Method to Characterize Potential UAS Encounters Using Open Source Data

A r t i c l e Me t hod to Cha ra ct e ri z e Pot e nt i a l UAS Encounters Usi ng O pe n Source Da ta Andre w We ine rt * M I T L in c o ln L a bo ra t o r y , L e x i n g t o n , M A , 0 2 4 2 0 - 9 1 7 6 , US A ; a n d r e w.we ine rt @l l.m it . e d u Abstrac t: As un m a nned aeria l s ys te m s (UA Ss) in c rea s i n gl y in te gra te in to t h e US n a t ion a l a i rs p a c e s y s t em , t h e re i s a n in cr ea sin g n eed t o ch a r a c te ri z e how c om me rc ial an d r ecrea tion a l UAS s m a y enc oun t e r ea c h ot h er. To in for m t h e dev elo pm en t a n d ev a l u a tion of s a f et y c r i tic a l t ec h n ol ogi e s , we dem on s tra te a m et h odo logy t o a n a l yt ic a l ly ca lcu l a t e a l l p ot entia l r e la tiv e geo m et ries b e twe e n diff er en t UA S oper a ti on s perf orm i n g in s p ection m i s s i on s . Th is m eth od i s b a s ed on a pr ev i o u s l y dem on s tra te d t ech n i qu e t h a t lev er a ge s open s our c e ge os p a t i a l i n for m a tion t o ge n er a te r epr es en ta tiv e u n m a n n ed a ir c ra ft t r aj ector i es . Usi n g open s our c e da t a a n d pa r a l lel pr oc e s s i n g t ech n i qu es , w e per fo r m ed t r il li o n s of ca lc u lat i on s t o e s t i m at e t h e r ela t i ve h or iz o n ta l dist an c e b et w ee n ge os p a t i a l poi n ts a cros s s ix tee n l ocat i on s . Ke ywo rds : un ma nned a eria l v eh i cl es ; dr on es ; a e r os p a ce control ; s i m u l a tion ; g eos pa ti a l a n a l ys i s ; open s our ce s of twa re 1 . Int ro ducti on Th e con t i n ui n g in t eg ra t i on of u n m a n n ed a er i a l s y s tem ( UAS) oper a tion s in t o t h e Na ti o n a l Air s pa c e S y s tem ( N AS) r equires n ew or u pdat ed r eg ul a tio n s, pol ic i es , a n d t echno logi es t o m a i n ta i n s a fet y a n d en a bl e ef fic ien t us e of t h e a irs pa c e. On e en a bl i n g t echn ol og y t o h elp a ddres s s ev e ra l U A S a i r s p a c e in t eg ra t i on ga p s ar e a i r s pa c e enc oun ter m odels , w h ic h h a v e b ee n f un d a me n t a l to qua n t ifyin g a ir born e c oll i s i on r i s k f or m a n n ed a n d u n m a n n e d oper a t i on [1 – 5] . Th ese m ode l s r epr es en t h o w a irc ra ft be h a v io r a n d t h eir r el at i ve g eom et ri es e vo lve duri n g cl os e e n c ou n te rs. T he y h a v e s u pp o rte d t h e dev elop m ent of s ur ve i l l a n ce a n d com m u n i c a ti on r eq u irem en ts [ 6 , 7] . 1 .1 . Moti v ati o n Mit iga tion s for a i r b o rn e coll i s i on r i s k a n d opt i m i z a tio n of a ir s pa c e oper a ti on s a r e s tro n g l y dependen t on t h e dis t ri bu tion of ge om et r i es a n d b ehav i or of ai r c ra ft enc oun ter s . Fo r exa m p l e , col li s i on a v oi da n c e s y s t em s a re de s i gned t o det er m i n e, c om m u n ic a te , a n d coor din at e av oi d a n c e m a n euv ers wh en t h ey det er m in e t h a t a maneu ve r is nee d ed t o a vo id a coll i s i on . The s e s ys te m s a re t h e l a s t a n d thi rd la yer f or airs pac e con fl i c t m a n ag em en t a n d a re em pl oye d a f te r s epa ra tion pro vi s i o n a n d s t ra te gic m i tiga tio n h av e fa il ed. Colli s i on a void a nce s ys te m s m ay leve ra ge v ehi c l e- to - e v e ryth i n g ( V 2 X ) com m u n i c a tion t ec h n ol ogies t o i m pro v e perf orm an c e a nd s a fe ty. H ow a n a i rc ra ft b e h a ve s wi l l in flu enc e t h e dev elop me n t of V 2 X r o utin g p rot ocol s , l in k b ud get s , a n d en erg y re quirem en ts [ 8 ]. Fas t - ti m e M on t e C a r l o si m u l a tio n s a re of t en ut i li z ed t o ev a l uat e t h e per form a n c e o f av i a ti o n s a fet y s ys te m s, su c h a s det ect a n d a vo i d (D AA) f or UA S, f or cl os e enc ount ers b etw ee n ai rcra f ts [2 – 4] . The desi gn a n d e ff ect iv en es s of t h ese si m ul a ti on s ar e depen d en t on how cl os e enc oun te rs a re def i n ed. Th e r elat i ve ge om etr ies a n d se p a ra tion be tween a i rcra f t a re i m po rtan t cri t e ria wh e n def i ni n g t h es e en cou n t ers . S i m u lat ed enc oun ter s are gener a ted b a s ed on w h a t s a fe ty f un c tion is be i n g ev a l ua te d and t h e per for m an c e or b eh a v i or of t h e a i r c ra ft in v ol ve d. For e xa m p l e, en c oun ter s m e a n t t o pr om pt c oll i s ion a v oi danc e m a n euv ers m a y n ot b e s uita bl e t o e v a lu a te a s y s tem a t te mp ti n g t o m a in ta i n well cl ear. 2 o f 15 E n c oun t ers a n d m an n ed a i rcra ft b eh a vior h av e h i s to ric a l l y be en ba s ed on a n a bu n danc e o f ra d ar ob s er va tion s, w i t h t h es e m odels r ef i n ed f or deca des [1 – 3] . H ow ev er, a s UAS a r e n ot r out i n e l y oper a t i n g b eyo n d vis ual l i n e of s i gh t, w e c a n n o t c h ar acte ri z e UAS en c ou n ter s us in g observ ed a i rc ra f t b eha v ior. Wh i le in dep en d en t tra jec tor ies of r epres en ta ti ve U AS b eh av ior ca n b e g en era ted [2 , 3] , a n a l t er n a tive a ppr oa c h t o ch a r a cter i z e t h e ge om e t r y a n d fe a s i b il i ty of pot en t ial UAS v s . UA S enc oun t e rs is r eq u i red f or t h e dev elo pm en t a n d e v a l u at i on of D AA sa f et y s ys te ms . 1 .2 . Sc ope W e a dopt ed a s i mil ar sc ope a s t h e ASTM s ta n d a rd [ 9 ] a n d t h e Fe deral Av i a tio n Adm i n i st ra ti o n ( FAA ) pr opos ed 1 U AS R em ot e I dent i ficat i on (Rem ot e ID ) r u le f or con s ider i n g cl os e a irbo rn e enc oun t e rs in volv i n g UASs. Out of s c ope w a s es t ima tin g t h e fr eq u en cy of pot en tia l e n c oun te rs an d n on - D AA c on c ern s , su c h a s a i rw ort h i n es s . Th i s s c ope w as in form ed b y t h e F AA UAS I n t e g ra ti o n Of fice, a n d t h e s t a n da rd s a ctivi ties o f Int ern a tion al Civ i l Av i a tio n O r ga n i z a t i on ( IC AO) , ASTM F3 8 , RTCA Speci a l Co m mi tt ee 1 4 7 , a n d RTC A S peci a l Committ ee 2 2 8 . Th e Airbor n e Coll isio n Av o i d an c e Sy s t em ( ACAS X ) un m a n n ed v ar ian ts [ 1 0, 11] w er e c on s id er ed a s D AA r ef er enc e a r c h itectu re s, as t h ey a r e b ei n g sta n d a rdi z ed by t h e a f ore me n ti on ed or ga n iza t i on s . Th e s cope en co m p a s s ed comm er ci a l a n d r ecre at i o n al UAS s weigh i n g gr ea te r t h an 0 .5 5 po u n d s w it h no r estri c tion s on UAS si z e, p erf orm anc e, o r oper a ti n g al ti tude . W e a s s ume d t h at e n c o u n te rs con s is t of onl y t w o a i rcra fts , b u t t h a t t h e g en era l poli c y for m a n n ed f or m a t i on f li g h t w i l l ap p l y to UASs . W e pr ioritize d r es ea rch t o D AA a n d col li s ion a v oi dan c e s ys te m s desi gn ed t o mi ti ga te d th e r is k of m ida ir coll isi on . Thes e pr iori tize d sys tem a re t h e t h ird a n d f i n a l l a yer fo r a irs pa ce con f l i c t m a n a gem en t a n d a re em p loye d a ft er s epar ation pr ovi s i on s a nd s trateg i c m i ti ga t es hav e fai l ed [ 12]. 1 .3 . Obj ect i v es and C o nt r i buti o n W e f ocu s ed on on e of t h e m a n y ob je cti ves iden tified b y t h e av i a tion com m u n i ty t o su p p o rt in t egr a tion of U ASs in t o t h e a i r s p a ce, qua n t ita tive l y def i n e a cl os e enc oun ter b e t ween UAS s . Sa t i s f ying t h i s o b j ective coul d l ea d t o or enh a n c e e xi s t i n g r i s k - ba s ed m in im u m oper a ti n g per fo r m a n c e s t a nda rds ( MO P S) for a D AA s y s tem [ 12 ] . I n r es p o n se , t he pri m ar y con tri bu ti o n was an a n a lytica l m et h o d t h at us es f r ee l y a va i lab l e op en s ou rc e da ta to estima te r a n ge a n d a z i m uth b e tw e e n pot ent i a l UAS opera ti on s . We a pp l ied t hi s m eth od t o c a l c ul a te t h e di s ta n ce b e tw ee n v ar iou s r e a l i s ti c s h or t a n d m ed iu m t er m UAS in s pecti on opera t i on s . W e f ocus ed on in s p ectio n of long li n e a r in fr a s tr u c tu re a n d poi n t o bsta c l es due t o t h e i n du s try de m a n d and t o demon s tra te t hat a va ri e ty o f da t a s ourc es ca n b e us ed with t h i s m eth od . Th e r es u l ts can eas i l y b e ex te nde d with ot h er us e c a se s or en h a n c ed us i n g d igita l elev a tio n m od els t o es t i ma te potenti a l v er tic a l s e p a ra tio n . Th es e r es u lts directl y i n for m ed t h e s c opi n g a n d g enera tio n of s i m u l a ted Mo n te C a rl o en c o u n te rs of t w o UASs t o s up por t D AA dev elopm en t w i t h i n R TCA S C - 1 4 7 2 . H ow ev er, dis c u s s i o n of t h e se Mo n t e Car l o e n c ou n ters were out of s c ope fo r t h i s pa p er. Additi on a l l y, w h i l e D AA sy st em s c an be ob s t a c l e a w a re [ 1 0] , our r esea rc h doe s n ot dir ect ly s u pp o rt a UAS c a pa b i l ity t o a v oid ob s t a c l e s . Ra t h er, t h es e r es u lts ca n i n for m i f o b s t a c les sh oul d b e r epr es en ted as pa rt o f s i m ula te d U A S enc oun t e rs w h en de s i gn i ng or ev a lu a tin g D AA c a p a bil i ties t o m itiga te t h e r i s k of a mi da ir c oll i s i o n b et w ee n a irc ra ft . W e i n t en d t o r elea se t h e s oft w a re use d fo r t h is a n al ys i s un d er a per m iss i ve op en - s ou rce l i c e ns e . Th es e con t ri butio ns a re in te n ded t o s u p p ort c u rre n t and exp ec ted UAS D AA s y s te m dev elo p m e nt a n d ev a luat i on , s pecifi c a ll y es tim at i n g t h e proba bil i ties a s so ci a ted with e n c oun te rin g a l ow -a l ti tu d e a i r c ra ft base d on g eog ra p h y or defin ing t ota l a l lo w a ble s ys te m s la te n cy of a s a fe ty cri tic a l s ys tem t ha t s a t i s f i es perf orm a n c e- ba s ed r e qu irem en ts . Th e r es u l ts in form how t o ge n er at e r epre se n t a ti v e U A S t r a jectori es [ 3] a n d pa i r t ra jec to ries t o get h er t o s im u l a te en c oun ter s [ 2 ]. Th i s pa p er is c om p l i me n te d b y a n ot h er ef for t t o propo s e a qua n ti tati ve m et ri c t o a s se s s t h e perf orm a n c e of a s m a ll er UAS s a f e ty s y s t em [8 , 9] . 1 h t t p s :/ / w w w .re g ulat i ons .g ov / d o c ket ? D =F AA- 2019 - 11 00 2 h t t p s :/ / w w w .rt c a .or g / s c-14 7/ 3 o f 15 2 . Ma te ri a ls a nd Me tho ds Our ex per ime nt wa s b a se d on c a l c u l a tin g t h e dis ta n c e b et wee n a n y giv en point s a l on g di ff e re n t s ur v ei ll a n c e or i n spe c tion t ar get s for a UAS. The e x p er i me n t d esi gn wa s b ased on a n a p p ro a c h to ge n er a te r epres en ta ti ve UAS t ra jec to ries t h a t t ak e i n to a c c ou n t t he i r opera tion a l in te n t b y lev e ra g i n g open s our c e data s et s , su ch a s O pen Stre et Ma p (O S M) , “ a knowl e dge col lecti ve t h at p rov i d es u s e r- ge n er a te d s t re et m a p s [ 1 3 ] . ’’ Fo r pa i r s of la t itu de a n d lon gi tud e c oor di n a tes fr om diff er en t featu re s, w e ca l cu la te d t h e r ela t i v e geo m et ry b et w een t h em . Th is con t r asts a n a lt er n at i ve a ppr oa c h of ge n er a tin g r epr es en ta tive UAS t r a jec tor ies b a s ed on o pen s our ce f eat u r es a n d c h a r a c te ri zi n g enc oun t e rs b et w een t h es e t r a jectori es i n a s i x degr ee of fr eedom s im ul a ti on . Th e c l os ed f o rm a n a lytica l a ppr o a c h is s i m i l a r t o w h a t E dw a rds a n d Ma c K a y us ed t o det er m in e s ur v ei l l an c e r eq u i r em en ts for UAS D AA [ 7 ] . All da t a u s ed were f r ee l y a n d ea s il y a c c es s i bl e fr om t h e i n ter n et a n d t h e s oft w a re w e dev el o p e d f or t h is a n a l ys is h a s b ee n r el ea s ed un der a per m i s s i ve open -s ou rce lic en se . O u r desc ri bed m e th o d a n d s u b s equen t r esu lts a re r eprod uc i ble, giv en a cc es s t o t h e a p p ro p riat e MATLAB t o olbo xes . 2 .1 . Use C a ses a nd Dat a Sour ces W e e v a luat ed us e ca s e pa irs f or s ix tee n loc a tio n s. Th es e a r e a s i n c l u de al l loca tion s a s s oc i at e d w it h t h e UAS I n t egr a ti on Pi lo t Prog ra m (I PP ) 3 , m a jori ty of st a te s w ith FA A UAS t est s i te s 4 , a f e w s t a t es wi th in FE MA R e gion 1 , a n d t h e t erri to ria l is l a n d of Pu er to Ric o. Al l ge os pat i a l da ta us e d w e re f r eely s our c ed fr om t he publ ic dom a in . Fo r l oca tion s , t h eir a dmin ist ra tiv e b oun d a rie s w ere s o u rc e d f r om Na t u ra l E a r th D a t a a t a 1 : 1 0 m s c a l e. Th e a n a l ys is f ocuse d p rima ri l y on UAS in s pecti on s a s l o n g li n ea r in f ra s truc ture[ 14 – 16] a n d poin t o b s ta c l e s . Thes e r e a l i s tic us e c a s es a re s om e t h e m o s t m a tu re a n d w ell un der s to o d UAS oper a ti on s , a s i n di c a ted b y t h ei r e v a l u at i on a s pa rt of t h e UAS IPP , F AA UAS t es t s it e, or FAA Pa t h fi n d er a ctivi t i es. Poin t fe a ture s were sourc ed fr om t h e FAA di gita l ob s ta c l e file (D OF) 5 an d l oca t ion s of 6 30 0 wi n d t ur bin es were s ourc ed fr om t he Uni te d St at es Wind Turbin e D a t a ba s e[ 1 7] . W h i le t he FA A D OF m ay in c l ude w i n d t urbi n es , w e w a n te d t o a s s e s s t h e s ens i tivity of t h e r es ul ts b et w ee n a ge n er al ( F A A D OF ) a n d a s p eci fic da ta s et ( USWT D B). Speci fic ally, t h e FAA D O F h a d 4 8 3, 2 7 9 ob st acles b u t w e o n l y con s idere d t h e 3 2 1 ,6 99 obs t ac les t h a t wer e a t l ea s t 50 f eet t a l l . The soft w a re t o pa rs e t h e FAA D O F h a s b een r elea s ed un d e r a perm issi ve o pen s ourc e l i cen s e 6 . E lect r ic power tr a n s mis s i on li n es opera tin g a t h igh v olta ges of 6 9 - 7 6 5 kV w ere s ou rced f ro m th e U. S. D epa r t m e n t of H om ela n d Secu r i ty (D H S ) H om ela n d Infr a s truc ture Foun dat i on Lev el D a ta ( H IFLD ) 7 . R egula r r a i l w a y t r a c ks w er e sou rced f r o m t h e Geo fa b ri k O SM ext r a c t s 8 . Four t y p es of pi peli n es (cr u de oil, hy dro car bon ga s liquids, n a tu ra l ga s , a n d pet rol eum p r od uc ts ) w er e s o u rc e d f r om t h e U. S. E n er gy I n for m a tio n Adm i n i s tr a ti on ( E IA ) 9 . Fe der a l a n d s t a te fr ee way s a n d p ri ma ry r oa ds were sou rced f r om Na tu ral E a r t h D a t a 10 . W hi le e l ectric p o wer li n es , r a i l way s , a n d r o a d s a re m os t l y a bov e gr ou n d , t h e m a jori ty of oil pip elin es a re b u ri ed u n de rg roun d. Th i s r es u l ts in r el a ti ve l y s t r a i gh t e r in fr as truc ture la yo u ts . Poly gons of golf c our s e p er ime ter s w er e a ls o s ourced fr om t h e Geof a br i k O S M ext r a c ts a s a r epr es en ta tiv e r ecr ea tio n a l fe a t ure. Ot h er r ecr e a ti onal fe a ture s s u c h a s b eac h es a n d la ke s we re con s idere d b u t ultima tel y not in cl ud ed t o m a n a ge com pu t a ti on r esou rc es. A gr i c ul tura l la n d u se f ea t ur es s u ch a s f a rm s a n d v i n eya rds were n ot i n c l u ded b ec a u s e w e heuri s ti c a ll y as s es se d t h at O S M 3 h t t p s :/ / w w w .f aa.g o v / u as/ p ro g rams _ part n e rs h i p s/in t e gr at i on _p il ot_ p ro g ram / 4 h t t p s :/ / w w w .f aa.g o v / u as/ p ro g rams _ part n e rs h i p s/t est_ si t e s/ 5 h t t p s :/ / w w w .f aa.g o v / a i r_tra f f ic / f li ght _in f o / ae ro n av/d ig it al_p ro du c t s / d o f / 6 h t t p s :/ / gi t h ub.c om/ Ai rs pac e - En co un t e r- M o de ls / em - c ore/ t re e/m as t e r/ ma t lab / u t il ities-1st pa rt y/ f aa d o f 7 h t t p s :/ / h if ld- geo plat f o rm .o p e n d at a .arc gi s.com/ da t ase t s/ e lec t ri c-p o w er- t ran smi ss io n - li n es 8 h t t p s :/ / d ow n lo ad.geo f ab ri k.de/ n o rth-a meric a.h t m l 9 h t t p s :/ / w w w .e ia.g ov / map s / m ap _dat a/ C rude Oi l_Pip eli n e s_U S_E I A.z i p 10 h t t p s :/ / w w w .n at u ral e art h da t a .c om / d own lo ads/ 10m - c u lt u ral - v e c t ors / r oads / 4 o f 15 did n ot h a v e su ff i ci en t cov era ge a n d w e coul d n ot fin d a n a ppr op ria te a l t er n a tiv e d a t a se t wi th n a t i on w i d e cov er a ge. Lin e v ect or a n d p oly go n fe a t ures w er e i n t erp olat ed t o e n for c e a con s i s t en t s pa c i n g b e twe e n poin t s . Int e rpol a ti on wa s c a l c u lat ed b ased on t h e a rc l en gt h b etw ee n poin ts a l on g t h e v ecto r u s i ng a li n ea r c h or dal a pp r ox ima tion . Th is w a s m or e ef fic ien t t h a n us i n g a p iecew i s e cub i c H er m i te in t er p ola tin g p olyn om i a l (pch i p ) us ed b y pr ev i ou s m odel l i n g ef fo r ts [ 1 ] . Th e s pa ci n g of 500 fe e t wa s s elect ed b eca us e it pr eser ve s de tai l s a lo n g cur ves a n d w a s equiv a l en t t o t h e 500 f ee t h or i z o n ta l dim ens io n of t h e n ea r mi d -ai r coll ision (NMAC ) s a fe ty m et ri c , w h i c h is c om m on l y u s ed t o ev a l u at e a i r b orn e col li s i on r is k. Th i s s pa c i n g al s o h euris t i call y de t er mi n ed t o b e s uff ic i ently e ff ic i ent, as a li n ea r r educ tion in sp a c i n g r esu l ts in a n on - l in ear in c rea s e in com pu ta ti on t i m e. Thi s t r a d e-of f i s f ur t h er di s c uss ed in Section 4 .1 . 2 .3 . Pr o ces si ng a nd W or k f l o w Th e w or kf lo w w a s or gan i z ed in t o p r e - proces sin g, ge om et r y ca lc ul a ti on s , a n d r es u l ts a ggr egation; w ith e a c h com p o n en t en c oded b y a dedic a ted MATLAB s c rip t. Fir s t, p r e - proc e s s i n g con s is ted of t h e f oll owi n g: 1. D ow n loa d open s ource da ta fo r us e c a se s 2. Filt er d a ta b a s ed on a dm in ist ra tiv e b ou n d a ri es 3. Fo r FAA D OF , c r ea t e s m a l l ci r c l e v ect ors cen t ere d on r epo r ts p oin t s w i th a r a di us of t h e h or iz on ta l pos i tion un c ert a i n ty 4. I n t er pol a te da ta t o h a ve a f ix ed s pa ci n g of 5 0 0 fee t b et ween poi n ts 5. Ag gr e ga t e a l l v ec to rs in to a s in gle a rra y of la t itu de a n d lon gitu de p oin t s 6. Rech eck a n d con fi rm t h a t a ll poin ts a re w i thi n a d m in ist ra ti ve b oun dar y Next , di s t a n c e ca lc ul a ti on s w er e c om pl ete d , or gan iz ed b y a dm in i s t ra ti v e b ou n da ry. A m a xi m um di s t an c e o f 60 n a ut i c a l m i les w a s s pecified t o r e duc e t h e qua n t i ty o f di s c r ete dist an c e com put at i o n s . As t h e s c ope focus ed on cl os e e n c ou nt e rs , p oin t s gr ea ter t h a n 6 0 na u tic a l m i l es ap a rt s h oul d n ot be c on s i dere d “ cl os e” fo r avia tion ope r a ti on s . The g eom etr y ca l c u l a te s con s i s ted o f t he f oll ow in g: 7. Cal c ul a te un i que pa i rs of feat u res (e .g., r a i l wa ys a n d r o a d s ) 8. Cr ea t e a s m a l l ci rcl e w i th a 6 0 n a u t i c a l m i l e r adiu s c en te red on eac h p oin t fo r one of t h e fe a tu re s 9. I dent i fy wh i c h poi n ts of t h e ot h er fe a t ure a re w i thi n ea ch s ma l l c i rcl e 10. Cal c ul a te the di s ta n c e usin g t h e WG S 8 4 r ef eren c e ell ip s oi d be tween t h e c en t e r of t h e s m all c i rc l e a n d a l l p oin t- in - p ol ygon s 11. D et er m i n e t he c los est poin t b y c a l c ul a tin g t h e m in imum fo r a ll com p uted di s ta n c es Af t er t h e ge om e t r y ca l c u l a tion s , t h e r esu lts w ere a gg r eg at e d a c r o s s l oca tion s a n d pa ir s of f ea t ur es . Gen era l s t at i s tic s s u c h a s t h e m ean, m edian , a n d ot h er percen til es w ere ca lc ul a te d . 2 .4 . Azi m ut h Az im uth i s t h e a n gul a r di s ta n c e a l on g a fixed r ef ere nce directi on t o a n obje ct. Th e a z i m u th , a l s o know n a s b eari n g, b et ween t wo ai r c ra fts is a geomet r ic v a r i a bl e us ed w h en de fin in g e n co u n te rs b et w ee n a irc ra ft s . Thi s a n gu l a r m ea s urem en t i s of t en us ed w he n con s i deri n g ai rc ra ft r ig h t - of -wa y r ul es r eg a rd i n g w h et h er a n a ircra ft s h ou ld m ane uve r l ef t or r i gh t t o avoi d a c oll i s i on . In dev elo p i ng t h is a n a l ys i s , w e or i gin a l l y ca l c u lat ed a z i m uth in a ddi ti on t o di s ta n ce b e tw een poin ts . H ow ev e r, th e a ggr egate a z i m u th dis tri buti on s pr o vided n o j us tif i cat i on t o fa v or on e sp eci f ic r ela tive o r i e n ta ti o n ov er a n other. Th u s , w e di d n ot c a l c u l a te a n gu la r di s ta n ce a s pa rt of t h is a n alys i s . 5 o f 15 3 . Res ult s Th er e w er e 1 6 un i qu e loc a tio n s a n d 2 1 un i que pa irs of feat u re s . Ac r os s a ll 3 3 6 c om binati o n s o f loc a t i on s a n d pa i rs of fe a t ures comb i n at i on s , a b ou t 2 .7 1 × 1 0 12 pa i rs of poin t s were c on s ide red. H i g h per fo r m in g c om p u tin g r es ou rc es fr o m t h e MI T Li n c ol n Lab ora tory Su perc om pu tin g Cente r [ 1 8] we re lev er a g ed fo r t h e t r i l li o n s of di s c r ete ca lc ul a tio n s. Thi s s ection is or gan iz ed in t o ge n er al s ta ti st i c s f ocu s ed on a v er a ge dist a n c e b et w een poi n ts , followed b y m o re det a il ed r esu l ts u s i n g p er c en t i l es . 3 .1 . Gen er a l S tat i sti cs Ta b l es 1 a n d 2 r epor t t he t ot a l pa i rs of poi n t s con sid ere d a n d t h e m ean of t h e clos es t poi n t o f a p pr oa che s for v a r iou s s ubs ets or ga n ize d b y l oca ti on (Ta ble 1 ) or us e ca s e s (Ta b le 2 ). Ta b l e 3 a ggr egates pairs of fe a t ures a c ros s a ll locat i o n s . Th e w ei gh ts us ed f or c a l c ul a ti n g t h e w ei gh t e d me a n w er e per r ow r a th er t h a n a cros s t h e en t i re t a bl e. P lea s e r ef er t o t h e s ource code for i m p lem e n ta ti o n det a il s . Ta bl es 1 a n d 2 s up po rt t h e follo w in g col loqu ial s t a tem en ts : • “ On a v era ge, a n y two f ea t u res of in tere s t a re cl os er t o e a c h ot h er i n Ma s s ach use tts t h an K a n s a s; ” • “ W h il e N ev ada i s t h e 7 th la rg es t s t at e b y a re a a n d New York is t h e 2 7 th , t h ere a re m ore pote n ti al w a y s for UASs t o enc oun ter eac h ot h er in Ne w York, giv en t h e feat u res of in t er es t;” a n d • “ On a v er ag e, r ail w a ys a n d r oa ds a re c l os er t o ea c h ot he r t h a n r a i l wa ys a n d wi n d t urb in es . ” T a b l e 1 . G e n e r a l s t at is t ic s f o r e ac h lo c a t io n . M e an s a re in na u t ic a l m il e s wit h e x t re m e s hi g h lig h t e d . ISO 3 1 6 6 -2 Cod e L oca t i on T ota l P o i n t P a i rs We i gh t e d Mea n U n w e i gh t e d Me a n US - CA Cal if o rn ia 3 . 4 6 8 × 1 0 11 4 . 9 8 1 0 .8 3 US - FL Fl o rid a 8 . 3 8 7 × 1 0 10 3 . 6 0 1 8 .5 8 US - KS Ka nsa s 9 . 7 1 8 × 1 0 10 4 . 0 6 8 . 6 3 US - MA M ass a c h u s e t t s 6 . 1 7 6 × 1 0 9 2 . 0 6 3 . 9 4 US - MS M is s iss ip p i 3 . 3 5 9 × 1 0 10 3 . 4 8 4 . 4 9 US - NC No rt h C a ro li na 4 . 5 9 1 × 1 0 10 4 . 1 5 2 0 .0 0 US - ND No rt h D a ko ta 4 . 9 0 6 × 1 0 10 6 . 2 8 9 . 8 6 US - NH Ne w Ha m p s hi re 1 . 0 7 8 × 1 0 9 3 . 8 8 9 . 9 2 US - NV Ne v ad a 1 . 0 6 0 × 1 0 10 1 0 .6 7 1 7 .8 1 US - NY Ne w Y o rk 8 . 9 9 7 × 1 0 10 3 . 3 5 7 . 8 5 US - OK O kla ho m a 1 . 5 1 4 × 1 0 11 3 . 9 8 1 0 .3 9 US - PR P u e rt o Ri c o 1 . 6 1 1 × 1 0 8 2 . 7 1 8 . 5 8 US - RI R h o d e I s la nd 9 . 3 6 2 × 1 0 7 1 . 6 8 3 . 6 7 US - TN Te nn e s s e e 3 . 3 3 5 × 1 0 10 3 . 3 0 1 7 .7 6 US - TX Te x as 1 . 7 2 2 × 1 0 12 4 . 5 4 1 1 .7 1 US - VA V irg in ia 3 . 4 7 6 × 1 0 10 3 . 0 7 3 . 2 9 6 o f 15 T a b l e 2 . G e n e r a l s t at is t ic s f o r f e a t u re p ai rs. M e a ns a re in na u t ic al m il e s wit h e x t re m e s h ig hl ig ht e d . Fe a t u re #1 Fe a t u re #2 T ota l P o i n t P a i rs We i gh t e d Mea n U n w e i gh t e d Me a n FAA O bs t a c le s G o lf C o u r s e 1 . 5 1 9 × 1 0 10 7 . 8 9 6 . 8 7 FAA O bs t ac le s P ip e lin e 2 . 2 9 0 × 1 0 11 2 . 2 2 5 . 7 6 FAA O bs t ac le s R a ilwa y 8 . 9 3 3 × 1 0 10 6 . 0 1 4 . 7 3 FAA O bs t ac le s R o ad 5 . 7 6 2 × 1 0 10 4 . 0 0 2 . 8 9 FAA O bs t ac le s Win d Tu rb in e 4 . 3 7 2 × 1 0 9 1 6 .3 6 2 3 .2 8 Ele c t ri c P o we r FAA O bs t ac le s 2 . 2 8 1 × 1 0 11 2 . 0 0 1 . 9 6 Ele c t ri c P o we r G o lf C o u r s e 6 . 5 3 7 × 1 0 10 7 . 8 4 7 . 9 4 Ele c t ri c P o we r P ip e lin e 7 . 5 3 2 × 1 0 11 2 . 4 7 6 . 4 3 Ele c t ri c P o we r R a ilwa y 3 . 4 9 2 × 1 0 11 5 . 8 7 5 . 4 3 Ele c t ri c P o we r R o ad 2 . 2 4 1 × 1 0 11 3 . 9 2 3 . 6 1 Ele c t ri c P o we r Win d Tu rb in e 1 . 5 2 5 × 1 0 10 2 8 .5 7 2 8 .7 3 G o lf C o u r s e P ip e lin e 3 . 6 8 0 × 1 0 10 2 . 4 5 5 . 2 2 G o lf C o u r s e R a ilwa y 2 . 5 4 0 × 1 0 10 3 . 2 8 3 . 8 8 G o lf C o u r s e R o ad 1 . 6 7 4 × 1 0 10 2 . 2 2 2 . 3 5 G o lf C o u r s e Win d Tu rb in e 8 . 2 5 8 × 1 0 8 2 8 .4 1 2 9 .0 5 P ip e lin e R a ilwa y 2 . 8 9 0 × 1 0 11 7 . 7 2 5 . 0 8 P ip e lin e R o ad 1 . 9 1 3 × 1 0 11 5 . 3 6 4 . 2 0 P ip e lin e Win d Tu rb in e 1 . 6 0 0 × 1 0 10 2 9 .4 9 3 0 .5 6 R a ilwa y R o ad 8 . 9 1 4 × 1 0 10 2 . 1 7 2 . 3 5 R a ilwa y Win d Tu rb in e 5 . 8 9 8 × 1 0 9 2 8 .6 4 2 8 .2 6 R o ad Win d Tu rb in e 3 . 7 1 2 × 1 0 9 3 0 .9 2 2 9 .6 4 Figur e 1 il lu s t ra te s t h e w eigh ted m ea n s giv en t h e n u m ber of poi n t pairs f or Ta bl es 1 a n d 2 . T h e w eighted m ea n for m os t l oca tion s w a s les s t han fiv e n a u tic a l m il es . Th ere w a s m ore v a riab i l i ty w h e n com pa ring a c ros s p a i rs of feat u re s . The m in i mum w ei gh t ed a v er ag e in Figure 1 w a s 1 .68 n au t i c al m i les a n d t h e m a x imu m was 3 0. 9 2 n a u tic a l m il es . Fi gu re 1 . I llu s t ra t e d we ig ht e d m e a ns f o r c lo s e s t p o in t o f ap p ro a c h f ro m t abl e s 1 a n d 2. 3 .2 . Per cen ti l es A s et of di s t a n c e pe r c en til es w a s calcu lat ed f or eac h pa i rs of fe a t ur es for a l l loc a tion s. A s a n exa m pl e, Ta bl e 3 prov ides t h e p ercen til es for Cal i fo rn i a . P lea se r ef er t o t h e s u p p l em en t a l m a te ri a l f o r t h e per cen til es of a l l 3 3 6 com bi nati on s o f loc a t i on s an d pa irs of fe a t ures . The per c en tiles can va ry s i gni ficantl y de p endi n g on t h e feat u re s . Ta b l e 3 s up por ts t h e follow i n g colloquial st a te m en t s f o r pot ent i a l UAS oper a tion s in Ca li for n i a : • Min im um: “ R ail w a ys a n d r o a d s a re s om etim es co - lo c a te d .” • Me a n : “ On a v er a ge a lon g a r a i l w a y , a U AS com es with i n 1 .9 3 n m of a r oa d b u t com e s wi th i n 2 6 .9 7 nm of a w i n d t u rbi n e. ” • Me di a n : “ At a n y give n poi n t a lon g a r a i l w a y, a UAS c om es us u a l l y w i thi n 0 .6 1 n m of a r oa d.” 7 o f 15 • Max i m u m : “ Th e cl os es t p oin t of a p proa c h b et w een UASs in spec tin g a r a il way a n d r oa d m a y exceed 60 n m . ” T a b l e 3. C lo s e t p o in t o f a p p ro a c h pe r c e nt ile s f o r US - C A ac ro ss a ll f e at u re c o m bin at io ns. M e an s a re n a u ti c a l m ile s wit h e x t r e m e s h ig h lig h t e d . Fe a t u re #1 Fe a t u re #2 Me a n 0 5 25 50 75 95 100 FAA O bs t ac le s G o lf C o u r s e 5 . 3 3 0 . 0 0 0 . 3 8 1 . 4 4 2 . 9 3 6 . 5 8 2 1 .5 1 5 6 .6 6 FAA O bs t ac le s P ip e lin e 4 . 0 5 0 . 0 0 0 . 1 0 0 . 5 7 1 . 3 9 4 . 0 6 1 8 .6 6 6 0 .0 0 FAA O bs t ac le s R a ilwa y 3 . 2 2 0 . 0 0 0 . 0 6 0 . 5 6 1 . 6 9 3 . 9 8 1 0 .1 2 6 0 .0 0 FAA O bs t ac le s R o ad 2 . 9 6 0 . 0 0 0 . 0 8 0 . 5 4 1 . 5 8 3 . 9 5 9 . 8 8 5 5 .6 1 FAA O bs t ac le s Win d Tu rb in e 2 0 .6 1 0 . 0 0 0 . 0 4 1 . 3 7 1 8 .3 0 3 5 .0 4 5 7 .9 3 6 0 .0 0 Ele c t ri c P o we r FAA O bs t ac le s 2 . 8 5 0 . 0 0 0 . 0 5 0 . 5 7 1 . 6 0 3 . 7 2 9 . 8 2 3 3 .0 7 Ele c t ri c P o we r G o lf C o u r s e 7 . 3 5 0 . 0 0 0 . 5 3 1 . 9 0 4 . 4 2 1 0 .1 8 2 3 .4 8 4 4 .5 0 Ele c t ri c P o we r P ip e lin e 5 . 7 3 0 . 0 0 0 . 1 4 0 . 8 2 2 . 1 0 5 . 9 2 2 3 .1 8 6 0 .0 0 Ele c t ri c P o we r R a ilwa y 5 . 4 4 0 . 0 0 0 . 0 8 0 . 9 0 2 . 7 2 7 . 1 3 2 0 .5 2 6 0 .0 0 Ele c t ri c P o we r R o ad 3 . 5 0 0 . 0 0 0 . 0 8 0 . 6 5 1 . 8 3 4 . 4 7 1 3 .1 3 2 9 .2 7 Ele c t ri c P o we r Win d Tu rb in e 2 9 .1 8 0 . 0 0 3 . 4 9 1 4 .1 9 2 7 .0 7 4 2 .6 3 6 0 .0 0 6 0 .0 0 G o lf C o u r s e P ip e lin e 3 . 2 9 0 . 0 0 0 . 1 2 0 . 5 8 1 . 4 5 3 . 1 2 1 2 .9 2 6 0 .0 0 G o lf C o u r s e R a ilwa y 3 . 5 0 0 . 0 0 0 . 2 6 1 . 0 1 2 . 0 3 4 . 1 8 1 2 .5 8 6 0 .0 0 G o lf C o u r s e R o ad 2 . 2 7 0 . 0 0 0 . 1 5 0 . 6 6 1 . 4 2 2 . 9 7 6 . 5 8 5 5 .6 8 G o lf C o u r s e Win d Tu rb in e 2 6 .2 1 0 . 3 6 5 . 2 2 1 2 .0 5 2 2 .9 8 3 7 .9 5 6 0 .0 0 6 0 .0 0 P ip e lin e R a ilwa y 4 . 9 2 0 . 0 0 0 . 1 3 0 . 8 7 2 . 4 7 6 . 5 6 1 8 .9 5 3 4 .7 4 P ip e lin e R o ad 3 . 8 8 0 . 0 0 0 . 1 2 0 . 7 1 1 . 9 6 5 . 0 8 1 3 .5 2 3 4 .6 3 P ip e lin e Win d Tu rb in e 3 0 .0 3 0 . 0 0 3 . 5 6 1 5 .0 4 2 8 .1 9 4 3 .4 4 6 0 .0 0 6 0 .0 0 R a ilwa y R o ad 1 . 9 3 0 . 0 0 0 . 0 3 0 . 2 0 0 . 6 1 1 . 5 3 1 0 .2 0 4 0 .3 8 R a ilwa y Win d Tu rb in e 2 6 .9 7 0 . 0 2 3 . 3 3 1 1 .5 0 2 5 .0 4 3 9 .1 4 6 0 .0 0 6 0 .0 0 R o ad Win d Tu rb in e 3 4 .1 1 0 . 0 1 4 . 4 9 1 8 .2 9 3 3 .0 1 5 3 .5 1 6 0 .0 0 6 0 .0 0 Figur es 2 a nd 3 ill u s tra t e t h e d is t ri buti on of v a riou s cl os et points of a p proa c h p ercen til es a c ro s s a l l loc a t i on s a n d f eat u res . Similar t o the Ca l ifor n i a -on l y res u lts , d iff erent fe a tu res a re of te n co -l o c at e d or w i t h i n on e n a u tic a l m i le a pa rt a cros s a ll loca tio n s . Th e m a jori ty of t h e m edia n s were l es s t h a n 2 . 6 n a u t ic a l m i les a n d t h e m a j ori ty of t h e 2 5 t h pe r c en til es w e re a b out 1 n a ut i c a l m il e or less . Wi n d t ur bin es oft en were th e farth es t a w a y fr om ot h e r f ea t u res , w hil e r oads were t h e m o s t of t en n ea r o th e r f ea t ur es . 8 o f 15 Fi gu re 2 . Clo s e s t p o in t o f a p p ro a c h pe r c e nt ile d istr ibu t io ns ac ro ss al l lo c a t io ns a nd f e a tu re s . Fi gu re 3 . Pe rc e n t ile d ist r ibu t io n s a c ro s s al l lo c at io ns an d f e a t u re s ; f ig u r e re s t r ic t e d t o t e n n au t ic a l m il e s. 9 o f 15 4 . Disc uss io n Th i s s ect ion s t a rt s w i t h a b r i ef dis cu s si on on t h e s en s i t i vity of t h e r es ul t s t o us in g a c l o s e r in t er p ola tion a n d t h en il lu s tra te s how ge og ra p h y or ur b a n pla nnin g in flu enc ed t h e r es u lts . T h i s s ect i on c on c l u des w i th a n exa mpl e of h ow da ta a v a il a bili ty a n d c ove ra ge c a n s ke w t h e r e s u l ts. 4 .1 . R esults Sen si tvi ty to S pac i ng bet w een Poi nt s To as s ess t h e s e n siti v ity of t h e res u l ts t o t h e sp a c i n g b etwee n i n ter p ol a ted p oi n ts , we r ep e a te d t h e a n a lys i s fo r o n e of t h e la rge st USA sta te s , C a li fo rn i a , us i n g a 1 0 0 i n s te ad of a 50 0 f oot sp a c i n g . Sh ow n b y Ta ble 4, t h e per cen t diff er e n c e ( giv en two nu m ber s , a a n d b ), for t h e com p u ta tion t i me , m ea n , a n d m edi a n wa s ca lc ul a ted as % D i ff er en ce = 1 0 0 × (a − b ) /b . ( 1 ) Th er e w a s m os t l y a n egligib l e di ff er en ce b et w een t h e m ea n a n d m e dia n s t a t i s ti cs wh e n com pa ring t h e u s e of 1 0 0 a n d 5 0 0 fee t . H ow ev er , t h e re w a s a s i gni fica n t p er cen t in c rea se in t h e r eq u i r ed com pu ta tion t i m e due t o t h e in cr ease d qua n ti ty of poi n t s t o con s ider. The t r a de -of f f o r r educi n g t he in terp ola ted s p a c i n g b et ween point s di d n ot prov i d e a s uff i ci en t i n c en tive t o r ep e a t th e a n a lys i s f or a ll lo ca ti on s . T a b l e 4 . P e rc e nt d if f e re nc e s f o r US - C A r e s u lt s wh e n c ha n g in g s p a c in g f ro m 5 0 0 t o 1 0 0 f e e t . Fe a t u re #1 Fe a t u re #2 T ota l P o i n t P a i rs Com p u t e T i m e (s) Me a n ( n m ) Me d i a n (n m ) FAA O bs t ac le s G o lf C o u r s e 1754% 2113% 4 . 2 % 6 . 1 % FAA O bs t ac le s P ip e lin e 1797% 2210% 4 . 0 % 1 . 0 % FAA O bs t ac le s R a ilwa y 1455% 2623% 1 . 0 % 4 . 4 % FAA O bs t ac le s R o ad 1800% 2705% 3 . 3 % 7 . 3 % FAA O bs t ac le s Win d Tu rb in e 282% 2442% − 3 .8 % − 4 .9 % Ele c t ri c P o we r FAA O bs t ac le s 1791% 356% 0 . 3 % 0 . 6 % Ele c t ri c P o we r G o lf C o u r s e 2303% 1681% 0 . 3 % 0 . 6 % Ele c t ri c P o we r P ip e lin e 2359% 1826% 0 . 2 % 0 . 4 % Ele c t ri c P o we r R a ilwa y 1916% 2001% 0 . 4 % 0 . 8 % Ele c t ri c P o we r R o ad 2363% 1909% 0 . 3 % 0 . 6 % Ele c t ri c P o we r Win d Tu rb in e 395% 280% 0 . 1 % 0 . 1 % G o lf C o u r s e P ip e lin e 2311% 2179% − 0 .3 % − 0 .2 % G o lf C o u r s e R a ilwa y 1876% 2699% 0 . 1 % 0 . 4 % G o lf C o u r s e R o ad 2315% 2383% 0 . 1 % 0 . 3 % G o lf C o u r s e Win d Tu rb in e 385% 389% 0 . 0 % − 0 .1 % P ip e lin e R a ilwa y 1922% 2712% 0 . 2 % 0 . 2 % P ip e lin e R o ad 2371% 2461% 0 . 2 % 0 . 2 % P ip e lin e Win d Tu rb in e 397% 346% 0 . 1 % 0 . 2 % R a ilwa y R o ad 1925% 2057% 3 . 9 % 3 . 4 % R a ilwa y Win d Tu rb in e 307% 338% 0 . 4 % - 0 . 3 % R o ad Win d Tu rb in e 397% 388% 0 . 0 % 0 . 0 % 10 o f 15 4 .2 . Geog r aphy Th e l on g li n ea r in f ra s tru ctu res of r a i l wa ys , m a jor r o a d s , p ip eli n es , a nd electric p ower l i n e s a re of t en n o m or e tha n a f ew n a u tic a l m i l es a p a rt. Th es e fe a t u re s a re n ot un i for m ly di s tr ibu ted a c ro s s th e env ir on m en t, r a th er ge og ra p h i cal f ea tu re s of m oun ta i ns a n d la ke s i n fl uen c e t h e loc a tio n a n d m an - m a de f ea t ures. Th is is exem p l i fie d b y Figure 4 for ge ogr a ph i c a l a n d m a n- m a d e fe a t ures a r o u n d th e W h ite Moun ta i n s N a tion al For es t. Fo r em os t, t he lon g li n ea r in fra s tr u c tu re t ra ve rs es t hro ugh t h e n a tura l m ou n ta i n pa s s s ou th o f Fr a n c on ia Notch n ea r Wood s toc k. It is m or e ef fic ien t t o b u i ld p ower li n e s a n d r oa ds t h rough v a l l e ys in s t ead of s t ee p a n d v a ried m ou n ta i n ou s te rra i n . The mou n ta i n pa ss a c ts a s a n a tu ra l con s tr a i n t o n t h e loc a t i o n of t he m a n ma d e features . The e l ect ric p o wer l ine s t o t h e w es t of t h e m oun ta i n s w e re li ke ly con s tr u c te d t he re t o m i n i m i ze cos tl y con s tructi on a n d m a i n ten a n c e du e t o c h all en gi n g t e rr ai n . A diff er e n t con s tr a i n t i s La ke Winni pes auk ee t o t h e s outh of t h e m oun ta ins , t h er e a re n o l on g l i n e a r in fr a s tr u c tu re f eat u res t ra ve rs i n g t h rou gh i t . Ins te ad t h e r a il w a y a n d ro a d s b o rde r t h e w es te rn ed g e of t h e la ke . For p ot ent i a l UAS oper a t i o n s , t h is ge ogr a p h y w i l l l i ke l y i n c re a se or decr ea s e th e li ke li h ood t h a t two UAS w il l en c ou n t e r e a c h ot h er. Fi gu re 4 . Fe a t u r e s ar o u n d t he Whi te M o u n ta in s i n no r t he rn Ne w Ha m p s hi re . Nev er th el es s , a s ill u s trated b y Figur e 5 , g eog r a ph i c a l f eat u res a r e not s olely r esp o n s ibl e f o r in flu enc ing t h e l oca ti on of m a n -m ad e f ea t ures . Th e env i ronme n t i n Figure 5 is r ela t ivel y fla t a n d con s is ten t, y et t h e l on g l in ea r in frast ruc tures a re w ith i n 0 .5 na u tic a l m i l e or les s of ea ch ot h er. Th e s e f ea t ur es a l ign with U. S. R out e 2 w h i c h w a s b u i lt in 19 2 6, f oll owed b y t h e Gre at N ort h ern R a i l w a y ( t h e ev en t ua l Am tra k “E m p i re Bu il der” ) r oute in 19 2 9. Th er e a re engin e eri n g des ign s ta n d ar d s to r educe t h e env iron me n t a l im p act of n ew t r a n s porta tion r outes b y l ocat i n g r a i l w a y t ra c ks a l on g s i d e a h igh w a y. Th e n ea rby t ra n s po rtati on s ys tem m i n i m i z es environ m en ta l im p a c t b y j oi n tl y us i n g l an d w h il e a ls o i n c re a sin g t h e ef fici enc y of m ul ti-v eh i c l e t rip s . 11 o f 15 Addit i on a l l y, Figur e 5 il l us t ra te s t h a t s peci fic f eat u res , su c h a s w in d t urbin es , ar e loca te d a t s p ecific loc a tion s t o opt i miz e t h ei r op er a ti on s . Th e w i n d t urbi n es a r e loc a ted t o m a x i miz e e n e rg y pr odu ction w h ile m i n i m izin g e n v ir on me n ta l c os t s . UAS op er a tion s coul d l ev er a ge t h i s wh e n desi gn in g r isk m i tiga tion s . UAS in s pecti on s of w in d t u rbi n es m a ybe a good ca n di da te t o p r o to t yp e s t r a te gi c m i ti ga t i on s b ec a us e our r es ul ts in d ic a t e t h at t h ey a re of t en far a way f r om ot h e r f ea ture s. Fur t h erm ore , w h il e o ut of s cope f or t h i s a n a l ys i s , t h es e r e s u lts ca n in fo r m pot en t i a l gr o u n d col li s i on r i s k a n d m iti ga ti on s . Fo r exa mple, c on s id er t h a t w i n d t u rbin es a re of t en m a n y m i le s a w a y f r om m a jo r r oa d way s w h i l e r a i l w a ys a re oft en c l os e t o m ajo r r oa d w a ys . If a UAS h a d a cri tic al fa i l u re , t h e l ikelih ood of a UAS c r a s h i n g i n to m ann ed v eh i c les on t he r oa d is p ot en tiall y les s i f t h e U A S wa s in s pectin g a w i n d t u rbin e t h an r ail w a y. Fi gu re 5 . Fe a t u r e s n e a r R u g by in n o rt h e r n No rt h D ak o t a. 4 .3 . Ur ban Pla nn i ng Ur b a n pla nn i n g an d t h e pre s en c e of ur b an c l u s te rs or de v elop ed la n d w i l l a l s o in flue n c e t h e in t er a cti on b et w een UAS oper a tion s . Figure 6 il l us t ra tes r a i l way s a n d go lf c our s es n ear Boston , M A . Th e r a il way s a re m ore prev a l en t i n t h e ur ba n cen te r wi th in di vid u a l li n es cl os er t o e a c h othe r. A s th e r a i l way s n a v ig a te outs i de t h e m a jor city, t h e li n es b ec om e more d is p ers ed wh i l e s til l s erv i n g m o re dev eloped r eg ion s. Conv er s ely , r ecre a ti on a l - f o c use d golf cour s es a r e loc a t ed in l es s dev e lop e d r eg ion s a n d n on e exi s t in Bos to n ’ s ci ty c enter . S in c e r a i l w a ys a nd go lf c ours es s erv e di ff ere nt s o c i e ta l n ee ds , it is n ot su r p ris in g t h a t golf c our s es ar e r a il w a ys a r e o ft en m il es ap a rt. A ddi t io n all y, gol f cour s es a re of t en a c c es s ed p rim a ri ly by r o a d s , ra t h er than ot h er m o des of t r a ns p ort a tion . Th i s r ef l e c ts t h a t t h e pote n ti a l cl os es t poin t of a p proa c h b et w een g olf c ours e a n d r oa d w a y i n s p ecti on UA S s a re cl os er t h a n t h os e b et w ee n g olf c ours e a n d r a i l way operati on s. 12 o f 15 Fi gu re 6 . Fe a t u r e s n e a r B o s to n in e a s te rn M a s s a c hu s e t t s . 4 .4 . Data A v a i l a bi l i t y a nd Co v er a g e La s t ly, F i gur e 7 il lu s tra te s e lect ri c power lin es , r oa ds, a n d FAA ob s t a cl es in s out h ern Rh o d e I s l a n d . Th e elect r i c power l i n e i s pa r a l l el t o t h e r oa d an d t he F AA r epor te d ob st acles a r e c o - l o c a te d w it h t h e pow er lin e. Th es e ob s t ac les a re t h e t ow er s s up portin g t h e pow er lin es t h em s elve s . A s desc r i bed in Sec tion 2 .3 , ea ch obs ta c le is repres en t ed a s a ci rcl e w ith a ra d i u s def i n ed b y th e h o ri z o n ta l pos i t ion un cer ta int y. Th e l a r ger t h e cir c l e, t h e gr eat er t h e u n c er t a i n ty. A ch a ll eng e is t ha t m a ny da t a s e t s do n ot gua r a n tee com plete cov er a ge of a ll fe a t ures. Thi s is s ue e x i s t s for b ot h fede ra l l y m a n a ged a n d open s our c ed da t a s et s . Th e i n for m a ti on a va il a bl e a cr os s da tase ts v a r i es t oo a n d cor r elat i n g da ta s et s ca n b e ch allen gin g. I n F igur e 7 , t h e D H S H IF L D elect r i c po wer l in e da tase ts do n ot s p eci fy t h e l oca tio n s of th e to we rs s up por ti n g t h e l i n es . Th e FAA D OF s im pl y s p eci fi es t h e locat i on of a t ow er a n d d oe s n ot des i g n a te if a t ow er i s us ed to su p port electri c po w er lin es . H oweve r, fr om a UAS o pera tion s per s p ec ti v e , a n in s pection of elect r i cal sys tem s coul d in c l ude b o t h t h e t ow er and p ower l i n es . Th e con se que n c e i s t h a t our r es u l ts m a y s ke w t o wa rds cl os er s mal l er dist a n c es, a s we do n ot deli n ea te i f t wo f ea tu re s a re com pon en ts of a s in gle s ys tem . 13 o f 15 Fi gu re 7 . Fe a t u r e s ne a r P o rt s m o u t h in s o u t he rn Rh o d e I s la nd . 5 . C o nclusio ns W e dem on s t ra te d a n a n a l yt ic a l m et h od t o ch a r a c te ri z e pot en tia l UAS enc oun ter s . B y ch a r a cter i z i n g en c oun ter s , w e c a n dev elo p a n d e v a l u at e s y s tem s t h a t m i tiga te a i rbo rn e c oll ision ri s k . Th es e s y s tem coul d b e ob s ta c l e aw a re, like ACAS sX u [ 1 0 ], s uch t h at w h en m a n eu v erin g t o a vo i d a n ot h er a irc ra ft , th e s ystem wil l a tt em pt to n o t i n adv ert en tly ma n eu v er i n to a n ob s t a c le. R ep re s e n ti ng ob s t a c l es as pa r t of t h e s i m u l a tion w ould b e b enef ic i a l f or sy s t em de v elopme nt , e v a l uat i o n an d deploy m en t. Th e sy s t e m s coul d a l s o b e c ooper a ti ve in t ha t a ir c ra ft exc h a n ge in fo r ma tion v i a a n a i r b orn e v e h i c le t o v eh i c l e li n k ; a n d t h i s li n k woul d need t o b e con s i dere d a s pa rt of D AA Mon te Car lo s i m u lat i on s. H ow ev er , ASTM [9 ,1 9 ] n or R TCA h a ve pu bl i s h e d s t a n dar d s t h a t p rov i d e r eq u irem en ts o n h o w t o r epr es en t obs ta c l es or p er f o rm a nce req u ire m en ts on a V 2 V s ys tem , a s pa rt of a D AA s y s t e m f o r s m a ll er UAS. Thes e D AA ca pa b il i ties a re cu rre nt l y b ei n g dra ft ed a n d dev el oped by t h e s ta n d a rd s dev elopi n g or g a n iza tion s an d ci v il a v iat i on a ut h oriti es . Th e p r es en te d r es earc h s upp o rt s t h e se s t a n da rd a ct i v i t i es b y det er min i n g w h i c h ob s ta cl es s h ould b e pr i oritiz ed for in c l us i on i n D AA s i m u lat i on s ; ass es s i n g i f s p eci fi c enc oun te r s cen ar i o s a re s u ita ble t o a s s es s a g ive n V 2 V te ch n ol o g y; a n d c h a rac ter izin g enc ou nt e r s c enar i os t ha t are l ikely r a re, r eg a rdl es s of UAS f li gh t h ours . Fo r exa m ple, wi n d t u rbi n es were con sis tentl y m a n y m il es a w a y fr om t h e ot h er fe a t ure s . E x c e p t f or w h e n con sider i n g FAA o b s ta c l es an d win d t u rbin es , t h e 5 th per c en ti l e d ist a n ce b e twe e n a wi n d t ur bin e a n d a n ot h er fe a t ure w a s at lea s t t h r ee n a utic a l m i les . I n c om p a riso n , t h e 2 5 th per c en ti l e dis t a n c e b etw ee n electr i c a l power t ra n sm issi on li n es a n d ot he r f ea tures w a s l es s t h a n on e na u ti c al m i le. Si n c e w i n d t u rbin es a re oft en m uc h farth er a wa y f rom ot h er fe a tures , it is les s l ikel y th at a n y pot ent i a l enc oun ter b et w ee n s mal l er UA S w ou l d occu r n e a r a w i n d t u rbin e, w he rea s , s impl y du e to t h e ge os pa t ia l dis t ri buti on of fe a t ur es , e n c oun t ers a r e m or e l i ke l y t o oc cu r nea r elect ri c a l po we r t r a n s m iss i on li n es . Th i s exa m p l e s u gge s ts t h a t t h er e is a gr ea ter n eed t o r ep res ent e l ectric al p o we r lin es i n D AA s im ulat i on s t h a n w in d t urbin es . Addi t i onal ly, if an ob s t a c l e da t a ba s e w a s s t o re d 14 o f 15 onb oard a UAS an d g iv en a s peci fic con cep t of o per a tion s , st ori n g l oca ti on s of w in d t u rbin e s m ay n ot b e a n ef fici ent us e of li m i t ed s t ora ge r es ou rc es . Likew i s e, th e r es ul ts ca n in f orm i f a giv en V2 V l i n k w o ul d s u pp ort di ff ere n t en c ou n ter sce n a ri o s . W h il e t h e re a re m any ot h er fa ctors w h en c h a ra c t e riz i n g a V 2 V lin k, s uc h pr o ba bil i ty of r ecep ti o n , upd a t e r at e, a v a i l a bl e s pectru m , an d t ra nsi t pow er , w e ca n ill u s tra te ho w t h e pres ented r es u l ts c a n b e lev er a ge d with r es p ec t t o e x pected t ra n s m i t r a n ge. Sp eci f ic a l ly, t h e ASTM Rem ote I D s t a n d a rd [ 9 ] dis cu s s es t h a t B lu et o oth 4 w ould h a v e a r a n g e of a b out 1 3 00 f eet or les s in a r u r a l env i ro n me n t, Blu et oot h 5 Lon g R a n ge c oul d h a v e a r a n ge of 3 2 8 0 fee t or l es s , a n d Wi -Fi Awar e coul d h a ve a ra n g e of 6 5 6 1 fe et or les s . Gi v en t h a t w i n d t u rbin es a r e oft en m i les a w a y f r om o t h er fe a ture s, r eg a rd l e s s o f f li gh t h our s , t h e r es ul t s s ugg es t t ha t a UAS, w ith a D AA com m un i c a tion r ange of on e n a ut ic al m i l e , in s pectin g a w i n d t urbin e w oul d oft en n ot b e w it h i n r a n ge t o c om m u n i c a te w i th ot h er UAS s. Acc or din gly, wi n d t u rbin e in s pec tion s m a y not b e a g ood us e ca s e t o dr i ve de v elop m en t o f a V 2V li n k f or D AA. Con v er se l y, s i n c e elect r i c pow er l in e s a r e of t en c l os er t o ot h er pot en tia l UA S oper a t i on s , a V 2 V li n k w i th a m a x imu m t ra n sm it r a n g e of on e n a ut i c a l m i le m a ybe enoug h . Th es e exa m p l e a n a l ys es a re pote nt i a l fut u re con tri buti on s t o t h e a via tio n s a fet y c om mu n i ty an d a r e e n a b l ed b y our re s ea rc h t o q ua n tita tivel y def in e a cl os e e n coun ter b etwee n UASs . O n ce U A S oper a t i on s b ec om e m ore r outi n e or con c ep ts of oper a ti on s a re b et te r es t a bli shed , t h is r es ea rc h c o u l d b e ext end ed t o c on s id er t h e f r eq u en c y of s p ecific en c ou n t e r s c enar i o s . Su p p l e m e n t a ry Ma t e r i a l s: Th e f o ll o win g a re a v a ila ble wit h th is p a p e r, T a ble S 1 : Re s u lt s f o r a ll lo c at io ns a n d f e a t u re c o m bin at io ns . A u t h or Con t ri b u t i on s: A ll a u t ho rs h av e re ad a nd a g re e d t o t h e p u bli s h e d v e rsio n o f t he m an u s c ri p t. Fu n d i n g: D istr ibu t io n st a te m e n t A : a p p ro v e d f o r p u blic re le a s e . Thi s m a t e ri a l is ba s e d u p o n wo rk s u p p o r te d b y t he Fe d e r a l A v ia t io n A d m in ist ra t io n u nd e r A ir Fo r c e C o nt r a c t No . FA 8 7 0 2 - 15 - D - 0 0 0 1 . A n y o p in io ns, f in d in g s , c o nc lu s io ns o r re c o m m e n d at io ns e x p re s se d in t hi s m a t e ri a l ar e t ho s e o f t he au t h o r(s ) an d d o n o t ne c e ss ar il y r e f le c t t he v ie ws o f t he Fe d e ra l A v i at io n Ad m in ist ra t io n . D e liv e re d t o t he U . S . G o v e rn m e n t wit h U n li m i t e d R ig h t s , a s d e f in e d i n D FA R S P a rt 25 2 . 2 2 7 - 7 0 1 3 or 7 0 1 4 ( Fe b 2 0 1 4 ) . Not wi t hst an d in g a ny c o p y rig ht no t ic e , U . S . G o v e rn m e n t r ig h t s in th is wo rk ar e d e f in e d by D FARS 2 5 2 . 2 2 7 - 7 0 1 3 o r D FARS 2 5 2 . 2 2 7 - 7 0 1 4 a s d e t a il e d a bo v e. U s e o f t h is wo rk o t he r t ha n a s s p e c if ic al ly a u t ho ri z e d b y t he U . S . G o v e rn m e n t m a y v io la t e a n y c o p y r ig h t s t h a t e x ist i n t hi s wo rk. A ck n ow l e d gm e n t s : T he a u t ho rs g re at ly a p p re c ia t e t he s u p p o rt p ro v id e d by S abr in a S au nd e rs - Ho d g e , Ri c har d Lin , Ad am He nd ri c ks o n , a nd Bil l O e hl s c hl ag e r f r o m t he Fe d e ra l Av ia ti o n A d m in ist ra t io n . The a u t ho r s wi s h t o a c kn o wle d g e t h e s u p p o r t o f th e ir c o ll e ag u e s, Ro d n e y Co le , an d Ng a ir e U n d e r h il l. The a u t ho rs a ls o ac kn o wl e d ge t he M I T L in c o ln L ab o ra t o ry S u p e rc o m p u t in g Ce nt e r f o r p ro v id in g h ig h- p e rf o r m a nc e c o m p u t in g re s o u rc e s t hat h a v e c o nt rib u t e d t o th e re s e a rc h re s u lt s r e p o r t e d wit h in t h is p ap e r. Con fl i ct s of In t e r e st : The a u t ho rs d e c la re n o c o n f lic t o f in t e re s t . The f u nd e r s h a d a ro le in th e d e c isio n t o p u bli s h t he re s u lt s . Refe re nces 1. Ko c he nd e r f e r, M . J . ; Ed wa rd s , M .W. M .; Esp in d le , L. P . ; Ku c ha r , J . K. ; G ri f f it h , J .D . Air spa c e E nc o u n t e r M o d e ls f o r E s t im at in g Co ll isio n Ri s k. J. Guid . C ont rol D y n. 2010 , 33 , 4 8 7 – 4 9 9, d o i:1 0 .2 5 1 4 / 1 .44867 . 2. We in e rt , A . J . ; E d wa rd s , M .; A lv a re z , L .; Ka t z , S . M . Re p r e s e n t a ti v e S m al l UAS T ra j e c t o rie s f o r E nc o u n t e r M o d e li n g . I n AI AA S c it ec h 2 0 2 0 Forum ; A I A A : O r la n d o , F L , U S A , 2 0 2 0 , d o i:1 0 . 2 5 1 4 / 6.2 020 - 0 7 4 1 . [ O nl in e] . A v a il a ble : h t t p s : / / d o i.o r g / 1 0 . 2 5 1 4 / 6 . 2 020 - 0 7 4 1 . [ A ccess ed : 0 5 - A u g - 2 0 2 0 ] . 3. We in e rt , A . ; U nd e rh ill , N. G e ne ra t in g Re p r e s e n ta t iv e S m al l U A S T ra j e c t o r ie s u s in g O p e n S o u rc e D a t a. I n P r o c e e d in g s o f t he 2 0 1 8 I E E E/ A I A A 3 7 t h D ig it a l A v io ni c s S y ste m s Co n f e re nc e ( D A S C ) , London, U K , 23 – 2 7 S e p te m be r 2 0 1 8 ; p p . 1 – 1 0 , d o i:1 0 .1 1 0 9 / D A SC .201 8 . 8 5 6 974 5. A v a il a ble o nli ne : h t t p s :/ / ie e e x p lo re . ie e e . o rg / d o cu m e nt / 8 5 6 9 7 4 5 . 4. Z e it lin , A . ; Lac he r, A . ; Ku c h ar , J .; Dru m m , A . C o llisio n A v o id a n c e f o r U nm an n e d A ir c ra f t : P ro v in g t h e S a f e t y Case . 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