SARP No. L4FO?
NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
WAll TIMl REPORT
June 1944 as
Advance Restricted Report L4F02
THE EFFECTS OF STATIC MARGIN AND ROTATIONAL DAMPING IN
PITCH ON THE LONGITUDINAL STABILITY CHARACTERISTICS
OF AN AIRPLANE AS DETERMINED BY TESTS OF A MOIEL
IN THE NACA FREE-FLIGBT TUNNEL
By John P. Campbell and John W. Paulson
Langley Memorial Aeronautical Laboratory
Langley Field, Va.
NACA WARTIME REPORTS are reprints of papersoriginally 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 55 DOCUMENTS DEPARTMENT
:!k": P. -
Digitized by the Internet Archive
in 2011 with funding from
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~7 2 4C7 OS
rAOA ARR No. lljF,02
I.ATIONAL ADVISORY COi'"ITT'" FOR AC OI-AUTICS
.',D'.A"C R STF. I ACTED REL PORT
THE ZIfFICTS OF STATIC IARGiT: AUiD FOTATICIIAL E'.PIIP::3 IN
F.'C.- "ITEE Ln.C-ITi'TDIjAL ST.-.BILI'Y CHAR.CTzRI.TICS
OF AA ,IRFLAET AS D:ETiLlliED DY TESTS OF A i.ioDEL
INl ThE UCA _F.. E-FLIGHT TUIil:EL
By John P. Cartrbell and John ';. Paulson
The effects of s.rti? ier.--!n &-id rotational ramping
in pitch on the lonritu.. inl s1 T iit ch.rs tterit ics of
an airpJnr.e have been .e te:.i.ne j bu' flithit tests of a
model in the ACA free-flic-t Tn te-fi ,- t in--?ta-
ticn, the rotational d1a;!n:in.- In :it :'- w< '.r.. ie l over a
wide r'o.r:J.e b U' usinf '1orij z on':-l tA. lis th~It ':-.-ier i e .ri area
from 0 tc. 21 per:.ert of thYe ".ing a.rea. A range of sta sic
margins from 2 to 16 percent of t.h *c n sr-?od':'nr:ic
chlord .,was covered in the t,-,st "r-r eaich te:-t condition
the odel a flon and the loncitL...dl.. stedines. char-
actsrist-ics vere noted.
It v.ias found in the investigation that Icnigituldinal
steadiness wrs affected to a m.ch r..:iter e:::ent b;:
chan-es in static m;argii tnaii by can-;s in rotational
dar;ning. 'he test lonc.tudif ,l C.-dinss a'v.s noted at
large. -:,.lulEs of static mar.-in. For- all valu.-s of rota-
tional LIsn.pinr, the stec'ldint t of t'ih model decreased as
the st.itic m!arpin was reducced.. T;'e model was especially
unstea'.v at low values of static ..ar'-in (0.05 or less).
Reduction in rotational dam.irin had little effect on
lon`itudir.nal steadiness, except ti;t with lov: values of
static iar.in (0.05 or less) tne longitudinal divergences
were soretino more violent vith the taillesL (low rota-
tional da.-.,ir.n ) conii ition.
Tn the applications of the model test results to
full-s-cile airplanes the Frsmall scale of the model and the
method of control make the iod.el tests conservative; that
is, th" ste.adiness of th.,e airplane Is expected to be some-
what greater than that of the i..odel for g-iven values of
2 NACA ARR No. L4F02
static margin and rotational damping in pitch. The model
test results indicate that the tailless airplane, in
spite of its low rotational damping in pitch, should have
longitudinal steadiness characteristics similar to those
of a conventional airplane with the same amount of static
margin, provided the static margin is greater than 0.05.
Full-scale flight investigations have indicated that
static longitudinal stability and rotational damping in
pitch are two important factors affecting the longitudinal
handling characteristics of airplanes. No flight investi-
gations have been made, however, in which both of these
factors were systematically varied. Such an investigation
was considered desirable especially because of the recent
trend toward tailless airplanes, which have inherently low
damping in pitch. An investigation has therefore been
carried out in the NACA free-flight tunnel to determine
the effects of large changes in static margin and rota-
tional damping in pitch on the longitudinal stability
characteristics of airplanes. Static margin is a measure
of static longitudinal stability and is defined as the
distance between the center of gravity and the neutral
point of an airplane expressed in terms of the mean aero-
The investigation was made with a free-flying,
dynamic model. The longitudinal steadiness of the model
was observed in flights made with variations in horizontal
tail area and center-of-gravity location that gave a wide
range of values of rotational damping and static margin.
In the investigation an attempt was made to determine the
relation between the observed longitudinal stability char-
acteristics in flight and the calculated characteristics
of both the phugoid and the short-period longitudinal
CL lift coefficient Li: fts
NACA A!:R Io. LLF02 3
S... 4it4hin- !_opent\
C pic tchi.n.-i ont c oeLific nt o nt
S .- S J
dCr rate of change of -oitci nl,-iroinent coo~ef'ic,'.ent
t 1per degree st ailiz.'g incid.cncs
it anle of incidence of horizontal tal.], ositi've
when trailing edge is acv:n, d; rr -es
Cmq rate of changee cf pitcaiin..-mo..-ent coefficient
with pitching ang.- :1 velocitE 1 t 7
p msas densityj of air, slu.-;s pe'; cubic foot
q pitching angular vloc t:, r di.ans per second
V airspeed, fee- per seccn-i
c ,ran serodT-.amrl ch rd, ir.:1t
-- sct-;t-c ar.i, cho, ds (:: t', for pro:-e ll'cr off)
x distance from center of sravit- to '-.ni.tr-.il r'3it,
S wing area, S,:IL.1re feet
kic radius of gyration about Y-a-xis, fet
b v.ing span, feet
T1/2 tim-e to damp to cne--alf amr:litude, recon
P per-iod of lon.'itv..dinal ozoillaticir, seco-Ldls
q .ang.le of pitch, dere es
The investigation w was ca-. rri'3d cut in th1e ,CA free-
fiilht tunnel, which is fully described in rcfer-unce 1.
NACA ARR No. L4F02
A photograph of the test section of the tunnel showing a
e~lel in flight is presented as figure 1. Force tests
made to determine the static stability characteristics
of the model were run on the free-flight-tunnel six-
component balance. (See reference 2.) A free-oscillation
apparatus similar to that described in reference 5 was
used to obtain values of Cmq.
A three-view drawing of the model used in the inves-
tigation is given in figure 2. The model was constructed
principally of balsa and was fitted with control surfaces
similar to those described in references 1 and 2. In
addition, a movable elevator was installed on the inboard
portion of the wing (fig. 2) to provide longitudinal trim
and control during flights with the horizontal tail re-
moved. Three geometrically similar horizontal tails
were used on the model. (See fig. 2 and table I.) For
the tailless condition, the horizontal tail was removed
while the vertical tail and the fuselage were retained
on the model. The center-of-gravity location of the
model was varied by shifting lead weights located in the
nose and the tail.
The period and the time to damp to one-half ampli-
tude for both the short-period longitudinal oscillation
and the phugoid, or long-period longitudinal oscillation,
were computed for each tail condition for a range of
values of static margin from 0.02 to 0.16 mean aero-
dynamic chord. Values of the static longitudinal
stability derivatives used in making the calculations
were obtained from force tests of the model, and values
of the rotational damping derivative Cm were obtained
by a free-oscillation-test method similar to that de-
scribed in reference 3. All the calculations were made
for a lift coefficient of 0.5.
The model was flown with various amounts of static
margin for each value of rotational damping and a rating
NACA APR No. L4F02
of lon itudinal steadiness was assigned by- the pilot to
each condition casted. Thie moe-l option n was observed,
wvith ccnt--ols fi::ed and alco duArir. controlled ilig-t.
One as ure of stesdi:'nesss C.ss the fre.quenlc win whi ch
ele.vaior defle tions hed to be ai!plie-d -o keep tlhe nodel
flyi-: sC:oothly in the center of tL: tunnel. For very
stead:' com.nit ions, elevator control was seldom! necessary;
for i..u:stead.- conditions, iove'.cr alternate up anrd down
elevator d'eflections were rc-quiire1 ab lost continuously.
Another I,-eaRsre of steadinrzs vta t'he nmanitiude of ver-
tical mot-ons of the !"cdel in tlim- tunnel while the model
vwas l) -eirng controlled. "Lar-,& vertical dis,:lac!emen s and
rapid r.otions ,'ere the usual ind'ications of unsteadiness
and CiCw,, easily co.ntrolle.: m'.otions o.i sirall m..-r-itude
were obtained in .stcacy-flij-_ht cor:nliti.ns.
!ot iorn-icture Iecords .'ere ta'en with a cc-,iera
mounted at the side of the test -sc:t:cn of th-e t~.:.r.nel
for Core conditions to sup:le, enT. th? pilot's observa-
tion? cf steadiness. -ost of t..e.-- records jwere made of
controlled rmnod.l motions becaL'eis ela-.'ator cront-rol wa
usuall- required to keep the :r.'.del flying, in the center
of tne tunnel.
Three differences between the ..-ethod of controlling
the longitudinal motions in model flight and, in airopans
fli.it i-sho..ild be noted:
(1) The mcdel is controlled -y abrut elevator de-
flectic:ns of 20 to 5, or .-iore, which are applj.ed. for vry
short 7.riods of ti:ne; vwhereas, the airplane conltrcl can
be applied slowly and smoothly. This difference probably
makes the model fligh-its m.-re j-.ntpy tnan tlose of an air-
plane with the same values of static margin and rota-
(2) For the model, abrupt elevator control is given
front a fixed neutral position and uncn release the ele-
vator returns to the neutral p3siti:n. V'ith thi's method
of co-ntrol it i ims iossitle for lon it-idinal motions of
the :-,orel to be induced b-i orci.lations of the elevator
itself as is som etimes the cass for airplanes.
(5) The model is usually controlled to .-.a intain a
constant vertical position in the tunnel rather than a
constant attitude as in the case oi an ai ?lans. 'his
method of control introduces la- ifficulties at ti-es
and causes motions that are probl well damped with
h pdr., o "el l apdwt
NACA ARR No. L4F02
controls fixed to appear lightly damped when the elevator
control is being used.
RANGE OF VARIABLES
During the investigation, the rotational damping in
pitch and the static margin were varied while the weight
of the model and the moment of inertia about the Y-axis
were held constant. The rotational damping factor Cq
was varied from -5.1 to -14.3 by use of horizontal tail
areas that ranged from 0 to 24 percent of the wing area.
(See table I.) The static margin was varied for each
tail condition by shifting the center of gravity known
distances ahead of the neutral point. The neutral points
for the different tail conditions were determined from a
consideration of the values of -- obtained in force
tests of the model. The maximum variation of static
margin for the different tail conditions was from 0.02
The weight of'the model was held constant at a value
of approximately 6.1 pounds, which corresponds to a wing
loading of 2.7 pounds per square foot for the model or
to a wing loading of 27 pounds per square foot for an
airplane 10 times the size of the model. The moment of
inertia of the model for all test conditions was such
that the ratio of the pitching radius of gyration to the
wing span ky/b was 0.17. This value of ky/b is
within the range of values for conventional airplanes
and is only slightly below the average ratio obtained
from values for over a hundred airplanes.
The flight tests were made over a range of lift
coefficients from 0.4 to 0.7. The lowest lift coeffi-
cient obtainable (0.4) was established by the maximum
airspeed of the tunnel. The highest lift coefficient
(0.7) was limited by the maximum lift coefficient of the
model. Most of the flight tests were made at a lift
coefficient of approximately 0.5.
ITA..A 2R :io. L FO2
L S 'U LT S
The r- ul.ts of the ca cul-t!-r ion's t.d to dc teirmine
the t _~.e tc 'i.i:p to one-hr.lf a. p liT; lre a.-:. ti. period' of
the n -i tudina l o '- llitins r. se ntc in fi"d u ? 5
and .I. sule. ar" iv. -: fo.- e ishort-;.ri-, i 1 C S .ill. -
tiori in. J"i-ure ani fo the lor -.ri or -r tu cid
os-illat icr in Tfi...-u.e The ste .-l i ss: r tin- a.-a i n-
by the ;i. lot to di:'ferenL fl].i' ht co:-. ft s n r-n Z ar sowrP in
table II. Dar from r'c' tion-, i i:cuir, r-corl s sinvi-.in" tn i r
historic' s cf tth- vr-iasl n,:t: n : p.it,:,ir-.t rcotion of
the .c iel vdthi diff 'r rent a yiroi'-t of rot.tic al .a. :.i.r.
and sL.ati,., r.mar.in are r'c-'sc.,o in ti.'.: .- ': to 7.
effect of Var iaton .' tt" ic i,-r:in
iThe r tings of table 1I --O Lr Ih.- t ti-.e L 'od.lin;-- s co
the .cilel decr a sed a the s -atic ir- ir. v's.s, r-educ :ed fo:-
all values of rotatironal ranpixgi. a-_e idi l ti, 5Lc;r. iDLZ-
larly unstealy at low values of. : .ic :.~ar.lin (belov'0. .0J.).
The, mC,:iel flew. v-j.ry steal. ly th 1rre v.lues of
static arr in, and ,only oc,.scaZs Lon 1 -levatlor df-i lect ions
were r-eluir.d tc. keep t e ,mo- el f i'inn. s..ootl in' te
tunnel. Th- timetime histories a th, bC'ottoi. of ft' 'L ure- -
an t s:'ov' th;at the ve rt icsl otio si of ti.e :,ondel d.'.;in.
controlled fl ight "ith lar atti. r .ar.'in were slov,
smoot' a:nd of small rn ni r I.. .e
"ii:o- levi values of sta-t:i' n- Shov.vr, the
motions :,eca-e faster, shal."-r.:r a': va "',--, show by
the r .eor t-i.ne historic in f :- :: ad c. Table II
shores thI:t, with 0.0' s-itic r'.in, ti-'e .-.o.el -s -- ry
un stea- tI vith any a;liLmont c f otst onal d :iir. F i ht
at this c condition ve-re .'.ery j':..ni -nj _rc tende ncie
tow.var.d l.onvitudc final diveri- n ,-.'- nted. ",,t fl'.ohts
wit tni; arm:ount of st io ar--in -A,.ed in c a, she's
because of the e-:tr,-me diffic lt : r p-erienc e: b-: the
pilot in applying elevator r cc00irol at te. e:-act instant
that it vwas needed to rev-:-e': lon i.-t di in.al diver-.ence.
At ti-r.s because of iunavoi.o.ble 1.t in thLe pilot's
res- ct io ns, thi= control \is a.:3_; i : i' in, sa:h a ,.'a; as to
re .nfor ie rather lth-n to oppose tie .- r-ren t :ctionsc
NACA ARR No. LFP02
In this connection, it should be pointed out that the
pitching velocities of the small-scale models tested in
the NAlCA free-flight tunnel are more than three times as
great as the pitching velocities of the corresponding
airplanes. It is expected, therefore, that the airplane
should be easier to fly than the model with the same
amount of static margin, and it is not believed that an
airplane corresponding to the model tested would neces-
sarily exhibit poor flight characteristics similar to
those that were noted in the tests of the model with 0.02
The results of the calculations of dynamic longitu-
dinal stability (figs. 3 and 4) show that reducing the
static margin increases the period of both the phugoid
and the short-period oscillation and reduces the damping
of the phugoid but does not affect the damping of the
The only agreement noted between the calculations
and the flight-test results was that the period of the
short-period oscillation was approximately the same as
the period of the controlled motion of the model. Theo-
retically, the damping of the short-period oscillation
is heavy and does not vary with static margin. -It is
possible, however, that the short-period motion could be
reinforced by elevator control movements or gust dis-
turbances in such a way as to prevent it from damping
quickly. If such conditions were present, an unsteady,
lightly dLamped longitudinal motion having approximately
the same period as the short-period oscillation might
Effect of Variation of Rotational Damping
The ratings of table II show that variation of rota-
tional dampsing had very little effect on the longitudinal
steadiness of the model. Decreasing the rotational
damping had virtually no effect on the steadiness at
large values of static margin but decreased the steadi-
ness slightly at low values of static margin. The time
histories of figures 5 to 7 show that the vertical
motions of the model during controlled flight with dif-
ferent values of Cmq were roughly similar for a given
value of static margin. With low values of static margin
'.--CA :. I o. 'I 02
( .. J C. th riln-"t" in-' d ri' r nc': s '.": :' S ii-' -
ti!me- :..o-: "-ioir:t with t!:- tr "!:. E -e flo-.r CT,4) condi-
': ic 11 effeo- cf c ..H n es 'n i t.L: cti .n:-'. .i- n in.-
on t:< .- -itudinal 2"ea-Ui e:s :, : 0- f.oj. i l ic ac -0at
ta ba Icrs irpl.cire, i c .:2: ,. ;.:1'._Leei t l-- -.' r-ota-
r n a nt- "I n71-
tiC na' c'J'-,:n. In Kr -' :" u1i ': : c' : ;it ,' .1 st -
ness c -asr-E'. it : ti .t s t .: l- _' .F i-I c --Irc itio,. l
air l a :: n t .ie Esi. st ti. ..e: ic.
TI the i--nve-, ti atioL n t-,o i I.i .: tive d.: t ,ere ob-
taini ;. co,'A r in t- th e E'l P..:t f c-an.er in rot. cit nal
dal.lpi.- oni t:e e ev-t r ef. ;rti-: ncss i:'- ii ed :. m;"aiitain7
a ,i-.in ude-r. e -a conicroii bi lit:. I ,a: nctec in the
fli.'i; trTc-, ho"'eve'_ r'.a: s t.a :', i ':ntal t.il area
( nld l :.e.S i:-.e lev Stor" e ff :ti; .in ) s --C u.C'aed, iIhe
mag7ni te of te elev.Atcr. co,-to"i. reflect ion. ;e. uLet ]
to -< .. th- >olu l iKr.; si isa -toriLy in the i:unn l
did ;n t inicr .ase in i. rec t irc- ti. n to the reductioii
in ei.' to eff- -''eie .s. I- r.-; a r 3r e.O.d t at, as
t _e o .-tioa. l ia:.,i::.r in iir:-'. s e .-ed, s : .
oDC w -"ul i -,'vator control .a.: r ..i.r tI'o obtain satis-
factor f lic-hts L".:: t .e m" .. .
f C!.- f. i
Tt 1c C laticn f r .I 1. 9 -:: t rt d in
the r-, t ti, u l d .ri.. ..c.r. CC La' r : tU me -i'd
of tl .... t-..'',-d s. ?idl u ic- in J1. .Cr.-: : t'-h po -iod
of t'Te ; ,-u oid. :edlu.-:r: '.- 'i .. of Cn eIi :e te
dar. .- of t":e s'irt-o' riod o: aiu.tion -.:- 1ii ,.lu,;
of' sta ic ;,,.-.:- in a :r- ....::". e t tl r( H .i.in:- :f t i, ..l i' i .'j .
oQ cll j on for the alo- r n': 'f Efr. ... -: i .
C- CL, DI. ir- .'- -:s:..
T'-.e results of the invs-ti l-icnr. do ter-Lin-In the
effec:U- c:- lonr.itulLirnci ts .. in o vary.i.-. as.atic
rarrrin zi-.d rota ioi al d1.i. n .- e S'L'i .ized iL the fol-
lo'::in r .r.arhi s. I Che :i :l _C-1 io-ns of -.hes e r -esults
co Lth' fi l-' cale air.l sne t-,- a.l i sacl'.e oC the -n:odcl 1
and the -r ethod o cont-ol ootac,ly i.e th- e io 3l tests
conservative; tat is, the t%7finac--: of to air' lane is
e:-.: ct:- to be so:ie':-h-h t r-r'-aterr tlS-,. that of the iodel 1
for'r i.ven values of t' ztic :nar-,n anrd o-otational dcaipin:.
NACA ARR 'No. Li F02
1. The best longitudinal steadiness was noted at
large values of static margin while the least steady
conditions were obtained with very small values of static
margin (0.03 or less).
2. Changes in rotational dajrring had little effect
on longitudinal steadiness except that for low values of
static margin (0.05 or less) the longitudinal divergences
were soiretivies m-ore violent for conditions of low rota-
tional d amp ing.
,5 The model test results indicated that a tailless
airplane, in spite of its inherently low rotational
damping in pitch, should have longitudinal steadiness
characteristics similar to those of a conventional air-
plane with the same static margin, provided the static
margin is greater than 0.05.
Langley I:emorial Aeronautical Laboratory
NTational Advisory Connmittee for Aeronautics
Langley Field., Va-.
1. Shortal, Joseph A., and Ostorhout, Clayton J.:
Preliminary Stability and Control Tests in the
FACA Free-Plight Wind TIunnel and Correlation with
Pull-Scale Flight Tests. 1 CA TF 3:. 810, 19i41.
2. Shortal, Joserph A., and Draper, John 7W. Free-Fljht-
munnel Investigation of the Effect of the Fuselage
Tength and th-e Aspect Ratio and Sizo of the
Vertical Tail on Lateral Stability and Control.
:ACA APR No. 3D17, 19i5.
3. .ar.pbell, John P., and T-athews, .,ard 0. : 7r :-erimental
Determination of the Yawin ,:ent Due to Yaw-in--
Contributec. by the .Ving, 7 "elage, and Vertical
Tail of a hidwing Airplane Hodel. :.CA ARR
To. 5P28, 91045.
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NACA ARR No. L4F02 Fig. 1
NACA ARR No. L4F02
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