Aerodynamics of Fuselage, Multhopp PDF

 

TECHNICAL

_-" NATIONAL

ADVISORY

MEMORAI_IDMS

COMMITTEE

.......

FOR AERONAU_XCS

I

-4 CO

.

CY_

7"O m

No.

AERODYNAMICS

1036

OF TEE _JSELAGE

By H. Mult Multho hopp pp

Luftfahrtfors

chung

18, No. 2-3, March 29, 1941 vox R. 0 delhourg, M_nchen un_ Berlin

Vol.

Verlag

h, _w

t

o

nL

Washington

December

.°

19}.2

f

 

ARy KAFB,Nil  I'ECH  I'E CHUEP, UEP,

1B

0144_.779.

T30ENIOAL

NO..

I_MORA._DUM

A_RODYNAMIOS

3y

THR

0Y

10S6

PUS_,LA@_*

}_ulth'o_p

E.

8UMX_iARY

a number of problems, with of the fuselage the wing an& tail, On th_ basis of simple calculating method's &erlve@ from greatly i@ealize& concepts. The present report _eals with particularly with the In_eractl0n

For

the

potential

fuselage

_heory,

a

alone certain

it

affords,

in

frictlonai

which, s_milar lif_ of to the iB no longer linearly relate_ _evertheless _here exists for

variance

lift

in

of _mali a wing to the angle of this frictional

with

yawed

flow,

ratio, aspect a_tack. lift some--

thing llke a neutral on oblong fuselages

of which the lift

increase

lift,

stab.ili%y point the position appears to be assooiatc_ _ith of the fuselage in proximity to the zero to the presen_ experiments,

according _he

_itching

with

• or or

moments

comparatively

the

unstable

of

the

fuselage

be &eterso far as _he flow c0n&itions in the neighborhoo_ of the axis of the fuselage can be approximate_ if the fuselage were absent, which, in general, is no% very &ifficult. minel

great

can

reliability

contribution

of

the

fuselage

to

the

static longitu_inal comparatively simple

of the it affords stability airplane the evaluation of which fornulas, offers little lifflcul_y. On the engine nacelles there in a_li_ion _ very substantial wine contribution moment in&uoel by the nonuniform listribution of the transverse displacement flow of the nacelle along the wing chor_; _hiz also can be retresente_ by a simple on a l_rge number of &iseimilar aircraft _he unstable fuselage _n_ nacelle moments agreement ficient throughout *"Zur vol.

with

for

the

within

the

formula. A check types regar&ing disclose& an

be sufrequirements. errors remalne_ The sco_e of instrumental accuracy.

wln_--tunnel

practical

is,

tests,

Aeredynamik _e _es s _lug _lugze zeug ugr rum umpf pfes es." ." 2_-_, Ma_rch 29, _p. 18, nos. 1941,

which

shoul6

Luftfahrtforzchung, 62--56.

 

I,'A.OA _e _echnloal

For

llft

the

of

was

of the

the

assumed

mathematical would

of

determination

distribution

fuselage

to

can

the

fuselage

be

fuselage

the

in

butione

from oa

values

portion

The

of

air

tive

by

fuselage

In bution an

_he firmed

As

the

at high--

the

vertical

in

dlre_%ional A

few

distlnotly of mot

the

this

the

or

tail

fin

the

a

(for

for

of

the the

an

rud&er

%hose ca or nega-

flow lift

low--wing

of

the

arrangement) magnitude.

on

satisfactorily

con-

fuselage

an_

leads

damping

to

rivet

%o in

a

at

sidewash

appreciable

attention

changes

phenomenon to

the

very results

unsymmetrical

of

con--

fuselage

yaw.

this

mechanics

flow

the the

produces

are

the

on of

flight

ions.

One aircraft

notoriously is

that

ODUOT

neglected of

%

distri-

moment

sideslip

demonstrating in

measure_ positive

considerable

very

measurements

phenomenon

wing--fuselage from

rolling

arrangement

intended

is

measurements.

surfaces

and

this is

effect

stability

itself

width.

or of

effect.

determined.

displacement

high--

moment

low-wing

combi-

anti. symmetrical

available

the

the

linear

the

the as

fuselage

sideslip,

&Iffer--

considerably

when _istrlbuted

appli-

flstri--

the

so

for

of

fully

fuselage

method

_NTR

of

by

_istributlon

sections

few

the

angle-

fuselage

over

wing, in

change the

basic

by

without

dlffer

evolved

are

found

4

the

methods

for

lift

a_ditional

wing

be

wing

the

a

in

two

determined

rolling

regards

ditions

a

of an

fuselage by

a

method

formula

elliptical

can

across

attendant

simple

wing

orthodox directly

case

along

with

the

this

causes

wing

a

all

equivalent

by

affords

distributions

on

an

conventional of

again

taken

lift

the

fuselage

the

the

sllt. Then a wing-

extent,

lift

from

the were

some

the

transformation

represented

the

lift

by

of

on to

i_self

of

oonformal

that

to

distributions

loa_

obtained differences

to

Then

customary

estimate&

combination

for

of

is

a

_istribution

which

then

fuselage

the

is

it

eSfec%

transverse

to a vertical distribution for

also,

particular,

as

easily

llft

the

cable,

flow

by

effect

distribution and of--attack distribution. computing

fuselage

the

lOS6

two--dlmensionai_

reduces

chord

No.

th_

which

removed

oomblnatlon

wherein

_he

be

cross section of the lift

fuselage calculation

nation,

wing

dlffioultles

entail,

ent

Memorandum

the

I O}T

phase fuselage.

lu

the

This

aerodynamics is

due

in

the

 

I_AC_ first by

instance,

itself

parse

are the

becomes includes

fact

the

that

comparatively

aircraft,

necessary this mutual

The

Hemorandum

search

interference

throughout,

as

woull

it

potential

theory

a

to

of

It

existence

parts

vlou_ly

the

while

such

eithor able merely

seemed

for

which,

by

a

metho_

be

The method construe_

increasingly

design

in _f

pear

somewhat

ance,

the

the

or For

general, to

_,_ore in

present

exclude_, merely

lan_ing

s_ress

lage

and

engine

aerodynamic

As matters forces an_

moments

wing

were

alone

stood

be

Justlfled

or

suitis

of

airplane

the

some'time

present

flight

of

by

because

_ttac_e_

for

Ob--

ap-

perform--

assumptlons

for

the

the

mechanics

of

flight

the

influence

of

the

which

an

analysis

across

fuse-

usually

on

the

the

distribu-

their

wholly unusual in_t_cod drag

measure,

of

aircraft.

llft,

maximum

presented

in

left

be

resistances,

part

most

are,

must

the

and

but

hence

calculations

may

explanation.

of

aircraft

stipulates

_.rlng under

the

also of fuselage

this

respect

between

a

directly

mechanics

induced

the

nacelles and loads along in

to

the

effect

for

afford

distribution

to

problems

for

the

speed,

cases

be

praotlcal

performance

As

changes

is

load the

drag

at times admittedly total amount of

a,_ _he

The

the

research.

important

many

task since

e_perimenta

tion in scarcely

and under

came

of

essen-

hereinafter

describe& s_ep which,

load

the

the

nacelles.

engine

the

fuselage

the

all

the

few

_ffects.

first

mechanics

aircraft

three--

appropriate

involve_

shoul_

The of

of

characteristics,

lage

am

have

will

aerodynamics

analysis

stress

must

firs_

methods

unwieldy.

a

out

secondary

demands

respect,

suggested

a

boundary

than

evolve

errors

itself

pressing

thi_

even

the

a

for of

bring

treatment

as

it

which

arbitrary

to

all

of

hence

solutions

more

phenomenon,

of

other

adduced.

disregardin_

estimation

wing;

real

bothersome

very

hardly

effects

its with

development

expedient

each

an

tests. to

the

with be

But

theory

exceedingly

which

coul_

therefore

formulas tial

problem

the

exact

entail

conditions;

proofs

with

is

dimensional

the

perceived. in combination

mathematically

problems

considered

structure

fuselage

evolve a interference.

3

fuselage

the

especially

to

for

lq'o. 1036

simple

apparently readily into evidence only

come

of

such

to

a

is

of which effects

Technical

model

ascribed

the

the

exact

effect

the

distribution

and

nacelles

of

the

fuselage

fuselage

fuseof

themselves.

discrepancies

with to

the

in and or

air the to

the

 

4

N_O_

_euhnioal

n_celles.

engine lations

In

indicate

contTaet

these

that

in

the

majority

of

on

the

wing

should

In

flight of

and

solve.

Is,

stabillty

in

flight

an_

symmetrical

so

noticeable conditions

at

wing

of

moment

the

tude

of

is

moment

wing.

an_

rudder,

the

_ownwash

of the

Hence,

Inmtead

quantities _ue

In

of in

The

important and

with

absence

greater

instance,

of p_rt

existing in

volume

all

analysis

VI

the other

on

ai_zh _

of

Duran_

of

the

_he

of citer

si_ewash these

occur conditions

lateral

of

of

of

the

the

modern

on

parts,

be

taken

hulls,

interference

airplane,

observer

_e

two

rotation and

of

of

parts

can

yaw

rotation

_he

dlreo--

manner.

in

vibrations

airplane

@ata

like the

ignored.

_henomena other

which,

appraisal

yaw

to

the

data

the

the be

the

of

to

cannot

the

of

_ue

of the fin

pure

pat.h,

knowledge

for

with

effects

proceefing

ya w

The

degree

fuselage

alrea_F

in

flight

of

lift

effect the at

_amplng a

the

angle

different

a

then

af

case.

of

_irst,

curvature,

change

in

of

the

affects

yaw

concep_

oonsi&ered:

_amping

discussion

the

simple

in

magni-

that of

si@ewash

a

location of

dihedral

_tabliizer.

_amping

problems, these

the

an_

l_ath

latter

3efore brief

a

of

some

aircraft

the

wit.hou_

the

considerable the

be

to

aircraft

s_ahility

a

the

order

the flow

flow

produoe

r e ea aotlon

unRer on the

un-

a

the

with

the

the

plays

upon

fuse--

In

But

to

the

by

i_

l_roduce_ siResllp

of

an_ of

modifications is

wing

as

of of

affects

manner

induced

elevator

shoul_

aircraft

yaw

it

neu-

the

effect

_leo

p

must

mechanics

comparable

important,

the case

on

etabillty

in

to

of the number

of

forwar&.

fuselage,

cases,

loa_s.

wing

the

dependent

the

many

namely,

tional

only

in

due

in

largely to

_,qually

&Istribution fuselage

the

yaw

relative

which

rolling the

in

wing

fuselage

the

as

the

fuselage

a

of

position

for

sidesli

are

loads

aerodynamics

under

auch

air

calcu-

interpretation type a large

the

the

present

treated

i_erablF

in in

the

fuselage

whioh

motions _irst,

rolling

be

important

the

effec_

the

anE the aircraft

cone

part. the

bo

particular,

shifts

flight

in

an

motlon's

nacelle

changes

that

point,

symmetrical

this

due

I08S

Eo.

with

therefore

arlses

also

There

lags

oases

the predetermination characteristics of

problems

tral

KemoranRuh

is over

as

"Aerod_cnamic

the

a

fuselage

necessary. from

compiled,

Theory.

the for #

 

NAOA

_echnical

the On analyzing the first result

flow

No.

Memorandum

1036

.5

conditions in fri_tionless parallel Is the tbtal oZ resultant absence

forces on the fuselage; the pressure distribution over the body merely free moments. These moments are affor&s free of

some

since

significance

of attack of angle bility quantities. the stability about

the

they

are

normal

axis is lowered by the an axially symmetrical

action

to

the

an_ hence enter the stathese moments is such that axis or about the lateral

fuselage sign of

The the

proportional

of

these free moments. the free in moment

On

flow fuselage is, of course, zero; on unsymmetrical fuselage forms or by appen&ages the axis for zero moment can be located at place. free moment any other The is _roduced by negative pressure on the upper side of the along

the

fuselage

axis

bow an_ on _he lower side sure lower side of 8._ the the stern (fig. i). The and

time

for the fuselage nay be substituting potential theory methods as developed Kaplan, and others. But for the task

I)

is

more

According to of revolution

Ifunk is

the

I

_ H

euitabie.

He

simply

determine@

slender fuselage forms and dependent on _he slenderness

unstable

=-

wit_

moment

of

the

values

a very

Ez

is

the

ratio air

_/D

volume

(fig. in

transverse motion of the tudinal motion. fuselage cal surfaces it is

1

d MR

q

&_z

ratio

2). to

In

of

slender

s vol.

(s.l)

the effect fuselage being accounted of finite length by the correction (E z -- Kx) which _epen_s on factor slenderness

If

built up by means of by Von Earm_n, Lo_z, in hand Munkrs method

which he obtained by. a comparison an_ accurately computable forms.

ratio, easily

body

much

value for very correction f_ctor

the asymptotic _hen a added

presside of

on

in various ways. can be compute_ no object a flel_ of singularities

free moments patience are

(reference

and positive" the apper

of the stern _he bow and

this

the

representation

fuselage

and that fuselage E l For other than axially

2 0

for the

volume

by

by longisymmetri-

 

6

Technical

EAOA

and

for

the

Memorandum

contribution

to

the

10S6

Ne.

moment:

yawing Z

The

1

dE R

q

dv

FL

(_.S)

2

O

longitudinal moment of the fuselage which considerably under the effect of the flow is taken care of later by more reliable while the formula for the yawing moment can be taken over, downwash no apas the wing affords contribution to the momentum of the fuselage the transverse axis.

unstable

still round

changes the wing

formulas, summarily preciable flow

along

a fuselage about the center of of the volume on surfaces of revolution fuselage the center of gravity of the volumles Rotations

of

gravity or

about

an

addi-

Z

/

R_ dx

/

or

0

are

neither

hR_

d x

0

accompanied

by

a

resultant

force

nor

tive moment so long as the conditions in i@eal flow are only considered. S% merely results in a slightly modifie_ transverse force distribution. If the rotation is not about the center sulti_g from the

of gravity local yawed

of the volume, flow exactly

the moment re-in thin center

the rotation is used in the calculation. So, if in rotations about the normal aircraft axis, for the center of _:ravity of the is, as instance, aircraft usually before the center of gravity of the happens, fuselage volume, the fuselage directly furnishes a negative contribution to the _amping in yaw by an amount of

gravity

due

to

Z

b where a_

Ax the

tual

the

volume

This theory

is

is

dw z

supplies behavior

tential

flow

distance

center all

o

that

of

of

the

alone.

aircraft

consideration a

fuselage As

the

center

of

gravity

gravity.

the

concerning

of

eoonas

s_ngle is

not t_e

of

the

fuselage. described flow

past

potential _ut by _e

the the

acpo-

fuselage

 

I_AOA

ceases

to

be

perfectly

accumulates flow

Technical

more the

forces

a%

in

moment

the

cation course

are

fuselage

is

secured

lift

or

urements

of

t hiB

of

attack

As

attack

the is

of

wing9

the

is

not

(figs.

etremglF

3

wing

of

=

of

readily

able

test

which _ata

has

fuselage

measure

that

layer

the

introduce

a

might

be

presumably sectional location

form it

form

of

the to

on

%]:e

of

angle

on

course

ratio

the

width maximum

for

a

suggests we

certain

get

the

of

on

its

we

put

unknown boundary of

it

width

soli_it_

force

anf of

experimental else,

we

bR

determination

R

lateral

place

avail-

conventional

separating

everything

Hence

the

temporarily

In

exact

momentum

with

fuselage

the

fuselage

the

the

_b.

fie _

&A

of

agreement

of

the

appendages.

oorresponQinglF

to

similar

However,

above

the

means

width

profitable

i

or

the

OCt relation

aspect

hence

f

depends,

of

a

(2.S)

wings.

factor

a

very its

good

sides;

for

lift

despite

2

in

such

sharp

substitutes

like

= .

by

is

denotes

correlate

which

for no

feature

something r e el late_

llft

a

small

_crivable

considerations

NAOA

unpub--

O:

i

result

the

from

%_.

ratio:

very

mothe

meas-

outstanding

linearly

of the

with

several

also,

frict.ional

aspect

is mo-

recorded

were

of

appli-

force This

appraisable

from

llft

even

cl d_

a

the

moment

The

suggestive

_

from

existence

an_

of

small a

the

of

subtracting

rest

as

frlc%ional

depenQence

itself, For approxlmately

after

used

_ata well

factor

point

cToss or fuselage.

the

measurements.

llf_

very

ms

was

for

that

_he

540,

Yw

from

_oi_%t

angle

and

the

additional

appreciable The

T/nfortunately

evaluations

neu_ra'l

remaining

scarce;

Z94

data

the_e

fact

very

are

lished

the

force.

Nee.

Reports

fuselage.

an_

in

an

becomes

material

other

results

contribution

correlating cross

the

frictional lift far aft at the the measurements

unstable

and

so

the

of

from

theoretically ments

This

and

balance

on

than

altered.

of t_%e inQuce_ proportionally

ment

si_e

V

IQH6

boundary--layer

symmetrical

one

on

conditions

1,To,

Memorandum

research_ on

the and

cross-the

 

8

_AOA

Tenhnioal

1

Memorandum

dY H

= -

-

i_o.

IOS6

fhRS

(2

7)

the evaluatei measuraments available indicate, Then by itself was plausible, relationship what a certain bet_¢een the form factor f an_ the position of the applied

point

(measure_

of

from

the

frictional

nose

of

lift

fuselage)

denotel in

xn

wlth

figure

5.

This

point

is located, as the frictional

may be expected, so m_ch farther back as lift is actually less developed. This relationship of xn with f has, at any rate, the aS-vantage cf obviating the extreme caution required in the estimation of the yawing due to yaw moment from the mrictional transverse force at the usual cen_er of gravity positions of the aircraft, seen that the It is further directional sSabilitF is so much more intimately relate& to this center the slenderness

of g_avity ratio of

position as the fuselage

f is

is greater an_ smaller. The

extent to which the fuselage bounlary layer leads to the of aerodynamic an_ moments in rotations formation forces of the fuselage about the normal or the transverse axis, is up to now utterly unrre_iotable ; their explanation is, of course, a matter of experiment.

ments

In this of the

the foregoing in free stream

instance fuselage

appraisal

fails,

of the no-because the

flow pattern of the wings causes a very substantial variation of the flow at the fuselage. To begi_ with, the previously _escribed frictional lift of the fuselage is likely to exist, orientates the flow not since the wing along the wing chor@ and even far aft of it with the result that flow component transverse to the no appreciable fuselage exists in the real zone of formation of the frictional lift. Hence there is some JuBtifloation in assuming that the theoretically anticipated moments will after_ar_ actually occur. First of fuselage alone stantial carriel

Lennertz

the fuselage wing all with in that the fuselage takes proportion of the lifting forces _ the wing section in its placs.

(refere_ce

4)

anl

Vanlrey

liffere the from up a very sub-orlinarily

(reference

AccorEing 5)

the

to _oint

 

Technical

NACA

'B of at

of

application

directly

_ue

the

same

only

momentum

so

that,

to

the

the

forces the

substitute

&ietributlon

moment

at wing,

the

wing

secti0n;

for

is

which

x

from

of

plane

fuselage located

is the

moment

from

solved

a

simple

unit

plane,

with

form

non--exlstent, lift

with

is,

of

_R

as

the

thus

the

right

of as

_

the

the

&istance

angle

reference

yaw

in

were this

a%

f_selage

in

flow

the

fuselage

width

segregated

this

angle

which

the

fuselage

dlstrl-

through

the

if

angles

at

_ressnre

passing

axis

fuselage

an_

the

ahea_

momentum

that

the

%he

over

portion

vertical time. Then,

at

fuselage

the

long,

sufficiently

plane

meets

the

be

%o

reference

integral

fuselage

_he

reference

point,

a

ass%une&

that

the

nose,

equals

in

fixing

direction

5he

bution

is

fuselage

after flow

woul_

the

of

8

1036

consideration.

_ex%

area

on

force

air

free

a

aerodynamic circulation

as

this

leaves

the

the

place

separating

the

to

go.

Memorandum

_ortion

8) X

&A

Yet, right;

if

the

_ngles

to

fuselage the

el i_.tAc

oF In&er

integral

is

(Vn

an_

being

axis)

Since

this

rate_

to

a

the

f _t.

=

&f

the

2].:,.%e,

Differentiation

1

axis

may

flow

at air

pVnm

of true

_7_ -

the

approximate_

right

angles

volume,

=

at

axes for

it._ _??l_r_x'mate

flow

be

bRs

e'ren

the

%0 _o

that

pv__

at

is,

_7r -hR

an the

m

right

angles

tc

ratio

of

ellipse.

a _se

cylin&er

for

all

the

&egenercross--

justlfie_. with

q

enongh,

components

}:oli_

_ppears

long

comprised

independent

fo:cmul_

form_

for

the

-- Vn_.)

Vn_

cylinder

section

n

Cv

is

fuselage

an_

two--d.4mensionai,

f

R

respect

%0

x

then

allot&s:

(3.3) _Ix

_

_x

 

I0

_AC_A

By

of

reason

_echnical

the

of

disappearance

b2

total fuselage lift is zero at both the desire& free moments a_Litionaily fuselage.

free

This

No.

Memorandum

moment

for

is

I036

so

the

its

computed

ends,

supplied any reference

hence gives by the point

0

and,

after

partial

integration:

°f .

_

b2_

(s.5

_Lx

o

For

of

surfaces

turbed

=

by

the

on

which

the

the

wing,

we

revolution

of

presence

get,

not

is

dis--

because

constant

qB or

the

same

result

as

=

EX

- T Munkle

for

-- 2 vol.

the

ship hulls. might be a_visabls It then rection _o these factor free fuselage pattern,

containing

length, except what slenderness to

flow

the

the

from rear

the en&

flow

at

of

effect

the

of

moments

to apply momenta on

finite

a

air-

cor-

1(unkls

fuselage

knowing relative value is primarily due to the fact the fuselage ends still varies somewhat

for the ratio

theoretical

that

the

free

(S.6)

difficulty to apply.

of not quite The reduction

assumed two--dimensional pattern; s_n_ while the contributes to the free fuselage almost nothing the portions directly before the o£ the fuselage

moment, wing, which certainly are not encompasse_ by this reduction through the effect of the finite length, contribute very large amounts. Hence the actual val_e for the correction factor is likely to be far closer to I than Hunkts quantity (E 2 -- K_ K _). So far the check on a large number of

measurements

tion

of

factor the

has in

fuselage.

the

shown prediction

small

of

nee_ the

for

such

longitudinal

a

correcmoments

 

NAOA

Technlcal

l_emorandum

presence of the wing is The to 5he wing circulation. The the angle of attack is:

q

dm

allowed change

for of

by

the

relating moment

with

(3.7)

_x

f

S

ii

1036

No.

0

The is is

d_ d_

0.

is

Behind

from

wing

alent

_--_

uprush.

in (fig. in A

V)

llen

=

of

ratios

an

the to

is

To

•

of

follows:

wing

downwash

the

stern in obtained:

_ing

greater

than

1

values

the

ca'

the

aspect

the

values

or serve

are

equivalent as

the

to

a

basis.

Since

_-_

yes

=

rises

value. of

Before the

somewhat

as

before

shown

the

in

a

_.ting

for

computed

llft curve Yor other

prev-

slope aspect _ropor--

fairly

not re-e_ge to a lea&lug with respec_ to means of these itself

is

•

For (c a

this

reaches

peak in wing proximity, this high value produced _ut integral She wing Che from certain point before it. The integration equation (3.7)is readily accomplishe_ by Cllr

stabilizer

d_

approximately

converted

values.

of

_--_

8)

the

yawed

_hat

&--_ _

(fig_

of

the

because

is

attack

hence

chord;

vicinity

to

of

region

reduces

assuming

calculation

anglo

the

wing

e_ge

estimate

ratio,

in

trailing

always

may

the

the

when

the

f_ow

to

exact,

exact

The

with

parallel

fuselage there is

the

flow

yawed

Altogether

8 ampect ca t = 4.5

tion

the

sufficiently

linearly the

as

practically

flow; at the and elevator

It

the

of

expressed

wing _

change

O)

the the

prediction same

of

arguments

the

zero

hold

moment

true

except

Cmo

=

that

cm t1_e

 

12

NAOA

Technical

No.

Memorandum

10$S

is usually conslderably • less. Given exact effect the llf% of the airplane pr.ece@ed by several zero directiom lift distribution calculations, the respective _ values are _etermlne_ an_ the integration with respect to equation (3.5) ce'rrie& out. The _isplacement flow _ue to wing

finite thickness wing the consideration may especially

true

if

Cmo

then

Is

value

location bution

of from

heretofore played in no part be ignore_ This is not altogether. engine nacelles involved, where the are quite intimately associated with _he which

the

wing

on

the

fuselage

the

The moment contrivery small. usually

fuselage.

brag

is

The arguments so far were largely l_atterned after conditions fuselage, that is, relatively at the airplane long bo@ie_ com-_are_ to win_ _hord. But the conditions are somewhat different on engine nacelles because they ueu_lly extend only forward beyond the decrease in nacelle wilth along

_

the wing. the wing

chorl

the

of

reason

the

normal velocities, induced by the nacelle, themselves _e-crease along the chord. Since these induced velocities are proportional to the angle of setting of the nacelle, it implies a curvature of the wing inflow _epen_ent on Ca, an_ in turn, additional wing moments dependent on ca. Hence which is

value

momen_ wing

moment

_ue

there readily

exists, besides computable from

_o

effect

the

of-_he

represents a further unstable • inal moments. I_ _s estlmate_ With

_v e_ge,

as _m

edge,

slope wing

at

according

Cm°

Integration the nacelle

=

to

nacelle

c_ntrlbution

as

airfoil

at

theory

longitu--

leading

trailing

(mean--line gives:

--

of the _ values over region itself exclude_,

a

which

_he

wing

Prandt --Birnbaum)

i--6

_acelle (3.7),

M?G, to

follows:

flow a_ of the center, and _h

two--_imensional

theory

but

the

the pure equation

"

the entire approxlma'tes

wing, _o

b/S =

/,dy=/ dy

of

the

order

a

moment magnitude

wing of

(S.9)

--_

--b/2 Hence

b.

under of

the

effect

of

the

nacelle

 

NAOA

Technical

Memorandum

Eo.

I03Z

13

(S.lO)

I

where readily

%G

is the_wing chord in the nacelle seen that this moment contribution when practical an_ wing negligible nacelle involve&,

To

illustrate: e_ge

i

=

(UGh

O)

is

linensions

are

nacelle not protruEing an& _he width of which

bayou&

wing

lead-

the

trailing

wing ing

center amounts to about Z/4 of e_ge, gives a moment contribution

1 _

region. I% is far from

0.5

b b@ @

that

at

the

at

of

%@_

The manner of moment fistribution over the wings is exactly predictable on the basis of this simple calnot culation, since the mutual in_uotlon of the separate wing sections pro@uces v_rious _isp acemente, but little touches the total values as a rule. It is clear that this additional

wine

nonent

termination, wing.

celle

Moreover effect to the

when

also

must the

nacelle

inclu&e_

is

practical

of

stability

the

neutral

stability

longitudinal

points;

check

an

Cmo

Ee-

angle

@Ith

the

stability

the

_x_

point

practical

author compute_ these values on which the displacement of

stuli_s

the stability as _isplaoemente

with

a Xn

To

at

the

noted, when computing the naairplane, that the transverse is Alrea_y under the influence the nacelle moments must be often

always recommen_el to represent aircraft components of separate tral

set

in

it should be on a complete engine nacelle

flow so that of the fuselage, increase_ in proportion. In

be

as

we

l

use for

forwar_

it

is

contributions in neudisplacement

get

aMa

of a

these

formulas,

series of neutral stability

the

_w types, point ha@

 

14

Technical

NAOI

been

from

_etermlned

Memorandum

_ifference

No.

iOS6

measurements

in

wink--

tunnel _ests. Table 1 gives the results of this checkp with the note, however, that _he measured displacements stability point, at 5he determination of which neutral certain uncertainty, is inevitable instrumental reafor sons, laSion

n _ewln_ termintunnel. e_ before ha_ from beethe

TABL_

I.-

_US_LA@_

Design

O_

DISPLAORM_NT AND

NAOELL_

the

NEUTRAT. _0_

start

STA3ILI_Y

8_.VERAL

_w

10o

Type

A:x:n t

Measure& A

B

.....

Nacelles

.....

Fuselage

.............

_nbo_rd

Ou_boarl 0

Pus elage P_opeller

D

..

]_'us elage

Nacelles

.

•

Nacelles

.....

.

.

......

.............

}_ount

........

.............

Nacelles

....

Fuselage

.............

Boom

2.0

........

_us e el lage

Tail

•

.....

.

.

........

.........

.

........ @

.

.

the

POINT

DU_

TO

TYPRS.

=

zOO

a

ealcu--

_.Ae._. cl ca

0 omput 2.3

. 2.2

2.4

4.1

4.1

3.7

3.7

2.4

2._

9.2

9.4

0.8

0.6

1.4

1.5

4.4

4.2

2.0

2.0

. 2. 2.0

2.3

5.6

...........

of

of

6.0

. 4.0

4.4

Fuselage

.............

4.0

4.1

Nacelles

.............

3.5

3.5

e_

 

N_CA

A

similar

lage-wing of

ch@ck

by

Muttray of not

forms

design

minimum of such

of

zero.

wher_

great at

Ac-tually,

there alone, for

readily

apparent

by

so

faire_

measurements 540,

show

that

any

wing

effect

In

on

_eveloped

here

engine

and

wing

the

separation monte do

quite

so

vlously

for plain

the

the

very on

against

the

ioc'atlon

are

merely

in

the

appraisal

the

the

the

at

of

measure_

far

of

curves wing

do m

--

the

of relative to

not

is

the

as

arrangeITA0_ Re-

which

end

the

checks

so

parallel

values,

5ables

of

This

5__0),

the

of

fusela'ge

midwing

slight,

shifted

ca

the

formulas

location

that

moments

_ifferent

_Isregarded.

the low--wing _igure 23 of

plainly

No.

scarcely

of

No.

(Rep.

not

Report

the

the

of

Muttray's

be

to

it ig is

forms

have

that

on

is

especially the records.

the

moment

contribution

tests

very

the _R

N_0A

size

the

follow

That here

therefore

_MR

fuselage

NAOA

the

by

hence

fuselage

restrlcte& of

_isoloscs

fuselage

other

not

which

rest,

of

out

pointed

_ith

additlonal

normal can

_.rorks

here,

dealt

value,

the

those of

stability

are

some

plotted

the

the

phenomena falsify

5@0

moments each

with

no5

No.

port to

to

well

is

fuselage

the

For

.and

ideal

value. dealt with

with

as

dependence

relative

quite

it

ca

fuse-

t'he

of

no

this matters

U.S.

confirmation

treated

ca

also

flow.

moments

nacelles

monoplane;

i_

fillets

for

ax_s

of

cited

He

certain

at the

the

conclusion

of

15

ScoWl

problems

the

a

exact y

the

design

comparison

root

are

the

fuselag@s

completely

into

series

significance.

relative to wing great significance well

the

i036

a

support

on

drag

several

flow

wing

6)

a

on affordeE

further

(reference

were

Vandrey also

In

theory.

No.

Memorandum

combinations,

our

is

Technloal

report.

value

Oh--

&eDen,s

_c a to

a

considerable

AIR

LOAD

UNDER

_he change

fuselage of

flow

wing'section. all

supplementary

upon

extent

the

DISTRI3UTION TH_

_LONG _. O_

INFLUENC

the

influences velocity

In

addition, flows

in

skill

it in_uce_

THE

_HE

wing

quantity forms at

of

a

the

operator.

_[ING

3V/S_LAGE

chiefly

and

the

a

_hrough

_irection

at

fixe_

bpunEary,

wing,

which

each

for means

 

16

Technical

_AOJL

ITo.

Memoran¢lum

i036

no velocity components at right angles to its surcan exist. Any metho@ for solving the fuselage efef course, these two actions. fect must, allow for A further effect &iff_cult to define mathematically arises from the boundary flow of _he fusela6e, which in many 5hat

face

_ecrease on the wing section llft close on _ertaln low--wing arrangements is responsible for a premature separation of  he wing flow to the thls a_Jaoent fuselage. However, boundary layer effect ehoul_ no longer be exeesslve on the aero_Lynamic-ally clean fuselages of _o_ay. oases results to the fuselage

in

a

an_

flow past the fuselage is suitably H_vi_e_ in a _isplacement parallel to the fuselage one flow axis an_ at righ_ angles to It. The first usually affords slight ±noreases of velocity in wing l_roximlty, so which are much greater as the slenHerness ratio of the fuselage is smaller. from the transverse of the The velocities flow fuselage, to the wing the slgnifieance of an normal have angle of attack change. The

Then

the

about

olrculation F =

the tween tlon

at

angle

effective the of

right

_he

angles

to

an_

With

lift

zero

is

section

(4.1)

_eff

Hirection

section.

wing

wing

c vt _eff

attack

of

flow

local

a

being the

zero

as

_n

_irec%ion

llft

stream we

angle

the

Hireccomponent

get

wzl

=efz

be-

= -+-

( 4. s)

whence F

_he butions

normal

with

_F

_he

that

is,

lift

_irection;

the

=

local angle

_

angle between

WnR

Or

wn

spee_

wn

=

the

Wn

is

v

+ of

(4.3)

bull%

wnR

+

up

three

contri-

wi

attack

the

from

fl_ght

supplementary

of

(4.4)

the

wing

an_ normal

path

section, its s_eeH

zero un&er

 

I_ACA

SB

the

effeot

induced

of

Technlcal

the

fuselage

from

speed

the

No.

_emoran_m

and

w i

usually

the

layer

vortex

17

1036

negative

produced

behind

the

win_. The Eutt

lift

density

per

length

unit

is

according

to

the

law

a--_oukowsk_

_A

hence dA

--

= pv

&Y

comparison very

dissimilar

that

the

ent

product

in

flow

transverse

win_

with

a

span, fuselage

3/4

chord.

_Ing

leaving induced

angle

speeds

extent 9,

finite

le_gt'h

where

of

cross

sectlon

a

Such ern

conformal

changes. span v of

of

at

fuselage elimlnate_, approxlmate computing

rational

the

manner.

is

a

along

elongated

the

of

for

the

instead

hereby WnR

course

This in

since

from

are

possibility

product one

as

changes

Intro6uoe&

independ-

So,

very

a

the

propor-

almost

figure,

with

reflected

fuselafe

slenderness

ratio

fuselage at

to

are

can one

the

of usual

be

the

into

a

so

usually very

transformed

known

manner.

wing

in of

_

in--

4

=

the

slit

(fig.

rectifying

are

a

circle

methods

circles

But or and

by

fuselage i0).

applie_

readily

closely. %o

obtaine_

that

vertical is

which such

approach also

the

%rans£ormation

sections

least

normal transformation,

changes

conformal

forms in

attack

wn

the

section

speed

adde_ the wing

for

WnR

speeds

means

any

and

for

length,

from

resulting

to

cross

error the

w n

Justified

the

the

is

of fact

illus%rated.

The

or

of

following

fuselage.

decisive

the

along

of

the

same

Then

affords

figttre is

the

only

tu n_ n_ t i o on n as s tu

attac-_,

epee_

fuselages unusual

velocity

of

finite

of

having

normal of

largely

of the

V

ratio

seems

it

cylinder

The

is

flow reveals

angle

normal

the

(4.8)

velocity

an&

slenEerness

product

the

ratio

inflo_.t

fuselage

the

the

this

of

ct

displacement

circulation

to of

the

slen&erness

longitudinal tional

of

wn

mod-

to or

ellipses

divergent ellipse then

by

treated

_ith

u--

z +

l y

(4._)

 

18

NACA

as

comple_

lage

Technical

coordinate

axis

Memorandum

in

the

No.

plane

at

IOS6

right

a_ugles

to

and

'_ = _ + iy coordinate

the a

in

slit

vertical

the

plane

resulting

(4.8)

where from

fuselage

the

conformal

merely

is

tranmformation

= _ (u) the

z

component

transverse

to

of

here

_u_

conformal

iS

in

the

is

further

_

formal

length

we reduce

value

problem.

for

the

the

the

is

of

the

the

the

of

lift

if

flow

is

downstream

to

of

the

the

wing

c_

v

fuselage

a

the

fuse-_

compliance

Con--

surface.

a

form

where

_or

this

a

potential

potential by

the

rolling-_p _oundary

boundaryfunction

wing,

afforEs

downstream process values

of of

with

- _im ¢ X. .--_ _-- _

F  

7),

(reference

sufficiently

Denoting

disregarde_. from

a

induced

again

effect

the

in

formulas of

a

induced

satisfied.

distribution

the

for

f_selage

introduction

conditions

wing

the

of

elng_l arities

fnselage

themselves

Trefftzte

to

The

the

the

introducing No

the

distribution

of

applie&

be at

order

load

of

of

of

presence

the

of

evident.

to

s_ppleme_tary

vorti_e_ far

of

knowledge

brings ate

two-dlmensional

from

derivation

axis

-_

the

nee_

revert

_hlch

the

reason

the

uonditions

con_itlons

purpose

to

of

advantage

transfornation

these

Eq

by

on

fuselage

the

boun_ar_

-_

solution

pTinclpal

infinlte

of

equal

flow

displacement

_he wing the presence where taken into consideration.

the

within the

°The

is

part

toward

pre&icate_

Here of

real

_(u)

plane.

C4.9)

supplementary

_Rv

the

flow

speeds along must also be

lags

=

funotion

parallel

the

fuselage

the

w_2

pure

fuse-

(4._i)

 

NAO£ the

J_-_

about

circulation

_ _:_tion

above

line,

Technical

She

any

an_

wing

section,

wing one

below

19

1036

one

after

wing

the

along

integra-a

stream--

is :

r(y) -   An_,

wi_h

wing,

exactly

w i

we

Since

the

presence

flow

we

from

plane _

(y) -

half

as

wi

2

(y) at

great

(4.1-2) the

poin$

of

the

ge_

of

again

consideration

of

No.

Memoranlum

now

_he

for

on

remain

fuselage the

must

in_ucel

tr_usform

Gonformally

U

_z _z

p_ne

_,

be

taken

into

supplementary the

where,

wing

potential of

_(¥,

course,

the

z)

_mounts

unchanged:

(4.1_)

while

(The

the

conformal

mean

value

to

zero.)

close

sU i

(y)

is

t6

the

slit,

metrical of

airfoil

of

above

reenSers

and

below

the

%he

derivation

wing

is

always

Hence

readily

air

-clu

factor

_efined;

represent.ing load. theory

since the

distributions,

follows

at

no

fuselage,

the

speed

at

remains conventional

right for

angles symformula

 

'20

_AGA

Technic_l

_

so

that

fected

the

calculation

with

th_

Altogether in

the

U

in

usual we

the

llft

get,

No.

Memorandum

(4.z_)

_

y-

"z

plane

_istrilratlon

when

10S6

can

be

ef-

method.

transforming

equation

(4.3)

plane

I

(4.1a)

47T

whereby

r(_)

_ r[y

(7)3

t(y) = t [y (_)]

To

_impllfy

the

calculatlon,

we F

-] (4.19)

for.m

(4.2o)

by

$ 1

--i

hence

(4.21)

 

_AOA

a@vantage

_he of

tho

that

wing

of set

of the wing is readily

angle

_echnical

liemorand.um

_ivi&ing

the

lift

No,

lOSS

_istribution

into

an angle with the fuselage anl fuselage together set at apparent:

at

axis the

and same

(4.24)

+_

_-_o

that

Then:

_io)

-

(4._5)

an_

yRmetho_ This except that

2_ little the wing It is :

and

is no different the wing chore

R _u

factor

the

while

care where

span

AIR

must the

in

LOAD

the

is

_etermined

from the other usual multi._lled by _he

is

twist

(_y

be exercized in lift distribution

the

_

plane

DIS_I%IBUTI0_

Since the distribution closest relation with the it

(_.28)

\¢u/

first.

-- _2) locating is to

follows

ON

THE

is

volocity velocity

_ivi_e_

by

it.

5he points on be determine_.

from

_USELA@R

over the fuselage _Istribution lift Wi_h the potential

previously for %he additional of the wing, the local flow

methods, correction

duo along

width is in over the area ¢

introduce&

%o _he action the x-direction

is

 

22

17£0_

Technloal

Hemoran&um

v

=V

+v

l_o.

I036

(5.1)

x

with vx

according

Then,

=

_x

3ernoulliJs

to

P [(v _o + 2_-  V'  V'= = = P + -_-

which,

allowance affords

with

or_er

only

for

P

an_,

after

-- Pc

integration

vz)_

the

small

---

pV

along

(9 -

+

theorem:

a

Pc)ax

vy_

+

of

terms

(5._)

vz_]

the

first

(5.s)

_x

of

strip

= -

+

the

fuselage

wall:

(5.4)

pv_

--CO

wing

The_

the

even

on

extent

to

loads.

the

which

Since

_Ifference cern, terms

is

VxS

since

they

the

upper

rye

are

cont.ur

lower

that

Vxa

in same

behin&

in&icatlon

strip

the

is

of

principal

omission (5.2) of

the of

up

takes

by

equation order

far

up

si&e the

an

is

taken

seen

the

_

fuselage

forces

an&

+ of

potential

single

the

easilF +

the

fuselage

for

of

it

of

course

air

fuselage

the con-

of

the

is

Justlfie&,

_agnitu_e

the

quadratic

above

an@

below. The easily use_

in

the

lage

is

represents&

%_('_) of

the

is

of

&etex-mination

accomplished

wing

the

by

a

prediction

expanded

in

_

by

of

on

the

fuselage

vertical

_aylcr

series

slit from

+ (r-

is fuse-

the U-91ane, the poeltlen hsIght

in

T_:

=

con%our

¢onformal transformation same llft &Istribution. The the

....

 

I_AOA Technical

_nd

f oi-

"g <

Hemoran_um

No.

10.36

23

g_

1

while

in

both

(5.7)

cases

= 2 WiCY = o) The aspect relationship

The of

U

this plane,

ourve then

_o (-_) is then of as of y (_) being known, original fuselage on the presents no _ifficuity.

(5.s)

shown in figure Ii. the transformation contour in the

of the distribution solution air load along air load is again divided into two parts, one giving a free moment, _he other only a lift with the resultant a_ _/4 of the center section, wing l_or the &is_ribution of _he air loads upstream an_ _ownstream from the wing only the first porportien is involved. The dis-tribution then follows immediately from the formula (H.3). _or

the

the

fuselage

In _he corre_pon_ing

the

region of the wing to the chordwise

is the lift _istribution

_istribute_ of the wing

portion which woul_ lie in _he fuselage zone if the fuselage _vero net the_c. The very local lift coefficients high pro_uce& in the neighborhood of the fuselage nose are, however,

considerably

and

_rop

_-_ d_

very

compensated rapidly

_o

zero

according

at

the

to

(S.3)-

nose.

wing

The

_istribu_ion so obtained along the entire fuselage needs to be a little but withou_ particular care, compensated, since the transverse force8 an_ moments in the fuselage follow only

not lif_

after integration very susceptible

an_

the

fuselage

from these _istribu%ions| %o small errors, so long longitudinal

moment

as

assume

hence are the total the

values

 

NAOA

_4

computed

in

shown

figure

in

the

PRACTICAL

The

foregoing,

_o.

1036

distrlbutione

are

then

as

I_.

LII_T D ISTRI3UTION

FOR

ALLOWANOE

application

previous

Hemorandum

OALGULATION'.O_

WITE

The

Technical

sections

of is

the

TEE

YUS_LAGV,

theoretical

predicated

on

results

of

following

the

the

necessary

data: I.

_.

The

A

twist, the latter being appropriately meaBure_ or reduoe_ relative to the fuselage axis in the zone of the wing as reference axis. Also of importance is the so-called twist, %hat is, the position aerodynamic of the zero lift direction of each wing eectlon an_ not of the wing chord relative to the referwing

ence

axis.

sketch

of

tion The for

the section For the

chord

of

and

the the

fuselage wing

on

showing

the

the

exact

fuselage.

thing then is to obtain the function _ (u) conformal transformation. To this end we plot the through _he fuselage the wing root at 3/4 ohor_. fuselage of circular with radius we get section R first

R _

--u + --

(6.1)

U

c1_ du --=

The

trace

of

the

wing

in

I__

1 the

u _

_--p ane

R

the

loca-

factor

2

follows

at

 

NAOA

4B

Tophnical

Memorandum

_B

1036

}To.

(8.4)

for

which

z =

0

arrangement)

(midwing

R2

= y

\_) The

formed

fuselage

in

two

transformed formei

in

with

into a

a

slit

the

transforms ellipse

(z

the

=

with

the

circle

is

_hen

trans-

U--plane

the

an_

The

is

then

equations

(6.7)

tranz--

intermediate

function

(8.7)

to

a

circle

Rm

4

=

semiaxes

line of

cf

the

centroii@

A m -- - Bm

(S

4

A

and

3

then

becomes

a

_A+_

and

(6.10)

B)

circle

(6.9)

2

transforme_

of

radius

into

the

vertical

slit

= = u_ + __2 _rom

firs_

u I

Rs _his

is

= u_ + --

_i _ =-

The ellipse with radius

in

13).

connecting

• E)

section

U1--p ane,

the

(fig.

the

u

which

in

(6.6)

cross

ellipse

circle

affords

transformation

= _ + y-_

The

vertical

(6.s)

Y

elliptic

stages:

simplifies_to:

it

by

(6.1o) then

follows

that

 

_eohntcat

NAOA

2B

1_ o.

Memorandum

1 03 6

(6.11) n I and

_z_

which

multiplied

by

-

u R_ _

=

other,

each

u_

-

(R_ _

(8.1_)

R_ s)

give

(6.13) or,

of

because

Es

(6.7)

2A A--B

and

_

u

(6.9):

+

--------A B (u s +

A--B

Ba ) =

0

(6.14)

hence 1 A--B

Thls

is

%he

conformal

function

that

changes

the

el--

U--plane eLirectly into the vertical slit in the U--pl_ne. The correlation between the points of the U--plane, that is, especially %he coordinates of the wing ariel those of the U--plane is obtained by elementary calculation by means of equation (8.15). It is best to put llp_e

in

_he

u

where point _

a from

-- _.

=

z +

y

=

a

cos

is the arlthmeti¢ mean the two oentroi¢Is of

_

+

Ib

(6.18)

sin

of the distances of the ellipse, while

the % =

Then

V_ _ -- a _ + _he the

i

_--coordinate of lift ¢listribution

bs -

b

cos

_0 +

the transformed then becomes

ia wing

sin

(s._)

_o

neede_

for

solving

 

NAOA Technical 1

F --J_(_) --

M.emorandum No. iOS6

sin

(Ab

_ -- ]3 a

sin

27

_)

F T"

3

A

a

(6.z8)

)

A--B

It

likewise

affor&s

in

the

same

manner:

a.'-E._- 3 Herewith reads

the

cenformal

( 6.19 )

,h.,_._._

factor

for

the

llft

distribution

(6.2o) i +

_uselage cal

fGrm

require

Having _u ing

sections

'

this

a

diverging

special

establisheQ

_._e again

t

(_)

_)_

markedly

conformal

the

ana

_(_)

(a 2 -

from

the

ellipti-

function.

y,

correlation

between

are

obtaineC.

readily

Y

anQ

_ollow--

f.orm

ot(_) io

anQ

ae

function

is

introduced.

_O poser

anQ by

of

_.

For

Then

_R

in

the

writer

the

the

equation

ensuing

of

solution (4.24)

(reference

calculation

by

8)

the

means yields

base of the

_

=

distributions the

method

equation

pro-systems:

 

_8

NAOA Technical

l.:emorandum

J/o. 1038

3vnVon

(e. Sl Sl) )

m+1

i

 

The

buy

an&

from

the

re,_l

Applying _,ring, we

1 as

Bun,

(reference

report

aB

well

 hU

anal

_n

can

read

8).

the thus computed first form

circulation

v_lues

b

'Y = V-. BThen _ fuselu, ge fucelage the value equation

be

to

the

(8.2s)

normally in the fuaelage region; on a section the _Lietribut.lon along _he wicl_h then has the form of a semiellipee, also at fuselage center being, as easily foun_ from (5.5):

_ecr.e_eee of

elliptical

7_I

=

Y m

+ _--

b/2

m+

(B.2,1)

_

2

with

w

i

_i o m

+

_ =

I

(cl'_

t_ L_ 1

where

hR

is

the

height

m ++--_--i-_  _ _m

and.

+

bR

-

m 'o@. +__.+ _s+ bt"¢'o "¢ @._.

1

wiclth

the

_.

the

of

fuselage.

 

I_0A

few

A along data

am&

no

are

available of

so,

by

a

a

in

the

Ca

incl_de Plotting

of

 6  6. . slightly

At below

dca

for

becomes

for

ca

=

0

than

affor&e_ at

high

whlch the

the

pressure in

structure margin

to

the

sir

In ments be

a

always

that

be

very

accurate

that

at

near

the the

to

the

O

as--

_irectly an_

It

for

ben&ing the

imply

a

the

3ut correct

that

as

in

further

wing.

of

points

of

moments

of

effect

so

pull--out

aEv_ntage

sole

of

the

lift.

ca_e

all

ca

the

been

high

the

to

_istribution

method4

this

regards

the

of small

the

to

affecte_

of

the

the

the

and fuselage

measurements.

of

the

the

as

these

it

is

the

wln_

itself

tu/_nel in

must

be

_iffer-small the a_e_ _raw

somewhat tunnel,

boundary matters

wi_ens

course,

in

necessary

really

a

of

of

the

process there

numbers

transition the

in

care

manifest

measure--

obstacle

comparatively

tunnel9

turbulent; by

the

the

must,

both

attac_

weighing

airfoils

Reynolds

of

greatest of

with

In the

angle

The

with

calculations The

because

with

laminar

the

obtaine_

usual

the

associated

scattering

ha&

reliability

case.

Involve_.

somewhat

of

carefully.

is

particular

from

loa_

always

at

ei_o

slope

accor¢ ing

chalacter

not

_oos

safe

_

3ut

assumptions

different

an_

more

this

b_h_vior

loa_

it

accuracy

measurements

tack

ha_

comparison

the

enees

an_

combination the

relative

fuselage

3)

in

throughout

the

(case

also.

ongth.

_velghed

cannot

_

negative

very

the

the

constant

obtaining

entirely

lift distribution loaves one on

the

hence

wing

 

alone.

to

shown

the while

smaller

for

as

equal

computing

as

_ynamic

tD

local

by

distributions

wing

owing

of

fuselage

consiste_

8_fety

"wing

lif_

at

theoretical

necessarF

of

the

Eence

for

obtaine_ to

of

affori_l

is

calculation

graph

alone,

are

the

the

value

ca

wing

_eterminel.

it

in

a

positions

metho_

&ifference _rihe_

the

for

combination those

conventional

0

greater,

the

and

gives

under

solutions

makes

alone

=R

high

been

the

of

15.

measurements,

&istribution

actually

wing

that

medium

with

llft

however

the

=

c_

distributions figures 14 and

experimental

against

is

values

the

of

figure

fuselage

has

which,

case ca

the

29

lift in

comparison

confirmation

values,

the

a

10S6

I¢o.

solved shown

which

fuselage

certain

comparison

total

of

are

for

measurements

influence _ven

Memorandum

model examples an& fuselage

wing

I_o

Technical

the

unusual  w  wh hich la_-er arc

zone

is flow also of

_-

 

SO

NADA Technical As

hid

regards

in

the

the

Mem.oran. t_:r..t

theory

falsify

the

:_ctually than

the

1

the

half of

attac ¢

at

the

largo

lesser tion

suggests.

tion

of

available

the

time

apply

a

suitable

distribution little

from

not

preferably

de----d_

is

fs.r

circular

nacelle

region

conditions

in of

the

case

the

a_gle

from results change some

the

than

in in extent

on

3ut

pre-

changes.

an_ to load

hits

this

are

los_.

Ca max

on

the

U.S.

midwln_

a

which

the

the

subtract

oomblnatlons

the

be

fl_w the

Is

accord

respecting

type

wing

and,

_.ring

arc

of low--placed is of attach

as

with

is

reduction

stated

the

me&iliad

be

that

past

very

small,

before,

the

the 3/_

downwash the near

flow

can

difthe

considerably

by

a

anticipate_[ at

a

usually

governe_ nacelles

somewhat

to

_ecroases

displacement

distribution

wi_h

dealt similar

wing

itself

the

applying

a

_ir

to

rate

the

by

total

f_tselage.

must

width

lift

the

any

at

a

are

oxpodlent

a_

o£

lift

solu-

available

is

of

in

14).

the

longitudinal

the

to

of in

calcula-

inluceE

better,

because

types

nacelles effect

its the

the

built

(fig.

Although

fuselage the

better

engine

ferently. since

_w

fuselage

_he

factor

the

permi_

the it

prubably

near

_,ffects resulting

to

of

extent

wing--fuselage

being

explore@

the

the

caBes

expecteE

quantitative neither

enough

of

condithe

be

than

Impossible;

magni_ulce

is

lift

very

attaclr.

measurements,

what

the the

of

eim_le

yet

reductio:_

or,

primarily

On

to

reliable

particular,

fuselage

the

flow

the

in

to

greater

since

arrangements, to

as

is

wing, for

anglo

theory.

lift

particularly

of

being,

sufficiently

the

decisive

numerous

order

the

concerns,

due

is

airfoil

for

satisfactory,

facts

the

whole

miiwlng

measurements of

is

induced,

dc____

A

these

t

on

of

change

Eiction

error

--co

behln&

therefore

proximity

the

far

3/4

of

are

W X--'_

&ownwash

This

amounts

fuselage

For

at

wing.

nature

this

of

_ownwash

tions

=-- 2

results

effective

anglo of

fundamental

_ssunptlon

Wi

can

one

itself

1036

No.

wing.

at

the

The

accurately angle

of

t

in

flow region.

inlependent

na_elie wing,

which

accompanying defined

attack

to in

the w

 

I_AOA

nacelle

zone

measured

of

and

c a

the

on

are, in a more

general,

Bution

along can

be

may

result

acts

wing between of lift in tors

are

safe

side

ditions

a

the

small

as

regards

OF

now

we

of

the

fuselage

less

no

flows

fuselage the

ated

is

rolling

moment

the

elsewhere

Sideslip

is

l_ge flow profuoes uhan_e

in

attack.

signs

on

the

seems

at

Jacent is

to

still

total

wing

mutual

fect r

as

follow

solution of

the

this

of

of of

the

transverse

this of

the

the

of

foregoing; To begin

but

a

location to

the

of

wing,

of the

an

ad-

arm, for

there

the

effect

wing

by

change

lever

of

the

sections. requires

change the

anti--

portions

yaw

with

follower

is

wing

fuse--

the wing, hence a

attack

in

t_e

occurs

which

compensating

in

which

displacemen_

phenomenon

moment

As

with

aSsoci-

of wing_

the

sufficient

attaok

unthe

decisively

mathematically

flow.

symmetry calculation.

fuselage.

angle to

con-

on

by

Individual

effect

the

flow

airplane

is

results

the

angle

the

the

the

rolling

result

the

YAW

T0

component

sides

without

a

on

As

fuselage

appreciable

on

effects

_&wing @)

normal

restricte_

interference _o

the

the

an

one

our

important.

the

upon

solely

first

when

decrease these fac-

if

accompanying

accompanie_

Although

load it

of

very

for

in

as

distribution

moment.

%hess

Their

wing

two

region

DUR

phenomena

of

depending components

Then

symmetrical

transverse

of

lift

rolling

the

angle

symmetrical

MOMENT

(reference

course,

to

which, velocity

different a

of

proportional

the

of

occur

leaves

with

Just

location

the

air

the

stresses.

_escribe&

are

with

flow

been

on

the

wing.

the

always

to develop distri-

may

a corresponding wing. Even

fuselage.

effects

explained

in

utilizel

a_

indirect

there as

have

alone

the

flowrepeateily

the

structure

used

in

nacelle

on

ROLLIE@

are

of

in the

largely

the

subsequent

wing

method

change the

set

and of

ON

noteworthy

symmetrical

of

wing

dealt

of

minor

probably

3_JSELAG_.

the

the

same

increase

the

to

the

plate

the nacelles outer zone

characteristics But

A

it

an&

in

the

effect

worth the effort regards the air load

effect lift

the

not

is

a

discounted

_,31FROT

Up

like

that

Since

forces

chord,

the

modification

obtained.

As

followed,

under in

it

31

1036

distribution

nacelle

the

distribution nacelle

lift

this

transverse

small, method.

accurate

the

assuming

is

the

and

moments

fuselage

so

by

No.

Memorandum

difference

nacelle

bending

Technical

case

under of

first the

ef-

symmetrical

 

NACA

32

Zechnical

Hemoran_um

No,

10.36

is flow the flow transverse to the fuselage assume_ to be two--llmensional the section through the fuselage at 3/4 wing chor_ bein_ &ecisive for the calculation. Then the conformal transformation affords the flow transverse to fuselage

this

So

section.

if

u = y + i,, is the COml_lex coordinate lage section, then _(u) edge,

horizontal

in

this

i_

(7.1)

for the plane about this fuze-is its reflection on a knife case. Then

=Vv

-- Iv Ivz z

(7.2)

a measure of the tion. Sufficiently

velocitF flow about the remote from the fuselage,

_.lhence the angle section follow_

attack

i,

of a_

change

for

the

fuselage we

get

indivi&ual

wing

('_.4)

V

_hus

--,/

_

can

heCral-ang e of dihelral angle. Then

a

for

the

two

additional

be the

complete

rolling

summaril}, wing,

lift

moment. factors:

sec-

regarEe&

a

as

supplementary

to

fictitious the

fi--

geometrical

&Istribution could be achieve& But it woul& also have to include first, the usual assumption 1 X_

would ity,

no

longer

requiring

be a

sufficiently

greater

value,

--

o.

valid so

that

in

fuselage the

lift

proximvalues

 

N_0A,

5B

TechniCal

Memoran&um

No.

wing

be

1036

SS

i

in

inner

the

5y

than

the

flclen_s are

ignore

both

an_

metho_

any

also

vicinity.

the

a_

other

it

being.

elliptical

normal rise in

win

K

_Is%ri--

the

to 5he

&Isap--

the fuselage llft ooef--

5he

seems

Then

lower

lift

%he

require

Fortunately

whence

time

little

_

computin_

wou._

component velocity en%aillng a flow,

for of

would

of

it

counteracting,

yaw

for

the

that

of

fuselage

in

nomena to

5op

the of induoed

pearancs %he for

• ue

customary

On

bunion.

of

region

two

phe-

to

promising

the

rolling

moment

is:

wing

-

=

47

f

l

fCn)

z

(7.6)

--1

the

integra%ion

the

contour

by

the

_iffer,entiation

ferent

aileron

tour.

3ut

ellipse

so

f(_)

factor of

wing. so

widths

usually

the

cloeely

that

The

being

far

as

are

available

mo&ern a

more

as

yet

f

factor aileron

upon

_epen&en_ u_n

be

obtaine&

calculations for

airfoil accurate

%he

forms

on

_if--

particular

con--

approach

solution

an

seems

superfluous.

Integration within 5he

out

_oo

conformable

(7.5)

fac%o_ is

ve-ry

thir_

of _I

over -- _

power

5he in singe

small, of

easier

if

carrie_

range

2

instea&

is

y.

_o%al _he

2

wing

sp_n,

integration.

while

The

om_ttlng remaining

the error

 

NAOA

34

Hence

by

Technical

Memorandum

No.

1036

pu%ting

_c L _T

e_

the

_J

2

na_

(7.7)

h

D,¢o

in_egra

-f_ -f _ C_ C_))_° _°_ _ after

of

evaluation

the

complex

In%egral

gives

-/J (_ ( _) _hen the :B af affo for_ r_

ellip%ic

(/

y _ty =

fuselage

l

z

9

section

L

u_ 2

rolling

zT

as moment

the in

location

B [u ju2

yaw

finally

_he

(7.8)

eemiaxes

A

an_

_)]

_ (A_ _ _,)

2

of

the

(A _-

-(A_ -( A_ - _) in(. + _ ;fith

- y_(_)

with

E_-_Ju_-

_,

A--B

_t

wing

reads

- (A_ - _'))SI SIF F(7.9) .#

on

the

fuselage,

the

 

N_40A

Technloal

}._emorandum

No.

1036

35

i

b _

2 _I a_

A

+(sin hR 2

for

< z_ <

)

hR 2

or

&c

1

L

hR(h R

d7

2

c'

+ b_

b R)

w 2

_.z_ b

z_

>

2

A

ao_

I

hR(hR

2 cI

amount

The

of these data material is, at

wing--fuselage relative to

combination the fuselage.

model

_sed

NACA

the

dCz d7 is

the

wing

difference an@

mi@wing

between

=

(7.1o)

with measurement the time, very

data from are those describes the rolling

for a tions

by

hR2

z_

. .

appraisable 730 which

I_o.

-- 2_ 2_--bq-_-I

-- 2-

A

_or a comparison of available

only

Eote

b +2 I_')i

the NACA moments

the scarce.

Technical yaw

in

at different height _or the dimensions

posiof the

0. 0324 0324

the

rolling

moments

in

yaw

of high--

and

0.035_

between

lo_-wing

in--4°< region

_

of

and

midwing

< 4°   that the root wing

is,

arrangement in

fillets

the is

zone

(fig. where

certainly

IV). Withthe flow in the still completely

 

EAOA

Z6

Technical

_omora_um

No.

IOS6

adherent, the mean value from the exact result of our calculationR.

neasurements gives th_ N.r. Schlich_ing reported similar results. He found that the rolling moments in yaw a definite course when the win G root is faire_ show so as to prevent separation of flow at any point.

OF

E_¥ROT

Up been

%o

very

the

horizontal

tall

on

the

wir_g,

is,

attack

due

at

usual

not

TAIL

ON

now the fuselage'tail i_erference little explained, Theoretically

on

the

_SELAGE

tha_

to

surface.should

an

fuselage wing

discernible

inc.reaso

and

flow

positions. whe_,

prediction of the tunnel measurements

as

tall at

a

si|ailar

to

is

those

angle

chan_._e in

effect

freq.uently

efficiency _ifferent

effect has phenomena

e'ffectivo

hence

This

so

be in

the

of

ticn -d_

is

naturally

the

case,

is based uDon tL_il settin,';e

the

windrelative

fuselage. This phenomenon a further to the represents ob_st_cle in the e_perlmental solution of the flow conditions at the horizontal tail surface. Furthermore, a change

in

the

_ownwash

mw

or

in

the

quantity

d mW _m defining

the

surface is _istribution and

which

stability

to

generally

However,

since

relative

to

contribut-ion

be expected at the wing

the

results

only

dc n _ d_

the

of

the

because of the under the effect in

a.reduction

dlfforence

of

wind tunnel, the modlfied noticed at all_ P,ince two each other and practically

the

tall

downwash

fuselage cancel

of

of

the

alcove

horizontal tail air load fuselage

changed of the

is

this

factor.

product

_.efine_

by fuselage effects work each other.

in

the

no% against

will

be

 

NAOA

_echnioal

Seemingly, boundary

of

of

in

pronounced since

a

of is

tion

in

a

considerable strip

Eoerner

region

as

a

of

contraction

of

S?

IOS6

wing, is

tail

especially

blanketed,

b_r

the

i0)

to

treat

section

in

the

values

in

many

load

air

fuselage,

the

as

a

Eaturally

fuselage.

into

inroad

cut--out

the

at

the the

blanketed (reference

}To.

is the effect importance fuselage, which is more

then

strip

this

prompted

the

vicinity

tail

the

greater

of

considerable

result there

much

layer

the

Hemoran_um

the

tail

distribufact

which fuselage

and

which

affords

don quite

rational

The for

-d_

fuselage

central

fuselage

usually

horizontal

the

It

tail

found

was

to

asI_ect

the

on

_he

_ut

of

but

a

faces. by

of

a

sli_

a lift distribution circulation increases

and

decreases

of upper eidewash wash

the

plane

wing

of with

by

a

wing

also

_late.

the

with

reflection

this

induced

ti_e result the wing

in

such wing

'

with--

In a

side-

way

that

portion

a

signifies

knowing

that

-dy

velocities

span_zise is _ against

governed

wing 8.

This

sur-

is a

pro-

surface

c'ontrol

angle

peril'on.

of

wing

sidewash

formed advancing

And

of

the t_il

lateral

center.

difference

that

dihedral

trailing

lower surface, the center above

estimation

a

at

of figure

Consider

_S then on the

anf

from

the

-dy

end

to

horizontal

the of

certain

the

in

the on

to

Denoting

and

a

the

the

mechanics

_he fact

interference.

the

equal

the

magnitude

fuselage

is

on

also

of

on

the

involved, cases

analysis

&oubled

for is

&ownwash

having

is many

one--sided

an

zurfaces

area

motions

out

large

in

divi&ed

surface.

wing--fuselage

fairly

a

tail

si&ewash

order

act control

the

system in

and

like

value

arrangement

fuselage

rule

is

tail

central

significance

fiigh_

The

the

best

the

special

not only similar

duces

The

fuselage

asymmetrical

By

the

den -d_

the

on

unsymmetrical

lateral

ratio

upper

If

surface

be

of

effectiveness

influence

ignored.

that a completely bo_ne in mind. be

fact must

great

arrangements.

tall is

of

is

cases.

fairly the

grea_ siie-

sideslip. the

angle

of

symmetry

the

order

d.ihedral

forme¢1 of of 8

at

by the

this airplane

magnltu_e wing

o" =78

in uced

of center

with this

above

sidewash _

a

si_.ewash the

wing

rough on is

 

TechniCal

E_0A

3B

a result

Aa

of

the

}_emorandum

sideslip

both

1036

No.

sides

of

the

wing

mani-

to the _nount of m 8, of attack which is almo.qt completely equalizel by the inlucecl flow. So for a c_irsory it can be assume_, that the wine appraisal in the insicle zone acts like a gaid.e apparatus imparting a twist of this to the flow. A fictitiou_ &ihe_ral amount angle is create& in the wing center section uncSer the fusel,_ge effect as explainel elsewhere, which is predominantly lepenlent upon the location of the wing relative to the fuselage. Since the absolute _mount of this fictitious fest

a

chcngo

in

angle

liheclral is far greater for high-- an_ low--wing arrangements than that customary on geometrical iihelral a very considerable influence of the fuselage on the slle_ash is to be expected. conformably

0n the high-_ving arrangement the to the great _ositive fictitious

ref_uce

contribution

the

towarcl d.irectional corres pon6ingly on

of

the

lateral

si_e_ash shoul_, _._iheclrai angels,

control

system

stability ooneilerably anl the low-wing arrangement,

increase Suitable

it ref-

assessing the or_.er of magnitule are as yet ackin_. _ossi_le to compare the si&eit might-be wash with the fictitious clihe_ral at a d:istance from the wing center which can be o6rrelatel with the lateral tail surface _imensions. l_uch more promising at the moment appear syctematic measurene_ts i_ whAch first of all, the wing positio_ relative to the fuselage, the ratio of tail height to fuselage height an_ the setting of the wing relative to the fuselage r:_ust be molifiel. _ess significant are the effects of the wing form, of the ratio of wing chorl to fuoelage _viith and height, tail _esign a_ so for th, erence

_ata

A

few

_entionel _uce_ tail

for

first HACk

measurements Technical

in figure surface to

18. the

Note

are

a_ailable

No.

930,

in

which

0nly the contribution d_irectional stability

the

are

aforc-

repro--

of the lateral ie in_icate_..

effect of the poeitio_ of the wing telling relative to the fueol_ge, the conduct of the high--wing arrangement being fairly critical, while on the low-wing arrangement probably some separation pheno_ena at _he wing root obliterate the picture a little. ¥igure 19 rsveale& s onething si i_ _i ar. For the hlgh-wing arranger_ent the ef_t

cSisciosos

fect

of

the

low--Wlng in

the

the

si_ewash

is

arrangement

fuselage lihelral

about

i-_ -- ---0.3,

appears

proximity there

aPl_ro aPl _ro_i, _i,_ _ at ely

is

an

adherent.

increnent

to

i-_ =-0.4, iT so

For _ _ _ eft

as

long

of

the the

for

the

the

flow

effect

of

order

of

 

NAOA

magnitude

angle

0.09

of

according

sent

with

flow

which

of

angles

with

the

along

Qn

with

lateral

of

wing

span.

co_tro

amounted,

of

=

_ dV

which on

of

0.09,

without

the

the

framework a

slight

probablF

associated

distribution

contribution

same same

model value

=

m

at

local

to

show

_ownwash

neat

dihedral

dlheclral arrange--

again

is

the

5 °

the

values

stability

surfaces

to

arrangement

attack, The

about

due

all

_9

high-wing

outside

probably

sideslip

1036

to

The

whole,

the

angle

effect

the

equivalent

attack,

separation.

increase

is

No.

our estimates. falls somewhat

to

&ihedra

negative

Hemora_&un

_echnioal

of

without as

O,

on

wing

the

as

the

is

mi_wing

to

be

ex-

pected. Ae the

concerns

following

the

mechanics

should

stability

directional surfaces

is

to

be

of

noted

be

asymmetric

in

this

contribution

i_rovided

of

with

the

flight

respect:

motions

While

lateral

the

the

control

factor

d_ &7

the

damping

change

during

in

yaw

of

angle

to

yaw

the

7,

I

because

the

sidewash

d.ownwash

at

temporal

displacement

in

She

directional

from

that

the

is,

the

on

effect

this

the

the

two

duced.

of

sion values

yaw

the appraisal the static

standard

the the

conception types similar

rolling

result, remains

of

yawing obtains

moments

depending straight

in upon or

yaw

in

in

the

where

yaw

must two

(reference

because flight is

accor_ be

previous

the

the

stability

in

motions

whether

yaw,

lateral

concepts in

curves

in

damping

two

be

not

but

change

further of

unsustainable|

Something

a

_

n0t

motions

involved

damping with

the

yaw vibrastability,

_iving is

associated _or

a

change

should

yaw

of the lateral

spiral

on

sidewash

of

concurrent

in

stability

different the

_amping

against

is

This

tail.

and In

aircraft.

altogether

the

the

motion

consists factor

exactly as arrives, with ao certain surface,

the

directional

of

of

studies fore

Ing

stability

the

yawing

course

for

it the

wing

tail

on

that

obtain

d7

the

stability

es_eoially the aircraft.

effect

+.

horizontal

neglected, tions of

extent

must

there-with

Introdiscus-

different

flight

path

dUr"

9). i

 

40

NACA

These manner

In

a

problems

@uring decision fuselage

be

design

of

or

sidewash

and

of

the

1036

considered

in

lateral

the

against

for the

No.

l_emorandum

should

the

particularly, the

Technical

a

divi_ed

a

or

conditions wing

appropriate

central

under

should

surface.

control the

receive

tail,

effect

of

particular

attention.

Translation for

J.

by

National

Vanier,

Advisory

Aeronaut

ComT._ittee

ics.

REFERW,

I.

flunk, 2ep.

2.

3.

M,:

Max

g0.

184,

Jacobs,

_a_tman

_T.,

and

of

and

_'_selage

Rep.

Airship

Wing in

the

i_._o. 540,

Lonnortz,

J.:

des Rumpf.

NACA,

Hulls.

Ward,

Kenneth from

Variable 1931.

E.:

Interfer-

Tests

of

209

Varlable--Density

Combi-

Tunnel.

1935.

Beitrag

zur

theorotischen

Einflusses

Z._.a_li.M.,

Vandroy, F.: seitigen

Airship

in the Tests EAOA, I_o, 394,

Model ReD.

_T,A.@.£.

gogonseitigen

on

Forces

192_.

NACA,

Tunnel.

nations

5.

Aerodynamic

Abbott, Ira H.: Density _lind

ence

4.

The

N 0KS

7,

Bd.

yon Aug.

Bohandlung Tragfl_che

19S?,

pp.

Zur

thoorotlschen Bohandlung Ein_'lusmes v0n Tl-agfl_Igel und

Luftfahrtfor_chung,

34.

14,

July

20,

und _49-_76.

gegen--

des

Rumpf. 1937,

pp.

347-

355.

6,

l_uttray,

H.:

The

T.H.

_illets.

7.

TreTftz,

E.:

Nulthopp, von 3,

764,

Z.f.a.H.H., H.:

Die

Tragfl_geln. 1930,

No.

Prandlische

Theorie. 8.

Aerod_namlc

pp.

_ACA,

Wing--Fuselage

1935.

Tragfl_chen-B_. I, June

Berechnung

der

L uftfahrtforsohung, 1'53--).69.

of

_spect

und 1921,

Propeller-pp.

206-218.

kuftriebsverteilung Bd.

15,

April

 

NACA

6B

9.

auf

i0.

H.:

_[ulthopp,

Koerner, die

Die

Yragen

&or

S.:

Anwen_ung

Bambor,

_influss

gation

J., of

anl

cular

Fuselage

yon

Rumpf

Yaw

of

Recbangular--l_AOA and

a

Fin.

on

1036

41

_ragfl_eltheorie

In

R.

House,

_ffect

torlsticB.

_er

Vorb Vorber erei eitu tung ng. .

unf

Jahr_uch 1939 p. 231.

Stabili%_.

M.

No.

_lugmechanlk.

Luf_fahrtforschung, ii.

}[emoran&um

Technical

_er

0.:

Luftschraube

auf

Deutschon

investi-

_/in_-Tunnol

Latoral-Stabili_y 2301_--Wing

T.N.

No.

730,

0harac--

with I_AOA,

a

0ir-

193%.

 

NAkGA

Teohnloal

Memora_lum

Figure I.+ Positive

No.1035

Fuselage pressure

F£go.

in

-

1,3,4,5

flow. Negativepressure ideal

i

-Q

'

i

Sj

J

'''

f I

0 Figure o u

F 3.-

¢'

6

Li.ft

Normal Reotangulaz_

of

J

q'

8' the

E

#' ¢

fusel_e

-_e rt ..... -_ _aUA _ po •

_'

&lone.

-4u

_

_o

\

_8

\

o_

° Figure

4.-

Moment

curves

friotional

Ftmelage

fo_ms:gAOA-Report

of

rlgure

llft.

3g41ift.Insoribed slendernns

i

4_ 5

-

_G Ne,utral sta_il£sy point of f_iotion_l numbers i_llo&t_ r&t£o.

 

_i _iC, C, i

1;o.1036

tZemortndum

Teolmioal

S,6,8

Figs.

t.C

.e,-

 

-,-----X _

_ntrol

orlon

.,_

_

o_

 

.

q _.c_ St_ea=. direction of_o_aZ >airplan_direotion

--

./

etre_=

-

C

';_

_ _._az-e 2.-

_unkls factors unstable moments of revolution.

( Yigure

correction for the of surfaces

(NAOI Report

6,-

fusslaKe

Hcment oonsitez_tion for tefinin_free moments.

184)

5 L

f

\

Figure

8._

Nor_I

values

therfusela_e

for width

_ruah

bofore

the

wing.

is oo oons nsta tan_ n_._ ._t we w t e _t:

To

the

axtent

that

 

NACA

Teohnloal

He_orandum

¥ig8,,

_To.1036

7114,15,1_

.6

I

I C _IEure

7.- Curve of _ fuselage.

alon6

3 14.-

Lift _Istrlbution of a with mid-wlng arran_nen ciroular fuselage and reot_n6_lar wing, A=6.DimensionB correepond to the oondltlon9 in NACA Rgport 540. 1 _In_ an_ fuselage(TH) _R   1

_Igure

=0.073

(avere_o_-

O. 054.) in flow

2 Wlng

sot at an anEle,fuselaEe direotlon _-_R = 1 _o___a . O.050(avera_ed-

0.049)

caz,t 3 Wing

alone

_ = 1

ca Wtng'///_eola&e

.4

_cemblnatlon

_

Wing

alone

.3

_aR=o(Ye-dl stributlon)

"2 .i

i

:

....

'_

,

0 .I .: Ylg_ve 15._Igure

16.- R_latlon of llft angle of attack.

to

---_in_

i

-'r'--

Lift distribution win_ arrangement.

.0 oi low-

alone

l_oasurod ca values correspond to calcul_tlon differences within scope of instrumental

accuracy.

_e

 

NAOA

Memors,ndum

Teohntoal

1036

No,

Figs.

 ,I0,II

d

I

0-"

.

axially

_

z

J

_,

o /_

nymetrloal

abou_

_

oi_oula_

oyltnde_

(II_)

I

(_.

U- Pta.e

-__--

.-'.....__---.._ I

Z;Z'

_lt V

FiEu_e -

of

_Jle

g

i0.-

fusel_e

onto

&

Oonformal

transformation oross

veztioal

8eotlon sllt.

ram,

6

V

I

Vz,,_,,UA.tevery

Foin F

Fi_re seo_ion _ansformed

ii.of

Poten_i_l the

on

the oonformally fuselage.

 

Technical

NAOA

Memorandum

No. I036

XA dz

Figs.

_

Figure

i_,1_,17,18

Air

IS.-

load

fueela4_e. distribution

long

•///////_ J_ fuselage moments _\\\\\_ lift rom f_elage - -- Total variation

J-plane

__Pl_

u,- mane --- -

13.-

_Figure

transform_tlon ....

Iz

L

_

-8_

-

'__o ......

-__ _

_ ., .,_._

conforms/ on

of

fusel_ge

-. elll elllpt ptio io sections.

Z Figure

-

Method

A_-_, .. .... ..

V__ . _

----- r

17.-

Rolling moment

in

yaw under fuselage effect. (Teats from NACA-T._. ?30) + High win_ &rran&ement o Mid wing arrangement Low win_ &rran_ement --- Theoretical v&luea for hAghand

low-wlng

Figure

arrangement.

18.-

Contribution of fin and toward directional

rudder stability effect.

by

fuselage

(_AOA-T.N. 730) Wing

_" 8

dihedral

oli

Mid

Hl_ wlng .Lu_ arrangement arrang'mont Low wing arrangement

Of i

Mid wink arranKsment High wing &rrgngement Low wing arrangement NA AC CA A-L a aa a_ _e eY

- 4-_4-_-6S 6S - I_