FILE copy NO.2-W AIm No. 3H31

NA llONAl ADVISORY COMMlmE FOR AERONAUTICS

ORIGINALLY ISSUED August 1943 as

Advance Restricted Report 3H31

THE EFFECT OF MASS DIS'mIBUTION ON THE LATERAL S'XABILITI

AND CON'rnOL CHARACTERISTICS OF AN AIRPIANE AS IE'lERMINED

BY TEsrS OF A moo. IN THE FREE-FLIGHT TUNNEL

By John P. Campbell and Char.les L. Seacord" Jr.

Langley Memorial Aeronautical Laboratory Langley Field, Va.

WASHINGTON

IL COpy To be returned to

the liles of the National Advisory LorrJOIttee

for Aeronautics Washington D. C.

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.

NATIONAL ADifISO!{Y COMMITTEE FOR AERONAUTICS

ADV faCE R~STRICT"'3.:D RBPORT

THE EFFECT OF 1::A3S DISTR.IBUTION ON TIill LATERAL STABILITY

AND CONTHOL CIlAHACTIm,ISTICS OF MJ".AIRPLANE AS D:CTEHHINED

BY TESTS OF A TIODEL IN THE FrrRn:-FLIGHT TlHrNEL

By John P. Campbell and Charles L. Seacord, Jr.

SUMjJARY

The effects of mass distribution on lateral stability

and control characteristics of an airplane have been deter-

mined by flight tests of a model in the NACA free-flight

tunnel.· In the investigation, the rol~ing .and yawing mo~ents

of inertia. were increased from normal values to values up to

five times nor~al. For each moment-of-inerti;a condition,

combinations of dihedral and vertical-tail area .. reprc.senti~g ,

a variety of airplane configurations were tested.

The results of the flight tests of the model werc_ .cor-

related with calculated stability and control characteristics

and, in gene.ral, .. goodagre-ement was obtained. The tests

showed the following effects of increased rollinG and yawing '. ,

moments of inertia: no appreciable change in sp\+ral s ta~ .. \ '.

bili ty; reduc tions in o'scilla tory stabili ty that tlore .

serious at high values of dihedral; a reduction in\ the

sensitivity of the model to gust disturbances; and \~.reduc-. ..

tion in rolling acceleration provided by the ailerons,. whic:q

2.

caused a marked increase in time to reach a given angle

of bank. The general flight behavior of the r.1.odel became

worse wi th inCl"easing moments of inertia but, wi th combirla­

tlons of small effective dihedral and large vertical-tail

area, satisfactory flight characteristics were obtained at

all moment-of-inerti~ conditions.

INTRODUC'l'ION

A recent trend in design has been to distribute weight

along the wings of an airplane inste~d of concentrating it

in the fu~elage. This pedi stribution of ,,'!eit;ht, which

has been brought about largely by changes fro!~· single­

engine to twin~enbine design and by the increased use of

wing glli'1S and vd.ng fuel tanks, ha.s resulted in f,reatel'

rolling and yawinr; moment:::: of inertia fOl~ the a1rplarie and

has thereby increased the difficulty of 6btaining satisfac­

tory lateral stability. BecHuse of this trend, theoretical

investigations (references I and 2) have recently been

made to determine the effects of large increases· in moments

of inertia on lateral stability. rphe r'8nults of these

investigations· indicated that the y;ange of values ,':If

dihedral Bnd vertical-tail area for sat1sfactorj osclllatory

stability becomes progressively smaller wi th increr.lf3ing

moments of inertia.

In order to verify experimentally· the re 31.1.1 t 3 of such

theoretical investigations and to deter:m:!.ne the effects of

3

the indicated stability changes on eenera1 flight behavior,

an investlgation has been carried out.in the NACA free­

flight tunnel VIi th a 1/10- scale, free-f1yj_ng dynamic model

loaded to represent a wide ranee of values of rolling and

yawing moments of inertia. For each moment-of~inertia

conditioll, a range of dihedral qng}es and vertical-tail

areas that represented, a variety of airplane confiGuratLms

was covered.

Calc:.~lations were made to deternine the theoretical

stability and cont.rol characteristics of tll.6 particular

model. tes ted in order that the results obtained by theor~T

and experiment could be correlated.

m

q

SYIVIBOLS

radius of gyration about x radius of gyration about

moment of inertia about- X

moment of inertia abou.t Z

mc-ss, sluGs

lift coefficient .(L/qS)

axis, feet

axis, feet

axis,

axis,

slug-feet2

2 slug-feet

. lateral-force coefficient (Y/qS)

yawing-moment coefficient

rolling-noment coefficient

11ft, pounds

lateral force, pounds

(yavvine ~(loment) \ qbS I (rollin.s momen.L9 \ ~" S ' '-1 0 ..

dynamic pressure, pounds per square foot (~pV2)

4

b wing span, feet

c wing chord, feet

S wing area,' s'quare feet

rate of chance of yawing-moment coef·ficient viith angle

of sideslip, per radian (0 Cn/O p) rate of change of rolling-moment coefficient with 8.ngle

of sideslip,- per radian (OC7.,/o[3) rate of change of lateral-force coefficient with angle

of 8ideslip, per radian (oCy/O'~) rate of change of 'yawing-moment coefficient with yav'Ting

. l'

i.7

"

velocity, per unit of rb/2V

rate of change of yawing-moment coefficient with rolli.ng

velocity, pel' unit of pb/2V

rate of chang~ of rolling-moment coefficient with rolling

velocity, per unit of pb/2V (~C ;. 'A .EQ) \ u 7., . u 2V

rate of change of rolling-moment coefficient with yawing

velocity, per unitoi' rb/2V

angle of sideslip, radians

yawing angular velocity, radians per second

airspeed, feet per second

p rolling angular ~elocity, radians or degrees per second

p air density, slugs per cubic foot

P perlod of lateral oscillation, seconds

t time, seconds

5

~ angle of bank, degrees

0/ angle of yaw, degrees

5f

flap deflection, degrees

R Routh's discriminant

D"E coefficients in stability quartic equation, given in

reference I

APPARATUS

The investigation was carried out in the NACA f'ree-

flight tunnel, which is equipped. for tes.tlnc free-flying

dynamic airplane models. A complete description of the

tunnel and its operation is given in refel'ence 3. Force

tests J'l1ade to determine the static lateral-stabj.li ty deri iJ-·

atives were run on the free-flight-tunnel six-component

balance described in reference 4. A photo[raph of the.

test section of the tunnel showing a Eodel in flight is

given as figure 1.

A three-view drawing of the model used in the tests

is shown in figure 2" and photographs of the model are

presented in figures 3 and 4. The l/IO-scale model,

which in over-all dimensions represented a m.odern fighter

airplane" was constructed principally of balsa and was

equipped w:i. th movable control surface s similar to those

described in referen~e~ 3 and 4. For all tests, the

model was equipped with a split flap 60 percent of the . "

wing span and 25 nercent of the wing chord. The flap

was deflected 600 •

6

The rolling and yawing Moments of inertia of the model

were varied by shifting lead weights from the fuselage to

the wing tips. The effective dihedral was chanGed by alter-

ing the geometric dihedral anfle of the outer panel, as

indicated in figure 2. Four geometrically similar vertical

ta'1ls (fig. 2) were used on the model to produce changes in

?ertical-tail area.

tIETHODS

Stability and Control Calculations

Boundaries for neutral spiral stability (5 = 0), neutral

oscillatory stability (R = 0), and neutral directional sta­

bility (D = 0) were calculated for all moment-of-inertia

conditions by means of the stability equations of reference 5.

Values of the static lateral-stability derivatives, C , np

CL' and f3

Cy ,used in the calculations were obtained from fopce -13

tests of the model. The value of the rotary derivative C nr

was obtained from free-oscillation tests of the r.1oo.el in the

free-flight tunnel (reference 6); wherea~, the other rotary

derivatives, Cn ' Ct ' and Ct ' were estimated from the charts . p p r

of reference 7 and fran the formulas of reference 1. Values

nf the stability derivatives used in the calculations are

given in table I. All the calculated boundaries are shown

011 the stability chart of figure 5.

7

The period of the literal oscillation was calculated

for some conditions by une of formula (21) given in

reference 5.

The banking motions of 'the model following abrupt

aileron maneuvers with different moments of inertia ~ere

calculated for a condition of small positive dihedral

and large vertical-tail area. For these calculations

the method of reference 8 was used and the ~odel was asswned

to have freedo~ only in roll.

Testing Procedure

The model was flown at each test condition and its

stabili ty and control characteristics were noted b:r the,

pilot. In addition, notion-picture records were made

of 80111e flights in order to supplement the pilot's observa­

tions wj, th quantitatIve sta'b:Lli ty and control data.

The spiral stab1lity of the yr;.odel was determined by

visual observation during sideslips across the tunnel with

controls fixed. Increasing inward sideslip was taken as

an indication of spiral instability.

General oscillatory stability characteristics with

controls fixed were noted by the pilot, and the damping

and period of the lateral oscillations after abrupt rudder

deflections were recorded by the cameras for each test

condition.

8

. The directional stabili ty was judged by the yawing

behavior of the model after gust disturbances and by the

amount of adverse yawing produced by aileron control.

The steadiness, or the reaction of the model to the

normal gustiness in the air stream, was noted for all test

conditions. This chaFacteristic was apparently. not very

closely related to other stability characteristics and was

therefore judged independently.

The effectiveness of the ailerons in rolling the model

was noted by the pilot and was r,1easured from camera records

of abrupt aileron maneuvers. The effect of adverse yawing

on aileron control for the various test conditions was

determined by visual observation.

Throughout the investigation, an effort was m~de. to

determine the best combinations of dihedral and vertical-

tail area for each moment-of-inertia condition and to

establish on the lateral stability chart (-C L against C ) ~ np

the boundaries between regions of satisfactory and unsatls-

factory flight behavior. Flight-behavior ratings based on

the pilot's opi~ion of the general stability and control

characteristics of the Model were recorded for each test

condition. Although the accuracy of these ratings depended

upon the pilot's ability to recognize nnsatisfactory condi­

tions, it is believed that the ratings give a true indica-

tion of the effect of changes in the variables involved because

each rating was based on a number of separ'ate flights.

9

. ,RAnGE OJ? V,ARIABLES

The parameters varied during the investigation were

rolling and yavJing moments of iner~~a, effective dihedral

f-c'[, "), and effective vertical-tail area. ('cn ). \ ~ .p~

The

weight of the model was held constant to simulate an alT'-

plane wing loa~lin['; of 30 pounds per I:qual'e' foot. All the

tests were made at an air8peed of 51 feet per second,

which corresp'Jnded to a' lift' coefficient of 1.0 .

. Because the rolline and yawing Moments of inertia

were 6hanged by varying the radii of gyration, Ie and X

kZ' while the' weight was held constant, the inertia changes

in this invest!gation are expressed in terms of

These ratios or their reciprocals a~e the conven-

tional nondimensional expressions for radii of gyration in

stability calculations.

In making the noment-of-inertia chane;es, kv/b and J ..

kZ/b Vlere varied in such a manner that the·value of

~\? k \ 2 \~ -'(bX) reaained constant. C~1anC'ing the Y:'10rlOnts of

inertia in this way corresponds to 'chanping the proportion

of weight carried in the ~ngs. In the tests with,high

values of ISc/b and kZ/b, the 1':lodel., therf.lfore represented

an airplane with·such loads as guns, ammunition, ,anc~ fuel

tanks installed in the wings instead of the fuselage.

10

Three moment-of-inertia conditions were tested corre­I

sponding to the values of kv/b al1dkr>/b in the follovIing table, . .J~ I..

in which the relative valuef! of m.oments of inertia are also

given in order to afford a better indication of the magnitude

of the inertia changes:

I COnditiOnl kX/b

!0.127 1.00 '\0.197

'\ I ! .200 2.49 1 .247

A

B

C

1.-· .f.J

"]:,-, (CoLdi­tion A)

1.00

L57

2.67 L · 286 ., 5.08 \.322 r------'oO.------___ ~----..;..-------·-These moment-of-inertia conditions are represented on

the graph of kX/b agains t kZ/b in figure 6 by the po ints

A, B, and C. Condition A is intended to si~ulate an aver-

age mass distribution for modern single-engine fighter'

airplanes~ Condition B represents ths probable upper

limit of moments of inertia for present-day conventidnal

airplanes. Condition C represents the. extremely high

values of the parameters kX/b and kZ/b that result in the

case of airplanes with very small span or with excep-

tionally large loads in the wings. Condition every

nearly simulates the moments of inertia of a flying wing

wi th uniforr.l spanwise f,1.ass distribution.

11

In order to illustrate the trend of present-day

airplanes toward higher mor.ients of inertia, various

other points are also plotted in figure 6. The squares

connected by arrows show this trend in successive models

of single-engine fighter airplanes of the SUl,,6 design.

The triangles represent mass distribuUcns of sever'al r.!odern

twin-engine and multiengine designs.

An example is f.lven in fi[ure '6 to show the effect

on mpments of inertia of adding large bombs 'Jr extra fuel

tanks to the wings oj'> a typical fighter airplane. rrhe

position of the maSA distribution of this airplane on the

plot is changed from Y to Z by th.e addi t:ton of a

2000-pound bomb or fuel tank midway out. on each vv'ing. It

is evident that an installation of this kind substantially

increases the rolling and yawing moments of inertia.

Three values of dihedral were used in the tests: a

large positive dihsdral; a small positive dihedral, and a

moderate negative dihedral, which are reppesented by the

symbols L, S, and N, respectively. The value of C~ for ~

each dihedral varied slightly with vel ... tical-tail area, as

shown in figure 5. The four vertical tails used in the

tests and desirnated by the number'S 1, 21 C, and 4 (fig. 2)

provided a range of C from 0.01 to '0.12. n{3

Exact values

f6r each model confi~uration were deter-of Cn and C"[, {3 {3

mined by force tests 'of the. X"lod61 and are shovm in figure 5.

12

The various configurations are represented by combinations

of symbols, for convenience. and brevity; for example, condi-

tion S3B has snaIl positive dihedral S, vertical tail 3,

and moment-of-inertia condition B.

Hl;;SUL'fS AHD DISCUSSION

Spiral Stability

The spiral stability of the model was not e.ffected by

changes in moments of inertia. The flight tests agreed with

theory in this respect for, as indicated in figure 5, the

theoretical spiral stability boundary is not changed by

vari8.tion of ky/b Ratings for spiral stability Jl.

for the va~ious model configurations are presented in

figure 7.

It was interestin~ to note that, for the negative

dihedral dondition, increasin8 the moments of inertia

did not ma terislly increase the difficu·l ty of flying t.he

" "110 de 1. It might be expected that, because of the spiral

instability with negative dihedral, increasing the rolling

moment of inertia, and consequ~ntly reducing the rolling

acceleration produced by the ailerons, would cause diffi-

culty in recovering from a banked attitude. Such was not

the case, however, probably because the acceleration of the

dropping wing after a gust disturbance was also smaller with

the increased inertia. At tines this reduced rolling

13

acceleration even caused ati apparent improvement in ~piral

~tability because ~he model seemed to diverge more slowly

following-a r,ust dist;urbance.

The flight-test results emphasized the fact that, for

the range of conditions tested, spiral instabili t-,v has

virtually no significance in determining general flight

characteristics. It can be seen from figure 7 that the

model was spirally unstable with both the small positive

and ~he negative dihedrals. Yet eVEn with the negative

dihedral, no rapid spiral dive~gence was not~d and the

model was not appreciably harder to fly than with the

large positive dihedral.

Oscillatory Stability

Increasing the moments of inertia definitely reduced

the oscillator7! stability of the model and forsoT'1e model

confir;ur'a tions introduced concH tions of dangerous 08cilla-

tory instability. The data of figure 8 show craphically

the changes in the daMping of the lateral oscillation with

change in mass distribution for various combinations of and

dihedral/vertical-tail area. Inasmuch as an accurate

quantitative measure-of the damping could not be obt-alned for

all conditions, the results a~e-presented in the form of

qualitative ratings for darJping at each condition. The

approximate quantitative equivalents of these rntings are:

14

,-.... -- .. ----;--.------------r-------------.. -.. -- .. -------, Qualitative

rating Approximate i

quantitative e(~liVa~~~t! Rating

A Stable

BSlightly stable

C Jeutral

D Slightly unstable

E Dangerously unstable

Damps to one-half amplitude in less than two cycles

Damps to one-half amplitude in two cycle s or l~lore

Zero danping

Builds up to double amplitude in more than one cycle

Builds up to double amplitude in one cycle or less ------_. ------_._-_._--"'--------- ----- ---_ .. -

A comparison of the theoretical oscillatory stability

~oundaries (R = 0) in figure 8 with the ratings for damping

of the oscillation obtained in the flight tests of the model

indicates good agreement between theory. and flight results.

Figure 9 shows that increasi.ng the.moments of inertia

causecl~n increase in the period of the late~al 08c11la-

tion, as indicated by theory. The exp~ri.mentally deter~

mined values for the period were slir:;htly smaller than the

calculated values.

The ratings in figure 8 show that, al t 1>:; ugh increasing

the moments of inertia reduced the oscillatory stability for

v;i..rtually all mo~el conflgurations, the marnltude of the

reduction varied greatly for the different combinations of

I

dihedral and vertical. tail area. In general, the effects of

15

moment of inertia on the oscillation damping we're more

pronolmced. wi th the large dihedral and the si'?1all vertical-

tail areas. This variation in the magnitude of inertia

effects with model configuration was in good agreement with

the variation indicated by the shifting of the theoretical

oscillatory stability boundarles shown on the stability

charts (-C L against en ) in figure 8. With increasing " .. ~ momen ts of inertia the b()Lmda:d.e s move upward and lnward

on the charts and there'J~r S}-lOVl the grea te st inertia. effects

at large valueo of -C, and small values of Cn • It &~. . ~

appears both from these boundary shifts and from ·the flight

ratings for oscillation clamping that a complete picture of

the effects of increased mOMents of inertia on osciJ.latory

stability can b~ obtained only by an analysis of tho effcicts

over a wide. range of model configurations.

dihedral, the effect of lncreased moments of inertia. on

08ci11a tory stabili ty was rela ti.vely s~-:1al.l for all values

of vertical-tail area. Even for the condition of l~ast

osclllatory damping with this dihedral (cond:i.tion S1C),

no unstable 03cill8.. tion::! were noted although the danping

was very light. With the two largest vertical tail~

(tails 3 and 4) and the small dihedral, the oRcillutory

stability for conditions Band C, though less than that

. for condition A, was conroidered satisfactory.

16

Large positive dihedral.- With the large positive dihedral,

increasing the Moments of inertia caused pronounced reductions

in oscillatory stability for all values of vertical-tail area.

Condit'ions of dangerous oscillatory instability were encoun­

tered with the smallest tall (tail 1) at loading condition B

and with ail tails. except the largest (tail 4) at loading,

condition C. These unstable conditions were considered

dangerous hecause sustained flights were inpossible as a

result of oscillations that increased in anplitude despite

intensive efforts of the pilot to control the model. For

some conditions, such 8S L3B and L4C, unstable oscillations

were encountered 5,n flights wi th contro'ls fixed, but. these

oscillations could be term~,nated at will b~J control appl~ca­

tions and were therefore not considered particularly danger­

ous.

The pronounced effect of moments of inertia on oscil­

latory stabllity with the large positive dihedral is illus­

trated graphtcally in figure 10 by photographically. recorded

time histories of fliChts at cond:itlonsL3A, L3I3,. and,L3C~

The two upper s,ets of curvc,;s in f:tgure 10 are pe.cords of· the

latera.l oscillations wi th. controls fixed, which were started

by abrupt rudder. deflections. A comparison of the curves

shows that changing frof;] mOY'lEnt-of-inertia condition A

moment-of-inertia condi tion B caused t~'le model to become

to

oscilla torily uns table, in. flir;hts . vITi th controls fixed. As

:' .. -

17

pointed out in the preceding paragraph, however, this

instaaili ty was not espec-ially. dangerous when the lateral ," ...

controls were used properly.

The two lower sets of curves in figure 10 show that

increasing the morn~rits of inertia from condition A to

cond! tion C produced an ill1stable 08cilla tion that could

not be stopped by aileron and rudder control. 1. tcondi-

tion L3C, the oscillatlon not only continued to build up

despite aileron-cont~olmovementB but also was of such

strength that its period was .not appreciably al tared by

~he control applications. The flights at this condition,

of course, were of Very short duration and were usually

terminated by an abrupt sideslip to the floor of the

tunnel after the model had attained a very steep angle

of bank. The notion-picture record for condition LoA,

which is in sharp' contrast vdth that of conditiOn L3C,

shows the positive'and almost instantaneous effect of the

ailerons in returning the model to level flight wi~h

normal moments of inertia and serves to emphasize the

magnitude of the instabilit:;r that effectively nu:llified

the aileron control at condition 13C. The apparently

unstable yav!ing motion shQ,;vn in the rec.ord of condi tion

L3A was probably caused by the fact that the ruddel1

control applied sim,ultaneously wi th the ailel'on control

19

used to bank the model was not always of the required magni­

tude nor in the proper direction for returning the model to

unyawed flight.

Negati'le dihedral.- VJith the negative dihedral, the

effects of Moment of inertia on oscillatory stability.were

less than w:!. th the posi ti ve dihedrals and were 31':1all for

all values of vertical-tail area •. With this dihedral, the

lateral oscillatidn appeared to have a satisfactory rate· of

damping for all conditions except with tte smallest tail

(tail 1). A peculiar and sometimes violent form of insta-

bility vias encountered at cond:i.tions rHA, NIB, and IUC.

The instability, which appeared to be more directional than.

oscillatory in nature, was usually evidenced by yawing

motions that increased in r1agnitude even when the ailerons

and the rudder were used for control. . In so~e fliphts at

this unstablecondi-tion, the model yawed to a large angle

and then rolled off abruptl;! with the leading wing going

down. It was interesting to note ,that the flight behavi.or

of the model wi th the negative dihedral and tail 1 ir:;proved

wi th increasing mor1ents of inertia. This snrprising effect

appeared to be a direct result of slower, and therefore more

easily contI'olled, yawing motions of the moq,el with the

higher r10ments of inertia.

The ratings for damping of the oscillation in figure

8 for conditions NIA, N1B, and NIC are given in parentheses

19

because of the lillcertalnty as to whether the instability

was oscillatory or directional in nature. It should be

noted that these condltioI1S .on the stability diagram fall

very near the boundary for neutral directional 2tability

(D =- 0) • In the negative dihedral ranee, and in fact for

all spirally unstable conditions, the R =- 0 boundary is

not an indication of neutral oscillatory stability because

E, one of the coefficients of the stability equation, is

nega.ti VB. An exa~ination of the roots of the stability

equations for several negative dihedral conditiona, however,.

reveals thHt oscillatory stability theoretically exists

well below the D = 0 boundary. It appears, therefore,

that over the neeatlve dihedral range directional diver­

gence will occur beforeo~cillatory instabilit~ as indicated

by the flight tests of the model.

Reaction to Gusts

The reaction of the !!lodel to the normal gustiness

in the air stream was improved by increasing the moments

'of inertia. VIi th the high values of kX/b and kz/b, the

model was less sensitive to gust disturbances during

smooth flight and appeared to be steadier both in roll and

in yaw than with the lower moments of inertia. This

effect, Which was apparently purely inertial, was considered

beneficial frm:l a staoill ty standpoint, but like sone aero­

dynamic stabilizing effects VIas detrimental to lateral

control, as will be shown in the following section.

20

It should be pointed out ,that the benefici~l effects

of high moments of inertia, on 'the lateral steadiness of

the model were present only during smooth fli.ght. Once

the smooth flight of the model was int.errupted by a partj.c­

ularly violent gust or control 'disturbance, the high moments

of inertia prolbnged the effect of the disturbance Rnd

increased the difficulty of returning to steady flight.

Lateral Control

Increasine the mOMents of inertia caused T'1.ark6d

increases in the time to reach a ~iven angle of bank with

aileron control. It is eviden't. from the time histories

of I3.brupt aileron maneuvers shown in figure 11 that this

reduction VlaS caused by decreased rolling acceleration.

The model accelerated so slov.rly' during aileron maneuvers

at conditions Band C that maximum rollinf, velocities

could not be rer,ched durinr; the limited time and space

available for the maneuvers.

Figure 11 shows that the tent results,were in excellent

agreement with calculations of the pure banking motion

of the model. ThesGcalcula tions, which \vere based on

the assumption that' the model had freedom onl~T in roll,

indicate that the maxirlUm rolling velocity is not affected

by changes in'moments of inertia. Complete calculations

of the banJdng motion of an airplane wi th three degrees

of frE?edom (unpublished data) show, however, that increasing

21

the moments of inertia reduces the final rolling velocity

as well as the acceleration in roll. In any event, it

appears that, with a very high rolling moment of inertia,

the reduction in rolling acceleration alone is sufficient

to lengthen noticeably the time required to attain a given

angle of bank with aileron control.

The ~eBt data of figure 11 are made applicable to

the airplane by additional scales for rolling velocity

and .time. By means of these scales, a better indication

can be obtained of the eff~cts of high moments of inertia

on the angle of bank reached in a given time or on the

time required to reach a given angle of bank for the full­

scale airpl&ne.

General Fli8ht Behavior

. 'rhe general flight behavior became worse tNi th increas­

ing r.lOments of inertia, as shown by the flight-behavior

ratings in figure 12. It appeared that oscillatory sta­

bility was the predominant factor influencing the pilot's

opinion of the general flight behavior, as is indicated

by the similarity of the ratings on figures 8 and 12 for

corregponding test conditions. The magnitude of the

detrimental effects of increased inertia on general flight

behavior, as on oscillatory stability, was dependent upon

the model configuration; the greatest effects were observed

with the large positive dihedral and trie least effects

22

were noted wi th the large vertical tails (t'ails 3 and 4) used

in ,combination with the negative or small positive dihedrals.

Combinations of dihedral and vertical-tail area that'

gave satisfactory flight behavior at the different moment-

of-inertia conditions are indicated in figure 12 by approxi-

mate boundaries that separate satisfactory and unsatlsfactory

regions on the stability charts. It is apparent from the

manner in which the boundaries shift that the number of satis-

factory. combInations of 'dihedral and vertical-tail area

d~creased with increasing inertia. One model confi~~ation

(~mall positive dihedral and vertical tail 4), however, pro-

vided good general flight behavior for all moment-of-inertia

conditions tested.

CONCLUSIONS

The effects of increased rolling and yawing moments

of inertia on the lateral stability and c.ontrol charac ter-

istics of an airplane as determined by tests of a model

ip the free-flight tunnel may be surnmarized as follows:

1. In general, the test results were in good agree­

ment with t!leory ,in regard to the effects of'moments of . ,

inertia on lateral stabili~y nnd control.

23

2. Increasing the moments of inertia did not

affect spiral stability and did not increase the

difficulty of flying at a condition of spiral insta­

bility.

3. Increasinr, the moments of inertj.a reduced

oscillatory stability. . With negntive or ~mall

positive dihedral the reduction in stability was not·

great even with the small vertical tails. With the

large positive dihedral l however, large increases in

the moments of inertia introduced dangerous oscillatory

instability, especially with the smaller vertical tails.

4. ijJi th high noments of inertia, the model was

less sensi ti ve to gust dis6J.rbances and consequently

flew more smoothly than with the normal !:"toments of

inertia.

S. Increasing th~ moments of inertia reduced

the rolling acceleration provided by the ailerons

and thereby caused a marked increase in the time

required to attain a given angle of bank.

6. The ceneral flight behavior became worse

with increasing moments of inertia. The greatest

effects of increased inertia were observed at

conditions of large dihedral and small vertical­

tail area.

24

7. Satisfactory flight chara~teristics for all moment­

of-inertia condi tions 'U·ere obtained wi th the small dihedral

(Ct. P = -0.038)· and the large vertical tail area (Cn~ = 0.11).

Langley Memorial Aeronautical Laboratory,. __ Na.tional Ad~i13oPY ·Commi.ttee for Aeronautics.,

Langley Field, Va.· ..

25

IBFERE1JCES

1. Bamber, Hillard J.:., Effect of Sone Present-Day Airplane Design Trends on Requirements for Lateral Stability. T. N. No. 814, NACA, 19'~1.

2. Bryant, L. W., and Pugsley, A. G.: The Lateral Stability of Highly Loaded Aeroplanes. R. & M. Ho. 1840, British A •. R. C., 1938.

3. Shortal, Joseph A., and Osterhout, Clayton J.: Preliminary Stability and Control Tests in the NACA Pree-Flight Hind TUrLi1el and CorreIa tioD with Full-Scale Flight Tests. T. N. No. BlO, HACA,H)4.1.

4. Shortal, Joseph A. and Draper, Jo1m 1Jj.: Free-'. Plight-Tunnel Investigation of the Effect of the Fuselage LenGth and the Aspect Ratio and Size of the 'Vertical Tallon Lateral Stability and Control. IIACA A.R.R., April 194~~.

5. ZiTnm.erman, Charles R.: An Analysis of Lateral Sta.blll ty in Power-Off F'light wi th Charts for Use in Desic;n. Rep. No. 589, NACA, 1937.

6. Cal'lpbell, Jo1m P. and Mathews, Vial'd 0.: Experi­mental Determination of the Ya.wing MOMent Due to Yawing Contributed by the VJi.ng, Fuselage, and Vertical Taj.l of a Midwing Airplane ?:iodel. NACA A.R.R. No. 3F2f3, 1943.

7. Pearson, Henry A. and Jones, Robert T.: Theoretical Stability and Control Charact~ristics of Wings with various Amounts of Taper and' rrwist. Hep. Do. 635, NACA, 1938.

8. Jones, Robert T.: A Sir.1plified Appliea tion of the Hethod of Operators to the Calculation of Dis turhed r':1otions of an Airpl~ne. Rep. No'. 560, NACA, 1936.

26 .

Cy i3

-0.196

-.201

-.226

.. ·.326

-.426

-.526

-.626

TABLE I

VALUES mil STABILITY J)ERIVi,TIVES US::::D

11'1 COMPU'l\o.TIONS " ,

IC L -is a dependent t_ ~

. ...,

va~~~ ~h, 1 ""I . ~ ~ ~,~~ -"~!

C CLp C~ CLr i °nr 4------.1---..,.----- --------11------------1-----

ni3

-0.0040

-. 00~22

.0065

. 0415

.0765

.1115

.1465

-0.47 -0.0520

-.47 -.0517

-.47 ... 0503

-.47 ·-.0431 .

-.47 ... 0336

0.2530

• 253~S

.2547 '1 !

.2619 I 02714 • I

-.0217 I .2833 I

-.47 -.0070 • ~~980 I

... 0.0472

-.0484

-.0790

- .103t3

-.12f30, i·

_ 1 to.':)!:;! • ...J..L-'k./ '-".

-----"'------------~----.-- ..... ~.--.".---... -~---...... -... - ., .•..

NA

CA

F

ig.l

NACA

o 5 10 /5 1,1 I I I I I I I I I I I I I I I

Scale J In.

Tip dilledral) 6° voriedto 14°o!7d -4"

VertiCal Area Ilspec/ tall (%5) ralio

-+-'-~"---I--~-I

/ 5.2 /.9 2 7.B 1.9 3 105 /.9 4 15.5 /.3

.----46.8"---+l---------~·1

'--Sp/;/ f'/apj 0606 025 cJ Or=60°

f.<---35.911--~------~-a---J 1+---Q35 b--->,:j~ Toll 4

/'.-~ I Tcl/I 3 ///~III Tc1l1 2.

11/ . III Tail I ~----_r-----~Ulld/~

FiGURE 2. - Dra w/!7g of model used i!7lree-f'light-tu!7nel mass -discrlbution investigation

HAC! Figa.,3 , 4

Figure 3.- Side view of model used in m&ss-di~tribution investigation in the NACA free-flight tunnel.

~igure 4.- Plan view of model used in mass-distribution investi6ati0n in the NACA f r ee- flight tunnel .

'.

NACA Fi 95 .. 5,7

I I I I I I

A)8p Mor;;enl"- Of-1n9rio cO/~d/l'I'Qns I IV,S,L DIIJedrals 1 i I 0f~ Ilnslabk 1,2,3,4 Vemcal tolls I' I I

. .... . £=(}I SpI/'V'1 slobl/;ty boundary . R=O Oscillatory stabiliTy boundary

./6 D=O Directional stabllll"y bounda.ry --. ~IT=O I J (condll'lon C)_

<:) 1114 /' Vy ~£=O I. I ...., .

~V iY .rAIl conddlons) -°S4 ./ ~ .... R=O ,. 1-

~z~ y r' CConcl;tlon B) " ./ /

~ --ON3 ~

~ V L I °S3 I

/ ~ r§L3 ONe .Y f?:=O

D=O I

J ~ 7 OL2 ~

/ (condl!;on A) ON/

.lc

.08

.04

7"7

~~ ~ V ~ ~

rr-r-,..,. ~ '7r-1 ~ ~." ",0=0

o

-.08 -.0";; 0 .04 .08 .12 ./6 .20 .24--Cl.

". 13 Flt3UR,E 5- SlablMy chari showlnq stablilly boundaries one! model

configul7:]/;ons. CL = /.0 for all boundaries and configurations."

.16

,/2 c+

c+ C'l9

.re

c+ .04

c+-

o -.08 -.04

c+

C+

/'

~ o

-cr, '(3

.04

A Slbble 8 Neutral C Unsfoble

.:/ E=O

./ V-

B y

/ y

->,VA-

V A

A I

i

'D8 12 .16 ,20

Ft5URE 7. - SPlrol - stabtli/y I()/Jnqs fOr .dtffe/enl model conflqula/lonS. q=/.O. (Averaqe I'O/mqs fOr all moment- of-mer/;Q . conqdlons.)

"...... <IJ

o U <f)'

-1: o VI c o \J)

>

/I

.x u o .0

! I

NACA

36

.32

28

24 ffZ

D 20

J6

.12

.08

D4

@@© Mcment-d-If7ed!o test conditions 117 free-f//q/}/­tLianel l/wesligoll0/7

~ Effect c/actll17g2,oOO­jJOum IxYnb cYmellollA /Jo/fway oot on exh WI/Kl cf tiq/7/er olr;:¥one

I I ; 1

I I

Fig. 6

o--+-D Smqle-enql/Je /Jq/7le;-­olrptJl7es(4r1ows show trem 1/7 success I ve mexiels if ..:.nme deslqn)

I I ! 1 ,

I

!

1 I ;.¥

v· /!.iZl 16

NVlI7-e/7QI/eOnd mull1-el7qll7e OIIJJ/oil~

i Ai

I I

~

L F

--

V ~ -.. - .--

----

I ------

- ~ ~ ~I C\l C"') --.. o

~~ 6.

101 PIT ~

-

I I

I I

! 1 I

I

!

_ ... __ .-

--

" .x. u o

.D

°0 .04 .C8 J2 J6 .20 .24 ·.28 .32 AX

--s-I1GLlRE 6. - Ron::;e if values d!!..i... oild "!!"z-covered //7

Invesflqatlon. b b

NACA ,/2

.08

.04-D::()

o

-.04

,/2

.08

Cn,8 .04

D=O

-0

-.04

.12

,08

.04

D=O

o

A+

~'

B+

~E) ~ ~ I7-r-,...

~

A

B

(!j -r-~ ~ -r-;..,.

A-

-'"

A -----

B i

(c0

~ ~ I7-r,.., ! I

A+ At

A ~

, B-

lB .-C ~

~

~ '''1"i r-;.;., ~ ..... .

/...~ B-

/-B+ /'

/ D+

--

/ L

P'- /' £ ~

~ ~ I~"'"

-8-+ V

~.

L ---

/1 8

/ E --.

k<' J

E

~+'" ,/

E '77-r-, ~ ~

Fig.8

M0/J7817t-ofiir,el1!d C0/7o'1/Jo/J A t !

V R=O

Lotera/-osCi//o/lon roll n qs A Stobie 8 . S//qht/y stode C N€utro/ o .:3I19/;!/Y uns/able E wnqel'ous/y un3to. de

I

/ R=O I

'/Womel7T-ot-llA9r/la COl7dJllon B_

-

/- R=O .. I

I I I i

MOl77elf7tofili7el'tia comillol? C ~

II

:s:. v o

..0

-:08 o .04 .0:9 .12 )6 .20 .24--Ct'(3

nGURE 8. - Rolll7qs for damlJI/lQ of' /aterol osc;//otlon . for different test condltlol7S, CI.. =1.0. (Ratings p:Js5fbly

mfluenced by directIonal 5tability enclosed In parEntheses':

o Q) Ul

16 -

14

12 -

10 --

_ 8 ~

4

2

o

Fig. 9

I I ! Jertic~1 tail I l ! I

1_ 01 Measured L-- --I

, -- 1 Calculated (ref. ~) L l' + 4 Measured \)

1--- ____ J -- --4 Calculated (ref. 5) - -,'-'6 . Il I ;

~ e--++ ! ---+-' --+-I -~--l

5i-t 'I: II I I: /' ~--r---t i I I I 1/

4 '--t-i--t- I i / I/-.Jj'---+----I -.,-t-+--~--L/ ! I If--l--4

3 ----+' i +iJ / ----LjJv1,,~l--f Lt ,:-;,-

I I : I ! I ome~v~o -lner la I' ! ,condltlon C

! I I I I " ! ---T--------r--,-1 +-.-t-.- t--l-~~~l--+----I

2- Mom~~t~0f-i""~t+a __ l_ . i 4---+----1 con'il tJ. 0!1 .4.. I I ~ I

i I '. \ I ' I I ---.. T--.T----~t- -___ ~-.-_i.----. ......:...: --~--I

1 '0 I ! '. Momont~of-inertia I I !. d't: B

1- ---------I----I--t-"-"n,~OJn -1-f----r---t--T---1-----r--L-- ----t--

ol __ ~l'~j~' ~1~1 __ ~il ~I~I~I~'~ o .08 .16 / .24 .32

k:c b

Figure 9.- Effect of moments of inertia on period of lateral oscillation. Small positive dihedral. CL = 1.0.

NACA Fiq. 10

/0 . L t'cJundn }3A 1 , JI7I)o~ U· _ -+.---1

~ .. ~,~ ~ _~ .k'" -A '-%-

o ~f ~t ~~~~.~ -/0 1'0-" '4> - Yo -+--+--+-~--+---+----+----If---+-~---l-~

-20 r-~~-4-+-4--+-~---+---+----+----If---+-~-+-~+-~

M(J.'i!~dO

wll­scale 0

•

. ) 1.0 I I,~ 2n 2;S 30 .35 40 I j I I I I I I Ilf r I 2 J 5 6 7 8 .9 10 II 12 13

lime, sec

fi$URE 10 - llme hlsmnes of' bon/rlnq Q/id yawl.l'Kl mollons or mOdel showing el'l'ect of IfJCreased fY:O/7Jenfs if IIler//Q on dOlTljJInq of" btem/ osc;/Iailon. LOlqe pos/!;f/e dihedral. I/etf/co; tall 3. CL = /.0,

. NACA

CJ

8? & ~ Q. ~ ~ ~ 9} s: th ~ ~ 0 C(

Fig. II

flill- MtX/el .::cole Ii OG

30

25 8 0

20 6 0

15 4 0

10

/

! II

I

II

/ .{

/

-Y ./

5 2 0 / tv'K

0 o ~

~ ~ l0

f'-'

v-v -- 1-

i l/ ~-!..--

.~ I+" /-l --

v+ -~-~-

~ ,..__r -- , :;;.x

v X"'"

V

COI7d;l7o/)' Expenmel7To/ Calculote d 54A 0 S4B + --S4C x -----

ole

o Mode/O

/'

r~ j

lJY V v*" P> 1--)(-'

.2

/

Z V

~ V /'

----.-x'"

.3

/

/ v i

I

V I / I

V / I

Y /' /' ./

V]/' ./ ,./

~/

.4 .5 .6 .7 rull-I .--~-'-----r--r--....,-----'----r--r-~.--r--.scale

o I I I 1 I I I

.2 .4 .6 .8 1.0 12 1# 16 18 2.0 lime, t, sec

;=;Gf.lRE II. - 77me histOries of a6ru,Dt ol/erO/7. maneuvers . with cilfterent momel7/-of-ll7er/;o conal/Ions. :Small paslove dlIJedrol. Jlel'llcol tOil 4. Cc:1.0.

X­u o .n

NACA .Ie

.08

.04

o

-/)4

.12

,re CIfJ

.04

o

-.04

,/2

.08

.04

o

A

A-

~ ~~

D ~~

I"r-~ ..,..~

~ h-,...

A-

8+' r

'('>-81) p-,.,.. -n

. D+ ..,.,., ~ "'r7-r-r- "7-,...

'8+

~ t>..~e~ .~ r-,..,.

B-

c-'77-J~ ~ tT-7-,..

..

\ ; . I \ ,4+ ; I \ A \ \' j

\ I V M+ /

v>V ~-.... '" ~

[>Y ~'f ~ . .,.,-r1"

/ ~ ~ ~ ",.

~ ~ t-~ ~ ,

,

\ .' , \

A , ,

if \ .... / - \

V ~ A-1/.) ~

~

~ '-'

-rr-,- :-rr ./ ~ c-

~ /- D ~ ~ -,.,..,..,..,

~

~

./ ./

v

.~ ~~~

V k"'l'"

Do; 0 r;;;..,.c

l'r E:O_

V~ //

KR=O

F' 12 10.

1 £=0

I 1

A1bmenl-o/-//W'/ia condilion A

R=O

/7/9/7/-bel7aJ/lor /"01/ A Good +-H B FOIl' C'Poor

/79S

D r;lqht Imj:X)SSlbA. TTTT rrrn BOUl7at7/,YJ

for sollsfoclory '. f/lQnt beIJClvlor

/1 Best I7!qnt "_)I1Jef(av~or

I I I /Womel7:!;o/'-!/7fJI1Ja _

cC"'7d)/lonB !

I o ~ -o

~ ~ 0=0 . ,I / R=-O

f\: A~ t. l~~ ./ E=O ,-I- I~ Vl./ ~ ~

B+,~ '/ r V . MOIn?I7i-oT-il7erlld

condl/;ol7 C_ rr-r,..,... tM TT

/ V/): . ..>

.J ~ ~ ~p.

~~ .D··· ~ ~ ~ "-

~ ~ D=O , . ~.' -.04-. -.08 -.04- 0 .04 .08 .12 ./6 .cD .24-

-CZ{J . FiGURE 12.- Fl!9ht·behavlol' mflngs fbI' different lest

condllions. CL =/.0 . . .