20040625 - apps.dtic.milreport documentation page form approved omb no. 0704-0188 i maintaining the...
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REPORT DOCUMENTATION PAGE Form Approved OMB No. 0704-0188
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1. REPORT DATE (DD-MM-YYYY) 2. REPORT TYPE 3. DATES COVERED (From - To)21-11-2002 Final Report 26 September 2001 - 26-Mar-02
4. TITLE AND SUBTITLE 5a. CONTRACT NUMBERF61775-01-WE087
Configuration Studies Supporting Design / Assessment of Sensor Craft
5b. GRANT NUMBER
5c. PROGRAM ELEMENT NUMBER
6. AUTHOR(S) 5d. PROJECT NUMBER
Dr. Rajendar Kumar Nangia
5d. TASK NUMBER
5e. WORK UNIT NUMBER
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATIONNangia Aero Research Associates REPORT NUMBERWest Point, 78-Queens RoadBristol BS8 1QX N/AUnited Kingdom
9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR'S ACRONYM(S)
EOARDPSC 802 BOX 14FPO 09499-0014 11. SPONSOR/MONITOR'S REPORT NUMBER(S)
SPC 01-4087
12. DISTRIBUTION/AVAILABILITY STATEMENT7
Approved for public release; distribution is unlimited. D
13. SUPPLEMENTARY NOTES 20040625 09714. ABSTRACT This report results from a contract tasking Nangia Aero Research Associates as follows: The objective of the proposed work is tosupport on-going research at the Configuration Aerodynamics Branch (AFRLNA) for design/assessment of a Sensor Craft configuration. The sensoraircraft is subject to challenging flight envelope (mission profile). The design at present is relatively "fluid". Box wings of different layouts arise. It has tocruise and loiter (very high LID) for substantial periods and needs to carry a large percentage of its all-up-weight in fuel. The high aspect-ratio wingstherefore need to be fairly thick. This implies emphasis on efficient aerodynamic and structural loading. A particularly critical aspect is the design ofjuncture and LE/TE design. Obviously there are many geometry parameters that arise implying substantial computation. It is proposed to commencework on this configuration. Suitable geometry parameters have been discussed with VA scientists. In the first phase with seed funding from EOARD, it isproposed to:1. Set up the methodology of the design problem including flight envelope (Mach #, altitude & scale effects). Indicate important/critical design regimes.2. Set up appropriate geometry with thick aerofoil sections including junctions.3. Solve for design (under appropriate constraints) of the wings with mutual interference and allowance for juncture effects.4. Two typical cases are to be done, showing the effects of main parametric variations.5. Results will show the forces, moments and pressure distributions. Longitudinal behavior is the first interest. A restricted effort will be directed towardlaterals also.6. Compiling a report on the techniques used and results obtained with conclusions and suggestions for further work.7. Draft report is to be sent for comments before issuing the final version, which is the main deliverable.Parametric and optimization and further studies will be done when and if further funds are made available.15. SUBJECT TERMS
EOARD, Sensor Technology, Aeronautics, Aircraft Design
16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF 18, NUMBER 19a. NAME OF RESPONSIBLE PERSONABSTRACT OF PAGES Wayne A. Donaldsona. REPORT b. ABSTRACT c. THIS PAGE UL
UNCLAS UNCLAS UNCLAS UL19b. TELEPHONE NUMBER (Include area code)+44 (0)20 7514 4299
Standard Form 298 (Rev. 8/98)Prescribed by ANSI Std. Z39-18
RKýN--AERG/REPORT12M2-.10Issue 1, June 2002
CONFIGUR-ATIOIN& AERODYN-AMITC DILSGN STUDIES OF JOITNED-WIN-G HIGH ASPECT RATI 10SF, NSORCiRAFr CONCEQPT
Dr. Rt K. Naigia
SUMM ARY
Unanned Sensor Crafl air vehicesl have benpooed sth h-br-adin -opnntQfuture inteni~nce.suclance,. and reconnaissance (MkR) hiff~astructure to provide:revolution-arv capabilif=e. Sw ucrh=4 Tmust tAkeadvanitage of hi:gh aspectrqtio (AR) witiias for
Re .rodvnamniec efficienrey, d Also be reuired to enclose, .allantenna In a dimnd~ aireraftpnhrmAlag pr~oportion of fuel must, betri4 n 1er~ i thghatdchudes for a few
days in each fli.1gh-L This implies. that a Iwide CL--altitu de -capability is required.
Ths eort isý conberned writh configu r-tioný and design studie of hhili AR Sensor CmaftIMplication-s of 61ca fi~h nvelope- on W~ing, Design aspect have been mentioned. Three,different ty'pes, of jo-ined-mring laiyouts have been proposed. 'The, configur-ation differnce aisedue to orientation of the ou~ter wving ti-p, v;hethr it is (coVentional) aft -5v ept or tonvard-swejpt,and the. dihedral of each wig
Results are presented for wings -with uncamhered, sebtions and then with designed, camber -andtwist. trimr-ed 'for neutral stability. Lavouts -with fonward-s-,ept outer ti00s gVve spanwise
Idadirs at ~~~~off wd--ign cdindifionK vc th:7 wide fih rvI-ýSuch Configllra-tlon may' hiv'e less terndency for Wvirg-dipp at hi~gh lift. UesuW;t of- the invrse
deinapplication are shown-here, -arnd fuirtheer wNork is propo gedh s everal. areas.,
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WRFTTFENAPPROVA-L OFrTHE A.TTHOR.
RELATED FORMAL PUB3LICATIONS
L NANXGIA, M,K PALNE-R. M.L. TIULMANN, C.P., "On Dish"m and Optitiiisatfon MfUioaeto A] lAspect-Ratio, 'iOined-Wig Typ Aircrofr', CEAS- Aerps ce Agtndvrnarics, Research Cfrc ew(ýoa
Aeatutca Scit~ 1- lme2O2.Canbide~UK- (PAPER 85)
2I NANGIA, R.K_.PALMFR.11 ]KE~ & TTIMANN', CY., 'On D-sien of Unconn ntiaral High Aspect'Ratio-ioined-W, kg- Type .Aircraff;, Pac252 CAS-ý2002, Toronto, Canada, Septcrnbtr 1062
3. NAN RICARK, PALER ME & TLm.ANN., CY,~ "UrconventibnI 14ig ASO pect Rat m o lond-Wing AircraftWilth A1t- ;5 Fomwar Swept Wngj-ipsý', Paper 'for 41' AMAA Aervpce Siece Metn & Ex~biihC6 -2
:3L-~200 3., Reno NV, tUS4zA
CONTR-ACTUAL D)ECLAPLATONSý
-The Contractor Dr. R,. K. NAi~ irb eti~ hot,:o Ibc btal of ivi kmnwledEc and b-licit, cr'irl data &i'nr~dh~rwid uidcronrct o. GI7S-tIAVOS7is cr l~et ominutc. ;a=iý comp! j es w'-iti allrqiefet ot aet-
DATE: 'I? LA Nimae arnd T~itle ofAtithorized offici PV,\,
-1 ccreitv Ch~at rhut'ý wcme no shknictions tu dclare ais deilned h FA I5122 7741, duTim2i th ofit--"a -&Thi5 marract'
DATE- 1531- 02L N-ame and Title ufAuthorlzed Offleini; Zr- ~ /J t
2
CONTICNTS.
S U.MMA.RY
DISTRM M-OT-O ISTRELATED FORvMLAL PUIJCAT!N
CONTE\NTs
I. NT-RODUCTIO. ]BACKOROUND ,& WORK pROGR.AMME,,
1.1 BaL~rur~. WdercontextL2. Bref oteonr Work
12. Tm~odie to Pr-esenlt -WorL1.4. Present Vkrýýk Progf'rammeI-$- Lkyout Of Report
2.CMPUTATIONAL &, MOELLING ASPECTS, METHODS U-S.E
3. FLIGHT ENVELOPE'&' CO'NFIGURATIONr CONSUIDERATIOS
3.1. FILght Envel~ope.. Reynolds humber Effects-~2.ReereceCofigrayon(ARL wit oAft-Swept Tips Cni. iAllgePI,&M
3ý3. TWO PO~SSible Alternati-Ve Layot wth F 'rwarS~tTp.Cnis T f
4. BASIC PLANNFO.M EfFF:CTS. SPANW'lISE LOADNGS sTA-TIC STABILITYCONSIDOERATIONS, Config. ATI, Ma-,h 0.6
4J1. Basilc'Planfotrm Efftects. Unambre- Cs4.2. Designied Case4.3. Desi~xed Case at Low Speed (Mac 0.1-)
5. BASIC PILAN-\FORM~ ErfE.CTS, SPANIS L )GSSTTIC SABILIT
CONTSIDERATIONIS, ConfiggF1 El ach 0.6
51.- B~asic Planforrn Efteci- Uncam berezd Case, 15%t/5-1. Desti2nedCase, 15% L/c5-31. Basic Pnnflorjn Effects I. Uncunberod Cws. 17.20/ tic5.4. Desic'ned Case. 17.2%/ Vc
6. BASIC PLANFORM EFFECTS, SAWIELOADINGS, STATIC ST'ABILITYCONTSDEP -AT!L)NS, Config, FT2, Mach 0, 6
61. B asic Pf ?ahrui Efe cts.Un abere-d Casm I % t/c62. Designed Case. IP/o t/c
7. FURTHER VO1RK
8, CONCLUDING REMARKS
ACKNOWLEDGEMENTSREFERENTCESýLIST OF SY-MBOLS & ABBREVIATION'S
FIGURES 1,3;-3 3.111-7i'3.2.1, 41.11-5,4-2,1-4' 13-5.15 .215 .315 54156.1 A-5, 62.1-5 (54 Total)
L1. PTRbDUICT1 ION. BACKGROLNID, & WORK PRzOGRAmw.f
1A.1Backg-ronndJ WiderC Ctext
Follov~ina the, U-SAT-EPOARE) sponsor'ed NWn -aSine WS isit (Dec 21000) to theUS ir orc Reeach ab~raerv(AFRL)2 at Wri,`ý-:Jatter;son Air Forme Base, -a 7proi-ainnie of
work-.!o support thde labo-ratory'.s J4o1TTITTIC was idLEned.
The AFRL_ (Ref~l) is aiztivzly engaged in fi4nd,-= nA! and (more visibk ap*plid issues that7spearhead" future- ad2vancýe-s in technology.v Several piicsareben unC ke, om i
or~eraio w th is-nduty Onc' of the prmary AF ra'zTnivlved insuch acth-iaie 1' theA~roymCncfitrin Branch led bylkMr. Dieter Muhihop~p. Th~e prpjectzs include short-,l
ti-and longer- term-vsors e.g.
Current- & Short-term
- UAY. UCAV systerms ar2 being designed w-ith the aim of suppres~ing enemy defences fn~trisking pilots). The design,-s ar- not, necessarily biahhv' mnaoetnmbile.
Current- & Mid-term
-The AWACS are to he replaced by ESR Se-nsor Sircra"ft. Long endurance at high alti~tudes willrqire bigh t/ -25%) Wings swept al 30 &'Zg, The projccted L./T is 30 for aspect, ratio 2to 30. This-rriay imrply joined. onz.nfigurarions %;ith aprcaklaminar flow.
- Non-Planar Configurations, W~inglet4Silt-Wing, 4-Engined version.
Lonertem.Assessments Currenit Pribrities iublectiol Revision
- Further continued improvements to existing projeces..- UAN Wings. Ob~ldiqu wintn.- Highl Ma;no eiivrable, Air- to-Air Vehicles.
-Supersonic, Combat LIAV&s-SVINR of UAV's.- Wing-in-Ciround (WI10) Craft- Directed Energy Concepts.
1.2. A 86i0 Note on Our Work
The author has worked in Configuration AerodY nantIcs and related R & D for the beýst part ofthree decades- Clients include. Briftish Aerospaze, DEflA / QimneiQ, Rolls- Royce *& AFRL.Projects include. Omhat (RAF advanced trainer). Conzord~e, Flarriler, Ewio-fighter, AdvaricedSTOVL. Stealty Wines. Advanced. SST. Blendd 'Wing Body (WMV8) Aircmrat. HSCT, UAVWvings, Oblique Wings and Joined wings. More "fmanna"work relates to Inverse DesiotMethods, Vorte~x flows. hhh li~ft on 2-D &_3-D wings, and Stiore Se~paradTion (incl. STOVL jetsý).
Several special techniiques, have been developed for)- &eAlina with desion, & assessment ofun-usual -advanced econfiairatons_ Propulsion issues have been addressed e4g_ Intake Design.inclusion ofASTOVYL Jets.
Aecsof worlk have, been presented. in contractor reports, at .Iteriiatini (AAAS,CEAS),INTATO (AGARD & WrO) meetings~aan in Aerospace Journials (e'.g. Re&s2-16').
1.3. Introduction. to Present NWork-
The over-riding0 objective is to suppnort thievwork rormeof the Aerodynamic Config-urationBranch in design / ses~rOF several, types olf con~f'-igrations. Followimay communication~svwith the laboratory, the first con-fiLguration of interest is, te 'Se nsor rfwilojondxnsfdihc-drallan~hidral "box-viint" wih xension:' in frontal. viewv).
p F 1ýZirOD5 were Proposed(Fig.L.3.1)_ Some= of -he dea cr Lardin t .ex:riwnb %esc2rc
geViliwa 'dicd sw, confirmed to C-af tnhePsTtý
"vq~'jle~t"con vcanion-l aircralt -in tersof afrodyrtaniic (lreAR feasibiflity) and srcuaefficiency. Thczrear howve,-Nr so=e advers probleMS also 0eg 5a nv-Se flow.s etc lack -of 4ielVolume, junctiorn flow&-5
emphasis -6n re-vis i ingj soe of theie ocpts and &evising newer applications. Some harvebeen Figt32, eg. P FigdtbP2ane. Lockliecd Fuel TznkeGltliid NS)Sehir-~raf etc. Rf.I92)Sre~ e feaur wings bi~ined at thle tips,.;otherspart -,-ay.the tip'-wivngs can- b-c a-ppropriately a-ft- oIr fowad-wetTo,replace the AWVACS aircraft- appoa is for remiotely-ýcontroblled UAV sensor-craft. Suchcraft take avnaeof. high AR asi wel aseco ganatnai the- aircraftI diamondplaniforim- Sucbh aircraft C~ar-ry a large. p i-TiOrti of fuLC and are eXpe-cted to 16Iitur" at hkgHalt i TUdeL'S- for a few days in, eac6h lih.This inplies~ n wvide CL - altitude cýapability, Tft"1diaio n T' shapes offer useful sfealth azc- "ine. The -~a eroftoiI sh-apels need t o be thki k fo fuel1tiankaee. The cruise MAchnurnber ej ee to be Thigli" subsonic. Tfhe low-speed netr-fýieldperfoiinmnce is more akim to that of a (vcry) high aspec ratio wing glider. Take.-off and lapdiL.phases are critical.The desisin demands -obviously "'conflict" and this has led to a ciiallennn -work probgrixnrnCtowards 'suitable layouts.The sensor airraft as-en-iaqged in.Fig-1-3. is subject to a, challengirgfih neoe(ismprofile), At prcseri-L the design is, reltvl w:i~~Bx"wnso different layouts -arise- Thesensor crafi has To cruiseabnd loiter (very high UD or substantial periods and needs to carrv alarge P~erctntlgeoQf` its all-up-weight (AUW) in firel. The hihaspect-ratio.Nwings (sweep abu-u.t
1-3Y~) therefojre need to be fai~y thi6c_ Thi imles emphasis ona efficient aerodynauric and.strtictur.-l l6'ding- A partkcularly critical aspwc is the, desi-e of -the wingzjuncture anid LB TEdesign, Obiously there are =4nY zenietry Parameters that -arise implying, substanacomputations..
1.4. Present Work Programme
Suitable gearnetry parameters of the joined-wing coduiiguration have b>een discusse d with theAFRL togethaer with some preliminary results
In the first fhase- with '~seed"~ fundina b EQARD, the' follow~ing aspects have'been' proposedsein-pp Desigi ouinRptii & Prese-ntation delivebls)
1, Set u iemetholdology Of the_ design probilem ixicludingq flight envelope (N-kklt altitudeScal efects4 Indicate Important!f Critýical D Esi g reri mes.2.Set up appropriate geormetryit thic A lrfi sections inclu~dng juncions.
3. Solve for deSign (under appropriate con-straints) of The wvings 'with mrutual interference andallowance for juncture effet&
4. Two t-na cL-,ret e oe showci-n thle effects of the madin Parametric variations.5. Results vill isho-wthe fOrcesO~! moet n nesr istributions, Longitudinal be~haviour isof primart, int-ere st. A restricted effor will be directed toward laterals also.
6, Compiling a Report on the technique-s used and results obtained wvith conclusions andsagg&estions for further work.
7, Draft repor, is to be se-tt for coniments before issuib- the finil versio, which is the main
8. Presentation on fidings and- future wc-tk- possiblliti~s~at the AFRL laboratory durring, a '0O5visit (this effectively constitutesenrtlher Deliverable).
In -0eev of the rebfivzeiy small f nancial scqyjze of the pirsent fun-dinea. more &daietý,-d Ontinecessarv parametvic mc~~~~ad othecr studies wNill be subject to lau-her fivnds behiqsAnctioned.
2 1L5.. Layout of Report
The icmafindet of this :ý=-ort is in Sections 2 to 8 as follows:
Section 21 describes hriefiv the method and prceue b application.
Section 3: deals -v-i'h-th aaticipate6d f Iligh -t envelone and Ceornetry aspects of confimurtionsfeasile (Al wit af- wetoter tipst and FTI & FT1 boh it forward-swp ue
lips).Secin4 reer toth calcucations nenluaks of the type AT].
Section 4 refers to the IJcu ati ns On binfiqurTirsoThty FL
Section 6 refers to the. ciletilations- on.ofgrain of the type FT2l
Section 7 describes the scope offfindier wvork and Devellopmcent of Techniqqes.
Siection:8 rnemionoiConduiding Remarks.
2. COMP1UTATfIO3NAL & MODEI-TNG AS1PECTS,W1 MIOI)S USE]
Ont novel laouts. ufien, the experiecei-tw te comýplexities "d~f,) an a.utoma ed 'lstnds-off`design proce ýss en used wk7fithcnfed (uniquo solutloitS dobe). Thereforev wNv hdVe1chosen, a- proce-ss tat allws5 a mgalatudrtadn ib ane ihraoal manuzal
:1 P~1anel and Euler codes are befing utilisei rlrr enjabe a~seýs ent C the.u- dormymi p a-naneeover the ranT of low to hi gh spt¶L& M ost~ of:. the early work 1 cn bet accomp Ii s hed with ;a panelmethod, This is cotisider-ed adequate for design work at this st7nge- as [~light 'Mach number is ofthe order of 01.6.
The Euler or Nav~ie"-Stokes! solvers at- -subsonic sptMl Pimpl CPU: hours rT'her xban inutes fR,the pael code-s. Their usage.is appropriate *when aefiniitive cofgrainlave be&Vj arrved at
The camber and twis5t design, undef force and mom'ent constraint~ls. -IS" via previoutsly v'alidatedattained suction design methods (Reýfs.2, 6, 7,-8, 9ý: 10i I114 In vjew ofth1eq_ veiy-, high aspect ratios,involved, this process has been simpilda~ssarsrce sto abradtitmds
An inverse' design mnethod sing 3-D membrane analogy (Ref;3) can "tailor" <and `fine-tue"aerofoil shapes for -more optitn1Unipressure distributLions asreued
717
3. FIGHTENVEOVREYOL1)SINO. & CONFIGURATION CONSI1DERAI S
3.1.. F1liht Envelope, Reynolds Number Ef1fects.
Precious, wvork conducted at the AIFRL indiented that the. main. sizng drivecr aspeet i. hnegration of a 'rontbic' antennia. This lead L--o veTry thi`ck zlerfi.Thpald nrag
pe.rmntn e dem-atds lead to the desinofhcaeoii tcorltoheL.ewen1 d2 1%`) opera-ting, at h iih CL value s, F ig.331.1.
Mission Profile iuid Requitrernents are shown in Fig3.11.12.
The AFRL studieg indicated igt6ni nasufmrsdnFg.L3
Fiv.3 an4~ idea o Alzitude and Weiirzht reltinships dutibg a tpMmission. ThReyýnolds number variatzin is aLdso dcpicted.. Fig.3.1 shows the Mach huimber and CLrelationships (Cl based on th. -front wing z4-ea, $ec-1 an 327). Tak~e-off, is near CL of 03alMach 0.2 (Re fA4x1 6 t.wi~ adn sa CL of 0.7 zt~l 1 R .6The Mac 0.1rieCare rm 5,8 to 0.85 (Re 0..44 x 10 /ft to 0.345 1061fq).
It is interesting to re~flzz-t that on conventional aircraft the cruise. C-L values are near 0.55 and take-off/ landing CL, values near 0.3 to 1.2.
As the thick, aerofoil sections give an appreciable r-an e of Cjr operation, weý now -have to focuson what CL to chose for dessiin. We need to have an idea bf the 1"attaine'd o tr ranges (orbands)" for '"attacht-d" flow,
Fig.1.L6 shows3 estimates of "attained operation reanies". fbr 15%o t/c, 35' aft- and forward-swept wigvdmngawn-pn of 200 ft, chord of 6.640006* ft (dimensions are baised onSection 3.2).
The curves c .oIrresponidin2 to cruise cOnditions ar.- mor-ý demanqding. The atsetwn~i~bandwidth bate'len 10_5;ý (raot) -`-V (mid) - 101 (up)r~ wHslt thi forwad swe1pt wing, g'ive's aban~dwidth of 6.3 6 (rotf) - .4' (mid) - 14' (tip),
Fig,3.1.7 refers -to 17272%C te se-ctiokms. T[he finctea5¶2 tf nd~ 'the bandwidths appreciably.
the miinimumn operating~design at of about 4' wouxld s'eem. reasoniable to start iwith at thig stage.Once confidence is built up in the techniques, hig Pher dsie -ft ang~q'. can be attempted a'swNell Mmaximnising cruise LID.
Ftor maximnising- LD, -The, lift-induced drag term C1 i must equ!Ial the profile- dr-ag teri C~yj(comprising planar w'ing ftiction~drag and wa-ve--drag, Ni an)DO il hrfreeetaneed to ascertain vjscous efifects.
IT is interesting to reflect on bow, such a craft of x cry high AR could be tested it a wAind tnnel.Because, of large Nkirig. r an and smnall locaf chords, a large wind tune .etowould ýbe ideallyrequir~ed. The pojpular turnnl ranige between 8,and 16 fft and1 'the2se- are thoudht to be ratlher o'n thesnrallside for these conflgurations. Another associated problem is the stiI~hess of the model in
a-r--elastic sense. Bending and twisti ng odess are hikely to. be present,
So theoretical work. needs to be pre-requisire before any large-scale experiment-al mnodels areattenipted.
-3.2. Reference Configguratio-n (AITRL) with _Aft-Sw-ept Tips -C n ig AT,
Fiv.3.2.1 sh6,.s, the general arrangeingnt of the c, ensor craft Nit 9' dihedra I on the fore-wvingand 9' anhedral on the afl-w,ýinc. The elscagesl ois essentiafly "notional' -at this stage. Notethe- location of c-ontrol surfaicts. These are not, suppo led to intcrfere 4ith the anternra-
BriefRefereace Projeced Planfarm Geoineinv
Fore-Wingi- of Aspect katio 300. 12', Tap rto LO Svv weep 35'Whine Span 200Rf,Foie-Vk mi Gr Area =1320 f12
Ca.n .ro QG0 )'t CA v
A t Vin~ of v X' prctaR ati c,2 Lý9 7. Tape ratio 10, S weepr -_35Wingý Span 150 ft (joined to thc forewiz at between.140 & 150 ft)Aft--Wrtwi Gfoss Ara ~95 7 t
'For eanse of modellilng we ba-e, chosenl seinuspan as 1 .0 Pand t-he most leadingr-point Ci~c_the fbmW-d wing 4p~x) is choseni a-s the reference point for pitching inionrints andnieasurýmemnfts. The reference- area is Lhe area of the forward ing The refereacr. leng-th isthe ca (which is the same~ for both, wi ngs).
A basic super-cti tic al a'Oero fail wNith. tkc 15% stream wi se is the startlin -point-. The cam beranMA twist v-ariations need to be designe~d.
A typical case "ith tic 17-N% has also been run.(Config. 1171 series).
Titnann et al (Ref 21) uiention the design of thik aerofbits and these cant be iticornorated,.a!s and when-z recju ired.
13. Two Pwssible Alternative Layauts :Witb Forw~ard-Swept T*p, Con figp. FT- & FT2
To6 improve handlinse and to reduce. the2 "build-Op" of loaiding'_ on the sNwepf t~ip, particul,_Aryduring "offdesizn" the a-uthor ha prop-ose-d (Fg321 nop ton.f -a fbfwatrd-swept wiqgtup. Two arvang-ennents arise:
Config. FTI
The -front -vinz has dihedral and the aft wing has-anhedrak. The wingl-Tip has 4dihedral., joined
either to the fr-iaor the aft-ýNing Withisuitabie "cranks,
Thsariation imnplies th at the firorat- ing wiilIl ha-ve &mh dral and tkhe aft-wine wNiVll bave dihedra'l.Thiý!S %N vill ensure th at th e spar' o f I h e af--', g wvril scsntC'i ally, rem.ain "uribezft'". From A pricti calIview-point, we will need to as~sess the fuslag and itake itite-gration.
We nw ned o lok a eah cnfiaraton ritur and as~ses th-e relative rnerits of the variouslayouts.
For configtirationrs that have a consideraby largae~ flight eeopthe off-design, cnsideratioW,-become very impor*,ant- It is desirabIe thatt, fora agiven, pitch stablity leývel. the tendencc- for flowvsepar ation doescý_ not increase with increnusinu. agle of attack.,
In each Nas;, w need to assess angle of a~akand camber effw:s tribr to design'.
The, dcsi=ns are essentially "Iirst-cuf-C to demonstrate the rnjor ef-flccts. Obvio~usly the addidonnof fusel"Iamcan intak~es 'w1l haelcaleff.ctsq and'these ca.- be inrtroduced at a Iater.st.Aee.
Th e ptc hi"-n o tionent' Oe c: Is ina y b e vmore s; ifnfi.ca n t
4. 13ASIC PLANFORMi EFFECTS sr Ws7 LOADENGS,% 'STATIC STABILTITY
C ONTSf)E RAT I NS Config.ATI.. MachC06
4.1. Basir Plan-form Effects, Un-canihred Caise
Fi:g.4.i.1 shows the -general kir-fnienrnt and a 3-D) verspective.-c This ha9s be.enmiodelled F.8 3
w-ing comppirnents:- front, aft and the outer tip. FigA.L2 ýsh 0 s the miciatnhbered iaarofoil shapes,
ltig.4.13 shows§ the CLF and Cmn (about the most !c ad`I-, point) chiarai:ý:isticsý:. Al,(ýso shon.zn aethe contribuifon-s daie to th-ý 3 comipO'nent. wingcs. Note that it he forward winaz carries niore lifft
ehtite -ec nd in as n-pj1hL be epctenýcd fr'im dwnwa' ccnsid~eratioans, The neut'ral point islocated: at X/s= 0 $552 (as: F~rc on F4. 1.1).
17ig.4.1.4, shows the spanwise lift loadhings due1 f 1k-, ifl 3 C.,-rnopncwnits andtheir suim. Tbe' 1forwVardVj2 wingi m~ore loaded toward the i~n-jundure. tAf* eitr-ln_ ispite of the ddowixiwsh- 'feTs "Oro af igcare or ading ,tnd this, is to Tue expecite2d on a
fbrnvrd-'swept whig;. Frc nairntimn drag, of Th tota - oIiuain -!I nae iiclf1dinz. s.7ýdqsppear ihevr hwing tsp.
fig.4.1.5(A-d) shows the1 chordwisa loadings alontg varipus Mvn& sections at cc 01, 125ý1,4.25c'and 5.250- The coTrrcSpoI~dinlg CL values are 0.0 SSO, 0.759 and 0 9336-1 owethe incre'asein LE loads asý a increases.
At a given d1esign condition (CL and- a), one. could. desig cber'and tWis orminimum dtaelliptic loading. but the tendency 'at off-des~ign will be to de~part fProm the elliptic loadinz-. Thisw.ill have imrplications on pitch .stability,
4.21. Designed Case
The mnmmCL dAesign point is related to landing. \Wehalve chosen tL =0 68 i.e. equivalentfiat wing tb of 4.5 ehv re t prahl liptic loading for te design. In %iewv of the
thick sections andý anticipated attached flow bandwidthsý the opeatol rangeesho-dld'extend toCL of 1,5.
The twist and camber para-meter variations along the wing-span, (of the three v'wings) a:e. shown
£ ~in Fig.4.2.1. Notethe iharacteris&i twist and camber & ffernhces~fot the fomrdrswept and aft-swNept wings. The front wvina has less twist and caniberT, comparedý with their rear wý.ing.
FigA.7422 shows the aerofoil d-es ign asbapes comnpared wi~th the uncamrbered case.
fig..4.2I shows !he Ci c~ad CM -- ,CL chaac:teristics. T~ht CG for this design i~s locate'd at x/sý
0-546. The-C6 position Icain .be. controlled easily if required. by velyv Small Lfadditional changes'in twist. This is hnwever not contsilderced wxorthvwhile in Aiew of the preliminary nature of -thestu-dy and considering that fuiselage and intakes still neeZ, to incoipoated.
fig.4.2.4 shows the spnwvise lifi loadings due to anol of attack. on the 3 wNiniz components and
their su._For tininimurn drag, a neair ellipticsu mig.ain is r quired, as sho-wn. As angle ofattack increases,. the tips show higher loadings.
Fig.4.15(n-c) showsa the chordvise loadittgs'aliong i- ariouzs iwinz section-s at cx ý3.25, 4.250 and"5-2' The -corresPohdinz CL v~alues sire 0.588, 0.76S anrd 0-946.
Notce the upper surface flat--top nature of thie cherdwis"e pressure distributions (cX uincainberedCase. Fig.4.1.5). Geclretry detals* near -the wnijuncture dould do with sonmc local
u-nprovennentst if required.
4.3. Dosigtiedt'ase at Low Speed (M-ach 0,15)
We have briefly examinied the lo'w speed capabflity Of thei designed layout of The previous
section, LE and IT flaps remgain to be included. oevr
Fig.4.3.1 show~s the CL -C'Cah'd C Lcharacteristics-. The ?vllch 0.6 dlesign has be-Enevlute a .1. h ~ for Thfis v sis.- Nat h 0. 15 is loca, d at Nxis 0.553, which is
'S~hOly acft o1~Cotrlprmabie Malch 0.6 iocationt at xiS OS5.'6. The pC(,i sitions, and Tesiuhinc-C1nO ca býe cimtr-o
5. BASIC PLANITORM EFFECTS,' SPANMISE LOADINGS, STATIC STABILITYCON IDERAIONS, Clonfiga. FIil Mach 0.6
5.J. Basic'Phinform Effec's, It efcrd Case, 5 tc
Fi.5l 1 hosthe genrwal3 rangmn an I Q-)prpci~ This has bceen 7moýdeleda 3-w~ne cornponents: -ftran;, aiard the outer tip. Fig3J5..2 sow theý unctinibere Aeroo$IC saps
F-,513sh6vs the CL and Cnj (about the mtostz leine point) characteristd-cs. Also show-n artethe conhnh-titons due to iu ~ciponenV wi~ngs. As previously, tfle fo war ingth cr carres morelift thaný the~ siec-nd, due tto dawivvtash torsidoeratios. The neutral 'point is locatedI it x/s,(As mrruked 'onFi.L1
fig_'5'.4L showvs the- sbIiwseli loadings, due toan1 of attack on the '2 wivnc xomponenTS 4ndtheir sum. The for-w.ard .-v_,- is more Ioad~towrd the- wing-juncture. -At thel centre-line,-spite of the downNwasli c-eff-ts, the. aft wing -2resmt loadiri -n hsis tobic ecedoforward-swept wring. For ntniat g d of~M the totýal ccdfigiration, a ntear cilipfic litft loading isrequircedt as ShownL ,Oil this l a-,out, relativch- lowe:- Joadimiýs appear- near the Nvingý tip and ov&rallthe- lif t loadings aire nte,4r % 1, lizCc (except ra r a very n- Sfnlliscontinuity near the! junctlure).
Fig.:5.1.5(a-d) show%ýs the.- zhorlvwisc loading.s alonz, vaios win, sections at er = 0*, 125", 4.250and 5--25'. The cotrresrondirna CL values 'are O.0 0_53, U.759 & 0,9364 Note the, increase'in Lt-loads as ct increases.
For this configuration, the minimium drag, elliptic loadking is~ morp easilyimatched not only at agiveni design condition (CL and ct), but also, overm an exttndd" off-design irange!.
512. D-Csigne4d Case, 15%t/vc
The mninfimnum CL desicn point is related to landing. We ave 6hosc 'CL,07 ~.euvlnflat w~ing a of 4.251'. W~e hacýve tried to kecep the sp anwv. 0loadings91 rin1i aT to tho se tcir dh, placase rather than per-fectly ell Iiptic. Thiis impl ies neutral saiity. In view -of -the thi ck seýctio rs' andanticipated attached illow bandw-idths, tbe operation~al varme should extend to CL of 1,5-
The twist and camber Parameter variation along the -,itig-span is shown in Fig5.52.1.
Fig.5.2.2 shbvws the aetofbil s;,hape s comp'ared with the UrcaniIbered' case.
Fig.5.2.3 sihowvs the CL - cE and Cm CL characteristics., The.CG' for ths design is located, at. x/s03523. Thet- COPosition can be controlled easily, ifrequired, by very small &adional changes
in twis t. This is. however, not conisidered. W"'rrhivhile ii i th peinay nature o hstudy and. corisidering that fusalnae and intak-es suiu nee-d to in COPo-rated
Fig!5.2.4.shows t Ihe span~ls- lI& loadings- due oanl fattack on the 3 w~ing components andthir sum.. For mninimnum drag. ,a hear, elliptic liiift io~ng is require. as shownv. As angle of
arttack- increases, the tips show loadings lower than the ell(iptical shape. The small discontinuityat the w~ing juncture has been allowved t&:"persist".
fig,51.5(zi-c) shows the chordwise laig lngvroswn sections atoci= 3251,_2, 5" and,5.25*, Thecorrespondinng CL vadues are 0.582, 0.761 a~nd 940.
-Note the upper surface flat-irip nature of tbe chordwise pressu.re distributions (clf. uncaruberedcase, Fig,.5.1.5). Geometryý -d&tails near the wing Juncture could do w~ith some localimprovements, if require~d.
The process continues to confirmn the ability to tackle ffhe main flow fýeatures, design and detaildesqign of hig-h aspeciT raio joined-wýing layouts.
5.3. Basic Planfarni Effects, Uncamherrd Case, 17.2%tic
Fi~.5.1 sowý ch eneral t, I "- 7 nT d ar I-f) perspective. This has, been mnodel led as, 3Fig.5onnotr3s , a~ot. itand the )u-er 7rIp.Fg.. h the -, mec erfi h~s
JFig.5.3 "AhowrNs the CL- andC (abo,_- tlhe. most leading- point) -charctrisrics. Also sho%ý an-,the enr~hm 2ns dn to the 3 oompn ,- wigs- As previously, thef.r: r wing cfArre 7oe
flft thaxn the secciid, due, to dbvwnw~ash consideriitions. Ric nturaIM!'l pit is: located at ,ds~ 0.5"S(as ma~ed en, Fig._5.L.1).
Fig3A hos te panise2i~_ladnzz dueý !o tnled of aftack- on th.- 3wing- components andtheirI: _`.T. f~wr wing is mo~rL Iloded tow-,ardis the vwing-jntr. At te centrz!line. in,
spite of (hE &awn--ash effieck; the aft in ciirneLs more loa~ding and this fs to 1c exp-cted on aforwýard-swept wi.For minimmum ~rag2 "of the; total configuration, a near elliptic lift Taiiirequird ý bon On this layoutit wrdelatoi -o2ig aper ner the wn i n vrlthe lift loaddings Ir~na heit c-.T wing ILEncture lOR(dings can b- improwcd, if requined.
Fig.5.. Sa'_d) showvs tie ihrdise Ioadi ,s alnc aroswnsetnsa 4056'.~ ~ ThLoý,S7Crr1n: values aize<O0O'0.7l9, 08ý)9 1,073.1 Raoe the increase zin U3 leoad s
cr inereases-
For this conf-gaton the niihimnm d Cg ~Hiptic loadin6 is, Morteý esil. ahenoonytagiv en design .con-dition (C L and az). but a!i6 ovIer 'an 'extne' ofesign range.-
5.4. IegndCuse1 1712%'tlc
We have chosen CL = 0-711 i.e. equivalent fla wing ~aof 4', We~have tried to keep the laigsimnilar to those for the planar case -rather than pe~rfecfly, elliptic. This imp.Iieiýs neutnibzstabilihy. Iinview of the thickt secttidbs and anticipated attached flow -bandwidths, the opdrafional rangeshould elxtetid toCL of 1 ,5+.
Thetwvist -and canrber paramneter vari ýio ralo ag thie %-ving~span is showýn in Fig.5A.4I.
Fig.5.;4.2-shows thd-aerofoil sh)apes comare-jvwith thevanceambered case.
Fig.5.4-3 S'hows the CL~ - -qand Cra - CL cactrtis.The: CC for ths dealgu is46ocated at /= 53. The CG position can be easily cotold, if fc'quiired1 by very =,all -addition al chanees
* in twist.
Fig.5.4.4 shows4 t..e spanwise. lift loadinlgs due to arngle f attack on the 3 wintg co'mponen~ts artdtheir sum. For Minimum .driag a near elliptic liift loading, is reqiipred, as sho~vm, As ande 4 ofattack incrasLes, h tips shbj:ý Sodg hwver thian ý,he ellipticAl shape,
Fig.5.4.5(a-e) shows the chordwNise lodigsaong aiou -ia sections, at a~ 40, $5adThe'correspondine CL vAlu'S are 0.711. 0 891 and LC?7
Note the ue~per surface flat-top nature- of the chordwise~pressure distributions (clf un~camberedcase, Fig~.L5.). Geometry detail near the wing juncture covuld do w;vith :sm localim~proven eras. if reqnired.
6. BASIC PLAITFORM E~FFECTS, S1ý,ANIVISE LOADINGS, STATIC STABILITYCOLNSID)ERATIONS, C~onfig,,,. FTF2,Macb 0,6
6.1. Basic PlanforvinEffeets. tlieambe'red, C~ase, 1-5%N t/&
Fig.6.11 ýshows the gene-ral =xiganieftnt and a 34)peDctie This h_- been mnviefled as 3udr-1Z c~ompongnt%: fron-t eft and the. outer tip. fig..6.12 thw~hcuremerdirfoil ha~s.
Fig.6.1.3 sh&ovs tb Cj1 ahd C., (about-tle mslein poidt chiarvcteristics. Also shown tireThe contributions due t8h EE COtiiPOn'e't wAings0. As preViot!sly, the forwaNrd iwing carries mnoreOif than the seceondl 4vd to dovwash onide atioiis, h neutitl po;inT islcte txs .2(as 'marked on Frig.6.l.1V
Fig,6.l.4 shovvs the spanwidse lift loadings due to angle oF attack- on the 3wing ccinponent -andtheir sum., The forward. wiin is more oaded twrshein-ueture.Ath ceýntelenspite of the dqwnwa-zsfi ef f~ees- tfh e aft 4wing caries rnorý Ioa di til and ihis is tob xpete on a.farward-Lswept vvngý FVor ruinim umn drag, of the total confgrtion=, aR nr ell iptic lift lo'ading isrequired. ds shown. For this Thvtt,. relatiNely lower loatdings appe~ar near the wing- tip anhd.overalltelflodn•aexerllpih
*Fg.61.5(a-A) shows the lhrws oadings along varjious -is g sNjý,tions at ca O~ 3.25ý4.2-56and 5,2$3. The c or6ndi~na CL values are 0.0; (1 iý55 C-704 and 0.942, Note the itceras InEloads as aL in'creases.
For this conflgurat.ion, the minimumh drag, elliptic lo~adingy is tnoiae easily matched not only at a.eiven designc~ondition (GL.and cc),. bd~t also overzam, ede~ofdsinrne
-6.2. Designed Cum., W5%tf
We have chose~n CL ý 0_754 i-.e. equivalent flat xivg -a of 4,251D. 'We have triezd to keep theloadings similar to those for tha planar case rathetr than perfectly elliptic. Th-is implies neurtralsuability. In view of the thick sections and anriciiated attached fflow-bandwidtý7hs, the operationaranac should extend to C'L 0-,l ý5.
The tmist and carnber parameter variation along thfe. wing-span is sho'wn in M0g.6.2.1. Forsimplicity, this has boon. talkenas being 6he samffe a~s that for tht easet of Sec'tion 5. 1.
Figg.6.2.2 sliows the'acrbfoil shapes compared with the uncainbered case.
Fig.6.2.3 shows the. CL - c and Cm -CL chiaracteristics. The C(Xi}for this design is located at xls=0.572. This represents a slightly statically uwktfblecase The 'CO prosition cjan bi ConitfoIled.easily, if required, by, very small -additional chianges in tw'ist.
Fig1.62.4 shows The spanwise- lift loadingps duie, lo angle of zatt ack on the 3 %xing components- andtheir sum. For mininmuni draft a near &lliptic Ilift l~oading is required. as shown. As angle o~fattack increaes, the tips show loadinigs approachingi the, ellptical s$haped.
Fig.62.5(a-t) s.hows the chordw'ise loadings along -tarious -. ing, sections at ct 3.25c'i *25.ý:and5-250. The corsonding CL 0,le. a 5 075. 0.754, C, -29
\Note the upper sutface fiat-top nature of the daordvise pressure. dlistributions (c.f. uneamberedds-e, fig(.6.i.5). Geomnetry detail near the vving junctur e could do. with local iinpn-ovemnents, if
required.
The process continues to confirmn the aibilily leo pin-jpoinvtbtheaain flow featuress and to tack-le Ithe'design of high a~pect ratiojoincd-wking tayouts.
14
7. FURTUER WORK
So f&i we have- bxkd t NMach 0G.6 dtesienL~ on iTheý 'diff~retat typDes of sensor-craft- jond-winlayouts. Stea trsigfic trci h~v,. e- -eged Burtherc is niorz to do!
Further work is seen in a number ol aspects, and4 these are liste'd ajs ~los
-Lower speedas. field, performancecosdrtnsParametric iemti studies.
-Appropriate wethod de-velopmen-t.Different design CL studies as requilredi.
-Different aetofo*Hs incorporation, ifreuW mm the' point of view of validtion with CFD)and'trainsonic coides-
- L/ T Flp. etfing- o~nitr retitosc seýMrintatiol% effects separael ad cotnbined
-Fus lqge/ I ntAe incorporation. additinl efects on forces aind momenrtss.
-Inclusion of- visos effetts, Sbar~iiSe pre~sure gradiients, control.
-Draz -vredictioti.
-OIftkdsi-n perfounanee.-Include ne'ro-elastics.
-Lteral ?and dlirectional characteristics estimation.-Creating ThUl 3-1) geometry model.-Choice oflt)ype of. conifigurations; (AT or t .- Aeres).
- Expeimental work-(various aspects;)
It is apparent t~hat wve are only at a starting post and a sizeable, interesting work- progrMammeremains!
-8. CONCLUJDING REMAkRX-S
*To replace the AWVACS aircraft, a pibposai is tbr renhotely-tontrolled UAV Sen'sor.-c'raft. Suchncnft tk-e ad atap~ of high aspect.r'atio (aR s well a.5 enitlsing an. antenna in the raircraftdiamonid planfbrrim The airoraft carry a large proportiOn of fEel and "'loiter~at high altitudes foriiýfevvw.dqvs;iheach fligrt, -iimpIying a wide CT, - vohitiide capability%
This report Thas been concerned widh con-.ignra-ion and desizgn- studie.s of hi-gh AR sensor-craft
Three different types of joined-wing Iay-muts have been roosed. The eonfigurfitiobi diFferen'cesarise due to th oietation. f thý outer w~ing tic, whethr it is conwehticii't Ay aft-swept or.forward-Swepta
Results- have been pre-sented for wvings with uncainbered sections and then %ith desiigned camberand twisted sections..
Layouts Mi04 oowr-wp uter tips gie painwise loadings which are poibrme tolrnat. off-design conditions over, dtehe flight' envelope. Suc-h configurrations may have lessleaden~v for W~ne-drop at high lift. More lcla*Eng occurs on, the front-w4ing near the ju'nCure'rather than at the outer wing ti.
Further worki has been proposed in several areas.
The author has- -Iauei cnweanýhlfltcnclcmensaddMtsin ih Dr.Charbel N, Raffoultl Mr Waynce Donaldso:n. Alr. DA M~ulhopp. Dr. C. Tiln-hn. Dr, D,.Moorho~use,'Dr. W, lk' Dr. C, Jobe &Dr. M. 01 (LS-•AFkL), The,, tceehn~cal 1eW I-f DT. M, Ei,
This m-ateria] is based- uponn workc supported by the Europ~ean Office of Aerospace'" Researchl andDevelopment. Air Force Offiice. of'Scientif-ic Res-ear=ch. AMr Foircei Rese-arch ILabomýrytr, nContract No. F61 775-01 -WFOS"cý7 (f;-OA RD. Contract.SPC-C) 4097),
Any! opinxions, findings and2 conclusions or reorcdtosepesdin th~is nmaterial arc thostof the author(s) and do not niec~ssarlly reflect the sesof the Euiropean Office. Vf Aerospae'eResearh and De-vlopmrrL--- Air For'ceý Offlibe of Scie-n-lfli R(,search. Air Forc-e RiesearchLaboratory.
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15. N-AI.GIA, R.K. & PALNMER, NIB., IlThlets-with Negative Scarf'fbr Acoust5ic Rcduetion,Aeroidyrtarici PC7rforma:nCeI Asses~sment at Tra..sonic Spee;,ds", AIAA '2000'--.-.09, August
16. AN A.RXK &,P INE MRE. `Aprplricaticmof Neg-uac S,:7rf to Hnet Des3i~n Th
IVW 7 LKOV1TCH~ v. 1TeJie n:A v iew'. JR. 6fAi. pp 161-78~ 1986.18, WOLKOVNITCH. 3. &, MVONTEALBQI R-- "A .9econd Look-,at the Joined Wit99,~ Book-:
"~Uncon-ventionmi AkircraftConicepts", Deift Uni. PTC.ss 1987.19. rFREDIM A.. "'A Ncw Large .Aicrera withi EB'X-Shaped Swfpt WXings SYMPO~iurn
Toulouse.= 1099920. Serlsuro:;s on wwvw.21. rz I .C.P. et al..~Dv1pin & Validatio of Airfoils for Global Ruata
Transpons", Al-AA-2000-4509, Xauus- 200(10.
-'- ---- -
LIST OF SYM BOLS & ARB REVIATIOTN.S
Only fihe geea smosa efed he'e Othffr sytnbols are of lclsniamewillhin thestzfeioi they avise in.
AR AspettRntoA Axial Forze along win,=-p~ne x-axis (far, de-rhition of Ck)
b =2 s. wine 50oanBlL Bounda.y Leytr
C: LoValXNRýCbotrdCitto a Aerodynami. V41-~ Chord,4
CA = A/fq SX a' Force- 01ooý'tCIEVtt, Measured in W11~ rpan-ýCAL = Local Axial Force CoefficientCrD D /(,q S), Dtzge Coe-flcieni-CDO Drag; a'fice 7ero lHt(e etCjjj Lift Induced Dr7-z
CoCentre 6fitCL = U(i: S)i, LiatCeiinCLL = Local Vift Coeftkent
CL~a Maxiulmn Lift Caeffilcient
Cmoj Cg a3t Zero lifT
CN N($NnmlF-c CoefflcientCoefficient of PressurWmag-Root chord
CE wing Tip chordD Drat~ forcet
k = ~) AC151CL2 LitT e rg Factor
L Lift ForceLE 'Leading Edge,LEF Lgaufinz Edge- FlapIr. Pitching, Mmentcr (Body Axis)&I Macb N-umbe-r
q 0.~5 PVý ~ad r mzss rer Aerofoil radius
Aeriofoil raidius nr~mWl to cR Reynolds'Number, basel or c.., (unless otherwisen staxed)
5- Wing semi-sP IanS Wing Area. takers he-re as ttr on: will + tip-wing) zrca-
r Aerofol thicknessTE Trafliqg EdgeTEE Trafliqg -Ede cFhqvrv A irstrea'm vekcitylX.~ Ohog ilN Wir. P Coodiats, x a o nc b od v a,ý
Note x, & xcc coinciadu whun static krin is ze~ro.)X, Location of Cen-tte of:Gravity or TMOnetr refertiice Poir.t 2alone X-axI's
Location of Cmcm ofpenr a-long m-a.ds
a. Angle of Attac%, wmanl Ny r-ef~rrd to the bod)y axis?. Taper Ratito
Aý LE Sweep Angal-p Air Dcnsit:y
~1 =Y15, o-dnesoa pni Distance
FIG, t3A JGINED-Wt�G CRAFT (WOLKOVTCH�
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