Aemis Pojec Analysis of ecovey buoy fo Aemis Auho: Ahu Sale Vesion and dae hisoy: v1.01, 1 May 003 Documen ID: Sucue-1-1.01 Execuive Summay I is planned o fi a ecovey buoy o Aemis, ahe han aanging fo Aemis o suface fo ecovey. This buoy is based on he Fiobuoy concep (Fiomaine 003). This will save he caiage of compessed ai anks, main ballas anks, and associaed valve gea. I will also povide fo ecovey even if Aemis is seveely damaged. I is necessay o model he design o deemine desiable design feaues. The scheme is applicable o 100m dephs, bu pobably no much moe. Analysis Model The ecovey buoy is modelled as a eel of line, whee he eel is posiively buoyan, and he line leads veically down and is fasened o a seabed objec (he landed Aemis). Befoe and duing deploymen The ecovey buoy is housed wihin Aemis wih he line fully wound up and aached by a shackle a he bie end o Aemis. One possible configuaion is o have i conained in a hoizonal cylindical bay. Deploymen will be achieved by opening he bay doos (like he space shule) o a lid. The aleady hoizonal eel will unwind ou of he housing. I conibues a saic lif dependen on he displacemen and he weigh of he line and he eel, and his will be accommodaed in he vehicle s mass and displacemen budge. Posiive buoyancy mus be mainained even a maximum opeaional deph. Mid-wae The exenal foces acing on he eel a a paicula insan ae diagammed below.
The equaions of moion ae: dv ( B T ) K v M 0 veical moion d d T K I 0 oaion abou hoizonal axis d v coupling, povided T 0 Whee (SI unis shown in paenheses): = Radius a which line is unolling fom eel (m) B = Buoyancy Foce of eel and line on eel (N) T = Tension in line; T 0, since i canno susain compession (N) M = Mass of eel and line on eel (kg = N/(m/s )) I = Momen of Ineia of eel and line (kg-m = N-m/(1/s )) K = Tanslaional Dag Coefficien of eel and line on eel (N/(m/s) ) K = Roaional Dag Coefficien of eel and line on eel (N-m/(1/s) ) Noe ha all of hese paamees ae funcions of he amoun of line lef on he eel (o equivalenly he amoun unolled), which is iself a funcion of he ime since elease. Howeve, K and K ae pobably only weakly dependen on his faco, and if he line is neually buoyan B depends only on he eel and is consan. Dag foces ae assumed o depend on velociy squaed, which is appoximaely ue fo ficional and ubulen dag. This and he ohe vaying paamees invalidae linea analysis of he avel of he eel upwads. Howeve, admiing squae-law conducances (V I ), a simple elecical equivalen cicui can be dawn, using he following equivalences. This povides a quick appeciaion of he main feaues of he dynamic behaviou. Mechanical Foce, Toque Velociy, Angula velociy Rigid objec, saic efeence Dag (squae-law) Mass, Momen of Ineia Compliance, spinginess Coupling Elecical Cuen Volage Node Conducance (squae-law) Capaciance Inducance Ideal ansfome
This cicui can be educed o a simple RC cicui by pushing he oaional newok hough he ideal ansfome. Fom his we can deduce ha (a) he ension T will neve each 0 so he coupling equaion will hold, and (b) he eel will acceleae monoonically upwads o an asympoic eminal velociy elevan o is cuen sae of unolling. If he conducances wee linea, he speed would follow v v final ( 1 e ) in he sho-em, whee = ime consan v final = he eminal velociy v In he acual case whee dag is popoional o speed squaed, he appoach o seady sae will sill be monoonic, bu he iniial ise will be fase han in he linea case. dv d Conside he seady sae when 0 and 0, so defining d d K 1 3 a dimensionless value in [0..] K hen he eminal velociies can be shown o be 1 B v final 1 K v final final and he ension in he line T is T B noe 0 T B 1
Tangling Loss of ension in he line leads o isk of he eel ove-unning iself and he line becoming angled, leading o cessaion of unolling and a sysem failue. The above analysis shows ha hee is neve any isk ha T = 0 in quie waes. Howeve, i is possible ha a downwad eddy will push he eel down and lead o loss of ension in he line. The highes pobabiliy occus nea he suface due o wave acion. Fou facos hen come ino play: (a) he eddy mus have a velociy a leas equal o v, (b) he line in he viciniy of he eel should be equally affeced by he eddy, (c) if he ension in he line dops o zeo a low anslaional dag coefficien K should lead o a apid upwad acceleaion and line auening, and (d) a high oaional dag coefficien K should educe he spin of he eel apidly. The wo dag coefficiens ae hus impoan design paamees. A easonable compomise would seem o be o choose min = 1 which gives T min = 0.5 B. The consain o achieve his is: K K 3 max and his occus when he line is fully wound and he eel has jus lef is housing. Pefoming some fuhe modeling, assume ha he eel has an ouside wound adius of 100mm, axial lengh of 00mm, and conains 100m of 5mm Ø line wound 40 uns pe laye. Then he inne adius of he eel is 77mm, and a he suface and T = / 3 B. Recovey Caying a buoy in Aemis will allow fo easy ecovey fom a boa. Thee will be no need o pu a dive in he wae o aach a cable as wih ecovey of a floaing vehicle; insead boahook ecovey of he buoy will be possible and consequen aachmen o a ecovey cane and winch. Unlike he oiginal Fiobuoy, he line and eel ae caied aound as dead load on he vehicle. Thus he size of he line is an impoan design paamee, as i deemines he eel dimensions and he dy weigh conibuion. Goss ovesizing is no an opion, hough loss of he vehicle is equally unpalaable. Le M we be he mass of he vehicle and is conained fee-flooding volumes. The load on he line when he eel is being deployed is mino ( B). Since he vehicle was neually buoyan befoe deploymen of he buoy, he seady load on ecovey is only B, unil he vehicle beaks suface when he load will become g.m we, dopping as fee-flooding aeas dain o g.m dy. A dynamic load also occus duing ecovey. Assume hee is a mass of M we a he end of he line, and he ecovey vehicle is moving veically in a sea lifing he suface end of he line up and down. Assume also ha he moion is sinusoidal wih an ampliude of A mees, and a fequency of f. Then he moion of he uppe end of he line is descibed by: z = A sin ( f ) dz ( f A cos f d d z ( f Asin f d
The highes foces will occu when he vehicle is abou o beak he suface and lile line is deployed. When he vehicle is a deph, he payed-ou line will ac as a sping o a complian ansmission line, and he foces on he vehicle will be lowe. Assume ha hee is no compliance in he line, and ha fluid esisance of he line and vehicle can be ignoed. Then he maximum upwad acceleaion due o he suface moion will be ( f) A and hus he foce on he vehicle will be ( f) A M we This needs o be muliplied by wo o accoun fo shock loads due o he line becoming slack on a down heave and suddenly becoming au on an upwad one. Tanslaing his ino dominan significan wave heigh H (= A) and peiod P (= 1/f): H 4 Fmax M we P Reduced loads can be achieved by a lengh of suiably sized shock-cod a he aachmen of he vehicle and he line, o by a complian cane design (eihe like a flexible fishing-od, a shock absobe in he line pah, o a oque-adjused slipping winch). If M we = 50kg, H = 5m, and P = 5s, hen F max = 400N, o 41kgf. This is compaable o he weigh of he vehicle. Design Buoyancy The eel should be made of buoyan solid maeial wih no inenal ai spaces, unless i caies a suface adio beacon. See lae egading he buoyancy of he line.. Reel If he oue adius of acion of he fully wound up eel o is deemined by he vehicle dimensions, l is he unolled lengh of line, d is he line diamee, and N is he numbe of uns pe laye, hen he opeaional adius fo any degee of deploymen can be deemined fom: N ( o ) (eas laye effecs as coninuous) d o d N The adius of he inne dum is heefoe dum d max..5 1.5 1 0.5 0 0.04 0.0 0 0 0 40 60 80 100 Lengh 0.1 0.1 0.08 0.06 Radius
Dag design I seems likely ha he oaional dag of a simple eel would be low wih espec o he anslaional dag. The poblem would appea o be one of inceasing he oaional dag coefficien wihou inceasing he anslaional dag coefficien. Given he buoy is housed in Aemis, a soluion ha does no incease he diamee seems desiable. One possible soluion is skeched; dag fins/idges simila o a cenifugal pump impello would be moulded on boh eel sides. Sabiliy The above analysis assumed ha he eel assumes a posiion wih is axis hoizonal, and avels upwads in his posiion. The hydodynamic sabiliy of his configuaion is no known a his sage, bu i would appea o be wise o keep he axial lengh less han o equal o he diamee of he eel. Some expeimens should be conduced o fuhe eseach undeaken. The spin may povide some gyoscopic sabilizaion fo his aiude. If his is consideed desiable, he effec can be enhanced by inceasing he Momen of Ineia I hough he off-axis mass disibuion. The above analysis has ignoed a hoizonal hydodynamic lif (Magnus effec) ha would be geneaed by he oaing and ising eel. I seems likely ha his would be small and no affec he behaviou much. Keeping he anslaional velociy low helps in his egad, since Lif foce = o v Line A line beaking sain 00kgf should be sufficienly song. Fo example ypical 5mm ope has beaking sain >30kgf and dy weigh ~0.95kg/100m. Baided ope may be pefeable o laid ope o minimize wis and kinking. Slighly posiive buoyancy may be moe desiable han neual buoyancy o avoid snagging of Aemis on he seabed by suplus line afe he buoy has eached he suface. This will change he analysis slighly by educing B as he buoy ises. Refeences Fiomaine (003). Fiobuoy web sie. 003. hp://www.fiomaine.com/