.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

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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

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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