Updated Vertical Extent of Collision Damage

Robert Tagg Ship Stability Research Centre, University of Strathclyde, and Herbert Engineering

P. Bartzis Ship Design Laboratory, National Technical University of Athens

Apostolos Papanikolaou Ship Design Laboratory, National Technical University of Athens

Kostas Spyrou Ship Design Laboratory, National Technical University of Athens

Marie Lützen Technical University of Denmark

ABSTRACT: The probabilistic distribution of the vertical extent of collision damage is an important and somewhat controversial component of the proposed IMO harmonized damage stability regulations for cargo and passenger ships. The only pre-existing vertical distribution, currently used in the international cargo ship regulations, was based on a very simplified presumption of bow heights. This paper investigates the development of this damage extent distribution based on three independent methodologies; actual casualty measurements, world fleet bow height statistics, and collision simulation modeling. The results from the three methods are compared, and a proposed distribution for the new harmonized regulations is presented.

1 INTRODUCTION

Modern damage stability regulations use probabilistic distributions of the physical extent of damages in order to evaluate the safety level of ships in the event of a collision casualty. These distributions have typically been based on accumulated statistics from actual collisions.

Current international probabilistic regulations for passenger ships do not use a vertical extent of damage distribution and instead assume an unlimited vertical extent of damage. The current international damage stability regulations for cargo ships use an assumed distribution for the maximum vertical extent of damage. Since source data for the vertical distribution was not available, this cargo ship distribution was based on a simple estimate of the average bow height from striking ships.

The International Maritime Organization (IMO) is currently seeking to harmonize the damage stability regulations for all types of vessels and efforts are underway to harmonize and update the passenger and cargo ship regulations. Since the vertical distribution of damage extents can have a major impact on the design of future ships there has been

much discussion and some controversy regarding this subject at the IMO.

In Europe the HARDER initiative, begun in 2000, is concurrently working to systematically investigate the validity, robustness, consistency, and impact of all aspects of the harmonized probabilistic damage stability regulations. The HARDER project, together with contributions from research outside Europe, have made investigations into the distribution of the vertical extent of damage with the hope of contributing to the efforts of the harmonization effort at the IMO.

This paper presents the results of the investigations of the HARDER project, and their external partners, with respect to the distribution of the vertical extent of damage.

2 BACKGROUND

2.1 International Damage Stability Regulations International regulations for the damage stability of passenger ships have been developed as part of the International Maritimes Organizations (IMO, and formerly IMCO) conferences on the Safety of Life at Sea (SOLAS). The first such conference began in

1914, convened largely in response to the loss of the Titanic and over 1500 lives in 1912, established subdivision and lifesaving standards for passenger ships. The conference regulations were never officially adopted by the participating countries, primarily due to the onset of World War I. The 1929 SOLAS conference proposed a “Factor of Subdivision” and “Criterion of Service” regulations for passenger ships which in effect established a maximum bulkhead spacing based on the ship length and the number of passengers. These regulations considered sinking, or floodable length, only and contained no requirement for flooded stability.

Since the original 1929 conference there have been numerous other SOLAS conferences, each of which have approved amendments and extension to the original regulations.

2.2 Probabilistic Damage Survivability Regulations The first international probabilistic based regulations, Resolution A.265, Reference [1], were developed for passenger ships and adopted by the IMO in 1971. These regulations are an optional alternative to the deterministic passenger ship regulations in the SOLAS convention. This work on the passenger regulations was followed by the adoption, in 1990, of subdivision and damage stability rules for dry cargo ships, Reference [2], also based on probabilistic principles and similar to the Resolution A. 265 regulations. While the probabilistic rules for cargo ships are generally based on the same overall principles and damage statistics as the passenger ship rules, there are significant differences in the two regulations.

One specific difference between the passenger and the cargo ship probabilistic regulations is the treatment of the vertical extent of damage. Where the Resolution A. 265 [1] regulations for passenger ships use an unlimited vertical extent of damage, the SOLAS Part B-1 Regulations for cargo ships [2] use a probability distribution for the vertical extent of damage.

The development of a rational probability distribution of the vertical extent of damage is the subject of this paper.

2.3 Recent IMO Developments In 1995 the IMO Maritime Safety Committee initiated an effort to harmonize the passenger ship and dry cargo ship regulations into a single standard, which might eventually be extended to all types of vessels covered by IMO regulations. Also in 1995, the Sub-Committee on Stability, Load lines, and Fishing Vessel Safety (SLF) favourably reviewed a

study submitted by the United States delegation, Reference [3], which presented an alternative probability for the vertical extent of damage based on a statistical analysis, not of actual damage measurement, but rather of the bow heights of all ships in the world fleet. During the most recent sessions of the SLF it has become clear that harmonizing the vertical extent of damage probability between the passenger and cargo ship regulations will be difficult. The cargo ship regulations include a somewhat more liberal formulation whose maximum value was based on the minimum required bow height from the Loadline Convention (ICLL’66). The current passenger regulations, both deterministic and probabilistic, are based on an unlimited vertical extent of damage. While the SDS working group unanimously endorsed the more conservative vertical damage probability for passenger ships, similar to the formulation presented in the US paper, Reference [3], some nations do not support using this new vertical damage distribution for cargo ships.

Figure 1 shows the two alternative formulations of the factor “v” for a 200m long ship. The factor “v” represents the probability that damage will not exceed a given height “H” above the waterline. This factor is also a function of the Subdivision Length (Ls) and somewhat different distributions could be shown for any specific Ls. These formulations are labeled “SLF 43” which is the formulation taken from the current draft harmonized SOLAS Chapter II-1 [4] and was based on the data from the US bow height study [3], and “B-1” which is the formulation from the current cargo ship regulations [2].

Vertical Extent of Damage - Ls = 200m

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Fig. 1 – Alternative factor “v” formulations for a ship length of 200m

2.4 Project HARDER The HARDER initiative, begun in Europe in 2000, was designed to systematically investigate the validity, robustness, consistency, and impact of all aspects of the harmonized probabilistic damage stability regulations on the safety of existing ships and on the design evolution of new ship design concepts for various types of cargo and passenger ships. The extensive research resulting from the HARDER project will provide a strong technical basis for the work being carried out by the SLF Sub-Committee on harmonization.

This paper summarizes work directly from the HARDER Project as well as research sponsored by the U.S. Coast Guard in support of the HARDER Project. The paper concludes with a proposed vertical extent distribution offered in support of the harmonization work being carried out by the SLF Sub-Committee, and it is hoped that it might contribute to formulating a vertical extent of damage probability that can be used in the harmonized regulations for both cargo and passenger ships.

3 APPROACH SELECTED

The approach presented here seeks to independently develop the probabilistic vertical extent of damage distributions using three different methodologies:

3.1 Casualty Statistics A database of actual collision statistics is used to construct the distribution of the vertical extent of damage. The original IMO database developed for resolution A.265 is used and is supplemented with data from more recent casualties. The IMO original database has traditionally been considered inadequate to develop the probability distributions for the vertical extent of damage due to the scarcity of records that contain the full descriptions of vertical extent. For this study several assumptions are used to expand and extrapolate this data. This work has been primarily sponsored by the U.S. Coast Guard.

3.2 Bow Height Statistics Using a methodology similar to the US bow height study [3], the National Technical University of Athens (NTUA), as part of the HARDER Project, performed a statistical analysis of bow heights of existing ships. Individual ships characteristics were taken from the March 2000, Fairplay Ship Database, which contains information for over 35,000 ships.

In addition also DTU has performed a bow height analysis based on vessels in the ship database from Lloyds’ Maritime Information Services, London (LMIS).

3.3 Collision Simulation Modeling As part of the HARDER Project the Technical University of Denmark (DTU) performed an analysis of the probability of damage extents using collisions simulation modeling. This work consisted of two tasks:

• The development of collisions energy

distributions based collision scenarios, generic worldwide equivalent ship traffic routes, and different ship types.

• The development of damage extent probability distributions based on collision dynamics and the assumed distribution of collision scenarios.

All three of these methodologies result in a presumed distribution of the vertical extent of damage. The overall approach of this paper is to present the three types of analysis, compare and contrast the results from the three methods, and to propose a unified distribution, which is offered as a basis for modified damage survivability regulations.

4 VERTICAL DAMAGE EXTENT FROM CASUALTY STASTICS

4.1 Database In order to develop the specific damage probability statistics for the 1971 passenger ship regulations, member nations of the IMO were invited to submit “damage cards”. Each of these damage cards represented specific technical information about a ship casualty. The bulk of these data were collected for casualties occurring in the 1950’s and 1960’s. Two other sets of damage statistics are used in this study to supplement these statistics with more modern data. The three sets of damage data used for developing the vertical extent statistics are as follows:

4.1.1 Original IMO Damage Statistics Summary tables for all of the original 352 collision damage cards were received from IMO. As indicated in the original analysis of this damage data as part of developing the regulations for resolution A.265, this data represents approximately 297 collision records that contain sufficient information regarding both longitudinal and transverse damage extents to be used in the statistical analysis.

4.1.2 Lloyd’s Register Ship Repair Statistics Data from 133 ships damaged in collisions between 1972 and 1982 have been developed and entered in a database. Individual collision damage cases were pre-selected from the Lloyd’s Register casualty database. The data for each individual case was collected directly from the repair survey data on microfilm at Lloyds Register. In cases where the specific measurements and recordings of the damage extents were not made at the time of the casualty, but detailed records of the ship repair were available, reasonable estimates of the damage extents were made.

4.1.3 Updated IMO Damage Statistics The data received from the IMO consists of damage cards submitted to the SLF Sub-Committee representing 41 additional ship casualties. Of the 41 damage cards (representing all types of casualties including groundings and other causes) there were only 12 valid collision cases with sufficient detail to supplement the existing database.

4.1.4 Combined Database With respect to the vertical extent of damage the following fields from the database of the struck vessel are of particular interest:

• L – The length between particulars of the struck

vessel, in meters. • B – The molded breadth of the struck vessel, in

meters. • D – The molded depth of the struck vessel, in

meters. • d – The midship molded draft of the struck

vessel in meters. • Z – The vertical distance from the baseline to the

lowest point of damage, in meters, • h – The maximum vertical damage height

measured up from Z, in meters • b – The maximum transverse penetration of

damage, in meters.

And for the striking vessel: • Ls – The length between particulars of the

striking vessel, in meters. • Bs – The molded breadth of the striking vessel,

in meters. • Ds – The molded depth of the striking vessel, in

meters. • ds – The forward molded draft of the striking

vessel in meters.

4.2 Vertical Extent of Damage Statistics The original IMO database has traditionally been considered inadequate to develop the probabilities of the vertical extent of damage, primarily do the lack of vertical extent data recorded in the database.

This section of the paper uses the original IMO database together with the new data from the Lloyd’s Register records and from supplemental IMO data. This data has been re-examined to determine if any meaningful data can be extracted with respect to the vertical extent of damage. In general, an examination of the data for “Z” and “h” in the database, representing the location of the bottom and top of the vertical extent of damage respectively, results in the characterization of the

vertical extent of damage into one of the following four damage types:

1 2 3 4

h

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Fig. 2 – Damage Types

The complete distribution of the vertical extent of damage is known directly for damage Type 4 only. For Types 1 through 3 the distribution of the vertical extent of damage is not completely defined since it extends beyond the limits of the struck vessel.

For this study the focus is on developing the upper limit of vertical extent, and in this respect the Types 3 and 4 both provide meaningful data for the upper limit (i.e. both have an upper limit of damage which can be found from summing Z and h together). There are 122 records in the combined database for damages of Types 3 and 4.

For Type 1 and 2 damages, nothing can be deduced about the upper vertical limit from the damage data for the struck vessel since the damage extends beyond the full depth of the vessel. However it has been presumed in these cases that the struck vessel was deeper, or the striking vessel was floating at a lighter draft at the time of the casualty, and damage would have been sustained up to the bow height of the striking vessel.

d D

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Fig. 3 – Development of Vertical Extent of Damage

The combined database contains 94 damages of Types 1 and 2, and which also include the striking vessel depth and forward draught information. This study proposes to develop statistics on the vertical extent of damage by constructing the presumed upper vertical extent as indicated in Figure 3. Data on the actual bow heights of the striking vessels is not known, however this bow height can be approximated from the depth of the striking ship, the forward draft at the time of the casualty, and a reasonable assumption for raised forecastle deck height. The previous bow height study, Reference [3], have indicated that about half of the world fleet of large ships have raised forecastle decks. Assuming an average height of 3m, and applying this on average to 50% of the ships, for this study all Type 1 and 2 damages use the following formula to develop the maximum vertical extent of damage:

H = DS – dS + 1.5m

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4.3 Results and Analysis from Casualty Statistics

4.3.1 Results Figure 4 indicates the resulting cumulative

probability of the maximum vertical extent of damage, as well as the individual data for the two groups of damage types. There are 216 damage records in the combined database that can provide data on the vertical extent. There are 94 of Types 1 and 2, which use the derived bow height formulation as developed in the previous section, and 122 damages of Types 3 and 4.

Fig. 4 – Maximum Vertical Extent of Damage

Figure 5 is a plot of all of the 216 damage records that contain data for the vertical extent of damage, plus the mean damage height as a function of ship length, along with the ± 95% confidence limits for the mean. Note that the overall mean damage height is about 4 meters and the mean height is gradually decreasing with ship length. It should also be noted that this data includes a significant portion (more then 20%) of casualties, which indicate that the uppermost vertical extent of damage is below the waterline. The decrease in the mean height for increasing ship length is mainly due to damage below the waterline for larger vessels. The previous bow height study, Reference [3], as well as the updated bow height study following, do not include any such data since it was assumed that damage always occurred up to the maximum height of the striking bow. It is presumed that damage of this type occurs when the upper portion of the striking bow collapses and does not cause any actual penetration in the struck ship, while the lower portion of the stem of the striking ship (often the

bulbous bow) causes the penetration damage in the struck ship below the waterline, or when the striking vessel is much higher then the struck vessel.

Ship Length vs Damage Height

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Fig. 5 – All Vertical Damages vs. Ship Length

4.3.2 Analysis of Results The resulting vertical extent data presented in Figures 4 and 5 have been analyzed in order to understand the underlying trends with a view toward developing a modified probability distribution for

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Cumulative Probability

the vertical distribution of damage heights, factor “v”.

Vertical Extent of Damage

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The combination of vertical extent data for all ship lengths was examined. It can be seen in Figure 6 below, that this data fits a normal distribution extremely well with a mean of about 4 meters and a standard deviation of about 4.8 meters.

Fig. 6 – Normal Cumulative Distribution of Damage Heights

When examining the plot of damage heights versus ship length (see Figure 5), in addition to the generally decreasing mean damage height, the data generally indicates a greater spread in the range, or deviation from the mean, of the height data for increasing ship length. In order to quantify the general trend of these vertical extents of damage for various ship lengths, a spread of linear regression lines has been fit to the data, as shown in Figure 7. The location of the fixed axis point was selected based on trial and error to provide a good fit for the linear functions. For each line the percentage indicated in the legend represents the percentage of damage height data points below each line.

Ship Length vs Damage Height

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Fig. 7 – Trends in Damage Heights vs. Ship Length

The data from the trend lines in Figure 7 can then be cross-plotted to yield the distributions of the damage

height for individual ship lengths. Figure 8 indicates these cross-plots for ship lengths from 50 meters to 250 meters. As indicated in Figure 6 for the summary data for all lengths, each of the distributions in Figure 7 are also approximately fit normal cumulative distributions. However, there is a significant uncertainty in the assumed curves.

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Fig. 8 – Damage Height Distributions for Various Ship Lengths

5 VERTICAL DAMAGE EXTENT FROM BOW HEIGHT STATISTICS

5.1 Data analysis and results One of the Tasks in the HARDER project was to perform a statistical analysis of the bow heights of the merchant ships that are currently in operation. The result of this analysis could be used as a basis for establishing a new formula for the calculation of the vertical extent of damage probability factor “v” for side-collision damages. The analysis has been performed on the basis of the well-known Fairplay® database, taking into account ships over 500 grt and over 50m length, with fishing vessels excluded. The main intention of this study was to determine the region (by identifying its extreme values) in which the new “v” formula should fall in. Below are reported the basic steps that have been taken in order to fulfill this objective. The complete results can be found in [5].

5.1.1 Distribution of ships and lengths The percentage distribution of each ship type in the whole database and the distribution of ships vs. overall length LOA have been identified at the initial stage of the study. These distributions are shown respectively in Figs. 9 and 10. The ships were

grouped into 10 major categories with the largest groups being the bulk-carriers, the tankers and the dry cargo ships. In terms of length, we note the existence of two peaks, one around the 80m and the other around the 180m. The number of ships in the database exceeds 35000. Data filtering was necessary to account for inconsistencies or incompleteness of the registered data for some ships. The analysis was finally applied on 31585 ships. Vertical Extent of Damage

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Fig. 9 – Considered distribution of ships

Fig. 10 – Distribution of ship lengths

5.1.2 Distribution of bow heights The distribution of bow heights above the waterline has been derived as a function of the subdivision length S . For each ship in the database we have identified a minimum and a maximum operating bow height above the waterline. For the minimum bow height we assumed that

maxmin

L

TDepthDraftDepthH −=−= . In addition, we have considered the existence of a forecastle with a height of up to 3.0 m and we have derived the minimum (as well as later the maximum) bow height considering three different cases: • Forecastle height of the entire fleet equals 3.0m, • Only 50% of the ships are having a forecastle,

which is equivalent with adding 1.5 m to the above , and min

• All ships are without forecastle. H

More critical than the minimum bow height is the definition of the maximum bow height since this will determine the probable uppermost height of damage and thus the formula that will correspond to the “v”=1 value of the probability factor. As the “worst” case scenario, we have assumed, in the first instance, that the minimum operating draft for all ships can be determined by extrapolating the MARPOL requirement for tankers, that sets:

S , trim S , and stern draft such that the propeller is always immersed. Any other draft should fall between the two extremes, as defined by min and max . The maximum bow height is given from the expression: minmax . To this value should be added the forecastle height depending on the earlier stated assumptions.

LmT 02.00.2min += L015.0≤

T TTDepthH −=

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The striking ship has been assumed to operate with a probability of 50% at each of the two, so defined, extreme drafts. Although this simplifies the analysis, it may not be very realistic for certain ship types and it may lead to overly conservative results especially for ships like passenger vessels or containerships where the probability of operation with a ballast draft as above defined should be considered much smaller than 50% on the basis of their operational profile. However, the presently adopted approach aims to determine the likely extreme values, which is of particular value to this study. This important matter is discussed also later when considering the final proposal of the “v” formula.

5.1.3 Cumulative percentage of bow height A characteristic example of the obtained bow height scatter of data is shown in Fig. 11 for passenger/ferry vessels. The cumulative percentage distribution of all bow heights (including minimum and maximum) is shown in Fig 12. It is noticed that the relationship is not too far from linear between the 10% and 90% cumulative percentage, however the two extreme ranges show a more sharp change of bow height.

Fig. 11 – Bow heights for passenger/ferries with

forecastle

5.1.4 The calculation of “v” The cumulative percentage distribution of bow heights for all potentially colliding ships is the basis for calculating the vertical extent of damage factor “v”. This factor should depend directly on the subdivision length and the height of any horizontal subdivision above the waterline restricting the extent of a possible damage. As the “v” factor represents the probability that the vertical extent of damage

will not occur beyond a specified height of horizontal subdivision above d, it connects with the cumulative percentage distribution of all possible bow heights up to some height above waterline. Therefore, in order to derive a specific formula for “v”, we have determined the relation of min-max bow heights vs. cumulative percentage distribution values for all ships, considering their dependence on the subdivision length.

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5.1.5 Relative size of colliding ships A basic principle behind the existing criteria for the specification of the vertical extent of damage is that

the two ships involved in a collision are of

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approximately equal size. Considering the extremely large and extremely small vessels, it may be deduced that it is more likely that the larger ships will be hit by smaller vessels and vice versa. In order to deduce the impact of a possible variation of the size of the colliding ships, a sensitivity analysis has been performed, considering the statistical relationship between the respective lengths of possibly colliding ships within certain length margin of up to ± 40m. It has been proved that it is not necessary to quantify precisely the relationship between the respective lengths of the colliding ships The cumulative percentage distribution of maximum bow heights for increments of ± 20m is shown Figure 12. The data is here fitted by spline curves, and forced to have a minimum bow height of zero for 0%. The cumulative percentage distribution of bow heights for all vessels is shown in Figure 13.

Fig. 12 – Cumulative Percentage Distribution

of Maximum Bow Heights ± 20m Length Increment.

Fig. 13 – Cumulative percentage distribution of

bow heights for all vessels

5.1.6 Comparison of formulae for “v” The derived formulae for the vertical extent of damage probabilistic factor “v”, considering the various scenarios with respect to the assumed forecastle deck are outlined in the following:

Fig. 14 – The calculated extreme values of the

probabilistic factor “v” and comparison with existing formulae. 1. Scenario without Forecastle Deck: “v”=0.00 (Hmin-d) = 1.2m “v”=1.00 (Hmax-d) = 0.12 LS (1-LS/500) ( ≤ 15m) 2. Scenario for 3m Forecastle Deck: “v”=0.00 (Hmin-d) = 1.8m “v”=1.00 (Hmax-d) = 0.144 LS (1-LS/500) ( ≤ 18m) 3. Scenario for 1.5m Forecastle Deck: “v”=0.00 (Hmin-d) = 1.5m “v”=1.00 (Hmax-d) = 0.132 LS (1-LS/500)( ≤ 16.5m) These formulae have been plotted in Fig. 14, along with the corresponding formulae derived by an earlier bow height study presented in SLF 39/5/3 by the U.S.A.:

4. SLF 39/5/3 (1994) submitted by the USA [3]: “v”=0.00 (Hmin-d) = 1.2m “v”=1.00 (Hmax-d) = 0.104 LS (1-LS/500) ( ≤ 13m) Finally it is of interest to remember the corresponding SLF 42/3 formulae, practically reflecting the current consensus among the IMO-SLF member states with respect to the i formulation in future harmonised damage stability provisions, and the current formulation of SOLAS Part B-1 provisions pertaining to the damage stability of dry cargo ships.

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5. SLF 42/3 (1998) formulae of the SDS Working Group [6]: “v”=0.00 (Hmin-d)=0.012 LS ( ≤ 3m) “v”=1.00 (Hmax-d)=0.04 LS +3 ( ≤ 11m)

Note, this formulation has later been changed in SLF 43/3/2 [4].

SLF 39/5/3 (USA,1994) formulae – max: vi = 1.00 (Hmax-d)= 0.104LS(1-LS/500),⇐ 13 m

SLF 39/5/3 (USA,1994) formulae – min: vi = 0.00 (Hmin-d)= 1.2 m Scenario for 0m F’c’sle Deck-max vi = 1.00 (Hmax-d)= 0.12LS(1-LS/500),⇐ 15 m Scenario for 0m F’c’sle Deck-min vi = 0.00 (Hmin-d)= 1.2 m Scenario for 3m F’c’sle Deck-max vi = 1.00 (Hmax-d)= 0.144LS(1-LS/500),⇐ 18 m Scenario for 3m F’c’sle Deck-min vi = 0.00 (Hmin-d)= 1.8 m

6. SOLAS Part B-1 formulae for dry cargo ships [2]: “v”=0.00 (Hmin-d) = 0 “v”=1.00 (Hmax-d) = 0.056 LS (1-LS/500) Struck vessel:

• Main particulars and structural design given Route / Area: Striking vessel: • Type • Length • Loading condition Collision scenario • Striking location • Collision angle • Velocity of struck vessel • Velocity of striking vessel Calculation • Energy to be absorbed (external dynamics) • Energy absorbed by the structure (internal mechanics)

⇒ Compare energy ⇒ Estimate damage

for (LS 250m) ≤ (Hmax-d) 7m, for LS > 250m, whichever is less

5.2 Discussion of Results The minimum vertical extent of damage is varying between 1.2m (with no forecastle) and 1.8m (with 3m forecastle). This is in agreement with the SLF 39/5/3 formulation, corresponding to the zero forecastle deck height scenario. These values are in between the current SOLAS B-1 provisions for dry cargo ships and the proposed SLF 43/3/2 provisions.

For ships over 250m in length the maximum vertical extent of damage is varying between 15m (no forecastle) and 18m (with 3m forecastle), standing about 2.0m higher than the corresponding SLF 39/5/3 formulation. This is explained by the fact that present sample data consist of a higher percentage of large ships, compared to the U.S bow height study data. The obtained values are also significantly higher than the current SOLAS B-1 provisions for the large dry cargo ships (more than double as high!) and the proposed SLF 43/3/2 provisions.

The present results clearly indicate that the current

SOLAS B-1 formulation is insufficient as to the assumed vertical extent of damage, especially for large ships, therefore revision of the formula is required (see, SLF 43/3/2). The results of the present statistical analysis will be compared with the damage statistical data analysis reported in the previous sections and further elaborated if a practical proposal of a new “v” formulation is to be reached.

6 VERTICAL DAMAGE EXTENT FROM SIMULATION OF SHIP-SHIP COLLISIONS

6.1 Monte Carlo Simulation Model In this section a short description of the collision simulation model is given. Given that a collision occurs, and the main particulars and the structural design of the struck vessel are known, possible collisions situations can be established by knowledge of the particular collision geographical location. If information about the specific ship route is given, the distribution of striking vessels and collision scenario parameters such as the collision angle, the striking location and

the velocity of both of the involved vessels can be determined, see Fig. 15.

Fig. 15 - Simulation diagram The calculation of the collision is separated into an external and an internal analysis. The external analysis or the external dynamics deals with the movements of the two vessels and the interaction with the surrounding water during the collision. The aim of the external dynamics is to estimate the fraction of the kinetic energy that is released for crushing of the structure. The present model uses a procedure based on an analytical method where the energy is expressed in closed formed solutions (Pedersen and Zhang, [7]) and where the hydrodynamic forces are approximated by simple added mass coefficients. The internal analysis or the internal mechanics is dealing with the deformation of the side of the struck vessels and the bow of the striking vessel. For simplification, the bow of the striking vessel is here considered to be rigid, which means that all energy is assumed absorbed in the side of the struck vessel. By incrementing the bow into the side of the struck vessel and calculating the resistance at each step, a relation between the penetration into the vessel and the absorbed energy is determined (Lützen, Simonsen and Pedersen [8]). The damage to the struck vessel can now be determined by comparison of the results from the external and internal analyses.

In practice, these calculations are carried out by a Monte Carlo simulation where the calculation is carried out for many different choices of striking vessels and collision scenarios to establish probability distribution for the damage at the struck vessel.

6.2 The Striking Vessel A database from Lloyds’ Maritime Information Services, London (LMIS) containing ship characteristics for the world fleet has been used for the analysis. The database consist of approx. 87,000 ships in service all over the world and is the complete database of all ships in service with an IMO number. In order to carry out the final collision analysis it is decided to leave out some types of vessels of the study because their number are either very small or their movement patterns are atypical. The ships left out are e.g. sailing vessels, twin hull/hydrofoil ships, drilling vessels, tugs, supply vessels and dredgers. Thus, the remaining vessels can be divided into 10 types: bulk carriers, cargo vessels, chemical tankers, container vessels, gas tankers, passenger vessels, reefer vessels, ro-ro vessels, tankers and fishing vessels. For the study of striking vessels it seems reasonable to leave out all fishing vessels. Even that these vessels normally are sailing in restricted and trafficked waters their velocity are slow and maneuvers atypical which in most cases will make them to be the struck vessel. Also vessel with a length below 50 m are left out, which gives the final number of vessel of approx. 41,000 and the composition of the database is then generally similar to the Fairplay database used in the previous section.

The database has been analysed to derive distributions of the ship types in the world fleet and to describe the distribution of length within each type. Furthermore, the database has been used to find empirical relations for lengths versus breadth, depth, displacement and service speed for each type of vessel, see Clausen et. al [9].

The percentage distributions of types of striking vessels and lengths of all vessels together are shown

in Fig. 16 and 17. Fig. 16 - Percentage distribution of ship types

0%

4%

8%

12%

16%

50 70 90 110

130

150

170

190

210

230

250

270

290

310

330

350

370

390

Length of striking vessel [m]

Fig. 17 - Percentage distribution of lengths of all vessels Unfortunately, the database contains no information about bow heights, but the following assumption has been made about raised forecastles:

• It is assumed that half of the world fleet of large

ships has raised forecastles deck with an average height of 3m. This is modeled by adding an equivalent height of 1.5m to all vessels.

To determine the bow height above water level the draught of the striking vessels is required. Here three levels of draughts are used: • Full load:

Maximum load line draught Tmax• Ballast:

The ballast draught for all vessels are taken to be the minimum operational draught specified by MARPOL Tmin = 2.0 m + 0.025L, where L is the length of the striking vessel.

• Partial draught: Tpart = Tmin + 0.6*(Tmax- Tmin)

Furthermore, the bow heights have been calculated with no trim. The assumptions for the distribution between the different draughts for specific ship types are:

0%

10%

20%

30%

40%

Bulk Carr

ier

Cargo v

essels

Chemica

l carr

iers

Contai

ner v

essels

Gas Carr

iers

Reefer

vesse

ls

Ro-Ro v

essels

Passen

ger ve

ssels

Tanke

rs

Full Partly Ballast Tankers, Bulk carriers 50% 0% 50% Cargo vessels, Reefers 40% 40% 20% Ro-Ro, Container vessels 75% 25% 0% Passenger vessels 100% 0% 0%

The actual bow height of the striking vessels can now be approximated from the depth, the draught at

the time of collision and the assumed raised forecastle. Taking into account the distribution of types and lengths of vessels in the world fleet the distribution of bow heights can be calculated. The cumulative percentage distribution of bow heights is shown in Fig. 18.

Vertical Extent of Damage

0

5

10

15

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Cumulative Probability

Hei

ght A

bove

Wat

erlin

e (m

)

Piecewise Linear No. 1Piecewise Linear No. 2Exponential e^(2.5x)SLF 43 (L=200m)B-1 (L=200m)

Fig. 18 - Cumulative percentage distribution of bow heights

7 COMPARISON OF RESULTS FROM THE THREE METHODS

Figure 19 shows the cumulative distribution of the maximum vertical extent of damage from the three methodologies described in Section 4, 5 and 6 of this paper. The vertical extents from the Bow Height Statistics (from Section 5) and the Striking Vessel Simulations (from Section 6) are somewhat similar since they are both essentially derived from databases of the world shipping fleet. The Casualty Statistics distribution (from Section 4) is a completely independent derivation since it is not based on ships in service, but rather on actual collision statistics.

It should be noted that the Bow Height Statistics (from Section 5) were developed based on conservative assumptions for a “worst” case scenario. It is anticipated that a future reanalysis for the most likely scenario will yield results similar to those indicated for the Striking Vessel Simulations (from Section 6).

In comparing the distribution from the Casualty Statistics distribution (from Section 4) with the Bow Height Statistics (from Section 5) it is encouraging to note the close correlation of results from completely independent methodologies. There is some divergence of the distribution in the lower cumulative probability range, between 0% and 40%,

but as discussed in Section 4 this is believed to be due to the actual occurrence of damage below the waterline, which cannot be accounted for with bow height derivations for vertical extent.

-10

-5

0

5

10

15

20

0% 20% 40% 60% 80% 100%

Cumulative Percentage

Bow

Hei

ghts

[m]

Casualty statisticsBow Height Statistics (Fairplay database)Striking Vessel Simulations (LMIS database)

0

5

10

15

20

25

0% 20% 40% 60% 80% 100%

Cumulative Percentage

Bow

hei

ght [

m]

Figure 19 - Cumulative percentage of bow heights. Comparison of data from world fleet data and damage database.

8 CONCLUSIONS AND PROPOSAL FOR A NEW VERTICAL DISTRIBUTION

8.1 Proposed “v” formulations Figure 20 presents three possible alternatives for a new formulation of the “v” factor, which correlate reasonably well to the distribution presented in Figure 19. The lower bound at 0% has been set at 1 to 2 meters in keeping with the generally agreed principle that the regulations should not encourage inherently dangerous horizontal subdivision near the waterline. Also indicated on figure 20 are the two current distributions of the factor “v” (see figure 1) for a 200-meter ship based on the current cargo ship regulations (SOLAS, Part B-1), and for current proposal for the harmonized cargo and passenger ship regulations (SLF 43/3/2).

Fig. 20 Proposals for alternative “v” formulations

8.2 Dependence on Struck Ship Length It should be noted that these two proposed distributions are not dependent upon the length of the struck vessel, but rather represent the distributions of the damage from all potential striking vessels. The previous criteria have assumed that the vertical damage extents, like the longitudinal and transverse damage extents are somehow related to the length of the struck ship. This implies that a given ship is more likely to be struck by ships somewhat nearer it’s own size, rather then by random ships from the distribution of the world fleet.

Although the distributions in figure 19, based on the Bow Height Statistics from Section 5 and the Striking Vessel Simulations from Section 6, use purely random distributions of striking ships, the Casualty Statistics from Section 4 do confirm some level of dependency between the struck and striking vessel sizes. (See figures 7 and 8.)

Figure 21 shows this relationship between the struck and striking ships for all collisions in the HARDER database for which the lengths of both of the ships in a specific collision are known. It can be observed that there is a general trend for small ships to be struck by small ships, and large ships to be struck by large ships. However, for a given length of struck ship this is not a near one-to-one relationship, and the band of striking ship lengths is quite large. This suggest that, while the data from both Section 5 and 6 could be reanalyzed to include some dependency on the lengths of the struck and striking ships, the one-to-one banded relationship that was initially assumed for the Section 5 data analysis (Section 5.1.5) has lead to very conservative values of maximum vertical extent, especially for the longer ships.

Figure 21 – Struck versus Striking Ship

Lengths (524 collision records)

8.3 Observations and Conclusions The following observations and conclusions are offered regarding the vertical extent of damage distribution:

• Very similar probability distributions of the

maximum extent of vertical damage have been derived using fundamentally different methodologies.

• The proposed formulations for the factor “v”,

derived from these new distributions, are significantly different from either of the linear distributions currently under consideration for the harmonized damage stability regulations at the IMO.

• The proposed vertical extent heights for the high

end of the distribution range (over 80% probability) are equal to or even greater than the SLF proposal, based on the previous bow height study Ref [3]; confirming that the current B-1 formulation is far too liberal (low) in this region of the distribution.

• The proposed vertical extent heights for the mid-

level ranges of the distribution (40% to 70%) have cumulative probabilities that are fairly close to the B-1 cargo ship regulations.

• It is possible that the resulting distributions may

contribute to resolving the current controversies involving the vertical extent of damage at the IMO, since these mid-level ranges (40% to 70% cumulative probability) correspond to critical horizontal deck heights levels of about 3 to 6 meters above the waterline, a range critical to the design of many modern cargo Ro-Ro ships.

•

0

50

100

150

200

250

300

0 50 100 150 200 250 300

Struck Ship Length (m)

Strik

ing

Ship

Len

gth

9m0

9 ACKNOWLEDGEMENTS

The work presented in this paper was carried out by the University of Strathclyde, the National Technical University of Athens University, and Technical University of Denmark as part of the European HARDER research project; and also in part sponsored by a United States Coast Guard research project conducted by Herbert Engineering in San Francisco.

10 REFERENCES

1. IMO Resolution A.265 (VIII), Regulations on

Subdivision and Stability of Passenger Ships as an equivalent to Part B of Chapter II of the International Convention for the Safety of Life at Sea

2. SOLAS, Chapter II, Part B-1, “Subdivision and Damage Stability of Cargo Ships”

3. SLF 39/5/3 – “Harmonization of Damage

Stability Provisions in IMO Instruments – Statistical Bow Height Study and the Probabilistic Vertical Extent of Damage”, Submitted by the United States, 16 December 1994.

4. IMO-SLF “Development of Revised SOLAS

Chapter II-1 Parts A, B, and B-1 – Report of the SDS Working Group”, Submitted by the Chairman of the SDS Working Group, SLF 43/3/2, 2000.

5. Bartzis, P. & Papanikolaou, A.: Updated Bow

Height Statistics & Revised Formulation of Vertical Extent of Damage. Deliverable D1.2 of WP1. Final report of NTUA-SDL to the HARDER Consortium, 15 March 2001.

6. IMO-SLF “Development of Revised SOLAS

Chapter II-1 Parts A, B, and B-1 – Report of the SDS Working Group”, Submitted by the Chairman of the SDS Working Group, SLF 42/3/2, 1998.

7. Pedersen, P. T. & Zhang, S.: On Impact

Mechanics in Ship Collisions, Marine Structures No.11, 1998.

8. Lützen M., Simonsen B.C. and Pedersen P.T..: Rapid Prediction of Damage to struck and Striking Vessels in a Collision Event, Proceedings of Ship Structures for the Millennium: Supporting Quality in Shipbuilding, Arlington, June 2000.

9. Clausen H.B, Lützen M., Friis-Hansen A.,

Bjørneboe N: Bayesian and Neural Networks for Preliminary Ship Design, The Eight International Symposium on Practical Design of Ships and Other Floating Structures (PRADS), Shanghai, China, September 2001.