443,
1974.
4. Wentz, W. H., Jr.: Effectiveness of Spoilers on the GA(W)-I Airfoil With
a High Performance Fowler Flap. NASA CR-2538, 1975.
5. Smetana, Frederick 0.; Summey, Delbert C.; Smith, Neill S.; and Carden,
Ronald K.: Light Aircraft Lift, Drag, and Moment Predictions - A
Review and Analysis. NASA CR-2523, 1975.
6. Von Doenhoff, Albert E.; and Abbott, Frank T., Jr.: The Langley Two-
Dimensional Low-Turbulence Pressure Tunnel. NACA TN 1283, 1947.
14
7. Braslow, Albert L.; and Knox, Eugene C.: Simplified Method for Determina-
tion of Critical Height of Distributed Roughness Particles for Boundary-
Layer Transition at Mach Numbers From 0 to 5. NACA TN 4363, 1958.
8. Pankhurst, R. C.; and Holder, D. W.: Wind Tunnel Technique. Sir Isaac
Pitman and Sons, Ltd., London, 1965.
9. Pope, Alan; and Harper, John J.: Low-Speed Wind-Tunnel Testing. John
Wiley and Sons, Inc., New York, 1966.
lO. Abbott, Ira H.; and Von Doenhoff, Albert E.: Theory of Wing Sections,
Dover Publications, Inc., New York, 1959.
15
TABLE
xlc
0.0
•002O
•0050
.0125
.0250
.0375
.0500
.0750
•1000
.1250
•1500.1750
•2000
.2500
.3000
•3500.4000
.4500
.5000
•5500
.5750
•6000
.6250
•6500
.6750
.7000
.7250
.7500
.7750
.8000
.8250
.8500
.8750
.9000
.9250
•9500
.9750
I.0000
I.- LS(1)-0413 AIRFOIL DESIGN COORDINATES
.... (Z/c }upper
0.0
•O1035
•O1588
.02424
.03325•03966
.04476
.05261
.05862
•06347
•06755
.07103
.07399
.07861
•08182
.08381
•08464
{z/c )1ower
0.0
•00495
•00935
.01448
•01907
•02226.02498
•02938
.03281
.03562
•03792
•03982
.04139
.04368
•04484
.04516
•04474
.08435
.08293
•08023
.07834
•07605
•07335
.07024
•06674
•06287
.05868
.05419
•04946
.04450
.03933
•03397
•02843
•02275.01692
.01096
.00483
-.00156
-.04353
-.04144
-.03810
-.03589
-.03334
-.03051
-.02745
-•02425
-.02097
-.01767
-.01441
-.01126
-.00831
-•00568
-.00347
-.OOl81
-•00080
-•00058
-.00135
-•00336-.00714
16
::;_GINAL PAGE IS
.'-._._POOR QUALFfY
TABLE II•- LS(I)-0417 AIRFOIL DESIGN COORDINATES
x/c
0.0
•0020
•0050
•0125
.0250
•0375
•0500
•0750
•1000
.1250
.1500
•1750
.2000
•2500
•3000
.3500
.4000
.4500
•5000
•5500
.5750
.6000
.6250
•6500
.6750•7000
.7250
.7500
.7750
•8000
.8250
.8500
.8750
.9000
.9250
.9500
.9750
l.0000
(z/C}upper
0.0
•O1300
•02035
•03069
.04165
•04974
•05600
.06561•07309
•07909
•08413
•08849
•09209•09778
.I0169
.10409
•10500
•10456
•10269
•09917
.09674
•09374
•OgOl 3
•08604
•08144
•07639
•07096
.06517
•05913
.05291
•04644
•03983
•03313
•02639
•O1965
•O1287
•00604
-.00074
(z/c)lower
0.0
-•00974
-.01444
-.02051
-.02691
-.03191
-•03569
-.04209
-•04700
-•05087
-•05426
-•05700
-•05926
-•06265-•06448
-.06517
-•06483-•06344
-.06091-.05683
-.05396
-.05061
-•04678
-•04265
-•03830
-•03383
-.02930
-.02461
-•02030
-.01587
-.Oil91
-.00852
-•00565
-•00352
-•00248-.00257
-•00396
-•00783
17
TABLE III.- LS(I)-0421 AIRFOIL DESIGN COORDINATES
xlc
0.0
•0020
•0050
.0125
•0250
.0375
•0500
•0750
•1000
.1250
.1500
.1750
.2000
.2500
.3000
.3500
.4000
.4500
.5000•5500
.5750
.6000
.6250
.6500
.6750
.7000
.7250
.7500
.7750
.8000
.8250
.8500
.8750
.9000
.9250
.9500
.9750
l.0000
(zlc)upper
0.0
.01560
.02377
.03599
.04912
.05853
.06606
.07771
.08664
.09388
•09993
.I0507
.I0943
.I1617
.12074
.12344
.12439
.12365
.12112
.I1657
.I1342
.I0965
.I0525
.10025.09470.08865.08216.07530
.06814
.06075
.05318
•04550
.03775
.03000
.02232
.01476
.00735
.00016
(z/c}l ower
0.0
-.O1071
-.01775
-.02653
-.03522
-.04137
-.04650
-.05463
-.06097
-.06612
-.07038-.07393
-.07690
-.08130
-.08381
-.08484
-.08455
..08288
-.07970-.07452
-.07104
-.06701
-.06247
-•05752
-.05226
-•04678
-.04117
-•03553
-•02994
-.02456
-.01953
-.O1500
-.Olll2
-.00805
-.00598
-.00515
-.00589
-.00886
18
ORIGINAL PAGE IB
O_ POOR QUALITY
.2
.I
z/c 0
-.I
m
i
I . ; ! ' I
i
ii[
II ! :_I
i i :"
..... i-I
I: i'
!_i i _
i,, Airfoil 0415
) ..... 1J ! I ,
' I i I i Ei I i , _ t
.2
.I
z/c
0
-.I
a|i i t iI z t
.....! ......l..... i il
; ,_ .I: i I '_:_!
; ! [ ,
-7-_. _.. i ._ : ...........
::i,- : _, i Airfoil 0417
-,-_-F--.._--.=__:-! --I .... ! -i--,--i r -! ,i ' _ _ _ I !
_- ! I , i : I
-.: ! :....,..A2:__I .. i ._:_L_:i: ......t_
z/c 0
--ol
--,2
0 .I .2 .3 ,4 ,5 .6x/c
0421
i
!
1.0
Figure I.- Section shapes for NASA LS(1)-thickness family of airfoils, i_
zt/
Zc/C
.12
.10
.08
.06
.04
.02
0
.02
,
-.020
Airfoil 0421
. I .2 ,5 .4 .5 .6 ,7 .8 ,9x/c
1.0
Figure 2.- Mean thickness distributions and camber line for NASA LS{I)-thickness family of airfoils.
/--Tunnel side walls
/. _ Diam.= 1.67cv.Jk ",\ '_':: ","Y/I/I/.,////
ORIGINAL PAGE i_
O_ Poor QUALII_
___,._ LAirflow A
•I __tA
-- Circular plate --_,_, _
7Tunnel center line
c/4
L
t -
1.50c
7_y
Airfoil positioningattachment
Top view Model attachment
S plate
_ Zero incidence
reference
End view ,section A-A
Figure 3.- Airfoil mounted in wlnd tunnel. All dimensions In terms of airfoil chord, c = 61cm (24 in.).
Static-pressure
Static pressure
Airflow_
Tunnel
Total- pressure probes
(tubes flattened )
_-_o °
probe __c---__ i i -_---
"042c_i _--I_ ,25c-- --,-F
probes __ _
b
F
-F021c
typ.)
k__L-T-
__ .OIIc
(typ.)
-- .0052 c
(typ.)
.042c
1.17c
.189c
(typJ
,_h,,_, Figure 4.- Drawingof wake rake. All dimensions in terms of airfoil chord, c = 61cm (24 in.). ,
ORIGINAL PAGE IS
OF POOR QUALITY
.03
Cd .02
0
0
Cm -°1
8
a ,deg
Figure5.- SectioncharaderlsllcsforLS(I)-0413airfoil. M = 0.15;transitionfixedat xl c = O.075.
Cd.02
0 24
2O
16
8
a,deg
4
0
0 12
1.2 1.6 2.0 2.4
Figure 6.- Sedlon charaderlstlcs for LS(1)-0417 airfoil. M = 0.15; transition fixedat x/c = O.075.
.04
Roughness0 Off
[] On
ORIGINAL PAGE I_
OF POOR QUALITY
.03
Cd
.02
.01
0 24
16
12
8
a,deg
4
0
Cm
0 12
-.4 0 .4 .8 1.2 1.6 2.0
c l
(a) R_2.0xlO 6.
Figure7.- Effectof Reynoldsnumberon sedloncharacteristlcsfor LS(1)-0421airfoil.M = 0.I5.
cd
.O5
...... , ,lii I tl I!! '''
, : 0 Off ].J _' iju =] ii ' _:.:_.LL.i_:i__iJt ]J_ -L.__,04 - -_ :_--.- [] On :] /li Jl I J;:i
: : _ r T. i !!rf!:g i:-ii_j -iJ !; ' B ] i', I1 i !i ; il! l: ,
i , I : L I ,,, i i ,_ _, j
i ; ! '' 'r_ ] '
_,1 i [I', _ li I: I ; .
@ / t ii _T: i I_ :. .%_7,,. ) / i , i: []]''t_ : ! 1 '!! '.'
,. . . _ ! E, :i _I :lJ '
"P _ I.LA_l ; ', ! ; r ii ii
[ i ' I ..il t b _ ,7_ _F_ • ,t "!'_ !:1 "i '4 i i !:4
O '! ;] I i : , J ii.:!l .: ! .!,![J_ ,_,ii _.J, :, .... 24
2O
16
12
8
a,deg
4
cm
cz
(b)R = 3.0 x I0_,
Figure7.- Continued.
.05
.04
,03
c d
.02
.01
c m
Roughness0 Off
[] On
Iii
t
(
o _ I ! i ' i: i ' i !
L _ t / i ¸ II ; ' / L__ i1...........I --I-;i_i............
i -i -,-_--_--_ .........
' II ', / : t .,,[l_J _, t +_
[ S-_ Ii'i__l_---_ _
c _ i i io i,i , i_ ,i,liil:il,i
-.I
-.2-.8 -.4 0 .4
I
I
n i •
....... i ....... '
i1I
411
.8 1.2
cz
(c) R =4.0x105.
1.6 2.0 2.4
24
2O
16
12
8
a,deg
4
0
-4
-8
12
Figure 7.- Continued.
,05 ---:
.04 -'i
iI
.03 !
cd .
.02 .-_:I
.01 -- ....
0
! I
i!l:1
td
lli!.I
0 ::;
Cm
lili-.28
...... ii
,ll,: ii]
!i_! !i[
:il
ii! _ii
i
;i _!LI, !i,
ill; i!!!!_i iiJlI! ,_ ,,,
!i :
!iir!i
1tl_i!!i
i1!_ iill
!2 !iii! i[!
' Ilili
iiii
i[]ii ....[tIl
CL
(d) R_6.0x10 6.
t Figure7.- Continued.
.... 16
i
12
I
t_
i;
ii;
T7 -4iJ
I
-a
:! -12
;i
2.4
24
2O
8
:,deg
Cd
.05
.03
.02
.01
0
C
Cm
0
Roughnesso Off[] On
,4 ,8 1,2
c l
(e)R _ g.OxlO6.
Figure7.- Concluded.
24
2O
16
I 2
8
a,deg
4
0
-4
-8
-12
2.4
Cd
.05
.04
.02
M
0 0.10
[] .15
.20
A .28
'.01
0 24
2O
16
12
8
a ,d eg
4
0
.I
C m
Figure8.- EffectRofMachnumberon sedioncharacteristicsfor LS(I)-0421airfoil.= 6.0 x 106;transition fixedat x/c = 0.015.¢
Cp
-q .8
_Lt
-4.0
-3.6
-3.2
-2.8
_2.LI _
I \
-1.6
-l.2
e,deg c I cd c m
o -2._ .035 .0128 -.0816[] .1 .363 .0132 -.08q60 _.O .?_N .016? -.0808
8.1 1.06q .0285 -.0?33
i
_'NN,L_..
_,_
>--< >-....<__...,
I ._ _. _r._ _ ..[ , .. ""('-_
, _z_, --Z,k---z _.
.I . L/'II
,.._,_
0 [] 0 AUpper surface
© [] _ ._Lower surface
IJ.0 .1 .2 .3 ._ .5 .6 .? .8
x/c
•9 1.0
{a) R=2,1x106.
Figure 9.- Effect of Reynoldsnumber on chordwise pressure distributions for LS(I)-0421airfoil.M = 0.15; transition fixed at x/c = 0.075.
e,deg10.!12.014.216.0
c l
t • 1951.3171.4281.475
cd
.0352
.0478
cm
-.0683-.0662-.0643-.0649
Cp
,1 t.O
(a) R = 2.I × 106. Concluded.
Figure 9. - Continued.
ORIGINAL PAGE 18
OF POOR QUALITY
Cp
-q.8
-q .q
-q .o
-3.6
-3,2
-2.8
-2 •½
-2 .(
-I.(
-l•2
l._0
a,deg c l cd cm
o -3.0 .OH4 •0118 -.0852
o 0.0 .38q .0121 -.090?
0 q.l .803 .01qq -.0909A 8.0 1.121 .0225 -.0810
0 [] <3 z_Upper surface
d) _ _ &Lower surfdce
• i .2 .3 .q .5 .6
x/c•7 .8 .9 l .0
(b)' R = _.9 x I06.
Figure 9. - Continued.
-tq
-13
-12
-1!
-10
-9
-8
a,deg cz cd cmo 10,0 1.2_8 .0330 -,0731
[] ]2.2 1.357 .0Y63 -.0682
0 IH.O t.Y25 -.0620
A 17.1 t.N83 -.0571
0 [] 0 Z_Upper surface
@ aJ ,$, &Lower surface --
Cp
-5
-5
....
1.!
....... z+_--.,z]'_ (_
".-- +_ i--_l |_i
+_"+ ..--+,,- -, L,+_.._i:.--d
.2 .3 .B • 5 .6
x/c
{b) R = 3.9x I06. Concluded.
.? .8 .9 1,0
"'_'_ Figure g. -Continued.
ORIGINAL PAGE IS
OF POOR QUALITY
-4.81
_t l oi
-q .i
-3.6
a,deg cz c d cmo -3,0 .05? •0106 -,0895[] 0,0 .422 .0113 -,09690 q.l .853 •0130 -.1000
8.0 1.205 .0190 -.0925
O [] O AUpper surface[] _, _,Lower surface --
-3 •2
-2.8
_z_i --2q ^
, \"\Cp _ ...... x
<1>
I \ - -_Z
-1.2 _ /--< >......<1
-.I i n-----I 1_1 l_[]_[
>/ .<)Z<_.l _l_Z1 .(.3/_...-[_-I ]--i _--_',-"<
.ILr_')[ ,_ .<>-.< ;,_-< >--_
t k 1J• L1 -"
A
g1,._
0 .I .2 .3
"1-- ]--I _rl_r
.>---__-,_- _', ,4
.q
%.
)_
.]."_(
k--- z
.5
x/c
]._'_ _ .
<-"_tt_ I l--i i'_
•6 .'/ .8 .9 1.0
(c) R=O.0x106.
Figure9. - Continued.
Cp
-lq
-[3
-12
-11
-tO --
-9--
-I
-5
0 P
0 • 1 .2 .3
a ,deg c z cd cm0 12.0 1.437 .03u_7 -.0770
[] 14.3 1.5u_2 -.0631
0 16.1 1.626 -.0639
a, 19.0 1.665 -.0611
0 [] 0 aUpper surface• [] @ S,Lower surface
_L
.q .5 .6 .'7 .8 .9
x/c
l.O
,{c_ R = 6.0 x I06. Concluded.
Figure 9. - Concluded.
0d
,_,ur_I.D OO
d "
o
<>
[]
0
o0
0_J
<_
[]
(9
•6 __.L _14--
_ooo
onO
\
..,."\
l
\
<
<
ORIGINAL PAGE IS
OF POOR QUALITY
CT
/7
' <> fD _)
El , <>- (_
i
tD _ O0 ,_" 0• t • •
I I I I _.¢..)
CO
o.
O_i
cO
N
_D
o_1
0
o_1
0
0
A
s'/
0
,w
0
0 •
--I,._ II
I,,--
_.o
o_f--o II
0 m
¢D xo 0
i,.,
I.i-
-2.8
-2.4 _ ___ _
Airfoil
0 0413
[] 0417
-2
-I.6
-I.2
-.8
Cp
_o4
i I
14_->--I< >I< r -_
I,, -NLj-
1•2 t
0 .I .2 .5 .4
__ 0 0421
0
,-p_,---_ ->-__.<
)I--(_-- (-_)-----(.)...___(.__=_
cZ1.15
1.13
cd0.0119
.0145
Cm
-0.1086
-.I 108
.97 .0164 -,0870
[] (>Upper surface
E_ 4) Lower surface
1.
•5 .6 .7 .8 •9 1.0
X/C
(b)a = 6°.
FigureI0.-Continued.
33
0RIGINAL PAGE ISOF pOOR qUALITY
-8
-7
_6
-5
-4
Cp
-5
-2
-I
i ,
/
0
Airfoil
0 0415
[] 0417
0 0421
-'<>-.....<
.I ,2 ,5 .4 _ .5 .6
x/c
(c) a = 12°.
Figure I0.- Concluded.
cz Cd Cm1.69 0.0194 -0,0958
1.59 .0262 - .0887
I.:56 ,0465 - ,0682
© [] OUpper surface
® m _Lower surface
.7 .8 ,9 1.0
3I
Cl,o
.8 I
I o-I -• i
I
CZa
.16 -- --
,12
.08 -- --
!l
1- ii
i i ,,.
I
......... - I .,
1.2
Cm 7. I
0
0
(a ,deg) c -0
z-4
- 808 .12
ft
---0
-.2
.02
cd o01
1 , ! ,
o4_.j
-- ! I _
' "%1i i _- i
, !
i i i
I i = 1
I
I I I
--_-'Oi
J' i
-- i t
i • !
cz=0.40
.16 .20 .24 .16 .20t/c t/c
0.08 .12 .24
Figure II.- Effect of thickness ratio on sedion characteristics for LS(I)-thickness family of airfoils.M = 0.15; R _ 4.0 x !06_ transition fixed at x/c = 0.075.
onO
'_' _ 0
¢-
!
m
c-
o
L_
E
e.--
e_ ii
ON
ipm 14,,,_
ow
0I.J 0
-- E
X
E
0
Eli
>I
M
o_
_;i;:._.?;yT;_t_::::...:+_T_.-., _. '
O rO l',- --
'_000
o no
_ 1,11
!!)t)4
i: iiilii *'+
tt _:t;ii :rail
!] il 1;i i)I!
,I x
_1 ;!itIt ::t_i; t;_;
ct i]iI
H :_!i!) :i::
!( I i 4i
ii _!!(i! _+÷÷
7_1 tt_l
ii ihi]i iii_
_+ ++++++ _+4
))i)il• :.LL
t! _!ii±_Li
II i_!
t,
i _ 2222
tliii "_IHI:
))II) )i-lii'it!!j:H ! ,.
'**:!k
i i ]Lill ,,.
!ii.....rltt
0_II
EP
N
0
Qm
iI VI::+.1
;il 1211
:]'.i t__:
::_r f}?,;;i 41:
!l,i':4i'( !_f
::: Lii
if!! _ti
.... +i
• .;. f.ff
; .... !i
i4-_ +,+
+i: it!:
_t,t .+÷
iT)))!'+.!L_:[:r'r*
+.,. :...... i-
:. + !,,
i_:_i74--
_.• ++l
+--- l''
211_ 11
4:IT in
+-+F -_1...... +
Od
A
0'*" II
boE x
e-e- o
_ om
_ °i
_ L_
0
I
0_ X
°"' '4:_
E_
0 L
C _
_ 0
_- ,i,--,
> E
I
II
A
lei.,-_
O
em-n
14---
0
IllCD
"-d
II
X0 -.--'
oO,m.lD_
U_
L_
CD
o--.,
0
L_
0
0m..-.,
g..u
!
L_
i,...u
I.I-
04
4
'_000
oDO
0
0
t.O
0
c_
0Q
0q
00
0
0
...
e-
mI
II ,_ed.o --
it
z/d
12o
8O
4O
0
/
im !..!:
f/
/ 1
/
f
Airfoil
0413
0417
\
\\
\
!DBIGB_' pAGE iS
120
8O
z/d
0
/
/
/
/
J7
R_ 4.0x I06
---....
\
120
z_80
4O
0
- i
/
R _ 2.0 x IOs
.8 i.2 1.6 2.0 2.4
c l
Figure 15.- Variation of lift-drag ratio with lift coefficient for LS(I)-thickness fatally of airfoils. M = 0.15; transition fixed atx/c = O.015.
2.4
2.2
2.0
1.8
1.6
1.20
0 Present family
[] NACA 2"50 series _
NACA
z_ NACA
r,, NACA
44 series
24 series ?ref. I0i
65 series'
(cz,i =0.4)!
,\k9
.04 ..... ,08 .I 2 .16 .20 .24 .28t/c
Figure 16.- Comparison of maximum lift coefficient for present LS(I)-thicknessfamily with older NACA airfoils. R = 5.0 x 105; airfoils smooth;tvl_< 0.17.
c d .02
Cm I
8
(1,deg
4
Cz(a) Airfoil 0413.
Figure 17.- Comparisonof experimentalandtheoretical sectioncharaderistlcs for LS(l)-thlcknessfamily of airfoils.= 0.15; R = 4.0 x 106;transltlon fixed at x/c = 0.075.
.04
,03
cd .02
.01
0
0
Cm --.I
0
0 Experiment
Theory (ref,5
ilf2I
lit
,8
cZ
(b}Airfoil0417.
Figure17.-Continued.
1
I
i
I
i
_i 24
!
-- 20
i''
i,- 16
_i_ 12
-- 8
deg
_-- 4
-T,
i
,ii
R -4i
: -12
-4--,-
4_
Ii
I[
2.4
cd .02
(_
.01
0 Ex peri ment
Theory (ref.5)
C m
0
0
0
0o
.....
.4 .8
cz
{c)Airfoil0421.
Figure 17.- Concluded.
24
2O
16
12
I4
0
a ,deg