The use of geared spring tabs for elevator control

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Title:
The use of geared spring tabs for elevator control
Alternate Title:
NACA wartime reports
Physical Description:
22, 3 p. : ill. ; 28 cm.
Language:
English
Creator:
Phillips, William H
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 )
Elevators (Airplanes)   ( lcsh )
Aerodynamics -- Research   ( lcsh )
Genre:
federal government publication   ( marcgt )
bibliography   ( marcgt )
technical report   ( marcgt )
non-fiction   ( marcgt )

Notes

Summary:
Summary: Equations are presented for the stick force per g in maneuvers obtained with a geared spring tab. A geared spring tab, as defined herein, differs from an ordinary spring tab in that, when the elevator is moved with the stick free at zero airspeed, the tab moves with respect to the elevator in the same manner as a conventional geared, or balancing, tab. The geared spring tab is shown to present the theoretical possibility of obtaining a value of force per g independent of speed regardless of the spring stiffness. If the geared spring tab is used in conjunction with an elevator that has zero variation of hinge moment with angle of attack, the force per g may be made independent of speed at any center-of-gravity location. A suitably designed geared spring tab will provide adequate ground control, small sensitivity of the control forces to slight changes in the elevator hinge-moment parameters, and substantially no variation of stick force per g with speed. The geared spring tab is shown to be most suitable for application to large airplanes.
Bibliography:
Includes bibliographic references (p. 20).
Statement of Responsibility:
by William H. Phillips.
General Note:
"Report no. L-30."
General Note:
"Originally issued February 1945 as Restricted Bulletin L5A13."
General Note:
"Report date February 1945."
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."

Record Information

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University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 003617535
oclc - 71340145
sobekcm - AA00006271_00001
System ID:
AA00006271:00001

Full Text






NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS





WA RTIM .E IRE PORT
ORIGINALLY ISSUED
February 1945 as
Restricted Bulletin L5A13

THE USE OF GEARED SPRInG TABS FOR ELEVATOR CONTROL
By William H. Phillips

Langley Memorial Aeronautical Laboratory
Langley Field, Va.












: : .M "* '"*


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.


iL- o


DOCUMENTS DEPARTMENT


NACA t-30


.i






































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






























lillp: www.archive.org details LiseolgearedsprinOOlang
11








NACA RB No. L5A13 RESTRICTED

ITATIONAL ADVISORY COMMITTE- FOR AERONAUTICS


RESTRICTED BULLETIN


THE USE OF GEARED SPRING TABS FOR ELEVATOR CONTROL

By William H. Phillips


SUMMARY


Equations are presented for the stick force per g
in maneuvers obtained with a geared spring tab. A geared
spring tab, as defined herein, differs from an ordinary
spring tab in that, when the elevator is moved with the
stick free at zero airspeed, the tab moves with respect
to the elevator in the same manner as a conventional
geared, or balancing, tab.

The geared spring tab is sho:.'n to present the theo-
retical possibility of obtaining a value of force per g
independent of speed regardless of the spring stiffness.
If the geared spring tab is used in conjunction with an
elevator that has zero variation of hinre moment with
angle of attack, the force per g may be -made independent
of speed at any center-of-gravity location. A suitably
designed geared spring tab will provide adequate ground
control, small sensitivity of th'- control forces to slight
changes in the elevator hinge-mo.i.ent parameters, and sub-
stantially no variation of stick force per g with speed.
The geared spring tab is shown to be most suitable for
application to large airplanes.


INTRODUCTION


An analysis of the elevator control forces obtained
with spring tabs was presented in reference 1. Two types
of spring tab were discussed: the ordinary, or ungeared,
spring tab (fig. 1) and the geared spring tab (fig. 2).
The geared spring tab differs from the ordinary spring
tab in that when the elevator is nicved with the stick
free at zero airspeed, the tab moves with respect to the
elevator in the same manner as a conventional geared, or
balancing, tab. Although the calculations and discussion
of reference 1 were concerned mainly with ordinary spring


RESTRICTED









NACA RD No. L5A15


tabs, the advantages of g-earsd spring tabs were pointed
out. The geared spring tab presents the theoretical
possibility of obtaining a value of force per g in r,.aneu-
vers that docs not vary v:ith spe d even though a stiff
spring IL uscd to provide adequate ground control. The
pres-nt r.:eort briefly outlines the theory of the geared
sprin. tab, gives formulas for us. in design, and indicates
more completely the practical possibilities and limitations
of th ; device.


DISCUSSION


Difficulties 'ave been experienced with conventional
types rf elevator balance on largz airplanes, because the
elevator must be- very cloc:'ly balanced and because small
chance's in the hinre-mn,-ent rarancters cause large changes
in th:' control forces. The oosEibility of using a servo-
tab to avoid these difficulties aes explained in reference 1.
In tests of a control surface equipr,,d withh a servotab,
which is defined as the system shown in figure 1 with the
?--ring. o'itted, the pilots considered this arrangement
unde-s.irble because the elevator did not follow smoothly
move-,:.nts of the stick v,h,-n the airplane was on the ground,
taxyin-, or making landing-s and take-offs. A banging
action of thu control was experienced because the elevator
did not ,:ovc until the tab had hit its stops. A spring
tab provides a mc-chanical connection between the stick and
the ele.vator that relieves this difficulty. V;hen a spring
tab is used, the'. force p.-:r g varies with specd. This
variation ma-,- be reduced to an acceptable amount by using
a tab spring sufficiently flexible to make the control
behave essentially as a servotab at normal flight speeds.
The ground control provided by this Ilexible spring might
be considered acceptable but a stiffer spring would be
very desirable, especially on large airplanes that have
elevators with high moments of inertia.

The equations for the stick forces with a spring tab
were presented in reference 1. In the appendix of the
present paper, these equations are extended to allow cal-
culation of the stick forces with a geared spring tab.
The force per g obtained with an ordinary spring tab has
been shown to vary with speed. As the speed approaches
zero the force per g am.proaches that obtained with the tab
fixed and, at very hib-h speeds, approaches the value for








iJACA RD !To. L5Al5


a servotab, With a gared spring tab, as the sperd
acnroaches zero the force p-r is shown to approach that
of an uquiva]lent balanclrx- tab and, at very high speeds,
is shown to approach the value for a scivotab. The reared
spring tab therefore provides a means of reducing the
force per g at low speeds while leaving the force per g at
high speeds unchanged. The force per g may theoretically
be made to rer.main constant throughout the speed range, no
matter vhat spring stifiness is uszcd. This arrangement
therefore embodies the advantage provided by either the
conventional balance or the servotab, namely, that the
sticl-force gradient does not vary with speed. The unde-
sirable sensitivity of the conventional balance to small
changes in hinge-moment characteristics and the poor
ground control of the servotab are avoided by the geared
spring tb.

Tn order to compare the merits of conventional types
of balance, ungeared spring tabs, and feared spring tabs,
the stick-force characteristics have be.;n cornputed for an
air-lane of tlhe medium-bomber class (weight, 50,000 Ib)
with th' various t'oes of elevator control. The results
of th:se calculations are shown in fi-ure 3. The charac-
teri.sics of the airplane and of Q.'-.e tab sF:teims that
wer'i u.s.-d in the calculations ar-e -ivan in tables I and TI,
res?',-.ct'ivelv. (All ,.nmbols are lefined in a-r-en-dix A.)
The stick forces of a clo..-l:, balanced elevator with con-
ventional balance (as, for example, a 'alancine tab) are
shown "i figure 7(a). The critical nature of the balance
is also shown by the large chances in stick-force gradients
caused b; changes in O'h //'6e and 60he /ba_ p of -0.001
per degree. Variations of this cr-cer of magnitude may
result from slight differences in contours of the elevator,
within production tolerances, on dif.frEnt airplanes of the
same t-pe. The characteristics of an ungeared spring, tab
are illustrated in figure 5(b). The spring constant has
been chosen to provide a fair degree of ground control
without excessive variation of force per g with speed at
normal flight speeds. The criter2.on for the choice of this
spring stiffness was presented in reference 1. For the
airplane under consideration, the spring stiffness is such
as to require a stick force of 100 pounds to deflect the
tab I radian at zero airspeed when the elevator is held
fixed.

The characteristics of a geared spring tab that was
designed to provide the same control-force characteristics








IIACA RB No. L5Al3


as the conventional balance are shown in figure 3(c). The
method of calculating the values of the hinge-moment
parameters and gear ratio that were used to obtain stick-
force gradients independent of seed is given in appendix B.
The sa-e characteristics will be obtained with any spring
stiffness.

The exact values of hinre-moment parameters re-uired
to 'gile the characteristics shown in figure 5(c) will not
be attained in practice. It is therefore desirable to
investigate the effects of changing the hinge-nimoent
parameters slightly. If the spring in the geared spring
tab had infinite stiffness, the system would be identical
with the balancing tab (fig. 5(a)) and the stick forces
would be equally sensitive to small changes in hinge-
mo.nent parameters. The spring stiffness must therefore
be liu.ited to a point at which normal changes in 60he, /6e
and dCh/ arT do not cause lar;g changes in the stick-
force characteristics.

In order to determine the effects of errors in the
values of 5Che,/5be and 6Ch /"6aT when a finite value
of sporirg stiffness is used, the stick forces have been
computed for a geared spring tab that has the same spring
stiffness as the ungeared spring tat of figure 5(b). The
effects of changing 6C0h /65e and 6Che, /aT by -0.001
for the geared spring tab are shown in figures 4(a)
and Ltb'), respectively. Some variation of force per g
with speed is introduced but the variation is considerably
smaller than that normally encountered with the ungeared
sorinr tab (fig. 5(b)). Inasmuch as a greater variation
of force per g with speed probably can be tolerated, an
increase in spring stiffness to i.nprove the ground control
annears desirable.

The chances in 6Ghe/a6e and 6Che/6aT cause changes
in the order of magnitude of the stick forces as well as
some variation in force per g with speed. These changes
are, however, much smaller than those that occur with the
conventional balance (fig. 3(a)). At high speeds, in fact,
they approach the changes that would occur if a servotab
were used.

The effect of changing the gear ratio of the geared
spring tab from its ideal value is shown in figure 4(c).








NACA R3 7o. L5A13


The effect of changing the 7g-ar ratio is nearly equivalent
to changing the value of 6. :he/'e. An error in providing
the ideal value of 6(A /.5e on an actual airplane may
therefore be corrected by suitable adjustmiient of the rcJr
ratio.

The geared spring tab .ised to obtain the character-
istics shown in figure 5(c) h-d values of the hinge-imo::ient
parameters 6ohe, /ar and icht ,T equal to zero. The
equations riven in an endix B show that this condition
must be satisfied if the stick-force *radient is to be
ind-enenrcent of sce,?.d at any center-of-gravity location.
The value of 6o0he/aT, in practice, rmqy be r.nade equal
to zero by use of elevators with a beveled trailing edre
or with horn balances. The value of 6ch./'aT is nor-
mally very small and may lic'.'ise he adjusted by varyin.-
the trailin.-edge angle. If the values of 6rh /aaT
and C-h./oaT are not e.qual to zero, the force per may
still be r'ade independent of speed by use of a geared
s'-rin- tab for one particular center-of--ravity location,
but the force per g will var;,- somewhat with spceei at other
cen '-r-of-rravity locations.
T'_. effect of an increase in altitude on the stick-
force radients obtained with a ge1rc-d spring tab is to
shift. forward the center-of -rravity location for zero
force per C (the maneuver point) and to leave the slopes
of the curves of force per g against cent.r-of-gravity
location -~',richanged. In this respect, the geared spring
tab .ia:, be shown to follow the s5ij rules as a conventional
elevator. The stick-force variation with speed in straight
fli.-ht is related to the force -er in maneuvers in the
sa'.;.w wjay for a spring-tab elevator as for a conventional
ele vator.

The application of spring tabs to airplanes of
various sizes was considered in reference 1. The results
of this analysis, in general, may- be apn-lied to the geared
sorinr tab. In order to avoid excessive stick-force
variation with speed with an ordinary- spring tab, the
s.rin- ,imst be sufficiently flexible tc makl'e the control
behave essentia21Ty as a servotab in the normal-fli"'r.t
speed ranr.e. The stick-'orce -ra.dient obtained with a
geared spring tab wist also equal that of a servotab if








!ACA RB ITO. L5A15


force variation with snoed ts to i.-e avoided. Because the
stick forces obtained with a ser:votab result from the
aerodynamic hinge rmic:ients on th3 Lab, some difficulty may
be ern.iountcred in providing suff-ciently heavy stick-force
rraJ'.lcits with normal tab designs cr airplanes much
smaller than. the 50,000-pound airplane considered in the
present report. The calculations of reference 1 indicated
that sufficiently heavy stick forces may be provided on an
airplane weighing about 16,000 pounds, but a large tab-to-
stick rear ratio and a tab hI.vin, a rather wide chord are
required. These features increase the difficulty of
preventing flutter.

Because the stick-force' 7radicnts obtained with a
spring tab on siall airr.laner are undesirable low, the
use of a bobwelght in conjunction .vith the spring tab has
been -ronosed to obtain desirable stick-forcG gradients
in stea'1; maneuvers. Flight tests showed this arrangement
to be unsati factoryy b-ceuse of l-l',nie 1 Ilh- tnc s of the
stick- forces for suidon or ra .id rc.vei.ents of the control
st.ick. The rEsFon for this undesirable control "feel" is
that the elevator may be suddenly rrove-: to large deflec-
tions 'e:,cause the aerodynamic hintge mno;-.ent? on the tab
are s-iall. After a certain tim-e la, the acceleration
builds up -and causes the bobweicht uioment to be felt by
the -i.lot. These effects are discussed more fully in
reference 2. The preceding consi.;i.erstic.ns indicate that
the geared sprring tab may prove u-.satisiactory on small
airplanes. On large airplanes, for .which sufficiently
lara.a stick forces result fro.: the aerodynamic hinge
imo:r:en;s on the tab, the geared spring tab should be
satisfac tory.


CO ICLUSI OS


An analysis of the characteristics of geared spring
tabs for elevator control has led to the following con-
c lus i on :

1. Py means of a geared spri-gC tab, it is theoreti-
cally possible to provide a valut- of stick-force gradient
in '"ancuvers that does not v-ry with s,-eed, no matter
what spring stiffness Is used. If the geared spring tab
is usod in conjunction with an elevator that has zero
variation of hinrrc moment with a:-1le of attack, the force








TACA RB No. L5A15


per g may be made independent of speed at any center-of-
rravity location.

2, A geared spring tab may be designed to provide
adequate ground control and small sensitivity of the
control forces to slight changes in the hin-e-mom:ent
parameters. The poor ground control associated with a
servotab and the sensitivity of a conventional balance
to small changes in hinge-moment parameters may therefore
be avoided.

3. The geared spring tab appears to be most suitable
for application to large airplanes.


Langley memoriall Aeronautical Laboratory
National Advisory Committee for Aeronautics
Langley Field, Va.







8 '?ACA RB No. L5A13


APP:. D T:." A

SYM3OLS


7 vIe irght

b span

S *w:inFg area

c chord

I tail length

ST tail area


-y'/ slonre of lift curve of wing


E d o,'nv:*:as&h angle

q d:-nam!'c ,Iressu're

C, lift coefficient

I elevator moment of Incrria


variation of lift coEffiiciont of tail with
6e elevator anrEl


T elevator effectiveness factor -


-K ratio of stick movement to elev,;ator deflection,
tab fixed; ncrrr.all].; positive

K2 ratio of stick r.icve-ent to tab deflection,
elevator fixed; norr.ally negative

K3 ratio of stick force to tab anrle at zero
airspeed, elevator fixed; norr.:ally positive







NACA -B Ho. L5A15 9

K4 ratio of stick force to elevator angle at zero
airspeed; elevator i' in deflected position
bv.r external i:Leans, t. i: deflection held at
zero by spelicatior c.f required force at
control stick; positive for balancing tab
H hinge morment /
Q H
Ch hinse-mo.ent coefficient -

60 elevator deflection (Cri osiLive down)
6t tab deflection from cleva tor (positive down)
xs stick deflection (positive for":ard)
F sticU: force (pull furcs -rositive)
a angle of attack: of wing
am an.le of attack of tail
p mass density of air
n normal acceleration in g units
@ acceleration of gravity (2.2 ft/sec2)
x distance bewv'een center of '-r-.vity and stick-
fixed nautr-il point in, straight flight
(positive l:hen cbntcr. cf F.ravity is rearward)



A = + g2L

sW


B = ;- Tl"
Bc q T
66c q T



---- variation of elevator hinge-moment coefficient
(dOT/T with angle of attack of tail, measured with
tab free







'NTACA RB No. L5AlI


cV^h
I?
T+- f
j5e f


variac.on of elevator hinge-moment coefficient
with elevator anglc, measured vith tab free


Subscript s:


t ab


elevator

tril


value for equivalent balancing tab








NACA fl 1c. L5Al1 11

APFI^NITX B

E'7.rTTTC,!T POR ETEVATOR T,'OCES I'.7H "-.ARED SPP.Tn- TA.U

rp' e ta- syFten. considered is shown in figure- 2. The
mchanicE] characteristics of thie linkale are co.:: letely
d'et r ,:red ',,%ben jfr-ur cnrstantr ar6 s':'cific,. These
constants are d3f2ned by tn. follo':in ,- eQuations*

xs K13 + 21t ()

F = K56 + 'e(2)


Equstin (2) apolics "ihien thei sir cd s zero. The
ratio Letv.-n tnh- tab deflection and the elevator deflec-
tiorn, ctick lixed, eq-als -- ana the ratio between the
K2
tab election and the elevator deflection at zero air-
1: T e ratio is defined
speed, zticl: free, equals ---. The ratio -- is defined

as the .In.:-age ratio of an equivalent balancing tab. VWhen
the sr-tem n i in eruillbriu:i, the relations between stick
force, elevattor hingre moments, and tst hinge moments are
riven in terns of the".e- confstants 'y the exprEssions

1',
AHe At -

K1 -L 2
K : (3)


A = + K6 t +


The chanCes in elevator and tab hinge moments for
any type of maneuver are given y the equations

( C he 0he Che 2
e = T + A6e + At- Jqb e e2 (4)







12 IJACA RB No. L5A13

Ft = aT + Ar- + A3t I rTbtct2 (5)


In th'-i resent report, as in refire-nce 1, the stick force
required in a gradual pull-up is used as a criterion of
the elevator-control charact..rist ic The stic l force
required' in a pull-up, or any other maneuver, may be
deter.:ired by substituting the ap:.:ropriate values for AaT
and 2%e and solving equations (7), (L), and (5) simul-
taneously. If the tab is assumed to have a negligible
effect on the lift of the tail, the values of AaT
and 5e in a gradual pull-up are


\, dw 2
a = + (n I- 1) (6)
j---- n qS
/dCL\






Pnr copv.enience, the solution o" these equations for
an -un-rcareld spring tab rYF = 0), ','-.ch was derived in
refere,-ne 1, is presented first. m' force per r is



d 'h KFK e "- hN e -2K; -'
-A 9 + E re q+ ee 2
] TII f Yl Th
ja ---2------ (8)
6F =L Lt ( 8)
u n 6Che
b1 2
K2 t e 2
C--- bt t+ 6-- qTb+tCt
1 6 t + 16 T








NACA R? No. T.,A15

where
'= +.. x I.

\ da /w





6e q


tf


and I --- J
() Vtf


arif the values


of and that would be measured on thz ele-
OT 6 e
vator v:ith the tab free and are 1-ivcn by the expressions


dCheh
d-eT/t f





d~e/tf


6Che






che
68e


6Ct 6he





S2ht Che
e t
6Cht


(10)


The force per g for a reared Fs.ring tab, obtained
by si.mnltaneous solution of equations (7), -I), and (5),
may be tpresred by the same equation a? was derived for
an ordinary spring tab (equation ('b)), provided that
certain substitutions are made for some ef the parameters.
These substituted values may be interpreted physically


S9)


The terr.e








TU1CA R7? iHo. L5A15


as. the cbararteristic: of the equivalent balancing tab
previously defined. The complete equation is


A + + bB q--be c e



/1- \ -
K1b t'2 r) t o

where te quantities with the s,..i'jcript b are defined
in thfe- following table:

Quantity Definitinn IPhysical
sipnificanrce
Ratio between
/ Kvc2 \ stick travel and
(?: ---- elevator deflec-
( )I-. cion for equiva-
lent balancing tab
Che. K' Ch j'" ACht btc-2
(^ ,Y 4 -e .. e 2
he.he '- '- r -e l'e`c Value of 6Che//8e
for equivalent
'e/ 2 h t- t C b balancing tab
+ L
1^ Bt be,-
ht 2 Value of oh,/, aT
e''fle 17,- t-Vt btct2 for
------- for equivalent
aIT/b 'a T aT beCe2 'alancinp tab
Value of 6Ch'/.6 t
for equivalent
balancing tab,
,. \ & tt -measured ,.with tab
-7h "-"he _h "ht btct2 link connected.
t/-b ,5t Y7, ,t bce2 Ph:ysical signifi-
cance may be visu-
alized as effect
of deflecting tab
as a trim tab by
changing length
_________of tab link


(11)








NACA R3 No. L5A153


The stick-force characteristics of an ordinary spring
tab were discussed in refer-ence 1. At very high speeds,
the stick force per g normal acceleration was shown to
aro.roach the valiz; obtained with a servotab and, at low
speein, the force per g was shown to approach the value
obtained with the tab fixed. By similar reasoning, the
stick-force r-radient with a geared spring tab ray be shown
to approach that of a servotab at 1igh Fpeedr and to
approach that obtained with the equivalent balancing tab
at low seeds. -y varying the wrii ratio, the force per .
at low speeds may be adjusted to any desired value without
affecting the force per g at high sre]>F. In particular,
the force per g at low speeds may be adjusted to the value
obtained at high speeds. The stich-force gradient, in this
case, is found to be independent of the speed.

The conditions that must be satisfied in order to
provide a force gradient independent of speed may be found
from equation (11). The assumption is made that the
ratio qT/q is independent of speed a condition aporoxi-
mately true at maneuvering speeds. The force per g will
be independent of speed if the ratio of the terms in the
numcr;tor that contain qT to the terms in the denomi-
nator t-at contain qT is the same as the ratio of the
remaining terms in the numerator to t'he remaining terms
in the denominator. For one particular center-of-Lravity
location, this condition may always 'e satisfied by
suitable choice of the Fear ratio. If it is desired to
provide a force gradient independent of speed at any
center-of-rrav ty location, the following relations must
be sat-. eied-



tf (12)



1 ---
Cht 2
b6)b -to







1'ACA RB No. L5A15


\d e/tf e

1 ( bc C / -
2 tb e
l --it b o
'b ht 2
1b-,- -t tct


(13)


In practice, equation (12 can bec satisfied only by
malin pChe/'aT and 6Cht/'T very close to zero.
Equ9at 1on (13) may then be used to ceter-iine the -ear
ratio: I'l /Yz that must be e!.:ploryed to provide a value of
force' per g wh-ich does not vary ,:..th speed.


An example of the application of equation
the ,i r.lane with the characteristics civen in
presented If the values for (il:) t -


15) to
table I is
and _-_b
\ C'e b


give-, in the preceding table are substituted in formula (15),
the following relation is obtained:


(d he
d-ke/t'


11 -- h "
F 1 t


"he KF 'he Cht btct2
-e K, t K 5e ece2


(K 2 Cht btct2
K 0 t 'e-e


(14)


All of the quantities are assumed to be known except the
gear ratio Kl/}"'5. It will be noted that, because the
quantities Kl. and K% always occur as a ratio and KT
'r3 1k "'








TACA RB Yo. L5A13


and K3 are both increased in the same ratio when the
spring stiffness is increased, no limitation is placed
on the spring stiffness.
If an attempt is made to solve e juation (14) explic-
itly for the r:ar ratio K4/T47, a fifth-degree equation
is obtained. This complication may be avoided, however,
by solving equation (14) by a methci of successive
appr:.iri--tions. This process is applicable because a
chan-e in the value of 1"4/K7 has a marked effect on
the value of the right-hand side of e umtion (14) and a
relatively small effect on the value of the left-hand
side. As a first approximation, the value of ?l/K is
assu:.ed to be zero where it occurs in the left-hand side
of equation (l3) and the equation (now a quadratic) is
solved for K4/K3. This approxijai.te value is substituted
in the left-hand side of the ealation, and the equation
is a-ain solved for TK4/K3. The -rocess conver1gs very
rapidly and this second ap-roximation generally will be
sufficiently accurate.

If the values for the airplane and elevator charac-
teristics riven in table I are substituted in equation (l4)
and the values of K4/'K5 on the left-hand side are
assumed to equal zero, the follo"5in' enjuation is obtained-

.-......03.= -0.003 -0.0)
1- (-0.h)(-o.5(!.c) (2.2)2 --0.003)

( 1.e0)(-0.:5)(7.-5) (0.8)2

K3 (34.0) (2.2)2
2 ( (7.350) (.8)
+ K-- (-0.035) (735) (.)2
W(i5 (354.0) (2.2)2

This quadratic equation has the solutions:

0.863
K_
4-- = 20.2
F3







18 NACA R3 No. L5A153

Of these two solutions, only the smaller value is of
practical interest. The lart.er vJl.ue would result in
excessive tab deflections that would cause the lift incre-
ment due to the tab, which has been neglected in the
present analysis, to reverse the direction of lift on the

surface. If the value -- = 0.386 is substituted in the
left-hand side of equation (1l.) and the equation is again
solved for Tr,/K3, the second a: .proximation for the gear
ratio is obtained as -K = 0.85. Further a-proximations
do not change this value appreciably.
The following criterion for determining approximately
the ,ini'nun value of the spring stiffness required for
satisfactory ground control was given in reference 1:

1 e
I s = 200 foot-pounds per foot per slug-foot2

For a geared spring tab, the variation of elevator hinge
moment with stick deflection when the elevator is held
fixed is given by the formula
1e "ChSK qTbece2 ,, 2
-He (1)bKS + eoe2 (K)b-t qTbtCt2
+ (15)
SXs K2 K2 K22


If it is desired to satisfy the criterion at zero airspeed,
the t:-rms containing qp may be neglected and the fol-
lowin, relation is obtained-

1 e
200


}.21

This expression may be used to solve for K5, which
detrr:1iines the spring stiffness. For the example under
consideration,







NACA RT ITO. L5A13 19
K2 (200) I
-( 1)b


(-0.45)(2co)(1.5)
-1.80 1 )-0. )
i.Co J


S95.0 pounds per radian

A value of 1:7 of 100 pounds per radian has been used
in thie e:--aplcp of this paper. hror,. the value of K/K3
deter n.ned previously, the value? of T' may be readily
obtained.







NACn RB No. L5A153


P I Fr-' 2 NC S


1. Philli.s, William H. :
Lievator Controls.


Ap]lic',tion of S-ring Tabs to
HlACA A-K No. L4E2c, 1'.9


2. Jones, Robert T., and GreenberC, Harry- Lffect of
I'j-.ge-l moment Parar.,eters on Llevator Stick Forces
in Raoid Maneuvers. 'fACA AiFR No. L4J12, 194.








NACA R3 Fo. LVAl3

TABLE I


ATRPLA C CHARACTERISTICS


'V, lb .

S, sq ft .

C, ft .

1, ft .

ST, sq ft .

be, ft .

ce, ft .

bt ft .* .

Ct, ft .


S-- rer radian
da../,,

de

da

T .

T..r.
-- per ridian


qT
q


I, slug-ft


2


50,000

1,000



. 55

. 200

51

* 2.2

. 7.55

. 0.8


* *

* .


. . . 4.5



. . 0.55


. . . 0.5


. . 1.7


. . 1.0


. . . 1.5


MiATTO0AL ADVISORY
CO'".ITTrP,C FOR ALRCU;'TICS








NACA PB ro. L5A15


TABLE II


CO"PROL-SSTE;, CT-ATACV'TZTSrTCS


Conventional Un-eared Geared
balance s'rilng tab sarinc tab
S(fir. 5(a)) (fig. 5(b)) (fig. 3(c))
Kl, ft r r rsdian 2.18 1.80 1.80

12, ft rer radian ------------ -0.45 -0.15

K3, lb :per radian ----------- 100 100

l4, ib -er radian ------------ ----------- J5

he

-- r deg 0 0 0
baT

he
:er deg -0.00058 -0.005 -0.003
5e

^-h
---P, ..-r rer -------------- -.0.003 -0.005



per -eg ----------- C 0
aT

r eg ---------- 0 0



.5e e- -0.005 -0._00
-- r, cr dec ------------ -0.005 -0.005


IATIOPAL ADVISORY
CO'iITTEE 102R AERO'H["ILICS






NACA RB No. L5A13


r@ee //nk/


NATIONAL ADVISORY
COMMITTEE FOR AERORNAUTII

Figure 1.- Mechanism for ordinary spring tab.


Sprin- 9--Free #I7n
J/ /


r


NATIONAL ADVISORY
COMMITTEE FOR AERONAUTICS


Figure 2.- Mechanism for geared spring tab.


Figs. 1,2









NACA RB No. L5A13


0
























0
0

















0 *
0
-4



S-4











t 0


0
u


0
-4
S
0





I -
Ci








C..


d










I.
.0

t,-


e1




O
a
Uk
0 @





0










ot.











L.
Cu

















0





U L
I
.0

&0


0 T



'it



U k

C..J


3 jaed
T urou 3


qd 'uolj'[ Aaou3
Jad onaoJ ,lc0Ae'[3


Fig. 3


TTndj








NACA RB No. L5Al3 Fig. 4








E!i
0












8 -
--- ---- I 0





S* *0






i o O





0
I4 0I
-------- go. ,o
0 0
0 0 0









t4 4
/ i
-- -- -- -- & o





S 0 0
;I .4

U 0'
















I // 2! / o B i
_V 0'
-- -__ s \o











q o sez
/ o

















0 -r










UNIVERSITY OF FLORIDA

3 1262 08104 948 7



UNIVERSITY OF FLORIDA
C"Ot,MEaTWS DEPARTMENT
L J. A4 PSTON SCIENCE UBRARY
'). rOX; 117011
'..;'E3SVILLE, FL 32611-7011 USA


It


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