Some notes on the determination of the stick-free neutral point from wind-tunnel data


Material Information

Some notes on the determination of the stick-free neutral point from wind-tunnel data
Series Title:
Alternate Title:
NACA wartime reports
Physical Description:
17 p., 3 leaves : ill. ; 28 cm.
Schuldenfrei, Marvin
Langley Aeronautical Laboratory
United States -- National Advisory Committee for Aeronautics
Langley Memorial Aeronautical Laboratory
Place of Publication:
Langley Field, VA
Publication Date:


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


Summary: The effect on static longitudinal stability of freeing the elevator is shown to be similar to the effect of altering the slope of the tail life curve by a factor that depends upon the aerodynamic characteristics of the horizontal tail surfaces. The stick-free neutral point may then be determined from stick-fixed data by taking account of the reduction of tail effectiveness. Two graphical methods for determining the stick-free neutral point, which are extensions of the methods commonly used to determine the stick-fixed neutral point, are presented. A mathematical formula for computing the stick-free neutral point is also given. These methods may be applied to determine approximately the increase in tail size necessary to shift the neutral point (with stick free or fixed) to any desired location on an airplane having inadequate longitudinal stability.
Includes bibliographic references (p. 17).
Statement of Responsibility:
by Marvin Schuldenfrei.
General Note:
"Originally issued February 1944 as Restricted Bulletin 4B21."
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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Full Text

yA- LI


'- February 1944 as
Restricted Bulletin 4B21



By Marvin Schuldenfrei

Langley Memorial Aeronautical Laboratory
Langley Field, Va.

PO. POX 117011
CA NSV\/LLE, FL 32611-7011 USA


.?W/. 4 t'"., : ig^"
'i^.!*-.^^'' '
***-*a):Li t I .*r,
'" -.aSP:


S 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 251


RB No. 4B21


Digitized by Ihe Inlernel Archive
In 2011 Witll lunding from
University ol Florida, George A. Smaihers Libraries wIll support front LYRASIS and Ihe Sloan Foundation

hlip: details somenoelesondeterOOlang




:'~%TrAL POT'7? FT0;' ''ID-TIT"-.'L DA7A.

By Mar'vin Schuldcnfrei

Tile effect on stratic'uiAr 'J stc:.iIllity of
freein., the elevator is t:orn1 to Le l,.iir-r tc. th: effect
of al:serini th e sl.op:? -..' t ae tall. lift urve by a facLor
that .iepe :n s u.ion ti1 u*irodyi--!n... -h r acterrst icO of the
horizon-el ; a-il surfrccrs. ".l'hz st~ck--rtree ncut'al point
may then be Qote.',i'.ne- fr-om SEti? --i: Ixel datL tby tLale'in
account: of the reducti'.on of tail c f lJct ivences.

Two rsphiz3l r,.eto:c .o;' d- r.L .t,'riing the scick-free
neutral. point, which r. sxu.s-o',s :o t.e m.thods
cornm.on1ly used to 'et'.,'ihe Ct".:. ,: c -f ;ed n trnl point,
are ,-, sen' A .a hc ret 1 .lr.. L. for co.,!:.uti nr the
st'ck--r..:e nr utr??. pol'it is a-s o .iv!n. T:-ese ..iethods
may o CpFli Ed to rieteri !ne ;:prot,.'te.. the ]nrcr:sse in
tail s.ize n,'c ss'-ri'- to .i the n: ')t' r oint (with
stic! free ,Er f'ix plane kavin. inadiquate ]c -i-- tuina2 J.:-l a.::il7 .


Th:. sticl:-flix:d leutrsal point vas d-fin-., in'
refer'nci- e 1 as the ce.nt-r-C f-.;pra'JIry i.3 tiC n c ,t :i','ich
the statili .-: as :,:-S ',uErd by t: rlcr of' th. c-i20;r of
pitching-.Tomr.nt coeff.?i:cnt 'r i p.ultt-. cta trt lift
co,-ff f ient CL, is n,:utrai it,. r, a r;'l:ne ta i"'ne;i.
Thr conditions are tat.d muh,- n; t i Jall:- as
dCm,/dCL = 0, Cm = 0. Thi :; --f:-.:: -c- -avit-y loc-:ation
is tl-e Ija itinf ( o.;cst re'rarward) li'ca tic.; ht ;licho varia-
tion of tri,:- sped with el-;.-tLor -'.'fle-tin ,e is
conve-tioln-.1 (that is, up defl.6ct on of the elevator
decreases trim speed and down deficctio,.n of' he elevator
increases trim spnecd). T'-.3 -:cni.dition thus defined is
dbe/dCL = 0.

Elevator deflection alone, however, does not neces-
sarily deterriine the variation in stick force that will
be felt by the pilot. The stick forces required to
chang. speed ar mada up of two components: that due to
direct elevator deflectioi, and that due to the change
in an.:;.e of attack at the tall V'hen the attitude of the
airplane changes in response to the control deflection.
The stick-force variation with respect to speed, conse-
quently, depends upon both .Ch/iat and ( Chb, 5e of
the ta', where cCh/bat is tih rate of change of
elevator hinre-T:cL-ent coeffici;it with tail engle of
attack: and eCh /5e is t-.' rate. cf chang. cf elevator
hinc-miLoni:ent c.offici:rnt with elevator deflection.

The neutral r'oint with the- stic.: irse (elevator
free to float) is related to th.=- vitIL th.e sticl; fixed,
for the conditions to be ;net wi~.rti th'- ti,: iree are,
mathematically: dCm/i-L '= r = ), Ch = 0. The
condition thus defined is bT/dCl. = 0, where 5T is
the trim-tab deflection. 'T'.-e rse"-l p.,p'-r ::how'.s how
the third condition Sh =0 rray te tker.n int.c, account
as an extension to the rrmethodrjs of' etl.r.-r:irilnr the. sticl:-
fixerd neutral point of ref.r 'ince 3.

For thli purposes of this rs.'crt it is assumed that
ACh/Pae and ch/,aC t are cunstint at any particular
lift coefficient being i n;r ctigated regardless of the
ar.ngl of attack at the tail or the elevator deflection,
that tab deflection has negligible efl.ct on tail lift,
and that the elevator is sLatically balanced. The
other qualifications in the use of the r.ethods are given
in reference 1. The symbols us-d in this paper are
defined as they occur in the. text and are suri mmarized in
the an-er.diz:.


The pitching r.ormnt contributed b0 the tail ard the
increment of stability concrlbuted by the tail are seen
to be directly proport onal to their slone of the tail
lift curve :.CLt/L-at from equations a17) and (18),
appendix A of reference 1.


The relation between the slope of the tail lift
curve vith elevator fixed and the slope of the tail llft
curve with elevator 'r-ee may be found o followIs: In
gs.'nercl, witL the elevEtor fixed, and at any dynamic

CLt + Lt
CLt--- at + e (1)

and the associated hinge-:nor:.enL coeff'ic int with elevator
statically balanced is

Ch UC S, (2)
S- + -- e ---i (2)
S t c ,e T'

If t'ie lc- artor is allowe-i to rLt, "-tri a lixed- trim-
tab setting, the Ileft-I-and ni e.-hl-r o' eil utic.n (2) may be
equated to sero, whence

S---t (5

e re eI

CorI,'.binir.n cquations (1' and I ) ,-i' ld-
/ / \

Lf t t .j,\ 5 '' i

If equa.tion ( i) is differ ntiasted c. .ch res:pt:ct to at

eLt 6C.
SCC' t C
S- (5)
S it(5)

The ratio of (dCL /da t to c t /'dat is then

6c t


60L b
6t bC

= 1 ( -O
'CLt 6 Ch
6 at

which r..ey be written as

k = 1 -R

if':- coefficient of ?.nrizontal

lift coefficient of horizontal
fr.;e to float

tril ..'ith elevator

t.~l .rath elvator

Ch elevator -ilne-rmorent coefficlien
at anrgle of attack of tasl with re.-p c t tc relative
win. at tail

6o elevator deflection with re.Zp-et r.c stbtilizcr
chyrd line

6r tab deflection wi'':. reslact to ,.Lcvator chorx line

1CLt rate of change of tall lift cccffrcie,-t iti; tail
a1t le of attack, elevator rixzd

/(I rate of h'bnce of tail lift coe ff.'inr 1 v.ith tail
( J, an g le of attack, elevator r- r

.C~ rate of chang-E of 1ail .lift co-rficient vwith
-t elevator deflection, at fixed





6Ch rat3 of charge of elevator "-iner-. c.n ert corffici-er.t
W. it-l tail angie of atta'-, ie', conr a -nd tb fL'ed_

h rate nf n' elevator bin '--r:,omort coe fi icr't
--- wih ele-ator dellect-ion, an _- cO '.Ltack end
'e tab fixed

C;h re te of c-hanr.-e of ele-atot r L....: -r.-rm;nt cocel i'-.:nt
'ih-'. t J deflection, ana ..e o0 tt a: l. eini Ije'i-D or
T defr ti mi f>y I- -

k tIevatc'r'-f re e ct v,-ie ; t:tcr --

SLt/6 'ihr -t
Ti =- 1 i -T ^^''
a, a t c 0 ,

Ti a t; b3c r n f'i'T e- ji',5 s ( .' tha-t -e u faecive-
nP-l cf th- tasl 1 t'i c 3Ieva 'r f;-.- 1.1 c in 'ft
a(ard -iernce ; ': o in ,.o .: ) is rel ed to
the eI'ttF-cti resq ci .s L> v.-u l < 'ator Ii r;; e c
fcct Dr k *-;ren c'r.t :ncn e'l. E3a or.C.I'r ::arv.Ta-i. c-r is S
of tn:' orn *-i.ta tail s.d .. '*. T t, ra1
be sen tnt-, tnise ilc cr 3 i' ric- r-ieT' of ue tr '.ni-ta st?bi licr se-tin and *a-1-n3.;ic r .:( at t'he
t il, "i tar- dy!isii -no.u su'. PS .- 1 i: 1 fri Ul a. or-r
o-er the, tail.

'Tic ner rel poin i t, L o 'r' ..P.. t. r be
deterin1r.d b;- rect ifyi-.p' iat:- fr .: ecn nti, al c.-sts
witi .*lsvator fix.d accor diLr to tl..: ,iv~i n ir.
equations (; :.

DET ,E-'1'lJATT _I 0 ST: -F i.TP.I I;'T

Sti:-t!h.i I

Assurne that ecnv-ntc..c.'L ic'hirn-acmen curves of
the forn shown in fiilu.r. 1 hive b-c-en obtain-d for a n.odcl
with elevator fixd. (Thes; car' as,, for' a fictitious


Tt has been shown in reference 1 that, if (dCm/dCL)
is plotted against Cm/CL for two elevator for stabilizer)
settings at a given CL (fig. 2), the location of the
center of gravity for neutral stability is the point
where fC /dCL) is equal to CmC L; that is, the neutral
point is the point of intersection between p strai'gt line
connecting these two plott,:d points and a line having the
equation CCm/dCL ) = Cm/CL. In figure 2, the neutral
point is given in choid.r fsrrw.rd or reE.rward of the center
of gravity about which the data are :5verl, depending upon
whether Cmi/CL is positive or negative st the noint of
inte..'section. The value of dC 1,dCL arnd r for
the tail-off curve is now plotted in figi;i' 2; thi: values
are taken at the same CL as for the two elevator set-
tings. For this exminple, CL is selected as 1.2.

From figure 2, it is apparent that the contribution
of the tail to stability is the difference, in ordinates
between the tail-off and tail-on points plocted, whereas
the contribution of the tail to pitching ,rmomnnt (plotted
as Cm/CL) is the dif'.rence in abscissas. If, then,
the action of freeing the elevator is represented cy a
decrease in tail effectiveness as has b.e n shown, these
values of the differences in ordinates rnd abscissas may
be multiplied by the effectivenss- factor k. The
result obtained is the equivalent of multilying by k
the length of the Osshel lines a of figure 2.

As an example in the use of this met-cd, asss.ume that
the aero-dynsm:ic characteristics 'have been
determlirnc for the tail of the airplane of fi,;ure 1 (the
meth)ds for obtaininp these characteristics w:11l .be
discussed later):

I?.h/6at = -0.0012 CLt /at = O,'oo63

6Ch/e = -0.0030 6CLt/66 = c.Oa:3

Then, from equations (6),

--0.0012 0.031
-0.7050 'J.068
= o0.C

R = 0.20
which indicates that the slope of the tail lift curvJ
with dhie elevator free is 80 p:-r.,cnt f that with the
elevator fix.ed. If this factor is nL.lied to the
dash-d lines of igUarj .2, a new Jirn i.. obtained; the
intarrecti'n of u:is ine with LhCe line

(dJ C
KcC /Cr
d x -
deter mines tlU. stick-eree ncutrIa p.oit. i-Yom 1 '.gur-e 2,
it ma:i be sPenr chat the st ,.cl-'-fF point is "lr-
ward of the sti?'i:-fixrd neutral uc,.:in. .hcut 0.01,
(or ".L4 percent) of ti-e rmean aserndlna',rnjaic chord for this
r.ethcd TI

It has -.een Fshown in rI f.,ri-n,::c 1 ta.t :f t!.h tan-
gents to or more elev'stcr (or sta'" iz r) cr'u."es at
a Eiver, li't. coeffricient sare -ext_.:r-ied u .!til the;- i:ee t
(fig. 7 ), the slope o t e h l J.'n ] -in this .c'int of
intersections. throrjuiih (Cm : = ) Z1-, tn- lJoca-
tion of the stick -fi:-:e-i nr--u' r l *Ij -;t jr "'i r",ds ior'a.9r d
or re.ri~erd of the center.-of-cra.ty Lt'ncat inr. 'bot which
the data are cominputed. The pri'u-- ,: i''.rolve.jd re
same ic those used to obtain ne-t'a&l ::;.irts l..- .-
of figure 2.

It can be shown that, if t -ie ti;:I--nt t3 tlhe t-il-offl
curve at the CL imder ccri dert --.r, is c-:-tnded tc a
point having the sa--e abscissa as th; -,oirLt of inter-
section of ti-'e tangents to the i v,-- tO:' C'-r".'u- e the
difference in ordinates of the twp.,o ;oii:ts b is oro-
portion l to the elevator-.- .- e e':ecti-'-ness lectoi- k
(fig. ). For the fi,.ed-- l,- vat:)r ccnaition, i = 1.0.
With the slr-.vator free, the a&lueC r;f i: det;:r'r, :ines s
new point throui which to d:ravw the li:fne t.-iro.'gh
(CO = 0, CL= 0) in order to fin- t-,e neutr.l po-int.
For the example under consi j'rati..r (fr;,. 5), the dif-
ferenc.- !et',,c.-en stick-free annd strL'i-fil. ed nt.utral points
is again se-en to be eq' :l to 'u;. p.r,-cenC of e.,* m r. n
acroi-'nari.ic chord.
"cEthdT IfE

A 'nathom tlicil anra.lyrsis to ter:iine th: shLft in
the neutral polnc Ctlus to frc!-5rng- tih elevator, 'mlwhich
takes into account the vari'nttion of' dil.nimic-ritess'u'e


ratio at the tail, has been made in reference 2. The
neutral-ooint shift has been shown to be

Anp = np p

( 'cLt\ qI ______- ( -
\ qt~ 0 o dcI./ d

qt L


whe re

n neu-ral--oint location, chcri"c behind Icading
P e.'f e 0'" mean ercodr>5.nic chord, stick-: fixed
(xo in ref.r'- nee 1)

n neutral-point locabloo, record. l-behLdii leainr
d -re of mean aer>' ,rmrmc cizrd, cticl. free

An sabift in neutral p-oint du5- to freein,-. elrv.ptor
(nfP np)

6CLt incr-ase in slope of tail lift curve due to
Tii- -/ ,-: \
freein- elevator IF--R

V tail volume -

St horizontal tall area
S wing area

Lt tail arm
e- mean aerodlra.:tic chord of win,

qt a d:-ncmin. pyre*ssire at tnil com iiared with
Sfrce-st'-eam .ynamlc prs.rure

qo rate of chanCe of qt/qo with aI.r;lane CL

dCL slope of lift c~irve for complete lrrplane
de rate of chqnri of aver':ie dov.-n'ash angle at
da tail with air-,,lne a.-.,le of attack

If qt/qo Las the constant value 1 (as for
windmilling conditions), equation (7) reduces to

np Gat dCL 'da dac,

Inasmuch as

S t dC (9)


O1- /at dat
SCL/'a dCL

then equation (7)
d2m dat
dit dCL (0)
n t- L (10)




dCm rate of c.ian;-e of Fpit.L:i:n._-no.,eort coefficient
with ?tabl]iz-er an.-Ie, at any .-,,rticular
it airrpline 'L' elevator fi-.ed

dat rate of change of tail angle of attack with
d, de'
L (1 -da
airnlr-ne lift coefficient .


Aerod,-nr.mic characteristics, such as "Chh/at and
OCh/iOr, mentioned in the present pap,-'r (except ior
dCm/dlt in equations (9) and (10))were -bhsed on actual
d:-.Ta.-:.r; pressure at t.e tail. Thus these would be the
values fcund in tests of 4i isolated tail surface. In
tests of a complete io-:el, however, the pressure
at the tail will influence the :ingre moment and lift
reducec, degree of elevator or stabilizer ':Lartion;
,..!ec the d-Imr.-iz pressure will vary, in general, :.'ith
airplane attitude. It is then necessary to det-rm.ine
the value of the tail characteristics and I un.IPr
con1it.ions v.Lere qt/qo at the tail varies, as I1 would
on the actual airel.an1.

The value of th. factor R has been t-hc-n to be
h/bat CI -e .,at
,_ -CLt/ mTh ratio -- is independent of
6Ch CLt:aht -0 1
o h /
the dync.ic-rressure ratio. The value of -il-,

be determined from el-'.-'vtor and stabilizer tests by taking
the ratio at any lift coefficient or fr-1ndi- the .avrage
at several lift coefficients of the air-llans, if tr!e
hin .e-moment-coe ff'ic::t variation is lin,'ar. ry the
'-'"I t!' 5e
same "r'-scsir ----- is indep-rrnden:t of Qt./q at
sc. Cit/
the tail if it is assumed that -~t/qo is fairly unLifor:n
over the tail sp'~ii and, further, C, /6e is directly
propor:tional to li_.m/dit. Thus

*CT1t.< e dZ:,./d6e

and the ratio is constant at any value of
dC/d t
airplane lift coefficient.

if the actual values of dCh Cat and dCh/dIe
(with respect to the actual '.alue of the dyi.nmic pressure
at the tail) are resir,-d f'orn wirn-tunnel data obtained.
from tests of complete models, the;; may be found from
the relationship

dC> (6uyis5e)e4
je t/ o

and, siri!larly,

Ch (OCh/itexp
t Ct tA/qo

Tf the values fo" dCL, /dL and dC- 'dot dusir-ed
frcr !'ir.d-tunnel data, th- follouinT relations siauply:

Lt dCi c_ t
oat qt,,

i ,r
and, similarly,

... --'DtS


Tt nay be edTantarcous at this point to indicate
the Dhysical significance of the operations p;rformried by
these methods for finding the sticl-fr.e neutral noint.


Basically, it is desired to obtain t,"o or more curves of
Pm plotted against CL for the urodel with the elevator
free to float. recause,with the controls free, an air-
plane must fly with zero elevator hinge .iiorient, flight
speed or attitude can be changed only by varying either
center-of-rravity location, trim-tab setting, or stab-
ilizer incidence, for any particular airplane configura-
tion. Control-free flight may be reproduced in the
wini tunnel by obtaining two or r.,ore pitchinr-nor-ent
curves with thE elevator free with different trim-tab
settings (or stabilizer incidences), and the neutral
points with the stick free may bc found directly by the
methods of reference 1.

This procetlure ;]16y also be used in flight to
determine neutral points w.ith ':levator' free. The air-
plans n.ay be flown .ith several center-of-.-ravity loca-
tions &nd the trin-tab setti.n;s required for trim may be
determined thro-iwhout the speed range. Because an
airplane can fly steadily only with Cm = 0, the out-of-
trim pitching-:ionrent curves as obtained fror wind-tunnel
tests need not b- determiner. ThMe neutral points inay be
determined directly as t'.: ci'nter-of--revity locations at
which the variation of ta'b arngl reluirei for trim does
not chp.-ne with speed (d3r-/'dG = 0). Si:-.ilar tests can
e -mad'e with a rwinr:-tunnel rodel if the elevator is
statically brlqnned and all csed to float freely with the
tab at various T;he r' .ient curves
obtained -.ight then be handled in the. manner r described in
reference 1 for the dcterminnticn of sticl:-fixed neutral
points. This method has been avc'ied, in Lenera.,
because of the necessity for thi, l.enth of the
test pro:-ram but r:ay be the o'nl-, satisfactory method to
follow for models having noiilineer hiiEge-',c.or'ent character-

By applying the methods p described it is
possible to determine the stic'k-free characteristics
graphically or m:;ithemneatlcally from the stick-fi::ed
characteristics, provided that tle :ilnCe moments of the
elevator -iave been determined during the elevator-fixed
tests trade vith various stabiliLer and elevatorr settings.

Although the lift chnrncteristics of the tail of
windn-tunnel models have b.en, fj'iud to represent fairly
clos,'ly those of th3 tail of tih-- ctLual airplane, the
hinge mo'-cnts have been found to be critically dependent

upon the accurate representation of the tail-surface
dimens:-ons, vith respect to such details as gap, thici-
ness, and trPilinr-ed.:- angle. Further, the effect of
scale msy disto-.t th3 n.odel hinge-mroment characteristics
even if the tail conf,-iuration is rc. roi uce-d with the
maxin-i-'m of Pccurnicy. It ':;a., consequently, been found
desirable at timss to test isolated tail surfaces of
relatively large scale and tc aly these id.ta in cDn-
junctior vtith s-nall--cole corplcte-;.odel data to
estimr.ations cf fling qualities of tii seirplane. It is
appare-nt that the ae8'od0'naic criaract:e-rstics of the
large-scale tail surface with respect to
stability may be repr-FsentrLd to i- fair degree of accuracy
by determiining the value of the cons ant k. The effect
of the frue-floating elevacor o:i uLe location of the
neutr-.l point may tht-n be found lb tr-i m,-thods described
if th' tail-fuselage interference effects are approximated.
The erfects of tail-fusela c inl-lcrle;nce have not been
subjected to rational analysis. So..ic a:proachi to thc
interference effect iay bo- mr :d 7'by testing the large-
seal,' trial surf-cc in the ures'en:.e or a stub fuslagd,
for conventional airplanes, or in the presence of stub
booms, for twin-boc,,- airplanes. If such tests are not
possible, the effect .n- t be estir:: tc.d.

,he effectiveness of a tail surface as r.easured by
the slope uf the tail lift curve with elevator fi:.ed may
prove to be different i1 cthe t.-sLc o" a la--Rg-scal e tail
model fro:n that obtained froi t?-ts of a small-scale
complete model. In this car? h-1c effects i-sy be t3.aken
into recount snd the wir,d-tu;nnel results corrected graph-
ically by considering that the difference is due to an
increase in the factor k or matematically .y the use

of equation (7) where A---- is the increase or decre-se
in 'CLt/aat obtaine-. from tests of th-e large--scale
surface over thlt obtained frcTm tests of the smr.all-sca.le
co;rplete model. Also the si- f t:O tail surf..ce needed
to shirt the sticl:-firid neutrall ncinc to any de:-sired
location may be determined approximately by considering
a larce-r surface as hain. an increased e effectiveness
and solvin-g raphically or :y .e4uatio (7) again.

Lanlcey [;enorial Aeronautical La'oratory,
l;atjoial Advisory Co,:;,nitt.e for .erion:ut ics,
Lanl-cy Field, Ia.


S li' fOLS

pitching--not.ent coefficient

lift coefficient

lift coefficient of horizontal tail,

lift coefficient of horizoiltal,
free to float

elevator hlr.Le-moment coefficient

anEle of attack of tail with res.ect
wind at tail



to relative

elevator deiec~icJo with respect tc. stabilizer
chord line (positive with T.E. dacv,'

t&b deflection with respect to chord
line (positive with T.E. down'

rate of change of tail lift coefficient with
tail enrgl of attack, elevator fixed

rate of chance of tail lift coefficient with
tail an;le of attack, elevator free

rate of chan-e of tail lift coefficient witn
elevator deflec icn, at ixed

rate of chan-rc of elevatcr h'nre-eorrent coef-
ficient with tail a..-le of attack, elevator
and tab fi:'ed

rate of change of elevatcer '! co3f-
ficirit with elevate' deflection, e.:'le of
attack and tab fixc-I






Ch-- rete of change of elevator hingn-rnorant coef-
SsT ficient with tab deflection, angle of attack
and elevator deflec t.on fixed

k. elevator-frece effectiveness factor (1 R)

6Lt,66,. 6m/o t
R -CLt/ b't b/Ceat

x original ce:-.tcr-of-- revity location about which
data are gi'vn, ciior:a behind leading edge of
rnean c rod-.nan:ic Pchord

np neutral-roint location, chords be-hind leadin
edre of m r:n a,'rod;'w.r;:ic c!cord, stick fiz.'d
(xo in rc'irincc 1)

nPf nrutral-point location, chords behind leading
npf edge of m.-an aerodynar.ic chord, stick free

An sli'ft in neutral ;o.cinc aue to, elevator
(npf n")

A incre-se in dope of t--l lift curve due to
St / OCL
/ t
freeing elev'a tor (nL-

(ct \ O c
V tail V.u.r (t 75

St horizontal tail area

3 wing area

It tail arm
c rean aerodpnamic ci:ord of v;iitg

it an&le of incidence of stabilizer (stabilizer
setting) with respect to Li,.rizontal reference
line of model positivee t.ith T.E. down)

qt average dynamic pr-esure- at tail comca3red with
q- free-stream dynamic pressure

rate of change of qt/oo with i.rplane CL

-- slope cf lift curve for cor-iolet! eiirplane

Srte of ce of cane of average dov.'nwsh angle at
do. tail with airpl rs cr nle of attack

Rate of chn'rne of pitcIin-T-no;.ent coefi'cient
dit with stabilize, -.rnile at ,-ny or rticular
airplane CL, elevator fixed

dm rate of chagr-e of pitchin7-.c-.v,&enl: coefficient
d6e 'th elevator angle at s.i r pricul.ur airplane
CL, stabilizer angle fi..frd

-- rate of change of tail n.-'.-e of atti..: v.itji
dCL i
airplane lift coefficient da
SL /


1,2 elevator settings

x referred to center of nr;.vitt', bout vwich data
are presented

experimental values




1. Schuldenfrel, Mqrir-n: Som, P.'ots on the Determ-ination
of the St ick-rjxed "rfutral Point froi.i Wrind-Tunnel
Data. ITACA R.B Tic. .IZC Srpt. 1943.

2. rotes, S. .: An Analysis of Static LnrritiiCLnal.
Stability irn RI.Etion to Trim and Control FI-rc .
Part TI. .En-'nr 0:. T- p. "T. 1.4. 519,
P.A.E., Scpt. 1i'9.


NACA Fig. 1

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dC C

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-- O *

-- 2 /-. ... .. r- .. '
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-- -....- i t--- ,,- ---- --- -...- -.
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0 4 03 rl Ui

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-- -- "-- --.--.-- --- o .g -. -,--- .

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I I C ty r4 *" t -1
lI I I O I I
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I I u I
i___I -t ; I
o -l 4c 3 -Ia

jI I I .

N / 22' 1
;^1 ~c
[4 *j


ITACA Fig. 3
"3 ';USTt.tjooo z.uau8oWT-8rx1tpTDTd
m *d ( M rl- o 3 en fo

II / i
r i I .. T 0 I \ / -- I- .,

__jI I *I / I -
S ',o

- r -- -- F -i -- --1

Si '
-f -- r 2-I .,- -

-,0 --1 i. -
I i I I 0 I l

I,__ ,_. .i -
- 1 .- -r-. .- I 5
-- '----- .
rI ;
.- --r -^------4-- :-- -- .--'--.- -----\


I i i i I

1 I
I T i / T -- : '
/I r -t --k- 4

II I s
I, .*' I# I, -

S' I ,i I I io
... -.. --'- .. .. -l. -- r1
l -' I i I I "

r-- i ,-, Ai /_ : Ic .-i i I' <

/ 1 I i ', t / I I ""
S------ ----' I --I---'- *II--- --.----- 0.--.-. --- -i .-
/ I I i 0

---t 4 -iIx-- .I I S ; ......- -. *" I
S' T I I I I i I

I, c / I 1
l/ i | | i I -- --
~ ~ ~L. /I _. ,-_ 1 -
,ri -. --

_ K i-0
I i I x I ... .. -'-- 1
I /l't / I" ,t i 1 / 11 11

-__- f-- --, 'r... ----I- -*----- --:'--'-
I l 'x / i-

I, .. . . . ,




3 126208106 4 9 0

.O. BOX 117011
:, .Ji,:-ISVI!LE, FL 32611-7011 USA

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