International Journal

on Marine Navigation

and Safety of Sea Transportation

Volume 6

Number 1

March 2012

1 INTRODUCTION

Ship-ship collisions are rare events that potentially

might have disastrous impact on the environment,

human life and economics. To find effective risk

mitigating measures the risk must be reliably as-

sessed. Proper assessment of the ship-ship collision

risk requires understanding on the complicated chain

of events. Simplifying assumptions on certain pa-

rameters are necessary as the research in this field is

not comprehensive. Especially, the important link

between the encounter of the colliding vessels and

the actual moment of impact contain obvious uncer-

tainties.

In this paper a case study is conducted to compare

models found in literature for dynamic parameters in

collision scenario. The case study concerns colli-

sions in which the struck vessel is an oil tanker. The

traffic is simulated by means of a Monte Carlo simu-

lation based on AIS data to obtain realistic encounter

scenarios for the analyzed area. The assumptions are

then applied to encounter scenario to obtain the

complete impact scenario. The deformation energy

released in the collision is calculated by analytic

method (Zhang 1999) and the damage extents are es-

timated with simple formula to normalize the results

of deformation energy calculations. The effects of

assumptions for dynamic parameters to collision risk

are discussed.

2 COLLISION RISK EVALUATION

2.1 Concept of risk

Risk is a product of probability p and consequences

c and is expressed with (Kujala et al, 2010)

∑

⋅=

(1)

where i denotes certain chain of events or scenario.

2.2 Tanker Collisions

In case of ship-ship collisions scenario is a function

of vast number of static and dynamic parameters.

The parameters used in this study are listed in Ta-

ble 1.

Uncertainty in Analytical Collision Dynamics

Model Due to Assumptions in Dynamic

Parameters

K. Ståhlberg, F. Goerlandt, J. Montewka* & P. Kujala

Aalto University, School of Engineering, Department of Applied Mechanics, Marine

Technology, Espoo, Finland

* Aalto University, School of Engineering, Marine Technology, Espoo, Finland

Maritime University of Szczecin, Institute of Marine Traffic Engineering, Poland

ABSTRACT: The collision dynamics model is a vital part in maritime risk analysis. Different models have

been introduced since Minorsky first presented collision dynamics model. Lately, increased computing capac-

ity has led to development of more sophisticated models. Although the dynamics of ship collisions have been

studied and understanding on the affecting factors is increased, there are many assumptions required to com-

plete the analysis. The uncertainty in the dynamic parameters due to assumptions is not often considered.

In this paper a case study is conducted to show how input models for dynamic parameters affect the results of

collision energy calculations and thus probability of an oil spill. The released deformation energy in collision

is estimated by the means of the analytical collision dynamics model Zhang presented in his PhD thesis. The

case study concerns the sea area between Helsinki and Tallinn where a crossing of two densely trafficked wa-

terways is located. Actual traffic data is utilized to obtain realistic encounter scenarios by means of Monte

Carlo simulation. Applicability of the compared assumptions is discussed based on the findings of the case

study.

Table 1. Collision parameters used in this study.

________________________________________________

Description Unit Type

________________________________________________

M Mass [kg] Static

L Length [m] Static

B Width [m] Static

Added mass coefficient, [-] Static

surge motion

Added mass coefficient, [-] Static

sway motion

j Added mass coefficient, [-] Static

rotation around centre of gravity

R Radius of ship mass inertia [m] Static

around centre of gravity

Surge speed [m/s] Dynamic

Sway speed [m/s] Dynamic

x x-position of centre of gravity [m] Static

y y-position of centre of gravity [m] Static

x-position of impact point, [m] Dynamic

in coordinate system ship A

y-position of impact point, [m] Dynamic

in coordinate system ship A

α collision angle [rad] Dynamic

coefficient of friction [-] Static

e coefficient of restitution [-] Static

________________________________________________

The static parameters can be derived from AIS

data, statistics and theory of ship design. Modeling

of the dynamic parameters is often based on statis-

tics of the collisions.

Ship-ship collision risk evaluation schematic is

outlined in Figure 1 for the case of an oil tanker be-

ing struck vessel.

Figure 1. Tanker collision risk evaluation schematic

The first step of the risk analysis is modeling the

traffic in the analyzed area. Modeling may be done

via simulation of individual vessel movements as

proposed by Merrick et al. (2003), van Dorp et al.

(2009), Ulusçu et al. (2009) and Goerlandt & Kujala

(2010) or alternatively by simulating the traffic

flows as proposed by Pedersen (1995, 2010) or

Montewka et al (2010). The encounter scenarios are

obtained as a result of the traffic simulation. The

impact scenarios may be then obtained with the

models discussed in detail in Section 3.3.

Second part of the risk analysis is the evaluation

of the consequences which begins with the estimat-

ing the released deformation energy that is absorbed

by the vessel structures. Collision dynamics models

to calculate the deformation energy can be divided

into two groups, time domain and analytical (Wang

et al 2000), based on applied calculation method.

Analytical closed form methods have been proposed

by Minorsky (1959), Vaughan (1977), Hutchison

(1986), Hanhirova (1995), and Zhang (1999). Mod-

els based on time domain calculations are proposed

by Chen (2000) and Tabri et al. (2009). In analytical

models the external dynamics and internal mechan-

ics are uncoupled while in time domain methods

these are coupled.

3 COMPARISON METHODS

3.1 Traffic simulation and encounter scenarios

The traffic simulation is described here shortly as

the simulation itself is not crucial regarding the

comparison of impact models. The simulation is de-

scribed in detail in (Ståhlberg, 2010)

The traffic in the analyzed area is obtained from

AIS data. The data contains traffic information from

the month of July 2006 in the sea area between Hel-

sinki and Tallinn where densely trafficked water-

ways cross. In Figure 2 the analyzed area and the da-

ta points are presented. The four main waterways in

the crossing area are named after compass quarters

in form of “from-to” as shown in Figure 2. The con-

sidered waterway combinations and resulting en-

counter types are listed with reference numbers in

Table 2.

Figure 2. Plot of AIS data points in analyzed area

The AIS data is filtered to distinguish the traffic

between waterways and ship types. The numbers of

passages through the analyzed area per ship type are

listed in Table 3. The Monte Carlo simulation

flowchart starting from the filtered AIS data is

shown in Figure 3. The result of the simulation is the

encounter situations based on the traffic data.

Table 2. The considered waterway combinations and resulting

encounter types with respective reference numbers.

__________________________________________________

Ref number Route Encounter type

__________________________________________________

1 N-S, E-W Crossing

2 N-S, W-E Crossing

3 S-N, E-W Crossing

4 S-N, W-E Crossing

5 W-E, E-W Head-on

6 E-W, W-E Head-on

7 E-W, E-W Overtaking

8 W-E, W-E Overtaking

_________________________________________________

Table 3. Number of passages per ship type and route.

__________________________________________

Ship Route

_________________________________

Type N-S S-N E-W W-E

__________________________________________

HSC 741 740 0 0

PAX 253 254 26 14

Cargo 5 4 768 742

Tanker 0 0 218 215

Other 3 3 36 35

__________________________________________

* HSC = High Speed Craft, PAX = Passenger vessel,

Cargo = Cargo vessel

The Monte Carlo simulation to create encounter

scenarios is run 10000 times for those combinations

of main waterways in which the tanker may be

struck vessel. In the utilized data set tankers were

recorded sailing only on “E-W” and “W-E” water-

ways. In this study the probability of a vessel in-

volved in collision is weighted with the number of

voyages in the area.

Figure 3. Flowchart of Monte Carlo simulation

3.2 Impact scenario simulation

With the encountering vessels’ characteristics

known the impact scenarios are simulated here by

applying the compared models for the dynamic pa-

rameters. The models may be considered to be the

“evasive maneuvering” model shown in Figure 1.

The compared assumptions are presented in Fig-

ures 4-7 and the distribution parameters are com-

piled into Table 4.

In “Blind Navigator” –model there are no maneu-

vering actions taken to avoid the collision and thus

the speeds and courses are unchanged from the en-

counter scenario. The collision location is assumed

to be uniformly distributed along the struck vessel’s

length. This model is used by Van Dorp & Merrick

(2009) and COWI(2008). Based on the analysis of

collisions in (Cahill, 2002) and (Buzek & Holdert,

1990) it seems extremely rare that neither vessel

takes any action.

Figure 4. Input distributions for collision angle, Lützen: initial

angle 90°, Brown (2002) quasi-equivalent to NRC (2001)

Figure 5. Input distributions for striking ship speed, Lützen

with initial speed of 15 kn

Figure 6. Input distributions for struck ship speed, Lützen with

initial speed of 10 kn, Brown (2002) quasi-equivalent to NRC

(2001)

Figure 7. Input distributions for location of impact along struck

ship’s length, 0 = aft, 1 = fore

Table 4. Overview of impact scenario models.

__________________________________________________

Impact Collision V

Impact

Model Angle, β Point, d

[deg] [kn] [kn] [x/L]

__________________________________________________

Blind β=β

U(0,1)

Navi

Rawson U(0,180) bi-normal idem to U(0,1)

(1998) N(5,1) V

N(10,1)

Truncated {2, 14}

NRC N(90,29) W(6.5,2.2) E(0.584) B(1.25,1.45)

(2001) {0, 1}

Lützen T(0,β

,180) U(0,0.75V

) T(0,V

) Empirical

(2001) T(0.75V

) See FIG 7

Brown N(90,29) W(4.7,2.5) E(0.584) Empirical

(2002) See FIG 7

Tuovinen Empirical Empirical Empirical Empirical

(2005) See FIG 4 See FIG 5 See FIG 6 See FIG 7

_________________________________________________

* Distributions are marked as follows, U=Uniform(min, max)

N=Normal(μ, σ), T=Triangular(min, triangle tip, max),

E=Exponential(λ), B=Beta(α, β, min, max), W=Weibull(k, λ)

Lützen’s (2001) set of assumptions implies that

the struck vessel is more prone to speed reduction

than the striking vessel while the impact angle is tri-

angularly distributed between 0° and 180° with the

tip of the distribution at the encounter angle. The

longitudinal impact location is given by empirical

distribution. Although there is no explanation how

the distributions for collision angle and velocities are

derived these are included into the comparison be-

cause of the existing relation between encounter and

impact scenarios.

Rawson et al (1998) model is based on statistics

of the grounding accidents with assumption that the

collision speed being similarly distributed as

grounding speed. Velocities of the colliding vessel

are distributed according to a double normal distri-

bution in which the averages are described to repre-

sent the service speed, i.e. no speed reduction, and

half of service speed. The same speed distribution is

used for both striking and struck vessel. Collision

angle and collision location are uniformly distribut-

ed between 0°…180° and along the struck vessel’s

length respectively.

Tuovinen (2006) compiled statistics from over

500 collisions. Statistics have been used here as pre-

sented originally, in form of empirical distributions.

Brown (2002) and NRC (2001) give quite similar

distributions. Brown gives lower velocity for the

striking vessel. These models both assume that strik-

ing vessel has higher velocity than struck at the mo-

ment of impact. It is noteworthy that these two mod-

els suggest much lower collision speeds than other

models. Collision angle is normally distributed

around right angle. In NRC model the collision loca-

tion is beta distributed so that midship section is

rammed at higher probability than the fore and aft of

the vessel while Brown suggests empirical distribu-

tion.

Overall, the distributions Lützen suggested are

the only ones taking the encounter into account in

any way and other models give same distributions

for dynamic parameters irrespective of encounter

scenario. None of these models indicate how to de-

termine which vessel is striking and which is struck.

It is assumed here that the probabilities of vessel be-

ing striking or struck are equal for all models as no

other probabilities were suggested in these models.

The compared models do not have the possibility of

initial sway nor yaw speeds, which in case of ma-

neuvering is unlikely.

It can be seen in the Figures 4-7 that models, with

exception of Brown and NRC, give distinctively dif-

ferent distributions for the dynamic parameters.

Considering the struck vessel speed being lower in

all the models expect Rawson it appears likely that

the collision statistics from which the distributions

are derived include collisions in which the struck

vessel is in anchorage or in berth. Tuovinen’s (2005)

statistics include approximately 6% of such cases

and 41% of open seas collisions. Brown (2002)

states that the share is significant as in about 60% of

collisions struck vessel speed is zero.

3.3 Deformation energy calculations

Zhang presented in his PhD thesis (Zhang, 1999) a

simplified calculation method for released

deformation energy in ship-ship collision. Zhang’s <