April 2012 

NASA/CR–2012-217560

An Exploratory Investigation of a 

Slotted, Natural-Laminar-Flow Airfoil

Dan M. Somers 

Airfoils, Incorporated, Port Matilda, Pennsylvania 
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April 2012 

NASA/CR–2012-217560

An Exploratory Investigation of a 

Slotted, Natural-Laminar-Flow Airfoil 

Dan M. Somers 

Airfoils, Incorporated, Port Matilda, Pennsylvania 
Available from: 

NASA Center for AeroSpace Information 

7115 Standard Drive 

Hanover, MD 21076-1320 

443-757-5802 

Acknowledgments

This research was performed under NASA Contract NAS1-01076 from August 15, 2001 

to November 30, 2004. 

This effort was sponsored by NASA Langley Research Center and the assistance of 

Langley personnel is gratefully acknowledged. In particular, the dedication of William G. 

Sewall is sincerely appreciated. 

The use of trademarks or names of manufacturers in this report is for accurate reporting and does not constitute an 

official endorsement, either expressed or implied, of such products or manufacturers by the National Aeronautics 

and Space Administration. 
ABSTRACT

A 15-percent-thick, slotted, natural-laminar-flow (SNLF) airfoil, the S103, for general

aviation applications has been designed and analyzed theoretically and verified experimentally in the Langley Low-Turbulence Pressure Tunnel. The two primary objectives of high

maximum lift and low profile drag have been achieved. The constraints on the pitching

moment and the airfoil thickness have been satisfied. The airfoil exhibits a rapid stall, which

does not meet the design goal. Comparisons of the theoretical and experimental results show

good agreement. Comparison with the baseline, NASA NLF(1)-0215F airfoil confirms the

achievement of the objectives.

INTRODUCTION

The wing profile drag is the largest contributor to the total aircraft drag at cruise conditions for most aircraft. The wing profile drag contributes about one third of the total drag for

transport aircraft. As the aircraft size decreases from transport through commuter to business

jets and other general aviation (GA) aircraft and finally unmanned aerial vehicles (UAV’s) and

sailplanes, the percentage of the total aircraft drag due to the wing profile drag generally

increases, primarily because the relative wing area increases, as shown in the following table.

To minimize wing profile drag, the figure of merit FOM applicable to aircraft having

their wing area determined by a minimum-speed requirement (usually landing speed) should

be maximized:

where cl,max is the section maximum lift coefficient and cd,cruise is the cruise section profiledrag coefficient. (See ref. 1.) Note that the figure of merit is expressed in terms of section

(airfoil) characteristics, not aircraft characteristics. The figure of merit can be interpreted as

follows. The wing area, and therefore the aircraft wetted area, can be reduced if a higher maximum lift coefficient is achieved, resulting in lower drag. The wing profile drag can also be

reduced if a lower section profile-drag coefficient is achieved. This figure of merit applies to

almost all classes of aircraft. For those aircraft having their wing area determined by a fuelAircraft Type

Transport ~ 1/3

Business jet ~ 1/3

Low-speed GA > 1/3

UAV 1/3 to 1/2

Sailplane > 1/2

Wing Profile Drag

Total Aircraft Drag

-----------------------------------------------------

FOM

cl max ,

cd cruise ,

= -------------------
2

volume requirement (e.g., business jets), reducing the section profile-drag coefficient is even

more beneficial.

Three approaches have become accepted for the reduction of wing profile drag. One

approach is to employ a high-lift system (e.g., leading-edge slat plus double- or triple-slotted,

Fowler flap) to achieve a higher maximum lift coefficient. (See, for example, ref. 2.) This

approach has several disadvantages. Almost no laminar flow can be achieved because of the

disturbances introduced by the slat, which results in a high section profile-drag coefficient.

The maximum lift coefficient is limited to about 4, which limits the reduction in wing area.

High-lift systems are complex, both mechanically and structurally, resulting in higher weight

and cost. This approach can provide a maximum wing profile-drag reduction of about 50 percent compared to a conventional, turbulent-flow wing with no high-lift system and has been

adopted for all current transport aircraft. Active high-lift systems (e.g., blown flaps and circulation control) have demonstrated very high lift coefficients but the cost, complexity, and

potentially disastrous failure modes have prevented their adoption for production aircraft.

A second approach is to employ a natural-laminar-flow (NLF) airfoil to achieve a

lower profile-drag coefficient. (See, for example, ref. 3.) By appropriate airfoil shaping,

extensive ( 30-percent-chord) laminar flow can be achieved on both the upper and lower

wing surfaces. The extent of laminar flow is limited to about 70-percent chord by the

pressure-recovery gradient along the aft portion of the airfoil and by leading-edge sweep. The

recovery gradient becomes steeper as the extent of the favorable gradient along the forward

portion of the airfoil increases. The recovery gradient eventually reaches a limit beyond

which trailing-edge separation occurs, resulting in a lower maximum lift coefficient and a correspondingly lower figure of merit. Leading-edge sweep restricts the extent of laminar flow

because it introduces crossflow instabilities that lead to transition. This approach can also

provide a wing profile-drag reduction of about 50 percent compared to a conventional,

turbulent-flow wing and has been adopted for most current general aviation aircraft, including

business jets, as well as unmanned aerial vehicles and all sailplanes. It does, however, require

more stringent construction techniques.

A third approach is to employ a laminar-flow-control (LFC) airfoil to achieve a lower

profile-drag coefficient. (See, for example, ref. 4.) By incorporating suction through porous

or slotted, wing skins, 100-percent-chord laminar flow can be achieved on both the upper and

lower wing surfaces. LFC systems are very complex, mechanically, structurally, and operationally, resulting in higher weight and cost. This approach can provide a wing profile-drag

reduction of about 75 percent compared to a conventional, turbulent-flow wing but has yet to

be adopted for any production aircraft.

For the present effort, a new approach, called a slotted, natural-laminar-flow (SNLF)

airfoil, is employed. The SNLF airfoil concept is similar in nature to the slotted, supercritical

airfoil concept (ref. 5).
3

SYMBOLS

Values are given in both SI and U.S. Customary Units. Measurements and calculations were made in U.S. Customary Units.

Cp pressure coefficient, 

c airfoil chord, mm (in.)

cc section chord-force coefficient, 

cd section profile-drag coefficient, 

cd' point drag coefficient (ref. 6)

cl section lift coefficient, 

cm section pitching-moment coefficient about quarter-chord point,

cn section normal-force coefficient, 

h vertical height in wake profile, mm (in.)

M free-stream Mach number

p static pressure, Pa (lbf/ft2)

q dynamic pressure, Pa (lbf/ft2

)

R Reynolds number based on free-stream conditions and airfoil chord

t airfoil thickness, mm (in.)

x airfoil abscissa, mm (in.)

y model span station, y = 0 at midspan, mm (in.)

z airfoil ordinate, mm (in.)

 angle of attack relative to x-axis, deg

x change in chordwise position of aft element, mm (in.)

z change in vertical position of aft element, mm (in.)

pl p –

q

----------------

Cpd z

c

--   	 
 

cd' h

c

--   	 
 d

Wake



cn  cc cos – sin

 Cp

x

c

-- 0.25 –   	 
 d x

c

--   	 
 Cp

z

c

--   	 
 d z

c

--   	 
  +  –

 Cpd x

c

--   	 
  –
4


 change in angle of aft element, deg

f flap deflection, positive downward, deg

Subscripts:

l local point on airfoil

ll lower limit of low-drag range

max maximum

ul upper limit of low-drag range

0 zero lift

 free-stream conditions

Abbreviations:

LFC laminar flow control

ls lower surface

NLF natural laminar flow

SNLF slotted, natural laminar flow

us upper surface

AIRFOIL DESIGN

OBJECTIVES AND CONSTRAINTS

The design specifications for the airfoil are contained in table I. The specifications are

essentially identical to those for the baseline airfoil, the NASA NLF(1)-0215F (ref. 7), except

for the constraint on the zero-lift pitching-moment coefficient, which is more negative.

Two primary objectives are evident. The first objective is to achieve a maximum lift

coefficient of at least 1.72 for a Reynolds number of 3  106

. A requirement related to this

objective is that the maximum lift coefficient not decrease significantly with transition fixed

near the leading edge on both surfaces. In addition, the airfoil should exhibit docile stall characteristics. The second objective is to obtain low profile-drag coefficients from a cruise lift

coefficient of 0.20 for a Reynolds number of 9  106 to a climb lift coefficient of 1.00 for a
5

Reynolds number of 6  106. Because this is a low-speed application, the flow is considered

incompressible (i.e., M = 0).

Two major constraints were placed on the design of the airfoil. First, the zero-lift

pitching-moment coefficient must be no more negative than –0.20. Second, the airfoil thickness must equal 15-percent chord.

PHILOSOPHY

Given the above objectives and constraints, certain characteristics of the design are

apparent. The following sketch illustrates a drag polar that meets the goals for this design.

Sketch 1

Point A is the lower limit of the low-drag, lift-coefficient range; point B, the upper limit. The

profile-drag coefficient increases very rapidly outside the low-drag range because boundarylayer transition moves quickly toward the leading edge with increasing (or decreasing) lift

coefficient. This feature results in a leading edge that produces a suction peak at higher lift

coefficients, which ensures that transition on the upper surface will occur very near the leading edge. Thus, the maximum lift coefficient, point C, occurs with turbulent flow along the

entire upper surface and, therefore, should be relatively insensitive to roughness at the leading

edge.

1.8

0

C

B

A

cl

.2

1.0

cd
6

A two-element airfoil concept is used to meet the design requirements. The pressure

distribution at point A is illustrated in sketch 2.

Sketch 2

Because the aft element eliminates the requirement that the pressure at the trailing edge of the

fore element recover to free stream (see ref. 8), the favorable pressure gradient can extend further aft. For the slotted, natural-laminar-flow (SNLF) airfoil concept, the favorable gradient

extends along both surfaces of the fore element to near its trailing edge. Thus, the fore element is almost entirely laminar. The aft element then provides the necessary recovery to freestream pressure. Because the wake of the fore element does not impinge on the aft element,

the aft element can also achieve significant extents of laminar flow.

The SNLF airfoil concept allows the extent of natural laminar flow to be increased

beyond the limit previously discussed. Thus, the concept allows lower profile-drag coefficients to be achieved without having to resort to the complexity and cost of LFC. The concept

also allows high maximum lift coefficients to be achieved without variable geometry. The

SNLF airfoil shape is not radically different from conventional airfoil shapes—no more than

conventional, NLF airfoils are from conventional, turbulent-flow airfoils. Unlike conventional airfoils with slotted flaps, however, the SNLF airfoil has no nested configuration; the

slot between the fore and aft elements is always open.
7

EXECUTION

The Eppler Airfoil Design and Analysis Code (refs. 9 and 10), a single-element code,

was used to design the initial fore- and aft-element shapes. The MSES code (ref. 11), a multielement code, was used to refine the shapes in the two-element configuration.

The airfoil is designated the S103. The airfoil shape is shown in figure 1. The airfoil

thickness is 15-percent chord, which satisfies the design constraint.

EXPERIMENTAL PROCEDURE

WIND TUNNEL

The Langley Low-Turbulence Pressure Tunnel (refs. 12 and 13) is a closed-throat,

single-return tunnel (fig. 2) that can be operated at stagnation pressures from 100 to 1000 kPa

(1 to 10 atm). The unit Reynolds number can be varied from 1  106

 to 49  106 per meter

(0.3  106 to 15  106 per foot); the Mach number can be varied from 0.05 to 0.47. The turbulence level in the test section is generally below 0.05 percent for unit Reynolds numbers up to

13  106 per meter (4  106 per foot) at Mach numbers up to 0.15 (ref. 14).

The test section is 914.4 mm (36.00 in.) wide by 2286 mm (90.00 in.) high. Hydraulically actuated circular plates provide positioning and attachment for the two-dimensional

model (fig. 3). The plates, about 86 cm (34 in.) in diameter, are flush with the tunnel sidewalls and rotate with the model. The axis of rotation coincided approximately with the midchord of the model, which was mounted horizontally between the plates. The gaps between

the model and the plates were sealed.

MODEL

The aluminum, wind-tunnel model was fabricated by Advanced Technologies, Incorporated, Newport News, Virginia, using a numerically controlled milling machine. The model

had a chord of 762.00 mm (30.000 in.) and a span of 914.4 mm (36.00 in.). Upper- and lowersurface orifices were located to one side of midspan at the staggered positions listed in

table II. In addition, an abbreviated, chordwise row of orifices was located near each tunnel

sidewall to monitor the two-dimensionality of the flow. All the orifices were 0.51 mm

(0.020 in.) in diameter with their axes perpendicular to the surface. The surface of the model

had been polished to ensure an aerodynamically smooth finish. The measured model contour

was within 0.1 mm (0.004 in.) of the prescribed shape.

The aft element was mounted directly to the circular plates, not to the fore element.

The mounting system allowed the aft-element chordwise position, vertical position, and angle

to be varied independently. For several test runs, the aft element was fitted with trailing-edge

pieces that simulated 0, 5, and 10 deflections of a sealed, lower-surface-hinged, simple

flap. The location of the flap-hinge point was x/c = 0.9610, z/c = –0.0184. Thus, the flap
8

had a chord of approximately 15 percent of the aft-element chord. (See fig. 1.) No orifices

were located in the trailing-edge pieces.

WAKE RAKE

A traversing, wake rake was mounted from the tunnel strut (fig. 3). The wake rake

employed 25 total-pressure tubes, 13 mm (0.50 in.) apart, and 2 static-pressure tubes. The

rake was positioned spanwise at the tunnel centerline (i.e., at the model midspan). The tips of

the total-pressure tubes were located 0.93-chord downstream of the trailing edge of the model.

A traverse mechanism incrementally positioned the rake vertically.

INSTRUMENTATION

Measurements of the pressures on the model and in the wake were made by an electronically scanned, pressure-transducer system. Basic tunnel pressures were measured with

precision quartz manometers. Data were obtained and recorded by an electronic dataacquisition system.

METHODS

The pressures measured on the model were reduced to standard pressure coefficients

and numerically integrated to obtain section normal- and chord-force coefficients and section

pitching-moment coefficients about the quarter-chord point. To obtain more precise coefficients for the test runs involving the aft-element flap, the measured pressure distributions were

extrapolated to simulate the pressures eliminated by the model modification. Section profiledrag coefficients were computed from the wake total and static pressures by the method of reference 6.

Standard, low-speed, wind-tunnel boundary corrections (ref. 15) have been applied to

the section characteristics. The wake-rake total-pressure-tube displacement correction (ref. 6)

has been taken into account.

TESTS

The model was tested at Reynolds numbers based on airfoil chord of 3  106, 6  106

,

and 9  106 and a Mach number of 0.1 with transition free. No transition-fixed measurements

were made.

The aft element was rotated –1.0 (nose down) about x/c = 0.8321, z/c = 0.0002 and

translated –0.0017c chordwise (forward) and –0.0017c vertically (downward) from the design

position for all the results presented except those for a Reynolds number of 9  106. For these
9

results, the aft element was rotated and translated chordwise the same amounts but not translated vertically.

DISCUSSION OF RESULTS

EXPERIMENTAL RESULTS

Pressure Distributions

The pressure distributions at various angles of attack for a Reynolds number of

3.0  106 and a Mach number of 0.10 with transition free are shown in figure 4. At an angle

of attack of –4.15 (fig. 4(a)), a leading-edge pressure peak exists on the lower surface of the

fore element whereas a favorable pressure gradient exists along the upper surface almost to

the trailing edge of the fore element. An essentially flat gradient exists along the forward half

of the upper surface of the aft element whereas an adverse gradient exists along almost all the

lower surface of the aft element. A short laminar separation bubble, typical of the low Reynolds number of the aft element (0.8  106), is discernible on the upper surface around 60 percent of the aft-element chord. As the angle of attack is increased, the pressure peak on the

lower surface of the fore element decreases in magnitude. At an angle of attack of –2.10

(fig. 4(c)), which corresponds roughly to the lower limit of the low-drag, lift-coefficient

range, the peak no longer causes transition near the leading edge. At an angle of attack of

–1.07 (fig. 4(d)), a favorable gradient exists along the lower surface of the fore element to

about 65-percent chord. As the angle of attack in increased further, the pressure gradient

along the forward portion of the upper surface of the fore element becomes less favorable

until, at an angle of attack of –0.05 (fig. 4(e)), it is slightly adverse. At an angle of attack of

0.97 (fig. 4(f)), which corresponds to the upper limit of the low-drag range, the gradient

along the forward portion of the upper surface of the fore element is still insufficiently adverse

to cause transition to move forward. As the angle of attack is increased even further, the pressure peak near the leading edge on the upper surface of the fore element becomes sharper and

moves forward (figs. 4(g)–4(l)) until, at an angle of attack of 8.12 (fig. 4(m)), it reaches the

leading edge. As the angle of attack is increased still further, the leading-edge peak increases

in magnitude (figs. 4(n)–4(t)). The maximum lift coefficient occurs just beyond an angle of

attack of 16.29 (fig. 4(u)). At an angle of attack of 17.27 (fig. 4(v)), the leading-edge peak

decreases slightly in magnitude and then collapses at an angle of attack of 18.04 (fig. 4(w)),

indicating that almost the entire upper surface of the fore element is separated. The upper surface of the aft element remains attached, however. The pressure distribution on the aft element changes little with angle of attack, except for post stall (fig. 4(w)), because the incoming

flow angle for the aft element is fixed by the fore element.

The pressure distributions for a Reynolds number of 6.1  106

 and a Mach number of

0.10 (not shown) are nearly identical to those for a Reynolds number of 3.0  106

 and a Mach

number of 0.10 (fig. 4). Those for a Reynolds number of 9.1  106

 and a Mach number of

0.10 are significantly different, however, as illustrated in figure 5. The pressure distribution

along the upper surface of the aft element probably includes three-dimensional effects, a conclusion supported by the pressure distributions near the tunnel sidewalls. The three dimen-
10

sionality possibly results from premature transition on the upper surface of the aft element

caused by the orifices or the sidewalls.

The effect of aft-element flap deflection on the pressure distribution is illustrated in

figure 6. The increased circulation on the aft element due to the positive flap deflection

induces higher velocities and, therefore, lower pressures on the lower surface of the fore element in the slot.

Section Characteristics

Reynolds number effects.- The section characteristics at a Mach number of 0.10 with

transition free are shown in figure 7. For a Reynolds number of 3.0  106

 (fig. 7(a)), the maximum lift coefficient is 2.00, which meets the design objective of cl,max  1.72. The airfoil

exhibits a rapid stall, which does not meet the design goal of docile stall characteristics. For a

Reynolds number of 6.1  106

 (fig. 7(b)), low profile-drag coefficients are predicted over the

range of lift coefficients from 0.16 to 0.39. Thus, the upper limit of the low-drag range is

below the design objective of cl,ul = 1.00, primarily to meet other, more important goals. The

zero-lift pitching-moment coefficient is –0.14, which satisfies the design constraint of

cm,0  –0.20.

The effect of Reynolds number on the section characteristics at a Mach number of 0.10

with transition free is summarized in figure 8. In general, the zero-lift angle of attack, the liftcurve slope, and the pitching-moment coefficient are relatively unaffected by Reynolds number. The maximum lift coefficient increases with increasing Reynolds number whereas the

minimum drag coefficient and the width of the low-drag range decrease.

Effect of aft-element position.- The drag coefficients within the low-drag range are

essentially unaffected by variations in the aft-element position and angle over the following

ranges: –0.0033c  x  0.0017c, –0.0033c  z  0, and –1  
  0.

Effect of aft-element flap deflection.- The effect of aft-element flap deflection on the

section characteristics is shown in figure 9. The low-drag range is shifted to higher lift coefficients with increasing flap deflection. (See ref. 4.)

COMPARISON OF THEORETICAL AND EXPERIMENTAL RESULTS

The theoretical results were computed using the method of reference 11. The computations were performed with transition free using a critical amplification factor of 9. Note that

the method of reference 11 does not model the effect of Görtler instabilities (ref. 16) on transition. A cursory evaluation of this effect indicates that these instabilities may lead to transition

in the concave region of the lower surface of the fore element.
11

Pressure Distributions

The comparison of the theoretical and experimental pressure distributions for a Reynolds number of 3.0  106 and a Mach number of 0.10 with transition free is shown in

figure 10. At an angle of attack of –3.12 (fig. 10(a)), which is below the low-drag range, the

magnitudes of the pressure coefficients are overpredicted but the pressure gradients are predicted well, particularly on the fore element. The circulation is predicted well on the fore element but overpredicted on the aft element, which probably causes the overprediction of the

magnitudes of the pressure coefficients on the lower surface of the fore element in the slot.

The method of reference 11 also predicts the laminar separation bubble on the upper surface

of the aft element. At an angle of attack of –1.07 (fig. 10(b)), which is within the low-drag

range, the agreement between the predicted and measured pressure distributions is better, particularly on the aft element. At an angle of 6.07 (fig. 10(c)), which is above the low-drag

range, and at an angle of attack of 16.29 (fig. 10(d)), which is just below that for the maximum lift coefficient, the magnitudes of the pressure coefficients are overpredicted but the

pressure gradients are predicted well. Overall, the agreement between the theoretical and

experimental pressure distributions is good.

Section Characteristics

The comparisons of the theoretical and experimental section characteristics for Reynolds numbers of 3.0  106 and 6.1  106

 at a Mach number of 0.10 with transition free are

shown in figure 11. In general, the lift-curve slope, the maximum lift coefficient, the width of

the low-drag range, and the magnitude of the pitching-moment coefficient are overpredicted.

The drag coefficient is underpredicted. Overall, however, the agreement between the theoretical and experimental section characteristics is good for a two-element airfoil.

COMPARISON WITH BASELINE, NASA NLF(1)-0215F AIRFOIL

The comparison of the experimental section characteristics of the S103 and baseline,

NASA NLF(1)-0215F (ref. 7) airfoils at a Mach number of 0.1 with transition free is shown in

figure 12. Note that the NLF(1)-0215F airfoil incorporates a 25-percent-chord, simple flap.

For a Reynolds number of 3  106 (fig. 12(a)), the S103 airfoil exhibits higher drag coefficients for lift coefficients lower than about 1.5 and lower drag coefficients for higher lift coefficients, less negative pitching-moment coefficients for angles of attack lower than about 11

and more negative pitching-moment coefficients for higher angles of attack, and a more rapid

stall than does the NLF(1)-0215F airfoil with a flap deflection of 10. The maximum lift

coefficient of the S103 airfoil is 12 percent higher than that of the NLF(1)-0215F airfoil with a

flap deflection of 10. For a Reynolds number of 6  106

 (fig. 12(b)), the S103 airfoil exhibits

slightly lower drag coefficients within the low-drag range, a narrower low-drag range, and

more negative pitching-moment coefficients than does the NLF(1)-0215F airfoil with a flap

deflection of –10. The minimum drag coefficient of the S103 airfoil is 7 percent lower than

that of the NLF(1)-0215F airfoil with a flap deflection of –10.
12

CONCLUDING REMARKS

A 15-percent-thick, slotted, natural-laminar-flow (SNLF) airfoil, the S103, for general

aviation applications has been designed and analyzed theoretically and verified experimentally in the Langley Low-Turbulence Pressure Tunnel. The two primary objectives of high

maximum lift coefficient and low profile-drag coefficients have been achieved. The constraints on the pitching-moment coefficient and the airfoil thickness have been satisfied. The

airfoil exhibits a rapid stall, which does not meet the design goal. Comparisons of the theoretical and experimental results show good agreement. Comparison with the baseline, NASA

NLF(1)-0215F airfoil confirms the achievement of the objectives.
13

REFERENCES

1. Maughmer, Mark D.; and Somers, Dan M.: Figures of Merit for Airfoil/Aircraft Design

Integration. AIAA Paper 88-4416, Sept. 1988.

2. Smith, A. M. O.: High-Lift Aerodynamics. AIAA Paper 74-939, Aug. 1974.

3. Jacobs, Eastman N.: Preliminary Report on Laminar-Flow Airfoils and New Methods

Adopted for Airfoil and Boundary-Layer Investigations. NACA WR L-345, 1939 (formerly, NACA ACR).

4. Pfenninger, Werner: Investigations on Reductions of Friction on Wings, in Particular by

Means of Boundary Layer Suction. NACA TM 1181, 1947. (Translated from

Mitteilungen aus dem Institut für Aerodynamik an der Eidgenössischen Technischen

Hochschule Zürich, Nr. 13, 1946.)

5. Whitcomb, Richard T.; and Clark, Larry R.: An Airfoil Shape for Efficient Flight at

Supercritical Mach Numbers. NASA TM X-1109, 1965.

6. Pankhurst, R. C.; and Holder, D. W.: Wind-Tunnel Technique. Sir Isaac Pitman & Sons,

Ltd. (London), 1965.

7. Somers, Dan M.: Design and Experimental Results for a Flapped Natural-Laminar-Flow

Airfoil for General Aviation Applications. NASA TP-1865, 1981.

8. Maughmer, Mark D.: Trailing Edge Flow Conditions as a Factor in Airfoil Design.

Ph.D. Dissertation, Univ. of Illinois, 1983.

9. Eppler, Richard: Airfoil Design and Data. Springer-Verlag (Berlin), 1990.

10. Eppler, Richard: Airfoil Program System “PROFIL00.” User’s Guide. Richard Eppler,

c.2001.

11. Drela, M.: Design and Optimization Method for Multi-Element Airfoils. AIAA Paper

93-0969, Feb. 1993.

12. Von Doenhoff, Albert E.; and Abbott, Frank T., Jr.: The Langley Two-Dimensional LowTurbulence Pressure Tunnel. NACA TN 1283, 1947.

13. McGhee, Robert J.; Beasley, William D.; and Foster, Jean M.: Recent Modifications and

Calibration of the Langley Low-Turbulence Pressure Tunnel. NASA TP-2328, 1984.

14. Wlezien, R. W.; Spencer, S. A.; and Grubb, J. P.: Comparison of Flow Quality in Subsonic Pressure Tunnels. AIAA Paper 94-2503, June 1994.
14

15. Allen, H. Julian; and Vincenti, Walter G.: Wall Interference in a Two-Dimensional-Flow

Wind Tunnel, With Consideration of the Effect of Compressibility. NACA Rep. 782,

1944. (Supersedes NACA WR A-63.)

16. Görtler, H.: On the Three-Dimensional Instability of Laminar Boundary Layers on Concave Walls. NACA TM 1375, 1954.
15

TABLE I.- AIRFOIL DESIGN SPECIFICATIONS

Parameter Value Reynolds

number R

Mach

number M

Maximum lift coefficient 

cl,max

 1.72 3  106

0

Lower limit of low-drag, 

lift-coefficient range cl,ll

0.20 9  106

Upper limit of low-drag, 

lift-coefficient range cl,ul

1.00 6  106

Zero-lift pitching-moment 

coefficient cm,0

 –0.20 9  106

Thickness t/c 0.15
16

TABLE II.- MODEL ORIFICE LOCATIONS

[c = 762.00 mm (30.000 in.)]

(a) Fore element

Upper surface Lower surface

x/c y, mm (in.) x/c y, mm (in.)

–0.00007 284.6 (11.205) 0.00160 281.0 (11.062)

.00117 288.2 (11.345) .00537 279.8 (11.015)

.00530 287.5 (11.317) .01277 278.9 (10.982)

.01210 286.4 (11.277) .02160 277.4 (10.923)

.02133 285.0 (11.221) .03307 275.8 (10.860)

.03307 283.0 (11.143) .04747 273.8 (10.778)

.04690 280.9 (11.060) .06410 271.4 (10.686)

.06440 278.8 (10.976) .08317 268.6 (10.576)

.08293 275.9 (10.863) .10433 265.6 (10.458)

.10440 272.8 (10.742) .12730 262.3 (10.325)

.12760 269.7 (10.617) .15253 258.5 (10.178)

.15287 266.1 (10.478) .18010 254.6 (10.024)

.17967 262.2 (10.323) .20820 251.0 (9.880)

.20813 258.4 (10.173) .23820 247.0 (9.723)

.23810 254.1 (10.003) .26920 242.3 (9.541)

.26890 249.7 (9.831) .30130 238.3 (9.382)

.30110 245.4 (9.663) .33413 233.6 (9.197)

.33460 240.7 (9.478) .36780 229.0 (9.015)

.36767 236.4 (9.307) .40200 224.5 (8.837)

.40180 231.8 (9.126) .43633 219.6 (8.646)

.43607 227.1 (8.940) .46987 214.9 (8.462)

.47030 222.4 (8.756) .50403 210.2 (8.276)

.50427 217.8 (8.576) .53743 205.7 (8.100)

.53787 213.3 (8.396) .57030 201.3 (7.924)

.57067 208.6 (8.213) .60297 197.0 (7.755)

.60277 204.3 (8.043) .63343 192.4 (7.573)

.63373 199.9 (7.871) .64890 190.5 (7.499)

.66373 195.8 (7.710) .66357 188.1 (7.407)

.69227 191.7 (7.547) .67793 186.2 (7.331)

.71880 188.3 (7.412) .69237 184.3 (7.255)

.74420 184.6 (7.269) .70627 182.0 (7.167)

.76697 181.2 (7.135) .71867 180.2 (7.095)

.78843 178.3 (7.019) .73120 178.5 (7.026)

.80773 175.5 (6.908) .74400 176.5 (6.948)

.82403 173.0 (6.811) .75557 175.0 (6.889)

.83857 171.0 (6.732) .76683 173.5 (6.830)

.85063 169.2 (6.660) .77820 171.7 (6.758)

.85993 167.9 (6.612) .78877 170.0 (6.691)

.86653 166.9 (6.570) .80767 167.2 (6.583)

.87070 165.8 (6.527) .82410 164.7 (6.485)

.87177 163.7 (6.443) .83797 163.1 (6.423)

.85030 161.2 (6.346)

.85937 159.8 (6.291)

.86643 158.8 (6.253)

.87060 157.7 (6.210)
17

TABLE II.- Concluded

[c = 762.00 mm (30.000 in.)]

(b) Aft element

Upper surface Lower surface

x/c y, mm (in.) x/c y, mm (in.)

0.74010 105.2 (4.142) 0.73910 106.2 (4.181)

.74393 103.8 (4.088) .74220 112.6 (4.434)

.74940 102.8 (4.048) .74893 111.7 (4.398)

.75683 101.7 (4.003) .76093 110.0 (4.332)

.76597 100.2 (3.945) .77743 107.5 (4.233)

.77720 98.8 (3.890) .79720 104.9 (4.128)

.79007 97.0 (3.818) .81970 101.7 (4.003)

.80447 95.0 (3.741) .84423 98.4 (3.875)

.81990 92.7 (3.651) .86960 94.9 (3.735)

.83567 90.3 (3.557) .89503 91.3 (3.593)

.85270 88.2 (3.471) .91947 88.0 (3.466)

.86967 85.7 (3.373) .94197 85.0 (3.348)

.88630 83.2 (3.275) .96207 82.2 (3.237)

.90293 80.9 (3.187) .97833 79.9 (3.146)

.91890 78.5 (3.091) .99010 78.1 (3.076)

.93397 76.1 (2.995) .99750 77.1 (3.037)

.94873 79.6 (3.133)

.96127 82.3 (3.242)

.97253 85.2 (3.354)

.98200 87.1 (3.431)

.98983 89.0 (3.503)

.99530 90.3 (3.556)

.99843 91.0 (3.584)

1.00010 84.3 (3.320)
18

Figure 1.- S103 airfoil shape.
19Figure 2.- Langley Low-Turbulence Pressure Tunnel.
20

Figure 3.- Sketch of model and wake rake mounted in test section.

CeilingFloor

Circular plate Model

Strut

Wake rake

Traverse 

mechanism
21

(a)  = –4.15; cl = –0.099; cd = 0.0105; cm = –0.135.

Figure 4.- Pressure distributions for R = 3.0  106 and M = 0.10 with transition free. Open 

symbols represent data for upper surface; crossed symbols, data for lower surface.
22

(b)  = –3.12; cl = 0.019; cd = 0.0099; cm = –0.139.

Figure 4.- Continued.
23

(c)  = –2.10; cl = 0.141; cd = 0.054; cm = –0.149.

Figure 4.- Continued.
24

(d)  = –1.07; cl = 0.253; cd = 0.0051; cm = –0.150.

Figure 4.- Continued.
25

(e)  = –0.05; cl = 0.368; cd = 0.0051; cm = –0.153.

Figure 4.- Continued.
26

(f)  = 0.97; cl = 0.482; cd = 0.0051; cm = –0.156.

Figure 4.- Continued.
27

(g)  = 1.99; cl = 0.583; cd = 0.0091; cm = –0.155.

Figure 4.- Continued.
28

(h)  = 3.01; cl = 0.694; cd = 0.0101; cm = –0.157.

Figure 4.- Continued.
29

(i)  = 4.04; cl = 0.804; cd = 0.0109; cm = –0.159.

Figure 4.- Continued.
30

(j)  = 5.06; cl = 0.916; cd = 0.0116; cm = –0.161.

Figure 4.- Continued.
31

(k)  = 6.07; cl = 1.027; cd = 0.0124; cm = –0.163.

Figure 4.- Continued.
32

(l)  = 7.10; cl = 1.134; cd = 0.0133; cm = –0.164.

Figure 4.- Continued.
33

(m)  = 8.12; cl = 1.239; cd = 0.0142; cm = –0.165.

Figure 4.- Continued.
34

(n)  = 9.15; cl = 1.348; cd = 0.0154; cm = –0.166.

Figure 4.- Continued.
35

(o)  = 10.17; cl = 1.448; cd = 0.0169; cm = –0.165.

Figure 4.- Continued.
36

(p)  = 11.20; cl = 1.552; cd = 0.0187; cm = –0.165.

Figure 4.- Continued.
37

(q)  = 12.21; cl = 1.648; cd = 0.0209; cm = –0.165.

Figure 4.- Continued.
38

(r)  = 13.24; cl = 1.738; cd = 0.0235; cm = –0.162.

Figure 4.- Continued.
39

(s)  = 14.25; cl = 1.828; cd = 0.0269; cm = –0.160.

Figure 4.- Continued.
40

(t)  = 15.27; cl = 1.899; cd = 0.0309; cm = –0.158.

Figure 4.- Continued.
41

(u)  = 16.29; cl = 1.969; cd = 0.0352; cm = –0.154.

Figure 4.- Continued.
42

(v)  = 17.27; cl = 1.927; cd = 0.1080; cm = –0.158.

Figure 4.- Continued.
43

(w)  = 18.04; cl = 1.263; cd = 0.3764; cm = –0.255.

Figure 4.- Concluded.
44

Figure 5.- Pressure distribution at  = –1.08 for R = 9.1  106 and M = 0.10 with transition free. Open symbols represent data for upper surface; crossed symbols, data for lower

surface.
45

Figure 6.- Effect of aft-element flap deflection on pressure distribution at cl = 0.3 for

R=6  106 and M = 0.1 with transition free. Open symbols represent data for

upper surface; crossed symbols, data for lower surface.
46

(a) R = 3.0  106.

Figure 7.- Section characteristics at M = 0.10 with transition free.
47

(b) R = 6.1 

 106.

Figure 7.- Concluded.
48

Figure 8.- Effect of Reynolds number on section characteristics at M = 0.10 with transition free.
49Figure 9.- Effect of aft-element flap deflection on section characteristics for R = 6 

 106 and M = 0.1 with transition free.
50

(a)  = –3.12.

Figure 10.- Comparison of theoretical and experimental pressure distributions for

R = 3.0  106 and M = 0.10 with transition free. Open symbols represent data

for upper surface; crossed symbols, data for lower surface.
51

(b)  = –1.07.

Figure 10.- Continued.
52

(c)  = 6.07.

Figure 10.- Continued.
53

(d)  = 16.29.

Figure 10.- Concluded.
54

(a) R = 3.0  106.

Figure 11.- Comparison of theoretical and experimental section characteristics at M = 0.10 with transition free.
55

(b) R = 6.1 

 106.

Figure 11.- Concluded.
56

(a) R = 3  106.

Figure 12.- Comparison of experimental section characteristics of S103 and NASA NLF(1)-0215F airfoils at M = 0.1 with transition

free.
57

(b) R = 6 

 106.

Figure 12.- Concluded.
REPORT DOCUMENTATION PAGE Form Approved

OMB No. 0704-0188

2. REPORT TYPE 

Contractor Report

 4. TITLE AND SUBTITLE

An Exploratory Investigation of a Slotted, Natural-Laminar-Flow Airfoil 

5a. CONTRACT NUMBER

NAS1-01076

 6. AUTHOR(S)

Somers, Dan M.

 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

 NASA Langley Research Center

Hampton, Virginia 23681-2199 

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National Aeronautics and Space Administration

Washington, DC 20546-0001

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NASA

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Langley Technical Monitor: James M. Luckring

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14. ABSTRACT

A 15-percent-thick, slotted, natural-laminar-flow (SNLF) airfoil, the S103, for general aviation applications has been designed

and analyzed theoretically and verified experimentally in the Langley Low-Turbulence Pressure Tunnel. The two primary 

objectives of high maximum lift and low profile drag have been achieved. The constraints on the pitching moment and the 

airfoil thickness have been satisfied. The airfoil exhibits a rapid stall, which does not meet the design goal. Comparisons of the 

theoretical and experimental results show good agreement. Comparison with the baseline, NASA NLF(1)-0215F airfoil 

confirms the achievement of the objectives. 

15. SUBJECT TERMS

Aerodynamics; Airfoils; Laminar flow; Wind tunnel experiment

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