Calculation of stick forces for an elevator with a spring tab

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Material Information

Title:
Calculation of stick forces for an elevator with a spring tab
Alternate Title:
NACA wartime reports
Physical Description:
15, 6 p. : ill. ; 28 cm.
Language:
English
Creator:
Greenberg, Harry
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:
Elevators (Airplanes)   ( lcsh )
Aerodynamics -- Research   ( lcsh )
Genre:
federal government publication   ( marcgt )
bibliography   ( marcgt )
technical report   ( marcgt )
non-fiction   ( marcgt )

Notes

Summary:
Summary: Formulas for the calculation of hinge-moment characteristics of an elevator with a spring tab have been developed in terms of basic aerodynamic parameters, spring stiffness, and airspeed. The formulas have been used in a study of the stick-force gradients on a pursuit airplane equipped with an elevator with a spring tab. Charts are presented showing the variation of stick-force gradient in accelerated flight over a large range of speed and the complete range of spring stiffness for various center-of-gravity locations, altitudes, and airplane sizes. It is shown that the stick-force gradient for the elevator with spring tab tends to decrease as the speed increases and for weak springs tends to approach the value corresponding to a pure servotab (no spring). This tendency is independent of altitude, size, or center-of-gravity location although the magnitudes vary with these parameters. The variation of stick-force gradient with center-of-gravity location is less for the spring-tab than for a linked-tab type of balance.
Statement of Responsibility:
Harry Greenberg.
General Note:
"Report no. L-129."
General Note:
"Originally issued June 1944 as Restricted Bulletin L4F07."
General Note:
"Report date June 1944."
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

Source Institution:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 003613059
oclc - 71197494
System ID:
AA00009404:00001


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Full Text

RB No. L4F07


NA'A rl/j


NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS





WAlRTIME RE PORT
ORIGINALLY ISSUED
June 1944 as
Restricted Bulletin IAF07

CALCULATION OF STICK FORCES FOR
AN ELEVATOR WITH A SPRING TAB
By Harry Greenberg

Langley Memorial Aeronautical Laboratory
Langley Field, Va.









MACA


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 129


DOCUMENTS DEPARTMENT


I-


r







































Digitized by Ihe Inlerrnel Archive
in 2011 wilh lundinc Irom
University ol Florida, George A. Smalhers Libraries will support from LYRASIS and the Sloan Foundalion


hllp: www.archive.org details calculalionoltsiO01ang





A...A .? :o. L-"F07

NATIONAL ADVISORY CO T:'ITTEE FOR AERONAUTICS


REST TCTED EULLETIiI


CALCTTLATION OF SPrCK FORCES FOR

AN 'ZL-'7ATOR "'TTH A SPRING ?AB

By Harry Greenberg


CUI. AY.


For:-ulas for the calculation of hinge-moment
characteristics of an elevator with a s-ring tab have
been developed in terms of basic aerodynamic parameters,
spring stiffness, ard airspeed. The formulas have been
used in a study of the stick-force r-radents on a
pursuit airplane t~quipped with an elevator with a spring
tab. Charts are presented showing the variation of
stick-force gradient in accelerated flight over a large
ra;ne of speed and the cor;plute range of spring stiffness
for various center-of-gravity locations, altitudes, and
airplane sizes.

It is shown that the stick-force -radient for the
elevator with spring tab tends to decrease as the speed
increases and for weak springs tends to approach the value
corres-ior dng to a ure ser'votab (no spring). This
tendency is independent of altitude, size, or center-of-
gravity location althDu.-h th.:. magnitudes vary with these
para:i.eters. The variation of stic1:-for-e rwI:dtent v.ith
center-of-7ravity iocaticn is less for the snring-tab than
for a linked-tab typ? of balance.


IITTR ODUTCTI O:


On most types of control surface, balanced or
unbalanced, the control force per unit deflection of the
surface increases approximately as the square of the
speed. On a spring-tab type of balanced control
(reference 1', the amount of aerodynamic balance increases
with soeed; this condition results in a control force that
increases less rapidly than the square of the speed. This
type of control can be used to advantage on ailerons since
it reduces the difference between the control force per
unit helix angle pb/2V at the high and low ends of the
speed range.








KACA RB :lo. L)F'07


The question has arirse as to whether th3 I:nown
a'.v.tages of the spring tab on the3 i]eron cold be
reali-ed for the eler.ator. The .purosC of t:.iz report
is to analyze th!:- ch'. acteristics of the spring-tab
control n-ed as an elevator. =- aegal expressions, o:;
which either the static or i.anc',ie-.rinc stick' for--s for
an eleev..ator with a soring tab ini be cPlc~ite'i, ar
de'.el.cped and a!pli.dl to the calculation of maneuvritn.
forces for a typical pursuit airplane. The mranc.uvc r..n-
stick forces for the same elevatoJr 3rarr.e:icnt -"ith a
ser-oi. b and with no tab are also -rcsPnt.' for co.:-''arison.
The effects of variations in sprir- stiffn.r ss, airspeed,
altitude, center-of-j -:\,itty loc:..tion, ai- l .ne Fize, 1nd
tab si.e are conscidleed.




Tri the pr inr-lor.cdd e!cvat oif--t, b arI r n 7ein er.t
referr;ed to Verein, the control is conrnectlai directly
to thli tab, as in a zeivota.., :an. to the- el'vatjor through
a sp-ing. (See fig. 1.) i.is ar-anr.3int rgves3 Lhe
control system characteristics that ar ;-e'e,'en t!hos; of
a servocontrolled elevator ani an or-.i;cLar, u'calancied
elevator. A ve-ik sprijrnr a.-irroac-les the cause of no spring,
or pu-.'- servoco.nLrol. A stiff spring appl-roaches the case
of a rigid connection, or ana crdinary unbalance. elevator.
AF t'.h s.Fee- is I ncrea-:If d, theL-. a. 'cd'na.:-,.ic fcrces
.ncr.-:; .. v,-_l e the:- so:-.inf ei'ffct r ,.i.ainI constant; effec-
tively, the spring becoi.cs "/cEl:?-r in co,.cparlson with the
aerol ; ran.ic forces adi, the cornditi on of pure servocontrol
iz a~, .'rc. ch d.

T:i f -'.Tre 1 C is an idle:- thait is "ree to rivot
st t'-e )iPr-- of the elevator r -. Th- control rod AC
operat'- t'ie tab throug-h t- i lin"':a-e "'? E and oprates
tl'- elevator throl-,,: h the spring arn: crap.k -,r. The
1n ti: crf nnd 9B are E.ss-um-rc'd qal in the analysis.


SY'"BOLS


A 'wins aspect ratio


AT teil aspect ratio







ITACA ::B No. T 07? 3

bI wi"ng span

One hinge-moment coefficient about elevator
h inge

1

Ch, hlirfge-noment coefficient about tab
i2 Kv t t/



CL lift coefficient of wi'g 1 L
qpV-S S

CLm lift coefficient of tail



Cm pitchinr-monent coeffiU: nt about airplane
center of gravity -it'i e



c mean chord of wing

Ce mean chord of elevator

CL mean chord of tab

F stick-force gradient in maneuvers F

Fs stick force

F1 force in spring; positive when in compression

F2 f'crc f"n control rod AC at C; positive in
sane sense as F3

F, force In control rod AC at A: positive as
in figure 1

g acceleration of gravity

He hinge moment about elevator hinge







ACAA PB No. L4F07


;:t IinLe :aiornent about tab iinfE
K linkage ratio (11/12)

kI spring constant, pounds per foot

12 k1, 12
"2 oSE


L lift of wing

? length of control stick

L distance between wing and tail

lift of tail
-T
71 length of arm S.

L2 lenlrth of arm DE

M ?rach number

m mass of airplane

n normal acceleration per g of airplane due to
curvature of flight rath; accelerometer
reading minus component of gravity force

q dynamic pressure

r gearing ratio between control stick and rod

Sw area of win-

3S area of elevator

ST area of tail surface

St ares of' tab

V a.r.speed

Sweigh t of airplane

x/c distance b-et-ween center of gravity of airplane
and neutral point in fraction of mean wing
chord ,







7ACA RB No. ,i.F07 5


a -anle of attack at win:

CT angle of attack at tail

6. de-le'; icri :f e-levrvtor

(is defleccf:' c: elevator control arm BC

6t d-f]ectlor. of tab with respect to elevator
o anilo of pitch of air-lanE

F' p.*,chins velocity

re nr.ndic'i:.-ionalEoa pir-hing velocity (e/27)

SIrr late-density nar, tmet-.r (m /pS ,b)

p na's -resity of air

S-.n0- 6' t, aT, _, a, and D9 are ued
as -uts:cri:ts, ca :crv2tive is idicated: for examol.-,
6rm ^n
Cma = 6 a nd = r ". a d:eriv.ative- or coof-
ficier.t is vritten r,'&th a bar a'ove it for exarrple, Cna
the tctal derivative or coefficient is indicated, that is,
the resul.iltant or effective value viichl takes into account
the f'loat'ng tendency and sorl.- action of the clev-tor
wit st ,ii: fixed.

.ll angles ar3 measurtd in- radians.


iLETHODS OF AIJALYSIS


'he -siz ;ss'umptions involved in the analysis are
as follows?

(1) l-nkage ratio is constant

(2) .erodynamic derivatives are constant over the
range of deflections involved

(7) effectt cf speed on the aerodynamic derivatives

is Even by the factor
ST -2







6 ."JACA nR ;,o. Lit.FL:


(L4) effectt of power i is :-ielctei

(5) Effect o!' c a:a:,-. n3 in orw- l w .rd s.:e.'? .utrij- e
u-.l -up is n elc; oted

(c) ifoc t of h c-'icontl tsi fi':itc. iit" 3 r:.nere

Asz.mpti:n (1) is -.'lid L.ecsA.jc th'e 11i -:ng eti)
-:',e njt c.'nge 1. iably Ka e' r :it i. i i t.1 sr al rarn-e of
ifl ect' enr.is ti.at .cc in f 11 L" .' ; ti i (') iO-
r ii ., 2cc r i'r. ", lo..-. e._ v.1 ,-tJ ..' 1 Lt s -, t.e
c.r"ti 'u. r .:.-r n ... t -" 'e -' i ,".-r .:ie', or 8 ': t b
. fl- e :' t r.s p to r", ..- i.t ll- i ? -.. li- l
i.:vc1' l --, !-,ti ,: t i; ;ter .-.'i on .1e c'. l' ,
e'. *: 5t .rcd &. rein. I'" : t:-.o -' ar.c : )i.tin ~: t'le
, a' c of' s :.,-.5 ~'. (...r.. ,,{ ,' "I t',.:' ,:., o.. :. :: ; .r.::-i: ly
coo:re t cr c tor i t :'. v L C of i; ... 1. n, thail
I; of '.ou tf'., val .- :- -. .- i. in th irj..;
IT. i' t', As cin i O .. ., '' -: c :-.' .:. r
d: '.: n- ; affe tr '- 2 in. : r, 2-; r2-n -
l: -E?.-d A.u r: g c- ,t" i C'.W tV'- r s Ar;
i._1 i .. a-. .l_-_', _lJy t l ie .'- --.: re. '''l-' l'.t. I-i.j ine:"e se
" 1r 1 .1 : :0 -h .f-. ,.' ta"c _. n _, -n .e c:
'..2 i"c.. : t t c ie:t ..... --. ... _n s .-d.
Fi. rit- ,-. 1 t." ...r..0 e j ic J .? :ily ,.. ,il_
.".i- 't.... li:,e r.'rr i:-.v ',.',,:' sL,- .-, -. ..tx '... .- n (;) i)
t' ; t ... I '
b- l'e-.': to ,e r":alj, :.. l'_ :.;... r t- .i= ," ". J ,iili
i -i *.. st5 t e .:tic';i 1 c ;I' i-t ll..1tly rt .ii i. j tE.u,
ae'n riinti t.ez r'f-rer.cc : >. .r rt- :f j 4 :tLL. .-
ti.on t:1; rrelJs t;.'-n" 3.: ;.1J po'. -''i -Jlw *vr I 'C" 11i2
i i



PFc"n:: t'e *-'r".c try :2 tUs: cI -.at r-tc.b carrr :c'.e.t,
i; i : 001io..-. ..t
a = ,- -(53 6,








nCh '-'o. r., E, t
a t th T







+1 + 1, \qSo (2)

















I7 + C
AC RB .;o. 1; -07
1ro I '-.b-.- p.nr.d.tion fo j e :,1il" cl r1-in of" the cab,




\ l .. 1




Co:;.bi r- ex -r'. s:.on3s fi) to ( ; .- iv '


"- U'.


17.T


4--
+ :-- -
." r
C'


C.
'*1~
I-ft


C.
I *


I,.. I
-. On' ,


.., ,
-. L ', ^a /


T'. :",'s.:-c uf t *: :
Sri C, F.: = il + Ce). :l' r. '-
-- % r. ( ; ; v
e..-,' ,,-. -


1:, 3C
= I
A:>.


+ *g;J


+ *N--.t
-' e ..t


+ ".
a-,.


+ U.-
',


If t'ie "s.u ie of- t rhe ero dyn:. C-ic c i, L.ri'n' t? on tc
ri,-ht-,2nd s id of eIuTitiMo: ( ) ..-, c '..r.nod from r c .w-
1.
spo. Jt,, t e sho':ld be ,ii t i 'l. I' r-- to

V-I -





L -n
anly "o hi.:h speedd, a c-crdiir::n to '-p ]&'? t Ce .r Y.I-
nati o;r, if

1 1' 2

tX. C
1-
*A~.^ ^

q", ce


i n


+ aT-,2
t.1 ,









NACA RB Ho. L.'iC07


euati i-_r. (5) may 1e w'.tten as


-. ( = 6,Ch
e


- t 'i
C-


StY-t /
+ Se' tC


,?


+ .-tCt
rt
L 5;r


. ...' .It ine- f'r i t -r c f '. ~-i & in
., t L.r I. (. ar'] c ." f r t.'..' IS L at.A i .el


( .e'\ -'- C. 6 i ;' '-- ...., T
., ~ ," "T/
'c =I T \

X 12 I L c
Ch k + N'" + + "---1
S.- e "-- tlc
Ch


"'.iici teterj.J-ne: t:he _..L 1


".t "-'.'" f~~t -- le,:;::tcr


f'lc,.c ;- i-' ;:. cnr.": to z. .:.,:,-rL,,1 .*:,-fle t c-i 's ?''t .n le
oj a tt.."k a.. '. e 3.s oni-, i t n -ctr.r.n .jd the
ttJ


-.. .at ion (7 e.1 c -.-'i ten -n a-cr viated


l ._ni .- a io,
for. :


5; : -, + .
t, I


(3)


Tl -n,


t t e)


f= 1( 'C'


-9 LLTCI
C-r
0 7,


(7)


(9)







;TACA RB No. L4F07


'.e 'f. stitution of eq!E.tions (8) and (9) in the expr-s-
sion for the control force i3 gives

--- 1'3


= Cae
6 e


+ p",
( -eSe


+ K(l + A)Che 6
et


+ 3he
et


Ce T)LT


(10)


which gives the fundamental control
tives Ch "-d Ch as


Chei
B6,


= Ahee
^e


hil.ve-moment deriva-


+ K(I + A)CY
'-6t


ar.d


=


+ V3C
"t


+ Che
aq.


(12)


Che
a


'.Then the stick is fixed, the elevator moves v:ith
c.anr-ts in anrgl; of attack; in accordance with equation (7).
,:s a result, thL. static-stabilicy derivative m and
the d.mpinr in .itchinC CmD_ are affected. They may
be calculated by


da ci dlaT
Cr C + Cm B--a. + C 1ti
a a 5- a ma dE da
U t


and


CmD : CmD
D3 D


dam daT
+ Cm --- + CI KB--
be dDA 't dDA


(l1)


(15)


(14)






10 MACA RB iNo. TLF07


The control effect ivenesc TC._ sirilarl;y depends
0S
on the ..:.ction of the elevator with respect to the control
.arn. 'L.. relrtion is


SC 4 v( + C -( .) (15)




b' e ..:. rion (11) tc i''I,, t' .';l: R rce l inu t
n'or'mal "c:?c '" ati in p.ll-u ;,ay b: c. lc.1.]'. e n
c.' .- ...la fto" t,-ii_- stic .--'c : "' : rei'. cnt, 't i. is taken
frcOm ''Lsti s on Fa .':. C e' "en-= i

S..-c I C I C. r
p ', rt' ij
sn -a -' -.' I ( '6
n r \ c, ( ) In C



.for ,.r'.ss-b.:.la : d L.~e',ato,' .ar ror~mula 1 ) total
de-ri.j'.-t ." a .re n ed. ''al -. of' C anJ Ch are
a D9
obtain,-,d tPC.
'T
a a'aT i 7)

Sh (C. --



T.: effect of co-y. rresFibil t ir.ust a,-ann be taken
into La-coint in uasin., ic.r l.rli (Io). ,ll tb derivatives
in t'ial: express.io should .b o r.lL.plicd byi if
\4 #
the d1t- uted in ,io:r.nut ing these ieri'.at ive. are based
on lo'.'-scr'cr .,easure,ne:nts. The factor cancels out except
In th-- s-cord and fourth cerms. The corrected formula is

PS,_wC .:_ .__ ,e c hLL 6 ,mD
r + ILC ;I
'n sr CL, i tr eD CL ,..2 CI

(18)








YACA RB No. LhF07 11


Spring, elevator, and tab deflections corresponding
to any acceleration are calculated by the following
formulas, derived by using equations (2) of reference 2:


s 'g LA Cm C:
-. -C I'D O
n 2V2 \LG -'" Cros/
2V2 Ot2COrr


a ag (2A,, daT
n 2V21C dDO)

A number of computati-os, based on typical airplane
characteristics, have been made to illustrate the effect
of s-ring stiffness on the characteristics of an elevator
with a spring tao. The following airplane dimensions and
derivatives are used:
W/S,, pounds oer square foot . l0
5, feet . . 7
ST/S .. 18

AT ........ ................. 1.5

C La .......................* *
daT/da . . .
daT/dD .. 6.6


CmnDG . .. -. 15.5
Altitude, feet . .... 20,.J3
' . . . 235.
The follovwing elevator and tab dimensions and derivatives
are used:

S., square feet .. . 17.
-e, feet . .... 1.48
-t/ . . 0.536
Se/ST . . O. 352
3!/Se i 0. 11n
'J @ m J J i i i









IACA RB No. LE4F07


. .


te
t .


t t-, Se
I1, f'co
K .
cb
16e
Che

Ch.




Chtt
Cht


S . o.04o
. . 0.5


CT t

Cy




O e
C
clT
C'rB


S '. 1.34

S. 0.115

.09

. -1.0o
. -0.0615


From equation (7),


k: + 0.130
A
-:2 C.(22


G.115
-, o.622
-- -- fl& --fl


hrom equation (10),


-0.1.E7k2 0.0067
-I2 0.622


e a
"Om


C0.115, + 0.0025

--2 0.622


Prom equations (1i) to (13),

0. 0655
C = -0.252 06
M*a -X2 0. 22


1%

n"c


- -]5.5 o-bru
1 -k, C.,-22



= -1.106----- o.o615
-kp 0.822


These values can be substituted in formulas (17) and (18)
to obtain Fn.


. 'L&7
.-* .i.67

. 0.115

-0.115

. 15

. -o.5 5
0


Che
eis









iACA P.5 Ko. 14-0'7


T""''" ." 'T DI T C TP.I ON


"'Le computed values of the stick-force gradient in
mansuvers .' for the ass-red -':. lane and elevator
are r plott-i as a function of s-er' in figure 2, for
various values of t'-e -,-ri constant k1. The tc.p
curve, for :r.finite '-:'iri ti'-: vs, a;-:les to an
nrcdnrry unbalanced elevator, for v.hich the spr ln is
reiplaccd 1;- a ri -id :-'.. The bottom curve _. plies to
a ,''.- servocontrol, for v'hich the spring is remove.
The inter.r.r..aste cruves are for r:.; cases in v..,lil
spir:i-s of various stifines"es are connect-edL between
the control rod and elevator, i..i increase in stick-
foi-rce .wdient with s---:'ci for \'. :-i i v cer i low
values of E .*.i-- stiffness is based on the assunption
of t'1 effect of oC:..;::. ss' lity mentioned y.1viously
a3nd is not important for the purposes of this re,-ort.
Th. i.crtarat fact is that t-.e a':.tion of a spring
r du-.; t'- tiC ':-L -'.- '-*.l e;'. i t.'. '-cr 3.o~'v.n.
A ver / '-.ea.: s ri.- r- e E. t'- -fIO cc -* Tl .di it at.
t.e '.1 of L e Z) :d 'ra : ".. .-' only "liig tly
h'.-a b ;: -?.r.n -aet ,f t.,' u.'e :--v,:.on el. Un t'_- csTen
cr.rres Crn [d in t crr Ir le '.:-o- :-''ra i : (;r. s .' nr) in
f.' r ,e t : E t tic!'- fo.-,ie 1: e t..a.i the m'.ni..r-. v'S l
consiid.;r' ed d. ir.:'.. 'ue c ull '- incr-,e:- .ed 'b
ucin- i tir,' c.f in?- l' c i ? chO:... T ". '..'e n -
tlLe t,?*'.) o '1.'r: P0 :'r L '' .t.].e 1- f' r-' ? c I tl. r;'- ck-
foc"ce -.ient', Dc s 'j he 'cr, .- :" cr3''1 on t.'i tha
aCte corn.ensa ed .- t-he r. du t-fi't '-r.- ntede.
Ct!,er. -cn:-hos- c cf tP'-" in.- t'..-e t i':c: f3 :C -' .: .". : t.
lin!-ed bElan.--'ri t t,. ..-. u' l .. a li'.-t intr -ea
of St ij :-1 -"cr c "*''e:ie t i'; .- ':-: s. th' cahC cf the
to) rind botto!n s res f fi-s .-cr 2.

It :s so:-etim,' con id r-:.:d deirable to .eve di-rect
contr-ol until a certain :tis -: f'-or.' is :,e-c ::J after
v.;irch t;".e tab control b'c-;in oe i'".ncti,:. T'.iL direct
control is accoi.p .lshed by ,-j1los ir t.ie s in- 0- an
as.nunt that dce-nd3s n :hc e stic.-: force at vh'.ich it ic
desired to have the tab cc.Te i.i.o Tctini. Thi stick
force varies v.'ith accc le'-.tion n th:e '. ir:!t er h.own in
fi :'r'e 3. Thr curve -has th. IloC fcr infinite s:ring
stiffness up to a certain paont, Is ir: iciL'ed by E-.e
solid line, and thcn la: the Slo-: ccrrelonJing to the
spring stiffness used, as iniicatd by tl-e .i.lAe. line.








rACA RB .%o. LIJ.07


The p-.lnt wher 3 the slopr chancrs. of course depends on
t.e oL ]oad in the ss.P'n. S-uc an arreanga,.ient right be
useful in r;,a-ntaining reasonable ccnt-ol forces for pull-
cuts a.t ver,7 h:'ig'h po.) s.

r effect of i.n:reasjd airrnans zizn is shown in
figure The winr ledinr. and .'ont-'il ear-ir I re
assunr,:- th; ramne ss in fi-ure 2, but all lengths are
assu.-.i dou, led. The st ic' -f'or'. ;rrai ..ient for pure
servo-crper-tion (ki = 0) is so*.:ewinat higher than the
velue' considered :'esir:abtle and an., s.coreciable amount of
sEri i stifires-. would n.ax. : t.ie rt ic:-fCorce gradient tco
large. For this ca.e a ta-, rih ia'llr l ihon1c"d could be
used to eive lower s>.-ck Circes.

'";.c effect of altitude cn the v. .-iation of stick-
forc3 Cr-adient 'r.'th speed Is shrcv' il f .iLre 5. An
irncren.e in albude i.ed,.ces th stic!:-forc.e qrauient by
on amount that docs :-ot v.r--- a -:recl ably vrith speed.
The lcss in staici: fo,:ee in .o.'. de.rases as the spring
stiffness is J-croased.

'-he effect of' ientei-of-,ra"iJ.; .oca6Ccn on the
stick-force gradient fcr se'.'erali types ci balanced
cle-rat or is shown in figure 6. Th e elevator with
snrint, tab sho',s the nRallest c"ar~az of stick-force
Frad'lnts. Th linked-tab balance c'o.~En for comparison
was A;L U-:d to b so nl'ked to -rve the lame stic].:-
forc- r cr. i ent as the ele" toi' v.-t': zl'.! rin tab for one
particuvlar' centrer-oI-:Jravlty location = ) 0.05 ). The
varir.t:on of st ick-.fornce oridi enrt ":..th c eniter-of---ravity
location is less with t' nr-in- tia than vrith the
lin't,'. tab because hea r rei.'cei as well as Ohe;

this condition permits a sralllr C- f ror a given
'e^s
sti'k-feoce rra.dient. As s owv n jn eivation (13), the
variation in stick-forc-e r.jiint wil-. VC, which
de -e:ids on cenLer-of-t--ravity locations, is proportional
to C)
E6s








:IACA RB Ho. L1F07


CO'. ...LU IO S

Formulas have been developed for ith calculation of
hin.e-momeint characteristics of an elevator with a
S.linj tab. The analysis included basic aerodynamic
parameters, spring sti'finsc, an' airspeed and indicated
the following" conclusions:

1. The stick-force ._- a:ie"ts for an elevator with a
spring tab tend to L-.crease as the :;j.eed increoa~es. For
a weak sprinr, at hi L speeds, the stick forcc a_:.-roaches
ti.-t of a pure servocontrol.

2. The variation of st^cl:-force ,-radient with
center-of-r_'-vity location is less for an elevator with
a s r inj tab than :ith a 11i~.I i tab.

5. Increase in altitude reduces the stick-force
*. dients by a nearly constant amount over th-c speed
ran;-, for a .-iven --:-ing stilf.':iss, T- amount of
rcLuction in the stick-forco ;-i lecnt decreases as the
s-Crin- stiffr,..ss 1..creases.


Langl ":y !- -jris1 A.:ron.-uti" ,! Labur0 to'y
.li .i n ..i vi ?: : e-, Coi :.-. ttee for -,irorni't iCs
T.,a,-,i :: i.--l Va.






1. C-atuc, S. B.: HIot-:s on t-i, Sr rin;, Tab. Rep,
:Jo. d.A. loo,, ;.A.E., ajril 19 1l

2. C:rcenb'i-:r, FarrP;-, and Sternf-i.ld, Le.onard::
Tieorttical Invw.'tigatic.n of Lonitudinal
Stability of Airplanes '2ith Frc_2 Contbrols
Including Eiffct oi Friction in Control
3-st i.j CA ARR ivo. '-1 10.

5. Harmon, S. .: Det:.rri'initicn of thj Liffcc of
Horizontal-Tail Flex ibilityr on Lonr itu-lirnil
Control Charactcristics. LA- i ACS.: To. LO301,
1945.

















































































































li*







NACA RB No. L4F07 Fig. 1








as
I0



Zu


EE
1





i
0C o



ca



n,
0







f ~i)s







NACA PB No. L4F07


tS)





k.
*\
"-c"
s;
S




-s?






VS)


0 200 900


True airspeed, V, mph


Figure 2.- Variation of stick-force gradient with speed for
elevator with spring tab. kl, spring stiffness; wing
span, 42 feet.


600


NATIONAL ADVISORY
COMMITTEE FOR AERONAUTICS


Fig. -






NACA RB No. L4F07


160 -












40 Tab ocked- --
ILA


Tab free _


0 I-


Normal
NATIONAL ADVISORY
COMMITTEE FOR AERONAUTICS


Sccelerat/on ,9


Figure 3.- Effect of spring preloaa on stick-force gradient,


,Fig. 3






NACA RB No. L4F07


o0 ~ZO 400 600
True arspueed, mph
NATIONAL ADVISORY
COMMITTEE FOR AERONAUTICS.
Figure 4.- Variation of stick-force gradient with speed.
kl, spring stiffness; wing span, 84 feet.


Fig. 4






NACA RB No. L4FO"


( /it)









^~ ^-- o<------------------ --.-
o I
0-




0- 1






0 200 100 600
True airspeed, V mph
NATIONAL ADVISORY
COMMITTEE FOR AERONAUTICS

Figure 5.- Variation of stick-force gradient with speed at
sea Level and 20,000 feet. kl, spring stiffness; wing
span, 42 feet.


Fig. 5





NACA RE No. L4F07


q
\s,
f

Jl^
rS

Ch
r
1
k



\r>


-4


0 .0/ .02 .03


Center- of- gravity


/ocation


Figure 6.- Variation of stick-force gradient with
oenter-of-gravity location for various types of
balance.


Fig. 6







UNIVERSITY OF FLORIDA

31262 08103 307 7




I JN;VERSn[T OF FLORIDA
-OJCUMENTS DEPARTMENT
-* MARSTON SCIENCE LiBRARY
PO. BOX 117011
GAINESVILLE, FL 32611-7011 USA




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