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3. Angle
of Approach
The angle in which a ship approaches a dock not only influences the effective velocity but also affects which part
of the ship makes the initial contact with the pier. Generally, the ship will contact the dock at a point near the bow or the
stern. In such cases, the reaction force will impart a rotational movement to the ship and this rotational movement will
dissipate a portion of the ship's energy.
The proportion of the ship's energy dissipated by rotation can be approximated by the following ratio:
4. Hydraulic
E ect
In determining the energy to be absorbed by the fenders, it is also necessary to consider the effect of the water. As a ship makes
contact with the dock and its movement is suddenly checked, the mass of water moving with the vessel adds to the energy
possessed by the ship. Although there are a number of theories relating to the hydraulic effect, they all deal with the
length, beam and draft of the ship.
1. Weight
of Vessel
It is common to refer to the ship's weight in terms of dead weight tonnage (DWT) or displacement tonnage.
Displacement tonnage is the more accurate figure to use in computing kinetic energy because it is the total weight of
the ship and its cargo and equipment. If the dead weight tonnage is known, multiply DWT by 1.3 to obtain an accurate
approximation of the displacement tonnage.
2. Berthing
Velocity
Since the kinetic energy possessed by a ship is proportional to the square of the velocity, it is important that the velocity be determined with
accuracy. The velocity of a ship approaching a dock is affected by a number of factors:
the size of the vessel, •
the skill of the crew members, •
the wind and current conditions, •
and whether the ship is making an unassisted berthing or if it is being assisted by tugs. •
The angle of approach has a direct bearing on the determination of kinetic energy because the velocity used in equation (1) is that component of the
actual velocity that is at a right angle to the pier.
Since the velocity of a ship is usually given in terms of knots, it is necessary to convert that gure into feet per second as follows:
The velocity of a ship normal to a dock (effective velocity - VE ) is expressed in terms of the actual velocity and the angle of approach. All unassisted vessels
will approach the berth at some acute angle, usually 5
o
to 15
o
. Large tankers and ore carriers are guided to the docking facility by tugs and their approach
angle can be up to 90
o
. In these cases, the vessel is under control of the tugs and its velocity can be regulated.
The e ective velocity of a ship approaching a dock at an angle can be determined by:
Example :
A ship approaching a dock at 1½ knots and a 10
o
angle would have
an effective velocity of:
V
E
= (1½)(1,09)(sinus 10
o
) = 0,44 ft/sec
(2) V
E
= Actual velocity x the sine of the angle of approach.
Knots x 1.09 = Feet per second.
E
d
=
1
1 + (L
1
/r)
2
E
d
=
=
0,5
1
1 + 1
2
L
L
C.G.
Où
L
1
= the distance in feet from the point of contact to the ship's
center of gravity measured parallel to the pier.
r
= the rotational radius of the vessel from its center of gravity
(expressed in feet).
This ratio is often called the berthing coefficient, (C
B
).
Experience has shown that a ship normally contacts the pier at a point of ¼ of its length so that
the distance from the point of contact to the ship's center of gravity is also ¼ L. Therefore, the
ratio can be established as: