A comparison of the calculated profile drag coefficients of various low-drag wing sections

TECHNISCHE HOGESCHOOI* VLIEGTU1GP.0UWK.UNDE Kaaaakuaat 10 - DEUT

- 1 JUNI 1S53

' P " r : TECHNISCH?^ "^•"

LÜCHT¥AiiriT-TECHNISCHE HOGESCHOOL DELFT Kluyverweg 1 - 2 6 2 9 H S DELFT

T..»«ox «. n,...„ .,., REPORT N o . 3 5 .

LUCHTVAART- EN RUIMTEVAARnECHMIEK

BIBLIOTHEESC

Kluyverweg 1 - DELFT APRIL -1950.

T H E C O L L E G E O F A E R O N A U T I C S G R A N F I E L D

A C o u i p a r i s o n o f t h e C a l c u l a t e d P r o f i l e D r a g C o e f f i c i e n t s o f V a r i o u s Low-Drag 'Ving S e c t i o n s , "

b y

-E . I!, Dowlen. D«C.Ae, D e p a r t m e n t o f A e r o d y n a m i c s .

— o Go—

SlI lARY

The profile drag-coefficients of a number of low-drag wings v/ith straight trailing edges have

been calculated.

A comparison is made with other low-drag and conventional sections which indicates an increase in profile drag, for a given transition point position, with rearward movement of the position of maximum

velocity and with increase of trailing edge angle, Some experimental results obtiined at low Reynolds

number are included for couiparison.

A shortened method of calculating the

profile drag coefficient of an aerofoil is developed.

s Part of Thesis submitted for the College of Aeronautics Diploma, 1 9U9

-£-yiOTATION.

c = Aerofoil chord. t = A e r o f o i l thickness. X = Distance along chord. y = Distance n o r m a l to chord. s = D i s t a n c e along surface. Gp^ = D r a g coefficient.

Cr, = P r o f i l e drag coefficient. 0

u = Local v e l o c i t y inside b o u n d a r y layer. U = Local v e l o c i t y outside "boundary layer.

U-^ = Free steam velocity. p = Density.

V := K i n e m a t i c viscosity.

5 = B o u n d a r y layer t h i c k n e s s .

f^-; ^ . •

0 = Momentum thickness = / 77(1 - ^•è)&y.

R = Aerofoil Reynolds number = U^c/v.

R, = Boundary layer Reynolds numher = U„ö/v.

RQ = Momentum thickness Reynolds number = U'd/v.

Kg = Momentum thickness Reynolds number at transition. n = Constant in equation for skin friction coefficient. k = Constant in equation for skin friction coefficient. b = (1+n)k/R^'\

p = Correction f a c t o r f o r i n t e g r a l I^ = (n-0-2)/i|..

-0- 23 a = B'actor = (IJ/IL,) ^ ^ 0 T . E . I . =

X *

'(U/UQ)^

d(s/c).

(U/U^) d ( s / c 1 .

Suffix 'T.E.' r e f e r s to c o n d i t i o n s at trailing edge. Suffix 'T.P.' r e f e r s to c o n d i t i o n s at transition point.

ïtUHNiót^nc nOGESCHCX:)L VLIEGTUIGBOUWK.UNDE Kanaakuaat 10 — DELfT

-1 m\ 1353

3

-1. Introduction.

Prom the results of previous calculations (Ref.1 -k) it appeared that for an aerofoil designed with maximum velocity far back from the leading edge,

the drag (for a given transition point position,

thickness chord ratio and Reynolds number) was greater than the corresponding drag for a so called conventional section. This increase offset in part the advantage gained from the greater extent of laminar boundary la-yer on such an aerofoil. It was also suspected that the shape of the trailing edge (concave, straight or convexVmight have an influence on the profile drag

(Ref. 10).

In this report the results of a number of

calculations of the profile drag of various smooth wings in incomprossible flow are presented. The majority of these sections had straight trailing edges.

Wind tunnel tests were made on four o^ these aerofoils (at a Reynolds number of about 1 x 10"^) in order to compare experimental and calculated results. Thüse tests v/ere not conclusive but demonstrate some of the difficulties to be met when trying to fix transi-tion with wires at lovï Reynolds numbers.

2. Scope of Calculations.

The values of the profile drag of a nuuber of symmetrical aerofoils at zero incidence were calcu-lated by a method that is described in the Appendix. Some of the sections considered were of the N. A.C.A. 6 A series of low drr^g v/ings v;ith contours which are

straight in the neighbourhood of the trailing edge (Ref.5). Representative profiles are illustrated in Pig.1 and

pressure distributions are given in Pig.3. The four sections indicated by the prefix EGA also had straight trailing edges. These last were tested in the wind tunnel to check the theoretical calculations. Their ordinates are given in Table I and Pig.1, and their pres-sure distributions are given in Pig.2. Thickness-chord ratios of 10, I5 and 20 percent have been covered by the calculations and in each case values of profile drag have been computed for Reynolds numbers of 10°, 10' and I08

and transition points from 0*2 to 0-8 chords from the leading edge.

3. Results and Discussion of Calculations.

3.1. The results of the calculations are given in Table IT and are presented graphically in Figures i4.,5,6 as values of drag coefficient - vs - transition point

position for each aerofoil at Reynolds numbers of 10^, lo"^ and 10^.

An alternative method of presentation as used in Ref. 11 is shown in Figures 7 - 1 1 where >, is the ratio of the profile drag coefficient of the wing to the pro-file drag coefficient of a flat plate with the same

transition point position. The variation of y with Rey-nolds number is small and a mean value of .'1 has been taken.

-k"

3. 2, Position of Maxim-urn Velocity.

It is convenient to use the position of maxi-mum velocity on the aerofoil surface as a parameter rather than the position of maximum thickness. Most of the sections used were designed to have peak suctions at some fixed position. It is immediately obvious from the results that, for a given transition point position, thickness-chord ratio, and Reynolds number, rearward movement of the maximuin velocity position has the effect of increasing the profile drag of aerofoils for which the shape of the velocity distribution aft of the peak suction is similar (see Pigs. I4.-6, 12). This effect tends to decrease with forvmrd movement of the transition point position. Figure 12 illustrates the variation of profile drag with transition and peak suction position for I5 per-cent thick aerofoils at R = ^o'^. A line is drawn on the figure to indicate the variation in drag coefficient of

sections v/ith transition at the peak suction position. It is evident that moving the transition point aft by de-signing the section with a far back peak suction gives a smaller reduction in drag than that obtained with a

corresponding transition shift on a conventional type of section.

3. 3. Effect of Trailing Edge Shape.

The influence of the shape of the trailing edge on the profile drag of the section is illustrated in Fig. 13 where a comparison is made between N. A. C. A. 6I4A - 012 /straight trailing edges) and N. A. C.A. 6I4. - 012

(cusped trailing edge). It appears that the profile drag is reduced a little by reduction of trailing edge angle. The effect is more marked for far aft transition point positions (see Ref.5 for a comparison of the velo-city distributions on these two aerofoils). This effect can be associated with the fact that as the trailing edge angle is increased and the velocity distribution curve becomes more rounded, the value of the integral I2 (the

predominant factor in the expression for C^ (see the Appendix) ) increases and hence so does the^profile drag coefficient.

3. k' Equivalent Transition Point Position.

A convenient way of comparing the effect of changes in aerofoil shape on the profile drag is by consideration of the 'equivalent transition point posi-tion'. This is defined (Ref.10) as the mean transition point position required to give the same profile drag

coefficient as that of a conventional section with a specified mean transition point position, other things

(thickness—chjord ratio and ReyrLolds number) being equal. In effect, f:jr the same drag coefficient the transition. point on a lov; drag Vv^ing lies behind the transition point

on a conventional section. This rearward shift is plot-ted in Fig, 11+ for a niimber of wings, including those of Refs. 2 -ïj..'

Tvvo main effects are apparentt

-a. The rearv\fard shift of the equivalent transition

TECHNISCHE HOGESCHOOL.

VLIEGTUlGBOUWf^UNDE Kcmaolstiaat 10 — DELiT

-5-point is least for transition p-olnt-. positions near the leading edge.

b. The maximum value of this rearward shift is in the main a function of position of peak suction, al-though some effect of trailing edge shape is apparent

(cf, N. A. C.A. 6ij. - 012 and N.A. C.A. 6i+A - 012). U. Scope of Experiments.

Drag measurements were made, using a wake survey method, for the four EGA sections. The models Y/ere of wooden construction of 15 Inches chord, 30 inches between end plates in a spanv/ise direction, and were

tested in N0.IA tunnel at Cranfield. * Transition vras observed by the china clay technique, Spanv/ise wires O.Ql inches in diameter were used to cause transition in

the boundary layer. The wires were fixed to the wing surface by cellotape.

The results, corrected for wire drag are shown in Pigs. 15 - 18. Pig. 19 shoves drag as a function of

'V'ire Transition Point' i.e. on the assumption that transition occurs at the v/ire. It would appear from the delay in the drag rise as the wire is moved forwards that transition at the low Reynolds number of the tests

(1' 1 X 10^) is taking place over an appreciable region behind the wire and is not immediately provoked by the wire.

Tests were also made v/ith a grid of fine string placed upstream of the model to produce a turbu-lent stream so as to move the transition point forward vifithout the use of the vi^ires fixed to the surface (see Pigs. 15 - 18). Transition ims again found to be in-distinct and took place over a large region (this was checked by the readings of a surface pitot).

5. Discussion of the Experimental Results.

As already remarked at the lov; Reynolds num-ber of the ter.ts transition from laminar to turbulent

flow takes place over i^uite an extensive region. The transition points given by the china clay and wire tech-niques lie at different points in this region, the diffe-rence appearing to be a function both of the local pres-sure gradient and also of the boundary layer thickness. In general the v/ire transition point, defined as the wire position for vi'hich the drag just begins to increase^ with further forward movement of the v;ire, lies some

1 2 - 2 2 percent chord ahead of the transition indicated by the china clay. Jones and Brovm (Ref. 6) find that

the wire transition point lies som^e 1 3 - 1 ? percent ahead of the calculated transition -ooint. The degree of tun-nel turbulence is probably an important factor.

X 'ihe critical Reynolds number of a 6 inch aphere in this tunnel is about 3 x 10^.

f

-6-An^.exaroination of Pig. 19 shows that the shape of the curve"of drag coefficient variation with wire position as measured is similar to the calculated curve of drag coefficient variation with transition point posi-tion and lies roughly parallel to it. The same broad

conclusions about the effect of design maxim\im suction . « position apply.

Some flight tests made at the R.A.E. (Ref.3)>. • where tape was used to fix transition, exhibit curves

of very much the same shape as those found in the present tests, the tape transition point lying some 10 to 15

percent of the chord ahead of the calculated transition point. No such differences were observed in the tests of Ref. 5 at high Reynolds number, and it v\rould seem that further experimental work is required on the effect of

spanwise turbulence wires on transition.

CONCLUSIONS.

1. The calculated profile drag co»?fficients of the series of low drag v/lngs here considered are greater -in all cases (for the same transition po-int position, thickness chord ratio and Reynolds number) than the corresponding profile drag coefficients of conventional sections (Pig. lit.),

2. This increase is a function in the main of the position of maximum velocity of the particular section -far back positions giving higher drag coefficients - and is most marked for positions of maximum velocity aft of about 1+5 percent chord (Fig. 12).

3. This brings into question the desirability of designing wing sections with peak suctions further aft than about 0.1+5, in view of the practical difficul-ties of ensuring and maintaining the surface finish and freedom from waviness required for such extensive regions of laminar f lov»-. We must also note the adverse effects on control characteristics and G-r ^^^x. associated with the far back positions of maximum thickness required. i+. Changes in the shape of the trailing edge also produces changes in the profile drag coefficient. Pro-file drag is lowest for a cusped trailing edge and

in-creases as the trailing edge becomes more convex. The ",• increase is most apparent for far aft positions of transi-tion (Pig. 13).

5. The effect of thickness chord ratio on the profile drag is reduced for far back transition point

positions, especially at high Reynolds numbers (Pigs.7-11).

TECHNISCHE HOGESCHOOL

VUEGTUIGBOUWKUNDE Koooalstiaat 10 — DELrT

7

-6. Experimental results at low Reynolds number indicate a large region of transition, but confirm

q\ialitatively the predicted increase of drag coefficient v/ith far back peak suction positions and confirm the reduction of this effect as the transition point moves forv/ard (Pig. 19).

7. Further experimental v/ork is required to check the calculated resul-ts, especially at high Reynolds num-bers and in flight, Preliminary experiments to

investi-gate in detail the effect of spanv/ise v/ires are desirable. 8. The calculation of aerofoil profile drag may be considerably shortened with no significant loss in accuracy. The profile drag coefficient may be expressed as a function of two integrals of the velocity distribu-tion (see the Appendix).

-8-REFERENCES 1. 2,

3.

U.

6. 8. 9. 10. n. B. Squire A, D. Young N. E, V/ int e rb o 11 om H.B. Squire R.C. Lock A. P a g e W.S, V/alker L.K. Lof t i n , J n r . R. J o n e s A. P . Brown G. E. N i t z b e r g N e a l T e t e r v i n A. D. Youncr I , Sub-Gommittee of the Royal Aero-nautical Society Royal Aeronautical Society

The Calculation of the Profile Drag of Aerofoils, R and M 1838

(1937).

Note on Further V/ing Profile Drag

Calculations. R.A.E. Re-p. BA. ^

63k-(19i+0).

Note on Profile Drag Calculations for Low-Drag Wings v/ith Cusped Trailing Edges. R.A.E. Aero 2130

(19U6)

and Corrigenda (191+8). Experiments on Laminar-flow

Aerofoil EQH 1260 in the ¥/illiam Proude National Tank and the 9 x 7 ft. V/ind Tunnels at the National Physical Laboratory. R and M 2165 (19i4-2).

Theoretical and Experimental

Data for a Number of N.A. C.A. 6k

Series Airfoil Sections. N.A. C.A. T.N. 1368 (191+7).

Drag and Transition Experiments on Two Joulcowski Aerofoils in the Com-oressed Air Tunnel.

R and M 2110 (191+1 ).

A Concise Theoretical Method for Profile Drag Calculations,

N. A. C.A. ACR Fob. 191+1+. AI^.C 7707.

A Method for the Rapid Estimation of Turbulent Boundary Layer Thick-ness for Calculating Profile Drag. N.A. C.A. ACR LUG11+ (191+1+).

Skin Friction in the Laminar Boundary Layer in Compressible Flow. College of Aeronautics

Rep. No. 20 (191+8). Note on the Drag of Low Drag Wing Sections. Aerodynamics Data Sheets.

Aerodynamics Data Sheets. Wings 02.01+. 0 2 ,

-9-A P P E N D I X

Method of Calculation,

A1, The method used w a s essentially the same a s that of Ref,3> b u t w a s modified to reduce the labour involved. In R e f . 8 the expression:-/xT.E.

<^/°'.B.= w b « -

^

/ ("/"o)'""''""^tU)

0 T.E. ^' ••''T.P. ^H+2)(n+1) T.P. l/(n+1)

(O

is used to find the momentum thickness of t h e boundary layer at the trailing edge.

•By combining this relation f o r the turbulent boundary layer w i t h the equation

(6/0) 0'661+ '^•P- R''(U/U,,)^ 0 T.P. /-T.P.

I

(U/UQ)5d(s/c)

•''0 (2)

for the laminar boundary layer and v/ith the expression

C = 2(0/c)^ ^^ 1(U/U.)

0 T.E.

L

T.E.

2

wq c a n derive a n expression for the profile drag coefficient,

(3)

It w a s found that for a symmetrical aerofoil this relation could b e replaced v/ith no loss of accuracy b y the expression

t n+1 3'5(n+1)

C33 = i|a |b(1+p)I._, -f (0/c) (U/U )

"" ' - T.P. ^ T.P.

1/(n+1)

ik)

s This equation i s a c l o s e approximation to one that

can be derived from Ref.9.

-10-where

a = (U/U >"°'^^, (5) ^' T.E,

•b = i-^+n)]^ ^ ^ function of R Q and R, (6)

1+p = function of (RQ . ) and is a

correc-' tion factor, (7) lp = / '"'(u/u ) d(s/c) (8) and, as in (2)

(9/c:

0-661+ T.TD. R^(U/U^)-T,P, v/here /'T. ^. 5

:^

=1

"*(U/Un) d(s/c).

'O- (9)

The quantities b(1+p), b, n and a are given in graphical form in Figs.20 - 22 and the integrals I. and In may be rapidly evaluated for any given pressure distribution,

A specimen calculation is shov/n in Table IV, Here the integrals I^ and I2 are evaluated with respect to x/c rather than s/c. It was found that this sim.pli-fication resulted in an error in the calculated values of less than 1 percent for a 20 percent thick aerofoil

(Table III).

A direct com-oarison with the m.ethod of Ref. 3 was obtained by calculating the drag coefficient for an N.A. C.A. 65,1-012 aerofoil at R = 10^ with transition at 0'3c and 0.7c. The values obtained were O.OO652 and 0.00290 respectively. From Ref. 3 v/e obtain O-0065i; and 0.00286 (interpolated).

A Further Development. .A2.

form C

We can v/r it e "equations (1+) and (9) in the

^0 = a F

h' '-:

(U/Up) , R _{^ T.P.}

n-

• « • • (10)

Values of P are given in Table VII f or—vajrLoua^ values

of I. , I^ and (U/U,0

•1 ₀

T.P.

and R = 107,

and are plotted in the form of a lattice in Pig.23. Use of such a lattice and equation (10) enables the value of

C-Q for a given aerofoil to be obtained in a very short time, the calculation consisting mainly of the evaluation of the integrals I^ and To. Comparison of results

obtained using equation (TO) with those of Ref.2 shows equation (10) to give values of G D some 2 to 1+ percent too high (Table III). To cover a range of Reynolds numbers a series of such lattices would be required.

T A B L E I .

Ordinates of EGA Sections.

. / - 1 A / u 0 1' • 0 0 5 010 015 ' 0 2 5 050 0 7 5 100 150 200 250 300 350 lj.00 • I45O • 500 •550 600 700 800 900 950 000 y / o EGA 1030 ] 0 . 0 0 9 1 . 0 1 2 8 . 0 1 5 6 • 0 2 0 0 . 0 2 7 6 . 0 3 3 1 • 0 3 7 3 •Oi^.33 •01+71 •Oi;91 • 0 5 0 0 • OU83 •0IJ.31+ . 0366 • 0280 • 0 1 9 3 • 0 1 0 2 • 0056 • 0 0 1 1 y / c SCA 1050 0 . 0 0 7 1 0099 0122 0156 0 2 1 8 0 2 6 3 0 3 0 0 0 3 5 7 01+00 01^33 Oi+58 OU77 01^90 0iL^98 0500 01+96 01+86 01+38 0329 0 1 7 5 0091 0011

20 percent thick

s e c t i o n s have a l l

y/c m u l t i p l i e d by

tv/o.

EGA i n ^ n A As f o r 1030 u n t i l . 0500 .01+ÖU .OUU"! • 0 3 8 0 • 0 3 0 5 . 0 2 1 9 • 0121 ' 0 0 6 8 • 0011

T A B L E II .

CALCULATED PROFILE DRAG COEFFICIENTS.

AEROFOIL SECTION NACA 63A010 INACA 6i+AOlO INAGA 65AOIO NACA 63AC15 NACA 6i+AOl5 JNACA 65AC 15 EGA 1030 | E C A 1050 Ec, = ' ° ' T . P . 0 . 3 0 - 5 0 . 7 0 - 3 0 - 5 0 . 7 0 - 3 0 - 5 . 0 . 7 0 . 3 0^5 0^7 0 . 3 0 . 5 0 . 7 0 - 3 0 - 5 0 . 7 0 - 2 0.1+ 0 . 6 0^8 0 - 2 O'k 0 - 6 0^8 •00956 •00752 • . 0 0 5 5 9 . 0 0 9 6 2 •00765 ! . 0 0 5 6 9 . 0 0 9 8 0 . 0 0 7 8 0 •00571 .01071+ •OO813 .00571+ . 0 1 0 8 2 . 0 0 8 3 3 .00591+ . 0 1 1 0 6 . 0 0 8 5 9 . 0 0 6 1 3 • 0101+0 . 0 0 8 5 5 . 0 0 6 5 2 .001+82 . 0 1 0 9 2 • 0 0 9 3 5 • 0 0 7 3 3 • 0 0 5 0 5 R„ = 10"^ T . P . 0 0 0 0 0 0 0 0 0 0 0 0 ' 0 0 0 0 0 0 0 0 0 0 0 0 0. 0. 0 0 0 0 0 0. • 1 •3 •5 •7 • 1 3 •5 •7 • 1 3 5 7 1 3 5 7 1 3 •5 7 1 3 5 7 1 h 6 8 1 k 6 8 _ .__ _ % _ .0071+5 . 0 0 6 0 3 • OOi+36 •00235 •0071+2 •00611 •00/|42 0 0 2 9 0 007i+5 0 0 6 1 5 001+59 00291+ 0 0 8 1 6 00656 001+57 0 0 2 8 7 0081+3 00681 001+73 00291+ 0 0 8 5 3 00700 001+97 00306 00732 00512 00351+ 00225 0071+1 00572 001+11+ 00239 R, T . P 0 . 1 0 . 3 0 . 5 0 . 7 O ' l 0 ' 3 0*5 0 . 7 0 . 1 0 . 3 0 - 5 0*7 0 . 1 0 . 3 0 . 5 0 . 7 0 - 1 0 . 3 0 . 5 0 . 7 0 - 1 0 . 3 0 - 5 0 . 7 0 . 1 0.1+ 0 . 6 0 - 8 0 . 1 0'i+ 0 ' 6 0*8 = 10» CDQ 1 .00513 1 .001+03 . 0 0 2 8 2 . 0 0 1 7 0 .00517 1 '001+12 •00290 •00176 •00520 00i;19 00298 0 0 1 7 8 00578 001+1+9 •00296 . 0 0 1 6 5 . 0 0 5 8 5 •001+59 0 0 3 0 7 00171+ 00591 001+75 0 0 3 2 2 0 0 1 8 3 00521 00331 0 0 2 2 3 0 0 1 2 6 00531+ 1 00381+ 00261+ 0 0 1 3 3 j

T A B L E I I ( C o n t i n u e d ) . . / L E R O P O I L 1 SECTION IECA 2050 EGA 2050 m 511+-011 IECA 20 30A NACA 6 5 , - 0 1 2 NACA 6'+,-01 2 ^ c T . P . 0 . 1 8 0 . 2 7 0^1+7 0 . 6 7 0 . 2 0.1+ 0^ 6 0 . 2 0 . 3 0 . 5 0 . 7 =106 ^DQ . 0 1 3 3 8 • 0 1 2 0 8 • 0 0 9 2 0 • 0 0 6 7 1 •011+25 •01201+ • 0 0 9 2 5 . 0 1 3 7 0 • 0 1 0 0 0 • 00771 . 0 0 5 5 6 • ï^c=^0^

T.P. 1

. 0 8 • • 27 • •1+7 • • 6 7 • 0.2 j • 0^1+ 0*6

0-2 1

0-1+ 0 ' 6

0" 2 1

0-3 T

0 . 7

0' 1 1

0 . 3 0 ' 5

0.7 1

^T'O 0 0 9 7 3 00752 00521 0 0 3 3 7 0 0 8 9 2 00731 0 0 5 2 7 0 0 7 1 9 0 0 5 5 7 0 0 3 7 3 00870 • 0 0 6 5 2 • 0 0 2 9 0 •0077U • 00621+ • OOl+l+O • 0 0 2 7 7 %'

T.P. 1

• 0 8 ^ • 2 7 •1^7 • 6 7 0 - 2 0'I+ C . 6 0 ' 2 0 ' 1

1 0.3

0^5 0 . 7

=10^ 1

CDQ • 0 0 6 8 5 . 0 0 5 0 5 • 0 0 3 3 3 • 0 0 1 9 6

• 00585 1

. 001+90 • 0 0 3 3 3 • 0 0 5 8 6

•00535 1

• 001+25 • 0 0 2 8 5 .00161+ T A B L E I I I .

1 COMPARISON of RESULTS OBTAINED BY USE of F I G . 2 3 . |

••/iethod of C a l c u l a t i o n p i n t e r b o t t o m a n d S q u i r e . (v. RAE.Rep BAI63I+). P i g . 2 3 u s i n g v e l o c i t y d i s t b - a l o n g s u r f a c e F i g . 2 3 u s i n g c h o r d w i s e v e l . d i s t b - . T r a n s . P o i n t 0^1+ 0 . 6 0-1+ 0^ 6 0.1+ 0 . 6 Top • 0 0 8 1 6 • 00551+ • 0081+6 • 0 0 5 7 3 . 0 0 8 3 9 .00561+ B o t t o m • 0 0 5 7 6 . 00l+0i+ . 0 0 5 8 5 . 001+06 . OO58I+ . 001+06 % • 00696 • 001+79 • 0 0 7 1 5 • 001+90 . 0 0 7 1 1 . 001+85 / 20 p e r c e n t I t h i c k wing Vof Ref, 2.

T A B L E IV.

CALCULATION OF PROFILE DRAG FOR NACA 6 l | . , - 0 1 2 .

AEROFOIL AT ZERO INCIDENCE x / c 0 t 0 - 0 5 0 . 1 0 0 . 2 0 0 . 3 0 0-1+0 0 - 5 0 0 - 6 0 0 . 7 0 O'SO 0 . 9 0 I'OO U / U Q 0 1-099 1 -1 23 1-1i+8 1-162 1.171 1.136 1-093 1.01+3 • 9 8 9 • 9 3 5 -881 U/U^^ 0 1-1+68 1..593 1 • 738 1-823 1-882 1-66i+ 1-i|.28 1-183 • 9 5 6 i ^761+ 1 . 6 0 2 u / 0 , 5 0 1-613 1-789 1 . 9 9 5 2 - 1 1 8 2.201+ 1-890 I - 5 6 I 1.231+ ,

-h

0 0 - 1 3 7 -0 - 5 3 3 -\ 0 . 9 6 0 • 1 1^272 >

-h

— -1-257 -0 - 9 1 2 -0.51+5 -0 . 2 6 -0 -. « 0 a = 1 . 0 3 2 7 F o r R^ = 10 ! 1 2 3 |.i+ 5 6 7 8 9 10 j [11 12 13 i15 T r a n s , P t . ( ° / " O ) T . P . ( e / c ) X 10^ T . P . 1 n "b(1 + p ) I g b ( l + p ) 3^5 (ri + 1)

(u/u„)^'5(-^)

^ T. ? . {d/cf^^ X 10^ T . P . (10) X (11 ) (8) + (12) l / ( n + 1) DQ 0 . 1 1-123 1 • 1+16 5-1+9 617 0-211+ • 000382 -0001+80 U-25 1-636 6-71 - 000011 [-0001+91 •82U • 00771+ 0 . 3 1-162 1 • 569 9 - 7 7 1135 0 - 2 0 1 -0001+19 • 0 0 0 3 8 2 1+. 20 I . 8 7 S 1 5 . 2 2 . 0 0 0 0 2 9 i - 0001+11 • 8 3 3 -00621+ 0 . 5 1 . 1 3 6 Vl+66 11+-01+ 1595 0 - 1 9 5 - 0001+38 • 0 0 0 2 3 9 1^- 18 1-705 21+. 89 . 00001+2 • 0 0 0 2 8 1 • 8 3 7 . 001+1+0 0 - 7 .1-01+3 1 • 135 2 0 - 8 7 2180 0 . 1 9 0 -0001+52 • 0 0 0 1 1 7 1+- 165 1- 191 1+1-71 • 0 0 0 0 5 0 • 0 0 0 1 6 7 •8U0 • 0 0 2 7 7 = 0'661+JI/RJ(U/UO^^P = R ( 0 / c ) (U/U ) '^ T.B 0 TP. Prom P i g , 21 From F i g , 20 I 2 X (7) Prom T a b l e V From T a b l e VI 1 / ( n + 1 ) (13) X 1+a

T A B L E V. n

p-17

p.l8

0 - 1 9 p . 20 p . 21 p . 22

p-23

©•2i+ 0 1+^095 1+'13 i + ' l 6 5 L+^20 k' 23 1+-27 1+-305 :1+'31+ 1 1+^10 1+-13 1+'17 l+'20 h' 235 l+*275 il+-31 !+• 31+5 V a l u e s 2 k'^o h' 1 35 1+'17 1+^205 l+-2i+ 1+-275 1+-31 l+'31+5 3 •+•105 1+-11+ 1+'175 1+^21 i+-21+5 1+-28 i+'315 1+-35 of 3' 5 l n + l 1 1+ k' 11 .^•11+ 1+'18 1+-21 k' 25 l+^285 l+'32 1+-355 5 1+. 11 1+.11+5 1+-18 1+-215 1+-25 1+-29 1+-32 1+-36 . 6 i + . 1 l 5 1+. 15 1+-185 !+• 22 1+-255 !+• 29 1+-325 1+.36 1'" 7 [+•12 1+-15 1+'19 1+. 22 i+.26 k' 295 1+-33 1+-365 8 1+'12 1+^16 1+^19 k' 225 i+^26 1+^30 1+-33 l+'37 1 9 1+^125 1+-16 1+'195 l+'23 1+. 265 1+-30 1+' 3 3 9 i+*37 T A B L E V I . n 0 . 1 7 0 . 1 8 0 . 1 9 0 - 2 0 0 - 2 1 0 . 2 2 0 ^ 2 3 0-21+ 0 • 6 5 5 •81+7 .81+0 • 8 3 3 • 827 . 8 2 0 • 8 1 3 • 8 0 7 1 •Ö5I+ •81+7 .81+0 •833 .826 •819 .812 V a l u e s 2 • 8 5 3 .81+6 . 8 3 9 • 8 3 2 . 8 2 5 • 818 . 8 1 2 3 • 8 5 3 •Si+5 . 8 3 8 •831 • 8 2 5 . 8 1 8 • 811 of ' 1+ . 8 5 2 • ÖU1+ • 837 • 631 •821+ • 817 . 8 1 0 / ( n + 1 ) . 5 . 8 5 1 •81+1+ • 8 3 7 . 8 3 0 • 6 2 3 - 8 1 6 • 810 6 . 8 5 0 •81+3 • 836 •829 • 822 . 8 1 6 . 8 0 9 7 . 8 5 0 .81+2 • 8 3 5 . 8 2 9 • 8 2 2 • 815 ' 8 0 8 8 .81+9 .81+2 • 8 3 5 • 8 2 8 . 8 2 1 .811+ 803 9 .81+8 •81+1

•83J

• 8 2 7 • 820

•81iJ

807

T A B L E VII.

RESULTS OP CALCULATION OF VALUES OP CT. FOR ^0

V.ARIOUS VALUES OP I . , , Ig» ( U / U Q )

^1 0 . 1 0 0 0 - 0 9 7 0 . 0 9 5 0 ' 5 0 0.1+8 0.1+7 0 •go 0 ' 8 7 0 . 8 5 1 . 3 0 1 . 2 6 1 ' 2 3 1 .70 1 .65 1 .61 " T . P . 1 •OO 1 .20 1 .1+0 1 . 0 0 1 . 2 0 1 '1+0 1 .00 1 ' 2 0 1 •i+o 1 ' 0 0 1 ^20 1 •l+O 1 ' 0 0 1 ' 2 0 1 -i+O 10^ X CDQ/a l 2 = 1 -5 861+ 8 5 ^ 838-897 891 888 908 910 908 9 1 7 921+ 9 2 6 932 9 3 5 936 l2=1 -1 671+ 667 651+ 698 698 6 9 7 711 7 1 3 7 1 5 722 729 732 732 71+0 71+3 i o = o - 7 1+68 1+65 1+58 1+93 1+91 1+91+ 501+ 508 5 1 3 516 522 527 526 532 539 1 2 = 0 . 3 2lj.1 21+1 21+0 261+ 267 270 276 282 288 290 298 301+ 303 310 316 R e s u l t s a r e p l o t t e d i n P i g . 2 3 . / T . P . 3 I^ = ƒ ( U / U Q ) d ( s / c ) . .•T.E. / ^

I2 = J

(U/UQ)

d ( s / c ) .

COLLEGE REPORT Wo » 5

BASIC SHAPES OF AEROFOIL SECTIONS

^Z JMAQ4 G5AO10

^ _ X^K(i^

G^AOIO-^ --NACA G 3 A 0 I 0

4Z. . ECA J 0 3 0

ECA 1 0 5 0

FIG I

COLLEGE REPORT N 0 . 3 5

VELOCITY DISTRIBUTION FOR AEROFOILS

USED IN WIND TUNNEL TESTS

TixPEmMENTALLY DËÏiRMlNËD)

1-2 M

-«J/ü<

1 0 0-9 0-6 t'3 1-2 M

u/u,

I'O o«? 08 RfiTio

f

20 % t / c RWIO 0 - 2 0-4. % 0-6 0 Ö 10

FIG 2

C O U L E G C REPORT Wo 5>S.

VELOCITY DISTRIBUTIONS FOR NACA 6 A

SERIES AEROFOILS

\0% Vc ftATK)

% .

15% ifc RATIO

COLLEGE REPORT N o 3 S .

CALCULATED PROFILE DRAG OF N A C A 6A SERIES AEROFOILS AND OF FOUR SPECIALLY DESIGNED SECTIONS

PROFILE DRAG COEFFICIENT C _{O O}

F

R E P O R T NO. 3 5

CALCULATED PROFILE DRAG OF NACA 6A SERIES AEROFOIL AND OF FOUR SPECIALLY DESIGNED SECTIONS

PROFILE DRAG COEFFICIENT C o„ __r — t

COLLEGE R t P O R T No 3 5

CALCULATED PROFILE DRAG OF NACA 6A SERIES AEROFOILS AND OF FOUR SPECIALLY DESIGNED AEROFOILS

PROFILE DI^AG COEFFICIENT C _DO

2 0 1 - 8 X l ' f c I ' * i t I • O NFI< ^ — ^ ^ ^ — ^ IR 6 3 R

yy>

yyx^

SECTIONS A\y y

y^^^^

g^:=

^yj-'y'

0-^5::-_ — - ^ ^ 5 lO /5 TH«CKNESS/CH0«0 RRTfO { % 20

FIG 7

1

a o

I - 8

X »•*

11^ 1-2 i O MHCn fr<f R SECTIONS 1 1

A

^

^/7

y ^ y ^ j ^ j ^ ^ — y t^^^ i. (O »5 20

r*

C m tn O O O

:o

m

O H O > O H O

y

THICKNESS / C H O R D R A T I O / % ) _^ r* rn 3» o 2 o

8

r

i

COLLE.GE REPORT Mo 3 5

VALUES OF CORRECTION FACTOR "X.

go

1-6 l-fc 1.4 \'2. 1-0 O S iO iS SLO

THICKNESS/CHORD ftATiO C7o^ ECA - 3 0 ACROroiLS

COLLEGE REPORT NO 3 5

EFFECT OF VARIATION OF POSITION OF MAXIMUM

SUCTION ON THE PROFILE DRAG (VARIOUS AEROFOIL S") STRAIGHT TRAILING EDGES

Ft MO*'

' 0 0 9 • 0 0 6 •007 •OOG ^ -005 •O04 • 0 0 3

•ooa

•001 - S ^ O ' iS. ƒ NfiCft kSAOiS" ® _ NRG.R fc4fiOl5'. — . — . REROFOa NRCfl 6 5 R O i 5 E c n iSrSO

WITH TRANSITION tW PEAK SUCTION POSJTIOM O-J o a 0-3 0«V 0 - 5 0-6

POSITION OF PEAK SUCTION ( C H O R D S )

r

.OUte&e RtPORT NO 35

VARIATION OF PROFILE DRAG WITH CHANGE IN THE SHAPE OF THE TRAILING EDGE

'0\\ •010 •ooq 'O06 •00"T '005' •004 0 0 3 •0O2 OOI 0-1 0-2 0.3 o•<^ 0-5" TRRNSITION POIt^ POSITION (cHORDS )

0 - 6

z

o

REARWARD SHIFT OF TRANSITION ON LOW-DRAG WING

SECTIONS REQUIRED TO COMPENSATE FOR INCREASED

PROFILE DRAG OF SUCH SECTIONS (izy.THICK)

A MACA « 3 A 0 > 2 D NACA 6 4A012 •I. NACA «-fflOia

© ECA IZSO ® ECO 1 2 3 0 CfNflCA 64-0»a a EQH 1 2 6 0 A NACft 65r-oi2 X EC la^^o

TRANSITION POINT ON CONVENTIONRt SECTION (cHOROs)

r

COLLEGE. KEPOPT NO-öiJ".

EXPERIMENTAL RESULTS FOR

AND ECA I 0 5 0 AEROFOILS

ECA 2 0 3 0

O'Z 0-3 O ' l - O S 0 - 6 0 - 7 O a

C H O A O - V i i S C P O & m O N OP TURBULENCE W I R E S ( o - O I * o ) .

TRANSITION POINT POIisiT POSlTiOM

FIG 15

• O I £

O-T _OB

CHORD WISE P o e m O N O F TURBULENCE WIAE5 (O-Ol ' Q \ T R A N S I T I O N P O I N T l»OS»TION

COLLCA-E. REPORT N O . 3 5 .

EXPERIMENTAL RESULTS FOP ECA 2 0 3 0 AND ECA » 0 3 0 AEROFOILS

• 0 1 '^ • 0 1 3 j • ; • O i a • O i l • o i o D ' OOQ •. . 0 0 8 • 0 0 7 . 0 0 6 « , ^.> Sv \ "•N. 1 ^ i 1 ^ c n : \ , \

N

toao R = l-l X i<

1

1

o

N

• • •s. \ • } '

1

\

It

S P >

SN

1

\ ^ \

-9?

-i|

_si

> jb

i

S

^

Nj

V

1 1 1 1 ' 1 ^'

. WITH WIRE6 (coftRECTEO 1 POR V/IRE

1 1

^ wiTHOtrr DRRG ) 1 WIRE.S ( P L O T T E D ^ R&WNST ] OBSERVED TRANSITION P O S I T I O N . cnuc ULRT! _;o •

i

1

i O» O.e 0'3 O-A- O-S 0-(, 0-7 o 8

CMORO-wiSE Pos«Tior>» OF Tui^euLCNcE WIRES ( o ' O r ' o )

TRANSITION f»0»NT POSITION C I/^ 17

O-l _{oa 0-3} 0-4

f

TRRNSrriON POINT POSITtOM

0-5 0-6 0 - 7 0 - 8

CHORD-WISE POSITION OF TURBULENCE 'WIRE: ( ' o « 0 l " O ^

r

VARIATION OF DRAG COEFFICENT "WITH WIRE TRANSITION POINT* FOR ECA AEROFOILS EXPERIMENTAL

1

•o

H •

0

\i

. / / / <-^ /

i

f

\

( I

/ If

f

1

on

1/

' J

7

/ f N O O 5 O o o o

s

o

4

o

s9 O (A

g

*

o

z

t

O o

2 1

E O

1 i

Ui

a

ó

«1 o o

8

FIG 19

VALUES OF b(l+p) and b 7 0 0 ^ ^ ^ ^ ^ ^ ^^ ^ ^ ^ ' ^ ESTIMATION 7 0 0

600

1500 4 0 0 3 0 0 2 0 0

FIG

2 0

X 4- j s f e T r s ' ^ i o

COULE.GE f?E.PORT T^oTSS:

VALUES OF n F O R USE IN RAPID ESTIMATION OF AEROFOIL PROFILE DRAG

K

\ 1

1

c

f • 1 ' :ALCU 4 A C / \

s

-ATE

1

\ AC \ .D :R \ FR< No ! V > L \ 4G

s

14 • ^ ^ \ ITHOD GIVEN (ARC 849) , \ IN

0

3 / - - ] \ \ ! ! 1 \ ; ; j •

i

i i

i

! !

! 1

i i

s.

—^

_s

^ s ft y 6 ^ 10 ^ S € 1 Z ^ BQ (HUNDREDS)

COLLEGE REPORT NO 3 5 .

«_,•

VALUES OF a FOR USE IN RAPID

ESTIMATION OF AEROFOIL PROFILE D^AG

I0(> 1 0 5 i - O *

6 u

I i^ _{1 0 3} h d I-02 t O l t o o H \ \ >. • = 1-5 \

1

\ \ 0-9

(y-^)

0*9 TRniUNfr EOO-t l O

FIG

22

f

I