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NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
TECHNICAL MEMORANDUM
No. 1225
TEST REPORT ON THREE:- AND SIX-COMPONENT MEASUREIillENTS ON
A SERIES OF TAPERED VVINGS OF SMALL ASPECT RATIO
(Partial Report: Trapezoidal Wing)
By Lange/Wacke
Translation of ZWB Untersuchungen und Mitteilungen Nr. 1023/1, September 1943
Washington
May 1949 AF~~DC
T':'......, ~.~ . ~ -.-, - ~ !. r ~ ,. "Y ,- ... i"c .:,... ~-.;".'I-,All
. .- -;.; of " ... -- -- .... _.;;. I
TECH LIBRARY KAFB, NM
I !III~ 11111 11111 11111 lilllliill rlill [III 1111
NATIONAL .ADVISORY COMKI:'lTEE FOR AERONAUl:llib ",Pk4~~=-3--,-7 ____ _
TECHNICAL MEMORANDUM NO. 1225
TEST BEPORT ON THREE- AND srx-GOMPONENT .ME.ASOREMI!:NTS ON
A SERIES OF TAPERED wnms OF SMALL ASPECT RATIO
(Partial Re:port: 'I'ra:pezoidal Wing)*
By Lange/Wacke
The :present re:port, which forma the first of six articles on e:x::periments with airfoils' of as:pect ratio from 1 to 3 and various :plan fm'IDs, deals with the three- and. six-com:ponent IlJ.",asur'ements made on the tra:pezoid.aJ. wing series in the 2.15 X 3-meter wind tunnel of the DVL at the request of the Henschel Aircraf't Com:pany.
I. IN'IRODUCTION
The aerod.yna.mic behavior of wings with aa:pect ratio from 1 to 3 was studied in wind-tunnel measurements, first on the wing dlone, and later on the wings with fuselage.
As seen from figure 1, the swee:pback constituted the :princi:pal variation. The leading edge of the wing is either curved (elli:ptic wing), or straight (tra:pezoidal and. triangular wing). Common to all wings is the trailing edge :per:pendicular to the :plane of synnnetry. Since the test data serve as the aerodynamic data far the design of gliding bodies, this test series was to provide the :plan farm that affords a constant neutral :position :point for a large ca -range.
This first :partial re:port deals with the measurements of the tra:pezoidal wing series with equal as:pect ratio A = 4/3 and. equal s:pan far varying ta:per (fig. 2).' -,
II. DESCRIPl'ION OF MODELS
The models, of wood, were made at the scale 1:1; the surface was :polished. Three different wings were used: DT 1/2, DT 1/4, and. DT 1/8. The dimensions and. :plan forma are shown in figure 2. The wing section is the NACA airfoil 0012. '
*"Priif'bericht iiber Y- unCI. 6-Kom:ponentenmessung an der Zus:pitzungsreihe von Fliigeln kleiner streckung. Teilbericht: 'I'ra:pezflugel." Zentrale fUr wissenschaf'tlichea Berichtswesen der Luft~ahrtforschung des Generalluftzeugmeisters (ZWB) - Berl~Adlershof, Untersuchungen und Mitteilungen Nr. 1023/1, Se:pt. 15, 1943.
2 NACA TM No. 1225
III. TEST PROCEDURE
The measurements were made in the 2.15 X 3 meter wind tunnel of the DVL in the usual ma,nner on the six-component balance. (Figs. 3 and 4). To prevent the air from flowing through the wing at the two forward suspension points, the pre1imiIlBrY tension was provided. centrally in the plane of symmetry of the wing. The dynamic pressure was q = 100 kilograms per meter2, corresponding to 40 meters per second airspeed.
IV. IN'IERPRETATION
The forces and moments are defined by the standard DJlil L 100 and measured in the aerodynamic system of axes (fig. 3). The moment reference point for all three wings lies on the wing chord at a distance of three-fourths of the mean reference chord of the wing trailing edge (fig. 2). The reference axes for the moments are defined as follows:
Rolling moment: xe-axis = line of intersection of the vertical plane of symmetry of the body with the horizontal plane .of the tunnel (pos~tive toward wind direction)
Pitching moment: ye-axis = transverse axis along the wing (positive in flow ~irection, seen from the left)
Yawing moment: ze-axis = normal axis in wind direction (positive downHard)
All moments viewed. along the posi ti ve axes of rotation and for clockwise rotation are positive.
The coefficients of the forces and moments are:
A lift, kilograms
W drag, kilograms
Q transverse force, kilograms
L" rolling moment, meter-kilograms
M pitching' moment, meter-kilograms
N yawing moment, meter-kilograms
ca A = qXF lift coefficient
,
,.
f.
.:~
.....
NACA TM No. 1225
w drag coefficient
Cq = q X F transverse force coefficient
cL = L rolling moment coefficient qXF X l2.
2
cM = M pitching moment coefficient q X F X 7.m
cN = N yawing moment coefficient qXFx~
Reference quantities:
F = 0.75
b = 1
1.m = t = 0.75
q = f2v2 = 100 2
Angles:
wing area, (meter2)
span, (meters)
mean wing chord (reference chord), (meters)
dynamic pressure (kilograms per meter2)
angle of attack = angle between longitudinal axis along the wing and the xe-axis at rotation about the ye-axis
angle of yaw = angle between the longitudinal axis in wind direction and the xe-axis ~t rotation about the ze-axis .
Viewed along the positive axis of rotation at clockwise rotation the prefixes are ·positive. The results are tabulated in Table A.
(a) Tbree-Component Measurements
3
For each of the three wings the coefficients ca = f(~), ca = f(cw), ana Ca = f(CM) are reproduced in graphs 1, 7, and 13. Increasing taper is accompanied by decreasing Cal. Since the aspect ratio is constant, that is a consequence of increasing sweepback. The moment reference point lies in the range of ca = ±0.35 before the chosen moment reference point and moves quickly backward at Ca > 0.35. . The cause of it is the lift-producing transverse flow in the rear part of the wing observed in the measurements on the triangular wings. The effect of taper and sweepback is small. It causes a slight backward travel of the neutral point.
4 NACA TN No. 1225
Owing to the ca f decrease, the drag increases with increasing taper ~or constant ca , since the ~or.m drag, and especially also cWi increases at the correspondingly greater angles of attack.
The maximum lift is but little a~~ected by the taper, but that o~ the sweepback'on the ca max is considerably greater. While the ~low on the DT 1/2 separates very suddenly, it is very gradual on the DT 1/4 and the DT 1/8. The cause must be looked ~or in the decreased low-pressure peaks resulting hom the sweepback. The ca max shi~ts, for the very same1reasons, toward higher values with increasing taper.
(b) Six-Component Measurements
The coe~~icients o~ the six components are represented as fUnctions o~ the angle o~ yaw /3 and the angle o~ attack CL as parameter. As one can see hom the drawings ~ the course o~ the curves for the angle o~ attack CL = 0.620 (ca = 0), CL = 90 (ca = 0.3), and CL = 17.5 (ca = 0.6) is true to expectations wherever for large angles o~ attack the significant course o~ the curves is frequently interrupted. This applies partly to the transverse force and to the yawing moment. The influence o~ the yawed flow on the lift coe~~icient is small. Only in the regions of maximum lift coe~~icient does ca show a larger decrease with the angle of yaw. The drag also is independent o~ the yawed ~low. It becomes smaller only for angles of attack over 270 due to tae decreasing induced drag.
The transverse force with respect to the ~e OCq
determined by the ~or.m drag at the wing tips; a/3
of yaw is largely
is positive and dif~ers
very little ~or the three Wings. At ca > 0.3 the negative transverse dCq
~orce of the wing surface prepcnderates, 0/3 becomes negative.
Increasing taper is accompanied by decreasing rolling moment, which is likely to be due to the changed flow around the edge.
The pitching moment is not appreciably changed by the yawed ~low.
'-. Increasing taper acts unstable on the yawing-moment, since the
stabilizing ef~ect of the decreasing blunt wing tips decreases.
FURTBER REPORT OF TEE SERlJ!:S
Trapezoidal Wing with Fuselage Elliptical Wing (A = 2 + 1) Elliptical Wing with Fuselage Triangular Wing (A = 3 + 1) Triangular Wing with Fuselage
UM 1023/2 'OM 1023/3 UM 1023/4 UM 1023/5 UM 1023/6
,.
...
...
...
..
NACA TM No. 1225
A comprehensive report of the entire test data is being prepared by Voepel •
Translated by J. Vanier National Advisory Oommittee for Aeronautics
5
6 NACA TM No. 1225
... TABLE A
SuRvEY OF THE THREE- AND Srx-00MPONENT ME'ASUBEMENTS
ON THE SERIES OF TAPERED wnlG -
TRAPEZOIDAL WING
Angle Chart of Symbol Table
aP 130 ourves
Threer-camponent measurement Variable 0 1 1 Six-component
DT 1/2 measurement 0.63 Variable 2 2 Do----------- 9 ---do--- 3 2 Do----------- 17.5 ---do--- 4 3 Do----------- 26.1 ---do--- 5 3 Do----------- 30 ---do--- 6 4
Threer-component measurement Variable 0 7 5 Six-component
DT 1/4 measurement 0.62 Variable 8 6 Do----------- 9 ---do"'-- 9 6 Do----------- 17.6 ---do--- 10 . 7 Do----------- 26.2 ---do--- 11 7 Do----------- 33 ---do-~- 12 8
Threer-component measurement Variable 0 13 9 Six-component
Dr 1/8 measurement 0.63 Variable 14 10 Do----------- 9 ---do--- 15 10 Do----------- 17.5 ---do--- 16 11 Do----------- 26.2 ---do--- 17 11 Do----------- 38 ---do--- 18 12
Comparative ourves of the three wings
0a = f{a,); ca = f(ew) Variable 0 19 .., ca = f(cM) ---do--- 0 20 cL and cq = f(/3) Clca = 0.3 Variable 21
°L and cq = f(J3) Clca = 0.9 ---do--- 22 ..
T ,
F=a7SmZ,
1 ~ :»
F=a75m" f !:3 rr cc
I I 7!lfl I
.... I
, lo2I
~ 0
T i ta =.1.. C) . A1. ~ I\l
2 J . ti ,2
I I 1
I\J Ie) \J1
11' tWO 'L1 / \-1 I 111
I- 1500 '1 ~ 1225
1 1 DE F=o.7Sm" r
I ED
I 1 C) I <:) 10
~ .~ ~ ~ '" A..t I I '" , 3 I r,~ .,.
~ lJ ~ I. I •.
·11 /A=.:? ,
/000
I T ,
1000
i F=a7Sm I! 1 k~o.~ml!i I' 1225
CE I
I .Dn
. DT f1J
I ~ ~ ~ ::
~ '" I .
J 1 I ! ;j=t M: /:20 A=§ , i Prvf',1e AlACA WI2 ,
I .... I I ~ B68 TI' /000 1000 .,
Figure 1.
8
Survey graph taper series - trapezoidal wings .
nTyz F= 0'75m2
b = /.0 m
.em= f:; o.7S
4 A -= 3
.fa = 1 ~I E -t'a = 500 ~t = 1000
lJTJ4
F = Q75m 2
b = I.Om
/m= {=0.75
A=£ 3
.fa = / Lj "4 ~a -= 300 ~i = 1200
DT#J
F = o.75m 2
b = /,0 m
.em:: t =Q75
.L1.='£ 3
L'a _ / - - 8 til
~a = 167 Rl = 1334
. 1 NACA 0012 !
T. 11 !------+-h-(4----+-1+--..... ~
. b
Figure 2.
NACA TM No. 1225
to,.
IN
NACA TM No, 1225
9
Suspension of the model of the series of tapered wings - trapezoidal wing -in the medium wind tunnel of DVL
t
Figure 3. - DT 1 .2
Figure 4. - DT 1,4
I
• ·.
FloW /
Figure 5.- System of coordinates of the six-component measurement.
12
a,o
-5.41
.34
6.10
11.82
17·53
23.22
28.94
?9.88
30.84
32.17
35.33
38.54
41.55 I
NACA TM No. 1225
THREE-COMPONENT MEASUREMENT ON A SERIES OF
TAPERED wmas - TRAPEZOIDAL WING
TABLE NO. 1 TO CBART 1
Dr 1/2
o~ Ow oM
-0.1895 0.0177 -0.0096
.0061 .0080 .0014
.2029 .0190 .0065
.4230 .0533 .0119
.6526 .1155 .0014
.8985 .2149 -.0247
1.1240 .3433 -.0511
1.1710 .3734 -.0576
1.2020 .4961 -.0811
.9395 .5593 -.1092
.8140 .5369 -.1082
.6419 .5283 -.1078
.6341 .5548 -.1151
•
, \.
•
• .. • ..
I
Co
V \ ~~ ? "\ / 1
I \ / V , 1.0 \
\ ./ V P ... 1\ / j ,/ ....
'0
" /
/ ;' --.- // J LIt 72
~ I' ~ I r 1~5" / V ~ "a f (01:"
If ;/ IC c,. j(Cw)
,/ 1.1_ I
I / .II C,. T( (."711/
/ /'
/' V
-10 VJ 10 20 30 -10 'f T -20 • .; -fl2S ./ j iI 025" as a7S /.0 C'w _;5 CY'" j"
-0.
-q-I t , al a.2 a3 a4 Co -lJ..2 m
I I ! ! ! ! !
1 1 I I 1 1 I 1 11) I I I 1 1 1 I I 1 .1 I I I I I I I I I I I I I
Chart 1. Three -component mBlUlurement on a series of tapered wings -Table 1. trapezo1daJ. wing.
14
13° ca
-4 0.0166
-:2 .0158
0 .015:2
:2 .015:2
4 .0156
6 .0160
10 .0180
15 .0185
:20 .0:2000
13° ca
-4 0.3139
-e .3144
0 .314:2
:2 .3108
4 .3119
6 .3111
10 .3111
15 .3089
:20 .3000
NACA TM No. 1225
srx-COMPONENI' MEAS1lREMENT ON A SERIES OF
TAPERED WlNas - TRAPEZOJDAL WJNG
TABLE NO. :2 TO CHART :2, 3
cq Ow or. oM
-0.0033 0.0085 -0.00:27 0.0016
-.0015 .0083 -.0018 .00:21
.0003 .0080 -.0009 .00:20
.00:2:2 .0084 .0003 .00:23
.0030 .0089 .0004 .0019
.0035 .009:2 .0008 '.0014
.0058 .0099 .0018 .0016
.0087 .0103 .00:27 .0013
.0107 ,0141 .003:2 .0005
cq Ow °L OM
. -0.0047 • 0.0338 -0.0194 0.01:26
-.00:25 .033:2 -.0108 .01:27
-.0010 .033:2 -.0013 .0130
.0005 .0333 .0073 .0158
.000:2 .0335 .016:2 .01:29
.0018 .0338 .0:255 .01:23
.0035 .0348 .04:2:2 .0100
.0043 .0369 .0584 .0061
.0047 .0387 .07:28 .00:21
~
0.0033
.0010
-.0005
-.00:23
-.0036
-.0041
-.0055
-.0090
-.0106
~
0.007:2
.0033
-.0006
-.0043
-.0069
-.0098
-.01:23
-.0207
-.0:259
•
I
,
•
,
•
NACA TM No. 1225 15
Jl t----+--+--t--t-- a3-~I.S ~O.l5--t--+---;--+---t--+-__t--+---t-~
I I C
a '~Cq
t----t--+-~-+CH·~-~~~rCLr-+--t----t--+-~-+--t----t--+-~
Cw eN
I----+--+--+--+--Qe -f-/ - f-O.I+---+--+--+--+--+---+--+--+--+-~
r-- 0 Ca+_--If----+--+-~-+_-t____+-_+-~-+_-t____;-_+-_I_-+_~ oeq
- x CIN I'".O'Y+---+--+--o. / - -0.5 0.05 --'t---+--+--t---+---t--t-__t--t---I t1 eM
-9Cu+---If----+--+-~-+--t----+--+-·;--+--t----;--+--+--+-~
• CL
--/0
t---r--+---+---+--o./-~a5 -o.Os-r--+-~--~--t---+---+---~-+~ DTj/g
t----+-_+_-+_-t----+--+--+--t----+-_I_-+« = 0.63 0
'Chart 2. Table 2 .
I
Six-component measurement on a series 9f tapered wings -trapezoidal wing.
•
1
,
•
,
r
NACA TM No. 1225
r- 0 Ca o Cq
-xC t:. eM
--¢- eN • CL
10
Chart 3. Table 2.
I I - 0.115 0.30 1.5"-
I I I c. .~ ~~ .~ I
~M Cq
Ow CL eN
0.20 v.o-t- 0./0
/' ,..
./ /
/' V
0./O-Q5- -0.05
/ //
/ V
/ I"
......... ~ ./
r---. ./ -.,....( r- /' ~ 1"-c~ 10 .. (30 20
k
/ --~ --t':'--...... / r--I"-<>-
-t·) 10 -0.5- f-a05
DTfk lX =9°
I .
Six-component measurement on a series of tapered wings -trapezoidal wing.
1.7
18
(30 ca
-4 0.6480
-2 .6524
0 .6542
2 .6526
4 .6500
6 .6452
10 .6389
15 .6239
20 .6070
[30 C a
-4 1.0200
-2 1.0500
0 1.0490
2 1.0460
4 1.0070
6 1.0040
10 1.0000
15 .9690
20 .9390
NACA TM No. 1225
SIX:-COMPONENT MEASUREME:Nl' ON A SERJJl:S OF
TAPERED WJNGS - 'I'RAPEZOJl),AL WJNG
TABLE NO. 3 TO CEAET 4, 5
cq Cw cL
-0.0013 0.1154 -0.0355
-.0018 .1156 -.0202
-.0023 .1157 -.0044
-.0035 .1155 .0121
-.0050 .1158 .0278
-.0075 .1145 .0445
-.0100 ,I
.1128 .0760
-.0147 .1129 .1099
-.0187 .1121 .1367
C C Cr, q w
~
0.0018
.0015
.0009
.0012
.0012
.0016
.0006
-.0038
-.0081
cM
-0.0496 0.3197 -0.0211 -0.0368
-.0435 .3060 -.0183 -.0300
-.0403 .2963 -.0065 -.0363
-.0401 .2902 .0098 -.0383
-.0193 .2718 .0324 -.0346
-.0288 .2697 .0517 -.0346
-.0504 .2653 .0845 -.0349
-.0733 .2554 .1275 -.0394
-.0812 .2475 .1643 -.0403
~
0.0158
.0077
-.0006
-.0078
-.0145
-.0206
-.0340
-.0499
-.0623
~
0.0548
.0454
.0228
.0068
-.0231
-.0338
-.0508
-.0724
-.0981
•
I
r,
,
,
•
,
•
NACA TM No. 1225
~o Ca o Ott
f---X C,y A eM
~-9-C
• CL
10
Chart 4 • Table 3.
I I 18-
~/.5- ~a/5
I c.
j ,. Cq / /:' a
M ew CL V eM /
v ./
V QE- 'r-I-1-0.1 /
/ /
/
/ /
/ 0.1- 0.5- ~0.O5 V J
II I
'~ V """ ~ /
'0 -t-tr,.. () / ~~ T--, :r--f-- 90-~
/ ~~ -----r--c-~ / '" ..... V ~~ /
""'" ~ -al -Q5 -0.05
'" r-...... DT~ IX ,/7.{D i
. Six-component measurement on a ~eries of tapered wings -trapezoidal wing.
19
,
,
,
•
,
f"'
f
NACA TM No. 1225
-oea oeq
-x elY .A eM
--<> eN • CL
-/0
Chart 5. Table 3.
/ I
11.5- 1 V £lSO- -,.IS / I O~
I V CAl Cq J
c.., c'- I Ic,y
/ ) /
-0.20 Y.O- 'r-O.l
/ .....
.-V
/
I I
.(.10- ~5"- -0.05 II "- /
-~~\. ~/ \ /
....
\ II } ~
/ ~ /0 lJo 20
~ \ ~i\.
"'" DT~
-o . .tO~~ ---~ ~ cx=26./0 --:£lO5
~ ~ ~ ,
I'" -~
"-~~
Six-component measurement on a series of tapered wings -trapezoidal wing.
2l
,-
22
~o °a
-4 1.1310
-2 1.1480
0 1.1590
2 1.1320
4 1.1130
6 1.0870
10 1.0270
15 .8960
20 .7620
NACA TM No. 1225
SIX-eOMPONENT ME:ASUREMENT ON A SERIES OF
TAPERED wmGS - TRAPEZO]J)AL WING
TABLE NO. 4 TO CHART 6
Dr 1/2
0q Ow °L ~
-0.0187 0.5526 0.0257 ..0.0932 ..
-.0125 .5639 .0065 -.0944
-.0093 .5614 -.0120 -.0953
-.0045 .5555 -.0333 -.0950
-.0020 .5378 -.0471 -.0954
.0068 .5168 -.0637 -.0937
.0042 .4641 -.0594 . -.0868
-.0023 .4227 -.05ll -.0877
-.0210 .4400 -.0441 -.0999
~
-0.0068
-.0024
.0210
.0114
.0115
.0158
.0020
-.on4
-.0275
•
I
1
•
\
,
,
'NACA TM No. 1225
I Ca "'""- 0
c Cq Cw I--- )(
A eM I- -<>- 01{
• CL
-10
Chart 6. Table 4.
23
1 T 0.3_ 1.5_ _0.15".
j~ ca~ , c9. CM dw
CL
eN ~,. ;r-.., "-
~ ~).. 0.2- .I- f- 0.1 ........
i'-.. I--... v...... ~
~~
~ ..... ~ (.1- O.S: 0.05 Iloo.
r--r-- i-- w.-
1\
\ 4-\ V ~I!!.. V --- .... ;JiI;. ~
y~ 0 ~ /0 ....... ...... t--n ;.30 20 ...... ...... r--..... I--...
V y , ......
~ \ , ;t'
\ ~ l'
i\. - \ K -0.1 -o.~ -aos ~
\. v~ -~ --- DT Pf:
(X =30 0
I I Six-component measurement on a series of tapered wings -
trapezOidal wing.
24
aP
-5.43
.33
6.10
1l.85
17.63
23.26
28.97
31.99
32.86
33.85
34.85
35.83
37.85
39.90
NACA TM No. 1225
TEBEE-COMPONENT MEASUBEMENr ON A SERIES OF
T.A1'ERED WINGS - TRAPEZOIDAL WlNG
TABLE NO. 5 TO ClIART 7
Dr 1/4
c c a 'W ~
-0.1714 0.0160 -0.0076
.0138 .0075 .0006
.2006 .0180 .0072
.3980 .0496 .0057
.6140 .1082 -.0098
.8670 .2169 -.0435
1.0980 .4432 -.0757
1.1660 .5582 -.0870
1.1850 .5970 -.0905
1.1950 .6319 -.0928
1.2010 .6681 -.0958
1.2130 .7075 -.1000
1.1960 .7712 -.1043
1.1540 .8178 -.1109
..
(
,
•
· ..
~ I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I i 1.5
I
~". ~
I" ~ I ...... V I-"'" V f: .......... I"-
~ /' V ./
f'"" L
\ V- V ), /' V
\ V V DT}4 1 r
1\ II oV \ / /'
V .; ca f IX as I --'-
/ / ~ Ca Hew)
J ..... V ~ ,,1 ,7" \ 6. (..0 II '-ml
./ .....
V ,......."
-2 0 /1 1 «0
1 -fO ./ 10 ~o ~ 40
0.5 T' -f25 p- I 0.,25 q.5 dT5" i
i Cw
0.2 -0., 1 .: ae 0.3 0."1- em .. q.J
! ! I I
111111111 H 1111111111111111111111111 Chart 7. Tbree-comporumt measurement on a series o;f tapered wings -Table 5. trapezoidal wing.
26
13° °a
-4 0.0243
-2 .0242
0 .0228
2 .0229
4 .0238
6 .0248
10 .0237
15 .0250
20 .0251
13° °a
-4 0.2945
-2 .2965
0 .2960
2 .2970
4 .2980
6 .2965
10 .2935
15 .2850
20 • 2605
SII-COMPONENT MEASUREMENT ON A SERIES OF
T.APERED wnms - TRAPEZOIDAL WING
TAJ3LE NO. 6 TO CIrARrS 8. 9
DI' 1/4
a. co 0.62°
0q Ow c;:, ~
-0.0035 0.0085 -0.0004 0.0007
-.0028 .0088 .0005 .0002
-.0017 .0089 .0019 .0006
.0007 .0090 .0028 .0010
.0025 .0092 .0032 .0006
.0030 .0095 .0028 .0000
.0032 .0103 .0038 -.0005
.0065 .0114 .0051 .0004
.0090 .0135 .0056 .0000
0q Ow or. cl.J:
-0.0032 0.0319 -0.0150 o.ooBo
-.0028 .0315 -.OOBo .0081
·-.0023 .0313 .0015 .0085
-.0003 .0316 .0120 .0082
.0008 .0320 .0203 .0071
.0007 .0322 .0286 .0066
.0015 .0327 .0457 .0059
.0032 .0332 .0631 .0035
.0050 .0343 .0771 .0041
NACA TM No. 2225
~
0.0018
.0023
.0006
.0001
-.0020
.0004 , -.0000
.0005 1
.0004
cN
0.0047
.0035
.0015
-.0020
-.0049
-.0056
-.0091
-.0119
• -.0143
NACA TM No. 1225 27
I I f'J.20 1.0-r-O·r I
eM Ca ~I' I
C9 Cw CL
CN
~ oCa c Cq
f--XCW a 10- 0.5 ra05 A CM
~-<rCN
• CL
~
00; i_
..., -10 10 /30 EO
-0./0 -0.5-~-a05
Z;T~ a=a6Eo
-1,20 ,/0 0 -0,10
I Chart 8. Six-component measurement on a series of tapered wings -Table 6. trapezoidal wing .
•
,
..
•
NACA TM No. 1225 29
1 ~.o-
I ieo- -0.10
I CM Ca c
l q
Cw CL V ~
eN /'
I V " :--- 0 Ca
r:J Cq I /'
V :--- X Cw o./q- 0.5"-r-O.05
.a eM / v
:----¢-CN .CL /
V - .....
V / . --/0 V
""I( ),. / ~ ;9" 20 ~
...., r--r--. .. V
-alo -as- -0.05
DT~ '" =9°
-020 -1.0- -0.10
I I I Chart 9. Six-component measurement on a series of tapered wings -Table 6. trapezoidal wing.
30
13 0 ca
-4 0.6110
-2 .6130
0 .6140
2 .6150
4 .6160
6 .6170
10 .6020
15 .5850
20 .5730
13 0 ca
-4 0.9860
-2 .9990
0 1.0000
2 .9990
4 .9950
6 .9840
10 .9450
15 .8730
20 .8020
NACA TM No. 1225
SIX~OMPONENT MEASUREMENT ON A SERIES OF
TAPEBED WINGS - TRAPEZOIDAL wnro
TlffiLE NO. 7 TO CRAETS 10, II
cq Cw or. elM
0.0022 0.1083 -0.0226 -0.0097
-.0008 .1085 -.0092 -.0100
-.0037 .1078 .0046 -.0105
-.0059 .1090 .01.79 -.0105
-.0102 .1095 .0297 -.01.1.3
-.0157 .1.1.11 .0420 -.0124
-.0152 .1071 .0680 -.0114
-.0221 .1050 .1008 -.0136
-.0326 .1062 .1273 -.0185
cq Cw cL ~
-0.0162 0.3226 -0.0105 -0.0616
-.0062 .3222 -.0048 -.0644
.0007 .3201 .0020 -.0650
.0023 .3222 .0088 -.0650
.0045 .3273 .0157 -.0642
.0037 .3318 .0230 -.0622
.0018 .3351 .0282 -.0572
.0052 .3256 .0411 -.0539
-.0167 .3137 .0515 -.0486
em
0.0097
.0058
.0011
-.0037
-.0079
-.0080
-.0209
-.0288
-.0304
~
0.0209
.0092
-.0022
-.0123
-.0213
-.0266
-.0280
-.0294
-.0205
f'
:RAeA TM No. 1225 31
/ /
V .
a20-1-/.0- ~-o.IO ./ I V
/
CM Ca J V '1.
Cw e,- 1/ eN / ~o Ca
c Cq /v v
1--)( Cw (. .10-0.5-',-0.05
AV J:j eM
~¢- ell / • c'-
/ /
~~ ~ V
10 ~ ~ ~ 10 po 20 1/ ""I~ r---t'k -
/ r---...... .......... ........... -r--
I ~ r--.. ra..... ~ ..)...
"""'1: r--..
-a/~5 ~a05
DT%. a =17.6°
-120 ,-1,0
1--- 0.10
I Chart 10. Six-component measurement on a series of tapered wings -Table 7. trapezoidal wing.
NACA TM No. 1225 33
dz ! 1.0 0.10
1 -~ r----ad ' Cq """t> __
r--CM r--.. Cw CL
-eN
f--O en o Cq
0./0-D.5- ...... Ir -x CIA. -0.05 A eM V
.....
-~CN- ,......r-• CL L V
.,
/ ."
'" ./ v
~ ~ [J [ -- .........
-/0 ~ ~ ~ 10 -A~ 20
" ;f ~~ "\~ ~~ ~
""-- ...-
-o.lo-=aS-~O.O"
Drf/2 CC=26.2°
-a2~/'O ~o./o
I I I Chart 11. Six-component measurement on a series of tapered wings -Table 7. trapezoidal wing.
34
~o c a
-4 1.1950
-2 1.2010
0 1. 2070
2 1.2060
4 1.2000
6 1.1900
10 1.1450
15 1.0600
20 .9800
NACA TM No. 1225
SIX-COMPONEN.I' MEASUREMENT ON A SER:mS OF
....
TAPERED WINGS - TRAPEZOIDAL WING
TABlE NO. 8 TO CHART 12
Dr 1/4
c c Or, q w
0.0022 0.5978 -IJ.0015
.0025 .5996 .0014
.0017 .5990 .0019
.6017 .5964 .0055
.0032 .5945 .0066
.0013 .5931 .0074
-.0122 .5901 .0115
-.0042 .5460 .0154
-.0280 .5138 ~.0364
~ ~
-0.0933 0.0112
-.0940 .0055
-.0944 .0004
-.0947 -.0045
-.0966 -.0107
-.0951 -.0169
-.0906 -.0161
-.0882 -.0236
-.0820 -.0321
NACA TM No. 1.225
o Ca -oCq
)( Cw -AC",
-<> C,v r--e C/.;
-/0
Chart 12. Table 8.
r-- r--... r-... -~ a20- 1.0-kJ.lf r--. I ~
C'~ I
OM Cq t-- a Cw CL
GN
--"""'*-Q/O-O.5- 'r-O.05
~
J
./ V
...-" ., --~ ... -
~ - - (30 2r-.... ~ ~ '"I /0 , 20 ... ~ ~ ........
~ I~ ('..... .. ~ ~
~
" ~- - -~ .......... ~ "':t r--.
'"lII)o'
A
-O./~a;. -0. OS-
IJT~ 0{=3,gQ
-Q20 -/.0- -0'/0
i I I Six-component measurement on a series of tapered wings -
trapezoidal wing.
35
aP
-5.87
.34
6.12
11.89
17.86
23.37
29.11
32.09
34.93
37.91
NACA TM No. 1225
THREE-COMPONENT MEABUREMENl' ON A SERIES OF
TAPERED WINGS - TRAPEZOIDAL WING
TABIE NO. 9 TO ClIART 13
ca Ow
-0.1703 ~
0.0167
.0057 .0074
.1856 .0168
.3691 .0449
.5809 .1027
.7942 .2241
.9840 .3712
1.0522 .4677
1.123Y .5418
1.1492 .6022
OM
-0.0061
.0013
.0086
.0068
-.0107
-.0409
-.0598
-.0673
-.0785
-.0831
•. .
~
I I I I I I II I I ~51 I I I I I I I I I I I I I I I I I I I I I I I I : ~
I
Ca
.... r,. -... .JY
>-~
~ ~.o V ......... V v 1\ V
.,.. /'
V
\ v /' \ / / lJT}6
./ •
r-.. / /'
n~ / V ~ Ca jfw)
1\ I /' ;/ X Gz /fCw) ,
i 1ii V A Ca f(Cml
./ /'
/' /'
/'
-20 -~o ~ ~O 20 30 4f aD T ./
-45 -tU>5 . I V 1 0.25 " l~ 475 ~ Cw
-dz 01 0.1 {;;2 a~ 0.4- C'''' ; - ,. _. I I I I I I I
1111111111 +111111111111111111111 ! III Chart 13. Tbree-component measurement on B. series of tapered wings -Table 9. trapezo1dal wing.
13° C a
-4 0.0152
-2 .0145
0 .0138
2 .0152
4 .0153
6 .0146
10 .0145
15 .0146
20 .0135
13° ca
-4 0.2790
-e .2780
0 .2780
2 .2780
4 .2793
6 .2760
10 .2725
15 .2660
20 .2555
NACA TM No. 1225
SIX-COMPONENT .MEASUElEMENT ON A SERIES OF
T.APERED wnms - TRAPEZOIDAL Wll'iG
TABLE NO. 10 TO CB:ARrS 14, 15
Dr 1/8
C C c;:. q v
-0.0030 0.0088 -0.0000
-.0023 .0086 -.0000
. -.0013 .0073 .0005
.0007 .0078 .0018
.0027 .0079 .0023
.0037 .0090 .0029
.0045 .0098 .0034
.0075 .0llO .0063
.0105 .0130 .0068
cq Cw cr.
-0.0030 0.0288 -0.0160
-.0033 .0283 -.0081
-.0020 .0278 .0006
.0000 .0283 .0088
.0010 .0288 .0176
.0010 .0293 .0264
.0018 .0298 .0416
.0032 .0584 .0587
.0045
i .0728 .0720
~ ~
0.0017 0.0000
.0019 .0012
.0019 .0013
.0017 .0002
.0015 .0002
.0015 -.0007
.0016 .0034
.0017 .0064
.0014 .0100
cM cN
0.0078 0.0032
.0096 .0031
.0094 .0002
.0095 -.0013
.0079 -.0032
.0075 -.0039
.0063 -.0034
.0038 -.0025
.0014 -.0000
NAeA TM No. 1225
f--O Ca c Cq
~XCW II eM
~O Gil • CL
-/0
Chart 14. '"rl'l.ble 10.
,
I I 0.30- /.5"- ~O.15
I ~ ~ T
q( f--Ca Cq Cw CL
eN I I
0.20- 1.0-~O.lO
QIO- Q5-~o.05-
....t. .. 10 /)0 20
.DTJ& QIO -Q5-~-Oi05 ex =0.63°
I I I I Six-component measurement on a series of tapered wings -
trapezoidal wing.
39
NAeA TM No. 1225 4~
I i30- f-I.5 k{5
cMj cd
j I Cq
CW CL CN
0.20- 1.0-1-0,/0
./ .....
~V ......
:--- 0 en o Cq /
V f---X CW 0./0-fO·5-1-0.05
A eM ~/ :---9-CN
• C'-/'
7
/ v
/ ./
-10 )/ 10
,J' ;.3" EO
V
-0(0 -15 - I--o.o~ laTA?
I ex _9°
I Chart 15. Six-~omponent measurement on a series of tapered wings -Table 10. trapezoidal wing.
42
()o ca
-4 0.5800
-2 .5800
0 .5810
2 .5808
4 .5808
6 .5780
10 .5740
15 .5580
20 .5290
()o C a
-4 0.8920
-2 .8940
0 .8940
2 .8920
4 .8880
6 .8840
10 .8580
15 .8370
20 .7660
l
NACA TM No. ~225
SIX:-eOMPONENT MEASUREMH:NT ON A SERIES OF
TAPERED WTIlGS - TRAPEZOIDAL WING
TABIE NO. 11 TO CHARI'S 16, 17
c Ow Cr, ~ q
0.0057 0.1029 -0.0250 -0.0101
.0017 .1029 -.0104 -.0100
-.0037 .1029 .0027 -.0096
-.0073 .1029 .0144 -.0100
-.0106 .1031 .0259 -.0106
-.0133 .1040 .0375 -.Oll2
-.0232 .1062 .0620 -.0123
-.0302 .1043 .0962 -.0134
-.0312 .1000 .1258 -.0143
cq C Cr, "M w
0.0090 0.2859 -0.0192 -0.0499
-.0017 .2879 -.0079 -.0504
-.0073 .2769 .0016 -.0494
-.0147 .2849 .0105 -.0496
-.0226 .2835 .0237 -.0490
-.0313 .2807 .0369 -.0487
-.0142 .2989 .0475 -.0409
-.0265 .3047 .0617 -.0427
-.0335 .3017 .0821 -.04ll
'1l"
0.0026
.0017
.0004
-.0009
-.0018
-.0032
-.0021
-.0050
-.0089
~
0.0102
.0078
.0011
-.0022
-.0073
-.0104
-.0346
-.0370
.0338
"
NACA TM No. 1.225
f-- 0 Ca o Cq
I--xCW A eM
I---¢-C,y • CL
-/0
Chart 16. Table 11.
I I a80 1.5- f-o. I5
I J I
eM ,--Ca Cq Cw c'-
/ el/ V
I
0.20- /.0 ralO V /
/ v
/ V
~ /
V " I;
o./O~5-t-O.O~
/ /
V /
V ~
....., c-...... V /0
")Ii ~ "';r- (3D 20 / J..........
/ ~ ..............
/ ........., r--I r--
-,.10,5- --QDS DTjf
I C(':: 17..5T I I'
Six-component measurement on a series of tapered wings -trapezoidal wing.
0°
NACA TM No. 1225 45
J3Cl /.5"-I. r-O'f5 I
C ~ M Ca~ ~ Cq
CW CL CN
0.20- -/.0 ~./O
-0-. r-- ~
/ P"--~
_oea //, otJq
/ /'
--xC QIO-as- -0.05-ACM V --<>CAI. • CL :/
'J(
V /
~ ~ / -/0 ~ ~ ~ /0 /30 20
..... r ......
/ '-., """ "- " ~/
, , "'Id. '- ............ -
"- // "'- 1'0.... r-.. 1 ......
?'-- ~ 0r-A ~
-O.l()"':' o.S -/:-05- DT/fJ
I I F=26_Z 0
I I CharI: 17. Six-component measurement on a series of tapered wings -Table 11. trapezoidal wing.
40"
/30 °a
-4 1.1850
-2 1.1890
0 1.1860
2 1.1790
4 1.1700
6 1.1540
10 1.·1190
15 1.0580
20 .9440
NACA TM No. 1225
SIX-COMPONENT MEASUREMENT ON A SERIES OF
TAPERED WINGS - TRAPEZOIDAL WING
TABLE NO. 12 TO CHART 18
0q, Ow °L oM
0.0000 0.7014 -0.0118 -0.0912
-.0043 .6942 -.0047 -.0940
-.0080 .6B97 -.0001 -.0944
-.0137 .. .6884 .0022 -.0927
-.0227- .6887 .0058 -.0903
-.0333 .6846 .0132 -.0866
-.0378 .6726 .0276 -.0825
-.0628 .6485 .0536 -.0722
-.0588 .6127 .0496 -.0800
oN
0.ou8
.0079
.0033
-.0016
-.0055
-.0069
-.0154
-.0198
.0066
NACA TM No. 1.225
.
I-- 0 C !l Cq
-xCw A eM
-4 0 )1
• CJ.
-/0
Chart 18. Table 12.
d30- I 1.5-~.I5-
r I eM cJ~
, I
,....-- a Cq Cw CL
CA'. - ?--r--~ r-- r-a....
·c 20-1-/.0- Q.lO r--...... f"., ,
- r---i-.
JJ./O-k/.5-~o05= / '" / /
V -&. ./
V ~ ~ V
v .... ~
/ K ~ N /{J po ~ ""'i ...........
~ V ~ i>-- V
~ "I: "1-- -, " ~
~ ~ -0./0--=0.5 _ .. or-o-
'" .........-V
r.r
DT'/e ex- 9Ro
Six-component measurement on a series of tapered wings -trapezoidal wing.
47
I I I I I I • I I I I I I I I I I I I I I I I I I I I , , ,
"'-
Ca
,. V .--~ ~~ ~ ~ ,..... c;,.
k --1 r---/ v e::..- Va ~ v v\' (" In
/ V / "'" ~ V ./ '\.
h r: V ) ~ / "' l'-h ?/ V ~ V ~
~ ~ ~ V
as J ~ V I I I
I ~~ /" c.. : fjOC) DT 1ft 0--
i ~}:,- r--
I A ~ I J& ~ f--
J ~ ~ "Ca;f(C,,)DT ~ -I " IllT~.6--
f--
~ ... IDT }8 0--
~ io""
-10 ~ () 20 a~5 ;~ ",,"U
-a.z5 ~ 0.25 O.!JO r--~~ 1--' I
~ !7 I I ,
I I I I I rl I I I I I I I I I I I I I I I I I I I I I I I I I I Chart 19.- ca = f(a.) and ca = f(CwJ curves of trapezoidal wing series •
•
NACA TM No. J.225 49
1.5
Ca,
-.. ~ ~
..........
~ :t
. I " \
\ ~~ \
1.0
b ~ \ i\ \\ \
'\ ~. ~ , \ . /'15
Oa =f(CM) DT 12 e>-
IJT.P4 --- -< DrYs ~
)-
-0.2 -0./ ..... eM -t
-0.5
I Chart 20. - Ca = f(CM) curves of trapezoidal wing series.
NACA TM No. 1225
0./0
Cq ~~t-GL
I~ ~ ~
~ ~ 1n,05 ."
~ ~ ~ V
l.d V'
!~ \?
~.~ ..
-10 ...... ~ 10 20
... j3C'_
~~
0( Ca =0.3
-aos CL DT 12 0-_
DTf+ ----D1 '18 -¢-- -C'I ])1 Ye If---
1)T ~: Il---
7)T /, 0--
Chart 21.- cL and cq curves of trapezoidal wing series.
NACA TM No. 1225
L '/
J
V I
1/
/
0.10 ~ / ."
V Cq
)) ~)-
/ ./ V
CL
I L~ ~ V L
V V V
~DTJI.q 0-0.05- ~
/ V V v-I- DT'I4 .-
lJr fI2 ~- V ~ V C DT YE )(0-
~ ~ q DT 14 A-- c( ~
lY Ca =Q9 DT fa 0--
'" ~ ~ -0 ~ ~ /0 r--
~ 20
A r'- r-.... (J~
~ V ~ ~ ~ ..........
'" L / "'1:,
/ ............. ~ ---- ~ r--
'" V -'-.....l I'-t r-......
"" '" ,0.05 I"--
Chart 22.- cL and cq curves of trapezoidal wing series.
