Charts for the determination of wing torsional stiffness required for specified rolling characteristics or aileron rever...

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Title:
Charts for the determination of wing torsional stiffness required for specified rolling characteristics or aileron reversal speed
Series Title:
NACA WR
Alternate Title:
NACA wartime reports
Physical Description:
25 p., 8 leaves : ill. ; 28 cm.
Language:
English
Creator:
Pearson, H. A ( Henry A )
Aiken, William S
Langley Aeronautical Laboratory
United States -- National Advisory Committee for Aeronautics
Publisher:
Langley Memorial Aeronautical Laboratory
Place of Publication:
Langley Field, VA
Publication Date:

Subjects

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

Notes

Summary:
Summary: A series of charts are presented by which the wing torsional stiffness required to meet a given standard of rolling effectiveness may be quickly determined. The charts may also be used to obtain quickly the aileron reversal speed and the variation of the loss in rolling effectiveness with airspeed. The charts apply to linearly tapered wings and elliptical wings of tubular-shell construction having various aspect ratios with aileron span and location of ailerons as variables. In the derivation of the charts, induced lift effects have been taken into account and the form of the wing-torsional-stiffness curve has been assumed.
Bibliography:
Includes bibliographic references (p. 24-25).
Statement of Responsibility:
by Henry A. Pearson and William S. Aiken, Jr.
General Note:
"Originally issued December 1944 as Advance Confidential Report L4L13."
General Note:
"NACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution of advance research results to an authorized group requiring them for the war effort. They were previously held under a security status but are now unclassified. Some of these reports were not technically edited. All have been reproduced without change in order to expedite general distribution."

Record Information

Source Institution:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 003806597
oclc - 124083737
System ID:
AA00009419:00001


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ej-' .L


-U-I
I,


ACR No. L4L13


NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS


WATRTIMIE REPORT
ORIGINALLY ISSUED
December 1944 as
Advance Confidential Report L4LI3

CHARTS FOR THE DETERMINATION OF WING TORSIONAL STIFFNESS

REQUIRED FOR SPECIFIED ROLLING CHARACTERISTICS

OR AILERON REVERSAL SPEED

By Henry A. Pearson and William S. Aiken, Jr.

Langley Memorial Aeronautical Laboratory
Langley Field, Va.


t: tItt~~

-A


..1


WASHINGTON

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


L 187






































Digitized by the Internet Archive
in 2011 with funding from
University of Florida, George A. Smathers Libraries with support from LYRASIS and the Sloan Foundation


http://www.archive.org/details/chartsfordetermilang








NACA ACR No. LTL13


NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS


ADV..!i;CI_ CONFIDENTIAL REPORT


CHARTS -:-F, THE DETEREI.i..TIlON OF vVING TORSIONAL STIFFNESS

REQUIRED FOR SPECIFIED ROLLING CHARACTERISTICS

OR AILERON REVERSAL SPEED

By Henry A. Pearson and William S. Aiken, Jr.





A series of charts are presented by which the wing
torsional stiffness required to meet a given standard of
rolling effectiveness may be quickly determined. The
charts may also be used to obtain quickly the aileron
reversal seed and the variation of the loss in rolling
effectiveness with airspeed. The charts apply to
linearly taoered wings and elliptical wings of tubular-
shell construction having various aspect ratios with
aileron span and location of ailerons as variables. In
the derivation of the charts, induced lift effects have
been taken into account and the form of the wing-
torsional-stiffness curve has been assumed.


INTRODUCTION


In order to insure adequate rolling control at high
seeds, present structural requirements for Army airplanes
(reference 1) specify that the computed aileron reversal
and divergence seeds be at least 1.15 times the terminal
velocity of the airplane. The accuracy of such compu-
tations depends on the availability of aerodynamic data, on
a knowledge of the wing torsional stiffness, and to a
smaller extent on the method of computation used.

Since the terminal Mach number for fighter airplanes
is approximately 0.85, aerodynamic data should be
available at a Mach number of about 1.0 if accurate
results are to be obtained in rolling-performance calcu-
lations. A yach number of 1.0 is.considerably higher
than that at which high-speed wind-tunnel data are
available or to which they can be extrapolated.









2 CONFIDFNTIAL NACA ACR No. 14L13



Data available on the torsinoal stiffness of wings
ave Indicated that the- calculated values of wing
Yorsio nal stif" necs arc likely tu vary considerably from
-be toet values. Unoublished test data have indicated
that, for wings of the a-ne model, significant differences
.n tri >ual stiffness can be expected as a result of
differ.rces in "abrication.

heny methods are available for commuting speeds of
aileron reversal and divergence. (See references 2 to 10.)
These rmethods differ mainly in the combination of
assumnntions used rad in the degree of exactness attempted.
Tn Lmot cases, the foir- of the wing-t;.vt curve has been
assaued. to be linear or carabolic and the induced lift
effects have been eil'hr enLir.ely negected or antroxi-
mr.ated. In -one fc t0 e I;: roc's (-refeur..ces j, 6, 8, andl0)
the actual ::ing-trslIonal-3ti stress distribution is
required and e-ii 1 i le i est ilisl cd between elastic
end arod--..-ic :'-re s all *lon- th. .:ing scan; with the
excetion of ti r.t. of re:c .r .nce ., however, these
tl.etithod ei Ler -it lIuced lift u -ffcts or apn2oximate
them. Ihe iToplctatin of ti- c:-act r:.thod of reference 4
requires, cor....g the a,~tin r, g100 man hours.
Tnasi.luch a- the accuracy to ee ~' :ined by che use of the
rest exco ime tno, w vi ich includes induced lft effects,
is only a'bot 6 percent as cowparedi wi-th methods employing
ctrin ti ry, the use of cuhe ':1 exact rme;hod is
cons.cidred I'-icacti al when th e nossiEle inaccuracies in
the ard "na ni.c and structural quantities are considered.

So-e3 'cro'ver.ent in the roui'.rercnts can be obtained
Ly s ecif n t hat the loss in rolling, effectiveness due
to a>~i'n tw A. at either terminal velocity or high-soend
level fli'lt shall not exceed so-e i fixed percen'_..- of
that at I F:. eo,-ed. ch a c'sc afication .iould then
confo)rm better to maneuverabiliTy reire!iemets and would
not require as r:uch :xtraolation of the aerod':.-. ic
data, P rther irrr.ow:,..ent could be o.tainmd by requlring
that, fter fabri cat'ion, tbe tor-l onal stiffness of each
lwng nanel be greater than a specified value.

ChMarts re ,ivn in the CruP.ent laoer ironic which
the rc.q:iirtca inn tar:iona:.L st!ifness may be readily
obtained if a given loss in rolling ability is not to be
excci ed The charts -.,:, bt used to predict the aileron
reuve rsal so:ed ani tni los: in rolling effectiveness at
any other speed. The charts arc tased on the application


C ONFI I. 'AL








NACA ACR No. LlL15


of the usual lifting-line theory to wings of tubular-
shell construction and allow variations in wing tanpr,
aileron span, and aileron position to be taken into
account. In the derivation of the charts, the form of
the wing-torsional-stiffness distribution has been
assumed and as a result the twist curves for a given wing
vary with the aileron span and position in a manner to
be expected.

The advantages of the present method over others is
mainly in the speed with which results can te obtained.
More nearly accurate results are obtained than with
methods that assume the shape of the wing-twist curve to
be linear or parabolic.



SYM BOLS


Symbols used in the Dresent paper are defined in
the following list (see also fig. 1):

S wing area, square feet

c mean geometric wing chord, feet (S/b)

c wing chord at any soanwise station, feet

ca aileron chord

b wing span, feet

A wing aspect ratio (b2/S)

y ,-risoan station, feet

k nondimensional semis-'an station
\b/2/


Swir.- t.aer ratio; that is, ratio of fictitious
tip chord, obtained by extending wing
leading and trailing edges to tip, to root
chord

PG wing torsional stiffness as obtained by
application of concentrated torque near
win- tip; foot-pounds per radian


COIPT DEI7TTAL


CONFIDENTIAL









NACA ACR ::o. LLl5


t torque per unit span, foot-pounds per foot

Z accurflated or total torque, foot-pounds

o angle of '::ing tw:"st, radians

5 aileron deflection, radians

c/cr/d ra2te of c '- e o section pitching-.conient
coefficient with aileron engle as obtained
for incot..pressible flow, per radian

da/d6 rate of change of wing angle of attack v;ith
aileron ari~l3 as obtained for constant lift
at section

pb/27 heli: angle of roll, radians

Le rolling mo::rnt due to antis--..:-strical wing
t.' st, I'o t-pound

CL rcllfing-i:. :..nt coee 'fficient

C5 rate of change of rolling-_nir.ent coefficient
with aileron deflection, per radian

CI rzate of c: f e )f rolling-~ Orent coefficient
: ith heiix an.le pb/2;, per radian

C7: rate of cha nge of rolli ::-m.or-ent coefficient
with wing twIL.st at reference section, oer
rad an

7 derived constant for airplane (see appendix)

She1lix-an-le arar:. ter

t fr ction of ri gd- ..: rolling effectiveness
to be retainkdc7 by flexible wing

C rna;'.c )r.cassr, r inc Dor square foot -pV2)

p ocnslit, sl- s nor cubic foot

V true ~lrs-;d, fxct oer second

Syndicated airsoeed, miles _r hour


C )H :i.. AL


CO:; IDE ,TIAL









NACA ACR ":. LLL13


cpeed of sound, feet per secor.i


.a ch nunuber (V/a)


Glauert c r-.essibility coi-rection factor


Subscripts

y and k denote a oartfcular saanwise station


-utboirdd n of aileron

inboard end of aileron


reference station taken as r idaileron c..-n


refers to nartlcular sran le
of aile ~n san, region 1

refers to oartici.ar span.vise
of aileron, region 2

refers to particular saanui:se
of aileron snan, region 5


station inboard


station in way


station outboard


L limit diving speed

R reversal seed


CF.-.7


The desi-n of ilerons that will provide adequate
rolling control at high speed requires the determination
of (1) the w.in': torsional stiffness r-, uired to meet a
:-ven standard of ro'liii- effectiveness, (2) the aileron
reversal -:-.d, cnd (5) the variation wi ch airspeed of
helix angle of roll ocr unit aileron deflection. The
charts oresen-. herein ha-e been prepared in order to
facilitate the com-utation of these factors. L..- results
aoply to wings of tubular-shell construction, of various
asoect ratios and taper ratios (including elliptical
wings), and .'.it: various l-r. ths and positions of the
aileron alo.:- the soan. ..- various olan 'orms considered
are shown in f.ie 2.


CONFIDENTIAL


COi FIDE"I7IAL


/VT-F-2









NACA ACR No. L4L13


The derivation, which is given in detail in the
anrendix, is based on an aoolication of the lifting-line
theory to the wing plan forms chosen. (See figs. 1 and 2.)
In the derivation, the wing section aerodynamic coef-
ficients were assured to be unaffected by torsional
deformation and the shape of the torsional-stiffness
curve was assumeed to be inversely proportional to the
cute of the distance from the wing center line. It was
also assumed that the ratio of the wing chord to the
aleron chord was constant and that no twist occurred
about the aileron hinge axis.

e results, which apoly to wings having aspect
ratios ranging from 5 to 16, are presented in the charts
of figures 3 and i. Tn1 figure 3 the nondimensional
coefficient T is given as a function of ki and ko.
This coefficient T is directly prooortional to the
rollinig-molent loss due to the torsional deformation of
the wing and is inversly proportional to the dynamic
pressure.

Tf it is desJ ed to determine the wing stiffness
required at the reference section (mida leron) to retain
a specified rolling effectiveness, the following equation
may be aoolied:

dem/di b3 q
Tr = T (1)
r da/d6 ?Ad(- ) (-14


The d Tnaic pressure at reversal speed may be determined
from the equation


-5. (2)

da/d /A

If the actual variation of dcm/d5 with Mach number is
know, n, this variation may be substituted in equations (1)
and (2) in place of the Glauurt coropressibiiity correction

factor 1/ -I 2


CO 'I DEINTIAL








NACA ACR No. LL15


The coefficient '7 given in figure 4 is a nondimen-
sional quantity representing a helix-angle parameter for
a rigid wing. This parameter may be used in the equation


pb/2V d (-)
6 db6

to obtain the helix angle pb/2V of a flexible wing for
a unit aileron deflection.

The results given in equations (2) and (5) may be
used to determine the loss in aileron effectiveness with
airspeed due to wing flexibility. Because the relation

between b/2V and q/V 2 is linear, a straight line

drawn between the point representing the value for b/2V

at q/l-M2 = 0 and the point for zero helix angle will
yield the value of nb/2V at all intermediate values

of q.


APPLICATION OF CHARTS


Determination of torsional stiffness required at
the reir..:n': e t Li illn
requirement.- It is desired to determine the torsional
stiffness required of the wing at the reference section
(midaileron station) in order that at limit diving speed
at sea level the airplane will retain 0.25 of the
rolling effectiveness of the rigid wing. ''e following
values are given:

Fraction of rolling effectiveness to be
retained, / (by stipulation) . .25
Limit diving sneed, VL, miles per hour 553
Mach number, M . . 0.728
Wing span, b, feet .. .. 41
Aspect ratio, A . . 5.6
Plan form . . Elliptical


CONFTDiEIT'IAL


C0iI DEUITIAL








G CONFIDEI.TIAL TACA ACR No. LL13L


Distance to inner end of aileron, k$,
fraction of seispan . .58
Distance to outer end of aileron, ko,
fraction of semisnan . 0.945
Dynalic pressure at limit diving speed,
qL. pounds per square foot . 782.8
dc/dI . . 0.?6
dc,/dfi . . 0. 2


From figure 5, for an elliptical wing and with the
given values of ki and iko, T is determined as 0.249.
! Ln these values arc subs!ttuted in equation (1),



S = 0.2 x x 732.8
r .7 2 x (5.6)2 x 0.75 0.685

-= L6,'0i foot-pounds per radian

= 102,000 inch-nounds nor degree



Thus, if a concentrated to.: 'e of 10,2CO inch-pounds
applied outboard of the midaileron section produced less
than 0.10 wing twist of the reference section relative
to the wing Ioot. the wing would exceed the required
stiff Iess.

Dtterniration of aileron reversal speed.- The same
quantities uned ic thet previous examilte, together with
an experimentally determined value of the wing
stiffness mn (equal to 527,jOO ft-lb per radian,
r
= 0) may be used to obtain from equation (2)



_R 2 x 527,000
V\- C.2 9x x 1
.65 pouns p urf.6)

1652 pounds per -'iuare foot


CONPIDEITTIAL








NACA ACR No. LL-Ll5


From figure 5, which gives the relations between q/-l-'12
1
and VC the reversal speed at sea level is determined
to be 619 miles per hour.

Determination of variation of helix angle of roll
with s Cee.-d .- 1 i-L i l ..* ::. _. p- 1 .i ,. j r
airgI': -r the rigid wing ( = 1.0) is found from figure 4
and equation(3). Figure 4 applies to all normal taper
ratios and aspect ratios. For the airplane of the
example y = 0.91, and since da/d6 was assumed to
be 0.56, pb/V for the rigid wing is 0.328 radians
6
per radian deflection or 0.00575 radians per degree of
ob/2V q
aileron deflection. at this value of 0.
qR
If ---- = 1652 pounds per square foot, the corre-
Vl- 2
spending helix angle is zero. The helix angle for any
intermediate value of q/vi-?,: or airspeed may be
determined by drawing a strai._ht line through these two
points.

Discl.: r1n :,f e::''.i:-s.- In the application of the
charts to :.et.crr-.':ne n- ...r- stiffness, reversal speed,
or helix-angle variation, certain quantities will be
obtained from the geometry of the wings; other quantities
will be determined either ... Performance sDecification or
by the aerodynamic characteristics of the reference airfoil
section, which is located at the midspan of the aileron.

The values of b, A, ki, and ko can easily be
determined from the geometry of the wing. In equation (1),
the value of must be specified and q//l--'2 must be
known. An alternative method for determining the aileron
reversal '-..-: nmay be used instead of equation (2) in
cases in which the variation of dcm/d6 is not a function
of 1/11-72. This procedure involves the calculation
of at speeds greater than the limit divin r speed by
the use of equation (1). The values of dcm/d6 and da/d.
corresponding to the Mach numbers of the airseeds chosen
are used and a plot of J against Mach number is made.
As the Mach number is increased, s a oiroaches zero and
when reaches zero, the aileron reversal speed is
determined. These computations may be made for various


CONFIDENTIAL


COITFIDENTIAL









NACA ACR Ho. L4L15


altitudes to determine the variation of aileron reversal
soeed with altitude.

In equation (2) the altitude must be specified
and the value of the torsional stiffness mr must

be known either from tests or calculation. At present,
exoerimental values of mY are greatly referred
or e
since the calc'.ulted values may be considerably in
error. The experimental value of the wing stiffness
may be easily obtained by applying a unit torque
of about 20,000 inch-pounds to a section near the
win- tip and determining the angle of twist at the
reference section relative to the wing root. It is
recommended in reference 9 that in order to obtain
best results an antis:trmetrical torque be applied to the
other wing tip.

The quantities du/d3 and dcm/d6 are aero-
dynai c quantities that anuly at the reference
section. In general, they ;ill vary primarily with
flao-chord ratio and Mach number and secondarily
with other variables such as nose shape, gap, aileron
section, and cngle of attack. Figure 6 has been
preonred to show: average variations of these
quantities viLh flap chord and gap ratio. More
accurate values can, hc'aever, be obtained from specific
tests of the aileron section used or from reference 11,
which n'al"-es Lhe data obtained from a large number
of wind-tunnel tests.


DISCUSSION


The agreemr-ert that may be obtained between the
calculated valves of v.ing t:2ist and actual values
of wing t.iist :!hen the form of the1 wing-torsional-
stiffness distriLtion is assuc~d is illustrated
in figure 7. Co. nationss ee node for the
P-!.7B ?:"i.yS by usne of stifns c .ba fwurnished b-,-
the Army Air esi r oces r Technical Service Command,
;ri.,'.t Field, Ohio. The twist curve resulting from


C(.".'1fr:-'TTAL


CONFIDENTIAL








NACA ACR Yo. LJ-Ll5 CO:. IIDZ.:7:AL 1



these conutations is compared in fig-ire 7 vith a
twist curve cormuted by assuming that wing torsional
stiff. ness varied inversely with the cube of the
distance from the air-iane center line. In
calculations involving the use of a *'ing-tvist curve,
more consistent results vill be obtained b5 assuring u
cubic stiffness distribution than b- assui,:ing tne wing-
twist curve to be either linear or parabolic. Tr a
practical case the trailing-edge portion of the wing
usually contributes a negligible amount to the wing
torsioral stiffness, but the twist curves for a
given wing will differ considerably with aileron
span and position since the typist is dependent upon
the magnitude and position of the applied torques.
Such a variation is included in the results given by
the charts.

Equation (2) shows that, other things being
equal, an", increase in T lowers the aileron reversal
sr -ed. From figure 5, an increase in T is seen
to occur when the aileron sPan is decreased about
a given reference position. For an ellipticall wing
with ailerons exter., i.g from ki = 0.1q to ko = 0.8,
T is therefore 0.L67; whereas, for the same wing
with ailerons exten.1ing from ki = 0.2 to ko = 1.0,
T is 0.588. In both cases the reference section is
located at 0.6 semisnan.

In order to determine the wing stiffness
required to insure a specified rolli-.. effectiveness,
the largest value of q/Vl-2 obtainable should be
used.

If the present Ar-.- Air -)rce specification
is used as a guide namely, that the reversal
speed should be 1.15 times the terminal velocity
of the airplane calculations show that the value
of / to be used in equation (1) would in .rneal
yield overly conservative results for wicr torsional
stiffness. Another procedure for deter. inilg
the wing stiffness would be to specify a value
of ( at high-speed level flight. Either specifi-
cation is believed to be more useful than the current


COI.' UTID EITIAL








12 CONFI .. iTAL NACA ACR Lo. LI.T



one (VR > 1.15 V,) that yields results at Mach numbers
beyond which data would be comnletely lack ng and that
ouldntrodue omlicatio inLrcce c licti in the equaSions. As ;n
illutration, if an airplanee wore capable of reaching a
Yach nu:nber of 0.87, the design aach namnber vould
be 1.0. Vith Glauert's approximation, which Is us-d
v:ith the present method, the required .ing stiffness
would then be infinite. In recognition f this di fficuly,
Victory has introduced in reference 9 the concept of an
equivalent Yach number while still retaining the require-
ment that the reversal soeed be 1.15 times the terminal
velocity of the airplane. Reference 9, in introducing
this concept, interprets the present requirement that
VR > 1.15V L as referring to an indicated speed in an
inconipre ssible flow .

Grinsted, in -refi;reno. 12, has Si..ested an
alternative procedures nam ily, that the wing
stiffness be determined so that aileron reversal
would occur at limit diving coped and that this
value of a-ing& stiffness th-n be increased b- the
factor (1.15)2.

From a consideration of references 9 and 12,
together with current iirmy tir Force requirements, the
foll~ ng values of V/ and q/i -h2 are recom-nended
for use with the charts presented herein:

Method I.- th lir:it diving speed as a basis,
1 i i---
use 2 = and q/'1-L at limit diving seed at sea

level.

Method IT.- ith high-speed level flight as a basis,
use and the largest level-fliZht value of q/"'-i,
5
regardless of the altitude at which it occurs.

e- enrpl gi'en in the present report to thor with the various
snocifications that have been advanced, the wing stiffness
at the reference section has been coi-rOuted for the air-
plane used in the example. The following table shows the
sbiffnosn as obtained the use of the various require-
ments:


CO 1 LYT L








NACA ACR ro. LJL.L13


Requirement


Method I

L-


at VTi


.ethod TI
=f sats ma:

fliL-t seed


ximuin le-


Army iJr Forces,
VR = 1.15 VL

Victory (reference 9),
i'IR = i.0.9,o6 r

Grinsted (reference 11),
m 0 = 1.32 m9L where

S is the stiffness
tas:i =
assuming VR L \L


Sea-lev
bas-"c so


553



el-
.25



1.15 x 5


1.0 b x




1553

_..._] .~


el


[1-


(t-lb r rdia )


)


:Jed












-i




353


Also, for comparison, the follo : in nwuaerical values
of mn are listed for the airplane used in the exa.iole:


Source Conditi on
(1)

EzXerimental Amm'unitlon doers closed
E.."r-. rilental A-m'uni tion doors open
Calculated ammunition doors omen


(f c-l /ralc an)

527,000
351 ,ooo
209,0oo


'E::rerirmental data furnished by Army A Fr Force.,
Air Tec-inical Service Colmnand, :iI ; t Fiold, Ohio.
Calculated data r.., iepoublic Aviation Corporation.


COI; 'iDENTIAL


CO~~ICF~TT~L


St .iffn:,..


01, 000I






721,ooo








i1 CO'PIDITTAL NA.CA ACR T'. L .



CO'CL7DTNG ThAR S


Ch,,rts I ave beea r~reorred for use in ildterminin.l; the
wing torsio nai stiffn3sc foar v.i:Lig of ti'l .r- shll
corns ruct ioi wi th 1as3ct ratios rarnirn fro! 5 ico Vol an-!
taper rat os ranging fromr 0 to I ircluiin- rYe el3 1nt: C 1.
The loss in rolling effectiveness Ean the al .lcr)A
reversal src-ed *iaaT also'be clc.ullte 1 chioai
advantf.ge of the present method over areviuns net.cds is
tle seced witi w:i ch ic; r eSrlts ya y o obt ained. M or
accurate resv.lts ray :e ouai neu y tri use of this imiethod
than by the use of nmet] ods thait Esrui-e the shape of the
wang-trl st curve to bro linear r: ya.ic

Langley etemorial Aer tacticall Ia'oraory
iutiona] Advisor7 Colia'ttecs for .ronautics
Laxgl] 3y THl Va ,..


C :' :) : :A








NACA ACR No. L)L 13


APPFINDIX


DERIVATION OF CARTS


Although there are a number of types of air loadni
and inertia loading that contribute to the wing twist
about the elastic axis of wings in flight, so far as the
problem of rolling effectiveness is crnc-erned, Jnly the
twist due to aileron deflection need be considered. In
fact, since the distritutoan due to darpi n in roll is
likely to be almost the saie3 a3 the s&onw.ise air load
distribution resu!ltt.- from aileron deflection, only the
increase in section pitching mo:6cnt in may of the aileron
need be taken into account in deterI-i ning the wiLngr twist.

A strio of the wnrg dy in vay of the aileron
(see fig. 1) will have acting on it an Inccrement in
torque as follows:

cm (lc2
At c.y = ---5----d7 (AI1)


The factor 1/ i-_2 is introduced in equation (Al) in
order to increase low-soeed values of dm/dc for ilach
number effects. Tf the correct variation of dcm/d i s
available, the quanti: (dcm/d6)(l/!d-2) may cb
replaced by the actual variation with I.ach number The
accumulated increr.ent in torque at a particular station yo
in way of the aileron is

:7o
AT = At diy- (div
1t2

and, similarly, the accumulated increment in torque at
any station Yl inboard of the aileron is

Yo
ATy = at dy (a4)
'i


CC -IDENTIAL


CO-I7 iL.'AL









16 CONFIDENTIAL r GA ACi No. TI T 1



Tn thei der1E tion of the ch~rtl fIr t.e z dte r..l ITi: n
cf vig torsi)nal scifnf,-e required for specified.
ro li*ng characteristi-cs or aii ron .reer.,o':al soeeo, i c
desirable to use the win cent-r line ).s the reCference
n3. to define ;he to 'ioial stir or a Wn of
tu ; ,:ll r-s-Fell c i-st cti on as the co ( centC-.ated t-r
which, wxhen a-plied outb>o.rc o' a ,-vcn .nction, v) -
pri duce- a unit reflection vjith resnc ct to the rcfeir nc..
section. A]tihough this ,diflntion of *h. torsii:ul
stifess r':es the ea-riLcal devoiopier;. somc, at
longer, it is better cuitec to the test Droce4ures el-at
are nowv in use ihen tle bor ion-al-tiff ness varia tiJn
along toi :sran is to '-c duetr4 lCd. The aiglo ol tu.lst





72 L
T' o c t a- t j n" i 1
due to aincron cef.tctaion i a It n nation 13
way of -t sa:"or, (rcgin :. 1) 's .tus *iv n bi



= --- I t + cy ( +)
i

The t';ist at any station Yi in rei-n 1 inboard of tLe
a i r 'n is


9 n n 1. O ,:-i



Tn region c itboard of the all-ron -:c t1he ': -it is


r5 t / k d ; ,..c)
t> o


Gince r-' antitsv.rctri cal trquj; ti-. cng outbor'Cd of t'i.
ail < n tiol -. is constant to thi in; ti:). .y
-C
subst fiuttin,( e taiion (A!) in .equation (. .) and

r tru ci- --, a < "[ u'l'J.i *l)n ::,.:y b: obtai :.id.

This equation -a; tl :i e nut 'i.. r-'- c rcnient fjr',
by miltiolyir.I eac. t r.i.: ,' th, ri-,tio of th s 1il'n.j:.'
mn,> to t-e square of tro r.ean geriomtric


C) D IAL








!:AC. ACR TT. LjJ.L13 CO"TF'IDENTTIL 17



chord c. The resulting" e 1..-tion iay be rearranged to
give the following equal tion arplyingr to region 2 (for
convenien-c the factor 1/ 'I/1:-7' will be 'rouped with
instead of with dcm/di):

Sk2 2 kc\2

1- -. ; dk + / M ()
/.Cj

eT eiquations for thL wins twis at stations irboard
and outboard of the a1leron (qu.ations (A5) and (Ao))
si-ilarly become



__ __ /c\ (we
S/C --i dC -
q/ -b L'k^ *c/



G.O
6k3


do

Equations (AT), (AS), and (, ) define the anrle of
twist in the three regions in tecrns of tho chord and
stiffness distribution, subject to the assur.ptions
that dcm/d6 is a constant &alon the aileron oan and
that the aileron does not tvist about its hinge axis.
Inspection of figure 6(b) indicates that the factor dc;/, d
is essentially constant for flaD-chord ratios from 0.2
to 0.3 and, since the variation of allron-chord ratio
along the span will normally fall within this range, the
assumatio.n is justified. In order to evaluate
equations (A7) to (A9), the tvist carves will be obtained
in terns of the twist er at a reference section, which
will be taken at the midspan of the aileron. From
equation (A7) the twist at the reference section becomes


COP I''Tl !7 AL










!-GIkC' '73. T'l 'i


U /


+ i


.i th .e sti ff.'-i s 3 s ef 'i- d I the ..res; it r '
the torsii.l s. iffne'.s is in nite tc t. Li c --
1.i.e a Jecrea:'cs -: th Jist&nc to 'or .e iriit3 v tL.le at
t}.e cbip.. i.' ely' i o data or c-.-ic- fi i'rrr ... c.l:.-iec
'ndlcates thct :;f li, 1le ,rr os :ill rest in t.ist.
c~n:p-.tatflons if tle o'1sl.hal stzlf no.ts i': trl :t tion
aa1 on the svran i' as,.;l:..ed to bo


1' ...


(All)


;,hen equation (All) i" substltit:-d
nd (AQ. L:U follo'w:n; raios fr
4 n the various r. 1n::


1: c'
C' :i


t\- /


SL-


r II o bLrS?.cd


~~~ #: \~' i ~".---~

'; \ S ,iA ,2.
I i!-



I I
I 7 *


+ --


1
- 1 -


r \
H1


CI


I


-N

1j


*~ WI



A '1
' "
*l t :ii
+'


S'. I r


1'7


I' ,-.
*7 i


-I


( I


1-

i
1I\:j i
I
i-r?


F C = 'TIAL


3 -, ir:llr
-r

:-L"i ------C-3


(,,10)


~





,I I-
i


-i








1:ACA ACR I'o. LL13 CO:'- TD-ETTr!AL 1



It will :- noted in equations (A12) that only :-;:etrical
terms such as spanwise extent of aileron scan and chr
ratios c/c occur and that, in order to determine tle
resultant twist distribution, only these values need be
specified.

In reference 15 influence lines are prcsented f r a
series of tapered wings (see f2-. 2) of several as-ecrt
ratios, which nma-e postble the co:putation of a cef-
ficient of rolling-moment loss Cla ..e to any sort of
twist distribution. As a first step in the evaluation
of a loss coefficient Cl., the ratios of t6/6r were
evaluated for the series of wi.--s shown in fi.u c 2 with
ailerons cf various span.

The loss in roll'..r mo.,ent due to a twist -, at
the reference section, was then defined by the equation

Rolling mon:ent loss = L




where

dC
9 d9r
(Al4)
dCL/ dBr

e/9, 9r


The results shown in figure 16 of reference 15 were used
to determine C69 for the twist variations computed from.
equations (A12). T.,e coefficient C w was also determined
for elliptical win's of aspect ratios 6, 10, and 16, with
values of ki of 0.2, 0.5, 0., 0.5, 0.6, and 0.7
and for values of ko of 0.8, 0.9, .:.- 1.0 as well
as for the win; ulan 'orms shown in figure 2. 1.
numerical results of these steos are not iven herein
because they are only intermediate steps in the procedure.


CC .-r --:T.T IAL









20 CONFID IAL NACA ACR No. Li L.1



In the steady rolling condOition, the damping moment
equals the moi:et ii pressed '- t the ailerons minus the
loss in omnen; due to twist. In coefficient forln, tilis
relation rnay be expressed as

C b
C-o 2 qjb = C Sb CLerqb (15)


from which the helix anile per unit aileron deflection
6
is obtained as


C 7 C

(A16)
C 0


The coefficients C0l, C7, T and Cl will v.:-' with
Mach number but of these coefficients onl the variation
of C viith 1,ach number can readily be determiined from
wind-tunnel tests. At onresnt C' must be obtained
r)
either from results of low-soced te.ts or front results of
computations and C T rust al: ays be obtained by

coumutation. For this reason it would anpear reasonable
to use consistent values and to assu:re that each varies
with ;:ach nu:1ber according to 1/j Fro;"i equation (al0),
for a particular wing aileron coo>bination,


to
r1 ( Al17)


where the constant e1 equals tle ri :ht-iand sde of
equation (`10). Also, f!- eq :ton' (Al-) and (Al-), C9

is s -cn to Ie conc' .nt for a .art cular :rng-aileron
co-noination. '.1.hn these value:; of CA@ and Or are

substituted in equation (Arl), the f)llowinf equation
re sults:


C ON17TL i:'"T TAL








NACA ACR No. L4L13






rnb/27V
6


where the constant


CONFIDE1NTTIAL


~C,


____ _--
C-


Bt = C 3,


At the aileron reVersal seed,


d cm_-

C6 2mr
C5 nr,
01 Q "z~r


qi
T-- 2


and the value of the dynamic pressure is


q

l-M


2m r

dcm--2
dC-b
d6


C2
':'2


Mr 0
dcm b3
d6 A2


Cl5

da/d5


da/di
B2


By setting


B2
!da
C T-
Sd

the dynamic pressure at aileron reversal sPeed is


IR
1- '


2m,

dcm/dO b3
da/d5 A2


(A20)


(LA21)


CONFIDENTIAL


r l8


(A19)









22 COFFIDE -'TAL T .C.- ACR No. L



In o:e dterni'ntion of the values of T the ~ ces: ry
nrur -cci ci v all.e of L 'ere obtal b7 the } roc \re
outlined a.d the nezcs.-- lcs -- .-. ere t-en

rctl fr: ur 6 of ref ence 1. le; te
cf r .-:re plotted the results ;v.- ee ouId t3o I
es-'nt'Illlc th3 sa-uis for aspect rato-. o"' u, an. 16
aver.,e deviation a lessa t 1ha: 1 rcen. Te nval to
of di how ver, vary vit- lli.ln p ltion sn-1 '.in.
taper as fo2o1 in f l.2re 5.

Dr an inrini- ly ri d ..r.c, x .,; per
de:ree aileroI n eflectoin can 'e (obtaned from
equation (Aa8) as














vthlrc C;7, wa cbtair..ed fron fi' ... 3 of refr ncc I.
Fi ur e } ires t:e- vloues oif r i.. .i 0 >X:3 & .
Ey seccif ng t? Liat the f-ile :tn1 r etain o.1ic
fraction of the ri id vin ro i i1 effcctl venes; at;I
spe i-fid ca ynar,.ic orcsrs u (scay, t ....nal vel.cit'), tht.
fol ':-.in tO.qu tion r;s.ult3






y subst-itutin results frc e:j tt: n, (20) san (A. )
into cqua-lion (f.iE), the ;inj :;tit. ~ required
at tihe reference s ecti n :-n retn n i "1n i I 'fied valie


C : 7 -L.I








NACA ACR 2o. L4TL13


CO:'.; '--TIAL


of ro!li ; ability at e -'ven value of qi is
given by


dc,/d5 b3 q
mer d c./d 2A2 F_) _--2









NACA ACR No. L4L13


RT7 .. :;'ES


1. Anon.: Eandbook of Instructions for Airplane
Designers. Vol. I, Materiel Div., Army Air
Comns, 3th ed., Revision 7, Nov. 1, 1945, sec. II,
pt. V, par. 60-1, p. 654.

2. Pugsley, A. G.: The aerodynamicc Characteristics of
a Semi-Rigid .~ing Helevant to the Problem of Loss
of Lateral Control Due to Wring Twisting.
R. ,j 1 No. 1I90, British A.R.C., 1952.

3. Ccx, H. Roxbee, and Ougsley, A. G.: Theory of Loss
of Lateral Control Due to .ing Twisting.
R. & 1 No. 1506, British A.R.C., 1955.

4. Pugsley, A. G., and Brooke, G. R..: :e Calculation
by Successive Approximation of the Critical
Reversal Soeed for an Elastic ling. R. & M. No. 1508,
Sritish h.R.C., 1955.

5. Hirst, D. !.: On the Calculation of the Critical
Reversal S1eeds of Lings. R. & M. No. 1568,
British A.R.C., 19!T.

6. Shornick, Louis H. T'he Computation of the Critical
Soeeds cf Aileron Reversal, Wing Torsional
Divergence and Wing-Aileron ivergence. Meno. rep.,
3er. o. ENC--i-51/7'F'l, add. 1, Materiel Center,
Army Air :-9rces, Dcc. 19, 1942.

7. orton, '. H.: Critical Reversal Speed. Aircraft
Engineering, vol. XV, no. 177, Nov. 1943, pp. 319-524.

8. Rosenberg, Reinhardt: Loss in Aileron Effectiveness
Because of Wing -.ist and Considerations F.e.. riding
the Internal-Freosure Balanced Aileron. Jour. Aero.
Sci., vol. 11, no. 1, Jan. 1' 14, op. 41-47.

9. Victory, I:ary: The Calculation of Aileron Reversal
S-eed. Reo. ko. S.7.E. 5-7, Eritish R.A.E., 1944.

10. Harmen, Sidney V.: Determination of the -'fect of
.'ing Flexibility en Lateral maneuverability and a
Conmarison of Calculated Ro'lln Effectiveness
with Flight results. NACA nRR "'*. 4A28, 19i4.


C'NFI 7.jTTAL


CO.UITDF',TIAL








NACA ACR No. L4L135


11. Purser, Paul E,, and Toll, Thomas A.: Analysis of
Available Data on Control Surfaces Having Plain-
Overhang and Frise Balances. .-.'A ACR No. LilI,
19.44

12. Grinsted, F.:; Ti Effect of Compressibility on the
Estimation of Aileron Reversal .need.
Rep. No. S.M.E. 3192, British i.A.E., 192.

15. Pearson, Henry A., and Jones, Iobert T.: Theoretical
Stability and Control Characteristics of VWings
with Various Amounts of Taper and Twist.
NACA Rep. No. 635, 1958.


COU'IDENTTAL


COC 0"'T ?i DEiNT AL









NACA ACR No. L4L13 Fig. 1





----^-------J
a C

F 1

i









z q C








I !
80 -1 2
iCS ?














__ c
4Od Z .2







NACA ACR No. L4L13


CONFIDENT AL NATIONAL ADVISORY
COMMITTEE FOR AERONAUTICS


5//'gure 2.- /Winy p/o/7 forms used /'n oao/ys3A.
(/rwn reefere,/ce /3.)


CONFIDENTIAL


Fig. 2


- -- wwlww





NACA ACR No. L4L13 Figs. 3a,b








--=-- l~- 7--



L
---





----- I
t. N i, i. f i..i X I! f







-I- I I I 'l /I


-- -- -- -- c 1 1 n < s ij iiiiin 111111 j ii' ti- iii iiiin iiiiiiiii i n i 1 1111111 iiiiiiiiiii iiiiiiin -
't! ^^ ^ /^Z --- E^9P







NACA ACR No. L4L13


-< *
~tj
- t


z
o
0 [


Figs. 3c,d


It


:,I I | -


L4)


-I






NACA ACR No. L4L13 CONFIDENTIAL Fig. 4


/6




-- -5 ------- ------ -----

/2






















.2 .13 3 .,5 ,"


/Upre 4~- Fo/ai or dk-oq/e \ -rael for- \ a
N \i_ _
---------------.---
















6z--- --------- ex-- o-o---ea ---a- f--
------ ----------- --.v--~ I
_-----------------------


------------------------ ______'
-----------------^-^^^------1ii)- -
-- --- ------_ 8-












02 3 _-_ /-' tper /os



A _lct /lio I-ll ro/ny .-a 5 b .16
0 :^ ^
-- -- -CO --IDEN TI\^ AL
/'i .id-^V^^V^ ..ki xr. .o iern l t/


_ __





EACA ACR No. L4L13


I -4



---4-- "- --- -
\ !











-| i i---- i


idz
IX,
z
0











a %


I

^1$


oft/w'^>/


Fig. 5


I





NACA ACR No. L4L13


f I I


_ /iI ____ -/
I I


- ---_ -^ --
__
K ^


$ -
* u







\ iy~4
'1
") ^


h u
N








Na
\^^


Y N


Fi g. ,


I k 1





NACA ACR No. L4L13 Fig. 7



S--.


ck.
1 I_ ----_-_o_ -




S| II*- -^ --



-






C I
^ ^r- ^ .S'
^ *^ V ^
-~ ^ -\ -
c y '\ ^^
---- l -f ----^ ^ > ^
-------- 1----- ^ ^


+
*
; am yo who


w







UNIVERSITY OF FLORIDA

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T


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I
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