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B

4 C

b

B

30

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2. CALCULATING BERTHING ENERGY

(Continued)

c) Eccentricity – C

e

(Continued)

• for larger Bulk Ships and Tankers

K = 0.2L - 0.25L

• for Passenger Ships and Ferries

K = 0.17L - 0.2L

• for 1/4 point Berthing

a = 0.25L

The formula is based on the generally accepted assumptions that at the

moment of maximum fender deflection:

1.

Rotation only occurs at the contact point

2.

Ship's hull does not slide along the fender

3.

Forces such as wind, currents tugs are negligible

compared to the fender reaction.

The approach angle is usually taken as 7° with a maximum of 10°. If the ship

is berthing properly under control at the moment of contact with the fender

then the direction of travel will be at right angles to the berthing face.

Examples:

In the case of a two dolphin mooring where the dolphins are

1/3 L distance apart, the minimum C

e

is reached when the center

of gravity of the large ship falls halfway between the two

dolphins on contact with the fenders.

This is when a = 1/6 L

Therefore:

C

e

= (.25L)

2

= 0.692

The maximum in this case, would occur when the ship's center of gravity

falls in line with the point of contact with the fender or

a = 0 Then C

e

=1.

In the case of a continuous fender system and a large oil tanker

a = 0.3L

Therefore:

C

e

= (0.25L)

2

= 0.41

Generally C

e

ranges between 0.4 and 0.8

d) Virtual Mass Coefficient - C

m

When the ship is in motion and contacts the fender, the mass of the

ship has to be decelerated as well as a certain mass of water surrounding

and moving with the ship. This additional mass is accounted for in the

virtuaI mass coefficient - C

m

which is a function of: the block coefficient

of the vessel, its draft and its width.

Where:

C

m

= 1 +

p

x D

C

b

= block coefficient (see section 2.2c)

D

= Draft

B

= Width

an alternate formula recommended by Vasco Costa is:

C

m

= 1 + 2D

Since there is no conclusive experimental data, we would recommend

calculating C

m

both ways and using the higher value.

e) Softness Coefficient - C

s

This factor accounts for the relation between the rigidity of the ship and

that of the fender. It expresses that proportion of impact energy absorbed

by the fender. For a soft fender C

s

= 1.0 as deflection of the ship's hull will

be negligible and therefore all the energy will be absorbed by the fender. In

the instance of hard fenders, it is assumed that the ship's hull will absorb 2

to 7 percent of the impact energy so C

s

is taken as 0.98 to 0.93.

f) Berth Configuration Coefficient - C

c

This factor attempts to quantify the difference between an open pile

supported pier and a solid sheetpile or concrete crib structure.

In the first case, the water being pushed by the berthing ship is easily able

to be displaced around the pier. In the second case, the moving water is

squeezed in between the structure wall and the ship causing a cushion

effect. A reduction factor has to account for this effect.

For solid structures with parallel approach C

c

= 0.8. As the approach angle

increases from zero and as the under keel clearance increases then C

c

increases to 1.0 which is the value for an open type support structure such

as a pile supported pier.

2.3 VESSEL DIMENSIONS & TYPICAL ENERGY REQUIREMENTS

The following tables show typical weights and dimensions for the various ves-

sel classes. These are general and should be used only as a cross reference.

A berthing energy has been calculated based on standard conditions where:

1.

Velocity: 0.15 m/sec in all cases

2.

Eccentricity Coefficient: 0.5 (for 1/4 point berthing)

3.

Virtual Mass Coefficient: as shown

4.

Softness Coefficient: 1.0

5.

Berth Configuration Coefficient: 1.0

6.

Large under keel clearance / open berth

a) General Cargo

(1/6L)

2

+ (.25L)

2

(0.3L)

2

+ (0.25L)

2

800

56

9.0

4.0

3.8 1,115 1.6 1.02

1,000 58

9.4

4.6

4.2 1,390 1.59 1.27

2,500 83 12.4 6.7

5.5 3,470 1.58 3.15

5,000 109 15.0 8.4

6.7 6,930 1.57 6.23

7,500 129 18.0 10.2 7.7 10,375 1.59 9.48

10,000 142 19.1 11.1 8.2 13,800 1.56 12.32

12,000 150 20.1 11.9 8.7 16,500 1.55 14.73

15,000 162 21.6 12.7 9.1 20,630 1.52 18.02

20,000 180 23.5 14.0 10.1 27,400 1.54 24.19

25,000 195 25.0 14.5 10.3 34,120 1.50 29.35

30,000 200 26.0 15.7 11.0 40,790 1.48 34.62

35,000 210 27.2 16.2 11.7 47,400 1.49 40.50

40,000 217 28.3 17.3 12.0 54,000 1.47 45.52

45,000 225 29.2 17.9 12.4 60,480 1.46 50.65

Tonnage

(D.W.T.)

Length

(in meters)

Width

(in meters)

Height

(in meters)

Loaded Draft

(in meters)

Displacement

Tonnage (DT)

Virtual Mass

Coefficient

Berthing Energy

(Tonne-M)*

*These values are for general guidelines only.

They should be checked using actual site conditions.