Jornal of KONiN,3 4,5 00 IN 895-88 DOI 0.478/v0040-008-067-7 THE PROAILITY OF COLLIION DURING VEEL OVERTAKING PRAWDOPODOIEŃTWO KOLIZJI PODCZA WYPRZEDZANIA TATKÓW Gynia Maritime University 8-345 Gynia l. Aleja Jana Pawła II 3 E-mail: piotrliz@poczta.onet.pl Abstract. There are many close qarter sitations at sea, especially in narrow channels. The problem of overtaking on fairways is a complex isse. Navigation, when carrie ot in sch areas cases rece of a vessel s safety level, it is necessary to consier limits: ship s particlars, fairway s parameters, hman factor, vessel traffic. If these factors are not consiere ring overtaking, it will case ship ot of fairway or collision. The paper contains the probability of collision ring overtaking. Keywors: overtaking, collision treszczenie. Nawigacja na obszarach ograniczonych wymaga prawiłowej interpretacji i oceny bezpieczeństwa statk w trakcie jej realizacji. Nawigacja prowazona na tych akwenach wiąże się z obniżeniem poziom bezpieczeństwa, konieczne jest wzglęnienie ograniczeń: wymiary statk, parametry tor, czynnik lzki, rch statków. Niewzglęnienie tych ograniczeń poczas wyprzezania, może oprowazić o wyjścia statk poza tor wony lb kolizję. Artykł przestawia prawopoobieństwo kolizji poczas wyprzezania. łowa klczowe: wyprzezanie, kolizja
9. Introction Navigation when carrie ot in sch areas cases a rection in the vessel s safety level. The navigator, watch officer shol take into consieration the factors which have inflence on it. These limits are: ship s particlars an her manoevring characteristics, fairway s parameters: epth, breath, hyro-meteorological conitions, irection an spee of the win, crrents, waves, vessel traffic in the examine area an visibility. If these factors are not consiere by navigators in narrow waters, it will lea to the hazar of transport safety, as well as the risk of the ship getting ot of the fairway an as a conseqence, the possibility of rnning agron. Nowaays ais of navigation systems are se. ARPA Atomatic Raar Plotting Ai is a niversally se system whose aim is to plan an assess anticollision manoevres. However, when the istance between two vessels is abot a few of own vessel s lengths for larger ships 000 3000 meters, the watch officer makes a ecision base only on visal observation, goo sea practice rles an his own experience. In this case avices given by anticollision system are not sefl. The problem of making ecision abot availability overtaking manoevre in ncertain conitions is connecte with the evalation of system in orer to take on action. ystems object hman shol procee to execte tasks in ranom time moments. Probability it means the realization of ifferent ranom variables []. The system hman ship in case of too close approach in the fairway shol procee to execte the avoiance collision task, it means to execte ranom variables sch as an anticollision overtaking manoevre in restricte area. The measre of availability is the probability of ranom variables mltiplication. That system will be on permanent availability an procee to carry ot task an will not lose its ability to realization [3]. Apart from technical factors an environment parameters, availability also epens on the navigator s ecision abot anticollision manoevre kin of action.. Overtaking on the fairway Dring the overtaking manoevre on the fairway a navigator mst take into consieration the limits, factors which otline the safe manoevre area [4]: a external factors - traffic, position of other vessels ifferent types an particlars, spee of other vessels, - the fairway s parameters breath, epth, length, - hyro-meteorological conitions win, wave, visibility, state of sea, - ay time,
The probability of collision ring vessel overtaking Prawopoobieństwo kolizji poczas wyprzezania statków 93 b internal factors - own vessel manoevre characteristics, size of the ship length, raft, spee, breath, loaing or ballast conition, - navigational eqipment of own vessel, - overtaken vessel particlars corse, spee, size of the ship length, breath, raght, c hman factor - experience, - ecation, knowlege, - stress, - hors of work exhast. In orer to overtake safely another ship sitate on the traffic lane, it is necessary to fin the minimm istance to commence that manoevre, an also the vale of rer angles to alter the corse. The exection of an overtaking manoevre on the fairway alternatively in the traffic separation scheme will reqire from the navigator taking sch measres that the ship, as a reslt of the corse alteration, will avoi collision with the overtaken object an will not cross fairway limits. The ship carrying ot navigation in the restricte area is permanently availability to take a manoevre to secre proceeing the rote safely. In the consective time intervals some states may be istingishe: - expectations that the event sitation of collision will occr, permanent availability ring navigation, - the time interval after the ranom event collision possibility with another ship occrre, - taking action to avoi collision an keeping the ship in the fairway s bonaries. The occrrence of ranom event collision with another ship is pointe by ARPA. The watch officer is making a sbjective assessment of the istance an time of making a manoevre ecision in accorance with his own knowlege, experience an istraction factors, fairway s limits. The actions taken by the navigator after occrrence of ranom event have an inflence on final reslt of the manoevre: - avoiing collision an keeping in the fairway, - avoiing the collision an crossing fairway s limits, - the collision. De to the lack of precisely information, that ais the navigator in making ecisions in restricte areas, receive from navigational eqipment ARPA, anticollision manoevers shol be spporte by other avisory systems, which show the critical area aron the overtaken object. When that area is
94 crosse by a ship as a reslt of no making a manoevre or making a prohibite manoevre the se of nacceptable rer angles, crash stop, it leas to maritime accients. In practice the watch officer while assessing the critical overtaking istance, epens on his own knowlege an intition. I m [ m ] Obszar myszkowania statk 3. The probability of overtaking Fig. Overtaking manoevre in restricte areas The ship carrying ot navigation in the restricte areas shol be in availability to make an overtaking manoevre. When ranom event occrs collision with another object, it etermines the ecision of taking manoevre see Figre. That ecision shol reslt in overtaking object an keepingin the fairway []. Therefore it is essential to escribe the probability of overtaking manever. To avoi collision the vessel shol alter the corse. The angle of steering is given by formla:
The probability of collision ring vessel overtaking Prawopoobieństwo kolizji poczas wyprzezania statków 95 where: the angle of steering [ ], 0 the rer comman [ ], m the error of steering [ ]. In accorance with figre : tg where: sie istance of overtaking [m],, vessels breath [m]. < < arctg F tg P P F 3 That is necessary to fin the istribtion of ranom variable, assming that can be escribe by the normal istribtion N 0, σ. σ φ 0 0, arctg F N 4 Using the eqation: ' F f 5 As a reslt: 0 σ πσ arctg e f 6
96 The sie istance will epen on ranom factors, that is a reslt from the error of steering an the impact of istrbances like win an tie. The probability of overtaking manoevre PC in safe sie istance is expresse as: P C f, 0< < 7 where: PC the probability of overtaking manoevre, the minimm sie istance for overtaking [m], breath of the fairway [m]. The ensity fnction of sie istance f will make it possible to calclate the probability of safe overtaking the other vessel in a given istance in restricte areas. When limits of the fairway breath an the vale of sie istance as a reslt from hyroynamic interaction of two ships ring overtaking are known, it will lea to etermine that each manoevre is safe an possible to execte. For vessels breath: overtaking 57 m, overtaken 3 m, overtaking istance 300 m, the rer comman 30 an varios steering errors, permissible overtaking sie istance 57m, the right limit of the fairway 0m receive reslts see Figre : Table. Overtaking for 300 m an varios steering errors Overtaking istance [m] 300 300 300 Rer comman 0 [ ] 030 030 030 teering error m [ ] 3 7 0 PC 0,4 0,4 0,34
The probability of collision ring vessel overtaking Prawopoobieństwo kolizji poczas wyprzezania statków 97 4. Conclsion Fig. The ensity fnction f for varios steering errors The essential isse for overtaking manoevre is the time interval measre from the appearing of ranom event, which is the possibility of collision, to the time of making the manoevre ecision. In this time interval, the navigator has to ecie abot the action that will allow him to safely pass of the ship. The etermination of the permissible manevering area epenent on critical overtaking istance will make it possible to overtaking safely another ship being on i.e. the fairway. This area will also inform the navigator abot the minimm istance that the overtaking ship is able to approach to execte the manoevre, when limit factors are consiere. The moel of probability for overtaking manoevre in restricte areas was presente. The moel takes into consieration: hman factor steering error, rer comman, the fairway limit breath. References. rci Z., Lizakowski P.: Analiza ryzyka manewr wyprzezania w oparci o sieci ayesa. Problemy eksploatacji 4/009.. Jaźwiński J.: Polska szkoła gotowości systemów wojskowych. XXXVI Zimowa zkoła Niezawoności, zczyrk, 007.
98 3. Gcma L., malko Z.: electe problems an Methos of Navigational Risk Assessment. Proc. th International Congress IMAM 005, vol., Lisbon, Portgal 005. 4. Lizakowski P.: ystem antropotechniczny człowiek statek efektywność manewr wyprzezania w ograniczonej przestrzeni. XXXVII Zimowa zkoła Niezawoności, zczyrk, 009. D.c. Lizakowski Piotr, Gynia Maritime University, assistant, specialization: ship s overtaking in restricte areas, GMD.
The probability of collision ring vessel overtaking Prawopoobieństwo kolizji poczas wyprzezania statków 99