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NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS

MAY 2 1947 TECHNICAL' NOTE

No. 1270

EXPERIMENTAL AND CALCULATED CHARACTERISTICS OF SEVERAL

NACA 44-SERIES WINGS WITH ASPECT RATIOS OF 8, 10,

AND 12 AND TAPER RATIOS OF 2.5 AND 3.5

By Robert H. Neely, Thomas V. Bollech, Gertrude C. Westrick, and Robert R. Graham

Langley Memorial Aeronautical Laboratory Langley Field, Va. ~ -.- — -—•"""^ '•'

FOR REFERENCE •BBTto-iFBRSr^SWrTHIgTSS-M .

NBA C A

Washington

May 1947

11111' 3 1176 01433 9171


TECHNICAL NOTE NO . 1270

EXPERIMENTAL AND CALCULATED CHARACTERISTICS OF SEVERAL

NACA W-SEKIES WINGS WITH ASPECT RATIOS OF 8, 10,

AND 12 AND TAPER RATIOS OF 2-5 AND 3 .5

By Robert H. Neely, Thomas V. Bollech, Gertrude C. Westrick, and Robert R. Graham

SUMMARY

The aerodynamic characteristics of seven unswept tapered wings were determined by calculation from, two-dimensional data and "by wind- tunnel tests in order to demonstrate the accuracy of the calculations and to show some of the effects of aspect ratio, taper ratio, and root thickness-chord ratio. The characteristics were calculated by the usual application of the lifting-line theory which assumes linear section lift curves and also by an application of the theory which allows the use of nonlinear lift curves, A correction to the lift for the effect of chord was made, by using the Jones edge-velocity factor. The wings had aspect ratios of 8, 10, and 12, taper ratios of 2.5 and 3.5, and NACA ^4-series airfoils. For six of the wings the ratio of span to root thickness was held constant at 35 so that the root thickness-chord ratio increased with increasing aspect ratio . Thp aerodynamic characteristics of the wings with and without leading- edge roughness are presented for small values of Mach number and

values of Reynolds number between 1.5 x 10° and 7.0 x 10°.

Reasonable agreement was obtained between the wing force and moment characteristics calculated by the two methods and those obtained experimentallyj however, the method of calculation which allowed the use of nonlinear lift curves gave better agreement at high angles of attack. The two methods of calculation gave different spanwise lift distributions at maximum lift. Comparisons made at equal values of Reynolds number indicate that the values of the maximum lift-drag ratio (L/D)ma3C of 'the smooth wings increased-Wlth increasing

aspect ratio, throughout the range investigated in spite of the increased drag of the thicker root sections associated with the higher aspect ratios. The values of (L/l>)wajC for the wings of taper ratio 3 .5 with leading-edge roughness indicated the same trend; however, the values for the wings of taper ratio 2.5 with leading-edge roughness

HACA TN No. 1270

showed no gain when the aspect ratio was increased from 10 to 12, apparently "because of the larger increment of profile drag due to roughness on the thicker root sections of the wing of aspect ratio 12. The decrement in (L/D) due to roughness was considerably x ' max larger than the increment due to changing -the aspect ratio. The maximum lift coefficients decreased with increasing aspect ratio, mainly because of the associated increase in root thickness-chord ratio•

HSTR035DCTION

Elementary aerodynamic considerations indicate that wings of high aspect ratio are essential for efficient long-range airplanes. Structural considerations for such wings favor relatively thick root sections and high taper ratios. Sections •with large thickness-chord ratios have high profile drags, and high taper ratios usually result in impaired stalling characteristics. The aerodynamic advantages of high aspect ratio are thus partly offset by a design necessary to satisfy the structural requirements. Although the main aerodynamic effects of the design variables are readily calculated by lifting-line theory from section characteristics, considerable doubts have at times been expressed as to the absolute accuracy of the theory for determining an optimum combination of aspect ratio, taper ratio, and root thickness-chord ratio.

An investigation has accordingly been mado in order (l) to demonstrate the correlation of wing characteristics obtained by calculation and by wind-tunnel tests and (2) to show some of the effects of aspect ratio, taper ratio, and root thickness-chord ratio on aerodynamic characteristics. Seven unswept wings having KACA kh-series sections, aspect ratios of 8, 10, and 12, and taper ratios of 2.5 and 3.5 were studied. For six of the wings, the ratio of span to root thickness was held constant at 35 so that the root thickness-chord ratio increased with increasing aspect ratio and decreased with increasing taper ratio. The seventh wing combined the lowest aspect ratio and taper ratio with the highest root thickness-chord ratio of the other wings. The wing characteristics were calculated by an application of the lifting-line theory which allows the use of the nonlinear section lift curves as well as by the usual application of the theory which assumes linear lift curves.

SYMBOLS

G^ lift coefficient (L/qS)

NACA TN No. 1270

c^ section, lift coefficient (l/qc)

CD drag coefficient (P/q.3)

CD profile-drag coefficient (D0/qs)

Cm pitching-moment öö«?¥l<?ient (M'/^Sc*)

E Reynolds number (pVo'/n)

M Mach number (7/<t)

q. free-stream dynamic pressure ( TpV2J

p mass density of air

V velocity of air in free stream

L lift

I section lift

D total drag of wing

D profile drag

M' pitching moment ahout quarter-chord line

S wing area

c ' mean aerodynamic chord I '— / V Jo

c local chord

y distance from, plane of symmetry

"b wing span

H coefficient of viscosity

a velocity of sound

a angle of attack of wing root chord, degrees

NACA 'IN No. 15:70

cs root chord

ct ' conetruetlon tip chord

et twist~at construction tip

Subscript s:

min. minimum

max maximum

(L-0) at zero lift

WINGS

Seven wings of NACA kk-series sections with aspect ratios of 8, 10, and 12 and taper ratios of 2.5 and 3.5 were investigated. The wings had straight tapered plan forms with parabolic tips extending over the outer 5 percent of the semi span. There was neither dihedral nor sw»epj that is, the quarter-chord line was perpendicular to the plane of-symmetry. A typical^wing layout is shown in figure 1.

Six of the wings were constructed to have a ratio of span to root thickness of 35 with the root thickness-chord ratio varying between 0 .147 and 0 .2k't the saventh wing had a ratio of span to root thickness of 23.3 with a root thickness-chord ratio of 0-2k. The tip thickness-chord ratio was 0 .12. for all wlnga. Dimensional data for the wings are summarized in table 1. The designation for the vings is formed from numbers representing, consecutively, the taper ratio, aspect ratio, NACA airfoil series, and root thickness in percent chord. For example, in the designation 2.5~8-44,l6, the fir3t number "2.5" represents the taper ratio, the number following the first dash "8" represents the aspect ratio (approx.), the number following the second dash "hk" represents the NACA airfoil series, and-the final number "16" represents the root thickness in percent chord.

The wings were twisted to improve the stalling characteristics. For the wings of taper ratio 2.5, twistrwas introduced to give a Cj-margin of approximately 0.1 at the 0 .7 semispan station when ^ixo~s:

was reached at some inboard wing section. (See references 1 and 2.) For the wings of taper ratio 3.5,. calculations indicated that-the washout necessary to provide this cj-margin would cause excessive induced drag. The twist was therefore limited to 30 for thi3 group of wings.

NACA TN No. 1270 5

The wings were constructed of laminated mahogany and were finished with lacquer. Two surface conditions were provided for testing. For the smooth-model condition, the wings were sanded to an aerodynamically smooth finish. In order to simulate a rough- model condition, a leading-edge roughness similar to that established "by the Langley two-dimensional low-turbulence pressure tunnel was used. The roughness was obtained by application of No. 60 (0 .011-inch diameter) carborundum grains to a thin layer of. shellac along the complete span over a surface length of 8 percent chord measured from, the leading edge on both upper and lower surfaces. The grains were intended to cover 5 to 10 percent of the affected area. Some difficulty was encountered, however, in obtaining the same density of the grains for all wings. The roughness on the 2.5-8-^,24 wing was lighter than on the other wings and the aerodynamic characteristics of this wing are believed to be somewhat better than would be obtained with the desired roughness.

METHODS

Tests

The tests were conducted in the Langley 19-foot, pressure tunnel with the wings mounted as shown in figure 2. For all tests the air in the tunnel was compressed to a density .of approximately 0 .0055 slug per cubic foot. The test3 were made at several values of Reynolds lATttaS number between 1.5 x 10° and ].0 x 10°. The Mach number range was from 0 .06 to 0.25. The relation of Mach number to Reynolds number is given in figure 3 . The relation of Mach number to Reynolds number varied from wing to wing because the change in aspect ratio was accomplished by changing the chord while the span constant was held constant.

Measurements of lift, drag, and pitching moment were made over an angle-of-attack range from -k° through the angle of stall. Profile- drag measurements were made by wake surveys at 2k spanwise stations at several angles of attack covering a lift-coefficient range from 0 to 1.0. Flow separation on the smooth wings was studied by means of wool tufts placed at 20, k0, 60, 80, and 90 percent of the chord and spaced 6 inches spanwise on the upper surface of the wing. No studies were made of the flow separation on the rough wing.

Corrections for support tare and interference have been applied to all force-test data. Jet-boundary and air-flow-misalinement corrections have been applied to the angle of attack and drag • coefficient.'

NACA TN Ufo. 1270

Calculations

The characteristics of the wings were calculated from two- dimensional airfoil data "by the lifting-line theory. The required airfoil section characteristics at-appropriate Reynolds numbers were obtained from unpublished data from the Langley two-dimensional low- turbulence pressure tunnel. These section data were obtained at a Mach number not exceeding 0.17> so that compressibility effects are "believed to be negligible. The section data for the rough conditions were obtained for two sizes of carborundum grains so that the effect of idie variation of relative grain size across the span of the tapered wings could be taken into account in the calculations for the wings with leading-edge roughness. lift and induced drag characteristics were determined by a generalized application of the lifting-line theory which allows the use of-nonlinear section lift curves and by the usual, application which assumes linear lift curves. A correction to the lifting-line theory for the effect of chord of a finite- span wing was made by app3.ying the edge-velocity factor given in reference 3« The profile-drag and pitching-moment coefficients were obtained by using section coefficients at the corresponding section lift coefficients and integrating the loadings across the span. The procedure by which the wing characteristics were computed is given in detail in reference k. For the sake of brevity, the two applications of the theory mentioned previously are hereinafter referred to as the "generalized method" and the "linearized method".

Aerodynamic characteristics for the wings of taper ratio 2.5 were calculated by both the generalized and linearized methods for the smooth-model condition and by the generalized method for the rough-model condition. For the wings of taper-ratio 3-5» the characteristics were calculated only for the smooth-model condition by the generalized method.

RESULTS AND DISCUSSION

Comparison of Experimental and

Calculated Characteristics

The experimental and calculated lift, drag, and pitching-moment characteristics for the wings of taper ratio 2.5 and 3.5 are presented in figures k to 10 for the smooth-model condition. The experimental and calculated lift and drag characteristics for the wings of taper ratio 2.5 are given in figures 11 to Ik for the rough-model condition. Some of the important results of the comparisons are sunanarized in

HACA IN Ho. 1270

tables II and III. For "better accuracy, the experimental values of maximum lift-drag ratio (L/D) given in these tables were

read from faired curves of (L/D) against Reynolds number.

Typical calculated spanwise distributions of section lift coefficients at the predicted maximum lift, for estimating stall characteristics, are given in figure 15. Experimental stall characteristics derived .from tuft studies aro shown in figures l6 and 17 for all smooth wings.

In the linear lift-curve range, the characteristics calculated "by either the generalized or the linearized method would "be expected to "be the same. Differences in lift-curve slope and induced-drag coefficients were obtained, however, and are attributed to inaccuracies .in computing that arose in reading, fairing, and integrating plotted curves.

Drag.- A comparison of the calculated and experimental total- drag curves for the smooth wingB (figs, h to 10) shows that good agreement WSB obtained at low lift coefficients. Less satisfactory agreement was obtained at higher lift coefficients where the calculated drag was generally lower then the experimental drag. This effect was most pronounced for wings .of aspect ratio 8. As would "be expected, the same results are shown in a comparison of the calculated and experimental profile-drag coefficients. (Force-test profile-drag coefficients were determined by subtracting the induced drag coefficients obtained by calculation from the total drag coefficients measured by force tests.) The test values determined by wake surveys, however, are in excellent agreement with the calculated values. Possible reasons for discrepancy between force-test profile drag and calculated and wake .-survey drag are (1) errorB in corrections for support tare, interference, and stream misalinement, (2) inaccuracies in calculating induced drag and (3) inaccuracies in evaluating the drag at the wing tip from section data or wake surveys'".

Generally speaking, the agreement between calculated and experi - mental drag for the rough condition (figs. 11 to 1*0 was about the same as for the smooth, condition but was less consistent. In addition to the sources of errors mentioned before, errors in profile drag for the rough condition can easily arise from (l) inaccurate simulation of desired roughness in the wing tests and (2) inaccuracies in accounting for grain size in the calculations. These errors would also influence the lift characteristics.

For wings of the type investigated, the value of (L/D) is a max

predominant factor in determining the optimum design« As indicated in tables II and III, the calculated values of (L/D) were, for the

may case giving the greatest discrepancy, within 7 percent of the experimental

8 HACA TN No. 1270

values. From the preceding discussion of possible errors In the . determination of drag, even this largest difference "between calculated and experimental (L/D) appears reasonable.

Lift. - The differences "between the values of maximum lift coefficient-C-r obtained from tests and from calculation "by the

max generalized method (tables H and III) ranged from 0-02 to O.08 with an average difference of about 0.0^. The calculated values were generally lower than the experimental values. The maximum lift coefficients calculated by the linearized method are from 0 to 0.1^ lower than the. corresponding test values with an average difference of about 0-07- The maximum lift coefficient calculated by the linearized method is the wing lift coefficient at which some, section first reached maximum lift. The generalized method of calculation predicts the rounded lift curve peakB as were obtained by test in contrast" to the straight curves predicted by the linearizod method.

The agreement between experimental and calculate«! lift-curve slopes at-low angles of-attack (tables XT .-and III) is not altogether satisfactory. The correlation is good for the wings of aspect ratio 8. For the other wings, the calculated values were as much as k percent lower than the experimental values in some cases. Aside from experimental and computing errors, discrepancies may be due to the limi- tations of the edge-velocity factor in correcting for the effect of the chord in three-dimensional flow. The agreement between experimental and calculated angles of zero lift is excellent.

Pitching moment. - At zero lift the agreement between the experimental and calculated pitching-moment coefficients and momont- curve slopes is' generally good. (Sec table II.) At higher lifts, however, the experimental pitching-moment curves show larger increases in slope than the calculated curves. (See figs. k to 10.)

Sta]lina characteristics.- In order to obtain an indication of the stalling characteristics.öf the wings, an analysis of the type outlined in references 1 and 2 was made by comparing the predicted distribution of section lift coefficients at maximum" lift with the variation of section maximum lift across the span. A comparison of this type for the 2.5-10-W-.20 and 3.5-10-hk,l8.h wings is shown In figsjre 15. On the basis of the curves calculated by the ganoralized method, the maximum section lift- coefficients for those wings appear to be reached simultaneously over most of the span. The corresponding tuft surveys (figs. 16 and 17), which show trailing-edge separation or intermittent-separation over approximately tho same part r>£ the span, are accordingly in general agreement with the calculations; however, a more quantitative discussion of the agreement is not

NACA oasr No. 1270 9

possible In the absence of an experimental span load distribution and a correlation "between .section lift coefficient and tuft, behavior. The difference between the two calculated curves of figure 15(a) is sufficiently great to affect seriously any prediction of stalling characteristics. For this wing the generalized method predicts the maximum Bection lift coefficients to be reached simultaneously ever most of the span, whereas the linearized method indicates a considerable margin of safety at the outboard sections when the inboard sections have reached maximum lift.

The comparison indicates that the criterion of a c^-margin of 0.1 at the 0.7 semispan station, which appears to be satisfied on the basis of the linearized method, is not actually attained if it is to be assumed that the generalized method is more correct. If the margin cf 0.1 is necessary for good lateral stability and control, the stalling characteristics of the wing would be unsatisfactory according to the generalized method. On the basis of the tuft surveys alone, the stalling of these wings might be considered satisfactory since it 1B gradual and characterized by initial roughness and separation near the center and by fair flew at majcimum. lift.

Remarks,- Although calculated force and moment characteristics show some variations with respect to the experimental characteristics", the agreement is reasonable and is believed to be close enough to warrant their use in design. For calculating characteristics at high lifts, the method based on nonlinear section lift curves was more accurate than the method based en lin3ar lift curves. The results of the investigation indicate the need for more accurate methods for predicting flew separation on a wing. '_•

Effects of Aspect Ratio, Taper Ratio,

and Soot Thickness-Chord Ratio

The experimental characteristics of the wings are compared in figures 18 and 19. Calculated profile-drag coefficients are presented in figure 2C. The variations cf (L/^max with aspect ratio are shown in figure 21. The experimental variations of Cj\

and (L/D) with Reynolds number are given in figure 22. In the max following discussion the wings are compared at an essentially constant value of Reynolds number of approximately 3«9 X i0°. Although data included in table H and figure l8(a) are for a Reynolds number different from 3«9 X 10°, the comparisons shown by these data are essentially the same as for a Reynolds number of 3«9 x 106.

10 KACA TN No. 12?0

Drag. - The drag curves for the smooth wings (fig. 10) show the characteristic decrease in drag with increase in aspect ratio at moderate lift coefficients even though the profile drag was increased "by the thicker root sections of the higher-aspeot-ratio wings. Similar variations were obtained in the rough condition for the wings of taper ratio 3.5 and for wings of taper ratio 2.5 with aspect ratios 8 and 10. (See fig. 19.) The wing of aspect ratio 12 and taper ratio 2.5 had higher drags, however, than the wing of aspect ratio 10 except near the CT for (L/D) where the drags of the two

ij max wings were equal. The calculated data in figure 20 indicate that this effect is associated with the relatively large profile drag of the thicker root sections of the high-aspect-ratio wings in the rough condition.

The same variations in drag with aspect ratio are shown by consideration of the values of (L/D) in figure 21. For the wings

of taper ratio 2.5, both experimental and calculated values of (L/D) for the smooth condition increased with increasing aspect

' max ratio throughout the range of aspect ratios Investigated hut the values for the rough condition Indicated no gain in (L/D) when the aspect

max ratio is increased from 10 to 12. For the wings of taper ratio 3.5, the values of (L/D) for "both the smooth and rough conditions increased

max with increasing aspect ratio. Figure 21 also indicates that the harmful effects of roughness on (L/D) can readily exceed the

max "beneficial effects of increasing aspect ratio in this range; it may he noted, ho-wovor, that the roughness was somewhat extreme. Generally, there was little difference in (L/D) for corresponding wings of

max taper ratio 2.5 and 3-5 in the smooth condition hut in the rough condition the vaiues of (L/D) for the wings of taper ratio 3-5 wore

max consistently higher than those for the wings of taper ratio 2.5. This difference was probably due to the larger effect of roughness on the thicker sections of the wings of 2-5 taper ratio. The data in figure 22 indicated that Reynolds number generally had little effect on the OV^JJ^Y of the smooth wings and that increasing the Beynolds

number increased the (I>/Vt) „ of the rough wings.

Lift.- For "both smooth and rough conditions, the maximum lift coefficients of the wings with a ratio of span to root thickness of 35 decreased with increasing aspect ratio. An apparent decrease in Or

max due to aspect ratio alone is noted "by a comparison of wings 2-5-8-44,24 and 2.5-12-44,24 (fig. 22) hut this decrease was probably due to the fact that, when the two wings were at the same Reynolds number, the

NACA TN No. 1270 11

wing of aspect ratio 12 was at the higher Mach number. The wings of taper ratio 3-5 haA higher values of C^ than did the wings of

max taper ratio 2.5 "but the difference was usually negligible- The maximum lift coefficients increased with Reynolds number over most of the range- At the upper end of the range, the value of CL

max for some of the wings decreased, probably because of compressibility effects.

The lift-curve slope dCL/da for the smooth wings shots the

characteristic increase with irtc.^n.flTr>g_^p^jfr~ra,-h.-in (table II). For the rough wings (table III), the lift curves show little change in slope as a result of the large adverse effects.of. section -thickness ratio -

Stall characteristics.- The results of the stall studies in figures 16 and 17 show that all the wings have similar stall patterns. Separation of flow began at the trailing edge near the root and gradually progressed forward and outward until, at Cr > 30 to' kO percent

max of the wing was stalled. The effects on stall characteristics of increasing the taper ratio from 2.5 to 3-5 were very small.

CONCLUSIONS

The aerodynamic characteristics of seven unswept tapered wings were determined by calculation from two-dimensional data and by wind-tunnel tests in order to demonstrate the accuracy of the calculations and to show some of the effects of aspect ratio, taper ratio, and root thickness-chord ratio. On the basis of comparisons made at equal values of Reynolds number, the following conclusions are shown:

1. Reasonable agreement was obtained between calculated and experimental wing ,f orce and moment characteristics. The method of calculation which allowed the use of nonlinear section lift curves gave better agreement with experiment at high angles of attack than did the method which assumed linear lift curves. The two methods of calculation gave different spanwise lift distributions at mw-Mmum lift.

2. The values of maximum lift-drag ratio (L/D) of the smooth

wings increased with increasing aspect ratio throughout the range investigated in spite of the increased drag of the thicker root sections associated with the higher aspect ratios. The values of (L/D)m

12 NACA TH Ho. 1270

for the rough wings of taper ratio 3.5 indicated the seme trend; however, the values for the wings of taper ratio 2.5 showed no gain when the aspect ratio was increased from 10 to 12, apparently because of the larger increment of profile drag due to roughness on the thicker root sections of the wing of aspect ratio 12. The decrement in (L/D)__ due to roughness was considerably greater than the

increment due to changing the aspect ratio through the entire range investigated.

3. The maximum lift coefficients decreased with increasing aspect ratio mainly because of the associated increase in.root thickness-chord ratio.

Langley Memorial Aeronautical laboratory National Advisory Committee for Aeronautics ,

Langley Field, Ta., November 25,.19^6

REFERENCES

1. Anderson, Raymond F.: A Comparison of Several Tapered Wings Designed to Avoid Tip Stalling. NACA TN No. 713, 1939-

2. Soule, H. A.,-and Anderson, Raymond F.: Design Charts Relating to- the Stalling of Tapered Wings. NACA Rep. No. 703, 19^0.

3. Jones, Robert T-: Correction of the Lifting-Line Theory for .the Effect of-the Chord. NACA TN No.' 817, 19^1.

h. Sivelle, James C, and Neely, Robert H.: Method for Calculating Wing Characteristics by Lifting-Line Theory Using Nonlinear Section Lift Data. NACA TN No- I269, 19^7.

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NACA TN No. 1270 Fig. 3

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2.5-8-U.24

NATIONAL ADVISORY COMMITTEE FOt,AERONAUTICS

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Figure 3.- Relation of experimental Mach number to Reynolds number.

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Experimental (force tests) s

Experimental (wake survey) —^

Calculated (generalized and—N linearized methods)

^ \

<; x; A ^ \

/

-©—: fi^^^Fi

O G— j^' NATIONAL ADVISORY

CS. « COMMIT!

1 EE FOft AERONAUT

o >

CO

o

-2 .2 .4 .6 .8 1.0 t£ 1.4 /.$

(b) C against C . Do L 3


1.6 ^s-8-?^

1 A s s* J^f. i • •

? s /

1.2 s / / hi P

/

T'

i r\ j £ J f -\:

I.VJ

/ / EzperlUDtal'

Calculated-

(g*narallfc*d aethod)

0 " Jaloulatod— »Dsrallzad

/ 3 p • t

J f iwsthod) \ \ *j 1 I m I

•O j \ / i

4 I * T .1 f f 3

it

n t 1 .C

• f 0 /

J f. HKnONAL Aovtsom •

i>—' I—..J / TTi i i -a-

0 .02 .04 .06 .08 .10 -12 Co

.14 8 12 16

fa) C aeramst CL. a. and C -. ' ' L """" D' m

0 TI

On

Figure 8.- The experimental and calculated characteristics of wing 3.5-8-44,14.7 with smooth leading edge. R - 4.0 x 106.

3 CO

Q >

g CSD

O

.020

.016

.012

.008

.004

Q >

o

(b) C against C .

Figure 8.- Concluded. 4

00

1.6

1 A _>bi K U*T|

^1 r [*T3

1.2 / p

A 9/

1.0 ^ ^ •~^

<// >

^

/ — Ixp*ri«ntal—

ödxnOatod— (gSBOTBliJWd

Wthod)

\. r/

«rpurtJMOtiil-

OilaiilatBd —

Mthod)

J

1 .8

.6

? \, >f I /

\ \

/ '

I A 9 1 >

If \ _

4 / ^ F

,T

I / •

.2 d / i

J f II Ij

0 \ /' i / ¥

KATKMM. MVISOftY \

-2 x

t— f £ aMHirnEFM

1 1 «EMXUUT

1 es'1' _L

O .02 .04 J06 .08

CD

.10 .12 .14 -4 4 8

cc

12 16 0

(a) CT against C^, a, and Cra.

Figure 9.- The experimental and calculated characteristics of wing 3.5-10-44,18.4.with smooth leading edge. E. = 4.0 x io6.

3 m

i> o >

8*

O

.2 .4 .6 8

NATIONAL ADVISORY COMMITTEE KM AERONAUTICS

LO 12 1.4

o >

o

Do L"

Figure 9.- Concluded. 3 IP co

1.6 2" aq

1 A i-1

l.*T

.^^ <? P°

L2 y A" ,/ ^ }

J <] ̂»^ VA h t n ft A \-\J

—Caloalitftd

method)

/

}, Experlwntal .

Calculated

msthod.)

yA .8 4' / I

^ I ! 0 ^ Z^w i

.6 J ^ • P / /

A / It

.*T 1 W i

.2 / | /

(i

0 1 /

i / r i • ATlf^iftl \

-o 1 / <BHH1TT^ R* KMHWTKS i

0 D2 J04 .06 .08 .10 .12 .»4 ~4 0 4 8 12 .1 0 TI g q, •« c • %

>

(a) CL against CD, a, and Cm. s;

g Figur B 10.- The experimental and calculated characteristics of wing 3.5-12-44,22.1 with

smooth lfiariincr acitrp. "R = 4 fl vr 1fr3 r\a O

vO20

.016

.012

0^ "0

008-

004

u

-.2

« JQTC9 TOBl

D Make aurvey_«_

' Calculated (generalized

method)

NATIONAL ADVISORY COMMITTEE Ft» AEIKHAUTtCS

.4 .6 .8 C

1.0 1.2

s o >•

3

o

(b) C_ against CT. Do L


3

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M

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1.0 i v\ J\ Y /

! >• 4 yV

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•v

•v, Exparln»ntal V 4

.6 ', ! X

N Calculated {genaralizod mothodl /

if t /

r A .^

r 4 P \

.2 <• trj-

/ i i ' Y

1 /

0 \ i ) f

\ /

-2 1 A '

c r

MATIJMAL'AOVI^MY

r4 COMMITTEE FO 1 AEKWIJUmCS

1 1

2 era

0 02 04 06 08 JO J2 -4 0 4 8 12 16 20 5!

Figure 11.- Experimental and calculated characteristics of wing 2.5-8-44,16 with rough leading edge. R = 3.9 x 106. O

1.2 -

1.0 n/ *r" •0

^"•^

,/

A *

.8 .

& cx V

/ \ \ v. r /

t

.6 CL

/ \ x> \ (*

/

f \ V

Exparinenta] L •

i ? — uuomawu igraertuiieci aouioa; 9/

.t

6 /

.2 • {' /

0 T

i

I f V -2 \ J

. C Y NATIONAL ADVISORY

-A l COjMMITTEE FOR AERONAUTICS

o >

2 o1

o

0 02 04 06 08 .10 .12 -4 0 4 8 12 16 20 as

Figure 12..- Experimental and calculated characteristics of wing 2.5-10-44,20 with rough leading edge. R = 3.9 x 106.

3 Oq

to

ID

8

.4

CL

O

ki ^~

^

K X /

f cy v

\ V /

4 X px Exptriaontal -

ct/ rt /

i H • Ö'

? 1 I

v • J i T 1 \

\ ^

T

X < Y MTIONAL ADVISORY

COMMITTEE FOt AOMMUTICS

1 1 1 1 I 0 02 04 OS OS JO .12 .14 0 4 8 12 16

rigüre io.- Experimental and calculated characteristics of wing 2.5-12-44,24 with rough leading edge. R = 3.9 x ioß.

3 TO

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«^ O

3

—.—

ID o— -Q^^v •

£ y o yi

k K .6 / N IN r

1 y 1 N N

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a "I/ml

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2 i / V

1

n y \* I F

-2 /~ \ t ' ' lAflONAL ADVISORY

-4 COMMITTEE FT* AHWMWTTICS

i i i i i 0 02 04 06 08 JO .12 '4 0 4 8 12 16 20

Figure 14.- Experimental and calculated characteristics of wiog 2.5-8-44,24 with rough leading edge. R = 3.9 x 106.

Irr*

o >

*-\ o

-a o

3 ^

Fig. 15 NACA TN No. 1270

1.6

1.4

1.2

1.0

8

— °lmox

:•=•-

*~~ ~~ ~~*">

A Oj (generalized method)- X V

N

\ \

Oj (linearised method)— y\ \

\ \

.3 .4 .5 .6 Fraction semispan

(a) Wing 2.5-12-44,24.

.8 1.0

ci

1.6

1.4

1.2

1.0

.8

/ — clmax

/

s S ^•v

\ — c, (generalized method) \

\

\

NATI 5NAL ADV« »ORY CO r.

"" 1 AERO NAUTI C5

./ .3 .4 .5 .6 Fraction semispan

.7 .8 1.0

Figure 15.-

(b) Wing 3.5-12-44,22.1.

Calculated distribution_of c and c . over 1 U • max

semispan at CL max

TABIE I. - GEOMETRIC CHARACTERISTICS OF WINGS-

> O >

o*

Wing Taper ratio

Aspect ratio

ITACA airfoil Span (ft)

Area (eg ft)

M.A.C. (ft)

Geometric waehout

(leg) Boot

section Tip

eectiou.

2.5-8-44,16 2.5 8.04 4416 4412 15 27.994 I.99O 4-5

2.5-00-44,20 2-5 IÖ.05 4420 4412 15 22.393 I.592 3-5

2.5 -12 -44,24 2-5 .12.06 4424 4412 15 18.661 1.328 3.0

2.5-8-44,24 2.5 8.04 4424 4412 15 27.994 1.990 2.4

3.5-8-44,14.7 3-5 8.03 4414-7 4412 15 28.021 2.070 3*0

3.5-10-44,18.4 3-5 10.04 4418.4 4412 15 22.418 I.656 3.0

3.5-12-44,22.1 3.5 12.06 4422.1 4412 15 18.656 I.382 3-0

CO

o

NATIONAL ADVISORY COMMITTEE FOft AERONAUTICS

CO

TABLE II.- CALCULATED AMD EXPERIMENTAL CHARACTERISTICS OF VINOS WITH SMOOTH LEADING EDGE •K

Wing

°D m1n

Calculated

General- ized

Linear- ized

Experi- mental

(L/D) max (deg)

Calculated

General- ized

Linear- ized

Experi- mental

Calculated

General- ized

Linear- ized

Experi- mental

a. 5-8-W. 16 2.5-10-44,20 2.5-12-44,24 2.5-8-44,24 3.5-8-44 14.7 3.5-10-44,18.4 3.5-12-44,22.1

4.32 3-J9 2.87 4.32 4.00 4.00 4,00

x 10c 0.0080 .OO83 .OO88 .0084 .0076 ,0080 .0081

0.OÖ81 .OO85 .0087 .0084

0.0090 .OO83 .0091 .0081 .0074 .0082 .0088

29.4 32.0 32.6 28.0 29.8 32.4 33.9

28.8 31.1 32.6 27.6

-2.9 '3-0 -3-0

-3.6 -3.4 - 3.3

•2.8 -2.9 •3.1 -3.2

-2.9 -3.2 -3.2 -H -3.4 -3.5 -3.5 /

dCT "L_ .. 12& "mfT.nM

Wing Calculated

General- ized

Linear- ized

(L=0)

Experi- mental

Calculated

General-J Linear- ized lzed

Experi- mental

Calcu- late General-

ized

Experi- mental

Calcu- lated General-

ized

Experi- mental

n

o

^ r- ft L 1. - £ <;.5-o-i-t-io 2.5-10-44,20 2.5-12-44,24 2.5-8-44.24 3.5-8-44:14.7 3.5-10-44,18.4 3.5-12-44,22.1

3.49 2.87 4.32 4.00 4.00 4.00

lu- ll. 0823 .0827 .0848 .0795 .08IÖ *0833 .0852

ö .0815 .0028 .0836 .0780

.0860

.0870

.0705 ,08l2 .0852 .0870

1.41 1.31 1.35 1.57 1.43 1.37

1.4Ü I.36 1.26 1.30

1.54 1.43 s 1.27 1.37 1.54 1.45 1.33

0.0ÖY .006 .016 .014 .008 .008 .015

0.012 0 .021 .021 .011 .020 .015

-ö.Oyj -.087 -.085 -.083 -.092 -.089 -.085

-O.O99 -.095

RATIONAL ADVISORY C0MH1TTBB FOR AERONAUTICS

TABLE. Ill.- OALCtEATED AHD EXPKRIMEiraAL CHARACTERISTICS OP VIMS WITH ROUGH LEADIBO EDGE

Wing R

ümln ft/0) , max

afL^)) (dog)

dOL

dot CL max

Calcu- lated (generalized)

Experi- mental


Experi- mental


Experi- mental


Experi- mental


Experl- nental

2.5-8-44,16

2.5-10-44,20

2.5-12-44,24

2.5-8-44,24

3.5-8-44,14.7

3.5-10-44,18.4

3.5-12-44,22.1

3.90X106

3.90

3.90.

3.90

4.00

4.00

4.00

0.0129

.0137

.0145

.0137

0.0135

.0133

.0142

.0126

.0112

.0122

.0130

22.8

23.9

22.5

20.3

21.6

23.6

23.6

20.5

23.0

24.7

25.6

-2.7

-2.6

-2.5

-2.6

-.2.6

-2.8

-2.6

-2.7

-3.2

-3.2

-3.1

0.0778

.0760

.0763

.0701

0.0774

.0796

t

.0792

.0732

.0785

.0790

.0795

1.18

1.03

.88'

.91

1.22

1.08

.89 1

.99

1.26

1.10

.99

> Q >

Cv3 -<] O

HATI0HAL ADVISORY COMMITTEE FOR AERONAUTICS

Trailing edge

^—Lsoding edge

Trailing edge Root'Ohord Una (rtfltnence phntO

Charier cfKM /jha

Tip-chord lino

§'s- P°*d <f tongenctf

NATIONAL AOVBOftY COMMTTEE FM UMWUTtCS

Winq- tip plan form \ctetofi v/ew)

Figure 1.- Layout of typical tapered wing.

3

o r> H

o

i *

äü

2ft —

<Z0\

r/6 ~- '1- iL/D - £ /.<? ~ 7

/? jf &/- A -

4 ö /2 a

26

24

20

,/6

•12

.8

4

0

S-

Rxjghflw Cross fbv/6

'4- ö 12 ib 20 24 CO

3bfled (nlermitlsnto, dall 4 Ö 12 16 3} 34

00

2& 1 1 1 1 1

M -

2ß

Lo (*?!•} _ -,-ä — #—

*• L2 *>

*->*• - 3Z A "

"4 ö (2 16 2DM 00

CL=aQ5

3g3^W.'.';.'il.L*ra£Si

a?=Gö' cL=0Q3 ~ a?=äff c^ioi

o >

o

00=0.7* CfOÖS

Uft.ll "t

<2a^/ ä1^^ c^as

V- • • 11 •• .i'JW.'-'JA

QDmr CLH40

^ 3) ^TZ

W^/50* q=!27

ZZB

(XM3LT

q~i5ö (r~tä4- öf/35 a?=/T2- q~i4r oo=/io' q=&s oc=/6.r (a) Wing'25-8-44,161 (b)Wing 2,5-8-44,24, (c)Wing 2.5-10-44,204 (d) Wing 2.5-l2-44,24i

R~5.75x.lÖ. . R* 5.69x10'. R-4.61 x /0'. R-3.85 x 10*. JSSiiSSm

3 *

OS

Figure 16.- Stall progression for wings of taper ratio 2.5.

Fig. 17 NÄCA TN NO. 1270

Rough flow

2.8

2.4

2.0

CL 1.6

1.2 .8 .4

^ ^ ^

X'

8 12 16 20 oc

1 Cross flow

2.8

24

2.0 CL 1.6

1.2 .8 .4

^

Intermittent Stall

^ ^

8 12 16 20 oc

'L

Stalled

2.8

2.4

20

-

.... - ...

....

1.6

1.2 1

... .8 4

—

8 12 16 20 oc

CL=63 cc=4.6 Ci =.80 cc=6.6 CL=98 cc=8.5

CL=I.32 cc=l4.2 CL=I.36 oc=l5.0 C|_=l.23 oc=l2.7

CL=I.43 oc=l6.2 CL=I.4.4 cc=l7.0 CL=I.3I cc=l4.8

CL=I.5I cc=l8.3 CL=I.46 oc=l9.0 CL=|.37 oc=l6.8 NATWKAL AOVtSORV

COHWTTU r« AEMUVDCS

CL=I.5I cc=2Q3 C, =1.45 cc=2l.0 CL=I.36 cc=l8.8 (a) Wing 3.5-8-44,14,7. (b) Wing 3.5-10-44,18.4. (c)Wing 3.5" 12-44,-22=1.

Figure 17.- Stall progressions for wings of taper ratio 3.5. R =t 4^0 x 106.

Q r

o

to

o

.02 04 06 D8 Co

Figure 18.- Effect of variations in aspect ratio and root thickness-chord ratio on characteristics of wings with smooth leading edge.

3 '

00

(b) Taper ratio 3.5; R = 4.0 x 106.


crq

CD

O !>

CO

O

CL

l.*t

1.2 ^ X

«^ /

?k>>

ND >

f.O ! */ ̂

i— A -A r.

! i\ .8 j 1 *

$ k V

.6 v s\ UM

^ A ».5-10-44,20

• 8.5-12-44,24

V X

nac

\

V — 0 2.5-8-44,14—

/

.4 \

|— • 2.J-12-4J .31 •7

.2

0 "

-.2 NATKMU. ADVISORY ;i

-4 • I 11 1

0 02 04 06 08 Co

JO .12 8 12 cc

16 20 0 Cm

'J

>

%

to O

(a) Taper ratio 2.5; R = 3.9 x 10 .

Figure 19.- Effect of variations in aspect ratio and root thickness-chord ratio on characteristics of wings with rough leading edge. crcj

CD

(b) Taper ratio 3,5; R = 4,0 x 10


.6

4 t~>-

CO

2 >. O >

o

O

028 Wing

1

• 2,5-8-44,16

nP4 2.5-12-44,24 .l/£"r

/ /

.020 / L.E. rough

/ /

.016 /

/ /

'

y '

.012

> *K

^ -. -•- .

*

-"• L.E. smooth

.008 __ _

, ,-*•

~~* • *— - ' i

NATIONAL ADVISORY

004 CONMITT n 1 AERONAUTICS

] 1

3 > o >

o

CO

o

t£ .4 .5 .0 Z0 1.2 14 1.6

Figure 20.- Comparison of calculated profile-drag coefficients for smooth and rough wings.

13 oq

W O

Fig. 21 NfiCA TN No. 1270

(L/D)

36

32

28 max

24

20

L. E. smooth

L. E. rough

Experimental

Calculated (generalized method)

-— Calculated (linearized method)

8 9 10 II Aspect ratio

(a) Taper ratio 2.5.

12 13

(L^l

36

32

28

max 24

20

L. E. smooth _^- -

• —

L. E. rough

... NATIC >NAL ADVIS ORY CO» 1MITTI :E FOR AERO HAUTK :s

/£ 13

Figure 21.-

8 9 10 II Aspect ratio

(b) Taper ratio 3.5.

Variation of (L/D)_____ with aspect ratio. Ratio of span

to root thickness, 35.

NACA TN No. 1270 Fig. 22a

max

(L/D) 1 ' max

36

32

28

24

20

A 2.5-10-U,20

a 2.5-12-U,24

O 2.5-8-U,24

\ \ o

—rft—

•

A z \ T& L. E. smooth

_Q_ -O- G

^A •• -A

ACT

___ £3

<2 L. E. rough

o- '—o^

—O O —• -

— O -O

3 4 R

(ä) Taper ratio 2.5.

5 7*/0

NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS.

Figure 22.- Effect of Reynolds number on maximum lift coefficient and maximum lift-drag ratio of a series of wings.

Fig. 22b NACA TN No. 1270

1.6

1.4

Ci I 2

.8

36

32

H, 28 max

24

20

-tx -©•41

-9-

Wing

O 3.5-8-44,U.7

A 3.5-10-U,18.4

a 3.5-12-U,22.1

L. £. smooth-

L. E. rough


3 4 5

R

(b) Taper ratio 3.5.


7x10 6

: 1S0IM FOR« 69 (B (CUT)

• Ileely, Robert H. Bollech, 3. V.

AUTHOR(5)

DIVISION: Aerodynamics (2) SECTION: Wings and Airfoils (6) CROSS REFERENCES: Sings - Aerodynamics (99150)

A¥0= 54S0 ORIG. AGENCY NUMBE

TM-1270

REVISION

AMER. TITLE: Experimental and calculated characteristics of several IIACA 44-series wings witii aspect ratios of 0, 10, and 12 and taper ratios of 2.S and 3.5

IFORG-N. Tm.Es

ORIGINATING AGENCY: I.'ational Advisory Committee for Aeronautics, »'ashington, 1). C. .TRANSLATION,

COUNTRY U.S.

LANGUAGE |fORG'N.OA55 Eng.

a S.OASS. Unclas3.

DATE PAGES IUUS. 'ay'47 47 55

FEATURES ;jhctos, t£bles,diagrs, graphs

ABSTRACT Aerodynamic characteristics of seven unsvrept tapered wings wore ctatemincd by calc.ila

tiens from two-dimensional data and by Tdnd-tunnel tests, results of a comparison between the tests and calculations are shown by curves and indicate that reasonable agreement was obtained betTTeen calculated and experimental wing force and moment characteristics. The method of calculation which allowed the use of nonlinear section lift curves gave better agreement Tdth experiment at high, angles of attack than did the method which assumed linear lift curves.

MOTE: Requests for copies of this report must be addressed to N.A.C.A., Washington, 0. C

T-2, HO., AIR MATERIEL COMMAND AlR VECHNICAI DNDEX WRIGHT FIELD. OHIO. USAAF WMMl MAO 47 ZtK

unclassified ad number limitation changes · sections, aspect ratios of 8, 10, and 12, and taper...

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