Hinge moments of sealed-internal-balance arrangements for control surfaces

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Title:
Hinge moments of sealed-internal-balance arrangements for control surfaces
Series Title:
NACA WR
Alternate Title:
NACA wartime reports
Physical Description:
20 p., 20 : ill. ; 28 cm.
Language:
English
Creator:
Murray, Harry E
Erwin, Mary A
Langley Aeronautical Laboratory
United States -- National Advisory Committee for Aeronautics
Publisher:
Langley Memorial Aeronautical Laboratory
Place of Publication:
Langley Field, VA
Publication Date:

Subjects

Subjects / Keywords:
Airplanes -- Wings -- Testing   ( lcsh )
Aerodynamics -- Research   ( lcsh )
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federal government publication   ( marcgt )
bibliography   ( marcgt )
technical report   ( marcgt )
non-fiction   ( marcgt )

Notes

Summary:
Summary: The results of a theoretical analysis of the hinge-moment characteristics of various sealed-internal-balance arrangement for control surfaces are presented. The analysis considered overhangs sealed to various types of wing structure by flexible seals spanning gaps of various widths or sealed to the wing structure by a flexible system of linked plates. Leakage was not considered; the seal was assumed to extend the full spanwise length of the control surface. The effect of the developed width of the flexible seal and of the geometry of the structure to which the seal was anchored was investigated, as well as the effect of the gap width that is sealed.
Bibliography:
Includes bibliographic references (p. 20).
Statement of Responsibility:
by Harry E. Murray and Mary A. Erwin.
General Note:
"Originally issued August 1945 as Advance Restricted Report L5F30."
General Note:
"NACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution of advance research results to an authorized group requiring them for the war effort. They were previously held under a security status but are now unclassified. Some of these reports were not technically edited. All have been reproduced without change in order to expedite general distribution."

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University of Florida
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All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 003807480
oclc - 126864601
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Full Text


ARR No. L5F30


NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS





WARTIME REPORT
ORIGINALLY ISSUED
Augast 1945 as
Advance Restricted Report L5F30

HINGE MOMENTS OF SEALED-INTERNAL-BALANCE
ARRANGEMENTS FOR CONTROL SURFACES
I THEORETICAL INVESTIGATION
By Harry E. Murray and Mary A. Erwin

Langley Memorial Aeronautical Laboratory
Langley Field, Va.
I I' ," 1 1.-
DO:CU iEI.I-FS DEP. T, T
120 M.i4STGN SClEi JSCE l JcHR
-P.. P\lSOLL 1 70 Ui
G.,-_i IESVILLE, FL 32611-7011 US,"


WASHINGTON


NACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution of
advance research results to an authorized group requiring them for the war effort. They were pre-
viously held under a security status but are now unclassified. Some of these reports were not tech-
nically edited. All have been reproduced without change in order to expedite general distribution.


L 174


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Digitized by the Internet Archive
in 2011 with funding from
University of Florida, George A. Smathers Libraries with support from LYRASIS and the Sloan Foundation


http://www.archive.org/details/hingemomentsoflang








IIACA ARR No. L5F30

NATIOT'AT ADVISORY COMMITTEE FOR AERONAUTICS



ADVAiNCE RESTRICTED REPORT


HINGE TfrMFNTS OF SFALED-INTERNATL-BALANCE

ARRANGEMENTS FOR CONTROL SURFACES

I'- THEORETICAL INVESTIGATION

By Harry E. Murray and Mary A. Erwin


SUMMARY


The results of a theoretical analysis of the hinge-
moment characteristics of various sealed-internal-balance
arrangements for control surfaces are presented. The
an,:-lysis considered overhangs sealed to various types of
wiing structure by flexible seals spanning gaps of various
widths or sealed to the wing structure by a flexible
system of linked plates. Leakage was not considered; the
seal was assumed to extend the full spanwise length of
the control surface. The effect of the developed width
of the flexible seal and of the geometry of the structure
to vhich the seal was anchored was investigated, as well
as the effect of the gap width that is sealed.

The results of the investigation indicated that the
most nearly linear control-surface hinge-moment charac-
teristics can probably be obtained from a flexible seal
over a narrow gap (about 0.1 of the overhang chord), which
is so installed that the motion of the seal is restricted
to a region behind the point of attachment of the seal to
the winn structure. Control-surface hinge moments that
tend to be high at large deflections and low or over-
balanced at small deflections will result if a very narrow
s a1 is used.


INTRODUCTION


Experimental data on control surfaces having various
arrangements of sealed internal balances have been col-
lected and a correlation has been made of the hinge-moment
cherscteristics for small deflections (reference 1). The
data used in this correlation were for balances consisting










NACA ARR No. L5F30


of an over-h.ne,7 sealed to a wing structure by a flexible
seal made of thin rubber or fabric. The effect of the
overhang-seal combinations was assumed to be the same as
that of an effective, overhang chord equal to the chord of
the actual overhang plus one-half the width of the gap
closed by the flexible seal. Obviously, such an assump-
tion could be expected at best to account approximately
only for the effect of the balance configuration near zero
deflection of the control surface and to neglect the
effects of variations of the dimensions of the balance
chamber, the developed seal width, and large control-
surface deflections.

Because sealed internal balances are co.ning into
rather wide use on the closely balanced control surfaces
of high-soeed airplanes, a systematic investigation has
been made by the Stability Research Division of the NACA
to determine the characteristics of such balances. The
results of the investigation provided data that may be
used in obtain, better original designs of sealed
internally balanced control surfaces and that allow a
more accurate estimate of the change in hinge-moment
characteristics associated with modifications of the
balance arrangement.

The investigation included both a theoretical and an
experimental study. The theoretical investigation, which
is presented herein, has as its object the isolation of
the most important variables affecting the characteristics
of sealed balances and the determination of the effects of
as many of these variables as possible. The theoretical
analysis was supplemented by an experimental study (ref-
erence 2), which served as a check on the theory and pro-
duced data on many important details not adapted to
theoretical procedure.

For the general investigation, two types of internal
balance were considered, typical installations of which
are shown in figure 1. In one case the overhang was con-
sidered to be connected to the wing structure by a flexi-
ble seal capable of sustaining only tensile stress; whereas
in the other case the seal was a flexible system of linked
plates.

The theoretical analysis given herein presents results
showing the effects of variations of gap width, developed.
seal width, and shape of wing structure to which the seal
is attached for the flexible sealed balance and the effect










IACA ARR No. L5F30


of varying the length of the seal plate in a linked-
plate balance consisting of two plates.


SYMP: CLS.


cb overhang chord

!p pressure difference across balance

x,y coordinates referred to origin at overhang hinge
axis

h,k coordinates of seal arc center

L1 vertical clearance required for seal to develop
moments presented in figures 9 to 11, fraction
of overhang chord

g width of gao between points of attachment of seal
when 6b = 00, fraction of overhang chord

6b overhang deflection, degrees (See fig. 2 for sign
conventions.)

r radius of seal arc

p mass density of air, slugs per cubic foot

T tensile force in fabric seal per unit span

PR pressure coefficient across balance

V free-stream velocity

q free-stream dynamic pressure IpV 2

MB total balance moment of balance system of unit span

v volume of balance system at deflection 5b

6 control-'surface deflection, degrees

Mb moment of overhang of unit span ( cb2

Ms seal moment; incremental hinge moment resulting
from seal of unit span










NACA ARR No. L5F30


t thickness of overhnsr at hinge axis

m seal-moment ratio for overhang having t = 0 (Ms/Mb)

s developed seal width, fraction of overhang chord

Ach increment of section hinge-moment coefficient
resulting from balance

Cf control-surface chord

ca aileron chord

S le.dlne-e.ge angle of overhang

c airfoil chord

h control-surface section hinge moment
2
ch section hinge-moment coefficient (h/qcf2)

a angle of attack, degrees


ANALYSIS

Methods

The present theoretical analysis was an investigation
of the characteristics of various configurations of sealed
internal balances. These configurations consist mainly of
the two types illustrated in figure 1: (1) overhang
balances sealed to the wing structure by flexible material
capable of sustaining only tensile stresses and (2) over-
hang balances sealed to the wing structure by a flexible
system of linked plates.

The moments resulting frcm the types of balance shown
in figure 1 were determined by the following two methods:

(1) Resolution of forces The method of the reso-
lution of forces consists of finding the forces exerted
by each part of the balance system as a result of a
pressure difference across these parts. The moments of
these forces about the control-surface hinge are then
added to get the total moment of the balance system.










NACA ARR No. L5F30


(2) Volume displacement The method of volume dis-
placement consists of finding the rate of change of volume
swept by the balance with deflection. The moment of the
balance is then

MB = ) Ap (1)


Overhang Balance with Flexible Seal

The configurations investigated are shown in
figures 3 to 5. The moments of such balances can be
written as the sum of the moment resulting from the over-
hang and that resulting from the seal; therefore,


MB = : b2 + (2)


The moment exerted by the seal can be expressed in terms
of the se'al-moment ratio ms. Then



M B 2 I.+ -cb2 m (3)


or, in terms of an increment of hinge-moment coefficient,


PR /Cb t \2
Ach = ) 1 + s (
2 \cf [ 2cb


In order to obtain numerical values for Ach, an
investigation was made of the variation of the seal-moment
ratio ms with the two important balance dimensions the
width of the gap to be sealed and the developed width of
the seal. Such variations were investigated for seals
attached at the leading edges to the following backplates,
which simulate three representative types of wing structure:










NACA ARR Uo. L5F30


(1) Forizontal-line backplate (fig. 3)
(2) Vertical-line backplate (fig. 4)
(3) Circular-arc backplate (fig. 5)

The flexible sejls analyzed were assumed to be non-
porous, inextensible, perfectly flexible, and weightless.
These assumptions imply that the unrestrained part of the
seal forms an arc of a circle and has a tensile force,
per unit span, of T = pr acting everywhere tangent to
the arc. The moments resulting from these seals arise
either from the tensile stress in the seal (figs. 3, 4(a),
and 5(a))or from the seal lying along and equalizing the
pressure over part of the overhang (figs. 4(b) and 5(b)).

In order to apply the resolution-of-forces method to
the seals shown in figures 3, 4(a), and 5(a), the radius
of the seal arc end the noint at which the seal leaves the
backplate were determined. The investigation showed these
unknowns to be related to the other variables in the
balance system as indicated by the equations presented in
appendix A. After these unknowns had been determined as
suggested in appendix A, the balance systems were con-
structed as shown in figures 3, 4(a), and 5(a). The seal
moment was then computed from the seal tension and the lever
arm, which was measured from the construction. If the
resolution-of-forces method is applied to the seals shown
in figures 4(b) and 5(b), the lever arm of the tensile
force in the seal is zero. The reduction in effective
overhang chord caused by such seals was equal to the
amount of overhang covered by the seal; this amount can
be determined as explained in appendix B.

In order to apply the volume-displacement method to
the seals shown in figures 3, 4(a), and 5(a), the balance
system was again constructed graphically. The area swept
by the seal, which equals the volume for a unit span, was
then mechanically integrated and plotted against flap
deflection. The slopes of this curve could then be esti-
mated for use in the formula for MB. Because of the
difficulty of estimating the slopes from these curves, the
volume-displacement method proved to be the less accurate
of the two methods. If the effective-overhang reduction
corresponding to the seals of figures 4(b) and 5(b) is
found by the method of aopendix B, the moment resulting
from the seal can be determined in terms of the volume
swept by the effective-overhang reduction.










:IACA ARR No. L5F30


Pressure-distribution data showed that, at high angles of
attack, the deflection of a control surface from -6 to
-12 may be necessary before the pressure across the seal
changes sign. At such deflections the seal is extended
in a direction opposite that of the overhang. This
deflection range corresponds to the negative values of the
overhang deflection 5b. (See fig. 2.) As soon as the
pressure changes sign, the seal blows across the gap and
5b is again positive. In order to investigate this
phenomenon, seal moments were computed for values of 6b
from -12 to 200 except in cases of very small gaps, for
which the computation of seal moments for the entire
negative range was sometimes impractical.


Overhang Balance with Linked-Plate Seal

Figures 6 and 7 show linked-plate balances consisting
of two and three hinged plates, respectively. The total
moment of the balance system can again be represented by
equation (3) in which the seal moment is the moment of all
arts of this balance except the moment of the overhang
rigidly attached to the control surface. As indicated in
appendix C, the moments exerted by such balances can be
determined by both the resolution-of-forces and the volume-
displacement methods.


RESULTS AND DISCUSSION


An investigation of the seal-moment characteristics
of the various seal arrangements was made by the resolution-
of-forces method and was checked by the volume-displacement
method. Only the moment characteristics of the seals are
presented. The effects of the entire balance system can
be obtained from the seal-moment characteristics by means
of equation (4). Figure 8 presents the characteristics of
flexible seals for various gaps as given by the approximate
formula of reference 1.

Hinge moments of internally balanced control surfaces
normally become heavy at large deflections as a result of
a decrease in 6PR/66 with deflection. In order to offset
somewhat the effect of a decrease in 6PR/65 with deflec-
tion and to give the most nearly linear control-surface










NACA ARR No. L5F50


hinge moments, 6ms/66b should have a positive value.
(A positive value of 6ms/66b that increased with
deflection would be even more desirable but generally
cannot be obtained.) This positive value of 6ms/66b
may be considered favorable inasmuch as linear or nearly
linear control-surface hinpe moments, although not
altogether necessary, are generally desirable.


Flexible Seals

The characteristics of the flexible seals are pre-
sented in figures 9 to 11 for the horizontal-line, vertical-
line, and circular-arc backplates. A comparison of these
figures with figure 8 shows that, in general, large errors
in the seal moments may result from the use of the approxi-
mate formula. Corresponding large errors can also be
expected in control-surface hinge moments estimated by the
approximate formula, except when the seal effect is small
relative to the total balance moment. The seal character-
istics shown in figures 9 to 11 can be discussed best in
terms of the following seal variables: gap width,
developed seal width, type of backplate, and type of over-
hang.

Effect of gap width.- The effect of changes in gap
width can be seen best by reference to the curves for
s = 0.6 (figs. 9 to 11) for any backplate. These curves
indicate that an increase in gap width for a seal of con-
stant width increases the seal moment at small positive
deflections and decreases the seal moment at large posi-
tive deflections; the effect is, therefore, a change in
6ms/66b in the negative or unfavorable direction. If the
most nearly linear control-surface hinge-moment character-
istics over the entire deflection range are desired, small
s-os of the order of g = 0.1 should be used. In terms of
control-surface hinge moments, increasing the gap width
tends to result in high control-surface hinge moments at
large control-surface deflections and low or overbalanced
moments at small control-surface deflections.

Effect of developed seal width.- Figures 9 to 11
indicate that decreasing the developed seal width tends
to change 6ms/$ b in the negative direction, a change
which is unfavorable. This effect should be the most
important single consideration in the design of a flexible










HACA ARR No. L5F50


sealed balance. The seal must be sufficiently long that
it does not become taut (see fig. 12 ) within the usable
deflection range. The seal shown in figure 12 has a very
large radius of arc; therefore, a very large tensile force
is to be expected. Because this force is so directed as
tc unbalance the control surface, a sharp control-surface
hinge-moment increase is to be expected at large deflec-
t on s.

Very wide seals contact the balance-chamber boundaries
at large deflections. A reduction of the seal moment then
results at large deflections and this reduction also tends
t-. change oms/6b -in the negative or unfavorable direc-
tion. Because of the difficulties involved in the analy-
sis of the seal effect after the seal has contacted a
balance-chamber boundary, such effects have been determined
e-:pnrimentally (reference 2). Figures 15 to 15, however,
w-.'re included to indicate the ranges of gap, seal width,
srid deflection in which the seal moments presented in
figures 9 to 11 can be expected to be valid if the balance-
chamber depth is known.

Effect of backplates.- The effect on the seal moments
of the three backplates investigated is shown in figure 16.
Figure 16(a) shows that, for a small gap (g = 0.1), the
horizontal-line backplate tends to give large balance
moments at small deflections and small balance moments at
laLge deflections. The horizontal-line backplate therefore
tends to result in an unfavorable value of 6ms/68b ana
should be avoided. The vertical-line and circular-arc
'bsckplates, which restrain the motion of the seal to a
region behind the point of attachment of the seal to the
wiing structure and give a favorable value of 6ms/o6b,
should be used. IncreasirZ the gap width tends to reduce
the difference between the seal-moment characteristics of
the three backplates as indicated by figure 16(b), which
-shows, seal-momrent characteristics for g = 0.5. These
backplate effects are summarized for. only one representa-
ti?-e seal width, since other widths would give variations
similar in character but differing somewhat in magnitude.

Effect of overhang shape.- If the overhang is changed
from the thin line assumed in the analysis to a triangular
c-oss section as shown in figure 17, the angle at the
o-,int of attachment of the seal can have a value up to 40
and yet effect no change in the seal moments presented in









NACA ARR No. L5F30


figures 9 to 11 for positive deflections and for gaps of
about g = 0.15 or larger.. This result is obtained
because the added cverh-ng thickness does not touch the
seal. A rather large range of overhang shapes therefore
seems to exist, for which the presented seal-moment
characteristics will be altered little if any.


Linked-Plate Seals

The possibility of improving the hinge-moment charac-
teristics of control surfaces having limited overhang
chords by using l'nked-plate seals such as illustrated in
figures 6 and 7 led to an investigation of such seals.
Figure 18 indicates that the linked-plate seal consisting
of two plates (fig. 6) exhibits an unfavorable value of
1/66b.

Another problem is the practical consideration of
preventing leakaee around the moving leading ed-e of the
seal plate. One method of preventing leakage is to use
a third plate as shown in figure 7. This third plate
may be small with respect to both the original seal plate
and the overhang so that the seal moments still aporoxi-
mate those of figure 18. If more exact characteristics
of the three-plate balance are desired, the method of
a-ipndix C can be used.


SAJ.' LE


In order to show how the characteristics of a sealed
internally balanced control surface can be obtained from
those of the sealed unbalanced surface and to indicate the
-a1gnitude of some of the effects about which conclusions
have already been drawn, the effects of two balance con-
figurations on the hinge-moment characteristics of the
aileron section shown in figure 19 have been determined.
The characteristics of the unbalanced aileron section are
shown in figure 20. From equation (4) the incremental
hinge-moment coefficients were computed for two balances
having verticel-line backplates and the following
dimensions:

Configuration cb/ca g s
1 0.417 0.5 0.7
S 2 .521 0 .6i










IICA ATR 17o. L5F30


Theveeff ect e cerh-enz s i",en b the approximate
formula is
C
= C.521
Cs

for both config rations. The hinge-mtoment characteristics
of the bElance6 aileron are therefore the same for either
co'nfirur?-tion according to the saoroximate formula and are
s'ov.ninin figure 20.

The section shown in figure 19 has L1 = 0.5 in the
region in which the seal is located. Inasmuch as fig-
ure 116d) indicate. that a value of 1 = 0.51 is required
with configuration 1 and L1 = 0.26 with configuration 2
for a deflection r.nge nf 200, ample srpce is provided
f?r the seal to develo-, the mor.ents indicated by fig-
u-es 10(a) and 101f).

In order t-o .ho'. the corim.tstion procedure, the calcu-
lations of the in rE remental hinge nomrrent for configuration 1
are presented. TEq'stion ('l4) was written as follows to
represent cc.nfig.uration 1:


h = PRi0.0:68 (0.7,75 + 1l)

Table I sho.".s the compiutat ions required for obtaining
hinge m.roments of the baslnced aileron from this equation.
A slimil:r procedi.ure is .used icr configuration 2 and for
the approximate solution.

The cotmr,-.ted character ritictis of both configurations
are shown in figure 23. This figure i.':iicates that the
large -ao asn- rather short s,21 of configuration 1 result
in hesa'" hin-e moments at lsr.-e deflecti.on3 and that the
a? rcx:iri.ote r'le ,does not pro..erl:, represent this configu-
ratin. It c n 9 ic be seen tsat the approximate rule
represents configuration 2 re --on.bly well at large
deflecticns but leads to cons-iderable error at small
deflections when the seal lies alcnr part of the overhang.

COICITCLTSTICIS

The hince-moment characteristics of various arrange-
ments of sealed internal balances were investigated










1,ACA ARR No. L5F30


theoretically. The results of the investigation indicated
the followin- conclusions:

1. Increasing the gap width for a seal of constant
width or decreas'i": the developed seal width tends to
result in high control-surface hir.ge moments at large
deflections and low or overbalanced moments at small
deflections.

2. Backolates that restrain the motion of the seal
to a region behind the point of attachment of the seal to
the wins structure probably give the most nearly linear
control-surface characteristics.

3. V&r,'nr the cross section of the cverhsng from
that of a thin plate presents no important aerodynamic
disadvantage and, if such a change is desired for struc-
tural reasons, s considerable range of design is available
in which the seal moments are unaltered.


Langley Memorial .--ronsutical Laboratoryr
National Advisory Committee for Aeronautics
Langley Field, Va. April 50, 19l5










TIACA ARR ITo. L5F50 15

APP "nIX A

ITUATCONS OBTAINED WHEN NO PART OF SEAL LIES
AGATHST OVERII AIG

The following equations relate the quantities
involved in fixing the position of the seal arc when no
oart of the seal lies against the overhang:

(1) For horizontal-line backplate (fig. 5),


s = r sin-i .xl 2 a+ Y12
2r + (x x2)


1 F(x h)2
r _= L + Yi


(2) For vertical-line backplate (fig. 4(a)),


s = 2r sin- /x l)2 + (k + k
2r

S(Yl k)-
r = 2 x2 Xl) -x x2--
2 xl "2

Por circular-arc backplate with center at overhang
hi fe axis (fig. 5(a)),


S= 2r in /x xl2 + (Y5 Yl)2 + X2 sin -j
2r x2

2 2
1 Cb2 2 2
r = x2 1 x2 2
2x1x3 + y17 x22










NACA ARR No. L5F30


In these formulas, the first term represents the length
of seal in a free arc and the second term represents the
length of seal lying Fscinzt the backplate. If conditions
are such that no part of the seal lies against the back-
plate, all three cases may be solved by



s = 2r sin- l x22 + (1 2)2
2r



If these relationships are subject to a practical
condition for example, requiring that the seal width
remain constant the radius of seal arc and the location
of the point at which the seal leaves the backplate should
be determined in order that the system may be constructed
for a graphical type of solution. None of the equations
could be solved for any quantity other than s, however,
because of the inverse trigonometric functions involved;
curves of the equations were therefore plotted and the
necessary values were read from the curves.










ITACA ARR No. L5F50


APPENDIX B


EQUATICO!S OBTATIED !HEN P ,T OF SEAL LIES

AGAIIHS OVERIIANG


The following equations relate quantities involved in
fixing the position of the seal sarc when part of the seal
lies against the overhang.(The meaning of symbols used in
thEse equations but not defined in the list of symbols can
'e obtained from figures 4(b} and 5(b).)

il) For horizontal-line backplate, the equations are
or.itted since the case is of little practical importance.

(2) For vertical-line backplate (fig. 4(b)),


s = 270' + (d + x2 tan 6b)
tan 00 6b 57 3


+ (d cb + x2 sec 6b)


(.) For circular-arc backplate with center at overhang
hinge axis (fig. 5(b)'),


S= r(270 P) (cb + g) b(cb + g) + d
57.3 57.5 57.3

r
= tan-
(cb + g) (cb + g)(1 cos p) r cos P

d = (cb + g)(l cos p) + r cos g


In these formulas the first term represents the width of
seal in a free arc; the second term, the width of seal










16 N-NCA ARR TD. L5FS0


lying alor- the bsckplate; and the third term, the width
of seal lying alo.ni the overhang.

In order to find the amount of overhang covered by
the seal, the distance d must be known. This quantity
can most conveniently be found if d is plotted against
the seal width s for various overhang deflections.
Appropriate values can then be read from the curves.










NACA ARR No. L5F30


AFPI:TrIX C


AD TICATIC'I OF METHODS TO LI'I-FrD-PL/TE BALANCES


A linked-plate balance consisting of two hinged
;plates is shown in figure 6(a). Figure 6(b) shows the
f2or:ce breakdown of the system for the resolution-of-forces
m--th-rd. (The symbols used in this appendix and not
defined in the list of symbols can be obtained from
figures 6 and 7.) The moments exerted are as follows:


The mo'-ent of plate LM is

Ap A2
2


The mr.o.rent of normal force FN is



LpBA c b s /1 sin2 b A sin26b
2 t of ai f

TI-e a:-t of axial force FA is


Ap A2
2




S AD BA cos 6
E 2


S A
sin -8b cos 8b sin26b


)2 sin2b


2 s

1 2 sin6b


+ Ap A2
2










18 NACA ARR No. L5P30


For the volume-displacement method, the volume
enclosed by plates A end B is


s i/ 1A 2 sin2
v = in 26 + sin 6b
4 2 IV (B)


Then


dv AB cos
d6b


6b 2) cos 6b sin256b

1 (i2 in26b


- 2 ( sin26 +-
B/ 2


dv -o AB
M =AP2 dA
B d-bt 2


cos 6b 2) 2 cos 6b sin 6b
-2

/I- BA B sin26b


In terms of seal-moment ratio, with plate B con-
sidered as the seal,


B
m =-
s A


cos 6b


1 -2 A) sin2b) 2

---- ---- 2(i)n b
1 / sin2 b


In order to solve the three-plate linked balance
shown in figure 7(a), the system should be broken down
as shown in figure 7(b); the normal force FN and the
axial force FA exerted by plate LM and plate KL


at joint L should then be determined.
dimensions of the plates are known, FA
as


Since the
can be expressed


2
Ap A2
2









ITACA ARR No. L5F50 19



FA (e- 90 + LM tan (e 900)
2 cos (e 90 )



The value of FN depends only on the length of plate LM
and the pressure difference so that



F P LM
N 2


The vector forces FA and FN can be added graphi-
cally as shown in figure 7(b) to find the resultant force
and its lever arm, the product of which is the moment of
plates LM and MN. The sum of this moment and the
moment of plate KL is the total moment of the system,
which can then be checked by the volume-displacement
method.









20 NACK ARR No. L5F30


rF7R-iC7S


1. Rogallo, F. M., and Lowry, John G.: Resume' of Data
for Internally Balanced Ailerons. NACA RB,
T:rch 1 19 3.

2. Fischel, Jack: Hinge Moments of Sealed-Internal-
Balance ArrErngements for Control Surfaces.
II Experimental Investigation of Fabric Seals
in the Presence of Thin-Plate Overhanges.
NACA APR No. L5F30a, 1945























v- ccO a% i Lr N cm o o 4 o\ -7 a t-- cm o 0\ a Lr\ o
o N-- o .-4 LC\ C\j o oo 0 -4 t L\ M- M KN o -t
- ,+ C ,- 0 L- _-t C0 0 0 0 C0 r-i 0 ,- I .- %O 00 0 M --t t -41
S -0 0 0 0 0 0 0 0 0 0 0 00 -0 r-4 l -40 (
O.- 0 I *I a







c r r f- N' '-\ o I D N O u o O IK- O- \ o
X0 0 N L- O &f U\-4 f M m an a 0 -0 O'D t1-O O
co r-- \o (o0 o N o o E c- 0o NLI C- o 4I K' I
40 4- -4 r-4 0 00o 0000 0 -4 r-4 4 \N N CN N\



0. .

or\-f-t 'r-4l NA M s -4 0 -t (V -4 00 -4 i4 r-4 00 N\
\, r' -4 U o CO I- 1p o '. I\ LrcO ',0 cN arf'.o MN -4 0
S o o oooooo o o oo oo ooo o
o 0 1 1 1 1 1 I I



L L L N UL\ %LL ON UN Ws U~% Lill U'\ WN NLp Lr\ U\ tPN LrN
,or- C r- r.- r- tl- co a ll 0 cm E- r- o aN Co or- t^ E- E- t- cm
\ O N c\ i- r- -tc- E O 0 O\0 .-- .-( .-I N \. CO
- +-+3 O rN C,- 1- 4 N N CN (N (N N N .-4 0 -d:
0 0 r-i r- -l4 -I r-4 r-I-4 r-4 ,r-I r- l- r4-4 rl 4 il


l) _t0t O -tCO l\ W\O -=t- 110 OD \. tc\ CO m _:f c- 10 W\
0 O 'D. z CO Co ( \ O O CN Lr\ rOz -- r-4 r(\ r- r-i
Ui\ aj Lr VrN p "- -3 K\ ry -I o H (\ N --' Lr\ '. \4 o N- C- C) co
-XN 000000000000 0000000
0 0 t I # I



0 'I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
t- N-\ NI C C\j lP C-- 0 O N-U N- O tmo _zt N H .-






.0 0 C ON _: N 0 o' -m 0 f -D0 0C 0 Nm c0 0 O 0
n' 0 I r4 -4 I-l -l H.-4 I r-4 rq .- r-f N




0o r ir\ ( No O N4\ o L. L0 r cm N ur c\j --t N-P u o o
V\ -t H< UN -0 a, I m 0 -zt Cy" r- t CM N l r -4_t C)N -:d:t



b a o 0 o 0r c 1 t 0N 0 0 CNo c a3 o00\ \


r- O 8 o o r -4 O -OOOOIOO O HO rO OO O O <\J O C OO
l- O r- fl -t ^ -1 1 1 ll -l l- ll -Io J


NACA APP Io. L5FO


cn

::g


UE
'-4
C-'





CO


z







IJACA AFR ho. L5FZO


(a)Co7ntrol surface with flexible seol.


M/ine ax/s LOr r
NATIONAL ADVISORY
COMMITTEE FO AERONAUTICS

(b) Contrl surface with /hiked-p/oate ro/.

Figure I. Typical Pientalation a' oa m.tean fay
jrealed and bo/anced contrd /trface.


Fig. la, b


A/Al' 99 ^








IJACA ARR No. L5F30


-I--


A /rfe///

- -


-
-
--
- -


i i


NATIONAL ADVISORY
I)/ / COMMITTEE FOR AERONAUTICS
S 7 -- 7-._ '_. _..5 c /


(0} d^, posf///ve.


Fig. 2a-d





INACA ARR jNo. L5F30


=
i j
8


\


^ ^i



i \i


Fig. 3








IJACA APR No. L5F30


(0a .5eo/ c/'r of he overa .


/b} &S/ /47 oaoi/n /.e ove'rAnyA. eoN MVISOR
COMMInEE FOR AERONAUTICS
Fure 4. /,7/f'rno/ ,6a/oa/ce w/i/h sea/ e7 ad ver//co/-


Fig. 4a,b







NACA ARR [Io. L5F30


zBock~o/a

Leve'r O'372 ~/-


//7g? okI~


(a) Ses/ c/eor of /he ovkro/ay .


A/9P r


fb) Jeo/ v/y/'75 aoas/ /Aes o vrhNa7Oy. wNAL nSao,
COMMITTEE FOR MAiOLNUTlCS
CU/,re 6. /n7er/ oc?/ /oAce w/C ose/ wo) /
c/~c//r-

Fig. 5a,b








IIACA APR ho. L5F30


Fig. 6a, b


X- oxr/


Lever arnP77
NATIONAL ADVISORY
(A) / -- vrr do cCOMMIEE FOR AERONAUTI


o n G "6. ~- %//'c/>,/e /we. /7/oae / s. ZIW = LA ; AWN =


(a) do/o/ceG crra oe7s








NACA ARR No. L5F30


4O7x/.


"o -4,o


X


//,;7ge oxAS L


Zever ArrIr
) ,-c NATIONAL ADVISORY
r FW/, COMMITTEE FOR YIUTKS

/ ~f 6rv 7 L/-rec-p/or- bo/o/7ce cos//7y
of /Aree /o/oyes.


Fig. 7a,b


Kay Bo/,/xe 23C>Apvv






IJACA ARR No. L5F30


.0




4 ---------

< .5


II) :=--- :---:-== =-== == ==






_-_--------------------_---------------!RO!uni_

0 ./ .3 .4 .5 .6 .7 .8
Gop w/A/L,
F/ure E'/crf cseo/-/omenf c/AreAc/eTr-
/f/cs of /7n /iced/'n of overhong quo/
/o onye-ho/f y wi/ch. 77- =. / 7 g -


Fig. 8








NACA ARR No. L5F30


--H- -
'IT
4Z4

4r---" t *"


44
tI
\ **.'^ -H^"-
.*- i r -
- ; '+ < 4 '*5 *i -


T^ ;-F^^t


(a g=o. (b) g=o. .


S 1 l I


(c) g= o.z .








^':16 -: i--: -i,.:"





?/ .. .- 0 4. 8. /'" 6 .

.. Overhn7q deflecf/,


Figure 9.- /Mo1ant charcteri/sfcs of f/exible 5ea/5 /ith ihorzonta/- ine
bact plote5.


P,


1.5^
N --Tr


- 1 I 1 1 I


-12 -6
6h, 6dq


(f) O.S. O "ATI ADVISORY
COMMITTEE FOR AERONAUTICS


Fig. 9a-f









IIACA ARR No. L5F30


r 1 1 I ll l I i i N Ii I
;: :::::.:.. :::-i:... :.


I .l |I 4 q 4 1 1 1 1 1 1 1 -41 1 --


I l l l l l I I l l I i


FIgure /0 M/oment character/sf/c of flexb/e 5eals I,/ th verbtca/-


NATIONAL ADVISORY
COMMITTEE FOR AEIIIONUTICS


(a)7 _=O .


t'1'fIlt illlllll I. iJifi


(b)j-o.i.


.4 -


0
-/2 -8 -4


0


(e) go=.4


I I I I I H 1 6 1 1 11111 I II H 1 1 1 1 IIILN
4 8 Z 12 1 2 1 1 1--1 1-1-1- 1 1 r 1 1 1 1
-/2 -6 -4 0 4 8 12 /
Overhang def/ecf/on, 6& deg (
(fl g-o..5


- ,',


T i'


I


I


I


(c) g- o.2 (d) g = o.3 .


^


/ne bac'p/lafej. ,


Fig. 10a-f


Ll









IJACA ARR iJo. L5F30


--- -- --- -M ^ai a ft'"
TE
S .I : ._ ,_ o :,- 'r .


(lal ) 0_ t

(a) g- o


I-." ( 79: Z2.

4O + -
0 ::, '1 L-


(c g- -2.


I+1t -


yowl A, "el%
j' ~. ~ ~- ~ ~ ~^ ~ -e w c r
/'. -_,- =l; ^ ^ e^ ..-/ .







-FT":' D iII i!I -
-F -1 I I I.
. m j |TNT I I III I
11!| | II i

I 1 :I I 1
0:::::: : ^:I I:t
i -- ---- -- --- ---- ----- ----
o Z::::-;--^- ^^^^.^^-^---


O~I1 T LLmi ]IIIIIIm 0_, .
-1Z -6 -4 0 4 6 12 /6 20 -4 4 6 .2 6 0

) g I .4 OAOverhang o7f/ecf/on 6 6, do g 0
e)g 9-.4. q (0 r)gz c.5
Figure //- Ioment characteri5t/cs of flexible seoi15 jrh 0ccobar-


NATIONAL ADVISORY
CONNITTEE FI UiIOUuTICS


IT .


L-t


arc bacep/aftes.


Fig. lla-f


,' ,,a ns e m w-/






I;ACA A:R No. L5F30


I'.


Fig. 12








NACA ARR No. L5F30


4--
L 7 1 t Tr1 1. i








4 I6 .
/5eal w/dth, 5


() 5b = /4 *
Figure 13.- Vertcal clearance
horizontal- ine bacKp/late.


Seal 5.aot7 s
(d)6' = zo
required for flexible sea, 5 l.fh


/


Fig. 13a-d









(JACA APR [Io. L5F30


Fig. 14a-d


i--
-,


C -' ... 1...: .::^ T. :U





.6 .7 -- -- L


























5eal z'cth, ; Geol iyidth,
(G) 14. ( 2.0 COMMITTEE 5b 6E UTICS



A: ,.',; .-/ .- Verfica/ clearance required for flez/bl/e dea/l /tih
t'e rcal -l/ne bacKp/oteJ.
-5,-o/allat, 5 Jt l Zldth,




v--I-iallln bc loej









NACA ARR ho. L5F30


1
F-


(0) = 6.


(b) 6h = /0


*.2 ir


S- .:- a .. *-:


-5





: r ; 7 .9 10
ea/l ///dth, s
(C)6 b 1 /4


deal ///dt, s
(dl = 0 NATIONAL DV.ISOY
SCONNITTIE F01 UAMAITICS


Figure 15- Vertical clearance required for flexible eal/ w/ th
circular- ore bacKpO/fes.


Fig. 15a-d







NACA ARR No. L5F30


5


/_ /or/,'orn o/- //.,e -_ -_/
_ ac/p/ofe V. .- -er o/- /-e
S-boc/r/o f







-------C/-c-/or- -are
--- --- --b-- ocAro/of'e


(fo y = O. /;


S.4or/zon

i l0 l- | | |

.o e --,- -


1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
/l 0 4 / /6 cl
Over'hn.y ~oef/ech--'/o- v 6 s'e
(4) c9O= 5-3. = o.e.
NATIONAL ADVISORY
COMMITTEE FOR AERONAUTICS
/ re/ o.- MAormen/ charoac ~er/s */s of *w1o
SeO/s ho/? V/ shrse d//'t yrn h ocApo/aes.


51-PVT-11 I i l til trl-r--T1~ F1 -I-r-F-1-T -rr F


- I- I I -I I I -----I I I- II -----
L I, .tt I


^fo/-//i7he /
/ofe
V /er/i/-/ / Ie


I j i ;uo /oferc


VJ7


Fig. 16a, b


.






NAOk ARR nio. L5F30


1







i g
N


(O)
01s




b!


Fig. 17






NACA ARR No. L5F30


N



N
pt
F
Y,


I I I I I


NATIONAL ADVISORY
COMMITTEE FO0 AERONAUTICS







.6









-#" \
__\
- _:-4__ __ _

^EEEE^Ezz\

"rzzzzzz 'zm\


I -- I I I I 1 -I I I I I I I L
O 4 6 /2 /6 20 24 z
Ov/erA77g ce9d/eca/on,/ odeg
/29//re /8. A/o7me7< C c tr/?cAw,5sf's5 of
/7bAeed-p/o/e Jeo/s .


Fig. 18









Fig. 19 NACA ARR Io. L5F30













F



0



( IJ en



o/o \

g o

St


,O -







--4
0





-I-
0
U






lob
/::s








IACA ARRP o. L5F30


-4 0 4
//eron 0n/70/ E, ode&


8 /2 /6 20


Figure 20.- Hinge-moment characteristics of an aileron on an airfoil
section having two balance configurations with the same effective
overnang and vertical-line backplates. a = 00.


-.J:' -,5 -,2 -8


Fig. 20




. ......








UNIVERSITY OF FLORIDA


186






i) I I.' I r i ,


S:.LE, FL 317011 USA




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