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1. DETERMINING ABSORBED ENERGY OF A BERTHING SHIP

(Continued)

Therefore, Energy to be absorbed by the fender system is:

E

Fender

= E

Ship

x f

Where

f = C

e

x C

m

x C

s

x C

c

C

e

= Eccentricity Factor

C

s

= Softness Factor

C

m

= Virtual Mass Factor

C

c

= Berth Configuration Coefficient

These variables are covered in detail on the following pages.

Also, convenient charts are provided in Section 2.3 which indicate the

amount of berthing energy generated by various ship sizes under

standard conditions.

2. CALCULATING BERTHING ENERGY

2.1 KINETIC ENERGY EQUATION

The equation detailing the variables:

E

Fender

= 1/2 MV

2

x C

e

x C

m

x C

s

x C

c

2.2 VARIABLES

a) Mass - M

One or more of the following weights should be readily available from the

facility user:

Displacement Tonnage -

DT

This is the weight of the water displaced by the immersed

part of the ship.

Dead Weight Tonnage -

DWT

This is the weight that the ship can carry when loaded to a

specified load draft. (Includes cargo fuel, stores, crew, passen-

gers.) It is the most common measurement.

Gross Tonnage -

GT

This is based on the cubic capacity of the ship below the ton-

nage deck with allowance for cargo compartments above.

When calculating the mass -

M

, use the loaded displacement

tonnage

DT

. Typically DT is 30% - 40% greater than DWT.

Where:

M = DT

g

DT

= Displacement Tonnage (tonnes)

g

= Acceleration Due to Gravity = 9.81 M/Sec

2

b) Velocity - V

As can be seen from the Kinetic Energy Equation, the energy to be

absorbed is a function of the square of the approach velocity. For this

reason, DETERMINING THE VELOCITY IS ONE OF THE MOST IMPORTANT

DECISIONS IN THE DESIGN. The choice of design velocity (velocity compo-

nent normal to the dock) is a judgement based on ship size, site exposure

and berthing procedure. Environmental aspects such as wind and current

forces may be an influence.

Section 2.4 b)

describes how these forces can

be calculated. Consultation with Port Management, ship operators and any

other available information should be used when making the judgement.

The following chart is offered as a guide to assist in selecting a design velocity:

NAVIGATION CONDITIONS

1.

Easy Docking; Sheltered

2.

Difficult Docking; Sheltered

3.

Easy Docking; Exposed

4.

Good Docking; Exposed

5.

Difficult Docking; Exposed

c) Eccentricity – C

e

Usually the ship is not parallel to the pier face during berthing. As a result, not

all of the Kinetic Energy will be transmitted to the fenders. At impact, the ship

will start to rotate around the contact point thus dissipating part of its energy.

Schematic diagram of berthing ship

The following graph illustrates the relationship between the eccentricity

coefficient and the distance "a" (as shown above).

Alternatively, it is represented by the formula:

C

e

= K

2

Where:

K

= radius of longitudinal gyration of the ship

a

= distance between the ship's center of gravity and the

point of contact on the ship's side projected onto the

longitudinal axis (in terms of L - the ship's length)

The value of K is related to the block coefficient of the ship and its length.

It can be approximated by the following expression:

K = (0.19 C

b

+ 0.11) x L

and the block coefficient C

b

C

b

= DT

Where:

DT

= Displacement of the ship (tonnes)

D

= Draft (m)

B

= Width (m)

L

= Length (m)

W

o

= Water Density (tonnes/M

3

)

Typical Seawater W

o

= 1.025 tonnes/W

3

(64 Ib/ft

3

)

Typical Freshwater W

o

= 1.00 tonnes/W

3

(62.3 Ib/ft

3

)

DWT x 1000

VELOCITY

(CM/SEC )

2 1

20

0

40

60

80

5 10 20 50 100 200 500

5

4

3

2

1

Navigation

Conditions

DOCK

L

a

K

Center of Gravity

B

Ce

0

.1L

.2L

.3L

.4L

.5L

.2

0

.4

.6

.8

1.0

a

2

+ K

2

D x B x L x W

o