Experimental verification of the rudder-free stability theory for an airplane model equipped with rudders having negativ...

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Title:
Experimental verification of the rudder-free stability theory for an airplane model equipped with rudders having negative floating tendency and negligible friction
Series Title:
NACA WR
Alternate Title:
NACA wartime reports
Physical Description:
27 p., 19 leaves : ill. ; 28 cm.
Language:
English
Creator:
McKinney, Marion O
Maggin, Bernard
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: An investigation has been made in the Langley free-flight tunnel to obtain an experimental verification of the theoretical rudder-free stability characteristics of an airplane model equipped with conventional rudders having negative floating tendencies and negligible friction. The model used in the tests was equipped with a conventional single vertical tail having rudder area 40 percent of the vertical tail area. The model was tested both in free flight and mounted on a strut that allowed freedom only in yaw. Measurements were made of the rudder-free oscillations following a disturbance in yaw. Tests were made with three different amounts of mass, moment of inertia, and center-of-gravity location of the rudder. Most of the stability derivatives required for the theoretical calculations were determined from force and free-oscillation tests of the particular model tested. The theoretical analysis showed that the rudder-free motions of an airplane consist largely of two oscillatory modes - a long-period oscillation somewhat similar to the normal rudder-fixed oscillation and a short-period oscillation introduced only when the rudder is set free. It was found possible in the tests to create lateral instability of the rudder-free short-period mode by large values of rudder mass parameters even though the rudder-fixed condition was highly stable.
Bibliography:
Includes bibliographic references (p. 24-25).
Statement of Responsibility:
by Marion O. McKinney, Jr. and Bernard Maggin.
General Note:
"Originally issued November 1944 as Advance Restricted Report L4J05a."
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 - 003806635
oclc - 124093465
System ID:
AA00009416:00001


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Full Text

NckL-I* vi
."' ARR No. LAJO5a




-i NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS






JYARTIME REPORT
ORIGINALLY ISSUED
November 1944 as
Advance Restricted Report L4JO5a

EXPERIMETAL VERIFICATION OF THE RUDDER-FREE

STABILITY THEORY FOR AN AIRPLANE MODEL

EQUIPPED WITH RUDDERS HAVING NEGATIVE
FLOATING TENDENCY AND NEGLIGIBLE FRICTION

I:By Marion 0. McKinney, Jr. and Bernard Maggin

Langley Memorial Aeronautical Laboratory
Langley Field, Va.

UNIVERSITY OF FLORIDA
I DOCUMENTS DEPARTMENT
120 MARSTON SCIENCE LIBRARY
P.O. BOX 117011






WASHINGTON

I NAQA WARTIME REPORTS are reprints Mf papers originally issued to provide rapid distribution of
adv.uance research results to an authorized group requiring them for the war effort. They were pre-
1t.wly held under a security status but are now unclassified. Some of these reports were not tech-
4,taly edited. All have been reproduced without change in order to expedite general distribution.

J" .'" ... .
.. ... ..r;i ..
-. 1.. ... ,.:.... .. .. .. :
N 4ll:..!.~i. :...I.. .. ,;~ k ';.~::.'i






















il







ITACA ARP No. T4J059

NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS


ADVANCE FRSTRICTED REPOr.T


EXPERIi.,E1,TAL VERI TIC NATION OF THE RUDDER-FREE

STABILITY THEORY FOR AN ATF PLA"E MODEL

EQUIPPED WITIH RUDDEES HA VI I:G ECATIVE

FLOAT NG TEl DE ?!Y A [ITD IEGLI CI BL F I CTI ON

By Far on 0. FcKinney, Jr. and Bernard i.iaggin


SUir..RY


An invest.iaMion has been rmade in the Langley free-
flight tunnel to obtain an experimental verification
of the theoretical luddrr-frece stability characteristics
of an airplane miLdel equipped with convent nal rudders
having negative floating tendernits anrd negligible
friction. The model used in the tests was equipped with
a conventional single vertical tail having rudder area
0O percent of the vertical tail area. The model was
tested both in fr-3. fllrht and mr.ounted on a strut that
allowed freedom only in :,'-v. Yeasurements .fere 'made
of the rvuddrr-free osci.liat ons following a disturbance
in yaw. Tests were made with three different amounts
of rudder aerodynamic balance and vith various values
of mass, moment of inertia, and center-of-_rcvi ty
location of the rudder. lM'ost of the stability derivatives
required for the theoretical calcilations v':-r determined
from force and frec-oscillatton tests of t particular
model tested.

The theoretical analysis showed t-hat the rudder-
free motions of an airplane consist largely of two
oscillatory modes a long-prFri od osci llston somewhat
similar to the normal rudder-lixed oscillation and a
short-period oscillation introduced only when the
rudder is set free. It was fund possible in the
tests to create lateral instability of the rudder-free
short-period mode by large values of rudder mass parameters
even though the rudder-fixed condition was highly stable.

The results of the tests and calculations indicated
that, for most present-day airplanes having rudders of
negative floating tendency,the rudder-free stability










2 NACA ARR No. L1JO5a


chvractcristics tray be ezamrined by simply considering
the dynamic lateral stability using the value of the
direct.iunal-stability paiametear n for the rudder-free
condition in the conventional controls-fixed lateral-
stabili y eq-uations. Fnr very large airplanes having
relatively high values of tne rudder mass parameters
vw.th respect to the rudder aerodynamic parameters,
ho',ever, analysis of the rudder-free stability should
be ml3.e vi tn the complete equ'tians of notion. Good
arree.nent between c:lculnte.d and measured rudder-free
stability characteristIr. was obtained by use of the
g-nEral rudter-free stability theory, .n vhich four
degrees of lateral freedom are considered.

Then the assirnrtion is inide that the rolling
motions alone or the lateral and rolling motions may be
neglected in tLe onloulations of rudder-free stability,
it is possible to piedi.-.t satisfacLorily the character-
istics of the lon--period (Dutch roll type) rudder-free
oscillation for e; rplancs only when the effective-dihedral
angle is smrll. ''ith tnese s'implif-ing assumptions,
however, sat1sfactor-y pr-dictlon of the short-period
oscillation nme b.e obtained for any dihedral. Further
simplification of the theory based on tie assumption
that the rudder mo;.lent of inertia might te disregarded
was found to be invtlid because this assumption made it
impossible to cslculate the characteristics of the short-
period oscillations.


I NTEODTUCTI O I


SorIne military cirplcnes havs recently encountered
dyaninc i nstahlic]jY in the ridder-free condition.
Certain other airplanes live performed a rudder-free
oscillation c.led ''na':ir:g" in which the airplane yaw
and ru 3dr motions -.re sn coupled as to maintainn a yawing
oscilltirn of constant -niplitut>. These pncnomena have
bern th3 subject Df various Lhecretical investigations,
and the f.-ctors sff',ctlnj_ the ruiddr-free stability have
been explored and iefin'd in Lhe tiveoreeical analysis
of refer-:nces 1 to ?.

In reference 1 the .L.st corplete set of the three
sets of equations of the rudder-fr2e motion is developed.
Th- equations of reference 1, however, arc vary involved
and rather un-vieldy, and use of these equations to









NACA ARR No. tLJO5a


determine the rudder-free stability characteristics is
consequently laborious. Su-h equations are usually
simplified by neglecting certain i :grees of freedom or
certain parameters ani thus obtaining noproximate though
satisfactorily accurate solutions.

In reference 2, the equations were sirrollified by
neglecting the rolling motion-s of the .irplane. In
reference 5, vhich supersedes reference 2 for the rudder-
free theory, further simplification was obtained by
neglecting siCevise motion a9s 'ell as rolling motion.
An additional sirmlifying assumption of reference 3 is
that the rudder moment of inertia r'-i_.ht be neglected.
It was realized thst these 3;r,.plified equations were
not applicable throughout the entire rnnge of the
variablz-.s that could be obtained, but the r-sultz were
believed to bc,- generally applicable to airplanes of
that period.

In order to obtain an rre-'elin.nta l check of the
general ,nd simlpll fed cquat.lons, an e-:peri-rntal program
is being conduct.aAd in 1-he Langley rree-flight tunnel. The
results of the first part of this piogrirr. are reported
herein and are concerned with tre rudder-free dynamic
1
stability of a -scale airplane modlel in gliding flight
7
equipped with rudders having inset-hinge balances and
negligible friction.

The rudder-free stability characteristics of the
model were invest4ieted for varying snou nts of rudder
aerodynamic and mass balance. The model was tested both
in free-fli'ht and mounted on a stiut t1ht allowed
freedom only in yaw in order to determine experimentally
the differences caused by neglect of the rolling and
lateral motions of an airplane v.ith rudder free.

In order that the results obtained by theory and
experiment right be correlated, calculations wRere made
of the theoretical rudder-frae stability of uhe model
tested by equations. involving four degrees of freedom
and by equations involving f,-wer degrees of freedom.
In addition, the rudder-free stability of th. model was
calculated by an approximrate method that neglected all
of the rudder parameters except those causing a reduc-
tion in the directional-stab4lity parameter C- for
the rudder-free condition.









FACA ARR INo. LJO5a


Various force, hinge-moment, and free-oscillation
tests wcre r..n in orde, to determine as many as possible
of the stability derivatives required in the calculations
of rudder-free stability.


S..1BO LS


S -,ing arca, square fe3t

v free-stre'am irspeed, feet per second

'b irg pspn, feet

c vWi ny 3hcord, fest

hb, srsn of rf..er, feet

ni .',ss _' T.J r,,Ir&S

mr. nass c f ru.i'j r, slu c

'v, rediius of ;.-itin of mc-del ebouiL longitudinal (X)
1xic, fet

radiu_ of ;rattlon of model about vertical (Z)
aY-s, f.et

'"r radius of ,yretion of rudder about hinge axis, feet

X., ri instance from center of gravity of rudder system
to rlng r..xi; Fpositive 'hen certe1 of .raSvity
is back of hinge, feet

S distance fr-mr. mor'el enter r of gravity to rudder
hin,- e 11r: r t

D -!fferer til ri -r.-tr

s di staiie traveled in rpsns (~t/b)

P rc-riod Df 'oscill nations, seconds

T time rcu.i-,ed fjr r.cttirns to decrease to one-half
am.plitule, seconds

t ti'e, =.?onds









NACA ARR No. LtJOa


A, 9, C, D, E coefficients of stability quartic for
rudder-fixed lateral stability

Al' 1, C1, 01 E1, Fr G,,Hi1 coefficients of stability septic
for rudder-free lateral
stability

A2, B2, 2,D2,E2, F2 coefficients of stability quintic
for rudder-free lateral
stability

A5, B3, C,D3, E coefficients of stability quartic for
Srudder-free lateral stability

A4, B,, C,, D), coefficients of stability cubic for
rudder-free lateral stability

S root of stability determinant (% = a' ib')

ib' imaginary portion of complex root of stability
quart c

a' real root or real portion of a complex root of
stability quartic

q dynamic pressure, pounds per square foot -pV2)

p mass density of air, slug per cubic foot

L r:odel relative-density factor (m/gSb)

' rudder relative-density factor (mr /Fbrcr )
cr root-mean-square chord of rudder, feet

a anale of attacV, radians unless otherwise defined

p angle of sideslip, radians unless otherwise defined

angle of roll, radianrs unless otherwise dEfined

\ angle of yaw, radians unless otherwise defined

6 rudder angular deflection, radians unless other-
wise defined

r flight-path angle, radians unless otherwise defined








FACA ARR No. LiJO5a


p rolling engul- r velocity, radiens per second

r yarinrg angular velocity, radlens per second

v lateral component of velocity, feet per second
(U ft\
L lift coefficient (M-

CD drag coefficient \- '




Cy lateral-fore coeffic t (Lateral force
qY

C rollin-rpo."ent coeffieenrt (Roll-n: moment
qSb

laviIn.2 rioment
', ya'"in -~rom nt coeffi.i nt Zn
n \ qSb

.. Hings 'moment
C irnre-'orrent roeffTicient ( g = .I


C rate of c.has-ne of lateral-force coefficient with
a angl' of sideslip (tCy/6p)

r7 rrte of chang- of rollinE-moment coefficient with
S san]1.3 of sideslip 16C7/6)

07 rate of change of rolling-moment coefficient with
rolling anrulor-velocity factor 0,7/_)

C r-te of change of rolling-rmorent coefficient with
Srb)
.-":zng- nvular-vel cit:. .t'f.ctor. /(6 r/6


Cn f'.te oi' ch'anre 3f' yev-in-Timormnt oefficient with
rnile of -~'dslir 'OCn/~ )








NACA ARP No. L4JO5a


, rate of change of a'virng-morent coefficient wiAh
angle of yaw ( 1- -Ci

Cnp rate of change of yawirg-Tioment coefficient with
p / ^
rolling canular-velocity factor 2 )n2


Cnr rats" of change of yawing-mor.ent coefficient with
/ rb\
rowing arnul!ar-velocity factor i6 /r

C, rate of hinange of :/ya",ng-morrent coefficient with
C- rudder Lanulr deflection (6Cn/65)

Ch[ rate of charge of rudder hinge-r.oment coefficient
with angle of sideslip ('0,h/6 )

Cht rate of change of rudder hinge-moment coefficient

with angle of ya. Ch


Chr rate of change of rudder hinge-moment coefficient
.'i th yavin- Lng.ular-velocity factor 6 Ch,/')


Ch6 rate of change of rludder hinge-rroment coefficient
'n ith rudder angular d r'lection (6Ch/665)

Ch rate of chansige of rudder hinge-moment coefficient

with rudder anpular-v. l.ociy factor CKh/ v /b


APPARATUS


The terts were rrun in the Langley frze-flight tunnel,
a complete description of which is given in reference 4.
The model used in the tests .was o modified 1/7-scale
model of a Fairchild XF2K-l airplane with its center of








8 NACA ARR No. L JO5a


gravity located 25.0 percent of the mean aerodynamic
chord. Figure 1 is a three-view drawing of the model.
The mess and dirensional characteristics of the model are
given in the following table:


'eight, pounds . .. .
Radius of gyration, k foot ...
Wing area, square feet .
'1:ing span, feet .
'"ing chord, foot . .
Distance from airplane center of gravity
to rudder hinge line, feet ..
Height of rudder, foot . .
Root-mean-square 3hord of rudder, foot .


S .
0.73

475
0.66

...07
0.667
0.185


The vertical tril of the model was a straight-taper
surface with a ruldc-r of the inset-hinge type. The area
of the rudder behind tne -inge line ,was 0O percent of
the vertical tail area. Three different nose balances
were attached t t.e rudder in order to vary the amount
of aerorH'yna.mc balance. Sketches of these surfaces are
given in figure 2. The rass characteristics of the
rudder were varied by moving weights within the rudder
or along a thin metal strip that prCtroded at the base
of the ruoder trailing edge. The rudders were mounted
on ball bearings to reduce friction to a minimum.

The yaw stand .!sed in the tests was fixed to the
tunnel floor -nd allowed the model complete freedom in
yaw but restrained it from rolling or sidewise motions.
A ohotog:a-oh of the model installed on the yaw stand is
shovn as figure 3.


TESTS


To-ts .,-re imade to determine the period and damping
of the rudie-n-fre: latsral oscillations of die model
during: fre.: ,i-lnpg flight and vhen mounted on tha yaw
stand. o ::-Ls ':-ere performed to determine the effect
upon the ru'-der-fri--e stability of eliminating only rolling
motions.








ITACA ABR No. li.7OS-a


Scooe of Tests

The range of rudder aerodynamic and nass character-
istics covered in the tests is given in table I. The
test range investiabt3d was obtained by altering the mass
characterist'cr of the rudder by ard.ition of weights at
various locations. In this manner the mass, center of
gravity, and r-dius of gyration of the rudder were varied
si1.,ultan eo_ Ls7I This proced.1.re was followed for the rudder
equipped with each of three different amounts of aerodynamic
balance. All. tests v.ere run ?t a dyns.nic pressure of
l.00 pour ns per square icot, "hih corresponded to an air-
speed of aooroximat ly I10 feet ,er second. The lift coef-
ficient was anprox-iri ste l.f O.c.


Flight Test

Flight tests vwre made lor the nodel test conditions 1
to 5 anr; 10 to 15 n.f table T. These t ts were made by
flying the test odel freely w;ithn.n the tunnel as explained
in reference During a given fl] ht, a m-chanisn, within
the modp'l wa" so activated as to fr-.e che rudder after an
abrupt rudder deflection of saout 15-. The rudder-free
lateral oscillations resu.lting fr-,r; the rudder disturbance
werie recorded ty a n:cotioi.-.piture. cem7er:.. The,- period and
damipinj charaict .lti:s of t"he flight oscillations were
obtain.-d from th? rioti on-rci ture record and w,:re corre-
lated with correzpor:ning re;-ords from the :aw-stand tests
and with calculated charect-.ristics. Several runs were
made at each test condition and showed a variation of
period of aboui.t ? p9,rcent snd a v,.-isti on of damping of
less than 10 percent. Typic.i flight oscillations are
shov.n in fi ure .LI f.r a state ccnti tion arnd in
figure 1: b) Por in unst-ble cnr-.. ti on,


Ya'-S tand Te-ts

The yaw-stand tests v.w-r- marl5 for all test con-
ditions listed in table I. These tests ver nimade under
conditions reprodu:?ing those considered in the analytical
treatment of reference 5, in vhich the rolling and the
lateral notion of the a' plane center of grsakty are
neglected. For the yaw-stand tests, the model was attached
to the stand and the rudder vas deflected 15'. At the
given test airspeed, the rudder was abruptly released
and the resulting oscillations were photographed by means








FACA ARR No. 17JO5a


of a motion-picture camera installed above the model.
Record s of the period and damping of the sawing oscilla-
tions !were then obtained in the saine manner as for flight
tests. Appro:ximatoly the same scatter of period and
damping values was obtained in the yaw-stand tests as in
the flight tests. Plots of representative yawing oscilla-
tions obtained from the yaw-stand tests are shown in fig-
ure h(a) for a stable condition and in figure L(b) for
a neutrally stable condition.


Yethod of Analyzing Test Data

Stahili L theory Indicates that the rudder-free
lateral osc' lations are composed of two sucerimposed
oscillatory m'dceE, one of which has a shorter period than
thr oth=1 The t..::t os.illations, however, after a short
interval of tire r.'presented only one of these modes -
the one that subsided later because of the Doriod or damping.
Tn geiner-l, the s;-ti llty calculations showed that the
short-oeriod mnrr? ardo,-d to one-hialf amolitude in roughly
1/50 the pe-:;d of the other mo3e. Th3 test oscillations
therefore r..pres3nted th- long-period mnode for most of
the test conrit ions.


iraszureimnt of Stability Derivatives

The stalilit" -eri vatives necessary for the calcula-
tions are oiven onr tsble II and were ootained by the
following ?'-roedure : The partial derivatives of yawing-
moi;'ent coefficient vith respect to angle of yaw and rudder
deflect on, C3n, and were determined from force
tpsts of the model on the six-comnonent balance of the
Langley fre:--fli ht tunnel d-scribed in refrcnce 5. 'The
results of these tests are ore scented in figures 5 to 8.
The hiline-mo.rcnt derivatives d.ue to angle of yaw and
rudoer r, fle 1.-tion, ;h,,r nd 11, r'ere determined from
hir, e--ro!ent tects of the model rudder, the data from
which arc- pretent.dL in i'gurps ? to 11. The rudder
hinge-m:im-nt d ri.vative due to yawing angular velocity
Chr -:a- then calculated by the relationship


2 = 1
C1hr -b- Chj (1)








IACA APRE No. LiJO5a


The y:rnwinr-mnom-nt derivative due to y'win. angular
velocity Cn, 'l ig. 12) ."s determined by the iree-
oscillation I3tliaod idc-scribed irn reference 6, a id the
rudder hinge-m-rnment derivative due to rudder angular
velocity C was similarly determined. The measured
D5
values of the narameter ChD (-0.02 6 for rudder 1
and -0.01.2.L for rulders 2 eand ) did not agre? vith the
value of -0.1.2 as calculated :by tht n;etLiod presented in
reference 7 eyceot that the frequency -or the oscillation
was neglected. The rcau.se of tnis discrepancy was not
determined but is b'l.iev,.-d to have been the high
oscillstion frequency at which the. tests were
run (about 6 cycl-3s per scconrl at an airppced of .J.O feet
per second). This f'Tequ.-rncy -orre: onded arpro\rl:.tje]y
to the c]oculct d frequency of the rudd.er in the. ru."der-
fr,.ee tests of con1-litions 1 to ': in tsble IT.

"easuremrints indicated ttPft the fricti i n',1 drlqpin.l-
of the rudder wa~s ::-bout one-tenth of the air dam oi l,.
T"i.s value was cons idered ne.l i;ibT'. a.ind no attempt
:, :rade to irtr'oduce fri. tl in der- v*t. 'r l:itc the
-~_ l.iaticns. Four runs vaer? re1.3 with er:;; rtrdder and
tnr scatter o1 vali -s .of 0' was le s. th:'.i 10 percent.

The rarti-l *eriv't 've 'f the rollrn'--m:rent *:oef-
f cient with re.sct to the rolling veloc'ity
parsiametr 7 was d t--rined- fr.,r, th? charts of
P
reference S. The deri .'ciLt iv-s ,7 and C were
-r no
c.-rermlnred from the forimnlas riven in rerferen3e ,


*A;LCJ LA.TITO CS

Scope


Calculations were mide of the damiping and period
of the ruddl.r-free lateral O.)scilli ti on1 ,of the mndel for
the range of eir.milne arl rudaer parameters given in
table I. These zal!uleti ons were made by equations that
provided f',ur de'..rees rf freedom as well as the fewer
degrees of freeo-i. whi,-h re.-ulted from the n-elct of
rolling or the negle2t of rollins and lateral motions.
Other c-l..ul-.tti3n- wenre made to determine the effect of
v:-ry.:n_ th: effe ati ve-r!hedr:1 parae;rt.:r upon the
rudder r-free sta bil; ty h r act' r stics.







NACA ARR No. L4J05a


Method

The customary methods of stability calculation
(outlined in reference 5) were employed in the present
investigation. The equations of motion were set up,
rendered nondimrensional, and so treated as to obtain the
stability equations defining the period and damping of
the lateral-stability modes.

Equations of motion.- The nondimensional equations
of motion used in the calculations are given in the
following paragraphs.

The equations used for the rudder-fixed condition
are


(2 D Cy 1F + -CL) + (2 + C. tan 0)1 = 0

-C0 0+ 2j D2 + (-L D) =0 > (2)



(-C + (- C 0 + 2 ) D2 nc D O j 0


Equations (2) yield the familiar lateral-stability
equations of the form


Ak4 + B + CO2 + DX + E = 0 (3)

The general equations of motion for the rudder-
free condition four degrees of freedom) are








NACA ARR toT. LlTJJOr5



SL
D-C ) ~+ C + V L t '
Do + .. i, l = n


(-c1nS 1 + Q Cnlp + 2D- -Cr Q.-r = 0 -
!r \ 1)


rr

+ + -






Et uations o) 7L. -I 1 -' l t r -: ts' li t
ecuatiLcns ': th.. cr.

A+ + + t- ( )1

For tih rudd-r-free ii tion, .l nr ling ic
neg-lected i thiee (ei-ees of fr- .l' .r), tr: r irs.t-i-, r Cs c e


(2D CyF + (2pir)' = 0


+ [2 2 I -

2n r 'o )



-/ -- .r b -7.h
[ V r h '

L+ ,- -" r h 2
+~ ~ F~C ;r ^D r b0+^ ---^'/'4
+_ L.^- -h '-







14 NACA ARR No. LLJO5a

Equations (6) yield stability equations of the form

A2,5 + Bp' + Ck3 + D2\2 + E2% + F2 = 0 (7)

Wh-en the rolling rrotion and the lateral motion of
the center of gravity are neglected (two degrees of freedom),
the equations are
r 2

L
.- --,. +2 ( 0 1'8)


2Lb D- + 24r -C D C- C
i r / r'i
b-


+ LPr. -h5 2 Db D =


Equations "E) yield stability equations of the form

/ + B. + C + DL + E = 0 (9)


Tf, In. asd,'itJon to neglect of rolling and lateral
rotLj n cf the center of gravity, the rudder moment of
inert-a is al.-o neglected, the equations are

D- nr D C (Cn6)6 = 0

/ >(10)
K 7 D2 rD C c + Ch D Ch = 0
b2 (2 L.









NACA ARR No. Li 05a 15


Equations (10) yield s*abil'ty -eqution. of the fcrT


A + E2.2 + C + D = 0


Deterrmiinaton of feriold end 'rmp3'nt o'f 'i_',:_ 1
oscilltiion". The ro's of equao'n r -i ], 7 (T, 7,
TT, and (111 ar-) cf th- form, a or 1 .. + b'
Tile roots are us id in Ic..e follo;. n eq..'.. ti oni t,: d 'etLr-
mine the period -nd the t i.? to d.,' to one-hr-ol
ample i tude:


? = '12)


and

-1 o ; ., 5 -,

a _
T T A T )



R .L T 3 A ;' C ;," T ,,- *r0 .


The results of the test. n3 n 1'.: 1 l-ti ln. r :- r.:- rnted
in table II, vhi h list the crt r : -. -:-i. fe r- c i :. .- : l t
tne time to rha p to one-ha- f l" p11 i tti e i,:r 3r c-l, o, iL ti .in
in-restijated. Tr:e Cr'ec ro- cal of t-he ti"e: to d ,: n D J.n -
half amplitude was .c-h sen t- v lu-.:tc t'-.- d-, p] i ;
this value is di i-c t :rat.L than a!, iiv':rs- r':re3st; 'e
the degre..of stoa lit;. .e 1: ivi vt ':91u'j *- f t i.e r--ciprocal
of the ti.e t to drro to one-h:ialf a-'li t' c r.ef : fr to t..
time to increase to iouole a-.':l.i t:.'G


Cor.rel ti ton of rest s cnd .' -neral 2 :ua tirons

Calcillat; n s. 'Tr7e vtsQ -.. J t.i. ';ti On.: r..1 ad v 1 th
the general eq.a~t ions o1 r.otLon i nd:-i e : t LTt t t:-'ott.ons
of an airplane vi th r drid.-r f'r.: c;a, st of two aperic r.di,3
m"?des (convergences or di'.er ..,ncez) '-n-i two o. cill.tor/
nmories, one of which ;is_ ofI ci trl d 2 to 10 timLS t.-iL othicr.
As shcwn by' t'h re ult '.-reseated in table II,the23
calculations indicated thct, as Ion,: as tl, rudder radius








FACA ARR No. J4J05&


of gyration nnd mass unbalance ware small (conditions 1
to 9), the short-period mode was very heavily damped and,
consequently, the characteristics of the more lightly
damped long--eri d mo-de determined the nature of the
rudder-free oscillations. Table II Indicates also that
the characteristics of the long-period mode were only
slightly affected by the rudder parameters as long as the
rudder mass parameters were low (conditions 1 to 9).

rhlien the radius of gyration and the mass unbalance
of the rudder were larre (conditions 10 to 15), the
calculated period of the short-period mode increased
considerably and the d.'moing decreased. At high negative
floating ratios ;conditions 12 and 15), the calculations
indicated that the destabi li zing effect of high rudder
radius of :,-ration sand rrps unbalance was sufficient to
cause Icteral- in;: -tc&c I ty.

SlL t-Ls.t. T)ic results of the flight tests are
presPlited in tro]e TI. Tn.se data indicate that,for low
values of the rudde' r :.llss naramoters (conditions 1
to 9). the less '"" pe and hence thbe apparent mode had a
neris)' of ftout 1.5 seconds, w.hirh corresponded to that
calulaterd cfr the l-ni-oeriod mcde. For high values of
the rurddr m-Ess para-w:ters (conditions 10 to 15), either
the long- or th short -eriod mode was the less damped
of the two rod3es end rence determined the characteristics
of the apparent r.:otion, dependint- uoon the magnitude of
the r,.lddcer &erodrinamn'c parar' tt-r- Cp and Ch. For the
condition of h1ih rudder aerodyn,,mric parameters (condi-
tions 10 arid 11 the long-period mode was the loss damped.
Condition 12, however, showedV the short-period mods to
be the less da-.pec at som.;,.'hst lower values of the rudder
rnass parameters than those of condition 11, and condition
15 -ave an unstable short-period oscillation for even lower
values of rudder mass parameters.

Comomaris .n of theoretical and calculated results.-
Tho tests conf. rred the results predicted by the theory
inasmuch ss an unstable lateral oscillation was obtained
for test condr.iti n 1. The quantitative correlation of
measured valupe- of period and daTrping with corresponding
values calculated by the use of the general euattions is
sho-n in figure 15. The.. data show that the agreement
between measured anr' calculated values of period was
excellent for ill conditions tested. This agreement was
also shown In the correlation between measured and calcu-
lated values of dumping eycert for conditions 12 and 15.









iNJACA A"? Yo. L .JO 5 10


For conditions 1.2 andi 15, the aclcul..tion- indicated &
larger ce.;ree of i': nstA ility thiur. t'ut e:.i,-ou; nteired .' th;
te"ts, This s-ppre't rdi s -rcpJ;..:;, as exp : flne L'
furchor c'.lculat. :ns *"h.i';i sho;.rdL t -1nt ti: rud lr-f-c
stao'" litvy was 2.-1 ti'- al ., d-. pe dnrt aon r "'e rul-: :r' :s :.
characteriS tics 3 for. tihse test c-onJ ti on The r sc. -.
of the 'fu11her rsl l. tuiat ins ar-' P v n in -"E'. e il .,
Ehow thst +he d-..;re o n:st aci i t v e r.. g'i t :r-: i n r ,t
conli tion 1' woa 7n 2 cted 'c..y t'U.,-r to ':.e-.c r t r.-: -
what srall.er values of -nSF luLr]1 -e i t th-.1" Ls .'orz
the test. An .her r, sI- 1- :-1: :ti l t-A: dt.' .r -
ancy h1etwoen to: ts r.c t.i=c.r ....r ;:,v.-'1.tiro s 1.2 eand 1_
is tlit thn a'tus.] .:iCe ni F.,r Ltter lo"' -fr c'ency
condition' J nwi, "'.-t Tha; he-..r. ,i r n r! rh ,*s n ,.:- in
the calci i t ons En- c..:-: rn d T i hi h- r ? 1: ...r.-
'ents 'lore nf'or,,- tic is r.- -. r:.-I to 1.:- r r.'ire t':,1
effect of frequency ol te: o. 1i, t nr. on thi s jpra tcr.

Physical inter :r,'etct -n.- 'r, r:epr tn eF:xpl'L in :.ore
clearly the physical t s t T .' ttc.:, lor.'- anj short--..-riod
modes of ti-e rur'der-f iee nscil t ; ns, .Jd 1 tion.l ".o-i-
lations iv.ere mec'e of tr.e ia.der-fre : : i .: -r-fi.
stability character.'istic- ove'r i. ras--,e of Lih i '-1.l
In this wv'ry, itW v s r.-s l.e o cs :.-ve ar.lyt call t--
ch nige of literal st- t-bill ', :L ....., i s_ I hen th-.3 r.'.. -er
was 'ree.

A comniaris n of th, T.r s.l3 t? f t '-: trudTi'- -fi cx
and ruJder-frae c lo1.] S t. -ns i '"'L Le t'; t tL- z'.o'-t-
period mode of thte rul rj' -fre.- t.sc'. liatli on hm' r'o '"v 'nte r-
part in r.irider-f' ixr fl :ht s .,e T, :.- < ition 1,.
Ths mode, t -e-efore 's 3 n nantir.!y n- -. ; Lr,
create. d th3 new' d'J -g" e f i" ed I a'. 'c"" r
the rtud-dt.r wa'S fr3?d n i rc l', r"n r- Js1 .' Ss t' 1-
lati on of th. mdeuider -out its 'vn i- i tie. T:- '.l -
lat i.ns 'also shov-;e t'h.t t ; i~ya t:eri st: t -" th.
sho.3rt-pe iod mO were -m. v ..lt ua.i- in.i' -: '. t o- the
effective- dih -'.irs .:i 3t r -c v- ri .t n o" ti

calb ulat3,d val'.i s i a.,x-r o'- .i-. 1.. ?Z. ;. ..:.' -
period o .ill at n f.:'jr n. ,i- lt '. th .'. 'l av .-
diher.r-i. l no-.rs: .t r i: o ;'e ':1

P" 1 / T


.' c ._. _7 L c
-.03o .c.7. j -
-.12 .'.7 l-. t .i
-.16 .0o7 I 5








NACA ARR No. L4JO5a


The additional calculations indicated that the
characteristics of the long-period mode of rudder-free
oscillations varied with the effective-dihedral
pora:neter 0. in a manner similar to the variation of
the rudder-fixed oscillations with this parameter. The
results of these calculations are presented in figures
15 and 16 and indicate that the characteristics of the
long-perio'd rode for the rudder-free condition were of
the same order as th:.se of the rudder-fixed oscillation
but were of lower damninn and higher period. Inasmuch
as frtein- rudders of negative floating tendencies is
known to decrease the directional-stability parameter Cn
und a decrease in this factor is known to decrease the
dsaDnpDig and to increase the period of the lateral
oscill-tion (references 10 and 11), the long-period mode
of the rudder-free oscillations appears to be a modifica-
tion of the fa-riliar Dutch roll oscillation normally
encountered in controlk-fixed flight. The characteristics
of the long-Fprloc rudder-free mode may then be concluded
to be largely drpendrnt. upon tnei same parameters as the
rudder-fixed osc'llttory mode. For airplanes having rudders
of n.Egative floating tendency, then, instability of the
long-perio. ru.dder-free mnde should occur at smaller
values of effective dihedral than for the corresponding
rudder-flxId condition.


Correlation of Tests and Simplified Equations

'reclect of rudder psrarreters.- Inasmuch as most
present-da,' eirpolnez have low values of rudder mass
parameters, the long-period rrode is the predominant
factor affecting the rudler-frec stability character-
ist!cs for Eiroplnes having rudders of negative floating
tendency. Consideration of tne rudder mass parameters
would therefore not seeir necessary for these airplanes.
An anproximste scljtion for the rudder-free stability has
been obtained .by simply considering the controls-fixed
dynamic lsteral-stability equations (2), in which the
value of I' for the rudder-fi-ee condition is used.

Calcul.stions were made for the test conditions by
this epporcixiate method, and tht period aid damping
results are presented in table 11 and, for condition 7,
as points on figured 15 and 16. The value of Cn for








NACA APR No. L4JO5a


the rudder-frse condition was calculated by the follov.inz
relation fro-mr reference 1.

Ch
C n ni
n C -- C -
'J(rudder free) rudderr fixed, h5 "b


The values of period and dar-ping obtained with this
method are in good asreeiment ith the values calculated
by the general equaticns for test conditionss 1 to 9.
For conditions 10 and 11 the sorrelstimn is rather poor,
as was expected, because of the high values of rudder
mas. psarm.eters at these two contittions. Because tle
appr-oxintr, e r.thod cannot predict a short-period oszil-
laLio., this method failed completely' to predict the
imports'.-.t features of the rudder-free mot,-.ns for con-
ditions 12 anid 1, for which the snort-zeriod oscillation
v-, :b-.t ncutraliv darned. These calculations indicate
T' -.- .-thruh the predictions ,ielled by the approximate
.I.-L:3.d are 'rd st low values of the rud.j'er mass rarEmete.rs,
i 'more com Srl'e analysis is necessary at high values of
tle3 ruddcrr m sss parsireters.

FNe'.ret of rolslinz otion.- The s]i.r.xlifis&tion obtained
by ne p- c .. n rolling r': oion ',a; ,s !-nv:esti.: cL.. ed for the
-zlrsen :-. report by cor:pai ng; the- results ,, btaiLned by the
:.,-- 1. equo ti-nr wv.th chose obtained b. eqiauations
!" -i' LL.' i'n r'llin. equal ion 6). The -,I. I .- of period
S .... .i for the test con ti on. as I.''iilated by
erL. .s ticA (6) are presented in ttble II. In figure 17 the
crrsacteristi .s of the short-pericd rro.-e obtained by this
method are compared ith tho-e calculated by the generall
equations. The correlation o" the characteristics of both
t-'e lon.:- and s"hort-period m'iod:es cr icul-ated by the modified
equations with those obt-i ned ro-m flight tests or from
cJic-ula~tons by the general a uati Ins is fair except for
r...'itioTr's 10 :nd 11. Thi-s fact !nj.cht indi aL'e that trh
s -lifl f-i ,d rh.orr.y ,i' es ",oor ccrr itin for the case of
nnri-.:'"i.trl stability of the short-peri.o mode when the
Dpr.cd o.o the iong- and chort-perod modes i73 nearly
eq'... .

Equoi.tion (6- show ti-Et nEglc-ct of rolling eliminates
all of -e d'-]ivativos ini. lvrng rolling mome,?t as well
as tbos-- invo:>lin rollIng motions. The effect of C.








NACA APR :'o. IrJO5a


on the lateral stability cannot, therefore, be predicted
by this si.mplified method. The effect of dihedral on
the long-oeriod mode is to reduce both the period and
the da!ping, as is shown in figures 15 and 16. For
dihedral angles less than 5 C < 0.06 however,
neglect of rolling in the equations gives conservative
results,because these equations indicate less damping
than the general equations for low values of rudder mass
parameters (conditions 1 to 9). This result is obtained
mainly because with low dihedral the rolling component
of the, motion is small,

The effect on the stability of neglect of rolling
with rudder fixed ha: also been investigated. The
results of these calculations are given in table II
under condition 1L. and show reasonably good agreement with
th3 results obtained by the general theory for the rudder-
ftLed condition. This agreement is further proof that, for
low values of d.hedril, rolling ray be neglected in
making thest calculations. On the other hand, for air-
plane? having hip-h dihedral and large values of relative
densi ty nd radli of [.ration, the long-period oscilla-
tion might become unstable, as shown in references 10
and 11. The neglect of rollinE for these conditions
would invalidate the results for the condition with the
rudder either free or fixed.

;eglect of rolling and lateral motion.- In the
theoretical analysis of rudder-free stability published
In reference 5, the equations were further simplified
by necle-ting lateral notion of the airplane center of
gravity as well as the rolling motions. These simplified
equations also predicted a long-period and a short-period
oscillation.

Tests of the model in the rudder-free condition
were reads on th:- yaw stand in order to reproduce the
theoretical assumptions made in reference 5 (freedom in
saw about the i. rplane Z-uais and freedom of the rudder
about its hinge lin3). The results of those tests are
presented in table IT an1 indicate tLat,for low values
of the rudder mass p.rsa~eters (conditions 1 to 'Q), the
lon7-period mode was the less damped &nd hcnco determined
the characteristics of the apparent motion. For higher
values of the rudder mass parameters (conditions 10 to 15),
either the long- or short-period mode was the less damped,
depending upon the magnitude of the rudder aerodynamic









NACA ARR No. IJ1JO0a '1


parameters. For conditions 10 and 11, the long;-p e r in
mode was the less dariped :-:Jhereas for condliri ')i 12 .nd 1,
neutral damping of the short-period rode *v-is o':.tCin-i at
lower values of the rudder mass oaraneters.

Tt ma" be of interest to note th.-t i: unobli s'-:
cata from y;aw-st.ar.. test, mede. a- ni-c' v'-l. s of ':' ssZ
unbalance of the :-':d.dde tChn thhan hc' r;--: -nt.-d h-':.n, rn
unstable short-c-iod os.i.latic-: ,,a, ...t.t'-.r.?i. Thi'
unstab'-; oscillaori n could be st te,' L t." v'r'; s'.-r ll
disturt;nce and vo ulo r n.creas. in rl..i tdfie until it
became a constart-a rpli tuide oss- llaticn of fOsoat +1'0
yaw.

The results of col. ul--;tion. .rade by ,ti 11r-,n, the
equations of reft'-r'encc 5 are listed. n tsblie ITT nd hEve
been compared in fiTure 1j to meas..red values obtained
from the ypw-st.rnd tests. The rieta p-iseiited in liu.re 18
show that the equations of ref3rr.nce 5 closely predicted
the rudder-free dL.ta octa*ne.d in th'e ,sw-stand '-ests for
stable condi ti onrr L: '-. the rerersl theor,,, how/ev-: r, the
simplified c.,unt2. ons r -reJF cted,] insa -i lit.:; cf .th short-
period oscillati- c u:c c I _w:-r v'alu,-s of r.Li!.kl E mr'I.s a r ml terms
than did the yaw-stand lests.

A comparison of thi i,-v,.;- t.nd and fr.e-flight t:.t
results shows that the elirrinstiton of the rclling and
lateral motions results in ro-e,,'hat '.oner- perilo' t'nd
less damning than is obtar.ed in flight, :.s !o-loin as the
long-per:iod ercillatc.r. Is '"he controllin. I :er in' th~
at-are-nt moti -n I; f lit.'.. '..;n the cher-?ter' .t :.s of
the-. she-c-pc ond c.i .. l 1'icln ar- asop-rent in fi .ht,
tes~tS o.' the y-Av:' s .: c gtve': nearl. y I -t' t-'-t r:.:'
with rT cse frojn ,g t : s. a. '-!:-e cst iri- ;- t
for smerll efIee+.i. 'eirL' an -l.-es i-e let of the
roiling and. lateral rictiuon. ie'-s c.ot ,er 'F 1:*_; "arlue;r
for tl.e long-er~ri.od, rui:.der--fre cs 11sill o'n ar-nd r. rate
values for thn ,I rt- -.... tn 1i.ticn Li... i .t
co:-,irrr the z-n, ..ni n drs.'. f .he an -': ".c.-l
in-.-zst-a nation c:,'ra -r. n ni :- the If_' t f L : er..-:l, that
th-: characteristics of tie ;':,r't-eri od mde ',are
relat.'velv iniener..de t of ui: r.1, :hich s a :-asic
rolling derivative.

The data of qbSie IT indicate that the si.nlified
theory of reference 5, '.iich ne !. zt: ryollirn and lateral
motion, predicted the charLcteristis of 'he short-operiod
mode iust as well as dd the enp:3l ti.heor, and that use
of the simplified theory r.a! therefore jstified in this
respect.








NACA ABR No. LLJO5a


Nerglect of rolling, lateral motion, and rudder
moment of inertia.- A further assumption suggested in
reference 5 is that the moment of inertia of the rudder,
in add5t.ion to rolling and lateral motion, night be
disregorded in the calculation of rudder-free stability.
The results rf calculations made with the rudder moment
of inertia neglected are presented in tabl3 II and
indicate that, for airplanes with small amounts of
effective d'hedril, application of the theory gives a
rcasonchly -:ccure.te orediction of ths rudder-free stability
chsract ristics as long as the lorng-pri jod oscillation
.s t.-3 c !*tr ll' r factor in the aopp;,'a.nt motion. For
corit: ';3 '" which the sho:rt-petc oscillation is the
le s Jd''". -1 :td hj.,ev':r, the S.- .j'c'm : n r!iS m t be con-
s ier ,' .. ', in -i f- r r'- ?. .-": of ,::. ve floating
te n:' r 3, ,.'.s e the c a .. LL' l ion; 1 r..j2 i e tT.at, when
the ru.'.; m ricnent of ir: rti a is 1 .i.:l1-z 'd, the short-
peri.jr mrode is replaced. by a tea'ially dLrrped convergence.


COIC LUSIOi.IS


The fnl]ownIng conclusions were dr'vri "roT an
inv'sti.":tior. in three ticr'le: fr:-r;-fli'.t tunnel of the
rudde; --'.re.l. -stab.L. ty ,.sra'scter1 ti .s of an airplane
nmod'1 l ~ou;i p dr-1 v.'-th n ..'.'rerr'.e cf n -llat 'l floating
tend~n:!-ies .,d !ibin.n ne.lirible3 ricoion:

1 F)r Tm st rre~e t- % : -, ,ir r-,].n,- :onsiieration of
the r''".' r :' .-'s pc.ra t .-t rs ~ :i -, -' ari:- in an analysis
of tTr h" '--fr- stul r'-'" :". tC L-,.< : Th -.se
ch9:' r. .s OP -.: '. .i' .y >. nsidering
th-t ... *.ter I sxto' i t: ,', b07 u.ing the value of
the i :r-.'r t c. Zl- il Ly :J cio!,m,: r Cn for the radder-
free ccr' IL t io.n ii. the converttlonal control -fixed lateral-
stability ec u-at ors.

2. An.- l..:, of th- ruri .er-fr' stiabi lty of airplanes
having re -i .r ,'-- ,.. v'alC *f t, h? r:' .dder mass parare-
ters wl:t reco- t t he rur '"e -)rrd', .amic parameters
(such 3s -vould be enci,_.unterc in T.ry large airplanes)
should be made -rith the conri lete equations of motion
for the rudoecr-fr.ee cor,nitirn.

J. The rA.der-free stability+ characteristics of the
model tested were saLisfactorily calculated when all four









fACA APR ITo. LIJOCS


degrees of lateral fre.dornm .ere consi-lercd in the cal.u-
1Eti on0.

L. The roludl r-f rre .sh r..ct r st icr of t}-- :m-' '.el
tteted were predicted fftirl: well whn roll-in mori :ns-
or rolling ard later s!- notinrs ,ere ne;e. :1 ct.d in t_--
calculations Tnsta.br ty 01 tn- ru] ..r--f r: : t D t: ,, 1
ty e oscllt 11 .at on, how ve oC ld n t be- : r A! a t.d .,
this metrhcd.

5. Larg.-- sm irnt n-f r.i':.er c:.-s b-.-lan'. 0 use d
an unstable short-p- riod ra'-..er-fl, e eilll: jt on 'or the
model tested.

6. The ,:qsracter'istic. of thl- -hort-p3riod occil-
lation are found to b-a ''n.j,Dend nt of tihe airlJ.ane
effective dihedral and Lver.3 ratizsftoril]y or'e-dictc-d for
the model ter~ted by either the general stability eluastLins
in which all f'cur degrees of ] E,t 3l fr -ef.doi-n re considered
or by the mo'":' field stucbi.lit.; equ:; tons i.n .i!.ch ,-.ther
the effects of rolling rmtions s91'le1 or of r'llin tions
and lateral motionris of the ai'rl.nei center of cr' vi. t' are
neglected.

7 T1.hen the rudder ,- nor.-.ent .oF in nrt-i: was n-eglcted
in the calculations, t'ie cho3r~.teristic- cf the short-
period ruddar-fr--e osci 1 Lti ons f or- ruderrs havinn
negative floating t.er.Ji .r i coall .rot n- pr- :'ict :d.


Langley Memorial Aeronasut ic -l L'bor-.topr"
Fat. onal Advi sory Cornrit t -e for Ae-'-onr.a tit ?
Lsngle',y 'eid, V.








NACA ARR No. LJJO5a


PREFEBENTC ES


1. Bryant, L. '., ,nd Gandy, P. W. G.: An Investigation
of the Lateral Stability of Aeroplanes with Rudder
Free. L504, S. P C. 1007, British N.P.L., Dec. 18,


2. Jones, Rooert T., and Cohen, Doris: An Analysis of
the Stabillty of sn Airplane with Free Controls.
IACA TFep. In. 700, 1941.

5. Greenberg, Harry, and Sternfield, Leonard: A Theoretical
TInvestigation of the Lateral Osa4llations of an
Air-plane firLh Free Rudder vith Special Reference
to the Effect of Friotion. lIACA ARR, March 1945.

!. Shortal, Joscp l .., and Osterhout, Clayton J.: Pre-
liminary Stability and Contrcl Tests in the NACA
Free-r'li hlt 1.ind ..Tunnl. and Correlatln with
Full-Scale light Tests. I.ACA T!T ro. o10, 1941.

5. Shoital, .Toseoh A., tand Draper, John V.: Free-Flight-
Tt'nn3l Investigation of th3 Effect of the Fuselage
Length and the Aspect Ratio and Size of the Vertical
Til o1 Lateral Srab lity and Control. NACA APR
U7o. 5D17, IC'5.

,. Campbell John P., and ?.athe s, Ward 0.: Ex'erimental
Determination of the Yarin,.3 Yorrnt Due to Yawing
Contributed by the Wing, Fuselsae, and Vertical
T.il of a 'id ding Airplane "odel. NACA ARR No. 5F28,
1943.
7. Theodorsen, T:lodor-: *-eneral Theory of Aerodynamic
Lnstnbility and the ie.chan1sr. of Flutter. 1 ACA Rep.
dor. .17, 155.

8. Pearson, Henry A., and Tones, Rc.bert T.: Theoretical
Stabi.lity and Cjntrol Characteristics of Wings with
Various Armounrts of Taper and Tw' st. :ACA Rep.


3. Friaber, :illar-, J.; Effect of Some Fresent-Day Airplane
DesPigr Trendi on Feq'tirements for Lateral Stability.
ITAC A TIT No. clh, 19 1.








NACA ARR No. L4JO5a 25


10. Campbell, John P., and Seacord, Charles L., Jr.:
Effect of Wing Loading and Altitude on Lateral
Stability and Control Characteristics of an
Airplane as Determined by Tests of a Model in
the Free-Flight Tunnel. NACA ARR No. 3F25,
1943.

11. Campbell, John P., and Seacord, Charles L., Jr.: The
Effect of Nass Distribution on the Lateral
Stability and Control Characteristics of an
Airplane as Determined by Tests of a Model in the
Free-Flight Tunnel. NACA AFR No. 3H31, 1945.















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NACA ARR No. L4JO5a


TABLE II.- COMPARISON OF PERIOD AND DAMPINO FPOM FLIOBT
AND YAW-STAND TESTS AND CAiCULATTONS

Tests Caloulations

Rolling,
Rolling sldealip, Rudder
Teat General Rolling and and
conditions Flight Yaw stand theory neglected sidealip moment of parameters
neglected Inertle neglectedb
neglected

Iong-period asollation

S Period, P 1.72 1.80 1.69 1.6 1.66 1.6 1.60
Daping, 1/T 1.17 .90 1.12 .a .92 .9 _1.39
Period. P 1.61 1.78 1.60 1.60 1.6 1.6E 1.60
S Damping, 1T 1.09 .90 1.10 1.27 .8 1.5q
Period, P 1.48 1.66 1.40 1.70 1.60 1.61 1.60
SDmping, 1/T 1.06 1.00 1.10 1.32 .98 1.00 1.5,
Period, P --- 1.69 1.60 1.70 1.68 1.68 1.60
a -ping, f/T ---- .90 1.)8 1.26 .95 .9) 1.59
Period. P :--- 1.65 1.56 1.60 1.6 1.66 1.60
5 Damping, 1/T ---- .90 1.59 1.30 .9 .96 l.9
6 Period P ---- 1.62 1.6 1.60 1.62 1.62 1.60
Damping, 1/T ---- 1.00 1.1 1.26 .99 .99 1.59
Period, P ---- 1.86 1.7" 1.80 1.83 1.82 1.71
7 eping, 1/T ---- .0n 1.5 1.20 .88 .88 1.59
Period, P ---- 1.79 1.65 1.7 178 1.77 1.74
8 mping, 1/T ---- .90 1.55 1.2 .92 .99 1.9
Period, P --- 1.72 1.55 1.60 1.7 1.72 1.74
mping, 1 ---- 1.00 1.30 1.30 .97 .97 1.9
Period, P I.50 1.60 1.20 1 1.9 1.50 1.60
10 amplng. 1/T .90 1.05 .92 1.5 1.05 1.U1 1.9
Perloa, P 1.15 1.50 1.05 1.20 1.1 1.60
11 Daping, 1/T .8 1.20 .90 1.5 1 1.50 1.59
Period, P ---- ---- 0.96 0.99 1.06 1.16 1.60
2 Damping, 1/? ---- ---- 5.50 5.80 3.85 1.74 1.35
Period, P ---- ---- 0.7 0.98 1.1= 1.2- 1.74
1 Dmping, 1/ ---- ---- 5.22 5.19 5. 1.60 1.9
Period, P ---- 1.56 l.0 1.66 1.50 --- ----
I Dping, 1/T --. 1.00 1.87 1.L4 1.05 --- ----
Short-perlod oselllatiln

Period, P --- ---- 0.16 ---- 0.15--
Damping, 1/T -- ---- 5.66 ---- 4.92 L00
Perl.od, P .-- ---- 0.09 0.09 0.08
2 Damping, 1/T ---- -- 15.15 14.55 1.1 6 5L8
Perlol, P --- ---- 0.20 0.1 0.12 ---
5 Deainng, 1/T ---- ---- 4.45 5.L0 .l6 570
Period, P ----- ---- 0.10 0.10 0.10 --
4 Demping, 1/T ---- 32.50 50.80 52.50 152
Period, P --- --- 0.10 0.10 0.10 --
5 Damping, 1/T -- ---- 52.50 .80 52.20 1l7
Period, P ----- ---- 0.10 0.10 0.10 ---
6 Dmilng, ---- ---- 52.50 50.80 52.20 LI1
Period, P -- ---- 0.12 0.12 0.le --
7 Damping, 1/ --- ---- 2.50 50.80 32.0O 99
Period, P --- -- 0.1 0.15 0.1 ---
8 Damping, 1/T --- --- 2.50 50.80 52.20 9,
Period, P ---- ---- 0.15 0.15 ---
neping, 1/T --- --- 52.50 50.80 52.20 88
Period, P -- 0.80 0. 0.6
10 Dampingp. T ----- ---- 1.90 .88 .76 322
SPeriod, P --- ---- 0.87 0. 0.51 ---
11 Damp ng, 1/? -. -1.56 **. F7 U278
Period, P 0.83 0.888 8 .0.81 0.90 ---
12 ampl ng, 1/T .10 .00 -5.51 -2.75 -1.52 71
Peri o, P 0.92 0.90 0.86 0.92 0 --.
15 Damping, 1/T -.15 .00 -2.76 -2.19 -. 4 65 _
Period, P --- --- ---
1 Dmping, 1 ---- --- --- --- ----


P and T liven in seconds.
bApproximate method, all rudder prameters neglected


except those affecting C .


NArTONAL ADVISORY
COMMITTEE POP AEROBADTICS




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NACA ARR No. L4JO5a


FJgure /.- Three -view drawing of /te modified --scole
model of the fairchild XRZP?- Qirpltne.


Fig. 1






NACA ARR No. L4JO5a


Rudder /



Rudder



Rudder 3



Sections A-A


Rudder area Balaece
Rudder In percent inpercnt
vert/ca/-to/ rudder
oreO oreo
/ 40 0
2 40 3f
3 40 3"
NATIONAL ADVISORY
COMMITTEE FOR AERONAUTI


F/gure Z. .- 5Jetch of rudders used / f/Ae ruadder-freQ
stab ly d nveestigafbon in the laingley free-f/'gAt tunAe/.


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NACA ARR No. L4JO5a Fig. 3






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SNACA ARR No. L4JO5a


Ang/e of yogw, Y, deg


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NATION L ADVISORY
COMMITTEE OR AER NAUTIC

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Fig. 14






NACA ARR No. L4JO5a


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UNIVERSITY OF FLORIDA

3 1262 08106559 0




UNIVERSITY OF FLORIDA
DOCUMENTS DEPARTMENT
120 MARSTON SCIENCE LIBRARY
P.O. BOc. 117011
GAINESVILLE, FL 32611-7011 USA


















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