Ae Study of Canard

7/25/2019 Ae Study of Canard

1/12

EXTENSION

OF

A NUMERICAL SOLUTION FOR

THE

AEBODXNAMIC CHARACTERISTICS OF A

WING

TO INCLUDE A

CANARD OR HORIZONTAT TAIL

By Barrett L. Shrout

Langley Research Center

National Aeronautics and

Space

Administration

Hampton Virginia

CODE)

0

CATEGORY)


2/12

A method for predicting the aerodynamic lifting surface characteristics

of wing-horizontal tail configurations or canard wing configurations at

supersonic speeds is discussed.

The numerical solution has been programed

for a digital computer and is part of a complex of computer programs used

in the design

optimization and

waluation of aircraft configurations at

supersonic speeds.

The method is an extension of the Carlson-Middleton

numerical solution for lifting surfaces which is briefly rwiewed.

The

present method predicts lift

drag and moment characteristics over a

range of lift coefficients and for various control settings.

Theoretical

and experimental data are compaxed for wing-horizontal tail configurations

and for canard-wing configurations at various Mach numbers.

These compari-

sons show both the basic data with control deflections and some final

trimmed drag polars. Some data are also presented to show the extent to

which program limitations affect the accuracy of the analytic methods.


3/12

Subscripts:

SYMBOLS

weight ing fa c tor fo r par t i a l g r id e lements

mean geometric chord

drag coeff ic ien t D ~ S

l i f t c oe ff ic ie nt

L/S

pitching-moment coefficient

M

/qsT

pitching-moment coeff ic ie n t a t zero l i f t

increment i n

mo

fo r co n t ro l d e f l ect i o n

s t a b i l i t y l e v e l

measured i n t h e v i c in i t y o f zero l i f t

l i f t i n g p ressure co e f f i c i en t

drag

l i f t

coordinates of influencing grid elements

coordinates of field-point grid element

free-stream Mach number

pitching moment

dynamic pressure

grid element influence function

wing reference area

downwash strength

Car tesi an coordinate system x-axis streamwise

camber surface ordinate

angle of a t tack

horizonta l ta i l def lec tion posi t ive t r a i l i ng edge down

canard deflect ion posi t ive t ra i l in g edge down

fl ap or elevon deflect ion posi t ive tr ai l i ng edge down

wing

b o d y p lu s v e r t i ca l t a i l

h o r i z o n t a l t a i l


4/12

EXTENSION OF

A

NUMERICAL SOLUTION FOR

TIIE

AER0DYNAMI:C CW CT ERISTICS OF A WING TO INCLUDE A

CANARD OR HORIZONTAL TAIL

By Barr et t L. Shrout

NASA Langley Re search Cen ter

Hampton, Virginia

With the a r r iv a l of the supersonic je t e ra ,

th e ae rodynamic is t has rea l ized Ohat the c har ac t e r i s t i cs of a

conf igura t ion can no longer be considered th e sum of the cha rac t e r i s t i cs o f i t s component par t s .

Mutual

aerodynamic inter fere nce between components has a si gn if i ca nt e ff ec t on th e ov er al l aerodynamic charac-

t e r i s t i c s of a configuration ; as a consequence, ex tensive wind-tunnel te st in g must be done fo r configura-

t i on des ign and ana ly s is .

As an al te rn at iv e, th e aerodynamicist can use an al yt ic techniques fo r much of

the pre l iminary des ign and eva lua t ion work with wind-tunne l te s t in g used for f in a l ver i f i ca t ion .

NASA's Langley Research C enter has been working i n rece nt years toward t he development of a syst emat ic

method of ana ly s is fo r supersonic conf igura t ions ut i l iz in g high-speed di gi ta l computers .

From th i s

e f f o r t h as

evolved a complex of computer programs used to est ima te wave drag, sk in -fr ic ti on drag, and

drag-due- to- l i f t of supersonic a i rc ra f t conf igura tions . Unt i l r ecent ly ,

it

has been necessary to est imate

s t ab i l i t y and cont rol c har ac t e r i s t i cs us ing empir ica l techniques , or t o obta i n them from wind- tunne l da ta ,

The method and resu l t s of modifying th e l i f t i ng- sur face ana ly s is program t o pred ic t s t ab i l i t y and contra:

c ha r a c t e r i s t i c s f o r t a i l l e s s , w ing- hor iz ont al t a i l , and

canard-wing conf igura t ions a re presented i n th is

paper .

The experimental dat a presented were taken pr imari ly f rom referen ces

(7)

through

15).

DISCUSSION

A block diagram i l l us t r a t in g th e Langley supersonic ana lys is

computer program complex i s shown in f i gw e 1

I n b ri e f , t h e

conf igura t ion t o be ana lyzed i s reduced t o a numerical model i n which a l l wing coordinates,

thick ness rat io s, camber l i ne s, body contours, empennage, and so for th, ar e expressed i n

x

y, and

z coo rdina tes, as a computer card deck. This numerical model, o r components of i t i s t h en i n p ut t o t h e

sel ect ed computer program and the de sir ed component of drag i s ca lcu lat ed.

An i l l us t r a t io n of a t ypi ca l numer ica l model

i s

shown i n f igu re 2 .

The complexity of t he l~ume ricalmodel.

and t he a t t e n t i o n t o de t a i l i n t he de sc r ip t i on o f t he c onf igur a t ion a r e obvious i n t h i s d r aw ing.

The

drawing, which i s machine plo tt ed from a t ape made usin g t he numerical model as inp ut,

se rves a very useful

f u nc t io n i n t h a t

i t

prov ides a check on the accuracy of th e numerical model.

Misplaced decimals or

in co rre ct numbers become qui te obvious i n the se drawings, which may be three-view, obli que, or perspec-t,iiie.

The three pr inc i ple programs requi red t o es tab l i s h a bas ic drag pola r a re th e sk in- f r i c t ion drag program.

th e wave drag program, and the d rag -du e-t o-l ift program.

A

t yp i c a l d ra g po l a r , i l l u s t r a t i n g t he use o f

these three programs i s shown i n f ig ure 3 .

The wave dra g program ca lc ul at es th e dra g due Lo volume at

ze ro l i f t us ing the method of r e fe rence (1 ) . The method ut i l iz es a f a r - f ie ld approach by re l a t i

Lhe

drag t o th e momentum f low outward through a la rg e cy lin dri cal con tro l surf ace whose long itu din al

t h e f l i g h t p a th .

Skin fr ic t i o n i s evaluated by t he Sommer and Short T ' method of re feren ce

(2 )

witn th

ski n fr ic t i on of each component calcu lated and then summed. The drag-due-to- l if t cal cul at i on ut i l lz es

th e Carlson-Middleton method of ref ere nce 3 )

and uses a near-f i eld method whereby di ff er en ti al press ures

ar e calcu lated over the mean camber plane of th e confi gura tion .

The sum of th es e drag components yi el ds t he bas ic drag pola r. Performance analy sis , however, re qiu res

drag pola r fo r th e conf ig ura t ion i n a t rimmed condi t ion.

U nt i l r e c e n t ly , i t has been necessary t o

o b t ~ l n

pitching-moment curves and con trol increments f rom wind-tunnel data i n order t o es ta bl is h trimmed d rag

pola r s . The drag-due- to- l i f t program has been modif ied to provide cont rol increments fo r ta i l le ss

configuratio ns and to provide s t a b i l i ty lev el s and co ntrol increments fo r wing-horizontal t a i l coniigu?;ura-

t i on and for canard-wing con figur ation s.

The method u t i l i z e d i n t he d r a g -due - to - li f t p rogra m i s i l l u s t r a t e d i n f i gu r e

4

The mean camber pla ne i s

repre sent ed i n th e program by a gri d element system, each block of which

i s

i nc l i ne d t o t h e f low a t a n

angle determined by the camber plane i n th at region. For an uncambered wing, th e incl in at io n angles are

a l l z e ro .

Consider a p a i r of elements i n th e g ri d system. The forward element (coo rdi nat es L, N) gene rates a down-

wash

w

which a f fe c t s a l l the e lements i n the t r a i l in g Mach cone. The di f fe ren t i a l pressure ACp , a t the

f i e l d p o i n t L*, N* i s ca lcula ted f rom the inf luence of the e lement L, ( and a l l o the r e le me nt s I n t he

fo re Mach cone from th e f i e l d po in t) usin g the equati on shown. The term azc /ax i s the s lope of the

camber surface a t the f i e l d po int . The term A(L, N)

i s

a weighting fac to r fo r gr id e lement s iz e a l lowing

pa r t ia l gr id e lements to be used a long the leading and t r a i l i ng edges. The term

T

i s an inf luen ce func-

t i on ind ica t in g th e f ie ld point pos i t ion i n th e downwash of th e preceding e lements .

The ca lcula t ion

process begins a t th e apex and proceeds acro ss each gr id element row while proceeding toward th e tr ai l i n g

edge.

Thus th e di f fe r en t i a l p ressure of each e lement i n th e fore Mach cone of each f i e l d point has pre -

viou s ly been ca lcu la ted.

Simultaneously , ca lcu la t io ns a r e made for t he planform as a f l a t p la te a t

o

a ng l e of a t t a c k .

Once t he d i f f e r e n t i a l p r e s su r e s ove r t he su r f a c e a r e known, t he y a r e i n t e g r a t e d t o p r o -

vide for ce and moment co eff i cie nts .

A superposi t ion technique us ing th e f l a t p la te and cambered wing

da ta provides

f o r t h e v a r i a t i o n of d r ag w i th l i f t .

A

more de ta i l ed explana t ion of t he numerica l solu t ion can be found i n re fe rences 3) and 4 )


5/12

'_ 'he modif i ra tions made t o the program t o account fo r a hor iz onta l t a i l a re shown i n f i gur e 5.

The wing

2nd forebody a re rlandled i n a manner much t he same as t he or ig in al program.

The afterbody and horizontal

43 have been added and th e grid system extended a s shown on th e r i g h t si de of t he sk etch . The regio n

cutbonrd of t he body, a f t of the wing tr ai l i ng edge,

and forward of th e t a i l lead ing edge i s a reg ion of

~ e r ooadlng;

t h a t i s , t h er e i s no

s u r f ace wi th in th i s r eg io n to

s u p po r t a p r e s s u re d i f f e r en t i a l . Grid

elements on -che t a i l a r e s t i l l influenced by the pa rt of the wing with in t he ir fo re Mach cones, and these

v rn g p r e ss u res a r e inc lud ed in th e ca lcu la t io n of th e t a i l p r es s u re d i s t r ib u t io n s .

Some of tne genera l cha rac ter is t ics of the l i f t i n g sur face programs ar e l i s te d on f igure 5.

The mean

camber plane in put t o t he program may be cambered and twist ed or a f l a t pl at e.

The forebody may be

c-qbered ind th e wing p lanform i s arb i t rar y . For the hor izo nta l - t a i l p rogram specif ic a l ly , the t a i l may

b e o f a r b i t r a ry p lanform and co n t ro l i n p u t s may b e fo r e i t h e r a f u l l s l ab t a i l d e f l ec t io n o r d e f l ec t io n

o f e l e v a t o rs on t he t a i l .

I t

should be noted t ha t t he program i s r e l a t i v e l y e a sy t o u s e .

Inputs

cons is t p r imar i ly of lead ing and

-,r ail ing edge coordina tes f or th e wing-body and hori zon tal t a i l , and s treamwise camber l i ne s composed

of z coord inates a t specif i ed percent chord s ta t ion s . The gr i d system i s imposed within the program

~ n d n interpolation ro u t in e a s s ig n s a s u i t ab le d e f l ec t io n to each g r id e l emen t.

The grid system shown

o n tn e s l id e i s o n ly a c rud e r ep res en ta t io n ;

i n ac tu al pra ct ic e, depending on Mach number, a system 30 to

LO elements fo r the semispan and 90 to 100 elements i n length i s u t i l i ze d .

Computation time for a s ingle

Mach rm be r and cont rol de fle cti on ta kes approximately j minutes on a CDC 6600 se ri es computer, using

70 003 oc ta l st ora ge.

Figure 6 sl~owsa comparison between experimenta l fo rc e and moment c oe ff ic ie nt s and est ima tes made usin g

the hor izonta l t a i l p rogram.

The configuration i s a de lt a wing co nfigu ratio n with a ra th er close-coupled

h o r i z o n t a l t a i l .

t a Mach number o f 1.5 the agreement between theory and experiment i s exc ell ent .

No

:It-te~nptwas made - to cal cul ate th e minimum drag lev el fo r any of t he confi gurat ions i n th i s paper, ra th er

;he experiroental drag value a t zero l i f t fo r undeflected c ontro ls was added to t he estim ated drag-due-to-

l i f t v al ue s.

Drag increments due to contro l de f lec t ions , d rag a t l i f t , and the pi tching-moment data are

21-otted directly from the program output.

The da ta f or a Mach number of 2.5 a re more t yp ic al of th e

program es tima tes when compared with experiment, i n t ha t th e dra g-due -to-l if t i s

s l igh t ly underpred ic ted ,

and th e s t e b i l i t y l ev e l s l ig h t ly o v erp red ic ted . I n g en era l , t h es e d i s c r ep anc ie s can b e a t t r i b u ted t o th e

lir ldt ati ons of l in ea r theory, th e assumptions of small angles and completely attache d f low.

The overpred ic t ion of s ta b i l i ty lev el and th e underpred ic tion of drag-due- to- l i f t a r e compensating fac to rs

rihen a z rln. d rag ao la r i s ca l cu la t ed i n th a t t h e th e o re t i ca l d a ta t r ims a t a lo wer

CL

f o r a g iv en t a i l

d e f le c t so n b u t a t a, lower drag le ve l .

The theore t ica l t r i m drag polar i s shown by t he heavy l i n e and th e

exper2menLsl t r i m points by the solid symbols .

Figure 7 shows es t rmated and exper imental da ta fo r another hor izonta l t a i l conf igura t i on . I n th i s example,

,he configuration has an arrow wing and the sepa ratio n between wing and horizo ntal t a i l i s somewhat gre ate r

Ahan lo r tne prevlous confi gurat ion.

The s ta b il i t y lev el s again ar e somewhat overpredicted and the drag-

d u e - t o - l i f t s l l g h t ly u n d erp red lct ed .

I n th e case of t he da ta f or Mach number 1.41, the

C

increments

Ire overpredicted by about 25 percent.

Whether th i s d i s p a r i ty i n Cm , i s p e c u l i a r t o t h i s c o nf ig u ra t io n

br s g en e ra l ly t r u e fo r co n f igu ra tio n s wi th l a rg e s ep a ra t ion s o f wing and h o r i zo n ta l t a i l w i l l r eq u i r e

~ u r t n e r w e st i g a t i on .

Is mentroned e ar li er , th e basi c l i f t i n g sur face program was als o modified t o handle a canard-wing

;onfiguration.

F ~ g u r e shows i n schematic how th i s i s accomplished. The method i s much the same as

chat used Tor the inc lus i on of a hor izonta l t a i l except tha t , f or

th i s ca se , t h e co n t ro l s u r face i s ah ead

of t he wsng and the region of zero loading i s outboard of th e body, a f t of th e canard tr ai l i ng edge, and

rorward of th e wing leadi ng edge.

Note th a t a s f o r a l l t h e prog rams i n th i s s e r i e s , p a r t i a l g r id e l emen ts

o re u sed to b e t t e r d e f in e th e l eadin g an d t r a i l i n g edg es of a l l s u r f aces . I n ad d i t io n to th e f ea tu r e s o f

the o ther programs, th is p rogram al lows for an arb i t ra ry p lanform canard , bu t i s res t r ic te d t o def lec t ions

31 t h e en t i r e can ard su r face ; t h a t i s , t h e p ro v i s ion fo r d e f l ec t in g a t r a i l in g-ed g e can ard f l a p i s no t

lncluded a t the present t ime.

Figure 9 shows a comparison between theory and experiment fo r a d el ta wing con fig ura tio n with a canard

contro l sur face .

t

a Mach number of 1.41, th e zero li ft -d ra g increments and increments i n

Cmo

due to

co n t ro l d e f l ec t io n a r e p r ed ic t ed q u i t e we l l . The s t a b i l i t y l ev e l s a r e ag a in s l i g h t ly o ve rp red ict ed . The

d rag-du e- to - l i f t v a r i a t io n i s accu ra te ly e s t ima ted with th e ex cep t ion of th e d a ta f o r th e

15

canard

d e f l ec t io n . I n t n i s ca s e

i t

appears th at t he experimental value i s unexplainably low. I n general, between

l oo ~ n 5' contro l se t t in g , a s i za b le ex pe r imenta l d r ag in cr emen t o ccu rs a t a l l l i f t co e f f i c i en t s .

I n t h i s c a se , f o r t he hi g he r l i f t c o e f f i c i en t s ,

the experimental drag increment i s of the same order as the

-ncremenL between smaller control deflections. t th e higher Mach number, th e co rr el at io n i s much the

same; however, th e drag increment f or t he maximum canard def le ct io n i s i n bet te r agreement than i t was a t

the lower Mach number.

D7za f o r

2

second canard conf igura t io n ar e shown on f igure 10 . The conf igura t i on i s id ent ica l t o th e

previous conf igurat ion , except tha t

i t

has a trapezoidal wing.

The c or re la ti on between theory and experi-

,nent i s qu l t e good. The-s tab i l ity le ve l i s overpred ic ted by about

4

percent

c a t th e lower Mach number

2nd by about 2 per cen t c a t th e hig h Mach number. Drag -due -to-l ift i s s l i g h t l y u nd e rp r ed i ct e d a t t h e

Lower Macn number, and th e increm ent i n

Cm

fo r th e maximum contro l de f lec t ion i s s l ig h t ly overpred ic ted

a

both Mach numbers. Because th e ot he r Cm, i n cr emen ts a r e p r ed ic t ed s o we l l , t h i s in d ica te s t h a t t h e

r ~ r l a t i o n f

C

with canard de fl ec ti on an gle has become nonlinea r between 10' and 1 5 O and, of course,

the the or et ic al method used herein does not account fo r such non lin ear it i es .

rsg we shows a cor rel ati on between experiment and theory of the s ta bi li t y and contr ol parameters fo r

ne

two programs shown th us f a r .

The dat a cover severa l conf igura t ions i n addi t ion to th e ones which have

aeen presented i n th is paper . The c i rcu lar symbols are for hor izonta l t a i l conf igura t ions ; the square

synbols repre sent canard configu ratio ns. The sol id l i n e repre sent s pe rfe ct agreement between theory and


6/12

experiment. The Cmo increments show gen era lly good agreement; fo r th e most pa rt , th e estimated value s

a re between zero and 15 percent h igh. For the s t ab i l i t y parameter,

AC /AC~

t h e d a t a f a l l on e i t h e r s i d e

of t he l in e of per fe c t agreement ;

fo r a ma jo ri ty o f ca s es th e s t a b i l i t y p a ramete r i s s l i g h t ly o v e rp red ic ted .

Examination of the d ata fo r both parameters reveale d no pa rt ic ul ar pa tt er n re la te d t o Mach numbel-.

The

canard co nf i~ ur a t io ns enera l ly appear t o cor re la te bet ter ; however there were fewer of these co nf ig ur e t io ~s

examined and thus no conclusions ar e drawn as t o th e re la ti ve m eri ts of the two programs.

The the or et ic al method of t h i s paper assumes

a p lanar sys tem, tha t i s , a l l t h e g r i d e l em en ts l i e i n a

constant z plane. To in di ca te th e magnitude of erro r that occurs when th e configuration does not

sa t is fy th is assumption ,

data a re shown in f i gur e 12 fo r a conf igura t ion wi th a hor izonta l

t a i l l o ca t ed

above o r below t he wing pla ne.

The upper pa r t o f th e f ig ure shows the exper imenta l da t a for the two t a i l pos i t i ons

a t two Mach numbers,

The pre sen t method which, of cour se,y ield s a si ng le curve, i s shown by a s ol id li n e . For comparison,

a

pre dic tio n made using th e Nielsen-K aattari method (r ef .

(5 ) ) , which i s a ls o a p lana r method, i s shown.

The bottom pa rt of th e f ig ur e

shows the data as

a fun ction of a ngle of at tac k, with th e body-ta il moment

contr ibu t ion subtrac ted out so t ha t t he remaining increment i s the wing contr ibu t ion p lus th e e f fe c t of

th e wing o n th e h o r i zo n ta l t a i l . I t a pp ea rs t h a t t h e p r i n c i p l e e f f e c t o f t a i l l o c a t i o n on Cmo fo r t nis

c on f ig u ra t io n , i s t h e r e l a t i o n o f t h e t a i l t o t h e body, r a t h e r t h a n t h e r e l a t i o n o f t h e t a i l t o t h e w in g.

Regardless of t he cause fo r the Cm, change, th e pre sen t method does not account fo r

i t

and as can Se

s een fro m th e b as i c d a ta a t t h e to p of th e f ig u re , t h e e f f ec t can b e r a th e r s ig n i f i c an t . Thus , f u r th e r

s t ud y i s i n d ic a t ed i n t h i s a r e a .

Final ly , an a ttempt was made to modify the bas ic program to c a lcu l a te contro l cha rac ter is t ics for- ta l l le s s

conf igura t ions .

This merely cons is ted of ass ign ing th e des i red contro l de f lec t ion t o a l l g r ld e lements

which f a l l wi th in the f la p or e levon planform.

A

corre la t io n fo r two conf igura t ions wi th t ra i l ing-edge

contr ols i s shown on f igu re 13. The configuration on the le f t has trail i ng-ed ge contr ols over approximately

70 percent of the span. For the confi gurat ion on th e r igh t, th e contr ols extend approximately 30 percent

of th e span.

The drag-due- to- l i f t es t imate fo r both conf igura t ions i s cons iderab ly lower than the exper i -

mental dat a. This was unexpected because, fo r zero cont rol defl ect ion , th e modified program 1s th e sarre

as th e basi c program which genera lly gives much be tt er es tim ates . The increment i n

Cmo

f o r t h e c o n f ~ g u -

ra ti on with th e wide span f l ap s i s somewhat overpredicted. This diffe ren ce between theory and ex~ erl nle nt

can b e r e l a t ed to th e r e s u l t s o f r e f e r en ce

6 ) ,

where i t was shown th at contro ls i n the v lc in i t y of the

wing tlp,

opera t ing i n a reg ion where aer oel as t ic deformation and

f low separa t ion can occur , y ~ el de d

experimental increments only 70 percent of the estimate d increments . For the configura tion with tne s liort

span con tro ls, th e drag and moment increments fo r the 10 de fl ec ti on ar e good; f o r the 20 defiec:lon,

o n l y f a i r .

The s t ab i l i t y l ev e l s f o r b o th co n f ig u rat io ns a r e s l i g h t ly o v e rp redic t ed .

CONCLUDING REMARKS

A method has been discussed i n which the Carlson-Middleton numerical s olu tio n for l i f t i n g sur faces can be

exten ded to in c lu d e a h o r izo n ta l t a i l o r can ard. I n gen e ra l , t h e method s l ig h t l y o v e rp red ic t s s t - ,b l l l t y

lev els , and pred ic ts re la t i ve ly wel l d rag increments and increments i n C m due to contro l deflections.

The so lu t ion i s fo r a p lanar sys tem, and s ign if i can t er ror s may be in t roduced i n the pred ic ted dnL; i f toe

contro l s ur face i s wel l ou t o f th e wing p lane .

1)

Harris, Roy

V.

J r . :

An Ana lysi s and Corr el at io n of Ai rc ra ft Wave Drag

NASA TM X-947 (196 4)

( 2 )

Sommer, Simon C . ; and Short, Barbara

J .

Free -Fli ght Measurements of Turbulent-Boundary-Layer Skin Fr ic ti on i n the Presence of S evere

Aerodynamic Hea ting a t Mach Numbers From 2.8 t o 7 .0

NACA

TN D-3391 (1955 )

( 3 )

M i d d l e t o n , W i l b u r D . ; a n d C a r l s o n , H a r r y W . :

A

Numerical Method f or Calc ulat ing t he F lat -Pl ate Pres sure D ist r ib uti ons on Supersonic Wings of

Arbit rary Planform

NASA TN D-2570 (1965)

( 4 )

Carlson, Harry W . ; and Middleton, Wilbur

D.:

A Numerical Method fo r t h e Design of Camber Sur fac es of Supe rson ic Wings With Arb it ra ry Planforms

NASA TN D-2341 (1964)

(5 )

Nielsen, Jack N. ;

Ka at ta ri , George E.; and Anastasio , Robert F.:

A Method f o r Cal cul ati ng th e Li f t and Center o f Press ure of Wing-Body-Tail Combinations a t Subsonic,

Transonic, and Supe rsoni c Speeds

NACA

RM A53G08 (1953)

(6 ) Landrum, Emma Je an :

Eff ec t of Skewed Wing-Tip Co nt ro ls on a Highly-Swept Arrow Wing a t Mach Number 2.031

NASA TN D-1867 (1964)

( 7 )

Smith, Norman F.; and Hase l, Lo well E .

An

In ve st ig at io n a t Mach Numbers of 1 .4 1 and 2.01 of Aerodynamic Ch ar ac te ri st ic s of a Swepc-Wing

Supersonic Bomber Configuration

NACA

RM L52J17 (1952)


7/12

Driver, Cornelius:

Longitudinal and La ter al St ab il it y and Control Cha ra cte ri sti cs of Two Canard Airplane Configurations

a t Mach Numbers .o f 1.41 and 2.01

NAGA RM

~ 5 6 ~ 1 91957)

Spearman, 81 Leroy; and Driver, Cornelius:

Lomitu dinal and Lat era l S ta bi l i tv and Control Cha rac teri st ics a t Mach Number 2 O 1 of a 60 Delta-

~i.4

i rp la ne C on fi gu ra ti on ~ ~ u i e d ith a Canard Con tro l and With Wing-Trailing-Edge Fla ps

MACA

RM ~ 5 8 ~ 2 01958)

Hilton, John H.

r

;

and Palazzo, Edward

B .

Wind Tunnel I nv es ti ga ti on o f a Modified 112 0-sca le Model o f th e Convair MX-1554 Airpl ane a t Mach

Numbers of 1.41 and 2

O 1

NACA

R14

SL 53G3O (1953)

Driver, Cornelius; and Foste r, Gerald V.:

S ta ti c Longitudinal S ta b il it y and Control Cha ra cte ris tic s of a Model of a 45' Swept Wing Fig hter

Airpl ane a t Mach Numbers of 1 .41, 1.61, and 2.01

NACA RM ~ 5 6 ~ 0 41956)

Church, James D.:

Ef fe cts of Components and Various Modifications on the Drag and th e St at ic S ta bi li ty and Control

Ch ar ac te ri st ic s of a 42O Swept-Wing Fig hte r-A irp lan e Model a t Mach Numbers of 1. 60 t o 2.50

MCA

RM

L57K01 (1957)

Spearman,

N.

Leroy:

Sta t ic Longitudina l Stab i l i ty and Control Charac ter i s t ics of a 1/1 6- ~c a leModel of the

Douglas D-558-11 Resear ch Ai rp lan e a t Mach Numbers of 1 .6 1 and 2.01

NACA RM L53122 (1953)

Spearman, M Leroy; and Driver, Corn elius:

Eff ects of Canard Surface Size on St ab il it y and Control Char ac ter ist ics of Two Canard Airplane

Conf igura tions a t Mach Numbers of 1. 41 and 2.01

NACA RM L57L17a (1958)

Foster, Gerald V.:

In ve sti ga tio n of the Longitudinal Aerodynamic Ch ara cte ris tic s of a Trapezoidal-Wing Airplane

Model With Various V er ti ca l Po sit io ns of th e Wing and Ho rizo ntal Ta il a t Mach Numbers of 1. 41 and 2.01

NACA RM ~ 5 8 ~ 0 71957)


8/12

O P T I M I Z A T I O N r

ENGINE

AND w? IX

DIRECT

ANALY s

I

s

PERFORMANC~ -m e . . .id ESTIMATES

F ig u r e

1

Complex of com ~)u err og ra ms f o r s u p e r so n i c a i r c r a f t d e s ig n n ev ilu lo

MODEL

USED FOR W E

R G

ODEL USED FOR DR G

DUE

TO

LI T

F ig u r e 2 .

Computer drawings of numerical models.


9/12

DRAG

> fi

EAR

FIELD

L FT

F i g u r e

3

c o q p o s i t e s ys te m o f s u p e r s o n i c d r a g a n a l y s i s .

PAIR

OF LIFTING ELEMENTS

ARRAY

OF LIFTING ELEMENTS

F i g u r e

4

L i f t i n g - s i ~ r f a c e e p r e s e n t at i o n .

CAMBERED AND TWISTED WlNG

CAMBERED FOREBODY

ARBITRARY PLANFORM WlNG

ARBITRARY PLANFORM TAlL

SLAB TAlL DEFLECTION

OPTIONAL ELEVATOR DEFLECTION

F i g u r e

5

Wing horiz onto .l-

;:til

c o ~ ~ f i g u r s i i o n .


10/12

TRIM POLAR

Figure

6

Del ta wing cor i figurat ion with hor izonta l t a i l .

F igure 7 Arrow wing configu ration with hori zon tal ta i l .

CAMBERED AND TWISTED WlNG

CAMBERED FOREBODY

ARBITRARY PL ANF ORM WlNG

ARBITRARY PLANFORM CANARD

SL AB CANARD DEFLECTION

Figure 8 Canard wing c on fig ura tio n.


11/12

Figure 9 Delts wing configuration with canard

Figure 10 Trapezoidal wing configuration with canard.

HORIZONT L T IL CONFIGUR TIONS

C N RD CONFIGUR TIONS

T H EORY

- 5

a m

L E X P

. 2 5 v ,

0 - .25 - .5

A c m

A

L THEORY

Figure 11. Theoretical and experimental stability and control parameters.


12/12

HlGH TAlL

LOW TA lL

PRESENT METHOD

NIELSEN KAATTARI

HlGH

= L O W

Figure 12. Effect of vertical location of horizontal tail.

4

L

Figure

13.

Configurations with trailing edge controls.

Documents

Ae Study of Canard