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Wind rose, wind velocities and current patterns at Sognefjorden. Figure 6. The cruise ship Balmoral. In Figure 5 is shown an intensity plot of the AIS data and an annual counting of ships on the three main routes in the area. Since the ferry route route 4 is expected to stop service when the bridge is opened, this route is not described further.

An example of a cruise ship in Sognfjorden is Balmoral, a large cruise ship of approximately tons displacement. Balmoral is shown in Figure 6. In order to use the ship traffic data in the risk model, the registered number of ships on each route is assigned to a GT class according to their size and a traffic forecast for have been carried out. Forecasted values are based on the registered present values and corrected in order to account for national economic development and local initiatives concerning cruise ship operations.

COLLISION AND GROUNDING OF SHIPS AND OFFSHORE STRUCTURES

A general annual increase of 2. Furthermore, construction of new cruise ship harbors in Sognefjorden is expected to increase the number of cruise ships over the coming years. Hence, besides the general annual 2. In Figure 7 the estimated number of annual ship movements divided into GT classes is given for the forecast year These are however considered not having any influence on the structural damage in case of a ship collision. In the area where the bridge are planned to cross Sognefjorden there are presently four major sailing routes.

The main sailing route for commercial ship traffic is located in the centre of Sognefjorden. The main sailing route for commercial ship traffic is also used by a large number of cruise ships in the cruiseseason visiting a number of important cruise ports in the fjord. High speed passenger crafts HSC go from Bergen to Sognefjorden and use a sailing route closer to the northern coast line. Local traffic to Instefjord use a sailing route close to the southern coast line. This includes intensity plots, distribution of ships with. In connection with design and construction of the Fehmarnbelt Link proposed bridge and tunnel designs for a fixed link between Denmark and Germany detailed sip traffic studies have been made and an advanced ship collision risk model have been established, Rasmussen This reference reviews existing models, Fujii , Macduff and Pedersen , and estimated data input, RandrupThomsen in renewing the ship collision risk model.

The risk model deals with a set of ship accident scenarios including e. For the present use focus is on accident scenarios leading to ship-obstacle collisions collisions between the ship and the bridge. The basic concept in the ship accident scenarios is that the ships may based on the location on the considered route be at collision or grounding course, but will normally make proper evasive actions such that an accident does not occur, Pedersen An accident only occurs in cases, where a failure occurs and an evasive action is not made.

Hence, the frequency of an accident relates to the two probability contributions: 1 The probability of a ship being on collision or grounding course and 2 The probability that the navigator s does not make evasive actions in due time. The risk model is based on a modelling of ships on defined routes and a modelling of ship behaviour on these routes.

Since the focus of the present paper merely is on demonstrating how real ship data is transformed into a risk model, the focus will be on the route modelling part and other parts are described in more general terms. Figure 8. Intensity plot of current ship traffic in Sognefjorden and estimated sailing routes when bridge is present floating bridge top and SFT bottom.

Possible routes have been discussed with pilots from The Norwegian Coastal Directorate Kystverket having large experience in maneuvering in Fjords. Based on their statements and based on experience from AIS registrations from similar bridge crossings, the routes shown below are applied to the model.

Far away from the bridge there will be no difference from today whereas close to the bridge the ship location on the routes is influenced by the presence of a bridge. Hence, as a starting point the geometric modeling of the routes will be based on AIS registrations of actual observations on ships on the routes and a suitable probability distribution fitting to the observations.

The observed ship locations in form of histograms are shown below in Figure 9. In Figure 10, Figure 11 and Figure 12 are shown histograms and corresponding fitted probability distributions for the routes in Sognefjorden. It is seen from the figures that most ships are located centrally around the centre line of the route but also that some ships are moving quite a distance from the centre line. The fitting procedure maximum-likelihood fitting selects parameters from a uniform distribution U accounting for ships far from the centre. Obviously the routes are changed compared to the current ship pattern due to the presence of the bridge.

The total ship traffic volume must therefore be split.

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Figure 9. Histograms of observed ship locations on the three routes along Sognefjorden. Figure Distribution fitting secondary route. The ML-fitting to the selected distributions aims at maximizing the ML-function for the following resulting density function F x :. The fitting parameters maximizing F x are given in Table 1. Closer to the bridge crossing other distribution parameters for , and b are used. These parameters are based on observations from similar route types in resund resund Bridge and in Great Belt Great Belt Bridge in Denmark.

It is noted that fitting to observed data not in all cases will account for ships erroneously out of course due to the relative short period of registrations. The risk model allows for ships located more random in the area by requiring that the uniform distribution is a part of the resulting distribution. From other studies, Rasmussen and Randrup-Thomsen , different distribution types and parameters standard deviation , uniform ratio and uniform width b are found depending on the nature of the route open waters, narrow navigation channels, bridge crossings etc.

The situations are sketched in Figure 13 above. It is seen that a collision will occur, if the ships on collision course keeps the position and do not make evasive manoeuvres. Not making evasive maneuvers is taken as a human failure. It is assumed that the occurrence of a human failure is independent of the position of the ship and that a human failure will influence navigation of the ship for an average of 20 minutes.

During this period it is assumed that the ship will maintain the same course and speed as it did before the human failure occurred. It is assumed that the sailing course and speed is corrected after the human failure is detected. The annual number of collisions Ncoll due to human failure can be determined as. The present model uses an annual failure probability of 2 which also corresponds well with more general studies of human behavior, Kirwan Two scenarios dealing with technical failures are included: loss of propulsion leading to a ship drifting in a direction generated by wind and current and steering machine failure leading to a ship leaving the planned course taking a new direction.

Examples of the two situations are sketched in Figure 14 and in Figure However, according to general ship navigator experience and engineering judgments, the propulsion machinery on a ship is assumed to fail approximately once during a year in service. Furthermore, assuming effective sailing days per year to be relevant for a typical commercial ship, the frequency fdrift of loss of propulsion machinery becomes. The probability of human failure the probability that a collision candidate does not avoid the collision is estimated based on a large number of studies referred in details in Rasmussen The studies all find values for human failures in the region of between 0.

The frequency of loss of propulsion is adopted for all types of ships, although differences in reserve power and backup systems are present. Furthermore, the frequency is assumed constant throughout the passage of the investigated area. The risk related to loss of propulsion is beside the failure frequency also depending on wind and current conditions in the area and on the ability to regain control of the ship either by repairing machinery or by emergency anchoring all though not considered possible in Sognefjorden. Probabilities related to these issues are also accounted for in the risk model.

With effective sailing days per year assumed representative for a typical commercial ship, the frequency per hour of failure of the steering system becomes. This frequency or rate of steering failure is adopted for all types of ships and is assumed constant throughout the passage of the investigated area. In the risk model is included a scenario where a steering failure occurs immediately before passing the bridge leading to an immediate and significant course change.

The course change will be depending on turning radius and rudder angle. In the risk model is used a turning radius of 2,5 times the length of the ship. Additional scenarios for ships having steering failures further away from the bridge with only minor or no course changes is not included. It is assumed that this failure will be detected and repaired before reaching bridge passage area or that measures are taken engine machinery astern to avoid the risk. The frequency of loss of propulsion and the frequency of steering failure is studied and reviewed in details in the Fehmarnbelt link project as reported in Rasmussen These studies support the order of magnitude of the applied failure frequencies.

Only a fraction of the total collision frequencies originates from more serious collisions. The ship collisions will have different initial impact energy depending on e. For head on collisions HOB the impact energy will be considerably larger than for sideways collisions. HOB collisions tend to occur with higher ship speed than sideways collisions drifting ships having lost engine power.

For this reason the collision frequencies have been divided into HOB collisions and sideway collisions. Resulting frequencies distributed on single pontoons are shown in Figure 16 and Figure The navigational route goes between pontoon 8 and 9. It is seen that sideways collision frequencies are far smaller than HOB collisions frequencies but are having contributions from all pontoons also the ones closest to shore.

Dominating contributions to the overall HOB collisions are closer to the sailing route. It is noted that the most critical pontoon is no. This pontoon is critical since it is on a straight line from the main route from east to west having a bend east of the bridge. Navigators forgetting to turn at the bend will continue and collide in an area around pontoon 6. The situation is sketched in Figure The ship collision risk model described in the previous sections has been applied to both bridge solutions the SFT and the floating bridge.

Collision and Grounding of Ships and Offshore Structures | Taylor & Francis Group

Results in terms of collision frequencies with the pontoons and in terms of pontoon impact energy distributions are given in the following. The overall collision frequency for the bridge is 1. This includes all types of collisions including from minor glancing of the pontoons and collisions from very small. Hence, by knowing ship displacements and ship velocities related to the different ship classes it is possible to determine the resulting collision impact energies to be accounted for in the design of the pontoons.

The impact energy is expressed as. The resulting impact energy is represented by an impact energy distribution accounting for contributions from collision frequency for different ship classes and also accounting for variation of displacement and velocity within a given ship class. Resulting energy distributions for pontoon 6 are shown in Figure For the floating bridge the dominating energy distributions originates from the HOB collisions. Energy distribution percentiles for HOB collisions for use in design work are given in Table 2. Resulting frequencies for the two pontoons are shown in Figure 20 and Figure It is seen that sideway collision frequencies and HOB collision frequencies are of same order of magnitude.

Other less strict requirements shall be established if redundancy arrangements ensure that a collision does not lead to collapse of the bridge. It is demonstrated that the use of AIS data forms a solid basis for establishing a ship collision risk model that is able to evaluate ship collision frequencies. The very detailed information inAIS data data that has not previously been available makes it possible to determine design parameters in a more accurate manner than before. This includes estimation of impact energies and impact loads through detailed information about ship velocities and ship size parameters length, breadth, actual draught and displacement.

For the considered bridge designs it has been shown that the ship collision frequencies is of a magnitude that requires that ship collision loading shall be included in the bridge design. Suggestions for design parameters in form of impact energy distributions are made available.

Part Actions on structures accidental loading. Eurocode 0 Basis for structural design, EN Navig ational studies of vessel traffic conditions in the Fehmarnbelt. Fehmarnbelt Fixed Link. Fujii, Y. Traffic capacity. Journal of navigation. Heinrich, H. Industrial Accident Preservation. A Scientific Approach. Hndbok Bruprosjektering Eurokode utgave, Statens vegvesen, Joint Committee of Structural Safety. Probabilistic Model Code, Basis of Design. Kirwan, B. A guide to practical human reliability assessment. Larsen, O. Ship collision with bridges. MacDuff, T. The Probability of Vessel Collisions.

Ocean Industry: Pedersen, P. Randrup-Thomsen, S. Rasmussen, F. Simonsen, B. Mechanics of ship, grounding, Technical University of Denmark. Zhang, S. Mechanics of Ship Collision, Ph. The collision energy for HOB collisions are however significantly larger.

ICCGS 12222 – Collision and Grounding of Ships and Offshore Structures

For this reason, HOB collision energies for the two piers have been determined. The collision energy distribution for pier 1 is seen in Figure Energy distribution percentiles for HOB collisions for use in design work are presented in Table 3 above. SVV suggests that accidental loading like e. This means that for both the floating bridge and the SFT the design must take into account ship collision loading for pontoons where the collision frequency is above 1 The energy distributions are hence available for the bridge designers in their determination of design requirements for the pontoons.

This can be done directly by using the impact energy distributions together with force-indentation curves for relevant ship types. Zhang , Larsen and Simonsen suggest various force indentation curve representations. Or it can be done indirectly by determining a design ship on basis of the energy distributions and the related ship classes. Further, Eurocodes and Eurocodes gives requirements for designing for accidental loading depending on the consequence of a collision. Also Joint Committee of Structural Safety suggests methods for demonstrating sufficient safety.

Design in high safety class must be in place if the collision leads to a collapse of the bridge. Rasmussen Rambll, Copenhagen, Denmark. In this paper a general method for evaluating the effect of a VTS in terms of how much VTS increases the navigational safety is presented. VTS may also have an effect on minimizing the consequences of an accident if it should occur. In this case VTS may be able to inform other ships thus avoiding the accident to evolve further or VTS may be able to assist in search and rescue or in oil containment operations.

The effect of consequence minimization is not considered in this paper. The background for the study is the construction of the fixed link in Fehmarn Belt. However, the findings are of general interest, e. The Baltic Sea is one of the worlds most trafficked waters and the entrance through Great Belt and Fehmarn Belt is busy with many large oil tankers, bulk carriers and container vessels traveling through the area.

Around 25, ships pass through Great Belt each year and around 40, ships pass through Fehmarn Belt. These numbers are expected to increase in the future. With the construction of the Great Belt Bridge in and the future construction of a fixed link crossing Fehmarn Belt to join Denmark and Germany a great effort is put into analyzing and ensuring the safety for the ships in the region.

During work with navigational safety on the fixed link in Fehmarn Belt a range of risk reducing measures have been considered to ensure that the construction phase and the fixed link itself will be as safe as possible for the ships traveling through the waters. In the investigations it became apparent that relatively little is known about the risk reduction effect of a VTS system. However, this number is not verified in the literature; in fact the literature contains only few references dealing with the effect of VTS the few available references are described in section 2.

It is of interest to gain quantified knowledge about the effect of the VTS as VTS is one of the greatest risk reducers in navigational safety. This paper. In general the approach for quantifying the effect is applicable to other types of VTS where the results cannot be transferred directly. Examples of this include both coastal, river, and harbor VTS.

The VTS operates a Ship Reporting System offering information about conditions and incidents important to shipping and safety at sea. If necessary the service can provide individual information to a ship particularly. In general a study of the VTS efficiency is complicated by the fact that the number of accidents that would have occurred without VTS is unknown.

Meso-strategic events occur when the navigator has insufficient information about the traffic conditions or the situation otherwise is different than expected when planning the journey. However, as the paper was written in before the introduction of AIS, it is reasonable to believe that this new tool has made it possible for VTS operators in some cases to intervene in the tactical stage. Furthermore, early advice by the VTS operator might prevent a critical situation that requires immediate action from the navigator in occurring, such action will remove some of the accidents due to tactical events even before they arise.

A low number of observed accidents are typical to traffic safety studies. This problem has been handled in other studies using an approach taken from road traffic namely the Traffic-Conflict-Technique TCT. TCT is described in relation to navigational safety in Debnath, TCT relies on the fact that even though few accidents are observed, the number of near misses is greater than the number of accidents and the number of unsafe situations is even higher. A drawback of the TCT is the reliance on subjective judgments by the observers, a problem that could be relieved by using objective measures.

From AIS data which is also available in Great Belt it would be possible to estimate the severity of a traffic conflict, either using the methods described in Debnath, or by employing the ship domain theory Hansen, In this paper it is proposed to split the effect VTS has on the navigational safety into two different effects: 1 Increased awareness and information level: VTS informs about the intentions of other ships, general navigational conditions and special conditions such as slow traffic.

The fact that VTS monitors the traffic increases the awareness of the navigators. VTS encourages ships to communicate, relieving difficult situations before they occur. In the following sections focus is on estimating these two main effects of VTS. First an introduction to previous studies is presented in section 2, followed by a description of the approach taken in this study in section 3.

In section 4 the two effects of VTS are examined and combined to an overall estimate, before the conclusion in section 5. Throughout the paper numbers from Great Belt VTS are used to illustrate the method but, it is straightforward to replace the numbers and perform the analysis for any other VTS. Studies of probability of collision and groundings are numerous, see e. Mazaheri, ;T Nyman, VTT, , and the field of domain theory has also received a fair amount of attention Goodwin, ; Hansen, ; Wang, et al. In Hnninen, a review of how human factors influence navigational safety is given, including a Bayesian network analysis linking human failures to the effect.

Reports from before and after the expansion are treated alike as the analysis does not depend on the size of the area.

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A total of reports were written and of these concerned danger of collision or grounding. In the five year period 7 accidents occurred in the area, none of them with serious consequences. The VTS operators monitor the traffic and provide assistance to the navigators. An incident report is generated when a serious incident occurs, or if an incident is important for future learning. The nature of these reports varies from reporting small boats fishing in a no-fishing zone to machine failures on large oil tankers.

Around one third of the reports concern situations with a risk of collision or grounding. Such reports typically contain a detailed description of the involved ship s , a detailed account for the actions on the ship and by the VTS operator and maps with radar and AIS tracks of the episode. The reports are subjective in nature as they are written by the operators. Studies of AIS tracks from the area have also been performed but a direct comparison to the incident reports has not been conducted as little is known about incidents where no report was written.

To conduct the analysis, two effects of VTS on the navigational safety are considered:. In the five year period from to approximately , ships passed through the Great Belt. Under the current conditions with VTS present it is found from the reports that around of the , ships are involved in an incident with danger of grounding or collision. VTS has contact with all the navigators as they enter the VTS area and are hence able to inform the navigators about the navigational conditions and ensure that they are aware of the obstacles both permanent and temporary due to weather or traffic.

VTS operators also provide early warnings to navigators on ships that may meet another ship at a critical location, typically operators request navigators to contact each other to make arrangements for safe passage; such early warning contacts are made around 8 times each day but, are not recorded in a report. Furthermore, the navigators are aware that they are travelling in a VTS area and are under observation and it is likely that this will heighten their level of awareness.

All these factors influence the overall safety in the area in a positive direction. From the reports it is not possible directly to estimate how large this positive effect of increased awareness and information level is on the safety. VTS has an effect from increasing the awareness of the navigators and the information level available to the navigators macro-strategic and mesostrategic.

VTS informs about the general navigational conditions and about special conditions such as slow traffic or bad weather. Furthermore, the fact that VTS monitors the traffic increases the awareness level of the navigators in the area. There is an effect of VTS on acute accident avoidance tactical level. VTS can detect incidents which may lead to groundings and collisions and provide navigational assistance to the ships in these situations. The number of potential accidents that would have happened without VTS is denoted as AP , and the number of accidents that are actually observed is denoted as A0.

The relation between the two can be written as:. The two effects are investigated based on the reports from VTS during the period In this period around 25, ships passed through the Great Belt area each year, the VTS area can be seen in Figure 1 In July the VTS area was expanded to cover two sectors as illustrated in the figure, before this date. In this equation it is unfortunately only A0 that can be observed directly.

As pointed out in the previous section there are two major effects of VTS behind the reduction in the number of accidents: Increased information level and awareness Acute accident avoidance. The first effect reduces the number of critical situation that occur, and the second effect reduces the number of critical situations that turn into accidents. The effect of increased awareness and information level is important for the effect of VTS Raw unfortunately it is difficult if not impossible to get an accurate estimate of the effect.

Therefore the effect of VTS for varying influence of Raw is investigated in a later section. Of the , ships that have passed through the Great Belt in the five year period ships are mentioned in VTS reports concerning incidents with a potential for either collision or grounding. Figure 2 shows a diagram of how these incidents evolve. The process of categorizing the incidents in the incident reports is important, but also time consuming and somewhat subjective.

There are most likely a number of unpredicted incidents that do not lead to accidents and are therefore unreported. As there are no reliable counts of these incidents they are excluded from the analysis. During the five year period VTS has been in contact with 85 ships that are involved in a critical situation SC. These ships are either heading towards shallow water or are getting close to a critical ship ship situation. From the reports it is evident that some of these situations would have resulted in an accident without the intervention of the VTS.


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However, it is also evident that most of the situations would have been handled last minute by the navigator s or avoided by pure luck. A fairly common situation is when a ship approaches shallow waters and is informed by VTS, in this case it is likely that the navigator in some cases would have checked the map and location before an accident would occur. Situations where VTS was not able to contact the ship or where the VTS advice was ignored SNC are examined to estimate the fraction of critical situations that would result in an accident.

Here we see. Table 1. Unpredicted accidents accidents that could not be or were not predicted by the VTS Navigational assistance offered Communication not possible. Number of situations where a ship could not be contacted byVTS or ship ignored VTS advice in a critical situation Communication possible. Number of situations where a ship was successfully contacted by VTS in a critical situation Accidents where VTS was not able to contact the ship or VTS advice was ignored Accidents when communication is possible.

Two of these situations result in an accident ANC. Assuming that the fraction of critical situations that evolve into an accident when VTS cannot communicate with the ship or when VTS advice was ignored is. That is, the actual number of accidents avoided in acute situations AA is a small fraction of the number of situations in which VTS offered assistance. To illustrate the effect of increased awareness and information the number of avoided accidents AP A0 during a 5 year period is plotted in Figure 3 as a function of the effect of increased awareness and information.

In the other end of the scale with a high effect of increased information and awareness the number of avoided accidents becomes very high as a high reduction requires a high number of potential accidents. Unfortunately there is no evidence as to what the true number of avoided accidents would have been without the VTS. A comparison with the situation before the VTS was established is not accurate as routes have been changed partly as a consequence of building the Great Belt Bridge, the intensity in traffic varies, ferries have stopped operating and AIS has been introduced in the period.

Still a rough indication could be gained by examining historical accident data. In the 5 year period just before construction of the Great Belt Bridge started accidents involving Danish ships in the Great Belt area groundings and collisions have been counted based on these reports. A total of 19 accidents 9 groundings and 10 collisions involving Danish ships were found. A conservative estimate is to double the number of occurring accidents, with twice as many occurring accidents the number of avoided accidents would have been 32 2 19 7 , with a high estimate of 5 times as many accidents the number of avoided.

Adding the number of avoided accidents AA to the observed accidents, an estimate for the total number accidents that would have occurred without the acute accident avoidance effect of VTS is found and converted to a ratio of avoided accidents:. The estimate of Rac relies on an estimate of the fraction of critical situations that turn into accidents FA. Estimating the fraction of critical situations that would evolve into an accident without a VTS present FA is difficult. As the data material behind estimation of FA is limited the calculation of Rac has been subjected to a sensitivity study to illustrate the difference if one or three accidents had been observed instead.

From the reports where VTS did contact the ships it seems reasonable to believe that the true fraction is in this range. By rearranging equation 1 we get:.

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The influence of increased awareness and information level on the number of avoided accidents in a 5 year period is depicted above. Calculations are based on the estimate of Rac. By utilizing equation 2 the total effect of the Great belt VTS system is calculated for various combinations of the acute accident avoidance effect and the effect of increased information and awareness, the low medium and high estimates for Rac is derived in section 4. These numbers are very rough estimates and should be treated as such.

Values for the total effect of VTS can be found by combining equation 2 with the estimate of Rac for various values of Raw , values for the total effect of VTS can be found in Table 2. During the 5 year period 7 accidents have been reported in the VTS area; of these 5 accidents were not detected beforehand by the VTS. Estimate fraction FA of critical situations that will result in an accident without acute VTS intervention.

Estimate the increase in ships that would have been involved in an accident without acute VTS intervention. Choose value of effect Raw of increased awareness and information level Raw. If this is a general trend it shows that when a VTS system is present most of the accidents that occur are from dangerous situations that were not predicted or could not be predicted by the VTS.


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The positive side to this is that when VTS detects a dangerous situation they are most often able to prevent the situation from evolving into an accident. The procedure is based on. The procedure identifies the key number FA which is the fraction of critical situation that would evolve into an accident without VTS interaction. Operators are conservative when they contact ships, that is, some ships are contacted even when the incident would not have evolved into an accident. The estimate of FA contains, among other things, information about this conservatism, FA could hence differ between VTS system and between cultures.

The output from the procedure is the risk reduction from the acute accident avoidance. This number combined with an estimate of the effect of increased information and awareness results in the total effect of the VTS. Debnath, A. Traffic-conflict-based modeling of collision risk in port waters. Singapore: National University of Singapore. Effective Areas of Ships. Journal of Navigation Design of VTS systems for water with bridges.

Ship collision Analysis: The Analysis of Traffic Accidents. Gimsing, N. East Bridge. Copenhagen: Storebltsforbindelsen. Goodwin, E. A Statistical Study of Ship Domains. Goossens, L. Operational benefits and risk reduction of marine accidents. Journal of Navigation 51 3 : Analysis of human and organizational factors in marine traffic risk modeling literature review, s. Hansen, M. Safety ellipsis In preperation. Mazaheri, A. Probabilistic Modeling of Ship Grounding A review of the literature, s.

Olsen, D. Rambll Danmark. Rothblum, A. Safety, Human Error and Marine Safety. In: U. Orlando: U. T Nyman, V. Review of collision and grounding risk analysis methods which can utilize the historical AIS data and traffic patterns in seawaters, s. Trbojevic, V. Risk based methodology for safety improvements in ports. Journal of Hazardous Materials: Ship collision with bridges, review of accidents. In: Ship Collision Analysis: Copenhagen: Balkema.

Wang, N. Journal of Navigation: The procedure is based on incident reports from the VTS and uses these to quantify and combine two different effects of the VTS: The effect of acute accident avoidance and the effect of increased awareness and information level. The procedure is described in general and can easily be applied to quantify the effect of other VTS systems where incident reports are available.

The Great Belt is heavily trafficked and difficult to navigate. Even under such conditions the number of accidents and the number of VTS incident reports are limited. It is therefore evident that any estimates based on the incident reports are uncertain; hence also the estimate of the effect of VTS. The true effect of VTS is probably higher. Those methods are thought to be able to deal with wide ranging situations of collision candidates. However the case of small crossing angle has not been dealt with to a satisfactory extent. This paper introduces a method to estimate the number of collision candidates in a crossing between twowater ways which cross with a small angle.

Prior to this a holistic formulation for considering collision candidates is made and the existing method is reformulated. The method was examined by comparing its results with the results of traffic simulations. This examination suggests the rationality of the model. He used a closed region around a ship which is defined in the same way as Fujii defined. He also used collision diameter defined by Fujii in his formulation. No ratings or reviews yet. Be the first to write a review. Best Selling in Nonfiction See all. The Book of Enoch by Enoch , Paperback Unfreedom of The Press by Mark R.

Levin , Hardcover Save on Nonfiction Trending price is based on prices over last 90 days. The Book of Enoch by R. You may also like. Transportation Boats, Ships Nonfiction Books. Mixed Lot Books. Horror Mixed Lot Books. The test was carried out using the drop hammer machine.

Based on the test results, mean crushing strength and effective crashing distance of plated structures under impact have been evaluated. The results could be useful for structural design of vessels and automobiles against collision accidents. The detailed results were published in Journal of Ship Research, Vol. A total of six double skinned structural models, namely four mild steel models and two aluminum alloy models, have been tested in a quasi-static loading condition, varying the plate thickness and the initial colliding location.

The mild steel models were designed to represent side or bottom structures typical in double hull tankers or LNG carriers. The aluminum alloy models were designed to examine the internal mechanics in collision and grounding of aluminum alloy hull vessels for future designs. A same type indentor with a conical shape regarded as a striking body was used for the tests of all models.

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