On the Use of Rigging Angle and Canopy Tilt for Control of a Parafoil and Payload System

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1 Digil Geoge o Univei ul Puliion - Demen of ehnil nd Civil Engineeing Demen of ehnil nd Civil Engineeing 3 On he Ue of Rigging ngle nd Cno il fo Conol of Pfoil nd Plod em Nhn lege Geoge o Univei, nlege@geogefo.edu k Coello Geogi niue of ehnolog - in Cmu ollow hi nd ddiionl wok : h://digilommon.geogefo.edu/mee_f Reommended Ciion lege, Nhn nd Coello, k, "On he Ue of Rigging ngle nd Cno il fo Conol of Pfoil nd Plod em" (3). ul Puliion - Demen of ehnil nd Civil Engineeing. Pe 5. h://digilommon.geogefo.edu/mee_f/5 hi Confeene Poeeding i ough o ou fo fee nd oen e he Demen of ehnil nd Civil Engineeing Digil Geoge o Univei. h een eed fo inluion in ul Puliion - Demen of ehnil nd Civil Engineeing n uhoied dminio of Digil Geoge o Univei. o moe infomion, lee on olfe@geogefo.edu.

2 ON HE UE O RGGNG NGLE ND CNOPY L OR CONROL O PROL ND PYLOD YE Nhn lege * k Coello Demen of ehnil Engineeing Oegon e Univei Covlli, Oegon 9733 BRC Conollle foil nd lod if e onolled wih downwd defleion of lef nd igh foil ke. Lel onol i oined diffeenil defleion while longiudinl onol i eed olleive defleion of he lef nd igh ide foil ke. he wok eoed onide n lenive mehod o onol foil nd lod i vehile iling he foil no fo lel onol nd hnging igging ngle fo longiudinl onol. Uing nonline 9 degee of feedom imulion model, i i hown h no il ovide oweful lel onol mehnim nd igging ngle ovide vile longiudinl onol mehnim. NOENCLURE,, : Comonen of oiion veo of oin C in n ineil fme.,, ψ : Eule oll, ih nd w ngle of lod.,, ψ : Eule oll, ih nd w ngle of foil.,, : Comonen of veloi veo of oin C in n ineil fme.,, : Comonen of ngul veloi of lod in lod efeene fme ().,, : Comonen of ngul veloi of foil in foil efeene fme ( ). m, m : of lod nd foil., : nei mi of lod nd foil wih ee o hei m ene., : en m foe nd momen oeffiien mie. η : Rigging ngle. τ : Cno il. : nfomion mi fom ineil efeene fme o foil efeene fme. : nfomion mi fom ineil efeene fme o lod efeene fme., : eodnmi foe omonen on lod nd foil in hei eeive fme. W, : Weigh lod nd foil in hei W eeive od fme. : Conin momen omonen Join C. C : kew mmei o odu oeo dine veo fom join C o en m ene. : kew mmei o odu oeo of dine veo fom join C o foil no m ene. : kew mmei o odu oeo of dine veo fom foil no m ene o en m ene. : kew mmei o odu oeo of foil ngul veloi. : kew mmei o odu oeo of lod ngul veloi. NRODUCON * Gdue Reeh in, Demen of ehnil Engineeing, eme. oie Pofeo, Demen of ehnil Engineeing, eme.

3 Comed o onvenionl fied wing if onfiguion, foil nd lod i vehile e om nd lighweigh efoe lunh, ehii elivel long endune, fl low eed, nd im gound wih low veil veloi. o ome i vehile miion hee heii e uie ive, iull fo uonomou mio if wih long-em ening o eniive euimen delive euiemen. he mo ommon men o ee foil i hough defleion of igh nd lef ke on he foil. omini nd Ceimele [] efomed deiled ud on he un efomne of he X-38 foil nd demoned eion of leldieionl eodnmi oeffiien fom fligh d. hi d w ineed ino n 8 degee-of-feedom foil nd lod model fo fligh imulion vlidion. he noed h unde ein ondiion, dvee un e n e eeiened, whih he iued o foil ke efle. Jnn [] onideed un efomne of he LEX foil o uo he develomen of guided foil nd lod em. ligh e d of foil uning ngle w fi o fi ode file diven ke defleion ngle. lege nd Coello [3] lo onideed uning efomne of foil nd lod em nd like omini nd Ceimele [] found uning efomne o e omle funion of no uvue, igging ngle, nd ke defleion. he howed igh nd lef foil ke defleion ehii wo i mode of lel onol, nmel, kid nd oll eeing, whih genee lel eone in ooie dieion. hi onol evel i omle funion of igging ngle, no uvue, eodnmi oeie of he foil, well foil ke defleion mgniude nd i iull oheome fo uonomou em h mu uome onol ivi. While lef nd igh foil ke defleion i f nd w he mo ommon mehod of onol, ohe onol mehnim fo foil nd lod em e oile. o emle, mehod o ffe un onol fo foil nd lod em i o ee n mme in he uenion line lengh on oh ide of he foil leding o iled no. lo, igging ngle h oweful effe on he deen e of he em. Lge negive igging ngle led o lge deen e u e moe le highe fowd eed while igging ngle loe o eo led o lowe deen e u e le le high fowd eed. o longiudinl onol, he igging ngle n e dnmill hnged in fligh. While die no il nd dnmi igging ngle onol e on he ufe o offe vile onol mehnim he hve o de een uneloed in lieue. he wok eoed hee eloe he ili of no il fo lel onol nd dnmi igging ngle fo longiudinl onol of foil nd lod em. he e egin wih deiion of 9 degee-of-feedom imulion model ued o mke ediion nd i followed emloing he model o edi onol efomne of mll uonomou foil nd lod em. he effe of no il ngle on un e, veloi, ngle of k, nd glide e i doumened. Glide e eone fo onvenionl mmei ke defleion i oned gin glide e eone wih dnmi igging ngle. PROL ND PYLOD YE ODEL igue how hemi of he foil nd lod em. Wih he eeion of movle foil ke, he foil no i onideed o e fied he one i h infled. he omined em of he foil no nd he lod i eeened wih 9 degee-of-feedom (DO) model, oiginll develoed lege nd Coello [3]. he degee-of-feedom inlude hee ineil oiion omonen of he join C well he hee Eule oienion ngle of he foil no nd he lod. he no he i modeled olleion of nel oiened fied ngle wih ee o eh ohe hown in igue. Conneed o he ouod end nel e ke h loll defle he no downwd. he foil no i onneed o join C igid mle link fom he m ene of he no. he lod i onneed o join C igid mle link fom he m ene of he lod. Boh he foil nd he lod e fee o oe ou joinc u e onined he foe nd momen he join. Kinemi euion of moion fo he foil no nd he lod e ovided in Euion hough 3. ψ u v w () ()

4 ψ (3) he ommon hohnd noion fo igonomei funion i emloed whee ( ) in, ( ) o nd ( ) n. he kinei euion of moion e fomed fi eing he em he ouling join, eoing he join onin foe nd momen ing on oh odie. he nlionl nd oionl dnmi e ineill ouled eue he oiion degee of feedom of he em e he ineil oiion veo omonen of he ouling join. he onin foe i uni of inee o monio duing he imulion o i i eined in he dnmi euion he hn eing lgeill elimined. Euion eeen he nlionl nd oionl dnmi euion of oh he foil nd lod onened ino mi fom. 3 m m m m () he mi in Euion i lok mi whee eh elemen i 3 3 mi. Row -3 in Euion e foe ing on he lod m ene eeed in he lod fme nd ow 7-9 e he momen ou he lod m ene lo in he lod fme. Row -6 in Euion e foe ing on he foil m ene eeed in he foil fme nd ow - e he momen ou he foil m ene lo in he foil fme. Euion 5 hough 8 ovide he igh hnd ide veo of Euion. m W (5) m w v u W (6) w 3 (7) ( ) w v u (8) Euion i olved uing LU deomoiion nd he euion of moion deied ove e numeill ineged uing fouh ode Runge-Ku lgoihm o imule he moion of he em. he fou of hi e i o nlill inveige he onol eone ued die no il nd dnmi igging ngle. Cno il i modeled oing he no ou n ouod edge hown in igue 3. Cno il n e imlemened mouning onol line long lef nd igh ouod edge of he no. Dnmi igging ngle i modeled oing ll foil no eion wih ee o he mle link h onne he foil o oin C. hi i iued in igue. Dnmi igging ngle indue no hnge in ke defleion. REUL n ode o eloe he viili of no il nd igging ngle onol mehnim fo foil nd lod em, he model deied ove i ued o edi ed e onol eone

5 of foil nd lod if fo viou no il, igging ngle, nd foil ke eing. he foil nd lod if i idenil o he onfiguion ued lege nd Coello []. Phil mee e lied in le nd. eodnmi oeffiien wee oined fom lege nd Coello [] nd e lied in le 3. n ll e he em i lunhed n liude of f wih level eed of 5 f/ nd i emied o ele o ed e ondiion wih no onol inu. o he onfiguion unde onideion hi oe ke e. eeified ime fe lunh, he oie onol inu i injeed nd held onn fo he eminde of he fligh. ed un e e omued fo no il ngle fom. o 3. deg in inemen of.5 deg nd igh ke defleion fom. o.875 in inemen of.79 in nd e loed in igue 5. Cno il i onideed oiive when he igh ouod edge i moved lowe. neing moun of ue igh ke defleion odue ineingl moe negive un e wih un e of 77 deg/ ehed fo full igh ke of.875 in. neing moun of ue no il odue lge oiive un e wih mimum of 5 deg/ ehed 3 deg of no il. he eeme e of lge ke defleion wih no no il nd lge no il wih no ke defleion odue eemel lge un e. hu, no il ovide oweful mehnim fo foil nd lod uning. Lge oiive un e edied ue no il e eul of he ol no oll eniivi o no il. igue 6 how he euling no oll indued no il. ol no oll uikl eome lge nd ehe mimum of 6 deg.5 deg of no il efoe lighl deeing. Cno il i mlified nd eul in lge ovell oll ngle of he foil. igue 7 how he mlifiion fo of no il inu. he lge mlifiion fo of 83 ou.55 deg of no il. he mlifiion of no il ino lge ol no oll elin edied eniivi o mll no il. Commonl foil ehii oiive un e when he igh ke i defleed full, ooie h edied ue igh ke in igue 5. f igh ke nd oiive no il e ouled o h defleing he igh ke lo ull he igh ouod edge down, un eone dmill hnge fom ue igh ke eone. olid line in igue 5 how he ineeion of he onol eone ufe wih eo un eone lne. Bke defleion ue oh oiive nd negive un e deending on he moun of no il oied. Pfoil noie e highl fleile memne even when infled, o h defleion of foil ke on one ide lo il he no down on h ide. he moun of no il indued ke defleion i ongl deenden on onneion of he onol line o he no nd he nume of line on he no. hu, un efomne of he foil nd lod em i ued he diffeene of he wo oweful uning mehnim. o longiudinl onol, in fligh modifiion of he glide loe nd ol veloi of he foil nd lod em i lo deile. Commonl, eed nd glide loe i onolled defleing oh ke imulneoul. Dnmill hnging igging ngle in fligh lo onol glide loe nd eed. igue 8 how edied glide loe fom mmei ke defleion nd igging ngle. Glide loe i edued fom.38 o unde.8 ove he nge of mmei ke defleion while eduing igging ngle fom -3.5 deg o - deg onl hieve eduion in glide loe fom.33 o.37. igue 9 how h igging ngle defleion ove he nge of 3.5 deg o deg ield eduion in ol veloi fom 3.9 f/ o 9.7 f/ nd fom mmei ke defleion eduion fom.8 f/ o. f/. igue how h igging ngle defleion effeivel inee ngle of k hu eduing ovell veloi of he em. mmei ke defleion onl lighl le ngle of k. hu, deeed glide loe i no fom ineing he ngle of k like dnmi igging u ined fom ineing of lif hu eduing he ngle of k. Rigging ngle nd mmei ke defleion oh edue glide loe nd ol veloi of foil nd lod em u ue diffeen mehnim. Rigging ngle modifiion n effeivel edue he ol veloi of he foil em nd edue he glide loe euling in vile longiudinl onol mehnim. CONCLUON Due o he f h he foil no i fleile memne, defleion of he onol m on one ide of he foil m lo ee il of he no. Boh hee effe omine ogehe o fom he ovell uning eone. he foil nd lod em diued ehii high lel eniivi o ule no iling. he high eniivi o no il illue he imone of deign mee h le he fleiili of he no nmel uenion line uni nd ngemen nd onol line onfiguion. Cno iling n e eloied o elimine onvenionl foil ke fo lel dieion onol.

6 mmei ke defleion nd igging ngle modifiion oh demone he ili o effeivel le glide loe nd ol veloi of he em u in diffeen mehod. Rigging ngle modifiion le he glide loe nd ol veloi lgel leing he eodnmi ngle of k while mmei ke defleion inee he lif onl lighl ineing he ngle of k. n omion mmei ke defleion e moe effeive in leing he glide loe nd igging ngle modifiion moe effeivel le he ol veloi. Convenionl foil ke fo lel nd longiudinl onol ould e eled ominion of no iling fo lel onol nd igging ngle modifiion fo longiudinl onol. enefi of hi lene onol mehod i he oiili of deouling he lel nd longiudinl onol mehnim. PROL BRKE PROL CONNECON PON J K C REERENCE [] omini, C.., Ceimele, C.J., Lel- Dieionl eodnmi fom Lge le Pfoil e Pogm, Pe J PYLOD BODY J K [] Jnn,., eodnmi odel denifiion nd GNC Deign fo he Pfoil- Lod- em LEX, Pe -5. K igue - Pfoil nd Plod [3] lege, N., Coello., e of Conol fo Pfoil nd Plod em, Jounl of Guidne, Conol nd Dnmi, Vol. 6, No. 6, Deeme 3 [] lege, N., Coello., Comion of eued nd imuled oion of Conollle Pfoil nd Plod em, Pe 3-56, 3 3 J J 5 K K J 3 K 5 J J J 3 K K K igue Pfoil Cno Geome igue 3 Cno iling

7 igue 6 Cno Roll nduion B il igue ngle of nidene igue 7 Roll mlifiion igue 5 un Reone Bke Defleion on Righ ide nd Poiive Cno il igue 8 Glide loe

8 le Phil Pmee Pmee Vlue Deiion n 5 Nume of Pnel igue 9 ed e ol Veloi 5 deg Pnel ngle -5 deg Pnel ngle 3 deg Pnel 3 ngle - deg Pnel ngle 5 deg Pnel 5 ngle η -.5 deg nidene ngle.6 f Pnel e in Pnel hikne w.5 lf Pfoil Weigh w. lf Plod Weigh le en Coeffiien igue ed e ngle of k Coeffiien Vlue.9 B. C... B.7 C le 3 Eimed eodnmi Coeffiien Pmee ligh ligh 3 ligh 5 (deg) C ) L ( C ) D (

η : Rigging Angle. τ : Canopy tilt.

η : Rigging Angle. τ : Canopy tilt. ohei ligh ehni Confeene nd Ehii - ugu 3, uin, e 3-569 -3-569 ON HE UE O RGGNG NGLE ND CNOPY L OR CONROL O PROL ND PYLOD YE Nhn lege * k Coello Deen of ehnil Engineeing Oegon e Univei Covlli, Oegon 9733

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