The experiments here described were performed for the purpose of obtaining the essential facts concerning the distribution of the air force along the span. We did not follow, however, the time-consuming method of point-to-point measurements of the pressure distribution on the wing surfaces, but determined directly the moment of mean force about an axis passing through the middle of the span parallel to the direction of flight

Katzmayr, Richard

English

NASA Technical Reports Server

CASE RILE COpy 
TECHNI CAL MORANDUMS 
ATIONAL ADVISORY CO1MITTEE FOR AERONAUTICS 
No. 530 
TRAVEL OF TI CENTER OF PRESSURE OF AIRFOILS 
TRANSVERSELY TO THE AIR STREAM 
By Richard Katzrnayr 
From Beic1ite der Aeromechanisehen Versuchsanstal-t in Wien

Volume I, No. 1, 1928 
I
Washington
September, 1929
FILE Copy 
Advisory Cc%mvitfN 
for A6njraj 
a C. 
I
https://ntrs.nasa.gov/search.jsp?R=19930090889 2020-06-17T04:54:20+00:00Z
NATIONAL ADVISORY OOITTEE FOR AERONAUTICS. 
TECHNICAL MEMORANDUM NO 530. 
TRAVEL OF THE CENTER OF PRESSURE OF AIRFOILS

TRANSVERSELY TO THE AIR STREAM.* 
By Richard Katzmayr. 
Knowledge of the resultant direction of the air force to 
the wing section is a prerequisite for airplane stability calcu-
lations. It is also indispensable for the distribution of the 
load on the different members of the wing structure. Since air-
plane wLngs have a limited span, a knowledge of the distributionT 
of the air forces along the span is a second prerequisite, in 
addition to a knowledge of the pressure distribution along the 
chord. For the condition of minimum drag, the distribution'. 
along the span iselliptical. Tests with models and with full-.. 
sized wings show, however, that the elliptical distribution is 
rarely attained, the pressure distribution generally decreasing 
more gradually toward the wing tips, particularly at large an-
gles of attack. 
The experiments here described were performed for the pur-
pose of obtaining the essential facts concerning the distribu-
tion of the air force along the span. We did not follow, how-
ever, the -time-consuming method of point-to-point measurements 
* ll flruckpunktswanderungenbei Flügeln quer zur. Stromrichtung.11 
From Berichte der Aeromechanischen Versuchsanstalt in Wien, 
Vol. I, No. 1 (1928), pp. 47-57.
N.A.C.A. Technical Memorandum No. 530
	
2 
of the pressure distrithtion on the wing surfaces (the method 
employed by Mnerican and English investigators in both model 
and free-flight tests), but determined directly the moment of 
the mean force about an axis passing through the middle of the 
span parallel to the directiom of flight. The results thus ob-
tained can be immediately used in strength calculations of' 
wings and give values comparable to those obtained under the 
customary assumptions of an elliptical, rectangular, trapezoidal 
or other form of pressure decrease toward the wing tips. They 
also indicate the lateral travel of the center of pressure ac-
companying changes in the angle of attack. Lastly, they show 
hOw this lateral travel o± the' center of pressure is affected 
by changes in the aspect ratio, plan form, and thickness of the 
wing near the tips. 
The proper performance of these tests necessitated the con-
struction of special apparatus. As already mentioned, the ob-
ject was to determine the point of application of the air force 
to each half of the wing with respect to an axis passing through 
the middle of the span parallel to the chord. Figure 1 shows 
the arrangement of the apparatus. It consists of a hanging 
weight P connected with the wing model by two fine steel wires 
1 and 2. This weight enables the application of a variable hor-
izontal force to the model in the direction of the arrow q by 
shifting the support T. The magnitude of the pull Q can be 
determined by the formula Q = Q/Jj2 - m2 , when Q, 1 and m
N.A.C.A. Technical Memorandum No. 530 
are known, Q being the total force exerted by the weight P 
at the point of suspension B, 1. the length of the member BC, 
and m the deflection of the point B from its position of 
rest.. Such pendulum balances have been repeatedly used in. the 
Vienna laboratory for determining the forces exerted by air-
plane controls, the direction-al stability of airplanes, etc. 
They are simple, quick to set up, quite sensitive and accurate. 
In order to enable the use of the pendulum balance in -the 
contemplated tests, the wing models had to be cut in two at the 
middle of the span and perpendicularly to it. The two halves 
were then hinged together. The hinge had to perform three tasks. 
Its first task was to hold the two parts together with as lit-
tie friction as possible. Its second task was to carry the 
points of attachment for rendering the model immovable in the 
windtunnel. Lastly, it had to support a device to indicate 
whether the pulls Q 1/2 we±e in equilibrium with the air forces 
on the two halves of. the model. The hinge consisted of three 
metal parts a, b and c (Fig. 2), the middle one (b) being 
rigidly attached to one-half of the model, and the other two 
(a and c) to the other half. The three metal parts were twice 
drilled lengthwise, the axes of the holes being parallel and 
40 mm (1.5? in.) apart. The hole near the upper side of the 
wing served to receive the steel hinge pirn ci, which fitted 
tightly in the end parts a and c but loosely in the middle 
part b, so that the latter could move easily. A steel pin e
N.A.C.A. Technical Memorandum No. 530 	 4 
could likewise be stuck through the second hole near the lower 
surface of the wing, thus rigidly locking the hinge. The easiest 
possible operatiorr of the hinge was obtained by inserting thin 
washers between the three parts, around the hinge put, , so that 
the edges of the hinge parts did not come into contact with one 
another. The upper point of attachment of the model was provid-
ed by fastening a fork f to the upper end of the hinge pin d. 
The fork had a hole g through which a steel wire was passed 
to form a flexible union: with the upper support u (Fig. 1), 
which was connected with the lift balance in the usual maimer. 
The two lower supports V and w of the lift balance were re-
placed by fine steel wires attached to the rod i by means of 
the hole h. In order to keep the wires v and w continually 
taut, a third wire o was led to the bell crank d carrying 
the counterweight Q2 . The angle of attabk could be varied in 
the usual manner with the aid of the supports u, V and w. 
Moreover, the model was suspended from the drag balance by the 
wire r, which was also attached to the fork f through the 
hole g. The wires a and t, which likewise led to the drag 
balance, were left slack and served as a safety suspension in 
case the wire r should break. This method of suspension made 
it possible to move the wing halves back and forth about the 
hinge pin ci, despite the rigid mooring of the latter and, con-
sequently, of the model in the air stream. The hinge was at-
tached to the wing halves in such a way that the center of the
N.A.C.A. Technical Memorandum Ne. 530	 5. 
hole g in the fork f lay in the leading edge of the model 
and the line connecting g and h lay in the chord. This line 
was also parallel to the hinge pirr d. (Fig. 2). 
A brass bar k was firmly screwed to the middle part b 
of the hinge.. When the hinge was closed, there was a space of 
about 1 mm (0.04 in.) between this bar and the other two parts 
a and c of the hinge. This bar served as a stop. To the wooden 
model there was screwed a brass angle ir: carrying a set screw 
which could be screwed against the bar k. This bar and t1e 
angle n vere connected with a galvanometer through two wires 
and a four-volt storage battery. If the bar and the screw of 
the angle n came in contact, the galvanometer needle was de-
flected. This device served as an indicator of the state of 
equilibrium between the air force which tended to open. the wing 
halves about the hinge and the pull Q of the pendulum bal-
ance which tended to close them. Figure 3 shows the hinge ar4 
the contact device mounted. on the wing. 
In order that changing the angle of attack would cause no 
motion of the wing halves about the hinge pin, the three suspen-
sion points E, F and G (Fig. 1) were arranged in a straight 
line. It is obvious that the weight of the model exerted a mo-
ment about the hinge axis which had to be offset by a corre-
sponding component of the pull of the pendulum balance, in or-
der to maintain equilibrium at different angles of attack. 
This gravity component had to be determined therefore in still
N.A.C.A. Technical Memorandum No. 530	 6 
air before the power was turned on and then subtracted from the 
results obtained in the air stream. 
The dimensions of the hinge and the distribution of the 
screws were such that the same hinge could be used for all the 
different models. On wide models, however, there was a 10 mm 
(0.4 inch) slot between the wing halves at the back end of the 
hinge (Fi. 3). In order to avoid any error in the distribu-
tion of the air pressure in the middle of the span, thin silk 
•	 paper was paste over this slot before' the tests were made. 
Since the paper was not very stiff, there was no danger of its 
hampering the mobility of the wing halves. 
After it appeared probable that the results depended also 
•	 on the aspect ratio of the wings, reotangular wing models of 
the following dimensions were tested: 1210 x 120, 970 X 120, 
730 x 120, 610 x 120 (Figs. 5-8), 1210 x 200, 810 X 200, 
and. 410 x 200 mm (Figs. 9-11), the aspect ratios therefore, 
being respectively, 10.08, 8.08, 6.08, 5.08, 6.05, 4.05, 
and 2.05. Tests were also made with a trapezoidal wing which, 
by cutting, was given spans of 1210, 810 anci O5 mm igs. 
12-15), the.aspect ratios therefore being respectively, 6.8, 
5.13, and 1.84. Lastly, we tested a wing of common form in 
practIce, consisting of a rectangular middle piece to each en 
of which a trapezoidal end piece was joined. The span of this 
model was 1210 mm. Figure 4 shows the shape of the wing sec-
tion' or profile, which was the same for all the models, includ-
N.A.C.A. Technical Memorandum No. 530	 7 
ing the trapezoidal ones in which the thickness was kept propor-
tional to the diminishing chord. 
The test results are given in Tables I-XI and Figures 16-18. 
In addition to the usual data 2 
center-of-pressure coordinates e and. 
is the distance in millimeters of the 
dynamic resultant with the wing chord 
the wing. The latter is the distance 
half-wing from the center of the span
2cW and 2CM, the 
z, are given. The former 
intersection of the aero-
from the leading edge of 
of the air force on a 
measured perpendicnlarly 
to the direction of flow. For trapezoidal wings 2 CM is re-
ferred to an axis 10 mm (0.4 in.) behind the leading edge.. The 
distance e is also measured from the same reference line. 
With the aid of the coordinates e and z, it is possible to 
draw the curve obtained by joining the points of application 
of the air-force vectors on a half-wing in the plane of the 
chord for different •angles of attack (Figs. 5-l5) 
These curves show that, with increasing angle of attack 
cx. , the center of pressure moves toward. the wing tip. On 
small rectangular wings, this transverse travel is greater in 
proportion to the span, for small aspect ratios than for large 
ones. The reverse is the case for large rectangular wings. 
For small aspect ratios, moreover, the center of pressure lies 
nearer the wing tip at small angles of attack than at medium 
ones. For the rectangular wing with the smallest tested aspect 
ratio of 2.05, this phenomenon is reversed in that the air
N.A.C.A. Technical Memorandum No. 530
	 8 
force again, travels toward the middle of the span with increas-
ing angle of attack. The results show, however, that they are 
affected by the magnitude of'the index value. In fact, not 
quite doubling the index value has the same effect on the trans-
verse travel of the center of pressure as a diminutiort • f the 
aspect ratio. These remarks apply to rectanular wings. The 
phenomena are generally similar for trapezoidal wings. 'ith the 
latter, a reduction in the aspect ratio diminishes the travel 
of the center of pressure, as is the case with large rectangular 
wings. Direct comparisorn of the three trapezoidal wings is not 
possible, however, because the results (due to the different 
chords of the three models) are based on different index values. 
The wing with the combination plan form (Fig. 15) shows the 
greatest relative transverse travel of the center of pressure, 
amounting to 17% of the span, but behaves very much like the 
other wings in other respects. 
Moreover, the results show that, for the ordinary angles of 
attack, aspect ratios and wing shapes, the path of the aerody-
namic force very closely follows a parallel to the air flow 
passing through the center of gravity of the half-wing. These 
centers of gravity S are also' indicated in Figures 5 to 15. 
With large aspect ratios and large angles of attack, the travel 
of the center of pressure toward the wing tip is no longer neg-
ligible. This travel increases with increasing index values.
N.A.C.A. Technical Memorandum No. 530 
TABLE I. 
Wing 1. 
s/t = 1210/120 mm 
Area = 1412 Cm2 
Rectangular, X = 10.09 
p = 30 mm water pressure 
2 CA 2c. 2cM e z 
-3 15.1 3.00 14.9 171.0 274.5 
0 38.5 2.97 19.8 82.8 304 
3 55.8 4.07 23,4 61.0 289 
6 76.0 5.38 27.6 52.2 298 
9 91.1 7.11 30.8 45.0 298 
12 104.0 9.25 33.6 42.6 308 
15 111.5 12.75 35,0 40.25 330 
18 111.0 18.90 36.8 41.0 354 
21 81.4 27.20 38.3 42.4 - 
TABLE II.. 
Wing 2 
s/t = 970/120 mm 
Area = 1164 cm2 
Rectangular, X = 8.09 
p = 30 mm water pressure
a. 2°A 2c 2cM e z 
-3 13.0 3.04 13.74 128.0 177.5 
0 32.9 3.12 17.60 64.9 224 
3 52.0 3.90 22.05 51.4 225 
6 71.0 5.38 26.07 46.15 235 
9 88.5 7.63 30.5 41.8 234 
12 100.5 10.25 33.0 39.8 251.5 
15 107.5 12.82 34.8 39.2 260.5 
18 l0'.5 19.70 36.5 41.05 280.5 
21 73.8 26,5 39.7 56.6 360
9 
N.A.C.A. Technical Memorandum Na 530	 10 
TABLE III. 
Wing 3 
s/t = 730/120 mm 
Area = 876 cm2 
Rectangul'ar, X = 6.09 
p = 30 mm water pressure 
a 2°A 2CW 2ci e 
-3 12.73 3.25 12.9 123.1 155.1 
0 31.0 3.35 17.1 66.6 158 
3 48.70 4,28 2.3 53.5 181 
6 68.30 6.24 25.9 46.05 179.2 
9 83.30 7.99 29.55 43.15 178.5 
12 96.0 10.88 32.6 39.7 177 
15 101.8 14.13 34.1 40. 13.5 
18 96.0 20.20 34.7 44.0 194.6 
21 84.5 27.20 39. 47.3 236 
TABLE IV. 
Wing 4 
s/t = 610/120 mm 
Area = 733 cm2 
Rectangular, . = 5.09 
p = 30 mm water pressure 
a 2cA' 2cw 2cM e z 
-3 12.3 3.28 15,0 146.8 175.5 
0 30.0 3.41 17.45 69.9 144 
3 47.8 3.96 21.4 54.0 151 
6 64.1 5.60 25.5 47.7 150.4 
9 80.5 7.65 29.0 43.4 152 
12 90.8 lb.63 31.35 41.5 158.5 
15 98.31 14.05 33.4 44.3 166.3 
18 101.0 19.65 33.55 49.7 170 
21 77.8 27.0 34.5 53.5 214
N.A.C.A. Technical Memorandum No. 530	 11 
TABLE V. 
Wing 5 
s/t = 1210/200 mm 
Area = 2420 cm2 
Rectangular, X = 6.05 
p = 30 mm water pressure 
a 2CA 2c 2cM e z 
-9 8.27 2.25 13.4 324.0 450 
-6 25.6 2.32 17.1 133.3 310 
-.3 43.8 3.06 21.2 97.0 277.5 
0 61.6 4.63 25,4 82,5 271.5 
3 78.2 6.45 29.3 75.0 262 
6 93.0 8.89 33.6 72.2 267 
9 107.0 11.55 36.1 67.5 26.5 
12 113.3 14.87 38.8 68.0 283 
15 117.8 19.22 39.5 67.0 299 
18 117.8 23.95 41.4 7d.9 321 
21 n.o 28.10 41.8 71.5 333 
24 111.5 31.80 42.7 76.5 346 
TABLE VI. 
Wing 6 
s/t = 810/200 mm 
Area = 1620 cm2 
Rectangular, ?. = 4.05 
p = 30 mm water pressure 
a 2cA 2CW 2c1 e z 
-.9 4.94 2.285 13.32 - - 
-6 20,05 2.47 16.3 162.5 210 
-3 35.8 3.34 20.0 111.8 207 
0 51.6 4.70 23.7 92.0 198 
3 68.0 6.60 27.4 80.6 197 
6 83.4 9.26 31.76 74.6 192.5 
9 95.6 12.22 34.8 72.9 190.2 
12 104.0 15.4 36.83 70.? 189.2 
15 109.5 20.5 37.24 69.8 184.9 
18 109.5 25.6 38.16 69.6 187 
21 103.6 30.2 38.16 73.5 198.5 
24 102.0 34.2 40.9 90.7 201.3
N.A.C.A. Technical Memorandum No. 530	 12 
TABLE VII. 
Wing 7 
s/t = 410/200 mm 
Area = 820 cm 
Rectangular, X = 2.05 
p = 30 mm water pressure 
a 2CA 2cW 2°M z. 
-9 2.44 2.94 12.76 -	 - - 
-6 13.42 2.99 14.0 208.8 89f2 
-3 25.6 3.5 16.4 128.0 94,6 
0 38.4 4.76 19.0 104.0 94.9 
3 50.6 6.35 21.8 86.4 95.3 
6 63.5 8.91 25.0 78.9 93.1 
9 76..3 12.2 27.95 73.0 90,4 
12 88.5 16.0 31.3 70.9 86.4 
15 95.8 19.3 34.6 '72.4 86.6 
18 101.0 24.15 37.2 73.5 83.5 
21 101.0 27.8 38.0 75.15 83.5 
24 92.7 3.9 39.9 S6.2 90.9 
TABLE VIII. 
Wing 8 
S /tm = 1210/180 ITIIfl 
Area = 2184 cm2 
Tapezoida1, X = 6.72 
p = 30 mm water pressure 
a. 2c 2c 2c e z 
-9 5.05 2.515 - 12.2 - -. 
-6 24.22 2.58 .16.42 - - 
-3 41.6 3.25 20.03 200.0 176.5 
0 58.6 4.49 24.21 125.8 165.0 
3 75.3 5.92 27.8 103.2 204.0 
6 96.7 8.15 32.35 89.3 206.5 
9 103. 10.52 34.0 85,6 228.2 
12 .115.7 13.5 36.81 78.4 232.5 
15 125.ö 17.02 39.2 72.0 242 
18 118.5 22.2 41.8 69.7 283
N.A.C.A. Technical Memorandum No. 530 	 13 
TABLE IX. 
Wing 9 
S/tm 405/220 mnl 
Area = 891 cm2 
Trapezoidal, X =1.15 
p = 30 mm water pressure 
2c 2c 2c e z 
-9 2.8 4.01 11,4 - -. 
-6 12.9 4.04 13.01 222 - 
24.? 4.32 14.86 132.8 65.5 
0 36.5 5.50 17.12 103.6 77.5 
3 47.1 7.3 19.73 94.5 84.6 
6 58.4 10.1 22,5 85.0 89.0 
9 68.6 12.9 25.32 80.15 93.0 
12 80.8 16.85 28.8 78.5 94.0 
15 90.0 20.85 32.05 77.0 94.5 
18 95.4 25.22 35.6 8.4 96.0 
21 95.4 29.2 36.5 84.1 86.8 
TABLEX. 
Wing 10 
S /tm = 810/160 mm 
Area = 1296 cm2 
Trapezoidal, X = 5.05 
a. 2cA 2CW 2cM e z 
-9 2.315 3.16 10.18 - - 
-6 18.5 3.09 13.67 - 180 
-3 35.5 3.7 l7.2 77.6 179.2 
0 51.5 4.86 21.55 66.75 185.? 
3 68.0 6.49 25.? 60.7 188.1 
6 85.0 8.8 30.4 57.4 182.1 
9 99.5 11.1 33.9 54.6 178.8 
12 114.1 14.1 37.1 52.0 175.0 
15 126.5 17.35 4b.0 57.15 175.0 
18 132.7 21.3 42.6 58.05 172.0 
21 125.0 27.4 44.9 57.9 180.0
p = 30 mm water pressure 
N.A.C.A. Technical Memorandum No. 530	 14 
TABLE XI. 
Wing 11 
S/tm = 1210/160flUn 
Area = 2100 cm2 
Rectangular and Trapezoidal, X = 7.56 
p = 30 mm water pressure 
a 2cA. 2CW 2M e Z 
-9 6.66 2.24 12.8 - 
-6 24.78 2,34. .14.5 135.6 190.0 
-3 44.7 3.05 20.5 93.3 224.7 
0 63,4 4,29 24.6 79.0 236.4 
3 81.0 6.14 28.8 ?2.4 243,2 
6 95.2 8.32 32.2 70.5 252.5 
9 108.0 11.16 35.6 66.5 266.1 
12 115.6 14.3 36.8 64.3 280.2 
15 117.0 17.9 39.3 72.7 303.2 
18 117.0 23.6 41.8 72.7 316.0 
21 11.6 28.0 41.5 88.0 333.0 
24 96.1 33.8 - - 396.0
Translation by Dwight M. Miner, 
National Advisory Committee 
for Aeronautics. 
0 
a 
C
N.A.O.A. Technical Memorandum No. 530
	 Fis.l,2,4. 
Fig.2 
Fig.4
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am! 
II
N.A.O.A. Technical Memorandum No530 	 Fige.5,6, 7,8. 
	
1 10	 210	 310	 410	 510	
6O 
	
50	 3°	 120,t 
	
00 1 	 / 
-1210,s 
	
__ •	
/	 Io,t 
________ji 
—9 70, 
I 
	
L_50
	 21	
120, t 
	
—J-00I	 I 
730,s- J 
120,t 
__	 I 
610.t
100	 200	 300 
I	 I 
Figs.5,6,7,8.
400i	 500	 600 
I	 I
N.A.C.A. Technical Memorandum No.530 
100	 200	 300	 400 
L1001 
—15O
	
E24 
L200 1 	 - 
1210,s
Figs.9, 10,11. 
5f0
	 efo 
200, t 
	
_181	
200,t 
200--
I 
_	
200,t 
—410,s 
_16 
100	 200	 •310	 400 
Figs.9,10,11.
500	 600
N.A.C.A. Technical Memorandum No. 530 
190	 2O	 3?0
Figs.12, 13,14,15. 
4fJO	 5D0	 600 
1210, s
=l:12.5 
12 
0L2d0,t	
jqo jjiTI. 
-810s 
p-J2.5 
15	 1 
1 OO-j---,1	 010, t
Figs.12,13,14,15. 
-405,s	 ______________________________ 
____ 1210,s 
___________	
1:12.5 
____	
t 
P
I	 I 
100	 200	 300	 400	 500	 600 
I	 I	 I	 I	 I


Travel of the center of pressure of airfoils transversely to the air stream

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