Determination of the effect of horizontal-tail flexibility on longitudinal control characteristics

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Title:
Determination of the effect of horizontal-tail flexibility on longitudinal control characteristics
Alternate Title:
NACA wartime reports
Physical Description:
34, 10 p. : ill. ; 28 cm.
Language:
English
Creator:
Harmon, S. M
Langley Aeronautical Laboratory
United States -- National Advisory Committee for Aeronautics
Publisher:
Langley Memorial Aeronautical Laboratory
Place of Publication:
Langley Field, VA
Publication Date:

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

Notes

Summary:
Summary: An iteration method is given for determining the longitudinal control characteristics of a flexible horizontal tail. The method permits factors such as the actual spanwise variation of elasticity and the aerodynamic induction effects due to three-dimensional flow to be accounted for to any degree of accuracy appropriate to a particular case. An analysis is included of the effects of horizontal-tail flexibility on the tail effectiveness, the hinge-moment characteristics, and the control-force gradients in a dive recovery for two modern fighter airplanes. The effects of variations in speed, altitude, elevator stiffness, and center-of-gravity movements are considered. The result of these calculations for speeds below that at which critical compressibility effects occur indicate for the two airplanes significant effects due to the tail flexibility. It appears that the location of the flexural axis of the stabilizer too far behind the aerodynamic center of the tail may cause excessive control forces in a dive recovery at high speeds.
Bibliography:
Includes bibliographic references (p. 29-30).
Statement of Responsibility:
by S.M. Harmon.
General Note:
"Report no. L-45."
General Note:
"Originally issued February 1945 as Advance Confidential Report L5B01."
General Note:
"Report date February 1945."
General Note:
"NACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution of advance research results to an authorized group requiring them for the war effort. They were previously held under a security status but are now unclassified. Some of these reports were not technically edited. All have been reproduced without change in order to expedite general distribution."

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University of Florida
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All applicable rights reserved by the source institution and holding location.
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aleph - 003616150
oclc - 71296653
sobekcm - AA00006258_00001
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AA00006258:00001

Full Text
/ACbh C1


NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS





WARTIME 'l REI PORT
ORIGINALLY ISSUED
February 1945 as
Advance Confidential Report L5B01

DETERMINATION OF THE EFFECT OF HORIZOlTAL-TAIL
FLEXIILITY ON LONGITUDDIAL
CONTROL CHARACTERISTICS
By S. M. Harmon

Langley Memorial Aeronautical Laboratory
Langley Field, Va.


WASHINGTON


NACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution of
advance research results to an authorized group requiring them for the war effort. They were pre-
viously held under a security status but are now unclassified. Some of these reports were not tech-
nically edited. All have been reproduced without change in order to expedite general distribution.


DOCUMENTS DEPARTMENT


L 45





































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in 2011 with funding from
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-71 F ir S3


NACA ACR No. L5B01

IATIOFAL ADVISORY C'O[MITTEE FOR AERONAUTICS


ADVANCE CD;7IDEUTIAL REPORT

DETERP.I"ATIOIT OF THE EFFECT OF HORIZO'ITTAL-TAIL

FLEXI ABILITY ;I! L)UGITUDIlTAL

CONTROL CHARACTER ITICS

By S. ,. Harmnon


SWTP'ARY


An iteration method is given for determining the
longitudinal control characteristics of a flexible
horizontal tail. The i:etho" oermtits factors such as the
actual soasnmise variation of elasticity and the aero-
dynamic induction effects due to three-dimensinal flow
to be accounted for to any degree of accuracy appropriate
to a particular case.

An analysis is included of the effects cf horizontal-
tail flexibility on the tail effectiveness, the hinge-
moment characteristics, and the control-force gradients
in a r'ive r'c-,very for two rr.ciern fighter airplanes. The
effects of variations in speed, altitude, elevator
stiffness, and center-cf-grwavity riovemients are considered.
The results of these calculations for speeds below that
at which critical compressibility effects occur indicate
for the t'.-v airplanes significant effects due to the tail
flexibility. It appears that the location of the flex:ural
axis of the stabilizer too far behind the aerodynamic
center of the tail may cause excessivCe control forces in
a dive recovery at high speeds.


INTRODUCTIAI


The design of tail structures for high-spesd flight
requires special consideration of the factors that








2 CONFIDENTIAL NACA AUK NO. L.BU1


provide sufficient rigidity in torsion in order to
ensure satisfactory control and maneuverability for the
complete speed range. Reference 1 presents an analytical
treatment of the effect of horizontal-tail flexibility
on longitudinal control characteristics. The analysis
of reference 1 is based essentially on the assumption of
a semirigid tail structure having a linear spanwise
twist distribution and on two-dimensional section force
theory. The assumption of a semirigid tail, however,
does not provide for the establishment of the required
equilibrium between the aerodynamic and elastic forces
at every section; consequently there is, in general, no
assurance of the extent to which the arbitrarily chosen
twist distribution represents the distortion of the
actual flexible tail. In addition, the low aspect
ratios commonly employed on tails produce significant
induced effects on the aerodynamic forces, It appears,
therefore, that more reliable predictions of the control
characteristics of a flexible tail could be obtained by
taking account of the actual spanwise variation of
elasticity and of the aerodynamic induction effects.

The present paper presents a method for determining
the control characteristics of a flexible tail that
takes account of factors, such as the actual spanwise
variation of elasticity and the aerodynamic induced
effects, to a degree of accuracy appropriate to any
particular case. The method is based on an iteration
procedure in which the effect of the tail flexibility is
obtained by means of a series formed by the addition of
the incremental effects resulting from each iteration.
The rapidity of the convergence of this series depends on
the degree of rigidity of the tail, and the increments
for the higher-order iterations can usually be estimated
from a knowledge of the values obtained from the preceding
iterations.

In order to illustrate the iteration procedure and
to indicate the magnitude of the effects of tail
flexibility in some typical cases, the present investi-
gation includes an analysis for two modern fighter air-
planes of the effect of horizontal-tail flexibility on
the tail effectiveness, on the hinge-moment charac-
teristics, and on the control-force gradients required
in recovery from a dive. The results of these compu-
tations are given for sea level and for an altitude
of 30,000 feet for a speed range corresponding to
Mach numbers ranging from 0 to 0,72.


CONFIDENTIAL


_^__1__1_____ _


r___l








NACA ACR No. L5B01 CONFIDENTIAL 5


S'. B'DO LS


MI p itching-momient conLtribution of tail about
center of gravity of airplane, positive when
airplane noses up, foot-pounds: Mach number
when used to account for cormpressibility
effects

it tail length, measured from center of gravity of
airplane to elastic axis of tail, feet

e distance from aerodynamic center to flex:ural
center at a section for the tail, positive
when aerodynamic center is ahead of flezural
center, feet

p air density, slugs per cubic foot

V true airspeed, miles per ho-ur

q dynamic pressure, pounds per square foot

(1.4`7)2 ]

T total torque of tail, positive when stabilizer
leading edge tends to nose upward (the
dT
derivative -- represents the torque per
unit span at a tail section), foot-oounds

c wing chord, feet

b span (of wing, unless otherwise indicated), feet

S area (of wing unless otherwise indicated), square
feet

Ce root-mean-square elevator chord, measured behind
hinge line, feet

cw mean aerodynamic chord of wing, feet

y coordinate indicating fixed position along span
from center line

n coordinate indicating variable position along
soan from center line

CONFIDENTIAL







NACA ACR No. L5B01


A aspect ratio

A' fictitious aspect ratio employed in corrections
for compressibility effects (A'V-M2

E ratio of semiperimeter of ellipse to span of
airfoil surface, primed to indicate fictitious
plan form ti played in corrections for
compressibility effects

a two-dimensional lift-curve slope for tail
0t

cL section lift coefficient for tail; primed to
t refer to section lift coefficient of a
fictitious plan form employed in corrections
for compressibility effects

a+ geometric angle of attack of the tail, measured
"R from zero-lift line at section for assumed
rigid tail

e angular deflection of stabilizer due to tail
flexibility, positive when leading edge moves
upward, degrees

at geometric angle of attack of tail, measured from
zero-lift line at section for flexible tail,
degrees atR + 8)

6R elevator deflection at section for assumed rigid
tail, positive when trailing edge moves
downward, degrees

angular deflection of elevator section due to
elevator flexibility, positive when trailing
edge moves downward, degrees

6 elevator deflection at section in flexible tail,
degrees (6R + 0 0)

AR. change in 6R per unit change in normal
acceleration in recovery from dive, degrees
per g


CONFIDENTIAL


CONFIDENTIAL








NACA ACR No. L5BO1


change in Gt
r,


.per unit change in ncrrmal


accelerawLion in rec-ovry from dive,
de-crees oer g


('at



6 0


i'i


C,


c-ic


chacii e in. elevat :r contr l force oer unit
c2han e in noi,,ral accele 1 ration, p*u ..rLn.s
per g

acce leratio n i' gravity, v.2 feet oer second


rate :f charge crf section -anglc of attack ,.ith
elevate :r deflection f-.or constant lift at
Eectiin ifr as-sued Fri id a il


rate of chan je of section -hine-momrient coef-
ficient with secti .n lift c:)efficient for
constant elevator '"eflectijn for assumed
ri id tail


rate of chanh'e of section hinIe-moment cef-
ficient ;..ith section elevator deflection
of assumed rigid tail in degrees for
constant section lift



rate of char-ge of section .itching-irio:rent
coefficient with section ele-.ator deflection
of assumed rigid tail in degrees for constant
secti rin lif


airplane lift coefficient

three-dimensio.nal slope of lift curve for
airplane


rate of change of ele-at:r:' deflection with
airplane lift coefficient for trim for
assumed rigid tail, degrees


CO:r FIDEl:iT AL


" t -
1 L


CO1PFIDE!ITIAL


, C







6 CONFIDENTIAL FACA ACR No. L5B01

dE/dcy rate of change of downwash angle at tail with
wing angle of attack, degrees per degree

1
comoressibility correction factor, where
VI M2 M^ = Mach number

B compressibility correction factor +2
YE'A' + 2/

Ke elevator gearing ratio, as obtained with no
load on tail, radians per foot

VV airplane gross weight, pounds

H total hinge moment on elevator, positive when
leading edge tends to move upward, foot-
pounds
/ H \
Ch elevator hinge-moment coefficient qebe
e e

6Ch
R rate of change of Ch with 6R as obtained
for given movement of elevator control
stick

6Ch
rate of change of Ch with atR over tail
StR

Cm pitching-moment coefficient due to tail about
center of gravity of airplane (N/qSSc,

6Cm
- rate of change of Cm with 5R, as obtained
6NR for given movement of elevator control
stick

-Cm
atR rate of change of C, with atR over tail
-6 at R+5 R
"tR
-65a rate of change of BR for given movement of
\ "aR/ elevator control stick with atR over tail,
Cm -iCm/ atR
with. Cm constant -
6 0m /00


CON1'TDF7TTT AL








NACA ACR No. L5BO1


tty) total torque transmitted by the stabilizer
section at st&tl.n y, foot-pounds
(J bt/2 dit 9



h(y) total hinge moment transmitted b-; elevator
section st stiati-ol y, foot-pounds

dh



CTR(') coefficient of torsinrial rigidity for
t (r. )
stabi lizer at station q. equal to
6i/d,'
wh ere d/d-i is t}iE slope of thie 0 curve
at racT.on -q, pond-f et per d.- ee

CTRe(T) coeffIci e' of torsin -) rigid i -- for -levator
at E t.on e,.u! l to u: '--, "'here dA /d-

i3 3 o.. f c r.,-e z- tati:'rn q.
pou.,-fe tt rtner degree

dGI
-- rate of change of actionn e.levator tf'i.t with
dH tot l hin. e rn) r int t. a ioacl. d !A.l of
ele:,tar, su.r1I' 2. es irieaisured in sa ,Etic
te:zc, degrees ,er fot-p:jund

Subscripts

t tail

w 'jing

e eleva tor

s statilizer

R refers to assumed rigid tail

0, 1,2, etc. numerical subscripts used to indicate the
order of twist iteration


CONPT DEiTIAL


CONFI DEUITIAL








NACA ACR No. L5B01


PRESENTATION OF :ETHOD

Development of Formulas

7}- pitching moment due to the tail about the
center of gravity of an airplane, considered positive in
the nose-up condition, is given by the equation

/ bt/2
M = l-ltq / c7tct dr, + T (1)
\ J-bt/2 /

where T is the tail pitching moment about the flexural
axis of the tail, assumed to be po-ltive when the
leading edge tends to move upward. In conventional
airplanes, the value of T usually increases the
elevator effectiveness numerically by about 5 percent.
If the lifting-line theory of reference 2 is followed,
the lift coefficient c.t in equation (1) is givsn as
a function of the spanwise coordinate y in the form

2 c dc tct ]
ai-bt/2 c-

clt(y) = aat I ~ 5 db- (2)
L /cZt -bt/2 -

in which, for the flexible tail,

t = tR + 9

6 a5- + e

The integral expression in equation (2) represents the
induced downwash angle. The determination of the lift
distribution by means of the lifting-line theory for an
arbitrary angle-of-attack and chord distribution has
received much attention, and numerous methods
(references 2, 5, and 4) are available for obtaining the
solution of equation (2) when the functions at and 6
are given.

The basic consideration in the determination of the
spanwise twist distributions for the stabilizer and


CO:7;IDENTIAL


CONFIMID)'TIAL








NACA ACR No. L5B01


elevator, a(7) and Y(7), for use in equation (2) is
the establishment, at ever-y section, of equili briu
between the aerocyna-i c and the elastic forces acting on
the tsil structure. In the present analysis, 9 and
are determined on nte bsiss of the theory of pure torsion
of tubes (references 5 and 6 ). their r considerations
relating to the torsional effects of the axial stresses
induced by the restraints to the free ,.ar-pir of the
sections of the stabilizer Aind ele--ator and to the effects
of the bending of the ribs can i-e accounted for by
employing the proper par..aeters and following the
procedure of successive appro:r.inations or iterations
described herein under "Iteration .,-thod.'

The aerodynamic twisting mrncent fora s- yaun trial
airfoil section results from. the lift distribution
contributed byr the an.le of a tt=ack. vitch .acts at the
aerodyna-ic center of the section, and the lift
distribution contributed by the elevator deflectio-n,
which acts at its center of pressure. If the section is
unsymmetrical, the lift distribution due to camber
contributes a further increment e o the twisting .,oment.
On the basis of the foregoing assu.moti :ns, if a
symmetrical secLion is used, the applied tviisting n:mTent
across a section dn of the tail is

c N
dT (' ) + c -1 d 5)
IR/,t


In order to obtain the torsional Ir.ornent on the
stabilizer, the moment acting about the elevator hinges
should be deducted. from the total twisting rnmtoent on the
tail, because the elevator hinge moment is normally
transmitted to the fuselage through the torque tube.
The applied twisting moment across a section dr of the
stabilizer, therefore, is given by

dt(n) = dT(I) dh(p) (4)

where dh(r) is the elevator hinge mmr.ent at the
section r of width dn and


dh(r:)= Z + c i- (-- qcj jn (5)


11"?nr7Tp|[TirPT AT.


CO:PI DENTIAL






NACA ACR No. L5BO1


The expression for cLt in equations (3) and (5) is
given in equation (2).
The total torque transmitted by a stabilizer
section y is


t(y) = bt/dd (6)
Jy dn

Division of equation (4) by dir and substitution of the
value obtained for dt/did in equation (6) gives

t) bt/2 1,f
d ddT dh(\


where () and d (1) are given in equations (3)
dnT dn
and (5), respectively. Similarly, the total elevator
hinge moment transmitted by a section y is

hbt/2dh
h(y) : Ti d-8


If the boundary condition that the twist is zero at
the root is assumed, the angles of twist for the
stabilizer and elevator can be expressed in the form


0(Y) I-Ldr1 (9)



((y) d (10)
Jo dr

The torsional-rigidity coefficients for the
stabilizer and elevator, respectively, are defined as


COCiF'DENTIAL


CONFIDENTIAL








NACA ACR No. L5B01 CONFIDENTIAL 11


CTR ) tl
-., d.* dr j-


CT e Iri -


where t (n)l : h r,) refer t-: the tot&l torque
transmitted by- a section rn. S. ubsti turtio.n for d 'd
and d60idrl in equations (9) and (10) results in

S ti

t fl
.Z) = 1 t r dq (11)



,, /"y )
;oJ(.e ') =e1 (12)



where t(n) and h(j) correP ; nding t:: t (,) and hi )
are given by equations (7) anc. (3) r esrectively;.

Equations (2), 7), ( ill) .nd 112) express,
within the lirrmitations -.f the theory involved, the
equilibriumr cnCritions at each sectLion between th-e aero-
dynamic and ela stic torque-s. .,Ihen the aer,'d-namti c,
georrmetric, and structural paraie ter.s e:.x:1ressed in these
equations have been determined, the ti-wee u.il:n:wn
variable, s n, l0, and c>t remain. The s irL.ltane :us
integr -al equations resulting froci the required eq,.io 1 ibrirum
co ndition generally involve c i:I.licated funrctio ns for the
three u.n!rno,'n variables, In practical cases, i-owever, it
has been f:u.nd convenient to determinee the cnaracteriis"tics
of the flexible tail by worzling v.,ith the integral
equations t':ro.igh a procedure of successive approximations
based on an iteration procedure.


I te ration ii .. tho,

The first ancro.ximation to the tail configuration
is taken as the one corresponding- to an assumed rigid
tail; that is, 6 and g are both zero, and the elevator
deflection c and geometric angle of attack of the tail at


COFIJTDEITIAL







NACA ACR No. L5B01


at each section are equal, respectively, to 6R and atR
Corresponding values of c7t0(y) are then determined
from equation (2). Substitution of these values of cLtO(Y)
dT dh
in equations (3) and (5) gives --(9) and -(rj), and
dn dur
the functions t0(y), h0(y), B1(y), and fl(y) can be
determined, respectively, from equations (7), (5), (11),
and (12). The values thus determined for 81 and rl
can then be employed in turn to determine, successively,
new increments in the cl., 0, and / distributions.
The series resulting from the addition of the successive
increments permit the determination of tie control charac-
teristics for the flexible tail.

The general procedure for determining the elevator
effectiveness of the flexible tail is as 'cllwevi: Assume,
as a first approximation, that the geometric angle of
attack at(y) is equal to zero and the elevator
deflection 6(y) is equal to 6R. Compute c t0()
from equation (2). Obtain values for dT/dr and dh/di~
at several spanwise stations from equations (3) and (5),
respectively, with 5(y) = 6R and ctb(y) = cZ,(y).
Integrate equations (7) and (8) to obtain, respectively,
t0(y) and h0(y). Substitute the values of t0(y) and
ho(y) corresponding to t0(o) and hb(~I) into
equations (11) and (12), respectively, and obtain el(Y)
and '1(y) as a first approximation to the twist
distributions. For the second iteration (first twist
iteration), assume that 6(y) = /1(Y) 81(Y) and
that at(y) = 01(y) and compute the corresponding c0t7
distribution frcm equation (2). The substitutions and
integration in equations (3), (5), (7), (8), (11),
and (12) with 6 = 1 61 and c-t = ct in the
manner described for the previous iteration then provide
the second twist increments 02(Y) and 2(7y) For the
next iteration, assume 0(y) = 12(Y) 02(y) and
at(y) = 82(y) and obtain,as described previously, the
third twist increments, 93(y) and p3(y). This
iteration procedure is continued until the increments
for ct, 6, and / become negligible.


CONFIDENTIAL








NACA ACR No. L5B01


The foregoing procedure for obtaining the distri-
butions cit, 0, and is surmrnar.ized in the following
table, which gives the variables employed in each
iteration:
order of twist
"-- teration 0 1 2
Variable -

o a Si E0; i e;.
I I
tLI 0 U 2 C

t 0 1



In applications of the method ,f iteration, it will
be found that in minany cases various anproxim.tiion s may be
employed quite advantageously. Tithus for the first and
second iterations, the equivalent geometric angle-of-
attack distribution can often oe approximated by uniform
and linear distributions, respectively, sa that the
c I distribution rmay be obt-ained -directly fr:.i, the data
of reference 7. which gives results for a wide range of
taper ratios including the low aspect ratios commonly
employed on tails. In other cases, an ap:proximnation to the
cbt distribution can be obtained rapidly by the method
given in reference ".

The fact that the method of iteration is based on a
procedure in which the twist obtained from each iteration
is used to initiate the torque and the twist of the
succeeding iteration permits, in many cases, a rapid
estimation of the twist distributions for the higher-
order iterations. Thus, inasmuch as the twist for a given
torque distribution is directly proportional to the
magnitude of the torque, it follows that the propor-
tionality of the twists obtained at a section in succeeding
iterations will depend on the similarity for the two
iterations of the distributions of torque. (See equa-
tions (11) and (12).) Because the shapes of the torque
and hinge-moment distributions t(y) and h(y)
(equations (7) and (8)) for a particular tail are
usually not very sensitive to the spanwise variations
of 9 and X, the shapes of the twist distributions
tend to resemble the corresponding twist distributions
COIFITDEIITIAL


CONFIDENTIAL







NACA ACR No. L5B01


that initiated them. In these cases, therefore, the
twist distributions for a higher-order iteration may be
estimated from a knowledge of the values obtained in the
preceding iteration by taking the ratio of the twists
for two consecutive iterations at any suitable reference
station. The twist 8 at any station for the iteration
of order n is then given by


8n(y) =
8n-2
S reference station

A similar procedure may be followed to estimate the
increments in $ and cit for the higher-order
iterations.

The foregoing iteration procedure leads to series of
the form

cLt = ct0 + citl + cLt2 + ct3 +

S= 0 + e1 + e2 + 3 +


S= 0 + 1 + $2 + +

From the formulas derived in the preceding section, the
quantities cLtl, 81, and 01 will be noted to contain
the dynamic pressure q as a factor; cLt2, 82, and $2,
which are dependent on the corresponding values obtained
in the preceding iteration, contain q2; and so on. The
lift coefficient and twist at a section may each be
represented, therefore, by a power series-in q. The
coefficients of these series, which depend on the various
aerodynamic, geometric, and structural parameters, in
general vary with speed because of modifications in the
aerodynamic characteristics of the tail introduced
principally through the effects of compressibility.

By the application of these iteration procedures,
the elevator contribution to the pitching moment about
the airplane center of gravity is obtained from
equation (1) as follows:


CONFIDEi!TIAL


CONFIDENTIAL








NACA ACR ;l. L5B01 CONFIDENTIAL 15


f ib




where the ni irieri cal sub crinots reier to the orcer of the
twist it erat i on ad In = 2t t i ) + h- : ( See
equation: (7 and ) n-jci ?i n 1.1 t:;.a be written

:= i.:, + [ + + .(

The elev-tc.r r.-.er.,l se.-e Z .;, :taine fr: mr the
value *' the n.amlc pressure q .i.t *:ez the riht-
hand si e :f e:iuati.:on (li. e:ual to -er:.

In- a s' i ile r manner the elev..tc'r in e mo.,ernt f':or
the fle 1 ble tail be .:bt -ne.d as

H = E- + l: + 2 + (15)

where Hn =h( n ')

-.n iteration ':rtcedure .n:.:..m-L 1 t: th1 t eescri o ed for
the elevator effectiveness a I. I::e f. lo ed t:. det.er.iin
the effect o:f angle of attack ,of tlie tail .-.id e:-::re ssi :ns
for i.i -nd H similar in form' t:. equ ti:ons (1 1)
and (15 i will te o btaine d.

The tendency noted. e.-.:us l,- v. it regard to the
similarity in the respective distribut-ons for 9, ;,
and" c for the higher-crdier i tereti on?_s tiil le.ad in
many c "ae- t. cons ier- e ] e sir.',plificHt ion in the
iteration pr ocedure for deter innLec the effect of t.il
flex;:i'oility on the citc-hing rrmo.ment I1: and tae hi ge
im:.ent H. The i ncre.reents in .and I: f:r the higher-
order L-terat-ions can tnerefo're be obtained in these
cases b, means of the following r! f 1t i rlnshi ps :


E .(16)
Sin r.



H = --- (17)
Li i )


C IFIDElTTIAL







CnCa ACR No. L5B01


The forces and resulting twists on the tail structure
are directly proportional to the tail angle of attack and
the elevator deflection corresponding to the values that
would be obtained in an assumed rigid structure or
to atR and 5R, respectively. (See table III.) The
differentiation of equations (1),) and (15) with respect
to UtR and 5R and conversion to the nondimensional
form gives, therefore, for the flexible tail the parameters
6Cm 6Cm 6Ch 6Ch
C Cm, I, and -.
6 R' E tR 65R atR


Corrections for Compressibility

Inasmuch as the aerodynamic charteristics of the
tail are affected to an important extent by compressi-
bility, the effects of compressibility must be considered
in predictions for the control characteristics of the
tail. In the absence of experimental data, the following
corrections for compressibility, based on the theory of
small perturbations, which is discussed in more detail
in reference 9, are summarized for the parameters
involved in the present analysis. These corrections may
be applied at speeds below that at which the critical
compressibility effects occur or up to a Mach number of
approximately 0.60 in conventional airplanes.

The span-load distribution in a c-mnoressible flow
should be computed on the basis of a fictitious aspect
ratio equal to the true aspect ratio, reduced by the
factor l 2, and the resulting values of clt
obtained for this reduced fictitious aspect ratio should
be multiplied by 1/ T.-2. Thus, if the primes denote
values obtained for the fictitious airplane,

At' =A M2
and
ct'

ill I2
C 't ':


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NACA ACR No. L5B01


The values for the parameters z and tc)
% R/ z ,I
as obtained from low-speed data should be multiplied by
the factor 1/ .2

The slope cf the lift-coefficient curve in three-
dimensional incompressible flow is corrected for
compressibility by multiplying it by the factor

EAt + 2
B :
tE'vt, + e

in which the symbols Z and E' r.eur jesnt the potential-
flow correction for chord effect in inco.ipressible and
comoressible flow, respectively. This correction applies
specifically to elliptical plan forr-s but is approximately
correct for other plan forms. In incorpressible flow,
E is the ratio of the semniperimeter of the ellipse to
the span of the airfoil, as indicated in reference 10. In
compressible flow, the ratio E' is that for the
fictitious elliptical tail of span bt and aspect
ratio At'.

The derivative rd/daw for compressible flow is
computed on the basis of a fictitious tail length equal
to the true tail length increased by the factor 1/V M,1
and the fictitious aspect ratios for the wing and tail
equal to the true aspect ratios reduced by the factor
I .


APILICATIOH OF METHOD

Data for Calculations


Calculations were made by the foregoing procedure
of iterations for the effect of tail flexibility on the
longitudinal control characteristics for t, fighter airplanes designated airplanes A and B in
order to illustrate the method and to obtain quantitative
results for some typical cases. The computations were
made, for both airplanes, of the tail effectiveness, the
hinge-moment characteristics, and the control-force
gradients required in recovery from Jives at sea level
and at an altitude of 50,000 feet.


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NACA ACR No. L5B01


Figures 1 and 2 show the plan forms and dimensions
of the horizontal tails for airplanes A and B,
respectively. These figures also give the location of
the flexural axis as determined from stabilizer torsional-
rigidity tests made in connection with the present
investigation. The torsional-rigidity tests for air-
plane A were made by the Langley Flight Research Division
and for airplane B by the Langley Aircraft Loads Division.
Both the stabilizer and the elevator for airplane A are
metal covered, whereas airplane B has a metal-covered
stabilizer and a fabric-covered elevator.

The aerodynrnamic parameters for the two airplanes
were based on low-speed data corrected for compressibility
effects, essentially as described previously, ?'' basic
data employed in the calculations, the source from which
these data were obtained, and the c :-.,:essibility
corrections aoplied are given in tables I and TI, Average
values along the span were assured for the parameters

and I- which were obtained on the


basis of estimates for C/Ch~5R and C j/actR from
low-speed flight data. In the computations, the aero-
dynamic centers of the tail sections were assumed to be at
the quarter-chord points of the sections.

The tail-stiffness data for the calculations were
obtained from flexibility tests made on the stabilizer
and elevator of the full-size airplanes. In order to
clarify the relationship of the flexibility-test results
to actual flight conditions, the procedure for the
determination of the stiffness data is described herein
in some detail. The stabilizer tests were made by
applying a concentrated torsional couple at a section
near one tip of the stabilizer and mnesuring the
torsional deflections at several stations along the span
with reference to a station on the unloaded half of the
stabilizer. The elevator-flexibility tests were made by
loading bags containing lead shot or sand on one-half of
the elevator along a line one-third of the chord behind
the hinge with the elevator locked in position. Ir
spanwise loading on the elevator surface corresponded
approximately to a uniform distribution. T.- deflections
of the elevator on the loaded side were measured at


CONI!DEITI AL


COITFIDENTIAL








ITACA ACR No. L5B01


several stations with resC ect co a reference station
ta::en on-L the unlc added half of che elev atr.

Tests were als:, performed on one rib of the
elevator of airplane B at a station at:out -.5 feet from
the fuselagi e centter line to obtain the effect on the
di tortion 1alo ng the chard of a c hord i se loading that
simulated a triangular distribution nore closelyr thE.n
the one just descriLed (o ad mrncertated at one-third
of chord behind hin2er e Iii tne e tests, r' asr.er:enr' ts ..ere
taken of the deflecti.n- -t vetr;i sill intervals alone
the chord (5 dial a:-es for an 11 -i.-ichi chord). The
results indicated that v1ith botr h ty es of loading the
distortions :ai. ng the chord. 'er.. e el -iu anO- t i-at tie
deflect ins along toe chord follor i -. a str-saint litn.
It vas assumed, th r'-fore, that the i.ea u .u-d an.;ular
deflection due to tti'- leatjor il -.: bi iiity c. uld be
considered as an e.Aquivale-t chran.s in el '.;.'tcr dIefl-ction
with no change in the canTIL r of the elev/at.r sur face.

The tail-stiffness daci fo'r air. i:sne A are shtorn in
figure 5. The results f'r the stai;:i.liaer give in this
figure are based on a cncrentrrited torque of f'3 foot-
pounds applied :. the ri.zht half of the staliliLer at a
station 6.5 0 feet from the Lfu.ela-e c:'enter line, and the
data for the elevator are based on a total hin-e rm;iicoent
of 3.3 foot-..un-ds distributed on the right half of the
elevator in the manner descriced previously.

The tail-stiffriess data for ailrlane 3 are shown in
figure 4. The results -or the stabilizer given in this
figure are based on a concentrated torque of 50- foot-
pounds :applied to the left half of tile staliiizer at a
station 5.92 feet from the fuselage center line, and the
elevator data in figure L? are based on a total hinge
moment of 60 foot-pDunds distributed on the right half
of the elevator in the manner described, previously.


Procedure for Calculations

With the aid of the foregoirng dates, the srcanwise
distributions for clt, U, and 9' were detsermlined for
several iterations. The clt distributions were obtained
by the usual methods based on lifting-lin= theory. Tn
the comoucations, the stabilizers for the two airplanes
were assumed to act in torsion similarly to tubes so that


C'9PIIDEiNTIAL


CO'lII DEITIAL







NACA ACR No. L5BO1


the distributions of stabilizer twist resulting from the
aerodynamic forces were calculated by means of
equations (7) and (11) by use of the stabilizer torsional-
rigidity coefficients shown in figures 3 and 4. Because
the results of the elevator-flexibility tests for both
airplanes indicated the probability that the static loads
on the elevator did not act in pure torsion (see figs. "3
and 4 for d9/dH near root and tip sections), it was
believed practical in the present investigation to modify
the method described previously for determining '. The
twist distributions due to elevator flexibility were
obtained, therefore, by multiplying the total hinge
moment acting on each half of the elevator by the rigidity
factors dZ(y) shown in figures 3 and 4. This method
dH
for determining the elevator twist is strictly correct
only if the loading on the elevator surface in the static
tests simulated the loading in flight. For the present
investigation, however, the error from this source is not
expected to be important. Some computations with
different assumed elevator flexibilities, which are
discussed in the section entitled "Results and Discussion",
indicate that the calculated results are not sensitive
to reasonable variations in the elevator flexibility.

The increments for ct, 0, and V that were
obtained in the various iterations were used to compute
the pitching moment about the airplane center of
gravity M by means of equations (15) and (14) and to
compute the elevator hinge moment H by means of the
corresponding equation (15). The results for M and H
were then converted into the nondimensional form as the
derivatives 6Cm/6atR, 6Cm/65R, 6Ch/6atR, and 6Ch/-6R.
The details of the computations for determining 6Cm/66R
and 6Ch/66R for airplane B for a Mach number
of 0.60 at sea level are shown in table III.

The change in control force per unit change in
normal acceleration in recovery from a dive was computed
by means of the following formula:

Fn = a6 R + at -- tRKee2b (18)
(6,5R 5atR R)


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NACA ACR No. L5B01 CONFIDENTIAL 21


where CpR snd AatR refer to the changes in bR
and at- Fer unit change in norm-al acceleration in terms
of g and ,here Kf is the elevator gearing rati., In


d
1 Wp I1 (C.n
L&6R = -r t- j
q T tR IR
7FLR

+ Lt-- (19)





and


La = + 2.oZt (20)
r 4,a \ %,


In equation ('7) the tw terms on the' right-hand side
enclosed in thne brack:-ets represent the oprt 'of .,
required to trim the airaolare, and the third term
represents the part of ti'R required to balance the
effects of rotation of the tail during the steady chliSe
of the Ditching motion. In the.e equations, 'hL-J/. R,
"Ch/}-'ct, CCin 6R, R' ~AQtR, and (--J, are the
h -' citR, 'C.U-n..' L5 R.m' t

values for the flexible tail -,btained by the iteration
procedure. If values for these parameters for the
assumed rigid tail are used in equations (18), (19),
and (20), the ccntr l-force gradient for the rigid
tail FnR is obtained. The values for the d-riva-
5R
tive I ) for airplanes A and B were based on
d" L/R
flight results at an indicated airspeed of aoproxi-
mately 200 miles cer -hour. A value of --L equal
(dc^L


COniFTDEITTIAL







NACA ACR No. L5BOl


to -5.20 was obtained for airplane A based on a center-
of-gravity location of 28 percent of the mean aerodynamic
chord; whereas a value of -3.26 was obtained for air-
plane B based on a center-of-gravity location of
29.5 percent of the mean aerodynamic chord. The effect
on Fn and FnR of movements of the airplane center of
gravity was investigated by assuming different values
for dR .
dCL R
dE
The variation of -- with speed as determined by
daw
means of the theoretical compressibility corrections
noted previously, in conjunction with the design charts
of reference 11, indicated a negligible change in this
parameter up to a Mach number of 0.60. It was therefore
considered sufficiently accurate in the present compu-
tations to assume constant values for de/daw. The
/dR\
values for however, were corrected for compressi-

bility effects by multiplying the low-speed value by the
factor 1/B corresponding to an average between the wing
and tail.


RESULTS AND DISCUSSION


The results of the calculations are presented in
table III and in figures 5 to 9. Table III shows the
results obtained for the various iterations in
determining 6Cm/66R and 6Ch/o6R for airplane B at a
Mach number of 0.60 at sea level. Figure 5 shows the
spanwise variation of tail angle of attack at and
elevator deflection 6 resulting from an application of
the elevator control equivalent to unit deflection for
the assumed rigid tail, as obtained from table !II.
Figures 6 to 9 show tie effects of horizontal-tail
flexibility on the longitudinal control characteristics
for airplanes A and B for a range of true airspeeds
from 0 to 550 miles per hour at sea level and friomi 0
to 490 miles per hour at an altitude of 30,000 feet.
This range of true airspeed corresponds to a Mach number
range from 0 to 0.72. The speed for each altitude
corresponding to a Mach number of 0.60, which represents


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NASA ACR No. L5B03


the limit for which the theoretical compressibility
corrections employed in tne present corrputations are
believed to be reliable, is indicated, on figures o to '.
The resI.lt for the M"ach numbers higher than 0.i0 are
included in the figures in order to -ive an indication
of the trend of the flex.-ibility effects. The results of
the coimDutations for a ach nrier of 0.60 st sea level
are summ.rari -ed for both airclIan? s in tale IV.

Table III indica es that tlhe c-.,'onv.egence of the
iteratiocn procedure is very raniid. This con"ergence, as
indicated for rCI/; 5:. and C.-i% R for airplane .,
is tt:y"ic il for the other p-ir:niete in thle flex;1 ible tail
for both airolane. Thus, ii tn1 conributioc-n Otctained
for each successive iter nation is ex.r::sed a: a ratio of
that obtained for the Leroth-order twist iteration,

-r'iC,,/ 5F R
S1 -0.301 +0.0727 0.017 +U 0.008 $ 0.7
'- rr.FR '. .'"'r


SCh/ci. c
oC I .", ".;ol
0= 0.2411 0 0.0101 F D 0.;3u


The subsequent comrpari :son illustrates the number of
twist iterations required by the regular procedure of
iteration in order to determine the longitudinal control
characteristics f:or a flexible tail. The results obtained
from table III as given by equations ('21), whic'n utilized
three regular twist iterations, will be compared with
results obtained by the use of one and t.%o regular twist
iterations, respectively, in conjunction with the
relationship s given by equa ,ions ( 6) and ,17) for
estimating .. n and Hn f:r the twist iterations of
higher order than one and two, r-spectively. Thus, by
use of one regular twist iteration,


= 1- o.01 + 0.0905 0.0272 + 0.0081, = 0.771
o rr,/. R

22-)
6C h/5R
= 1 -0.241 + 0.0581 0.o01o +0.00558 = 0.3o6
bC hR/, R


C r- FI DIIT i AL


COITFIDENTIAL







NACA ACR No. L5B01


By use of two regular twist iterations,


1 0.301+0.0727 0.0176+0.00425 = 0.759

(23)

=1- 0.21 +0.0557 -.0129.+0.00300 = 0.805
6Chi-R/6

The comparison of the results shown in equations (22)
with those given by equations (21) indicates that the use
of one regular twist iteration in conjunction with the
simple relationships given by equations (16) and (17) is
sufficient to determine the effect of tail flexibility
to an accuracy of the order of 1 percent.

Figures 6 and 7 show for airplanes A and B,
respectively, the ratio of the tail effectiveness and
hinge-moment parameters as obtained in the actual flexible
tail to those obtained for the assumed rigid tail. These
figures indicate, for the complete range of airspeeds for
both airplanes, that the parameters 6Cm/66R, 6Cm/6~tR'
6Ch/66R, and 6Ch/ atR are reduced numerically because

of the tail flexibility and that the parameters
VatR
6Ch/6 R
and are increased numerically because of this
6Cm/6 R
factor. The numerical reduction in 6Cm/66R caused by
tail flexibility is due to the fact that the center of
pressure of the lift resulting from the elevator
deflection is behind the flexural axis (see figs. 1 and 2
for flexural-axis locations) and the resulting torsional
moment twists the stabilizer in a manner that reduces
the tail lift. The numerical reduction in 6Cm/66R is
also due to the negative value of 6Ch/I6R, which causes
the elevator to twist and thus to reduce the elevator
deflection.


CONFI DENTAL


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NACA ACR No. L5B01


The numerical reduction in 6Cm/6atR due to tail
flexibility resulted because the location of the flexural
axis of the stabilizer is ahead of the aerodynamic center
and because the value of 6Ch/datp is negative. The
respective numerical reduction in the values for cCa/6',
and 6Ch/ atR due to the tail flexibility resulted
principally from the fact that each of these parameters
for the rigid tail is negative and the elevator twist
therefore numerically reduces the hinge moment in each
case. The forward position of the stabilizer flexural
axis relative to the center of pressure of the lift
contributed by the elevator tended, however, to increase
numerically the value of 6Ch/c0,R due to the stabilizer
twist (6 is increased by -9); similarly, the location
of the flexural axis of the stabilizer ahead of its
aerodynamic center tended to increase numerically the
value for C-i/,-at.,

Figures 6 and 7 indicate that, in _ener&l, the
effects of tail flexibility vary with speed and altitude
approximately as the dynamic pressure modified, of
course, by the relative compressibility effects. This
variation with speed and altitude results from the raid
convergence of the oower series in q, which causes the
terms in q of higher order than unity to be compara-
tively small. In some cases, however, at very high
e 6 Ch/i atR
soeeds see figs. 7(b) and 3, for and FnFn,,
( 6ChR/o atR
respectively), the effects of the terms in q of higher
power than unity become comparatively significant.

Computations were made to estimate the effect on the
parameters shown in figures 6 and 7 of increasing the
elevator stiffness at each section by 12.5 percent of the
average elevator stiffness. The results of these
computations indicated that, for a Mach number of 0.60
at sea level, the ratios of the parameters Cmin/'6R,
6Cjh/6pR, and Ch/I6atR to the corresponding ratios for
the assumed rigid tail would be increased in the order
of 2.5 percent as compared with those shown in figures 6
and 7, and the corresponding ratio for 6Cm/IatR would
be increased by less than 1 percent; whereas, at
50,000 feet for the same Mach number, the effect of the


CONFIDENTIAL


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MACA ACR No. L5B01


increased elevator stiffness would be about 0.40 of the
corresponding foregoing effects indicated at sea level.

It can be noted from figures 6 and 7 that, provided
critical compressibility effects do.not appear, elevator
reversal for both airplanes A and B does not occur up to
a speed corresponding to a ,'ach number of 0.72.

Figures 8 and 9 present a comparison of the control-
force gradients in recovery from dives as obtained for
the actual flexible tail and assumed rigid tail. It
should be noted in these figures that the required motions
of the elevator control stick per unit g are not
necessarily equal for the flexible and assumed rigid
tails. Figure 8 gives the results for airplane A at sea
level and at ani altitude of 30,000 feet. This figure
shows the variation with airspeed of Fn and the
/d6
ratio Fn/FnR for values of R in incompressible


flow of -3.2 and -1.60. These values of -5.2 and -1.60
correspond, respectively, to cen.ter-of-gravity locations
at 28 percent and approximately 31 percent of the mean
aerodynamic chord. Figure 8 shows that flexibility of
the tail increases the control-force gradient and that
this increase for a Mach number of 0.60 amounts to
12 percent at sea level and 3.5 percent at 50,000 feet
altitude. This figure also shows that a rearward movement
of the canter of gravity of approximately 3 percent of
the mean aerodynamic chord causes a small reduction in
the ratio F / The results for the airplane B at

sea level and at altitude for values of -- R in


incompressible flow of -3.26 and -6.00 are presented in
figure 9. These values of -5.26 and -6.00 correspond,
respectively, to center-of-gravity locations at 29.5 percent
and approximately 25 percent of the mean aerodynamic
chord. The figure shows, 'or airplane B for a ran'-. of
airspeeds at the altitudes considered, a small increase
in the control-force gradient due to tail flexibility, or
approximately one-half of that indicated in figure 8 for
airplane A. Figure 9 also shows that a forward movemrn:n
of the center of gravity of approximately 't.5 percent of
the mean aerodvinamic chord causes a small increase in the
ratio Fn/FnR.

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IT ACA ACR IPo. LSBOl1


An e::amr. nation of equations (18), (10), and (20)
indicates that the control-force gradient in a dive
recovery ,as.y be influenced to an iimnDortant extent by the
C },/j s,
aerod'-namic Cparam eters --- C I and 6

The results of the present anaiy.is show for both air-
planes A and B that the first two of these paraneteirs are
affected by, tail fle:ibi lity in a manner to increase Fn;
whereas 6Ci6/',att is affected by this factor in a manner
to reduce Fn. As noted previously, the numerical reduction
in 'Cm/,'atp obtained in the present comvputa aions for
airplanes A and B is caused principally by the 1-,cartion
of the flexural exis of the stabilizer ahed of itr
aerodynamic c-nter and Lb' the nes eti e value
of C h/C, att. In order to obtain an indication cf the
importance of the change in oCrnm//"Ct due to tail
flexibility for the c:rtr.ol-f:,rce gradient in a dive
recovery, comoutations were made f.or the two airplanes in
which it was assumed that --- = which is roughly
octR '-,tR
equivalent in the present case to a rearward movement ,of
the flexural axis back to the aerodynamic center. These
computations indicated, for a Mach number of 0..60 at sea
level, that in the case of airplane A the ratio F,'/FnR
would be increased, from 1.12 to 1.26, and in the case of
airplane B this ratio vould be increased from 1.0'
to 1.075. On the basis of the present analysis it appears,
therefore, that the location of the flexural axis of the
stabilizer too far behind the aerodynamic center of the
tail, could cause excessive control forces in a dive
recov-.ry at high speeds.



COiC LUSI 0.TS


An iteration method for determining the effect of
tail flexibility on the longitudinal control charac-
teristics of airplanes was applied to two modern fighter
airplanes and was found to provide a practical procedure
for the determination of these effects.


CONFIDENTIAL


COITFIDEI'TTAL









28 CO;0'I,-2:'T. AL :TA.A ACR No. L5B01


The results of calculations to determine the effect
of tail flexibility on the longitudinal control charac-
teristics for two fighter airplanes indicate that the
longitudinal control characteristics are affected to a
significant extent at high szeed.s by this factor. The
follc. ng conclusions apply to results for these airplanes
at speeds below that at which critical compressibility
effects occur:

1. The magnitude of the ta l-flexibility effects,
in general, varied approximately as the d:-.r.c pressure -
modified, of course, by the relative compressibility
effects. In some cases at very high speeds, however,
the effects of the terms containing, the dynamic pressure
of powers ,grater than unity becalie co.mpaaratively
significant.

2. Tail flexibility was found to reduce significantly
the rates of change of pit'-hir_.; moment and hinge moment
with elevator deflection and tail angle of attack.

3. The control-force gradients in a dive recovery
were increased because of tail flexibility.

14. Rearward movemients of the airplane center of
gravity tended to decrease the effects of the tail
flexibility on the control-force gradient; whereas
forward movements of the airplane center of gravity
tended to increase the -agnitude of these effects.

5. The location of the flexural axis of the
stabilizer relative to the aerodynamic center of the
tail is an important design consideration with regard
to the. magnitude of the tail-flexibility effects. The
location of the flexural axis of the stabilizer too far
behind the aerodynxamic canter could cause excessive
control forces in a dive recovery at high speeds.


Langley Memorial Aeronautical Laboratory
National Advisory Committee for Aeronautics
Langley Field, Va.


CC' F :D:- T I'A







NACA ACR No. L5B01


REFERENCES

1. Collar, A. R., and Grinstead, F.: The Effect of
Structural Flexibility of Tailplane, Elevator,
and Fuselage of Longitudinal Control and Stability.
Rep. No. S. M. E. 5227, British R.A.E., Sept. l192,
and Addendum, Rep. No. S. M. E. 3227a. Oct. 19L2.

2. Glauert, H.: The Elements of Aerofoil and Airscrew
Theory. Cambridge Univ. Press, 1926.

3. Pearson, H. A.: Span Load Distribution for Tapered
Wings with Partial-Span Flaps. NACA Rep. No. 535,
1937.

4. Hildebrand, Francis B.: A Least-Squares Procedure
for the Solution of the Lifting-Line Integral
Equation. NACA TN No. 925, 1954.

5. Trayer, George W., and March H. WV.: The Torsion of
Members Having Sections Common in Aircraft
Construction. IACA Rep. No. 35, 1950.

6. Timoshenko, S.: Theory of Elasticity. First ed.
McGraw-Hill Book Co., Inc., 1934.

7. Anderson, Ray:mond F.: Determination of the Charac-
teristics of Tapered Wings. iJACA Rep. No. 572,
1956.

8. Schrenk, 0.: A Simple Approximation Method for
Obtaining the Spanwise Lift Distribution.
NACA TM No. 918, 1940.

9. Goldstein, S., and Young, A. D.: The Linear
Perturbation Theory of Compressible Flow, with
Applications to Wind-Tunnel Interference.
6865, Ae. 2262, F.M. 601, British A.R.C., July 6,
1953.

10. Jones, Robert T.: Correction of the Lifting-Line
Theory for the Effect of the Chord. NACA TN
No. 817, 1941.

11. Silverstein, Abe, and Katzoff, S.: Design Charts
for Predicting Downwash Angles and Wake Charac-
teristics behind Plain and Flapped Wings.
NACA Rep. No. 648, 1939.


CO NFIDENT IAL


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TACA ACR No. L5B01


12. Ames, Milton B., Jr., and Sears, Richard I.:
Determination of Control-Surface Characteristics
from NACA Plain-Flap and Tab Data. NACA Rep.
No. 721, 1941.


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NACA ACR No. L5BO1


CONFIDENTIAL


TABLE I
DArA PR CALUrLATroNs PHYSICAL IAD GEOIETIR C CHRALcruIsrics
[Date furnlmbed by manufatourer]


Ie I t. *l I re- Tall Eleeator r.ek ratill
Airplane area n ynamic ire.. apan, c atord length a
*lrplrne i '3 a e: o : be e -^ | ri J n/ ( t)
tlb) ratio cnord :r c Lb ar t t
a.4, 1t) n, r. (q rt) (a, fI) alr) it)
ift) 'r


A 12,000 300 5.55 7.28 55 16 1.19 21.4 0.66
B 7.660 256 5.815 6.6. 1.1.1 15.2 1.01 15.5 .57









IABLE II
DATA FOR CALCOLATrOBS IAROYrTfN1lC PARAMIBRS


alue in .,rretiorn tor
Parameter Ir.cu pr ees le Source or data
rlI com prer an L Ltyv

Altiplane A

c'O r'Rctit M-0.0086 Reference lI Multiply by -


ao 0 ..9) Asaumed Do.

b6ch d'R I -0.00686 Linpubllised data based 3n Do.
t d Cb/oot = -0.00218 and
i6ch, cit,' -0.0O 2 dCh 6b = -0.00804 None

(at/AI 'R )-o.66 .Rferenee 12 Bone

dr do 0.50 Reference 11 Assumed cnatant

0.077 reference 7 Multiply Dy B
(.dB dCLR Based on unnuorllbad data Mu.ltipL by 1. B:
('dR dCL' R for c.g. at 28 percent M.A.C. averede for wing and *11

Airplane B

(m/6 -O.0091OO Reference 12 Multiply by -
ct 1/_-M5-
o 0.09 Assumed Do.

(-ch."6r.-' -0.060b5 ELstlated frrm unpublianed DO.
''Lt fli ht JaLt Eb.sed on
.C 6-tR = -0.000511 and ----- -
Sc" '"c I' R -0.00625 "r, dci = -0.u06b5 one


'tR RR) -t 0.5c, beferernrce 1Ie None

a( ao .'0 Referir.:e 11 Aa Lied constant


Referernc 7
Eattmatea from .npucrllahed
rllArt a.ta for c.g. at
-).5 percbret .A.C.


Multiply by B

Multiply by I/a;
a&erage for wing and talA


NATIONAL ADVISORY
OlMMIiTEE POR AERONAUTICS


aVal.e giAven to f3r a sectin at L.5 ft. from fu3elg6e center line: appropriate veluas ere used for otber
sec tions.
Average *:onatranTr valj were used.
CONFIDENTIAL










NACA ACR No. L5BO1


-42


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NACA ACR No. L5B01


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NACA ACR No. L5B01 CONFIDENTIAL 34


T AB' IV.- COMPAlRIS 'i OF EFFECT OF iCHRII.'IITAL-TAI
FJE' ..FI.;I .T '. i GIT JDIpi L R 0 ROLC CHARACTERISTICS
FOR AIRP'L.AIE.3 A AI, AT' A .'A.!: 1' P.41BEFR
c'F 0.o0 AT ;EA E"'-L



FPgra'reter ratio Airplu A Alirpl1 9r 5


6rm /SR ,. 0.
6-',-I F/t_, IJ ''U i-

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tm tR


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FR
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,'ATITOIIAL ADVISORY
CO.T ITTEE FOR AERONAUTICS


CONF IDEI:T rA;






NACA ACR No. L5B01


CONFIDENTIAL


362' I ~--1-


f/ useaye,
t /


'_ CeC/~ lne
'-- F/e ura/ oxis



NATIONAL ADVI:ljRI
COMMiITEE FOR A-iiONAUTICS


o Location of test points
CONFIDENTIAL


Fiure / Plan form of ta'/ sem,'aDon showing siab/lizer
and e/evotor c//menr5,vs. A irp/'a ne A; hor/zonlo/
to// area, ss square feet; e/e vaor area, zz spoore
feel ba/once area, 7. percent of elevoaor areo.
ONFIDENTUAL


NATIONAL ADVISORY
o Local/or of test points comi FOR AERONAunTCS
gure 2.- Plan form of to/a sem/spon sho/wng stabi//zer
and elevator d/mens/ons. A rp/lne B; horizontal toll
orea, 4.1/ spare feet elevo or rea oS 1305 puore feet;bA/ance
area, 0.24 Spoare feet. NFcomEN AL


Figs. 1,2







NACA ACR No. L5B01


-9

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F/are 3.xperirne nta data for f/lexb,','/ of
/o.'zon.al Co.r. o Airane A. Dati from Je ts
Tr ade. by, L. F, ,Fsearch ,i/son..
7?L i/ -


CO FIDEI TL4L


_ H = 3.3 P-1h_


Fig. 3


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NACA ACR.No. L5B01


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/ ArIONAL ADY'i,0i f
/ COM IITE F0 AEO O UII CS
./ ---- -/ __ -- --.
,''4


O -O __NFI ENTI 0
0 2 3 4 6 7
D5/sance from taol cerner Ine, ft
F.'re 4.-(cxper/mental cata for flexiblily of
horizontal tal/. .A .-p/ane 8. ODaLa from tests
rnad y L iorl.ey Aircraft Loaos D/ls/ton.


Fig. 4





NACA ACR No. L5B01


12




ic-
-d0




NATI NAL ADVISORY
/ OMMITTIE FOR AIUQONAUTICS

I- CoNFDENTIA I IO
S / 2 3 4 5 6
Didsonce From fAol conerl/hen

Figure .- D,slrbuon of lod en y /e o aooc oa'a'ce/evor
def/eclion in a lexible Zoll resul,/tng omr an opp/-
colon of lte e levador control elu'va/en, to a~n
defledton for- he assumed rigid lo/. Airplane B.
Mach num ber.60ol sea /eve/l;, =/ o.Xf=0?


Fig. 5






NACA ACR No. L5BO1


S(ONFniENTI \L
/.4

/. --/







S-.0 .____ ____ __

,:1:


tO


.8


6





.2


0


FI
Atlude '
Sea le"e/


1 Indicates -.md,/ny speed
for /h'chA ca/cu/oaed
comroressibilAt correcticrns
are be,eved relmaie



NAli AL A DVSORf
CONFIDEJNTIAL. C(MuMirlI FRAE Al ONAuTIC


0 /OC 200 J00 400
True o'rspeed rqnph


500 600


() Effect/veness porarmetiers.
Fyore 6.-Effeci of norizonaa/-la/l flexbilbty
on7 /onlllud/ a/-contrc/ parameters. Airplane A.


Fig. 6a






NACA ACR No. L5B01


I-k
^*a

*-o


.6


.6



1 .4


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0
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4--

Altitude

Sea e ve/


SIndca/tes I/mitfln speed
for which cau/caoled
comnoress'h ibi correct ons
are beheved rehlail~e.



NfAION L ADVI ORf
COl FDEITLAL r.o MITTi OR A UTICS


-,300


9 /00 2906


,rue aorspeed, mph

i) Hinae-moment ,.jrometers.
Fgure 6. -Conwc/ded.


200 500 600


Fig. 6b






NACA ACR No. L5B01


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Sea level ...
30,000 \

-i Ind/COtes h ,mtn speed
for which ca,'cu/atcd
compressit/dyf corrections
are belie ved relaole



NATIO IL ADI O y
CONF DEN1 AL ____ CO IIiTEE FOR AER IAUnl


0 /00


Zoo 300 400 5
True airspeed, /r o n


'00 600


l) Effect/veness parameters
Fgure 7-Effecd of horizontal-tall f/exlblity
on /on /otdlna/- control parameters.Airplone B.


h -


Fig. 7a






NACA ACR No. L5B01


1u
0 U



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---- 3,000

< I diAcates /imbrrt, spede
for which calculaed
compress.,bil y correcrons
ore be/leved rel/ale/



NATION L AD; R,
Ot )NFilENTn,L COarinM t OR t B NTAUTI


0 /00 900 J0' 400 fOO0 600
True air.speed,mph
(o) Hinge- mornent parameters.
Figure 7 Conc/lded.


Fig. 7b





NACA ACR No. L5B01


SI I d 'i1ENT4L I I I
-- ., for f/,x ''e ~t/l
S- tFor r,'od ctal


0


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I ndicales /imIna speed
-- for ,h1ch co/cu/loeo -
compressi hbily corrections
are believed re /able

/13.- -J.2 Indicadoes values
-1.6 r (ddCi in_
i/ ncomrresshle flow
-- -1.6


/1 Z2O 300 400 SOO
7-re aorspeed,. n.ph


a') At sea /eve/. tb) A.t solitude of 3q0Od fee t.

F/gure 8.-Effect of horizonot/-ta/l flexibl/dlt on e/evoaor-
contro/-force grad/ents in recovery from dives.
4irp/ane A.


--rA ---- ---- --1--3.2
IT1A .__ ___ a=*"=^ if '


^
1^


Fig. 8a,b






NACA ACR No. L5B01







14




/0

o -----

6



S- ----
t"===
: / _


Fig. 9a,b


0 /00 200 JO 400 5~ 0 /00 200 300 400 SJO
True o rupeed, mph T7ru- airspeed, n ph


A)At se /e ve/.


(b) Af doflude of 30,000 feet.


F/yure Effec of horizonlo/-lal/ flexiblity on elevator
contro/-force yrad/ents in recovery from dive.
Airplane B.







UNIVERSITY OF FLORIDA






'- 'RSIy CF FLORIDA
CDOJCUMENTS DEPARTMENT
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