Ae Study of Canard
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Transcript of Ae Study of Canard
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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)
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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.
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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
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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 )
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'_ '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
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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)
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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)
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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.
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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 .
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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.
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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.
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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.