Boatright, William B

Rainey, Robert W

English

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CopyNo. 
CON FIDENTIAL	 RM No. L8K12a 
NACA 
RESEARCH MEMORANDUM 
ifiNGE-MOMENT MEASUREMENTS OF A WING WITH LEADING-EDGE 
AND TRAILING-EDGE FLAPS AT A MACH NUMBER OF 1.93 
By 
William B. Boatright and Robert W. Rainey 
Langley Aeronautical Laboratory

Langley Field, Va. 
CLASSIcATioN CHkNGD TO UNCIAss'IrD 
AUT,HOaiTL . JW.GROWLEY
	 DATE: fl-1L-S 
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NATIONAL ADVISORY COMMITTEE
FOR AERONAUTICS 
WASHINGTON 
January 14, 1949 
CON Fl DENTIAL. 
https://ntrs.nasa.gov/search.jsp?R=19930085565 2020-06-17T16:33:54+00:00Z
NACA RM No, L(12a	 CONFIDENTIAL 
NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
RESEARCH MEMORANDUM 
HINGE-MOMEI'IT MEASuREMENTS OF A WING WITH LEADING-EDGE 
AND TRAILING-EDGE FLAPS AT A MACH NUMBER OF 1,93 
By William B. Boatright and Robert W. Rainey 
SUMMARY 
Hinge-nionient measurements were obtained. from a semispan. wing with 
both leading-edge and trailing-edge flaps in the Langley 9-inch super-
sonic tunnel. The wing had a straight taper of taper ratio equal to 
0. 79, an aspect ratio of 3.14, and. constant-chord flaps (18.9 percent at 
the root)0 All tests were carried out at a ch number of 1.93 and. a 
Reynolds number of 1.31 x io6 based on mean chord of model. 
Leading-edge-flap test results show that the rates of change of hinge-
moment coefficient C with angle of attack a, are almost identical 
with values of the rate of change of hinge-moment coefficient with flap 
deflection 8 and are in excellent agreement with theoretical calculations. 
The slope3 of both tend. to increase at the higher values of the total 
angle of the flap plus the angle of attack as the theoretical- dalculations 
predict. 
For the trailing-edge flap, the test results indicate that dCh/da. 
and dCh/d8 are essentially the same for the small range of both flap 
angles and angles of attack that were tested. The test values of both 
dCh/da and dCh/d8 were somewhat lower than the values obtained. by 
theoretical calculations, as might be expected, primarily because of 
separation near the trailing edge. 
It is indicated from the results that, at least for the test Ich 
number of 1.93, a linkage system with a fixed ratio between the leading-
edge and. the trailing-edge flap might be used to reduce to approximately 
zero the resultant force required to deflect the flaps. 
INTRODUCTION 
One of the problems in the design of supersonic aircraft and missiles 
is a means for overcoming the large stick or servocontrol forces resulting 
CONFIDENTIAL
2	 COI1FIDENTIAL	 NACA RN No. Ll2a 
from control-surface deflection. A wing or stabilizer, which has both 
leading-edge and trailing-edge flaps connected by a linkage such that 
the hinge moment of one helps to counteract that of the other, has been 
suggested. In an effort to investigate the feasibility of such a linkage, 
hinge-moment measurements from a wing with leading-edge and trailing-edge 
flaps have been made at a Màh number of 1.93. 
SYOLS 
wing angle of attack 
8	 flap-deflection angle with respect to the wing (positIve when in 
the direction that will iiicrease the wing lift coefficient, up 
deflection for leading-edge flap and down deflection for trailing-
edge flap) 
A	 angle of sweepback 
wing taper ratio (ct/cr) 
p	 free-stream density 
e	 flap semiangle (measured in streaniwise direction) 
absolute viscosity 
A	 aspect ratio (b2/S) 
b	 span of model 
mean geometric chord of wing 
Cf	 chord of flap (perpendicular to hinge line) 
cr	 wing chord at root 
wing chord at tip 
Ch	 hinge-moment coefficient (_U 
\q(cf) - 
U	 hinge moment of flap about its hinge line (of opposite sii than 
when acting as a restoring iuoent) 
M	 stream Mach number
COEWIDWPIAL
NACA PM No, L8ICL2a
	 COEFIDENTIAL
	
3 
p ' stream static pressure 
q.	 d,ynamic pressure (0.7pM2) 
P	 Reynolds number (pV6)/it 
S	 total area of full-span model 
t	 thickness of wing 
V	 free- stream velocity 
Subscripts: 
LE	 leading edge 
TE	 trailing edge
APPARATtJS AND TT TE0] 
AU tests were conducted in the Langley 9-inch supersonic tunnel at 
a Mach number of 1.93 and. a Reynolds number of 1.31 x io6 (based on mean 
geometric chord of the wing). The tunnel is of the closed-return type, 
and the Mach number is varied by Interchanging nozzle blocks which form 
test sections approximately 9 inches sajiare, The air is sufficiently dried 
before each test for the effects of condensation in the supersonic nozzle 
to be negligible.	 V V 
The semispan model tested was of all-steel construction with both. 
leading-edge and. trailing-edge full-span flaps of wedge section (fig. 1). 
The geometric characteristics of the model are presented in the following 
table: 
Wing sendspan,b/2,inches 	 6000 
Wingrootchord.,c,inches.....o............, 	 4,81 
Wing-tip chord, Ct, inches .	 . . . . . . . . . . . . . . .	 2,81i. 
Flap chord, Cf inches
	 0	 •	 •	 •	 .	 .
	 0.91 
Wing area, S, sq.uare inches ...................	
.90 
Flap area, Sf , square inches	 7072 
Wing aspect ratio, A	 3.14 
Taper ratio, X	 ..........................	 0.59 
Wing thickness, t, inches .................... 	 0.30 
Angle of swoepback,A, degrees .............
	
.
	
9.33 
Flap seimiangle, e, degrees	 9,16 
C0I'FIDETIAL
4	 CONFIDENTThL	 NACA RM No. L8ICL2a 
Each flap was coupled to the wing through strain-gage bealn$, with Linch 
clearance between the flap and the wing 
The deflection of one flap was set at a value in. the range -5° to 50, 
with the other flap set at approximately zero, with the tunnel not running. 
Then, with the tunnel running, hinge-moment measurements were made through 
a range of wing angles of attack from _30 to 100 . Because of strain-gage 
trouble with one of the flaps, the tests were conducted with the leading-
edge flap at a given angle; the whole model was then rotated 180 0 , and the 
leading-edge flap became the trailing-edge flap. Neither flap remained at a 
constant deflection because of changing loads on the flap as the angle of 
attack was varied. However, all angles were measured from photographs of 
the tip taken simultaneously with the hinge-moment measurements. Both angles 
of attack and flap angles were referenced to the center line of the tunnel. 
The flap angles were practically the same as if the angles were measured 
normal to the hinge line of the fap since there was only 9.33 sweep of 
the hthge lines. 
The semispan model was mounted on a boundary-layer scoop-off plate 
so that the part of the' model near the root was free of tunnel-wall 
boundary-layer effects. One of the characteristics of semlspan testing 
is that the data include the interference effects of a mirror image of 
the wing being tested (due to reflections of disturbances back on the 
wing); thus the data presented correspond to those for a full-span wing 
where the control surfaces operate as flaps and not as ailerons. 
PRECISION OF RFULTS 
It was found from a survey along the air stream at three vertical 
positions that, for a Mach number of 1.62, the installation of. the boundary-
layer scoop-off plate alone caused a maximum change in static pressure of 
0.8 percent in the region to be occupied by the model. It is believed 
that this change in static pressure was even less at a Mach number of 
1. 93 . The maxinnim streanwise variation in static pressure for a Mach 
number of 1.93 with no boundary-layer plate installed is ±1.5 percent 
over the region occupied by the model, 
It is believed that the strain gages permitted accurate measure-
ments of the hinge moments to within Ch = ±0.003. This figure is based 
on observations of how well the zero readings checked before and. after 
each test and the linearity and the lack of hysteresis of the calibration 
curves. 
The angles of attack of the wing and. the flap angles were measured 
from photographs taken normal to the tip while the tunnel was running. 
It is believed that these angles are accurate to within ±0.25° with 
C OI\JFIDENTIAL
NACA RM No L8K12a	 CONFIDENTIAL	 5 
respect to the tunnel center line. This value is based on the consistency 
with which it was possible to recheck angle measurements taken from the 
photographs of the model. In figure 2 it can be seen that for a, = 00, 
zero hinge moment for the leading-edge flap occurs at 6 = 1.10 and, 
similarly in figure 3, that for 6 = 00 ,
 zero hinge moment occurs at 
a = 1.10
. Because of the manner of testing, that is, rotating the model 
1800
 when taking trailing-edge-flap data as compared with the position 
when taking leading-edge-flap data, ±0. !.° can be ascribed to model 
asymmetry. This may be seen by comparing (in figs. 2 and 3) the zero 
hinge-moment values of the leading-edge arid trailing-edge flaps with each 
other. The remaining part of the displacement of the curves is believed 
to be a combination of two other possible sources of error: (1) stream 
angle, and (2) misplacement of the reference axis. 
DISCUSSION 
The data obtained from these tests are presented in table I. It ras 
necessary to modify the test points, for more convenient analysis of the 
data, in the following manner: curves of the measured values of Ch against 
the measured values of a were plotted; and, at selected constant values 
of a, the corresponding hinge-moment coefficients were read. The values 
of flap deflection at the selected angles of attack were read from plots 
of the measured flap-deflection angles against the measured angles of 
attack, where smooth curves were faired through the points. (The accuracy 
was believed to be ±0.25° and also it was recogaized that other than a 
smooth variation of deflection under load with angle of attack seemed 
highly improbable,) Curves were then plotted of the variation of hinge-
moment coefficient with flap deflection for constant values of angle of 
attack (fig. 2). Th variation in hinge-moment coefficient with angle 
of attack for constant values of flap deflection (fIg. 3) was obtained 
by cross-plotting. 
Fore
 the leading-edge flap, for which the results can be expected to 
be independent of trailing-edge-flap position and for which there was no 
discernible interrelation for the small range of angles tested, the 
experimental value of both dCh/d6 and dCh/da was the same in the low-
angle region at a value of 0.030. At the higher flap-deflection angles 
and angles of attack there was a tendency for the slope to increase. An 
Interesting point is that, for the 9.16° half-wedge angle of the flap 
and a stream Mach number of 1.93, the leading-edge shock would detach 
(theoretically) at a total angle (flap-deflection angle plus angle of 
attack) of about 12.6°. No abrupt break in the curves was noticed at this 
point. The theoretical values of dCh/d6 and dCh/da for the leading-
edge flap are the same, and this value of 0.031 in the low-angle range 
with a gradual increaseto about 0.035 in the range from about 6° tb 12° 
compares favorably with the test results. These theoretical values were 
CONFIDENTIAL
6	 COTFIDENTIAL	 NACA RM No. L8K12a 
obtained, by use of the inviscid, shock and expansion theory over the two-
dimensional region of the flap (outside the Mach cones arising from the 
leading edge of the tip and of the root) and by use of the linear theory 
f or he region within these Mach cones. 
The effect of the leading-edge-flap position on the trailing-edge-
f lap results was expected to be small, and for the random variations of 
leading-edge-flap angles between -2.50 and 2.70, there was no discernible 
interrelation.. The trailing-edge experimental values obtained were 
dCh/d8 of -0.010 with no appreciable variation with a and dCj,jda. 
of -0.0095 for various 8 values.' In spite of any effect of the leading-
edge flap, there was very little scatter of the test points. The 
theoretical value of dCh/d8 for the trailing-edge flap was coinputed by 
the method outlined in reference 1 and, for a = Q0, was -0.015. The 
theoretical value of dCh/da of -0.011 at 8 = 00 was computed by 
assuming that the ratio of the thickness effect in the two-dimensional case 
and the three-dimensional case (computed from the linearized theory) were 
the same. The test results are seen to be somewhat lower than these 
theoretical values, as might be expected, primarily because of separation 
near the trailing edge. 
If a wing or stabilizer with both leading-edge and trailing-edge flaps 
were so designed that the hinge moment of one flap helped counteract that 
of the other, then for the design to be feasible the difference between 
dCh/da and, dCh/dö must be small. The results for the coafiguration 
as tested indicated that this difference was not large, the ratio of 
hinge moments for equal deflection of the two flaps varying only from 
about 2.65 to 3 . 35 throughout the test range of angle of attack, as shown 
in figure 1.. In order to reduce to zero the resultant force required to 
deflect the flaps, it can be shown that the ratio of flap deflections 
(which is equal to the mechanical advantage of a.ny suitable linkage) would 
vary accordingly from about V2.65 to f3.35, or from 1.63 to 1.83. An 
analysis of the forces involved in the linkage will show the relation 
between the linkage ratio for zero resultant force and the hinge-moment 
ratio for equal flap angles, namely that the former ratio is the square 
root of the latter. The smallness of the variation of the required 
linkage ratio suggests that a constant ratio of about 1.73 would reduce 
the resultant force required to deflect the flaps to a value close to 
zero. The constancy of this ratio for higher angles ITLight be in some 
doubt owing to the fact that the effect on the trailing-edge flap of 
larger leading-edge-flap deflections was not determined; however, since the 
leading-edge flap will deflect only 1/1.73 of the trailing-edge-flap deflec-
tion and the test results include leading-edge-flap deflections of -2.5 
to 2.5°, the results should be applicable to a range of trailing-edge-flap 
deflections from about _11.30 to	 The ratiobetween hinge moments 
may also be a function of Mach number so that a linkage of fixed ratio 
might hold hinge-moment values close to zero for only a limited range 
of Mach number.
C0NFIDNTIAL
NACA PM No0 LL2a	 CONFIDENTIfiJI 
CONCLUDING REMkRKS 
The experimental results as obtained for the leading-edge flap were 
in exceflent agreement with theoretical calculations. For the trailing-
ed.ge flap, the measured. hinge-moment values were somewhat lower than the 
theoitical calculations, as might be expected, primarily because of 
separation near the trailing edo. The smafl differences in d.Ch/d8 
and dCbJda for each flap suggest that a linkage between the two flaps, 
which would. reduce the resulting hinge-moment value close to zero s would 
be feasible for the test Mach number. However, the ratio between hinge 
moments may also be a function of Mach number so that a linkage of fixed 
ratio might hold hinge-moment values close to zero for only a limited range 
of Mach number. 
Langley Aeronautical Laboratory 
National Advisory Committee for Aeronautics 
Langley Field, Va.
REFERENCE 
1. Tucker, Warren A., and Nelson, Robert L.: Theoretical Characteristics 
in Supersonic Flow of Constant-Chord Partial-Span Control Surfaces 
on Rectangular Wings Having Finite Thickness. NACA TN No. 1708, 191i.8.
NCA PM No. L8L2a 
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.	 CONFIDENTIAL 
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Hinge-moment measurements of a wing with leading-edge and trailing-edge flaps at a Mach number of 1.93

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