REPORT No. 578

FLIGHT MEASUREMENTS OF THE DYNAMIC LONGITUDINAL STABILITY OF

SEVERAL AIRPLANES AND A CORRELATION OF THE MEASUREMENTS WITH

PILOTS’ OBSERVATIONS OF HANDLING CE4RACTERISTICS

By Hm’rmY A. Soud

SUMMARY

The dynamic .?on@wdhd dabildy characttmdicsof

eight airplmws m de@ed by the period and damping of

the hmgthdi?ud 08Wion8 were meamred in $igh.t to

&termine tha degree of sta&iMy thui may be arpated in

conventimud airplunee. An attempt w mm% to corretie the measured 81&&y with pihts’ opinbn.s of the

gemral handling characteristics of the airplanes in order

to obtain an indication of the most o?wirable degnz of

dynamic 8tabit&y. The rewL-?t8of the mea’urememh 8h0w

that the ptTiUd of 08Ci!%Lti5?Lincreaaea with qwexi. At

low speed-s a range of periods from Ii’ to %3 8ec0ruk tom

recorded for tti di$ermi airplunes. At high speeds tha

periods ranged from %9 to 6.4 8ecoruk. T’lw damping

8howed no d+$nite trend with epeed. A gened tmw%ncy

for airpiktx thui were 8tabk? with pmw OJ to kome

undable with power on wus noted. T/b maximum dhmping recorded was 8@.c&n4 to reduce the amplitwde qf

oscillation by one-hu-lf in 9 8econd8, or approximaMy

on+urth cycle. The opinions of two pilots concerning

t?u bundling churactenktti of the airplmwc appamn$ly

were not injk.enced by “the 8ta$i.My characte7%tic8 a

dejined by tlw period and damping oj the longitudinal

08Cikl-tiO?18.

INTRODUCTION

The theory of dynamic longitudinal stability of airplanes, although not complete for power-on flight owing

to a lack of lmowledge of the effect of the propeller

elipstieam on certain of the stabili@- derivatives, has

been developed to the point where it is possible tc

predict the power+ff stability characteristics of an

airplane from ita‘dimensions. (See~eference 1.) The

longitudinal motion of an airplane following a disturbance may consist either of a continuou9 divergence, i. e.,

static instability, or of two superimposed oscillations

of different periods and damping. Ii the present case

consideration is given only to the oscillatory motion

since no statically unstable airplane should be regarded

m Sfltisfnctcry. The periods and damping of both

oscillations me given by the theory but, as the shortpriod oscillation is so heavily damped that thare is

no probability of instability of the oscillation for conventional @lanes, it is usual to consider the dynamic

longitudinal stability characteristics to be ddned by

the period and damping of only the long-period, or

phugcid, oscillation. With the aid of the charts of

reference 1, the Mess and dimensions of airplanes can

be adjusted during design to produce, within limits,

any length of the period and magnitude of damping

desired for this oscillation. Aside born the desirability

of having the airplane stable for all normal-flight conditions, little is known as to the Iengtb of the period and

the magnitude of the damping that constitute satisfactory stabili~. Pilots exprew opinions of an airplane’s longitudinal stabili@- in terms of such factcrs

as “stillness” and of pitching or unsteadiness in flight

through rough air, but the relation between these

observed characteristics and the degree of stability as

defined by the period and damping of the phugoid

oscillation is unlmown. ‘

In the present tests, the period and damping of the

phugoid oscillations of several airplaneswere measured

and, in addition, the general handling characteristics

as related to longitudinal motions were observed. The

measurements were made to obtain inf~rmation on

the degree of stability to be expected in conventional

airplanes. The observations of the handling characteristic were made to determine whe~her there is any

defhite relationship between the stability as defined

by period and damping of oscillations and the pilot’s

impression of handling characteristic+ It was hoped

that the tests would provide an indication of the

degree of dynamic stability desired.

The theory of stability indicates that the period

and damping of the phugoid osoillatiom are affected

by engine power and elevator restraint as well as by

speed. It was therefore desirable to make the measurements for several conditions. The tests were made

with eight single-engine airplanes of d.illerent types:

69
70 REPORT NO. 57S—NATIONAL ADVZSORY COMMEITEE FOR AERONAUTICS

two high-wing monoplanes and six biplanes. The

weights ranged horn 1,440 to 6,100 pounda and the

engine powe~ from 95 to 575 horsepower. Where

feasible, the measurements of period and damping

were made for a speed range extending from 10 miles

per hour above the minimum speed to the maximum

speed in level flight for the following conditions:

1. Elevator i3xedwith throttle closed.

2. Elevator tied with full throttle.

3. Elevator free with throttle closed.

4. Elevator free with full throttle.

The hamdling charactefitics of each airplane were

rated by each of two tes”tpilots.

APPARATUS AND METHOD

The eight airplanes tested were the Fairchild 22,

the Martin XBM-1, the Verville AT, the Mw%in

T4M-1, the Fairchild FC2-W2, the Boeing F4B-2,

the Consolidated NY–2, and the Douglas O-2H. The

dimensions of these airplanes pertinent to their longitudinal-stability characteristics are given in table I.

The weights and center-of~vity locations given are

for the airplanesas flown in the tests sad do not represent full-load conditions. The NY-2 airplane has a

lixed stabilizer that limited the elevator-free runs to

one air speed.

The following procedure vm.semployed in the tests:

All runs were made at a mean pressure altitude of

approximately 3,000 feet. Steady conditions were

first obtained at a given speed. For the elevator-free

runs the stabilizer was adjusted to obtain trim at this

speed. The oscillations were induced by depressing

the nose of the airplane with the elevator until a

steady speed of approximately 5 miles per hour above

the initial flight speed was obtained. The elevator

was then immediakly returned to the original setting

for the elevator-iixed runs or freed for the elevator-free

runs. Adjustable stops were provided for the elevatorhed runs to assist the pilot in resetting the elevator

to the origimd position and in holding it fixed during

the oscillations.

The air speed was used for the determination of the

period and damping of the oscillations. The variation

of air speed with time was obtained by means of a

recording air-peed meter and timer started prior to

the start of the oscillations. The record of air speed

was obtained for at least two complete cycles of oscillation. The period of the oscillation was, of course, the

time between successive peaks on the air-speed record.

The damping factor ~ was computed by the equation

where P is the period in seconds, VI and Vg me the

true air speeds in feet per sewnd at successive maximums, and V’. the air speed at the intervening minimum. The time T required for an oscillation to damp

to one-half amplitude was obtained by the equation

~=–0.693

t

The period and the time to damp to one-half amplitude

were plotted as functions of the mean air speed duriug

the oscillation.

RESULTS AND DISCUSSION

The rwults of the measurements are given in iigures

1to 4. The figures show that the period and the damping vary considerably with speed for a given condition,

between different conditions, and among diiferent

airplanes. The condition with the elevator fixed with

throttle closed (fig. 1) is the only one which is completely covered by the theory at the present time and

for which the stability derivatives may be readily computed. For this condition, all the airplaneswere stable

in the speed ranges covered by the tests. The curves

show an ahnost linear increrise of period with the

velocity of flight and, with the exception of the results

for the O-2H airplane, there is very little diilerence

between the curves for the different airplanes. Longitudinal-stability theory indicates that the period may

be.approximated by the equation

P= O.142(2+a)’W

where V is the velocity in miles per hour, and a is a

variable dependent on the aerodynamic characteristics

but which does not change greatly for conventiomd

airplanes. Computations made on the basis of figure

1 show-that a consixmt value of 1.4 for a is satisfactory

for approximating the period of conventional airplanea

for the speed range of the tests for the power-off elevator fixed condition. The equation would then reduce

to

P= O.262V

The damping is a more critical stability characteristic than the period and, consequently, the damping

curves show more dispersion than those for the period.

The times for an oscillation to damp to one-half amplitude show a slight genaral tendency to decrease with

increasing velocity. h general, the number of cycles

required to damp to one-half amplitude varies inversely

as the period.

The effect of power on the stability characteristics is

shown by a comparison of the curves of figure 2, for

the elevator tied with full throttle, with the curves of

iigure 1. The periods of the oscillations are generally

longer with full throttle than with the throttle closed.

The damping is less, that is, the time required to damp

to one-half amplitude is longer. The power effects me

greateat at low speeds where the propeller thrust and

the ratio of slipstream velocity to forward speed are

greatest. All of the airplaneswith the exception of the
FLIGHT M3L4STI13EMENTSOF ~ STABILITY OF SIWRRAL AmPLJKrms 71

T4M-1 showed a tendency toward dynamic instability

at low speeds with power on. Four airplrmcs, the

O-2H, the I?4B-2, the AT, and the NY-2, actually

became unstable within the speed range covered by the

tests. The instability existed in the form of an increase

in the amplitude of the oscillations with time. No case

of instability in the form of continuous divergence from

steady conditions, corresponding to a positive slope of

the pitching-moment curve or static instability, was

encountered in the teds..

Figures 3 and 4 present the results for the elevatorfree tests. A comparison of figures 1, 2, and 3 shows

8

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Mean indfcufedvelocify,m.p.h.

FIOUREL—PefIcd rinddmnplng of fongftmlhal mciflalionnwith elevator fixed and

fmwa off.

that the stability characteristics are considerably less

affected by freeing the elevator than by applying power.

The periods are slightly shorter with free elevator than

with the elevator tied. The damping is decreased, but

only the results for the O-2H airplane show instability.

Ml the airplanes had statically unbalanced elevators.

For elevatora equipped with mass balances, as is usual

with more modern airplanes, the differences between

the elevator-fixed and elevator-free stability would

probably be less than that recorded.

For most cams power has the same general effect of

decreasing the period and damping with the elevator

free as with it fixed. The O-2H airplane is an exception. This airplane with the elevator iixed was stable

with the throttle closed and unstable with the throttle

open. With elevator free, it was unstable with the

throttle closed and stable with the throttle open.

Table II has been prepared to show the test conditions for which instabili~ was recorded for the wmious

airphmea. As will be noted, only the F–22 and the

T4M-1 were stable for all test conditions and speeds.

The FC2-W2 and the X13M-1 were stable for three of

the four test conditions. The F413-2, AT, and O-2H

airplanw were completely stable for only two conditions. The NY-2 airplane was unstable for only one

condition but, since this airphme had a fixed stabilizer,

the elevator-free runs were made at only one speed.

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Mean indkofed velocify,m.p.h.

Fmwm 3—Pdod and dnrnplng of fongftmhol cmfllatforu wfth elevator fixed and

power on.

The range for periods of oscillations given by the

results for all ted conditions extends from 11 seconds,

for the F–22 airplane at 60 miles per hour in gliding

flight -withthe elevator free, to 64seconds, for the O-2H

@lane at 102 miles per hour with the elevator fixed

and power on. It has been noted previously that, for

the power-off elevator-fixed condition, all airplanes

except the O-2H had approximately the same period at

any given speed. II all test conditions are taken into

consideration, howevar, fairly large variations of the

periods at a given speed axe noted. At 60 miles per

hour, the shortest period is 11 seconds and the longest

23 seconds. At 102 miles per hour, the shortest period

is 23 seconds and the longest 64 seconds. It is of
72 REPORT NO. 578—NATIONAL ADVISORY CO~ FOR AERONAUTICS

interest to note that for most airplanes and test conditions the mssimum period is about 45 seconds.

Tho times for the oscillation to subside to one-half

amplitude vary horn tinity for the cases of instability

previously discussed to 9 seconds for the FC2–W2 airplane in gliding flight at 118 miles per hour with the

elevator fixed. On the basis of the number of cycles,

this damping corresponds to a reduction of the amplitude to on-half in approximately one-fourth cycle.

The damping shows no definite trend with speed of

flight, so ramgesat different speedsare of no importance.

Table HI shows alphabetical ratings of the airpkmes

~ased on measured stability characteristic as compared

with pilots’ ratings based on observed longitudinal

hfeonindicofedvefou-fy,mph.

FIOUEE&—Petidenddewingof longitndfnal wfIlelions with eleva!or frw and

mm OfL

control and handl@ qualitiea. It will be appreciated

that any ratings made on the basis of the measurements

for comparison with the pilots’ ratings can only be

approximate and represent average conditions. The

ratings for the pexiod given in table HI consider the

entire speed rage. The shortest period is designated

A. The periods increase in alphabetical order. The

ratings for damping casider primarily the higher portion of the speed range where most flying is done and

whare most of the airplanes are stable. The greatest

damping is designated A.

The magnitude of the elevator forces and movements

required for normal operation of an airplane, through

their partial dependence on the slope of the pitohingmoment curve, are indirectly related to the stability aa

defined by the period and damping of the longitudinal

oscillation. The relationship has resulted in the use of

the loosely defined piloting term “stillness” to describe

the combined longitudinal stability and control characteristics. The general usage of the term has made it

desirable to make it one of the bases for rating the airplanes, although it is appreciated that the ratings given

depend on the interpretation of only two pilots and

might be somewhat different from those that would

have been obtained had more pilots been consulted.

h table ID, the stiffest airplane has been designated A.

60

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/ /,”

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~ / al I 1 1A I 1 1 1 1

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q 20 u / “

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k \ 5

Pmmrr 4.-Pmicd and dempins of IoI@tudhal willeffom with elevator frw ond

pm-er on.

Because stillmw does include the elevator force and

movements, pilots prepared separate ratings on the

basis of these two items. The airplanewith the heaviest

elevator control and the one requiring the greatest

elevator movements are designated A. A rating was

also prepared on the basis of the amount of pitohing

occurring during flight in rough air. In this case, A

designated the airplane doing the most pitching or

being the unsteadiest in flight in rough air.

A compmison of the different ratings prepared by the

pilots shows that’ the ratings for stiffness are ahnost

identical with those for elevator force. Aside from the

fact that stiffness iE given in four gradations and the

elevator force in three, the T4M-1 airplane is the only
FLIGHT MEASUREMENTS OF THE STABHJTY OF SDVER411 AIRPLANES 73

one for which there is actual disagreement. This airplane was the largest of the group tested and had a

wheel control. The pilots associate heavier forces with

a wheel than with stick control and rate airplanes for

stiffness accordingly. Apparently, at least for the

Committee’s pilots, stifheas refers primarily to elevator

force with consideration taken of the size of the airplane and type of control. The ratings for elevator

movement show that there is a tendency for large

elevator forces to be associated with large elevator

movements. The ratings for pitching in rough air show

no correlation with those for any other item.

In the vibration of springs, the period of oscillation

varies in an inverse ratio to the spring stifhs-s. By

nnalogy the airplane having the shortest period may be

considered the stiffest. From the listings on table HI,

it will be noted that the pilots’ ratings for stillness are

in almost direct opposition to the stiilness as indicated

by the period. There are too many variables involved

to determine the reason for the reveme order for the

two ratings, but the conclusions cannot be drawn that

this reveme order will occur for all airplanes. The

disagreement, however, indicates that elevator forces

and period are not closely enough related to the slope

of the pitding-moment curve to assume that high

forces and a short period will result from a large negative slope to the curve. Neither can the ratings for

damping be correlated with the pilots’ observations of

stitl?nms. Likewise, there is no apparent correlation

between the pilots’ ratings for pitching or unsteadiness

in rough air and either the measured periods or the

damping. It is also of interest to note, in connection

with the lack of correlation of the measured dynamic

stability characteristicsand the characteristics observed

by the pilots, that the instabili~ of the oscillations for

the power-on conditions for several of the airplanes

had no appreciable effect on their flying characteristics

and was not noted by the pilots prior to the tests.

It is evident from the foregoing comparisons that

the dynamic longitudinal stability characteristics, as

deiined by the period and damping of the phugoid

oscillation, are not apparent to the pilot and, therefore,

cannot be taken as an indication of the handling

characteristics of airplanes. If the most desirable

degree of dynamic stability is to be determined, factom

other than the handling characteristics.will have h be

considered. The reaction of the airplane to rough-air

conditions appems to offer a possible basis. The pitching in rough air, tim the present tests, does not appear

to be related to the phugoid oscillation. It may,

however, be related to the short-period oscillation, and

this possibility should perhaps be inv&igated. Fisher

(reference 3) shows that the structural loads imposed

by gusts are influenced by the stability derivatives.

CONCLUSIONS

1. The period of the phugoid longitudinal oscillations

for the eight si.rplanestested varied from 11 seconds at

low speeds to 64 seconds at high speeds. For the

elevator-fixed power~ff condition the period for conventional airplanes may be approximated by the

equation

P= O.262V

2. The maximum damping encountered in the tests

was sufficient to reduce the amplitude of oscillation to

one-half in 9 seconds, or in approximately one-fourth

cycle.

3. Four of the eight airplanes were dynamically

unstable with power on although all were stable with

power off and the elevator fied and only one was

unstable with power off and the elevator free, indicating

the importance of the effect of power upon the stability

characteristics.

4. The dynamic longitudinal stability of airplanes,

as defined by the period and damping of the phugoid

oscillation, has no apparent bearing on the factors from

which pilots judge the handling characteristics.

LANGLEY MWORIAL &EROIiAUTICAL LABORATORY,

NATIONAL ADVISORY Cormmrrwa FOR AERONAUTICS,

LANGLIIIYFIELD, VA., July 16, 19S6.

REFERENCES

1. Zimmerman, Charles H.: An Analyda of Longitudinal

Stability ’in Power-Off Flight with Charts for Use in Deisgn.

T. R. No. 521, N. A.. C. A., 1935.

2. SouM, Hartley A., and Wheatley, John B.: A Comparison

between the Theoretical and Meaaumd Longitudinal

Stability Charad.eristica of an Airplane. T. R. No. 442,

N. A. C. A., 1932.

3. Fisher, H. R.: The Normal Acceleration Experienced by Aeroplanes Flying through Vertical Air Currents. Part I. The

Calculation of the Acceleration Experienced by an Aeroplane

Flying through a Given Gwrt. R. & M. No. 1463, British

A. R. C., 1932.
74 REPORT &-O.678—I?ATTONAL ADVISOi3Y COMMITTEE FOR AERONAUTICS

TABLE I

CHAIUCTERISTICS OF AIRPLANES TESTED

AMe----------------------------------------------------------- Fairc#d

KBM-1

Bi9L3na

Vergff

BIPlane

Mfutsm

T4M-1

Biplane

DQIQuIl#

m--------------------------------------------------------------------- Hfgb-wing Biplane Blplone

monOplane

Biplane

.ti)-------------------------------------------------------

j~%f --------------------------------------------------

e timm ---------------------------------------------------------

Wi&l&fnS (lb./W. fL)-----------------------------------------------

Ob@p.)----------------------------------------------------

‘Ww+%%)___ -.----- .-. -. —-—--- .--- .—. —---------- .——.-....-

s@u~&y~-------------------------------------------------

)-------------------------------------------------------

Chord IOWYI (ft.) ----------------------------------------------------

2%kiGz::::::::::z:::::::::::::z:::::::::::::::::::::::::::

IWnK wttfng (dw.)------------------------------------------------

Airfofl tion -------------------------------------------------

J%

675

14.8

la 6

410

40.0

0.17

h42

6.17

2B

o

N-22

hoo

3.60

.s2

14.0

%4

2S6

2!6

–$L 8

29.7

—.38

242

MgI

9.5

13.9

810

810

4.17

4.17

&o

%X3

:+;

4.17

29a

L18

la o

1~ 6

13.3

2:

–2L 6

32.1

.03

236

4,610

w

13.4

la o

4,%

4m

13.5

1!24

82s3

.—-—-----

hs

.--—— ---

.---.-...--

----------

10

N-22

~o

.-..-.---.,

7.0

.. ... .. .. .

.. ... ... ..

-..--.-—-

c?6tm&

7.0

.26

0

Man aemiynamfodud (fL)------------------------------------- &m

LeadfEz @e to lemf@ ed20Of10= W@ {~**~k/~j~~~~~~ ~~~~~~~~~~~~ 6B

Tall dhnamfoox

Stab~arm @. ft.)----------------------------------------------- :;

span fk)------------------------------------------------------

Elovatcr mea (aq. fL)----------------------------------------------

Elevator hfnge to kadfns edge Of10~er *S {=&L/~j~~~:~~~~~El~~lE –2 o

M.@

c. g. lomtfon:

ReLatfm to K A. O. {~m~m} ~t of IL A. C--–----. —-------- { –g;

Rdative to tbmst axis (ftJ.__-.--.—_. ___–---.-..__..-_. –. 30

1217

19.u

17.0

217

12iw

13.02

23.8

23.1

A:

-g :

.12

SUuMN~JY’OF DYNAMIC~L~F STABLE AND

CONDITIONS AIRPLANES

TESTED

tATING OF LONGITUDINAL STABILITY AND

HANDLING QUALITIES OF AIRPLANES TESTED

r

mfffnas

Messmad obarnoterlstfm

Faetoiaaffaotfngstfffnws

El&

vator

AfI’plane -

th#

Clcsai

Efeveta frw p&dmma

tbrettle dcmd Afrplane

DIWIIP Effra.

force

7

8—_-._. s.

s— ----------- - s.

s—- ——----- . s.

s--------- u Mow M

s --—---------- U:iy:w 67

ub310w91 s.””

S:p–b: ----- u Mew 61

s__–.---.– Um&ohw 70

~P.~

Fafrchffd Z3----- S

AfMl~T-L_ :

NY-2

BmInK F4B-2---- S

s—.------—-- S—-———---

u ky 49

u Low 69

Um%hp m

u: *E 83

s“— -- .---—---

FafmMld 22-----------

Martin T4M-1----------

Comudated Nl-2______

$k@@:W#----------

-----------------

Don@w O+Ef_________

Frdrcbfld FIX&WL_. ... ..-

Martfn XBM-l -----------

Vervffle AT--- S

DouglM O-2H___ s

Fafrcbild FC%TV2 s

Martin XRM-l_ s s--------

A fs u.@to desfgnata afrplanm that are stfffest, rayba tbe greatest elevator

I-emand moromanL do recutpkcbfng in rough ek, an bare the .shotit fmlods

ndthe grmtwt damp@

I

.