Design of a One-Third Scale Multi-Tethered Aerostat System for Precise Positioning of a Radio Telescope Receiver

Transcription

1 Dsign of a On-Third Scal Multi-Tthrd Arostat Systm for Prcis Positioning of a Radio Tlscop Rcivr 1 Casy Lambrt, Aaron Saundrs, Curran Crawford and Myr Nahon Dpt. of Mchanical Enginring McGill Univrsity Montral Qubc, Canada, H3A 2K6 Tl: (514) , mail: Myr.Nahon@mcgill.ca Abstract Th National Rsarch Council of Canada s Hrzbrg Institut has proposd a dsign for a nw radio tlscop known as th Larg Adaptiv Rflctor (LAR). Th LAR tlscop is comprisd of a 200 m rflctor and a rcivr hld aloft at an altitud of 500 m by a tthrd arostat. Th position of th rcivr is activly controlld by a sris of tthrs connctd to winching systms on th ground. Computr simulations of th LAR positioning systm hav shown that th proposd dsign holds a grat dal of promis. To add confidnc to ths rsults and giv furthr assuranc that th concpt is practical, xprimntal validation is crucial. Thrfor dsign and construction was undrtakn of a on-third-scal modl of th multi-tthrd arostat componnt of th LAR to furthr study th dynamics and control of this subsystm. Th dsign procss bgins with an analytical study of th scaling procss. All variabls liabl to affct th dynamics of th systm wr idntifid and dimnsionlss groups wr formd by applying Buckingham s Pi Thorm. Onc th dsird physical charactristics of th scald systm had bn idntifid, componnts wr chosn to satisfy thos charactristics. Th ky componnts to b slctd includd th arostat, tthrs, snsing instrumnts and winchs. Th dsign procss for slcting ths componnts is discussd and an ovrviw of th construction of th systm is givn. Introduction In th intrst of drastically improving th capabilitis of currnt radio tlscop tchnology, th intrnational radio astronomy community is pursuing th dvlopmnt of an instrumnt commonly known as th squar kilomtr array (SKA). Th instrumnt will b comprisd of many individual radio tlscops functioning togthr as an array with a total of on squar kilomtr of collcting ara. Rsarchrs at th National Rsarch Council of Canada s Hrzbrg Institut of Astrophysics hav put forward a novl dsign concpt for th SKA known as th larg adaptiv rflctor (LAR) which is dpictd in Figur Th LAR concpt consists of two cntral componnts. Th first is a 200 m diamtr parabolic rflctor with a focal lngth of 500 m, composd of actuatd panls supportd by th ground. Th scond componnt is th rcivr packag which is supportd by a tnsion structur consisting of multipl long tthrs and a hlium filld arostat. Approximatly 50 LAR tlscops ar rquird to mak up th squar kilomtr array. Th position of th rcivr is controlld by changing th lngths of th tthrs with winchs and is prformd at both macro and micro lvls. At th macro lvl, th rcivr is movd to various locations on a circular hmisphr to allow th tlscop to point to diffrnt rgions in th sky. For sufficint covrag of th sky, th systm must b capabl of positioning th rcivr for a rang of znith angls from 0 to 60 o (0 θ z 60 o ) for th full rang of azimuth angls (0 θ az 360 o ). Onc th rcivr is in plac, th micro-lvl position control of th tthrd arostat systm rsponds to disturbancs such as wind gusts in ordr to limit th movmnt of th rcivr. It is clar that th viability of th LAR concpt hings on th capacity of th tthrd arostat positioning systm to limit th rcivr s motion within an accptabl rang. In an arlir study, Nahon 5 assmbld a mathmatical modl and simulation of th dynamics of th tthrd arostat systm which yildd ncouraging rsults of th accuracy of th positioning systm. Basd on th outcom of this study, a scond and mor dtaild stag of analysis was

2 initiatd focusing on xprimntal invstigation of a scald modl of th tthrd arostat systm. Thr ar two important goals of th xprimntal study: vrifying th dynamic positioning capability and dtrmining th oprational fasibility of th systm. From a dynamics prspctiv, th goal of th scald modl is to masur th bhaviour of th systm in attmpt to validat th dynamics modl and dmonstrat th accuracy of th positioning systm. From an oprational prspctiv, th goal is to us th scald modl to study th logistics and potntial issus inhrnt in oprating th tthrd arostat systm. In ordr to satisfy both objctivs, it was dcidd to construct th scald systm at on-third th siz of th full systm. This siz was chosn as it is larg nough to hav rlvanc to th opration of th full scal systm and it is small nough to b affordabl. Th tthrd arostat positioning systm and th dimnsions of th scald systm ar shown in Figur 2. 2 Hlium arostat Rflctor sction Tthrs Fd platform Phasd-array fd concpt Main Rflctor a) b) Fig. 1. a) Artist's concpt of th LAR installation. b) dtails of on of th main rflctor sctions and th prim-focus phasd-array fd concpt. 3 This papr prsnts th dtails of th dsign of th xprimntal tthrd arostat systm. Th dsign procss bgins with an analytical study of th scaling procss for our systm which involvs a dimnsional analysis of all variabls prtinnt to its dynamics. Th dtails of th scaling procss ar prsntd along with simulation rsults that confirm th dynamic similarity of th scald and actual systm. Onc th dsird charactristics for th scald systm wr idntifid, componnts wr chosn to satisfy thos charactristics. Th ky componnts to b slctd includ th arostat, tthrs, snsing instrumnts and winchs. Th dsign procss for slcting ths componnts is discussd and an ovrviw of th construction of th systm is givn. Scaling Procss Th tchniqu of using a scal modl to prdict th prformanc of a larg dynamical systm is a common nginring practic and svral mthods hav bn dvlopd to scal th physical paramtrs of th systm whil maintaining dynamic similarity. Th mthod chosn for scaling th paramtrs of th tthrd arostat systm uss th Buckingham Pi Thorm 7 to arrang th rlvant dynamic paramtrs into n m dimnsionlss groups. Whr n is th numbr of dynamic variabls and m is th numbr of fundamntal dimnsions usd in th dscription of th variabls. Th first stp of this procdur is to idntify th rlvant dynamic variabls, which ar givn in Tabl 1 along with thir rspctiv dimnsions. From Tabl 1 it is obsrvd that for our systm th numbr of rlvant paramtrs is n = 13 and th numbr of fundamntal dimnsions is m = 3 which ar mass (M), lngth (L) and tim (T). Thrfor 10 dimnsionlss trms, rfrrd to as Π trms, ar rquird to dscrib th systm. On possibl arrangmnt of th dimnsionlss trms is: m J F ρ E Π 1 =, Π2 =, Π 5 3 =, Π =, Π 3 5 = (1a) 2 ρ l ρ l ρ U l ρ ρ U 2 b ρul U tu fl Π 6 =, Π7 =, Π8 =, Π9 =, Π10 = (1b) 2 ρ Ul µ gl l U

3 3 arostat instrumntation platform winch #2 tthr R = 167 m winch #1 winch #3 R W = 400 m Figur 2: Tthrd arostat positioning systm for 1/3 scald systm. An inspction of th Π trms rvals som common dimnsionlss paramtrs: Π 7 is Rynolds numbr, R; Π 8 is th Froud numbr, Fr; and Π 10 is Stouhal s numbr, St. To nsur strict dynamic similarity btwn th modl and th prototyp, all dimnsionlss Π trms must b qual for th two systms. Using ths qualitis it is possibl to dtrmin th appropriat scaling factor, λ for ach variabl. Th scaling factor is ratio of th scald quantity to th actual quantity. For xampl th scaling factor for any lngth is λ l = 1/3. Th scaling factors for crtain variabls wr prdtrmind ithr by th on-third scaling condition for th lngth or by th nvironmntal tsting conditions availabl. Sinc th scald modl and th actual systm will both oprat in th sam outdoor nvironmnt, th scaling factor for th nvironmntal paramtrs (dnsity, viscosity, gravity) is fixd at on (i.., λρ = λµ = λg = 1). A consqunc of our inability to scal th nvironmntal conditions is that strict quality of all th dimnsionlss trms cannot b satisfid. A conflict ariss whn considring th Π 7 and Π 8 trms or R and Fr. For consistnt scaling of R, th scaling factor for th vlocity, λ U = 3, but for consistnt scaling of Fr, λ U = 1/3. In light of this conflict, w must dcid which dimnsionlss numbr should b matchd so as to provid closr similarity. Tabl 1: Rlvant paramtrs for tthrd arostat systm. Catgory paramtr symbol Dimnsion Mchanical lngth l L Componnts mass m M momnt of inrtia J ML 2 forc F MLT -2 dnsity ρ ML -3 tthr lastic modulus E ML -1 T -2 tthr damping cofficint b MT -1 nvironmnt vlocity U MT -1 dnsity ρ ML -3 viscosity µ ML -1 T -1 acclration du to gravity g LT -2 Rspons tim t T frquncy f T -1

4 This task is not straightforward sinc both dimnsionlss trms appar to hav rlvanc to th arostat systm. Th R can b intrprtd as a ratio of inrtia forcs to viscous forcs whil th Fr can b intrprtd as th ratio of inrtia forcs to gravity forcs. Thrfor, undrstanding which dimnsionlss trm is mor significant can b rducd to undrstanding which forc has a gratr influnc on th arostat systm, viscous forcs or gravity forcs. For stady fluid flow applications R similarity is mor important as gravity ffcts ar minimal compard to thir viscous countrparts. Convrsly, for fluid flow applications nar stram boundaris, Fr similarity is mor important as gravity ffcts dominat ovr viscous forcs. For th tthrd arostat systm, both th gravity forcs and th viscous forcs ar xpctd to influnc th dynamics. To invstigat this mattr furthr, it was dcidd to prform a quantitativ comparison of th dynamic similarity of th scald systms with propr R scaling and with propr Fr scaling. Onc th scaling factors for ach systm wr dtrmind, a prviously dvlopd simulation 5 was usd to simulat th rspons of th systm to a crtain wind fild. This simulation includs dynamics modls of th tthrs, arostat and rcivr. To assss th dynamic similarity, th rsults for ach scald systm wr compard to simulation rsults for th full scal systm. To do this systmatically, th input variabls such as wind spd must b multiplid by th appropriat scaling factor and th output variabls such as position and tthr tnsion must b multiplid th invrs of th appropriat scaling factor. Figur 3 and 4 prsnt ths appropriatly scald simulation rsults for th scald and full scal systm. If th plots of th scald and full scal systm ovrlay, this indicats that dynamic similarity has bn achivd. Th plots show th vrtical position rror of th rcivr and th tnsion in on of th thr groundd tthrs. Th tst cas considrd is on in which th opn-loop (uncontrolld) systm with a sphrical arostat is rlasd from a non-quilibrium initial condition, and th wind spd is rampd up from 0 to 10 m/s btwn t = 5 s and t = 6 s. From th rsults in Figurs 3 and 4 it is apparnt that th scald systm with Fr scaling shows much bttr agrmnt with th full scal systm. This implis that th gravity forcs ar mor significant to th dynamic bhaviour of th systm than th viscous forcs. Mor significantly to our fforts, th clos agrmnt in Figur 4 dmonstrats that although it is not possibl to maintain strict dynamic similarity, by maintaining Fr and ignoring R it is nonthlss possibl to accuratly prdict th bhaviour of th actual systm using a scald modl. Th physical paramtrs of th full scal systm shown in Tabl 2 ar basd on th prliminary dsign of th LAR systm 3. It is undrstood that it might not b possibl to find componnts for th scald systm that will giv th prcis valus for th various physical paramtrs. For instanc, a tthr matrial may not xist that matchs th spcifid dnsity, lasticity and damping charactristics. This dos not intrfr with th goal of this study howvr, sinc th validation of th dynamics modl can b prformd with any tthr matrial. Tabl 2: Physical paramtrs for scald modl with consistnt Fr scaling. Componnt Paramtr Full scal systm scaling factor scald systm tthrs / lash diamtr 18.5 mm λ l = 1/ mm dnsity 840 kg/m 3 λ ρ = kg/m 3 lastic modulus 16.8 GPa λ E = 1/3 5.6 Gpa damping cofficint kg/s λ b = (1/3) kg/s Arostat diamtr 19.7 m λ l = 1/ m mass kg λ m = (1/3) kg buoyancy N λ F = (1/3) N rcivr diamtr 6 m λ l = 1/3 2 m mass 500 kg λ m = (1/3) kg ovrall systm focal lngth 500 m λ l = 1/ m winch circl radius 1200 m λ l = 1/3 400 m 4

5 5 Vrtical position rror (m) actual systm 1/3 scal modl T (kn) Tim (s) Figur 3: Simulation rsults; Vrtical position rror and tthr tnsion, for th scald modl (dottd lin) and th full scal systm (solid lin), using R scaling Vrtical Position Error (m) actual prototyp systm 1/3 scal modl modl T (kn) Tim (s) Figur 4: Simulation rsults; rror of rcivr out of th focal plan and tthr tnsion, for th scald modl (dottd lin) and th full scal systm (solid lin), using Fr scaling. Systm Dsign Th stratgy for th dsign of th scald xprimntal systm was to us off th shlf parts whrvr possibl. Th arostat and tthrs wr slctd basd on th rquirmnts stablishd during th scaling procss and off th shlf availability. By contrast, no commrcially availabl winch mt our rquirmnts. Th winching systm thrfor had to b dsignd in dtail, basd on th rquirmnts prdictd by th simulation rsults. Arostat A basic study of thr shaps of arostats was conductd to dtrmin which would b most suitabl for th scald xprimntal systm. Th shaps considrd wr: a) sphrical, b) stramlind and c) variabl lift (kit). Th critria for slcting an appropriat shap for th arostat includd th following factors: arodynamic prformanc, survivability, cost, availability and ground handling.

6 6 a) b) Figur 5: a)two variabl lift arostats: Skydoc abov and Hlikit blow, b) Tsting Skydoc on th Columbia Rivr. Th sphrical arostat, as its nam implis, has a sphrical shap. This is th simplst typ of arostat as it has no prfrnc to a particular orintation and dos not produc any arodynamic lift in a horizontal wind profil. Th stramlind arostat has an arodynamic shap lik a tardrop to rduc its wind drag and a numbr of tail fins for dirctional stability. A third typ of arostat is trmd variabl lift rflcting its ability to gnrat a significant amount of lift in a wind fild. Th variabl-lift arostats gnrat lift through th addition of wings or lifting surfacs, or altrnativly by simply using th hull to driv lift. Two diffrnt variabl lift arostats, th Skydoc and Hlikit wr considrd. Both ar shown in Figur 5. Th smallr arostat on top is th Skydoc arostat. It is an oblat (flattnd) sphroid and its msh flying harnss givs it a pitchd orintation which allows its hull to gnrat lift in a wind fild. Th lowr arostat is th Hlikit and it is a combination of a sphroid arostat and a kit. It gnrats lift using its dlta wing. Th attraction of such arostats is thir ability to maintain a mor vrtical orintation in high winds. For a convntional arostat, only th drag incrass as th wind spd incrass and, as a rsult, th arostat loss altitud as th angl of th arostat tthr bcoms lss and lss vrtical. To valuat th prformanc of th two variabl-lift arostats, xprimntal tsts wr prformd whil towing th arostats bhind a boat. During th tsts, poor prformanc of both arostats was obsrvd. At high spds btwn 40 and 50 km/hr, th arostats bcam unstabl, and somtims dov violntly all th way to th watr surfac. Basd on ths obsrvations it was dcidd to xclud th variabl-lift arostats from furthr analysis and instad focus on mor convntional sphrical and stramlind typs. Th arodynamic prformanc of th sphrical arostat is charactrizd by a singl drag forc on th hull which is proportional to its constant sphrical cross sction. To compar th drag cofficint of a sphrical and stramlind arostat, a rfrnc R of 10 6 was chosn which rprsnts typical oprating conditions of th scald arostat. Th drag cofficint for a sphrical body is about 0.15, whil for a stramlind body of finnss ratio 2.4, it is in th approximatly Whn th fins ar addd to th stramlind arostat, its drag cofficint incrass to In addition to having a drag cofficint of about half that for a sphrical shap, th stramlind arostat also has a frontal ara 1.7

7 tims smallr for th sam intrnal volum of Hlium. Thus, th drag forc acting on a stramlind arostat is about 3.5 tims smallr than on an quivalnt sphrical arostat. Th rducd drag of th stramlind arostat has important advantags for th tthrd systm. From a static prspctiv, th loading on th tthr structur would b rducd and thrfor th dsign can b lightr and mor fficint, as was rportd in th original analysis of th LAR concpt. 3 As wll, th disturbancs to th tthr tnsion structur du to wind gusts should b rducd which would rsult in smallr position rrors of th rcivr. Sphrical bodis also tnd to b subjct to vortx shdding oscillations in stady flow 9. Ths could substantially dgrad th prformanc of th systm with a sphrical arostat. This again suggsts that a stramlind arostat may b prfrabl for our application as a stadir lash tnsion is considrd dsirabl. Ground handling and mooring ar among th most difficult problms ncountrd in th opration of tthrd arostats 10. Th support systm for handling th arostat nar or on th ground is oftn mor complx and costly than th arostat itslf. Th ground handling quipmnt for th stramlind arostat must accommodat its tndncy to rotat into th wind. If th arostat is unabl to rotat frly, th loading from vn mild sid winds is strong nough to gnrat vry larg forcs. If th mooring station dos not prmit th arostat to rotat frly, thn it must compltly shltr th arostat from th wind. In this cas, additional quipmnt is rquird to transport th arostat from th shltr to th launch sit. By contrast, th ground handling quipmnt for th sphrical arostat would b substantially simplr sinc it dos not nd to wathrvan. For this projct, gratr mphasis was placd on prformanc of th positioning systm, and so a stramlind arostat was slctd (Figur 6). This was don with th known pnalty of mor complicatd and costly ground handling quipmnt. It should b notd that, aftr this dcision was mad, furthr analysis rvald that th fluctuating lift gnratd by wind gusts on th arostat hull may caus significant problms 6. If this is indd th cas, a sphrical arostat may b r-considrd. Tthr Matrial Th tthr proprtis shown in Tabl 2 for th full scal systm prsum th us of Spctra as th tthr matrial. This choic was mad bfor th mor advancd Plasma and Vctran matrials wr availabl on th markt. Tabl 3 3,11 shows th inhrnt proprtis of ths and othr high strngth commrcial tthr matrials. It should b notd that th proprtis givn ar for a braidd tthr and thus diffr from th constitunt matrial proprtis. Basd on th tthr matrials in Tabl 3, non fulfill our initial rquirmnts for th scald systm (s Tabl 2) bcaus a suitabl tthr matrial would nd to hav with th sam dnsity as Spctra but only on third its stiffnss (charactrizd by its lastic modulus, E). 7 Figur 6: Aros Flightcam arostat

8 Tabl 3: Proprtis for braidd tthrs of svral matrials. 3,11 tthr matrial dnsity, ρ t (kg/m 3 ) ultimat strss, S b, (GPa) lastic modulus, E, (GPa) strngth to wight, S b /ρ t, (x10 5 m 2 /s 2 ) Kvlar Spctra Plasma Vctran Stl If th full scal systm dsign wr to b rvisitd, it is likly that Plasma or Vctran, rathr than Spctra, would b chosn as th tthr matrial. Thrfor, it would b logical to slct Spctra for th scald systm, sinc its lastic modulus is a fraction that of th othr two matrials. Instad, for rasons of safty, a compromis was mad to choos a tthr matrial that would provid th bst prformanc for th positioning systm and th highst factor of safty. Plasma was thrfor chosn for th scald systm as it has th highst strngth to wight ratio th highst stiffnss of th matrials considrd. As a consqunc of this choic, th scald systm may not hav strict dynamic similarity to th original full scal systm. This is not considrd to b a problm sinc th dynamics modl can b validatd irrspctiv of dynamic similarity. Th tthr diamtr for th scald systm was takn as 6 mm, which is clos to th scald valu from Tabl 2 of 6.17 mm. Th dynamics modl was usd to nsur that an adquat margin of safty would b maintaind during tsting. Two scnarios wr considrd: th first rlats to normal opration, and th scond rlats to survivability. Th first scnario considrd th full oprating rang (znith angls from 0 to 60 o, azimuth angls from 0 to 360 o ) and a maximum wind spd of 6 m/s (approximatly scald from th full scal oprational rquirmnt of 10 m/s). Th scond scnario considrd wind spds up to 20 m/s (from Environmnt Canada data for Pnticton, B.C.) with th systm at a znith angl of 0 o, whr tnsions in th tthrs ar at a minimum. Th maximum tnsions in ths two scnarios ar 6.46 kn and 7.02 kn, rspctivly. Th braking strngth of th tthr corrsponding to its ultimat strss of 1.26 GPa is 35.6 kn. For ithr scnario th margin of safty is abov 5 and so th 6 mm diamtr was dmd accptabl. Instrumnt Platform In ordr to monitor nvironmntal conditions and th prformanc of th systm, an instrumnt platform was incorporatd into th systm at th conflunc point of th tthrs sinc this is whr th rcivr of th actual radio tlscop would b locatd. Th snsors ar housd on a circular platform (Figur 7) which hangs frly on all thr tthrs using hangr fittings placd along its dg. Th onboard snsors ar usd to collct xprimntal data that can b usd to compar to th simulation rsults. Th complmnt of onboard instrumnts and thir functions ar as follows: 4 load clls usd to masur th tnsion in th thr primtr tthrs and th lash, wind snsors to masur th wind spd and wind dirction, 2-axis tilt snsor usd to masur th tilt of th platform, digital compass to masur th hading of th platform, diffrntial GPS systm GPS antnna and rcivr usd to masur th position of th platform; a similar unit on th ground complts th diffrntial systm, inrtial masurmnt unit comprisd of 3 acclromtrs and 3 rat gyros to masur highfrquncy motion of th platform, tmpratur prob to masur local air tmpratur, radio modm to transmit GPS data to th ground computr. Additional snsors ar mountd to a plat on th undrsid of th arostat to masur its intrnal prssur and tmpratur, as wll as its hading angl. All th snsors hav analog outputs which ar convrtd into digital RS-485 signals using A/D convrtr moduls locatd on th platform. Th RS-485 signals ar thn convrtd to RS-232 prior to transmission via a cntral tthr. 8

9 9 Figur 7: Top and bottom viws of instrumnt platform. Winch Systm Dsign Th winch systm for th scald arostat facility is mad up of th four main componnts: srvomotor, plantary garbox, drum and support fram. Its dsign bgan with a dtrmination of th rquird tthr motion and tnsion, as prdictd by th dynamics modl. Onc ths rquirmnts wr stablishd, th mchanical componnts wr slctd accordingly. An analysis of th dynamic bhaviour of th arostat systm was prformd throughout its oprational rang in ordr to dtrmin th most dmanding physical configuration for th winching systm. In this configuration, th znith and azimuth angls wr θ z = 60 o and θ az = 60 o, whil th wind spd and dirction wr 6 m/s and θ w = 150 o, rspctivly. Th corrsponding dmand on ach winch was quantifid by th rquird mchanical powr (tthr vlocity tims tthr tnsion). Th dtails of th PID control systm usd for this analysis ar prsntd by Nahon t al 6. Th gains usd to control of th tthr lngth wr tund so that th maximum mchanical powr rquird was 1.5 kw---rprsntativ of th 2 kw of lctrical powr installd at th tst sit for ach winch, multiplid by an stimatd systm fficincy of 75%. Th rsults for th vlocity, tnsion and powr at th critical winch (Winch #1) ar givn in Figur 8. Th rsulting valus for th maximum tthr vlocity, acclration and tnsion wr: v max = 0.24 m/s, a max = 6.3 m/s 2 and T max = 6.14 kn, and ths wr usd as th basis for th dsign of th winch systm. Th nxt stp was to dtrmin th rquirmnts for th mchanical componnts for th winch, which ar shown schmatically in Figur 9. Th lctromagntic torqu producd by th motor, τ m and th motor vlocity and acclration can b stimatd using th following quations: T τ max r Na = m, N αm max Nv = r, ω m = max (2) r whr N is th gar ratio and r is th tnsion radius of th drum. It is clar from q. (2) that th motor rquirmnts dpnd on th gar ratio and th siz of th winch drum (diamtr and width). Spcifically, th radial location of th tthr r, is dirctly proportional to th rquird torqu and invrsly proportional to th spd and acclration. For a narrow drum, r tnds to b largr sinc th tthr winds mor tims on th drum. Numrous combinations of drum sizs and gar ratios wr invstigatd to minimiz th rquird motor torqu, spd and acclration. A high gar ratio is rquird sinc th output is typically low spd and high torqu. A rviw of numrous motor manufacturrs producd svral off th shlf srvosystms that could mt th rquirmnts. Th dtaild rquirmnts for th motor and gar box ar givn in Tabl 4 and 5 rspctivly along with th chosn componnts. Th garbox was slctd basd on having high fficincy, low inrtia and low backlash. It is notd that th rquird gar output torqu xcds th manufacturr s continuous rating by 10%. This is not anticipatd to b a problm sinc th pak tthr load and vlocity wr usd to dtrmin th winch rquirmnts.

10 v 1 (m/s) a 1 (m/s 2 ) T 1 (kn) P 1 (kw) tim (s) Figur 8: Tthr spd, tnsion and powr for highst powr configuration for wind spd, U = 6 m/s. Onc th motor and garbox had bn slctd, th dtaild dsign of th winch fram and th communication systm was prformd. Figur 10 a) shows th winch drum housd in its fram with th gar box. Th main fatur of th winch fram is th ability of th drum and driv systm to rotat about a vrtical axis. This fatur is ssntial to allow th winch to accommodat th rang of tthr angls possibl ovr th full oprating rang of motion of th rcivr. T motor τ m, ω m, α m garbox, N ω d, α d drum r Figur 9: Mchanical componnts of winch systm. Figur 10 b) shows a schmatic of th communication systm usd to transmit commands from th control computr to th winchs. A PC basd systm was slctd bcaus of its vrsatility and low cost. Th basic opration of th control systm can b summarizd as follows: th PC rcivs data from GPS and othr snsors; this data is usd to calculat a position rror and thn gnrat and snd compnsating digital commands for all winchs to th motor controllr (low frquncy, approx. 10 Hz), th motor controllr rcivs commands from th PC and issus 3 sparat digital commands to th amplifir of ach of th thr winchs (high frquncy, approx. 500 Hz). Th winchs ar connctd in sris by fibr optic cabls and communicat in a SERCOS loop, th amplifir at ach winch convrts th control signals into th voltag and currnt rquird to driv th motor.

11 11 Tabl 4: Motor rquirmnts and manufacturr s spcs Tabl 5: Gar box rquirmnts and Manufacturr s spcs. Torqu (Nm) Spd (rpm) Acclration (rad/s 2 ) Gar Ratio Gar Output Torqu Rquird Rquird Bosch Rxroth MHD Alpha SP cont pak amp motor gar box winch fibr optic communication lin motor controllr PC data aquisition motion control softwar GPS and snsor data radio modm a) b) Figur 10: a) Winch fram with drum and gar box, b) Schmatic of PC basd motion control systm. Infrastructur A comprhnsiv infrastructur was constructd at th Pnticton. B.C. sit to support th xprimntal quipmnt. A hangar was constructd to hous th arostat whn not in us, as wll as a spcial-purpos tractor-trailr to transport th arostat from th hangar to th launch sit. Ths ar shown in Figur 11. In addition, powr and data lins wr laid from th main building to th rmot sit and a trailr was installd to hous th ground-basd componnts including lctrical junction boxs, computr, GPS systm and wathr station. Figur 11: Hangar and tractor-trailr usd to hous and transport th arostat.

12 Conclusions An arostat positioning systm is bing invstigatd as th basis for a novl radio tlscop dsign. A on third scal prototyp was dsignd and constructd to dtrmin th fasibility of this concpt. Dimnsional analysis was usd to obtain th physical proprtis of th prototyp. It was not possibl to satisfy both Rynolds numbr and Froud numbr similarity. Simulation rsults indicatd that Froud similarity was mor critical in maintaining dynamic similarity to th full scal systm. Th rsults of th scaling procss ld to th gnral dsign spcifications for scald systm. Th shap of th arostat was chosn to minimiz th disturbancs to th systm. Th slction of th tthr matrial dviatd from th proprtis givn by th scaling procss and was instad chosn for maximum stiffnss and strngth to wight ratio. Th dviation from strict dynamic similarity should not b a problm sinc th validation of th dynamics modl can b achivd with any tthr matrial. In th dsign of th winching systm, th dynamics modl of th tthrd arostat systm was usd to stimat th rquird tthr motion with wind spds up to 6 m/s. Th systm configuration with th most powr intnsiv rquirmnts was idntifid and th rsulting tthr motion and tnsion for this cas wr usd to stablish th torqu and spd spcifications for th winch. Using ths spcifications, a suitabl srvomotor and garing systm was chosn. Acknowldgmnts Funding for this rsarch was providd by th National Rsarch Council of Canada and by a grant from th Canada Foundation for Innovation. Rfrncs 1 T.H. Lgg. A propsd nw dsign for a larg radio tlscop, Astronomy and Astophysics Supplmnt Sris, 130, pp , B. Carlson t al. Th Larg Adaptiv Rflctor: a 200-m diamtr, widband, cm-m wav radio tlscop. Procdings of th SPIE Intrnational Symposium on Astronomical Tlscops and Instrumntation, J.T. Fitzsimmons, B. Vidt, P.E. Dwdny. Stady-stat analysis of th multi-tthrd arostat platform for th Larg Adaptiv Rflctor tlscop. Procdings of th SPIE Intrnational Symposium on Astronomical Tlscops and Instrumntation, P.E. Dwdny, M. Nahon, B. Vidt. Th larg Adaptiv Rflctor: A Giant Radio Tlscop with an Aro Twist. Canadian Aronautics and Spac Journal. Vol. 48, No. 4, pp , M. Nahon. Dynamics and Control of a Novl Radio Tlscop Antnna, A Collction of th AIAA Modling and Simulation Tchnologis Confrnc Tchnical Paprs, , M. Nahon, G. Gilardi, C. Lambrt. Dynamics/Control of a Radio Tlscop Rcivr Supportd by a Tthrd Arostat. Journal of Guidanc, Control and Dynamics, Vol. 25 No. 6, pp E. Buckingham, Modl xprimnts and th forms of mpirical quations. Transactions. A.S.M.E. Vol. 37, pp , B.W. McCormick. Arodynamics, Aronautics and Flight Mchanics, John Wily & Sons, R. Govardham, C.H.K. Williamson. Vortx-inducd motions of a tthrd sphr, Jourmal of Wind Enginring and Industrial Arodynamics, Vol. 69, No. 71, pp , S.P. Jons. Nonlinar Dynamic Simulation of a Moord Arostat. AIAA 7 th Lightr-than-Air Tchnology Confrnc, AIAA , Cortland Cabl Company, Inc. Tchnical Data Sht 105,