July 2012 

NASA/CR–2012-217559 

Design of a Slotted, Natural-Laminar-Flow 

Airfoil for Business-Jet Applications 

Dan M. Somers 

Airfoils, Incorporated, Port Matilda, Pennsylvania 
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July 2012 

NASA/CR–2012-217559 

Design of a Slotted, Natural-Laminar-Flow 

Airfoil for Business-Jet Applications 

 

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 

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NRA-03-LaRC-02. 

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and Space Administration.
ABSTRACT

A 14-percent-thick, slotted, natural-laminar-flow airfoil, the S204, for light businessjet applications has been designed and analyzed theoretically. The two primary objectives of

high maximum lift, relatively insensitive to roughness, and low profile drag have been

achieved. The drag-divergence Mach number is predicted to be greater than 0.70.

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

more beneficial.

Aircraft 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

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 in 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

Cp pressure coefficient

c airfoil chord, m

cd section profile-drag coefficient

cl section lift coefficient

cm section pitching-moment coefficient about quarter-chord point

M Mach number

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

t airfoil thickness, m

x airfoil abscissa, m

α angle of attack relative to x-axis, deg

Subscripts:

dd drag divergence

ll lower limit of low-drag range

ls lower surface

max maximum

T transition

ul upper limit of low-drag range

us upper surface

0 zero lift

Abbreviations:

LFC laminar flow control

NASA National Aeronautics and Space Administration
4

NLF natural laminar flow

SNLF slotted, natural laminar flow

AIRFOIL DESIGN

OBJECTIVES AND CONSTRAINTS

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

were distilled from the physical and performance characteristics of seven light business-jet

designs. The following aircraft were used: Adam Aircraft A700, Aerostar FJ-100, Beechcraft

Premier I, Cessna Citation Bravo and CJ1, Honda R&D HondaJet, and VisionAire Vantage.

The specifications encompass the requirements of almost all the aircraft well.

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

coefficient of at least 1.55 at a Mach number of 0.10 and a Reynolds number of 3 × 106

, which

corresponds to the tip chord at minimum speed. 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 over the range of lift coefficients

from 0.20 at a Mach number of 0.65 and a Reynolds number of 12 × 106, which corresponds

to the root chord at the cruise condition, to 0.40 at a Mach number of 0.30 and a Reynolds

number of 12 × 106, which corresponds to the root chord at the climb condition. (The second

specification regarding the upper limit of the low-drag, lift-coefficient range, which corresponds to the high-altitude, cruise condition, is not critical for the airfoil design.)

It should be noted that, while the cruise Mach number is lower than those of larger

business-jet and transport aircraft, higher cruise speeds do not yield significant time savings

because the typical range of light, business jets is only about 2000 km (1000 nm); the negative

impact of higher speeds on fuel efficiency outweighs the small gain in block time. The dragdivergence Mach number at a lift coefficient of 0.25 for a Reynolds number of 12 × 106

,

which corresponds to the root chord at the high-altitude, maximum-speed condition, should be

greater than 0.70.

One major constraint was placed on the design of the airfoil. The airfoil thickness

should equal 15-percent chord. No constraint was placed on the pitching-moment coefficient.
5

PHILOSOPHY

Given the above objectives and constraint, 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.

1.6

.4

0

C

B

A

cl

cd

.2
6

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

distribution at point A is illustrated in sketch 2. (The sonic pressure coefficient at this Mach

number is −1.01, denoted by the horizontal, dotted line 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. 6), 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 section 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. 7 and 8), a subcritical, singleelement code, was used to design the initial fore- and aft-element shapes. The MSES code

(ref. 9), a transonic, multielement code, was used to refine the shapes in the two-element configuration.

The airfoil is designated the S204. The airfoil shape is shown in figure 1. The airfoil

thickness is 14-percent chord, which is less than the design constraint of t/c = 0.15, primarily

to meet the cruise Mach-number objective.

THEORETICAL PROCEDURE

The pressure distributions and section characteristics are predicted using the method

of reference 9 at a Mach number of 0.10 for Reynolds numbers of 2 × 106, 3 × 106, 4 × 106,

and 6 × 106 and at Mach numbers of 0.30, 0.50, 0.60, and 0.65 for Reynolds numbers of

4 × 106, 6 × 106, 9 × 106, and 12 × 106. The computations were performed with transition free

using a critical amplification factor of 9, although, because of laminar separation bubbles predicted near the trailing edge of the fore element, transition was fixed on both the upper and

lower surfaces of the fore element at 97 percent of the fore-element chord (i.e., x/c = 0.80).

Note that the method of reference 9 does not model the effect of Görtler instabilities (ref. 10)

on the laminar boundary layer. 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.

Computations were also performed with transition fixed at 2-percent chord on the

upper surface and 5-percent chord on the lower surface of both elements for all Mach numbers

except 0.10 for which transition was fixed at the same locations on the aft element and on the

upper surface of the fore element but at 10-percent chord on the lower surface of the fore element to account for the more aft location of the stagnation point at high lift coefficients. Note

that all the fixed-transition locations are specified relative to the chord of the respective element.
8

Because the right sides of the figures showing the transition locations and section

characteristics contain several curves, an explanatory example with transition free is given in

sketch 3, where the various curves are plotted with different line types. Note that the transition locations on the aft element are downstream of those on the fore element.

Sketch 3

DISCUSSION OF RESULTS

PRESSURE DISTRIBUTIONS

The pressure distributions at various angles of attack with transition free at a Mach

number of 0.10 and a Reynolds number of 3 × 106

 are shown in figure 2 and at Mach numbers

of 0.30, 0.50, 0.60, and 0.65 and a Reynolds number of 12 × 106

, in figures 3, 4, 5, and 6,

respectively.

TRANSITION LOCATION

The variations of boundary-layer transition location on the fore and aft elements with

lift coefficient are shown in figures 7 through 11. In general, within the low-drag, liftcoefficient range, laminar flow extends essentially to the trailing edge on both surfaces of the

fore element, to about 60-percent of the aft-element chord on the upper surface of the aft element, and to the trailing edge on the lower surface of the aft element.
9

SECTION CHARACTERISTICS

Mach Number and Reynolds Number Effects

 The section characteristics at a Mach number of 0.10 and Reynolds numbers of

2 × 106, 3 × 106, 4 × 106, and 6 × 106 with transition free are shown in figure 7. For a Reynolds number of 3 × 106

 (fig. 7(b)), the maximum lift coefficient is predicted to be 2.13, which

meets the design objective of cl,max ≥ 1.55.

 The section characteristics at a Mach number of 0.30 and Reynolds numbers of

4 × 106, 6 × 106, 9 × 106, and 12 × 106 with transition free are shown in figure 8. For a Reynolds number of 12 × 106 (fig. 8(d)), a low profile-drag coefficient is predicted at a lift coefficient of about 0.2, but no low-drag range of lift coefficients is predicted. Thus, the design

objective of cl,ul = 0.40 has not been met. The zero-lift pitching-moment coefficient is predicted to be –0.133.

The section characteristics at Mach numbers of 0.50 and 0.60 and Reynolds numbers

of 4 × 106, 6 × 106, 9 × 106, and 12 × 106 with transition free are shown in figures 9 and 10,

respectively.

 The section characteristics at a Mach number of 0.65 and Reynolds numbers of

4 × 106, 6 × 106, 9 × 106, and 12 × 106 with transition free are shown in figure 11. For a

Reynolds number of 12 × 106 (fig. 11(d)), low drag coefficients are predicted over the range

of lift coefficients from 0.22 to 0.52. Thus, the lower limit of the low-drag range is higher

than the design objective of cl,ll = 0.20. For a Reynolds number of 9 × 106 (fig. 11(c)), low

drag coefficients are predicted over the range of lift coefficients from 0.19 to 0.59. Thus, the

upper limit of the low-drag range is higher than the design objective of cl,ul = 0.40. Within

the low-drag range, no wave drag is predicted. The zero-lift pitching-moment coefficient is

predicted to be –0.162.

The effect of Mach number on the section characteristics with transition free is summarized in figure 12. In general, the zero-lift angle of attack is relatively unaffected by Mach

number. The lift-curve slope, the minimum drag coefficient, the width of the low-drag range,

and the magnitude of the pitching-moment coefficient increase with increasing Mach number.

Based on computations performed using the method of reference 9, the drag-divergence Mach

number with transition free is predicted to be greater than 0.70, which meets the design objective.

The effect of Reynolds number on the section characteristics with transition free is

summarized in figure 13. In general, the zero-lift angle of attack, the lift-curve slope, and the

pitching-moment coefficient are relatively unaffected by Reynolds number. The maximum

lift coefficient (fig. 13(a)) increases with increasing Reynolds number. The minimum drag

coefficient and the width of the low-drag range decrease with increasing Reynolds number.
10

Effect of Roughness

The effect of roughness on the section characteristics is shown in figures 7 through 11.

The maximum lift coefficient at a Mach number of 0.10 and a Reynolds number of 3 × 106

with transition fixed (fig. 7(b)) is predicted to be 2.10, a decrease of approximately 1 percent

from that with transition free. Thus, the design requirement has been satisfied. In general, the

magnitudes of the zero-lift angle of attack and the pitching-moment coefficient decrease with

transition fixed primarily because the roughness on the aft element induces trailing-edge separation on the upper surface of that element. The lift-curve slope is relatively unaffected by the

roughness, but the drag coefficients are, of course, adversely affected. The drag increase is

larger than that for a single-element airfoil of the same thickness, however, because of the

greater wetted surface length of the two-element configuration and also because of the separation on the aft-element upper surface.

The effect of Mach number on the section characteristics with transition fixed is summarized in figure 14. In general, the magnitude of the zero-lift angle of attack decreases with

increasing Mach number. The lift-curve slope and the minimum drag coefficient increase

with increasing Mach number. The magnitude of the pitching-moment coefficient is relatively unaffected by Mach number. The drag-divergence Mach number with transition fixed

is predicted to be greater than 0.70, which meets the design objective.

The effect of Reynolds number on the section characteristics with transition fixed is

summarized in figure 15. In general, the magnitudes of the zero-lift angle of attack, the maximum lift coefficient, and the pitching-moment coefficient increase with increasing Reynolds

number. The lift-curve slope is relatively unaffected by Reynolds number. The minimum

drag coefficient decreases with increasing Reynolds number.

CONCLUDING REMARKS

A 14-percent-thick, slotted, natural-laminar-flow airfoil, the S204, for light businessjet applications has been designed and analyzed theoretically. The two primary objectives of a

high maximum lift coefficient, relatively insensitive to leading-edge roughness, and low

profile-drag coefficients have been achieved. The drag-divergence Mach number is predicted

to be greater than 0.70.
11

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

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

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

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

c.2001.

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

93-0969, Feb. 1993.

10. Görtler, H.: On the Three-Dimensional Instability of Laminar Boundary Layers on Concave Walls. NACA TM 1375, 1954.
12

TABLE I.- AIRFOIL DESIGN SPECIFICATIONS

Parameter Value

Mach

Number

M

Reynolds 

Number

R

Maximum lift coefficient 

cl,max

≥ 1.55 0.10 3 × 106

Lower limit of low-drag, 

lift-coefficient range cl,ll

0.20 0.65 12 × 106

Upper limit of low-drag, 

lift-coefficient range cl,ul

0.40

0.65

0.30

9 × 106

12 × 106

Zero-lift pitching-moment 

coefficient cm,0

—

Drag-divergence Mach 

number Mdd at cl = 0.25 ≥ 0.70 — 12 × 106

Thickness t/c 0.15
27

(b) R = 3 × 106.

Figure 7.- Continued.

15

(b) α = 4°, 6°, and 8°.

Figure 2.- Continued.

14

(a) α = –2°, 0°, and 2°.

Figure 2.- Pressure distributions at M = 0.10 and R = 3 × 106 13 with transition free.

Figure 1.- S204 airfoil shape.
27

(b) R = 3 × 106.

Figure 7.- Continued.

15

(b) α = 4°, 6°, and 8°.

Figure 2.- Continued.

14

(a) α = –2°, 0°, and 2°.

Figure 2.- Pressure distributions at M = 0.10 and R = 3 × 106 with transition free.
27

(b) R = 3 

× 106

.

Figure 7.- Continued.

15

(b) 

α = 4°, 6°, and 8°.

Figure 2.- Continued.
18

(a) α = –2°, –1°, and 0°.

Figure 3.- Pressure distributions at M = 0.30 and R = 12 × 106

 with transition free.

16

(c) α = 10°, 12°, and 14°.

Figure 2.- Continued.
27

(b) R = 3 × 106.

Figure 7.- Continued.

15

(b) α = 4°, 6°, and 8°.

Figure 2.- Continued.

14

(a) α = –2°, 0°, and 2°.

Figure 2.- Pressure distributions at M = 0.10 and R = 3 × 106 13 with transition free.

Figure 1.- S204 airfoil shape.

17

(d) α = 16°, 18°, and 20°.

Figure 2.- Concluded.
27

(b) R = 3 × 106.

Figure 7.- Continued.

15

(b) α = 4°, 6°, and 8°.

Figure 2.- Continued.

14

(a) α = –2°, 0°, and 2°.

Figure 2.- Pressure distributions at M = 0.10 and R = 3 × 106 13 with transition free.

Figure 1.- S204 airfoil shape.

17

(d) α = 16°, 18°, and 20°.

Figure 2.- Concluded.

16

(c) α = 10°, 12°, and 14°.

Figure 2.- Continued.

18

(a) α = –2°, –1°, and 0°.

Figure 3.- Pressure distributions at M = 0.30 and R = 12 × 106 with transition free.
27

(b) R = 3 × 106.

Figure 7.- Continued.

15

(b) α = 4°, 6°, and 8°.

Figure 2.- Continued.

14

(a) α = –2°, 0°, and 2°.

Figure 2.- Pressure distributions at M = 0.10 and R = 3 × 106 13 with transition free.

Figure 1.- S204 airfoil shape.

17

(d) α = 16°, 18°, and 20°.

Figure 2.- Concluded.

16

(c) α = 10°, 12°, and 14°.

Figure 2.- Continued.

18

(a) α = –2°, –1°, and 0°.

Figure 3.- Pressure distributions at M = 0.30 and R = 12 × 106 with transition free.

20

(a) α = –2°, –1°, and 0°.

Figure 4.- Pressure distributions at M = 0.50 and R = 12 × 106 19 with transition free.

(b) α = 1° and 2°.

Figure 3.- Concluded.
27

(b) R = 3 × 106.

Figure 7.- Continued.

15

(b) α = 4°, 6°, and 8°.

Figure 2.- Continued.

14

(a) α = –2°, 0°, and 2°.

Figure 2.- Pressure distributions at M = 0.10 and R = 3 × 106 13 with transition free.

Figure 1.- S204 airfoil shape.

17

(d) α = 16°, 18°, and 20°.

Figure 2.- Concluded.

16

(c) α = 10°, 12°, and 14°.

Figure 2.- Continued.

18

(a) α = –2°, –1°, and 0°.

Figure 3.- Pressure distributions at M = 0.30 and R = 12 × 106 with transition free.

20

(a) α = –2°, –1°, and 0°.

Figure 4.- Pressure distributions at M = 0.50 and R = 12 × 106 with transition free.
27

(b) R = 3 × 106.

Figure 7.- Continued.

15

(b) α = 4°, 6°, and 8°.

Figure 2.- Continued.

14

(a) α = –2°, 0°, and 2°.

Figure 2.- Pressure distributions at M = 0.10 and R = 3 × 106 13 with transition free.

Figure 1.- S204 airfoil shape.

17

(d) α = 16°, 18°, and 20°.

Figure 2.- Concluded.

16

(c) α = 10°, 12°, and 14°.

Figure 2.- Continued.

18

(a) α = –2°, –1°, and 0°.

Figure 3.- Pressure distributions at M = 0.30 and R = 12 × 106 with transition free.

20

(a) α = –2°, –1°, and 0°.

Figure 4.- Pressure distributions at M = 0.50 and R = 12 × 106 19 with transition free.

(b) α = 1° and 2°.

Figure 3.- Concluded.

21

(b) α = 1° and 2°.

Figure 4.- Concluded.
27

(b) R = 3 × 106.

Figure 7.- Continued.

15

(b) α = 4°, 6°, and 8°.

Figure 2.- Continued.

14

(a) α = –2°, 0°, and 2°.

Figure 2.- Pressure distributions at M = 0.10 and R = 3 × 106 13 with transition free.

Figure 1.- S204 airfoil shape.

17

(d) α = 16°, 18°, and 20°.

Figure 2.- Concluded.

16

(c) α = 10°, 12°, and 14°.

Figure 2.- Continued.

18

(a) α = –2°, –1°, and 0°.

Figure 3.- Pressure distributions at M = 0.30 and R = 12 × 106 with transition free.

20

(a) α = –2°, –1°, and 0°.

Figure 4.- Pressure distributions at M = 0.50 and R = 12 × 106 19 with transition free.

(b) α = 1° and 2°.

Figure 3.- Concluded.

21

(b) α = 1° and 2°.

Figure 4.- Concluded.

22

(a) α = –2° and –1°.

Figure 5.- Pressure distributions at M = 0.60 and R = 12 × 106 with transition free.
27

(b) R = 3 × 106.

Figure 7.- Continued.

15

(b) α = 4°, 6°, and 8°.

Figure 2.- Continued.

14

(a) α = –2°, 0°, and 2°.

Figure 2.- Pressure distributions at M = 0.10 and R = 3 × 106 13 with transition free.

Figure 1.- S204 airfoil shape.

17

(d) α = 16°, 18°, and 20°.

Figure 2.- Concluded.

16

(c) α = 10°, 12°, and 14°.

Figure 2.- Continued.

18

(a) α = –2°, –1°, and 0°.

Figure 3.- Pressure distributions at M = 0.30 and R = 12 × 106 with transition free.

20

(a) α = –2°, –1°, and 0°.

Figure 4.- Pressure distributions at M = 0.50 and R = 12 × 106 19 with transition free.

(b) α = 1° and 2°.

Figure 3.- Concluded.

21

(b) α = 1° and 2°.

Figure 4.- Concluded.

22

(a) α = –2° and –1°.

Figure 5.- Pressure distributions at M = 0.60 and R = 12 × 106 23 with transition free.

(b) α = 0° and 1°.

Figure 5.- Concluded.
27

(b) R = 3 × 106.

Figure 7.- Continued.

15

(b) α = 4°, 6°, and 8°.

Figure 2.- Continued.

14

(a) α = –2°, 0°, and 2°.

Figure 2.- Pressure distributions at M = 0.10 and R = 3 × 106 13 with transition free.

Figure 1.- S204 airfoil shape.

17

(d) α = 16°, 18°, and 20°.

Figure 2.- Concluded.

16

(c) α = 10°, 12°, and 14°.

Figure 2.- Continued.

18

(a) α = –2°, –1°, and 0°.

Figure 3.- Pressure distributions at M = 0.30 and R = 12 × 106 with transition free.

20

(a) α = –2°, –1°, and 0°.

Figure 4.- Pressure distributions at M = 0.50 and R = 12 × 106 19 with transition free.

(b) α = 1° and 2°.

Figure 3.- Concluded.

21

(b) α = 1° and 2°.

Figure 4.- Concluded.

22

(a) α = –2° and –1°.

Figure 5.- Pressure distributions at M = 0.60 and R = 12 × 106 23 with transition free.

(b) α = 0° and 1°.

Figure 5.- Concluded.

24

(a) α = –2° and –1°.

Figure 6.- Pressure distributions at M = 0.65 and R = 12 × 106 25 with transition free.

(b) α = 0° and 1°.

Figure 6.- Concluded.
27

(b) R = 3 × 106.

Figure 7.- Continued.

15

(b) α = 4°, 6°, and 8°.

Figure 2.- Continued.

14

(a) α = –2°, 0°, and 2°.

Figure 2.- Pressure distributions at M = 0.10 and R = 3 × 106 13 with transition free.

Figure 1.- S204 airfoil shape.

17

(d) α = 16°, 18°, and 20°.

Figure 2.- Concluded.

16

(c) α = 10°, 12°, and 14°.

Figure 2.- Continued.

18

(a) α = –2°, –1°, and 0°.

Figure 3.- Pressure distributions at M = 0.30 and R = 12 × 106 with transition free.

20

(a) α = –2°, –1°, and 0°.

Figure 4.- Pressure distributions at M = 0.50 and R = 12 × 106 19 with transition free.

(b) α = 1° and 2°.

Figure 3.- Concluded.

21

(b) α = 1° and 2°.

Figure 4.- Concluded.

22

(a) α = –2° and –1°.

Figure 5.- Pressure distributions at M = 0.60 and R = 12 × 106 23 with transition free.

(b) α = 0° and 1°.

Figure 5.- Concluded.

24

(a) α = –2° and –1°.

Figure 6.- Pressure distributions at M = 0.65 and R = 12 × 106 25 with transition free.

(b) α = 0° and 1°.

Figure 6.- Concluded.
26

(a) R = 2 × 106.

Figure 7.- Section characteristics at M = 0.10.
27

(b) R = 3 

× 106.

Figure 7.- Continued.
28

(c) R = 4 × 106.

Figure 7.- Continued.
29

(d) R = 6 

× 106.

Figure 7.- Concluded.
30

(a) R = 4 × 106.

Figure 8.- Section characteristics at M = 0.30.
31

(b) R = 6 

× 106.

Figure 8.- Continued.
32

(c) R = 9 × 106.

Figure 8.- Continued.
33

(d) R = 12 

× 106

.

Figure 8.- Concluded.
34

(a) R = 4 × 106.

Figure 9.- Section characteristics at M = 0.50.
35

(b) R = 6 

× 106.

Figure 9.- Continued.
36

(c) R = 9 × 106.

Figure 9.- Continued.
37

(d) R = 12 

× 106

.

Figure 9.- Concluded.
38

(a) R = 4 × 106.

Figure 10.- Section characteristics at M = 0.60.
39

(b) R = 6 

× 106.

Figure 10.- Continued.
40

(c) R = 9 × 106.

Figure 10.- Continued.
41

(d) R = 12 

× 106

.

Figure 10.- Concluded.
42

(a) R = 4 × 106.

Figure 11.- Section characteristics at M = 0.65.
43

(b) R = 6 

× 106.

Figure 11.- Continued.
44

(c) R = 9 × 106.

Figure 11.- Continued.
45

(d) R = 12 

× 106

.

Figure 11.- Concluded.
46

(a) R = 4 × 106.

Figure 12.- Effect of Mach number on section characteristics with transition free.
47

(b) R = 6 

× 106.

Figure 12.- Continued.
48

(c) R = 9 × 106.

Figure 12.- Continued.
49

(d) R = 12 

× 106

.

Figure 12.- Concluded.
50

(a) M = 0.10.

Figure 13.- Effect of Reynolds number on section characteristics with transition free.
51

(b) M = 0.30.

Figure 13.- Continued.
52

(c) M = 0.50.

Figure 13.- Continued.
53

(d) M = 0.60.

Figure 13.- Continued.
54

(e) M = 0.65.

Figure 13.- Concluded.
55

(a) R = 4 × 106.

Figure 14.- Effect of Mach number on section characteristics with transition fixed.
56

(b) R = 6 × 106.

Figure 14.- Continued.
57

(c) R = 9 

× 106.

Figure 14.- Continued.
58

(d) R = 12 × 106.

Figure 14.- Concluded.
59

(a) M = 0.10.

Figure 15.- Effect of Reynolds number on section characteristics with transition fixed.
60

(b) M = 0.30.

Figure 15.- Continued.
61

(c) M = 0.50.

Figure 15.- Continued.
62

(d) M = 0.60.

Figure 15.- Continued.
63

(e) M = 0.65.

Figure 15.- Concluded.
REPORT DOCUMENTATION PAGE Form Approved

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Contractor Report

 4. TITLE AND SUBTITLE

Design of a Slotted, Natural-Laminar-Flow Airfoil for Business-Jet

Applications

5a. CONTRACT NUMBER

NNL04AD45P

 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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14. ABSTRACT

A 14-percent-thick, slotted, natural-laminar-flow airfoil, the S204, for light business-jet applications has been designed and

analyzed theoretically. The two primary objectives of high maximum lift, relatively insensitive to roughness, and low profile

drag have been achieved. The drag-divergence Mach number is predicted to be greater than 0.70.

15. SUBJECT TERMS

aerodynamics; airfoils; laminar flow; wind tunnel experiment

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01- 07 - 2012