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2. CALCULATING BERTHING ENERGY (Continued)
b) Fender Spacing (Continued)
iii) From the site conditions.
The fender spacing can be determined using the wind and current forces and
equating them to the fender reaction forces. Use the following formula:
N = Ra + Rc
Where:
N = Number of fenders required
Ra = Load due to wind (see below)
Rc = Load due to current (see below)
R = Fender Reaction at rated deflection
Wind Loads
The wind loads can be calculated using the following formula:
Ra = 1/2 x da x (Vw)2 x Cw x (A cos2 Ø + B Sin2 Ø)
Where:
Ra = Force due to wind (kg)
da = Force of air ( = 0.12 kg. sec2/m4)
Vw = Wind Velocity (m/sec)
Cw = Wind pressure coefficient
A = Area of the front projection of the vessel above sea level (m2)
B = Area of the side projection of the vessel above sea level (m 2)
Ø = Angle of wind direction relative to the centerline of the vessel.
The wind pressure coefficient is relative to the angle of wind direction as
shown in the table below:
Current Loads
The loading on the vessel due to current pressure is calculated as follows:
Rc = 1/2 x dw x C x (VC )2 x L x D
Where:
Rc = Reaction load due to current (kg)
dw = Water Force Coefficient ( = 104.5 kg. sec 2/m4)
C = Current Pressure Coefficient
Vc = Velocity of the current (m/sec)
L = Vessel Length (m)
D = Vessel Draft (m)
The Current Pressure Coefficient is relative to the angle of current direction and
to the water depth to draft ratio.
c) Normal Operations
i) Stand Off Distance
The allowable standoff distance will be governed by the loading/unloading
activities and the normal operating procedures of the ship and pier while
berthed. Operating constraints such as crane reach, roll, yaw and freeboard
are major considerations in the design. The fenders must provide adequate
protection yet accommodate the design.
ii) Vertical vs. Horizontal Mounting
There is an ongoing concern as to when the fenders should be mounted hor-
izontally and when vertical. In general, vertically mounted fenders provide
the best coverage for piers which experience tidal fluctuations. Where the
operating procedures require that the vessel slide along the pier face, hori-
zontal Bolton fenders provide good protection. A combination of horizontal
and vertical arrangements are often used.
iii) Tidal Variation
The change in water level due to tides will have a significant impact on the
operation of the pier and consequently the pier design and the fender design
as well. Protection in all cases must be achieved for both the largest and
smallest ships.
iv) Range of Ship Sizes
While the energy absorption capacity of the fender system is chosen for
the design vessel,the fender system should be suitable for the full range
of ships expected to use the facility. Fender stiffness on the smaller
vessels may have an influence on the arrangement of the fenders. Also,
if barges are to use the facility, special attention must be given to their
fender requirements.
v) Frequency of Berthing
A high frequency of berthings normally justifies greater capital expenditures
for the fender system.
d) Accidental Impact
The fender system is less expensive than the dock structure and it
should be recognized that damage to the fenders is less critical than to
the vessel or the structure. The design should incorporate a reasonable
level of energy absorbing capacity. If the fender system fails, it would
be an advantage if the structure were designed so that it could inexpen-
sively be repaired. The mode of failure of a fender and its effect on the
dock structure should be considered.
e) Ongoing Maintenance Costs
Maintenance costs can be an important factor and should be considered
when analyzing the overall costs of the various fender options. Maintenance
costs will vary with fender type.
f) Ease of Installation
A well designed fender system will be as easy to install as possible.
This will minimize initial capital costs and reduce down the road
maintenance costs.
R
Wind
Direction Ø° 0° 20 40 60 80 100 120 140 160 180
Cw 1.08 1.03 1.18 1.09 0.98 0.94 1.0 1.15 1.28 0.99
Current
Direction Ø° H/D = 1.1 H/D = 1.5 H/D = 7.0
0 0 0 0
20 1.2 0.5 0.3
40 3.1 1.3 0.6
60 4.1 2.1 0.8
80 4.6 2.3 0.9
100 4.6 2.2 0.8
120 4.0 1.8 0.7
140 2.8 1.3 0.5
160 1.0 0.5 0.3
180 0 0 0
C
H = Water Depth D = Draft