Effect of hinge-moment parameters on elevator stick forces in rapid maneuvers

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Title:
Effect of hinge-moment parameters on elevator stick forces in rapid maneuvers
Series Title:
NACA WR
Alternate Title:
NACA wartime reports
Physical Description:
16 p., 11 leaves : ill. ; 28 cm.
Language:
English
Creator:
Jones, Robert T
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: The importance of the stick force per unit normal acceleration as a criterion of longitudinal stability and the critical dependence of this gradient on elevator hinge-moment parameters have been shown in previous reports. The present report continues the investigation with special reference to transient effects for maneuvers of short duration. The analysis made showed that different combinations of elevator parameters which give the same stick force per unit acceleration in turns give widely different force variations during the entries into and recoveries from steady turns and during maneuvers of short duration such as abrupt pull-ups.
Bibliography:
Includes bibliographic references (p. 16).
Statement of Responsibility:
by Robert T. Jones and Harry Greenberg.
General Note:
"Originally issued November 1944 as Advance Restricted Report L4J12."
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 - 003806616
oclc - 124093069
System ID:
AA00009409:00001


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YI.-




LI .-


ARR No. IAJ12


NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS




' WARTIME REPORT

ONIGALLY ISSUED
November 1944 as
Advance Restricted Report LTIJ12
j; ; .


EFFECT OF HINGE-MOMENT PARAMETERS ON ELEVATOR
STICK FORCES IN RAPID MANEUVERS
By nobert T. Jones and Harry Greenberg

Langley Memorial Aeronautical Laboratory
Langley Field, Va.

UNIVERSITY OF FLORIDA
DOCUMENTS DEPR RTMENT
120 MARSTON SCIENCE LIBRARY
P.O. BOX 117011
GAINESVILLE. FL 32611-7011 USA


WASHINGTON


*ACA 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-
I iti. ly held under a security status but are now unclassified. Some of these reports were not tech-
.:. ay edited. All have been reproduced without change in order to expedite general distribution.


L 185





















I







-1 |









NACA ARR No. L4J12

NATIONAL ADVISORY COmTTITTE: FOR PEROCPUTT CS


ADVANCE R STPICTZD RtPORT


EFFECT CF IIHT,'j-.CE,? PARA!!TL'kS CIN ETEViTOR

STICK FCTCES IfI RAPID E.:ATTPERS

By Rooert T. Jones and Farry CGrenberg


S I I 1. ...R


'.e inportan2e of th.., tik!. fcre pr unit normal
accelerabion as a criterion of 1on-ituL1dinal stability and
the criticall dependence of this ..rad-iert on elevator
hinco-moment parameters have bear shown in previous
reep.ts. The rent report conti-nu.'-- he investigation
with .necinl re-ference to transient effects for maneuvers
of she'rt d.u.ration..

The analysir rmalc s-'o''ed t-.at d'.'faer.nt combinations
of elevator pararrieters w -.ch vi;e the 1 es'n sti I; force
per urit ar-eleratio'. in turns rcje widely di.ff rent
force ver.intions during t':.e entries into and recoveries
fro: steady turn and during mancouva of short duration
FsuhL as a'rup pll-ups. a. coin In.t'!c, of relatively
lcarC negative values of th'. re'stcrin- tendency Cn and
the flo?.ating tendency Ch, ap-roaching those of an
at
unbi l.nc d elevator, results in a stick .force that is
hI ...'rng th- nitial stage or p'. ]-up and then
der.,ea ss, and may even reverse, as the acceleration is
reduced at the end of th. ,..ian-nver. The stick force per
unit acceleration is greater for abrupt th?.n for gradual
control movements.

If the negative value of O :h is reduced so that
the corresponding value of Ct becore.s slightly posi-
at
tive, the reversal of force may be eliminated and the
force tr.ay be brought nearly in -hase with the acceleration.
There,; is a limit to the pr-rmissible reduction of the value
of Ch however, because as U6I approaches zero the
stick force per unit acceleration .may become lower for
abrupt than for gradual maneuvers and may thus lead to
undesirably low stick forces at the beginning of the
Maneuver.










2 NACA ARR No. L4JI2


INTRODUCE i ON


'The stick force per unit normal acceleration as
measured in steady turns or pull-outs, wnich was proposed
as a criterion of longitudinal handling in reference 1,
is now generally accepted as a basic measure of longi-
tudinal stability. The critical dependence of this stick-
fore g-radient cr, el].vator hinge-mo..ient parameters and on
mass unbalance of the control system was shown in
reference 2. It was found that a givenn stick-force
gradient can be obtained by any of a series of combina-
tions of tesc parameters satisfying certain prescribed
relations.

T%.urther consideration of the problem and some recent
flight ex-perieince, hov.ever, have shown the need for inves-
tigati n tOhe transient effects that occur during the
chan;-e fror., steady unacceleratQ-a flight to steady accel-
erated fliC'-t. Th.et. transient effects cause a difference
bet:,eeln the stick-force -,radients in a steady turn and in
a mareuve-r of short duration such as a pull-up.

The purpose of the present report is to investigate
the vorirtion of elevator stic': force and norr'al accel-
eratiun luring the transition 1 .ol preceding the
steady turn -and also during turns or pull-ups of short
daraticn. The effect of combinations of hinge-moment
pararnetorv is considered, each combination is chosen to
give the sE-e stick-force gradient i.n a steady maneuver.
Tim.r: Iistories of the stick force and normal acceleration
are fund for prsdetermincd variations of elevator deflec-
tioni. An attempt is made to explain and to suggest a
rem'.dy for the largc variations of stick force with time
observed during pull-ups of short duration on different
airolanus in flight. A previous analysis, somewhat
similar to the present one, was .-.ade in England (refer-
enc 53) but included a smaller range of hinge-moment
par'ar~et os.


SY1VB30LS


A aspect ratio of wing


b wing span











MACA ARR No. L4J12 3


-h elevator hinre-monept coefficient (H--)


CL airplane lift coefficient (Lift


Ci pitcbin---mrnomerit coefficient about airplane center
(Pitchin. .*nopment
of cravit7 -- -- ---.-I
C-\ r 3, ,

c w.inE chord

ce elevator chord

D differential operator (/-,is S

FS stick force, L-.ounds

Fl, ... Fe caEes reprerentinc-,. particular combinations
cf hIin.'e-mro. Tnent npa;.a.etcrs

F stick'-force rradiLent in '-ac.ver- (
n- J

g rccel--ration of .TravitY

H -,incc morrment; positive when tends to lower elevator

Ho r".ass -ioment of elevator control ; .stem about
:--' ;or hince positive when trnds to lower
e- a t or
h =



k,. radius of *-,-ration of air'-lane about Y-axis

Ih tail length, half-chords

m ima&ss of airplane

n normal acceleration per a of airplane due to
curvature of flight paTh; accelerometer reading
minus component of grav5.ty force

q dyna;:,i c pressure

S ':ing area











NACA ARR No. L.J12


Se elevator area

s distance traveled, half-chords (2Vt/c)

STrariod of elevator motion

t t ir:e

u independent variable uspC! in Duhamel's integral

V v'-.Icci -T

ya.c distance bset,.een center of gra.vit'v an aerodynamic
center; nositie when stable

dt'/d-: dellecticn of elevctor per unit movement of stick,
radlans ,cr. foot

Sanul].e of attacl:, r.&dians

at angle n' att.tacl -it tail, rad.ans

Sdcicflecti.on of elevator; positive downward

6 ing-lc of nitch of airplane

S r..-,c.t oP stability equa-:ion

- qairplane-density parameter (n'/pSb)

p i1qsS density of air

u'"1 'zr c m'un
u'n-.s i ,t r n


b,':-ri'lDt? a( Da, D2., at, DB, 6, and D6 indicate

derivativ,-w for example, m. = --. A dot over a

sy mhol ni c a t e different iation with respect to time.


TLT HOD OF Ai.ALYSIS


The following assumptions are made in the present
anal-sis:










NACA ARR No. L4JJ.2


(1) VEriuaion in forward speed is negligible

(2) Stability d.criv-ttives E-re constant; that is,
any possible ncnlincarit-- of coefficients is
:ne, igibl.

f) effects s of rower are nerl-1ible

(4) Ff"fects of control-s-.sr rnem. ,.ci.ent of inertia are
ne.- li i: le

(5) Cont-ol-systfom iss unmbalance is ll11 located at
air:.plani center of grav'i.t y

The c ,uatIon? of motion DL an irplar.e subjected to
a .)- scriled elev tcr .not ic- .an c,.-: cbt ined from refer-
ence. 2. If for'Iwa- d s- d is jssmild c.'-tant, there are
three e.4.atioin.- 1" imotion. Th fi.t two eqat ions
deter:,.-! Cn the n.ction of Iths a3:,I",clan' if 1thrE control
motion is seci f led T.'e t ..iril ..iation ceterrines the
hin'~ie-A.omcnt ceff cienL, which tid-,ernds or. the motion of
the con':rcl Surf ace ani 'he air;.lane. These e'-quations
ar,


(2- + EA1)a I


= f, (1)


= -0M6


+ i, 20 k/C) De


+h +,T) h) + CD2 h + (Ch. + h) C- + h f'hp ))6 = ( )


iquationls (1) and (2) arc. used to snlve for a in
ter-is o.f .: The solution can be expressed in determinant
for;1- as


-2!., Cm6

CLa
6 G + 2A.,.D

'C:a + 0mDaD + CmD2aDi
I


(41)


CmD9 2-,4Iky2D


-I- a -2)2
a j + ,]
M'O "1TI m-) ,,










6 NACA ARR No. I4J12

If c is -iven as a function of time, the solution for a
is 'oi.-nd b-- the method of operational calculus es follows:
First a is found for a unit change in f. This solution
is u1'taiine- from

-21A4 mCrn.. e"s 1
a = = 2C + (5)
F(D) F'( ) F(0)

,jln rc' P(P) ir the ceteriinant river in equation (L)
ani \- represents the roots oi F(D) = 0. The solution
foa: ao equation (5)) may be deoLoed by a's). The
val'i of a for a riven variation of 6 is then given
by Di am l's internal, vh.'.ch is

ps
o = f(s) (0C) I Vfs u) 6'(u) du


"a similar poccd,.u'e DB can be found for a pre-
scribed vr.riat'on of 5. The ar.gl of attack at the tail
can then 'e found from

6at
at = --a + h O
at da

Th normc.l .-_ccleration, which h is considered positive
upD,'7i., -i .proportional Lo the change in angle of attack a
and 1 .: :ven by
V2 JLa
n = C- 2.1

Th;c v&lue of the stick force can be obtained by
subort:.tutiing the derived values cf a and D9 and the
giv-n value of 6 in the hin -.:;-.oment equation
(equ..t-ai (3)). Th,' relation between the stick force
and Ch is simriply
1 23 C d6
F, = -pV -' C -
t 2 0 E h.-id7

Th- .ssu.icd variation elevator deflection with time
is il"lutrated in fiFgue 1 anJ can be represented analyti-
call, by
S= 1 1 2os










NACA ARR No. LJJ12 7


The crlculat-ons werere made for a pursuit airplane
for five different combinations or the hinge-moment
parameters C Ct and h; for three different dura-
tions of thie maneuver T; and for three different center-
of-gravity locations. These five different combinations
of the hinpe-moment parameters ;jere selected to give, for
one center-of-gravity location, the smr.e stick-force
gradient in1 a stcsdy turn, es determined by the formula
for stick-force gradient in a gradual pull-up or steady
turn given in reference 2, which is

PSec!cg d5 _A. 4 Ab Ch CmC nh mDO
Fn -- + CDe +
4 ax Cr D C m C
1a /m5

The locus of points in the C a't plane corre-
sponding to a "alue of the stick-force gradient of 5 pounds
per g and a center-of-gravity location 7 percent chord
ahead of the aerodynamic center is shown in figure 2 for
a masE-balanced and also for a mass-unbalanced elevator.
The amount of unbalance corresponding to the line marked
h = I5 -ould require a pull of 15 pounds on the control
stick for bala.ice. The five points mr.rked Fl, F5
represent the combinations cf the hinge-moment parameters
used in the calculations.


N, r'EPICAL VALUTES USED I1T ANALYSIS

The followirg parameters were used in the analysis?


L . . 12 .5

Cn . -0.548, -0.195, or -0.0 46
Xa. . .. 0.0 .2c, or O.C 6
OmDa .. 8.
D2 . . 23 .2


C"DE


. . .. -15 -5










8 NAC A ARR No. IJ.Tl2


Ikv, Ltalf-chlords . . 1.5
C . . .54
, -r . 6.6
6F/I:-, radic&n of elDvator motion per foot of stick
ravel . . 0.5
Ch . .. 51 Chat
.. . .. t
Ch . .. -10.55
T)h at
P-h . . -1

The fo-]loi.; d-lr-en?lonrs ard -!.sity were assu-ed:

c, font . . 7
e, . . 2
C uariVS e feet ., . . 3. 50
p, slui/ca it; at altItude of 10, CO feat 0.00176

The efor-igo-ng. airplane deriv'etIves are for an air-
!lane b-aI. i.- a ujin i o&aiiii of 7C -ounds per sQuare Loot.
Five cc-. !Etiont o" ?1inrge-mcnent par-ameterE selected to
pgila a sticl.-fjrce r-diant cf 5 r.unds. per g in a steady
pull-up when t:he ce.ater-of-mravit location is 71 Percenb
cho'd .hea-A of the aerodynrmic center (see fig. 2) are as
i oll:.vws :


Cacc he h I h


F I -0.1 -0.270 0
Fr 0 -.065
r 0 0
-. I- 17 5 5
S 0 0 1.65


All there values were used in co.lculating the variation
in stick force during.7 a maneuverr for xa.c. = 0.075c.
For '-iualitative co:!-nLriso.-i, case F1 may be taken to
reorpc.!ent a normal elevator. with a fairly high trailing










NACA ARR No. 14 J12


tendency end a moderate amount of blunt-nose inset-hinge
bAlance. The characteristics of F2 or F3 could be
achieved by the use of a sharp-nose inset-hinge balance,
a horn balance, or a beveled trailing edge; F4 combines
4 larae amount o" inset-hinge balance with a bobweight at
the control stick-:; F5 is the case in which the stick
force is due entirely to th. tobweight. Two more-rearward
center-of-gravicy locations (xa.c. = O.042c and 0.01c)
were also assumed, and the stick force in maneuvers was
worked out for cases '-., F,, and F .


RESULTS


Ou'rves of stick force and normal acceleration for a
varying elevator deflection are shown in figures 5, 4,
and 5 ror T = 2, and 1 seconds, respectively,
for V = 400 miles per hour, and for xa.. = 0.0750.
In these curves, the stick force for Pl reaches a
m ...imu.-i value be -re the peak acclera-Ion o':. reverses
direction in the latter part of the cy,.[e. 'Q'.t effect
becomes more, tro i .unced as the di.r tic of *o r,* Stlu."r
bec-.omts short r. '"he curves for 2, r' I ..-- T,)
sh-ow a progre:si.ely smaller phazs. dif'feren.e between the
stick force :nd the acceleration. The stick-force curve
for [ is .ost nearly in ohase with the acceleration
curve.

The effect of center-of-.ravity location on the
stick-force gradient in steady turns or pull-ups can be
shown in diagrams of the type of figure 2. Figure 6,
for exaiaple, shows that the "maneuver ooint" (c.g. loca-
tion for zero sticl: force per g) for case F1
is 4.2 percent chord ahead of the aerodynamic center
(point where Cm = 0). For center-of-gravity locations
behind the nmaneuver point, the stick-force gradient for
case F1 is negative. The stic-: forces fo F5 and F5,
however, are unaffected by ccnter--of-gravity location.

The time histories of the stick forces in a 2-second
maneuver for the cases shown in figure 6 for xa.c. = 0.02c
and 0.031c are plotted in figures 7 and 8. In figure 7,
the stick force corresponding to F1 (c.g. at maneuver point)










NACA ARR No. LtJ12


is oositi-'e at first ard then reverses and becomes nega-
five. The nipxi-"uyr vci.u.es of the positive and negative
rorc-jEr re ar-proxim.-tely equal. As the center of gravity
is :io-ed Ibhind the iineuver point for F1 (fig. B), the
ne. at-ve f,..iTr.i, o''ce is greater than the positive; this
inzreaae -"'orld bc e::nect3d since a negative force is
required tn hold the airplare in a steady turn. The
5ti27k forces for F3 and F5 remain positive. The
cle rntor 4.cflecton required to :.produce a given accel-
era c-or, hov:ev;r, decrease: as the center of gravity
moiVi s r a- v.E'&Cd.

Lir)lLr.ne s.,ecd has no eff.jct on the shape of the
sti:-f'ore and soc-.:eratiori 2-arves, if compressibility
effects are nelect,.j ani i. the product of speed and
du.'ation of' ir..;uver "s ::ed 3onLstant; for example, the
shape of L-e c-a'ves ni figures to 5 is unchanged if
the seed :"s hal.v:1i rid T:e diCation -s doubled. The
effleCt of ic- .Li'- .oed'; t'hereforo is the san:e as the
6f.-c't oj' irc".sil. cuatLon in the same ratio.


D.CSOCUSSI:O


-efo-e trick var'rus clevstor cases and degrees of
stb:'.lit, fc,' x:bich F"'-1 cn.pt'lations were made are dis-
cus6ed, .t apne':--rs .-eslrable to ex.pain the effects of
the separ&t? para-r.rtercs that comr.ine to give the resultant
elev.'tor !c.rcor in ni.- l-1.ps. These effects, as already
sE'ted, are the vir'ation of hinge-mre:ent coefficient
with elevator deflection, as indic-ted by 0Ch; the varia-
tion of 1:nre-rorrent coefficient Witub angle of attack at
the tail, as indicated oy 0. ; The variation of hinge
mo;-.ent "ith angular velocity or the elevator about its
hinge; the m:.r unbalance (jbo:veight effect); ard the
effectLtce rromient of inettia of th- elevator system.

ETcausr3 pre li-irary computatior..s indicated that the
inertia cf the elvrwtor -ysteni had a negligible effect on
tne stir; force for th. shortest maneuver assumed, it was
neglected in the an.lysis. ror airplanes larger than the
onu co-side.r'-d in this rt port cnd for other special cases,
inertia of the clt vator system may be an important factor.

Th.e influence of the important parameters is shown
in figure 9, which gives a br,'akdown of the factors


.1










NACA ARR No. T1J12


contributing to the st ck-fnrce curve for care F[ in
figure 5. Case Fe was chosen because it was the only
condition in which all the parameters were combined.

Figure 9 shows that the effect of C06 is to
produce a component of stick force in phase with elevator
deflection. The magnitude of tnis component of the stick
force depends solely on the elevator deflection at a
given speed ard .s independent of the duration of the
maneuver.

The normal acceleration produced by the elevator
decreases as the duration of the- 'raneuvtr is male shorter.
The stick force per unit acceleration due to the Ch5 term
therefore increases as the maneuver becomes more rapid.

The effect of the mass unbalance of a bobweight is
to contribute a component of force that is in phase with
and solely dependent on the nor.rial acceleraticn of the
airplane. The stick-force gradient dum to the bobweight
is thre'cfore independent of duration of maneuver. Although
figure 9 deals with a mass unbalance that tends to depress
the trailing edgc of the elevator, in the general case the
unbalance may be of the opposite sign so that push instead
of null forces result.

The effect of Ch t is similar to that of the
bobweight since the component of force caused by Cht
is nearly in phase P..ith the acceleration. The slight
difference in phase between the values of at and n is
the effect of the rate of change of airplane angle of
attack. For maneuvers of short duration, this slight
phase shift causes a noticeable difference between the
action of Cat and of a bobweight.


The component of force due to the angular velocity
of the elevator may be very important for maneuvers of
short duration. It has the effect of reducing the stick-
force gradients in cases in which the mraximum force
occurs after the elevator has reached mrraximrum deflection.

The cases for which the results are presented in
figures 3 to 5 were chosen to show the effects of dif-
ferent combinations of the hinge-moment parameters










NACA ARR No. L4J12


subject to tbc designer's control. The paraireter C-hD
is t'-, same icr all cases. In care Fl, the desired
rtick icorce for a steady turn is achieved by a balance
of relative]: large negative values of Ch. and C-t.
hbe stic- forces3 Cue -o there two parameters arc in
opr.o0.ite d1.rect-r-ns so that the ret value in a steady
turn s d'ue to t6e difference in their effects. In a
maneuver of the typ3 chown in firure 1, the elevator-
defloetion curie leads the normral-accelerat-on curve;
here C-- has the predoniratin- ef'f-ct in the initial
stac.ms of tle ,;ineuveir and the negative iCh, in the

later stai.rs. "Lis fact accounts for the high stick
for-ms in the .ret L.lf :' th,.3 nrar.-uver and the reversal
of force in the secoicn hiilf for esa F1. The difference
is :uor-, nc.ticeabic i: thc shcrtr maneuvers. As the
dura'or. of to :..n'iver lurclarses, Lht.e lag between air-
plane ruction anic el.'va.tor acflectio:i becomes greater and
the nr'ai.mu.. value of the arcelcrution for the given
elev-ator defle-tfon 'C,-cc'-pns senaler. Eoth of these
fact',rc tend t. reduce the irmrpo.rtanco of the Cht com-

ronent in .he .arly part of the maneuver and to increase
the ii..xinu. force required for a _iven maximum accelera-
tiio-. This varLation of ;ia;.i'nxn force per unit maximum
accck;rat'or shlovn in figure 10 is quite large.

Fc-' cane P2, t.he desired Pticl. force for steady
turns is achirvca through the action of Ch. alone. All
cur"" for 72 wcv.ul3' have the s.,.e ms; Pnitu.e for any
,citin o:" n.ano 3c Pr.1 ,Jn'.li bt in T.h se with the
] v-tor-,e' f. :c-ticn curve h-ut .i'or the contri f'uticn
of Tf I- eDff ir.crce.aes with the rapidity
of tbe el'.etor mov.m.ent and causes e. phase shi;'t in the
forco cur'et relative to the elevator deflection, wnich
results i'i a slight in.cra :_e in the tiseximum value for the
shorL, st L..ncuvL.r. A elisht push force near the end of
the mur.neuvr is produc.cd by C Figure 10 shows that
in casL T2 the ma::il..um fcrce per unit manxi-muai accelera-
tion ancra.ses as th ma-neuver is shortened although not
co -Lnuch :As in C sEC .

The balance is Pchieved in case P5 through action
of Cht alone. In this case, the maximum stick force











NACA ARR No. LTJ12


attributed to Chat is nearly in phase with the accel-

eration and, consequently, the maxim-um value occurs after
maximum elevator deflection when the elevator is being
moved back to its original position. The forces at the
beginning of the maneuver are consequently smaller than
in cases FI and F2 and may be too small for satis-
factory handling qualities. The effect of Cho is to
decrease the maxin.um force by an increasing amount as
the maneuver becomes shorter. The discontinuity in
the PF3 curve (and also in the F^ and F5 curves) for
the 1-second maneuver results from the disappearance of
the ChD5 comoonent at the completion of the elevator
hD5
motion. Figure 10 shows that the mra:xinum force per unit
maxi:-urn acceleration for case Fz decrease's as the
maneuver is shortened; this effect is primarily a result
of the action of C"D".

For case F the stick force for steady turns is
achieved mainly by a balance of negative "I and

bobweight effects. As a result of the large mass
unbalance required, the maximum force in the 1-second
maneuver occurs at the end of the elevator motion.

The stick force is achieved solely through the action
of .nass unbalance, or a bobweight, in case F5. Compu-
tations have been made for only the 1-second maneuver.
The action of the bobweight, as previously mentioned, is
similar to that of Ct but for a si,,ght phase shift.

The phase shift for a maneuver of short duration is suffi-
cient to reduce the adverse influence of ChD6. This
case would show a slightly greater decrease of maximum
force per unit maximum acceleration than case FP with
decreased duration of the maneuver.

The change of 'tick force with center-of-gravity
location for case FI, shown in figures 7 and -, is
caused by the greater angular response of the airplane
to a given elevator deflection that occurs with reduced
stability. The greater response changes the balance
between the Oh and Ch6 coiuponents. If the stick











NACA ARR No. L4J12


force is independent of CO as in cases F3 and F5,
the forr of the stick-forco curves is unchanged by varia-
tion of the center-of-gravity location. Figure 11 shows
that the variation cf maximum force uor unit maximum
ancal.,ration in a rapid man.une" with center-of-gravity
loccation becomes less as the value of Oh6 is reduced.

The adjustment of the elevator parameters so that
the s''.ck forces for steady turns ara directly propor-
tional to the normal arceloration produced and independent
of henftEr-oy.'-pgrvity location is generally conceded to be
deE irable. it ap ears ocsible from the analysis to
acco,..lish thesc. ccnditionr. by rmanina the stick forces
depend primarily on .at or on a bobv:eight, provided the

entrance and. recovery aie made slowly. It is not defi-
nitel-"- 'inorwn whet-er tLis c.nndizton of strict propor-
tion-Alit- 's desired in rraneuver: cf short duration. In
these c.sec3, ho-'ever, '..en the entry and racover.y are of
necess ty rvpid, ntrire proporti.orali.y between stick
force rnd accelcrLation Epp')ars impossible because of the
action of ChD. According to fi.gur- 10, a stick-force
r.radient that is independent of duration of maneuver but
varies somev:.at vi3th cenriei'-of-.ravity location can be
obtained, for a care intermediate between F2 and F .
This cpse would correspond to a certain amount of nega-
tive Cb and positive C(at and would also result in

hiFher stic]- forces at the start of the maneuver. A
",obtveigp't that increases the stick forces can be substi-
tuted for the positive Onat



COiTCLUDI'TG WRE-ARKES


A sEall stick-force gradient in steady turns can be
obtained with fairly large negative values of the
restoring! -endency 'h and the floating tendency 0hat
approacl'hin thome of an unbalanced elevator. Although
suitable for slw maneuvers., this combination of parameters
leads to a high initial value followed by a reversal of
the stick force in abrupt maneuvers. This difficulty can
be avoided and the stick force can be made to follow











NACA ARR No. LiJl2


closely in phase with the airplane normal acceleration
during both abrupt and slow maneuvers by decreasing the
value of Ch. and by making Chat slightly positive.


If Ch is made zero, the stick-force gradient
depends entirely on a positive value of Chat and is

unaffected by the location of the airplane center of
gravity. In thigh condition, however, the stick force
required to initiate a r.,anzuver may be undesirably light.
In order to prevent undesiiably light stick forces at
the beginning of a maneuver, a small negative Ch. must
be retained.

The use of a bcbweight in the elevator control
syste:.1 has an effect siriila-r to thet of increasing Oh
at
although, in raid lmanervers, there arc slight phase
differences in the sticL-force variations.


Langley remnorial Aeronautical laboratory
I'Lational Advisory CoTmmittee for Aercnautics
Langley Field, Va.


I- ,










16 NACA ARR No. LJ12


REFEREE TCES

1. tRlruth, 1. R.: -equirempents 9or Satisfactory Flying
Q1u elitics of Air-lanss. NACA ACR, April 1911.
(Classific3tion changed to Restricted Oct. 1945.)

2. Greenberr-, Harry, and Sternfiold, Leonard: A Theoretical
Investiga'Lion of T.on-.tudiial Stability of Airplanes
vith Free ControlE Includlng Effect of Friction in
Cortrol Syztem. T'ACA ARR RPo. 4301, 19i4.

5. T.7-, W.. Conbrcl 'Forces during Recovery from Dive.
J.A.C. Faper ?:3. 69, British R.A.E., April 1941.





NACA ARR No. L4J12


E I
i^


Q 'UOTIOGTJGp .OI AOTS
I--g --ON


L


Fig. 1











































j







NACA ARR No. L4J12


.)
Ca


.41

0
rt4


-.2


-.5 -.4 -.3 -.2 -.1 0
Restoring tendency, Ch.


Figure 2.- Lines of constant stick-force gradient
showing combinations of hinge-moment parameters
used. Fn = 5 pounds per g; xa. = 0.075c.
n


Fig. 2









NACA ARR No. L4J12


I4O

00*
.-0
*0
Ur-


44
0
o .-I


0-4





















0

-4

0

o


0 1


Fig. 3


2 5 4 5
Time, t, sec


Figure 3.- Stick force and normal acceleration due to rapi.
elevator motion. T = 4 seconds; V = 400 miles per hour
xa.c.= 0.075c.
















0
410
> 4J 0
o o to
-4 *0





rT4









-4

0


lime, t, sec

Figure 4.- Stick force and normal acceleration due to rapid
elevator motion. T = 2 seconds; V = 400 miles per hour;
a.c.= 0.075c.


NACA ARR No. L4J12


Fig. 4









NACA ARR No. L4J12


.2 .h.


.8 1.0 1.2 1.4


Time, t, see
Figure 5.- Stick force and normal acceleration due to rapid
elevator motion. T = 1 second; V = 400 miles per hour;
a.e.= 0.075c.


Fig. 5


'0
o -10
4. 0
e
. UT)

0 0


20


S


S
-
60
o

o,-4
o

-4


0)






NACA ARR No. L4J12


o.o42c
.01- -
-- O.Olc



F1 0



Fn to
o- -- ^ o_ 1/

5 .'1


^- NATIONAL ADVISORY
0 1- CO MITTEE FOR AERONA1 IIS0 -.2

-.6 -.5 -.4 -.5 -.2 -.1 0
Restoring tendency, Ch.

Figure 6.- Lines of constant stick-force gradient.
Fn = 0 and 5 pounds per g.


Fig. 6









NACA ARR No. L4J12


0 1 2 3
Time, t, sec
Figure 7.- Stick force and normal acceleration due to rapid
elevator motion. T = 2 seconds; V = 400 miles per hour;
xa.c.= 0.042c.


Fig. 7


r6


0
4.O
o0 .-r4


0
r4
Go
















0







0
a









.NACA ARR No. L4J12


Fig. 8


0

&j 0
*o
J 'O
*-Oi












o
r4 t













S



U
o -
I-I
%4
4D





0

















0
-4
41
a)
a

r1-

0
ci



0


Time, t, sec

Figure 8.- Stick force and normal acceleration due to rapid
elevator motion. T = 2 seconds; V = 400 miles per hour;
Xa.c.= O.Olc.


/ r





-8-- __ __ / __
0




-4

/ 3 ,-/


-8




.12















* / NIllONA ADVIORY
COMM TEE 3R AE ONAUT CS


I







NACA ARR No. L4J12 Fig. 9









20--


6 Component -
due to


12----- -










14 0
a -- ^-------- -
-4^ ^ ^ i- ^__ _
: y*N^


0 .2 .4 .6 .8 1.0 1.2 1.4
Time, t, sec
Figure 9.- Components of stick force for case F in figure 5.






NACA ARR No. L4J12


2


0
0i -- -- -- ---------- -- -- -- -- -----










8-\----





F
6------





4 0 a
2 ATIOP AL AI fISORY
COM ITTEE FOR A RONAl TICS
o I m\\


0 1 2 3 L 5 6 7
Duration of maneuver, T, sec
Figure 10.- Maximum stick force per unit maximum acceleration
against duration of maneuver. Xa.c.= 0.075c.


Fig. 10






















1=

Lo








\"



























0
1C- LiU'i











__ NuS


--V_--- --- i-I0










---- -----0"


C


/ Tw /a


NACA ARR No. L4J12


Fig. 11


0



0
9 o
4j



00




*.













o o
0 5












* 4
0
* U





















,-1
* 43


















rz


)


























































































4'.










UNIVERSITY OF FLORIDA
_Jt I' 4ENTS DEPARTMENT
i 2; MARSTON SCIENCE ULBRARY
P.O. BOX 117011
GAINESVILLE, FL 32611-7011 USA


4' ''9






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