Aerodynamics of Modified Wings

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NATIONAL ADVISORY COMMITTEE

FOR AERONAUTICS

'■? TECHNICAL NOTE

No. 1591

AERODYNAMIC CHARACTERISTICS OF A NUMBER OF MODIFIED

/ NACA FOUR-DIGIT-SERIES AIRFOIL SECTIONS

- By Laurence K. Loftin, Jr., and Kenneth S. Cohen

Langley Memorial Aeronautical Laboratory Langley Field, Va.

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NATIONAL ADVISORY COMMITTEE FOE AERONAUTICS

TECHNICAL NOTE NO. 1591

AERODYNAMIC CHARACTERISTICS OF A NUMBER OF MODIFIED

NACA FOUR-DIGIT-SERIES AIRFOIL SECTIONS

By Laurence K. Loftin, Jr., and Kenneth S. Cohen

SUMMARY

Theoretical pressure distributions have been calculated and the experimental aerodynamic characteristics determined at low speeds for a selected group of the NACA four-digit-series airfoil sections which had previously "been modified for high-speed applications. The experimental investigation which was made in the Langley two-dimensional low-turbulence pressure tunnel consisted of measurements of the lift, drag, and pitching-moment characteristics of each of the plain airfoils at Reynolds numbers of 3.0 x 10^, 6.0 x 106, and 9.0 x 10^. In addition, the effectiveness of flaps when applied to these airfoils and

■ the effect upon the aerodynamic characteristics of standard leading-edge roughness were determined at a Reynolds number of 6.0 x 10^. Also tested were three conventional NACA four-digit-series airfoil sections which had not previously "been investigated in the Langley two-dimensional low—turbulence pressure tunnel.

The results of the experimental investigation indicated that the maximum lift characteristics of the modified NACA four-digit-series sections having normal-size leading-edge radii and a maximum thickness of 12 percent chord located at U0 percent chord very closely approximated those of smooth NACA 61+-series low-drag sections of corresponding thickness and camber. When the leading-edge radius was reduced to one- quarter normal size, the maximum lift coefficients of the 10-percent-thick airfoils with maximum thickness located at 40 and 50 percent chord were

■about 35 percent lower than those of NACA 6^-^eries sections of corresponding thickness and camber. For airfoils equipped with 20-percent-chord split flaps deflected 60°, the maximum lift of the airfoils with one- quarter normal-size leading-edge radii more nearly approached that of NACA 61+-series airfoils. Roughness had no appreciable effect upon the maximum lift of these airfoils. The minimum drag coefficients of the airfoils with maximum thickness at kO percent chord and normal-size leading-edge radii were higher than those of the corresponding NACA 64-series sections. Reducing the leading-edge radius to one-quarter normal size and moving the position of maximum thickness to kO and 50 percent chord caused the minimum drag coefficients to be reduced to values about the same as those of corresponding NACA 6k- and 66-series sections, respectively. Increases in the trailing-edge angle resulting

NACA TW Wo. 1591

from rearward movement of the position of maximum thickness caused sharp decreases in the lift—curve slope and pronounced forward movement of the aerodynamic center.

INTRODUCTION

The increasing demand for high speeds in modern airplanes has focused much attention upon airfoil sections capable of operation at high. Mach numbers without Buffering the adverse effects of compressibility. One of the first systematic series of airfoil sections developed with a view toward high-speed application consisted of modified NACA four- digit—series sections. Descriptions and high Mach number data obtained in the NACA 11—inch high—speed tunnel were presented in 193^+ (reference l) for these airfoil sections. Since the issuance of reference 1, the modified NACA four-digit—series sections have been employed rather extensively in Europe, particularly in Germany, and have recently received favorable consideration in this country.

Low-speed aerodynamic data obtained in the NACA Variable-Density Wind Tunnel are available for several of the modified NACA four-digit— series airfoil sections (reference 2). The range of airfoil types covered by these data, however, is very limited. In view of the meager amount of data available for the modified NACA four-digit—series sections and because of the recent interest shown in them, an investigation of the low—speed aerodynamic characteristics of a selected group was undertaken in the Langley two-dimensional low—turbulence pressure tunnel. The airfoils chosen for test were those which appeared from theoretical pressure-distribution calculations to offer the best possibilities for high—speed applications. The results of the experimental investigation, together with the theoretical pressure-distribution data for a number of the modified NACA four-digit—series sections, are presented in this paper.

The aerodynamic characteristics of five of the modified sections are presented; three of these are symmetrical and two are cambered with the NACA mean line a = 0.8 (modified). (See reference 3«) Also presented are characteristics of three conventional NACA four—digit- series sections, data for which are not included in the systematic results of reference k for this series.

COEFFICIENTS AND SYMBOLS

CJL section drag coefficient

Cfl minimum section drag coefficient nnin

e NACA TW No. 1591 3

C2 section lift coefficient

C7 maximum section lift coefficient max

c7 design section lift coefficient 'i

Cj_ section pitching-moment coefficient a"bout aerodynamic center

CQI /r - section pitching-moment coefficient ahout quarter-chord point

<x0 section angle of attack

<x^ section angle of attack corresponding to design lift coefficient

dc^/da section lift—curve slope

V' free-stream velocity

v local velocity

Av increment of local velocity

Ava increment of local velocity corresponding to additional type of load distribution

Bp resultant pressure coefficient; difference "between local • upper-surface and lower-surface pressure coefficients

E Eeynolds number

Eg "boundary—layer Eeynolds number "based on "boundary—layer thickness and local velocity outside the "boundary layer

c airfoil chord length

x distance along chord from leading edge

y distance perpendicular to chord

yc mean—line Ordinate

a mean—line designation, fraction of chord from leading edge over which design load is uniform

NACA TW Wo. 1591

DESCRIPTION AND THEORETICAL CHARACTERISTICS OF AIRFOILS

Basic thickness forma.— The modifications to the NACA four-digit— series "basic thickness forms, completely described in reference 1, can perhaps "be "best described here "by an explanation of the digits appearing in a typical airfoil designation. Consider, for example, the NACA 0012-6^ airfoil section. The first four digits have the usual meaning attached to the numbers appearing in the designation of a conventional NACA four— digit-aeries airfoil section, in this case a 12—percent—thick symmetrical section. The two numbers following the dash describe the modifications.

The first number following the dash is an index to the size of the leading—edge radius. Leading-edge radii of three sizes, represented "by the numbers 33 6, and 9, were investigated in reference 1. The number 6 which appears in the illustrative example indicates the normal- size leading—edge radius employed with conventional four-digit—series sections; the number 3 represents a one-quarter normal-size leading-edge radius; and the number 9 indicates a leading-edge radius of three times normal size. The second number following the dash indicates the position of maximum thickness in tenths of the chord. Airfoils, which were derived in reference 1, have the position of maximum thickness located at k0} 50, and 60 percent chord.

In order to provide some "basis upon which to choose the airfoils to "be tested, theoretical pressure distributions were calculated "by the methods of reference 5 for a group of modified NACA four-digit— series "basic thickness forms. The results of these calculations are presented in figures 1 to 8 for the following airfoil sections:

NACA 0010-6^ NACA 0012-6^ KACA OOIO-65 NACA 0010-66

NACA 0008-3^. NACA 0010-3^ NACA 0012-3^ NACA 0010-35

In addition to pressure distributions at zero lift, these data include incremental velocity ratios from which the pressure distribution at any lift coefficient may be calculated. The method of making this calculation is described in reference k.

From the data of figures 1 to 8, the effect upon the pressure distribution of variations in the position of maximum thickness and size of the leading-edge radius are clearly evident. A decrease in both the peak negative pressure coefficient and in the variations of pressure over the forward part of the airfoil is effected by maintaining a normal—size leading—edge radius and moving the position of maximum thickness from 30 (original position) to lj-0 percent chord (fig. 2).

NACA TN No. 1591

Further rearward movement of the position of maximum thickness, however, appears to cause a second peak in the pressure distribution near the trailing edge (figs. 3 and 4) followed "by a rather sharp, undesirable pressure recovery. With one-quarter normal-size leading-edge radius, the magnitude of the peak negative pressure coefficient is not changed much hut its position is moved to the rear. The change in position of minimum pressure is particularly marked when the position of maximum thickness is moved from 40 percent to 50 percent of the chord (figs. 5 and 6). This movement of the position of maximum thickness decreases the peak negative pressure coefficient slightly hut results in an undesirably large pressure recovery near the trailing edge. On the "basis of these theoretical data and from a consideration of the probable low-speed characteristics, the NACA 0010-34, OOIO-35, and 0012-64 basic thickness forms were chosen for tests. The NACA OOIO-34 and 0012-64 were also tested in combination with a cambered mean line.

Mean line.- In the present investigation, the modified NACA four- digit—series basic thickness forms which were cambered employed the NACA a = 0.8 (modified) mean line (reference 3). This mean line is designed to have a uniform load distribution from the leading edge to the 80-percent-chord station and designed to be geometrically straight from about 85 percent chord to the trailing edge. The NACA a = 0.8 (modified) mean line was used because the peak induced velocities added by this mean line to the velocities over the basic thickness form are less than those associated with the older mean lines, such as the NACA 230 and 24 mean line; and the curvature of the airfoil surfaces near the trailing edge which results from the use of an NACA a = 1.0 mean line is eliminated.

Ordinates and load-distribution data corresponding to a design lift coefficient of 1.0 are presented in figure 9 for the NACA a = 0.8 (modified) mean line. If the ordinates and load are desired for a design lift coefficient other than 1.0, they may be obtained easily by linearly scaling the values presented. The method for combining the pressure-distribution data for the basic thickness forms and mean line to give the pressure distribution about a cambered airfoil at any lift coefficient is given in reference 4.

Designation of cambered airfoil sections.- The method of designating modified NACA four-digit-series airfoil sections which employ the NACA a = 0.8 (modified) mean line is illustrated by the following example:

NACA 0012-64, a = 0.8 (modified), c2. =0.2.

This system of numbers designates an NACA 0012-64 basic thickness form laid off on an NACA a = 0.8 (modified) mean line cambered for a design lift coefficient of 0.2.

MCA TN No. 1591

Conventional NACA four-digit-series airfoil sectiona.- Complete descriptions of the basic thickness forms and mean lines of the conventional NACA four-digit-series airfoil sections of which three were tested in the present investigation may he found in references k and 6.

APPARATUS AND TESTS

Wind tunnel.— The experimental investigation was made in the

Langley two-dimensional low—turbulence pressure tunnel. The test section of this tunnel measures 3 feet by 7.5 feet with the models, when mounted, completely spanning the 3—foot dimension and with the Juncture between the model and tunnel walls Bealed to prevent air leakage. Lift measurements were made by taking the difference between the pressure reaction upon the floor and ceiling of the tunnel, drag measurements were made by the wake—survey method, and pitching moments were determined with a torque balance. A more complete description of the tunnel and the methods of obtaining and reducing the data are contained in reference 7-

Models.— The eight airfoil sections for which the experimental aerodynamic characteristics were obtained are:

NACA 0010-35 NACA 0010-3^

NACA OOIO-3U, a = 0.8 (modified), cz. = 0.2

NACA 0012 . NACA 0012-6^

NACA 0012-6U, a = 0.8 (modified), cz = 0.2

NACA 2408 NACA 21+10

The models representing the airfoil sections were of 2k—inch chord and, with the exception of the 8-percent—thick section which was machined from steel, were constructed of laminated mahogany. The models were sprayed with lacquer and then sanded with No. 1*00 carborundum paper until aerodynamically smooth surfaces were obtained. The ordinates of the models tested are presented in table I.

Tests.— The tests of each smooth airfoil section consisted of measurements of the lift, drag, and quarter-chord pitching moment at Reynolds numbers of 3.0 X 106, 6.0 X 106, and 9.0 x 10°. In addition, the lift and drag characteristics of each section were determined at a

Reynolds number of 6.0 X 10° with standard roughness applied to the leading edge of the model. The standard roughness employed on these

NACA TR Wo. 1591

24-inch-chord models consisted, of 0.011—inch-diameter carborundum grains spread over a surface length of 8 percent of the chord hack from the leading edge on the upper and lower surfaces. The grains were thinly- spread to cover from 5 to 10 percent of this area. In an effort to gain some idea of the effectiveness of flaps when applied to these airfoils, each airfoil was fitted with a 0.20c simulated split flap deflected 60°. Lift measurements were made at a Reynolds number of 6.0 x 10° with the split flap, with the airfoil leading edge both smooth and rough.

RESULTS

The results obtained from tests of the eight airfoil sections are presented (figs. 10 to 17) as plots of standard aerodynamic coefficients representing the lift, drag, and quarter-chord pitching- moment characteristics of the airfoil sections, The position of the aerodynamic center, as determined from the experimental results, and the variation of the pitching-moment coefficient about this point are also included. The influence of the tunnel boundaries has been removed from all the aerodynamic data by means of the following equations (developed in reference 7):

cd = 0.990 cd«

H = 0.973 cz«

°*cA = °'951 ^c/V a0 = 1.015 a0»

where the primed quantities represent the measured coefficients.

DISCUSSION

The discussion is primarily concerned with an analysis of the effects, as shown by tests of the five modified NACA four-digit-series airfoil sections, of variations in the leading-edge radius and position of maximum thickness upon the aerodynamic characteristics. In this analysis, frequent use is made of cross plots (figs. l8 to 21) showing the characteristics of the modified sections as compared with those of the conventional NACA four-digit-series sections and NACA 6—series low-drag sections. The comparative results for the NACA 6—series and four-digit—series sections are shown in the form- of curves representing faired data taken from reference K, whereas the results of the present

8 WACA TN Wo. 1591

investigation appear in the cross plots as experimental points. Little mention is made of the results obtained for the three conventional WACA four-digit-series sections tested inasmuch as they follow closely the trends indicated in reference k for this series of airfoil sections.

Drag

Minimum drag.— The previously mentioned influence upon the pressure gradients over the forward part of the airfoil of a reduction in size of the leading-edge radius and a rearward movement of the position of maximum thickness has, as might he expected, a favorable effect upon the value of the minimum drag coefficient. An indication of the magnitude of this effect may he gained from figure l8, which shows the minimum section drag coefficient corresponding to a Eeynolds number of 6.0 X 10" as a function of airfoil thickness ratio for the five modified NACA four-digit series airfoils, for the conventional WACA four-digit series, and for the NACA 6k— and 66-aeries low-drag airfoils.

In the smooth condition, the minimum drag of the 10-percent—thick airfoils having leading-edge radii of one—quarter normal size and maximum thickness at kO and 50 percent chord was of the same order, respectively, as that obtained for WACA 6k— and 66-series low-drag airfoils of comparable thickness. This similarity in drag indicates the existence of considerable laminar flow over the airfoil surfaces. The small, though rather extensive, positive pressure gradient, which occurs over the surfaces of the 12—percent—thick airfoils having leading—edge radii of normal size and maximum thickness at kO percent chord, gives rise to a minimum 'drag coefficient which lies between those of the WACA 64-series low-drag section and WACA four-digit-eeries section of comparable thickness. The addition of the WACA a = 0.8 (modified) mean line to the WACA OOIO-3I1 and 0012-6^ basic thickness forms does not appreciably affect the value of the minimum drag coefficient. The faired data of reference k, which are presented in figure l8, indicate that airfoil thickness form and mean line have little effect upon the value of the minimum drag coefficient when the airfoil leading edges are in the rough condition; and the results of the present investigation (fig. l8) follow the same trend.

The airfoil basic thickness distribution appears to have a marked effect upon the manner in which the minimum drag coefficient varies with Eeynolds number (figs. 10 to Ik). The controlling action of the airfoil pressure distribution upon the extent to which the opposite effects of a thinning boundary layer and a forward movement of the point of transition balance each other as the Eeynolds number is increased suggests itself as a possible explanation. Some insight into the mechanism by which the airfoil pressure distribution influences the movement of the transition point with Eeynolds number may be gained from the theoretical work of Schlichting and Ulrich (reference 8).

NACA TN No. 1591

The results of this work show the existence of a critical boundary— layer Eeynolds number Be above which the laminar boundary

crit layer is no longer stable and may become turbulent. Furthermore, the value of the critical boundary—layer Eeynolds number is shown to decrease rapidly and the laminar boundary layer to become increasingly unstable as the pressure gradient along the surface becomes positive. In the presence of an unfavorable pressure gradient, the transition point is, therefore, most likely to move rapidly forward once the critical boundary—layer Eeynolds number has been reached.

In consideration of the ideas of Schlicting and Ulrich in relation to the increase of minimum drag with Eeynolds number shown by the NACA 0012-64 section (fig. 13), the unfavorable pressure gradient over this airfoil (fig. 8) would seem to be responsible for a rapid forward movement of transition which overbalances the normal thinning of the boundary layer and consequent reduction in drag that usually accompany an increase in Eeynolds number. On the other hand, the MCA OOIO-3U (fig. 10) and NACA OOIO-35 (fig. 12) airfoils which possess more favorable pressure gradients have a negligible scale effect between Eeynolds numbers of 3.0 x 10& and 9.0 x 10^. This fact indicates that the opposite effects of a thinning boundary layer and a forward movement of transition nearly counterbalance each other. The uniformly favorable influence upon the minimum drag of NACA 6-series sections of increasing the Eeynolds number from 3.0 x 10^ to 9.0 X 10^ indicates that E5crit of these airfoil sections, which have marked

negative pressure gradients, is sufficiently high so that no appreciable forward movement of transition occurs between these Eeynolds numbers; and, thus, the favorable effect of a thinning boundary layer predominates.

Low-drag range.- The range of lift coefficients over which low drag is obtained and the manner in which this range varies with Eeynolds number are about the same for the NACA OOIO-34 aad OOIO-35 airfoil sections (figs. 10 and 12) as for the NACA 6-series sections of comparable thickness (reference k). The low-drag range for the NACA 0012-64 section (fig. 13), however, is quite small at a Eeynolds

number of 3.0 X 10 and is practically nonexistent at a Eeynolds number of 9.0 x 10°. The more positive pressure gradients on the NACA 0012-64 section are probably responsible for the behavior of the low-drag range on this airfoil section.

The relationship between the drag and lift outside the low-drag range of lift coefficients is about the same for the NACA 0010-34 and NACA 0012-64 airfoils, both cambered and uncambered, as for the NACA 6*1—series low-drag sections of comparable thickness; a somewhat less marked correspondence exists between the drag characteristics of the NACA OOIO-35 section and a comparable NACA 66-series low-drag section. These comparisons are valid for the airfoils in both the smooth and rough conditions.

10 NACA TN No. 1591

Lift

Lift-curve slope.— Rearward movement of the position of maximum thickness of the NACA four-digit^series sections is accompanied by an increase in trailing-edge angle. In accordance with previous experimental work (references 9 and 10), the lift-curve slope decreases with increasing trailing-edge angle. The results of the present investigation (fig. 19) for the 10-percent-thick and 12-percent-thick sections having maximum thickness at various positions indicate the same trend, with the greatest decrease in the lift-curve slope "being about l6 percent.

From theoretical considerations, the lift-curve slope should increase with increasing airfoil thickness ratio; and the comparative data from reference k (fig. 19) for NACA 6i+-series low-drag sections, which have very small trailing-edge angles, indicate that such is the case. If, however, the trailing-edge angle is large and increases rapidly with increasing airfoil thickness ratio, the theoretical increase in lift-curve slope with thickness will be overbalanced by the opposite effect of increasing trailing-edge angle. The NACA four-digit series sections, data for which are presented in figure 19, have this characteristic. Since, with increasing thickness, the trailing- edge angles of the modified NACA four-digit-eeries sections become progressively larger than those of the conventional NACA four-digit-series sections, a more rapid decrease in lift-curve slope with increasing thickness would be expected for these modified airfoils. The amount of data available for the modified NACA four-digit-series sections does not appear to be sufficient, however, to define adequately this trend or to permit any definite statements as to the relative effects of roughness on the lift-curve slopes of the modified and conventional NACA four-digit-series sections.

Angle of zero lift.— There appears to be no appreciable difference in the section angles of zero lift of the NACA 0010-3^ and NACA 0012-6U airfoil sections cambered with the NACA a = 0.8 (modified) mean line (figs. 11 and Ik). The values are slightly more negative than those predicted from the theoretical mean-line data presented in figure 9 but agree quite well with the experimental values obtained for cambered NACA cA-series airfoil sections employing the NACA a = 0.8 (modified) mean line (reference 3)•

Maximum lift.- Some idea of the effect upon the maximum lift coefficient of variations of the position of maximum thickness and leading-edge radius may be gained from figure 20. This figure shows

the maximum section lift coefficients (E = 6.0 x 10°) for the modified NACA four-digit-series airfoils as a function of airfoil thickness ratio, with comparative data from reference k for NACA 6k-series low-drag airfoils. As might be expected from previous investigations, the lowest maximum lift coefficients were obtained for the airfoils having one-quarter normal-size leading-edge radii. The maximum lift coefficients of the two symmetrical sections (NACA 0010-3^ and OOIO-35) are about the same and do not appear to vary as the leading-edge condition is changed

NACA TN No. 1591 11

from smooth to rough. These results show that if the leading edge is sufficiently sharp, the usual Important influence of surface condition is negligible. The extremely low value of the maximum lift obtained under these conditions is shown by comparison with results for the MCA 6k-0l0 section. The maximum lift coefficients of the two modified NACA four-digit-serie3 sections are about 35 percent lower than that of the NACA 6k—010 section in the smooth condition and about 15 percent lower when the leading edges of the airfoils are rough. The increment in maximum lift caused hy cambering the NACA 0010—3^ section is about the same as that observed for the addition of approximately the same amount of camber to the NACA 6k—010 section. Even with camber, the maximum lift of the NACA 0010—3U section is about 23 percent lower than that of the NACA 6k-010 section; but with rough leading edge, the NACA 6^-010 section has a maximum lift coefficient which is about the same as that of the cambered NACA 0010—3^ section.

The maximum lift of the three airfoils having one-quarter normal— size leading-edge radii with smooth leading edges and equipped with 0.20c split flaps deflected 60°, more nearly approaches that of NACA 6k—series low-drag sections of corresponding thickness and camber. The decrement in maximum lift coefficient caused by leading—edge roughness is, however, so small for these three sections that in the rough condition the maximum lift of the three modified NACA four-digit—series sections is as good as or better than that of corresponding NACA 6k—series airfoils.

Moving, the position of maximum thickness from 30 percent to kO percent chord while maintaining a normal-size leading—edge radius reduces the maximum lift coefficient of the plain airfoil about 15 percent, as shown by the comparative data for the NACA 0012 and NACA 0012-6U sections. Clearly illustrated here is the important point that a reduction in thickness of the airfoil near the leading edge, such as occurred in this case, has a definitely adverse effect upon the maximum lift jjoefficient. although the leading-edge radius itself may not be decreased. The maximum lift coefficients of the cambered and symmetrical NACA 0012-6^ airfoil sections in both the smooth condition and with standard leading-edge roughness are nearly the same as those of the corresponding cambered and symmetrical NACA 6k—series low-drag sections (fig. 20).

The value of the maximum lift coefficient presented in figure 20 for the NACA 0012-6^ section is about 13 percent lower than that indicated by tests of the same airfoil in the NACA Variable-Density Wind Tunnel (reference 2). The value obtained in the present investigation; however, was very carefully checked and is believed to be correct. The discrepancy between the values obtained in the two tunnels may possibly have been caused by turbulence effects not fully accounted for on this sensitive airfoil by the effective Eeynolds number correction applied to the Variable-Density Wind-Tunnel results.

12 NACA TN No. 1591

The results presented in figure 20 show that, in the smooth condition at least, the maximum lift coefficients of the cambered and symmetrical NACA 0012-64 airfoil sections, when equipped with 0.20c split flaps deflected 60°, are somewhat higher than those of corresponding NACA 6k—series sections. This result may be explained by the fact that the trailing-edge angle of the NACA 0012-64 airfoil is larger than that of the NACA 6*1—012 airfoil since the experimental results presented in reference 3 indicate a slight improvement in the maximum lift of NACA 6-series sections with split flaps when the trailing-edge cusp is removed. The results for the cambered and symmetrical NACA 0012-64 airfoil with rough leading edges do not form a consistent comparison with results for the NACA 64—series sections. In neither case, however, is the modified NACA four-digit-series section worse than the corresponding NACA 64-series airfoil.

Between Reynolds numbers of 3.0 x 10& and 9.0 x 10°, none of the modified NACA four-digit—series sections show any appreciable scale effect on maximum lift.

Pitching Moment

Quarter-chord point.— The two airfoils cambered with the NACA a = 0.8 (modified) mean line have quarter-chord pitching moments (figs. 11 and 14) which agree closely with those predicted from the theoretical pitching-moment data (fig. 9)•

Aerodynamic center.— The chordwise position of the aerodynamic center for the modified NACA four-digit—series sections is shown in figure 21 as a function of airfoil thickness ratio, together with similar data taken from reference 4 for the conventional NACA four-digit-series sections and the NACA 6k—series low-drag sections. The forward movement of the aerodynamic center which is seen to accompany rearward movement of the position of maximum thickness on the modified NACA four-digit-eeries sections is in agreement with the trends of reference 11 which show that such a forward movement follows an increase in trailing-edge angle. Theoretical considerations indicate a rearward movement of the aerodynamic center with increasing airfoil thickness ratio, and the data for NACA 6k—series sections follow this trend; but the effect of increasing trailing-edge angle predominates in the case of the conventional NACA four-digit—series sections as evidenced by the forward movement of the aerodynamic center. (See fig. 20.) Since the trailing-edge angles of the modified NACA four-digit—serie3 sections become progressively larger with increasing airfoil thickness than those of the conventional NACA four-digit-series sections, a more pronounced forward movement of the aerodynamic center with increasing thickness would be expected for these airfoil sections; and the comparative results for the NACA 0012—64 and 0010-34 sections seem to show this trend.

NACA TW No. 1591 13

CONCLUSIONS

Based upon a two—dimensional investigation of the aerodynamic characteristics of five modified NACA four-digit—series airfoil sections

6 (\ at Reynolds numbers from 3.0 x 10° to 9.0 x 10°, the following conclusions may "be drawn:

1. The maximum lift characteristics of the airfoil sections having normal-size leading—edge radii and a maximum thickness of 12 percent chord located at kO percent chord very closely approximated those of NACA 64-series low-drag sections of corresponding thickness and camber.

2. The maximum lift coefficients of the 10—percent—thick airfoils with one-quarter normal—size leading-edge radii and maximum thickness located at kO and 50 percent chord were ahout 35 percent lower than those of smooth NACA 6k—series sections of corresponding thickness and camber. For airfoils equipped with 20-percent-chord split flaps deflected 60°, the maximum lift of the airfoils with one-quarter normal- size leading-edge radii more nearly approached that of NACA 6^-series airfoils. Boughness had no appreciable effect upon the maximum lift of these airfoils.

3. The minimum drag coefficients of the airfoils with maximum thickness at kO percent chord and normal—size leading-edge radii were higher than those of the corresponding NACA 64—series sections. Seducing the leading-edge radius to one—quarter normal size and moving the position of maximum thickness to kO and 50 percent chord caused the minimum drag coefficients to he reduced to values ah out the same as those for corresponding NACA 6k— and 66—series sections, respectively.

k. Increases in the trailing—edge angle resulting from rearward movement of the position of maximum thickness caused sharp decreases in the lift—curve slope and pronounced forward movements of the aerodynamic center.

Langley Memorial Aeronautical laboratory National Advisory Committee for Aeronautics

Langley Field, Va., Octoher 1, I9V7

14 MCA TW Wo. 1591

REFERENCES

1. Stack, John, and von Doenhoff, Altert E.: Teats of l6 Related Airfoils at High. Speeds. WACA Rep. Wo. lj-92, 193^.

2. Jacots, Eastman W., Pinkerton, Rotiert M., and Greehberg, Harry: Tests of Related Forward-Camber Airfoils in the Variatle— Density Wind Tunnel. WACA Rep. Wo. 6l0, 1937.

3. Loftin, Laurence K., Jr.: Theoretical and Experimental Data for a Wumber of WACA 6A-Series Airfoil Sections. WACA TW Wo. 1368, 19^7-

h. Afrbott, Ira H., von Doenhoff, Altert E., and Stivers, Louis S., Jr.: Summary of Airfoil Data. WACA ACR Wo. L5CO5, 1945.

5. Theodorsen, Theodore: Theory of Wing Sections of ArMtrary Shape. WACA Rep. Wo. lj-11, 1931.

6. Jacots, Eastman W., Ward, Kenneth E., and Pinkerton, Rotert M.: The Characteristics of 78 Related Airfoil Sections from Tests in the Variatle-Density Wind Tunnel. WACA Rep. Wo. 460, 1933.

7. von Doenhoff, Altert E., and Attott, Frank T., Jr.: The Langley Two-Dimensional Low-Turbulence Pressure Tunnel. WACA TW Wo. 1283, 19^7.

8. Schlichting, H., and Ulrich, A.: Zur Berechnung des Umschlages laminar turbulent. Jährt. 19^+2 der deutschen Luftfahrtforschung, R. Oldentourg (Munich), pp. I 8 - I 35.

9. Purser, Paul E., and McKee, JohnW.: Wind—Tunnel Investigation of a Plain Aileron with Thickened and Beveled Trailing Edges on a Tapered Low-Drag Wing. WACA ACR, Jan. 19^3i

10. Jones, Rotert T., and Ames, Milton B., Jr.: Wind—Tunnel Investi- gation of Control-Surface Characteristics. V — The Use of a Beveled Trailing Edge to Reduce the Hinge Moment of a Control Surface. WACA ARR, March 19^2.

11. Purser, Paul E., and Johnson, Harold S.: Effects of Trailing-Edge Modifications on Pitching-Moment Characteristics of Airfoils. WACA CB Wo. LlkL30, 1<M.

NACA TW No. 1591 15

TABLE I

ORDINATES OP NACA AIRFOIL SECTIONS TESTED

NACA 0010-54 NACA 0010-34

a - O.S (modified), 0, 0.2

(Stations and ordinates given in percent of airfoil chord]

Upper Surface Lower Surface

Station Ordinate Station Ordinate

0 0 0 0 -75 • 71U • 75 -7,%

1.25 .944 1.400

I.25 -944 -I.400 2.5 2.5

5.0 2.078 5.0 -2.078 7.5 2.611 7-5 -2.611

10 3.04^ 10 -3.044 15 3-7UU

4.244 15 -3.7W+

-4.244 20 20

28 4.853 28 -4.833 5.OOO fc.856

-5.000 -4.856 50 50

60 4.453 60 -4.433

ffi 3-733 l°o -3.733 2.767 I.556

-2.767 90 90 -1-556 95 .856 95 -.856

100 .100 100 -.100

L.E. radius: O.272

NACA 0012-64

(Stations and ordinates given in percent of airfoil chord]



0 0 0 0 I.25 I.813 1.25 -I.813 2.5 2.453 2.5 -2.455 5.0 3.267 5.0 -5.267 7.5 5.813

4.24Ö 7-5 -3.815

-4.240 10 10 15 4.807 15 -4.8I7 20 5.293 20 -5.293

28 5.827 28 -5.827 6.000 -6.000

50 5.827 50 -5.827 60

l°0 4 "480

60

So0 -4 480 5.320 -3.320

90 1.867 90 -1.867 95 1.027 95 -1.027

100 .120 100 -.120

L.E. rad Lus: I.582

[Stations and ordinates given in percent of airfoil chord]

Upper . Surface Lower Surface


0 0 0 0 .687

I.176 .790

I.062 .813

I.524 -.632 -.820

2.407 4.887 7.578

I.608 2.593 -I.I86 2.43,6 5.II3 -I.714 3.O94 7.622 -2.122

9-875 14.876 19.886

3.657 4.525

10.125 15.124

-2.1^5 -2.96I

5.172 5.98O

20.114 -5.512 29.917 30.083

40.045 50.006

-3.684 39-955 §9.994

6.279 6.186

-5.721 -5.526

60.031 5-735 4.915

59.969 -5.151 -2.549 70.064

80.100 69.936

5.700 79.9OO 8?.924 94-958

-1.83a 90.076 95.042

2.044 1.100

-1.064 -.610

100.000 .100 100.000 -.100

L.E. radi Lus: 0.272 Slope of radius through L.E.s 0.095

NACA 0012-64 a = 0.8 (modified), ct =0.2

[Stations and ordinates given in percent of airfoil chord]



0 0 0 0 I.IO7 2.356

I.928 2.664

-1.686 2.659 -2.237

4.825 3.625 U.295 7*678

-2.901 7.322 -5.525 9.825

14.859 4.832 5.645

10.175 15.161 ■

-3.640 -4.085

19.858 6.221 20.142 -4.561 29.900 6.974 30.IOO

40.054 -4.678

39-946 7.279 -4.721 L9.993 7.157

6.622 50.007 -4-497

-4.018 60.058 59.962 70.077 80.120

5.662 4.253

69.923 -5.296 79.880 89.909 94.950

-2.583 90.091 2.355 -1.575

-.781 95.050 1.271 100.000 .120 100.000 -.120

L.E. radi us: I.582 Slope of radius thr augh L.E.: O.O95

NATIONAL ADVISORY

COMMITTEE FOR AERONAUTICS

16 NACA TN No. 1591

TABLE I - Concluded

ORDINATES OF NACA AIRFOIL SECTIONS TESTED

NACA 0010-35 NACA 0012

[Stations and ordlnates given in percent of airfoil chord]




0 •75

1.25 2.5 5.0 7-5 10 15 20

50 60

l°o 90 95 100

1.267 1.844 2.289 2.667 3.289

4.878 5.000 4.867 4.389 3.500 2.100 1.178

.100

0 • 75

1.25 2.5 5.0 7-5 10 15 20

$ 50 60

Zo° 90 95 100

::ffi -1.267 -1.844 -2.289 -2.667 -3.289

-}'7Bl -4.878 -5.000 -4.867 -4.389 -3.500 -2.100 -1.178 -.100

L.E. radiuss O.272



0 0 0 0 1.25 I.894 1.25 -I.894 2.5 2.615 2-5 -2.615 5.0 3.555

4.200 5.0 -3-555

-4.200 7-5 7-5 10 4.683 10 -4.683 15 5-345 15 -5.345 20 5.738

5.941 20 -5.733

-5.941 25 25

8 6.002 8 -6.002 5.803 5.294 4.563 3.664 2.623

-5.803 -5.294 -4.565 -3.664 -2.623

50 go

50 60

l°o l°o 90 95

1.448 .007 .126

90 95

-1.L48 -.807 -.126 100 100

L.E. rad ius: I.58

NACA 2408




0 0 0 0 1.128 1.380 1.372

2.663 -I.I34

2.337 1.977 -1.493 -1.891 4.794 2.829 5.206

7.273 9.768 14.778 19.809 24.852

3.471 m 7.727 -2.111 10.232 15.222

-2.237 -2.338

5.320 5.677

20.191 25.JJ+8

-2.320 -2.239

29.9OO 5.869

30.100 40.000

-2.125 40.000 -1.869 50.039 60.068 4! 820

49.961 59-932

-1.585 -1.264

70.081 80.078 2.658

69.919 -942 79.922 89.946 94.967

-.636 90.054 95.033

1.575 -353 -.217

100.000 100.000 -.084

L.E. radJ Lus: O.70 Slope of radius thr ough L.E. ! 0.1

NACA 24l0




0 0 0 0 I.O98 I.694 1.402 -1.448 2.297 4.742

2.411 2.703 -1.927 3.420 4.169

5.258 -2.482 7.217 7.783 -2.009 9.710 14.722

4.765 5.665 6.276 6.668

10.290 -3.OI6 15.278 -3.227

-3.276 -3.23O 2^!^l4

20.239 25.186

29.875 6.875 3O.I25 40.000 49.951

-3.I25 40.000 50.049 6O.O85

6.837 6.356

-2.837 -2.460

5.580 4.551

-2.024 70.102 8O.O97

69.898 -1.551 3.29§ 79.903

89.933 94-959

-1.074 90.067 95.041

I.816 • 990

-.594 -.352

100.000 .105 100.000 -.105

L.E. radl us: 1.10 Slope of radius thr ough L.E. 0.1

NATIONAL ADVISORY


WACA TN No. 1591 17

1.6

1.2

.1+

0 • 2 a + • 6 . 3 1. 0

X ' X

(percent c) y

(percent c) (vA)2 v/V Ava/V

0 0 0 0 4.859 1.25 .756 .917 .958 1.558 2.5 1.120 1.025 1.011 .966 5.0 1.662 I.O92 I.0L5

1.066 .691

7.5 2.089 1.157 .561+ .485 10 2.U56 1.162 I.O78

15 2.996 1.188 I.O9O .587 .526 20 3.596 1.206 I.O98

28 3.867 4.000 1.217 1.105 .248 1.202 I.O96 .197

% 3.881* 1.185 I.O89 •^X 5.547 2.987

I.I65 1.079 1.062

.128

l°o 1.127 .100 2.215 I.O67 1.055 .074

90 XM • 995 .996 .047 95 .932 .965 .051

100 .080 0 0 0

L.E. radius J: 0.17I4. percent c

Figure 1.- NAOA 0008-54 basic thickness form.

NATIONAL ADVISORY


18 NACA ™ No. 1591

1.6

1.2

.8

•k

/ NACA 0010

s --£-, 7~ -~.

*""■

~"~ ~~ ̂ t^ \

■

"^

.2 • k x/c

.6 .8 1.0

X (percent c)

y (percent c) (vA)2 vA AvaA

0 0 0 0 1^28^ 1.25 1.511 1.108 1.053

2.5 2.01+i; l.*286

1.116 .966 5.0 2.722 1.134 .69O 7.5 5.178 1.277

1.269 I.130 .556

• 475 10 5-555 4.O56 li.iill U.Ö56

1.127 15 20

1.261 1.248 1.244

1.123 1.117 1.116

• 577 .516 .241

5.000 1.2l|2 1.115 .195

?0 J+.856 1.231 1.110 .155 4.433 1.211 1.101 .126

70 5.755 I.I55 I.O74 .098 80 2.767

1.556 I.O89 1.043 .072

90 .980 .990 .045 95 .856 .912 •955 .030

100 .100 0 0 0 L.E. radius 5: 1.10 perc .ent c

Figure 2.- NACA 0010-64 basic thickness form.

NATIONAL ADVISORY


NACA TU Ho. 1591 19

1.6

1*2

*) -8

.4

n .2 .4 x/c

.6 .8 1.0

X (percent c) (percent c) (v/v)2 v/V Ava/V

0 0 0 0 2.584 I.25 I.U67 l.li^O 1.068 I.295 2.5 1.967 1.273 1.128 .?x° 5.0 2.5§9 1.271 1.127 .684 7.5 2.989 1.252 1.119 .551

.470 10 5.3OO I.236 1.112 15

U.089 1.213 1.101 .372

20 1.200 1.095 I.O94

.312

2S ii.889 I.I96 .239 1.212 1.101 .193

50 5.000 L.867

1.229 1.109 .158 60 I.234 1.111 .128

l°o 4.389 1.226 1.107 .103 3.500 1.173 1.08?

I.O24 .076 .046 9.0 2.100 1.049

95 1.178 .915 • 957 .029 100 .100 0 0 0

L.E. radii is: 1.10 per cent c

Figure 3.- NAGA OOIO-65 basic thickness form,

NATIONAL ADVISORY


20 NACA TW No. 1591

1.6

1.2

• k

0

\

\ 1

0 • 2 • < + / •< $ . 8 1.0

X (percent c)

y (percent c) (v/V)2 v/V AVa/V

0 0 0 0 2.434 I.25 1.U89 1.150 I.O63 1.289 2.5 2.011 I.2L6 1.116 •959 5.0 2.656 1.2Ö6 I.I3I1 .687 7.5 3.O89 1.282 I.I32 .55U

471 10 5.Ü00 1.258 1.122 15 3.856

L.178 1.225 1.107 .372

20 1.209 1.100 .310

& k.^78 I.I89 I.090 .236 k.822 1.178

l.iau I.O85 .190

50 U.956 1.088 .153 60 5.000 1.211+ 1.102 .129

.104 l°o I.265 I.278

1.125 4.300 1.130 .080

90 2.833 1.135 1.-065 .01+9 95 1.656 .960 .980 .030

100 .100 0 0 0

L.E. radii, is: 1.10 per 3ent c

Figure I4..- NAGA 0010-66 basic thickness form.

NATIONAL ADVISORY


NACA TN Wo. 1591 21

1.6

1.2

7) -8

.1+

n

.2 • k x/c

.6 .8 1.0

X (percent c)

7 (percent c) (v/V)2 v/v AVa/V

0 0 0 0 3.857 1.25

1.U00 .892 .914 1.282

2.5 1.011 1.005 .950 5.0 2.078 1.113 1.055 .688 7.5 2.611 I.I67 1.080 .56U

10 3.014 1.200 1.095 .486 15 3.7U+

h.zhk 1.238 1.113 .389

20 I.256 1.121 .327

$ M33 I.265 1.1214. .21+9 5.000 1.253 1.119 .197

SO U.856 1.235 1.111 .159 60 U-433 1.205 1.098 .127

£o° 3.733 I.I57 I.O89

1.076 .100 2.767 1.556

l.Ol+l; .073 90 .990 •995

• 954 .01+5

95 .856 .910 .030 100 .100 0 0 0

L.E. radlu is: O.272 pe rcent 0

Figure 5.- NACA 0010-3l| basic thickness form.

NATIONAL ADVISORY


22 NACA TN No. 1591

1.6

1.2

t) -8

.4

0 .2 • 4 x/c

.6 .8 1.0

X (percent c)

y (percent c) (vA)2

v/V AvaA

0 0 0 0 4.068 1.25 .878

1.267 • 954 •977

1.016 1.309

2.5 1.032 .952 5.0 1.8Lk

2.289 I.O87 1.043 .679

7.5 1.122 1.059 .476 .382

10 2.667 l.ll^l 1.068 15 3.289 1.172 I.O83 20

4.878 I.I94 1.093 .323

l°o 1.214 1.229

1.102 1.109

.247

.198 -.162 50 5.000

I+.867 1.235 I.24O

1.111 60 1.11k

1.108 .131

l°o 4.389 1.227 1.176

.104

.076 3.500 1.084 90 2.100 1.01+6 1.023 .048 95 I.I78 .920 .959 .030

100 .100 0 0 0

L.E. radiu s: 0.272 pe] rcent c

Figure 6.- • NACA 0010-35 basic thickness form,

NATIONAL ADVISORY


WACA TN Ho. 1591 23

1.6

1.2

f) -8

.1*

n

.2 • 4 x/c

.6 .8 1.0

X

(percent c) y

(percfint-, n) (vA)2 v/V AVaA

0 0 0 0 5.154 1.25 1'^5 .865 .950 1.251 2.5 1.680 .997 .999 •ffl 5.0 2.495 1.122 I.O59 .685 7.5 5.155 1.186 I.089 .560

.1+84 10 3.655 11.495

1.229 1.109 15 1.282 1.152

1.145 .539

20 5.095 1.510 .529

$ 5.8OO I.329 1.153

1.145 .250

6.000 I.5II .198 50 5.827 1.281+ 1.153 .158 60

C480 l.2ltf 1.118 .128

K I.I92 1.092 .098 5.520 1.112 1.055 .071

90 I.867 .89J+

.992 • 946

.045 95 1.027 .029

100 .120 0 0 0

L.E. radiu s: O.591 pe rcent c

Figure 7.- NACA 0012-54 basic thickness form.

NATIONAL ADVISORY


2k NACA TR Wo. 1591

1.6

1.2

.8

.2 x/c .6 .8

(percent c) 0 1.25 2.5 5.0 7.5

10 15 20 10 ^ >0 >0 '0 to

90 95

100

(percent c) 0 1.813 2.1+53 3.267 5.813 k.2li0 4.807 5.293 5.827 6.000 5.827

4480 3.320 1.867 1.027

.120

(v/vr 0 1.072 1.270 1.330 1.325 1.322 1.313 1.303 1.297 1.300 1.280 1.2kk I.189 1.102

.889 0

v/V 0 1.035 1.127 1.153 1.151 1.1S0 1.146 l.l4l 1.139 1.140 1.131 1.115 I.O9O I.050

.996

.943 0

Ava/V

L.E. radius: I.582 percent c

Figure 8.- NACA 0012-6]+ basic thickness form.

1.0

NATIONAL ADVISORY


NACA TN No. 1591 25

2.0

1.0

\

\

1° c

.2 •4 x/c

1.0

ci1 = 1. 0 di = = i.4o° CmcA = = 0.219

X

(percent c) yc

(percent c] dyc/dx PR <w/v = pRA

0 0 •■««■«.«■MW • 5 .281 O.4753?

.44OOJ+

'

•75 •396 1.25 .603 •39531 2.5 1.055 •33404 [■I.O92 0.273 5.0 I.803 .27149 7.5 2.1+32 .23378

10 2.98I .20618 j

15 m .I6546 ■\

20 .I3452 25 5.257

5.742 .IO873 k.096 .274

30 .O6498 .04507 1? 6.120

6.394 L1.100

ll.l04

.275 1+5 50

6.571 6.651

•02S59 .00607

55 60

6.631 6.508

-.OI404 -.03537

.276

65 6.274 -.05887 1.108 •277 70 5.913 -.O861O 1.108 •277 75 5.401

4.673 -.12058 1.112 .278

80 -.18034 1.112 .278 85 90

3.607 2.452

-.23430 -.24521

.840

.588 .210 •147

95 1.226 -.24521 .368 .092 100 0 -.24521 0 0

Figure 9.- Data for NACA mean line a = 0.8 (modified).

NATIONAL ADVISORY


26 NACA TN No. 1591

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HACA TN Wo. 1591 27

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lffllISrjJ9?.B-..3J.Tt U013 0.BS.

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BIO; jja<|o i.siiaiuojf..

28 NACA TW No. 1591

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Aerodynamics of Modified Wings

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