This document analyzes berthing velocities and angles at four ports to inform fender design. It finds berthing velocities vary by port and do not correlate directly to vessel size. Wind has little effect on velocities. Berthing angles are typically smaller than design specifications, but flare angles are three times larger. Larger container ships have more curved hulls at fender level, allowing energy absorption across multiple fenders during berthing. Proper measurement of temperature and strain rates is important for accurately assessing fender performance under different conditions.

1. Measuring of berthing
velocities in container berth
and applying to fender design
Bridgestone
Seigi Yamase
7.Feb.2012

2. Berthing Velocity Standard data
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3. Container Vessel size distribution on 4 ports
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4. Berthing Velocity on 4 ports
4

5. Brolsma vs. 4 ports
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6. Berthing Velocity on 4 ports
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7. Frequency & Log-normal distribution
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8. Frequency & Log-normal distribution
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9. Wind effect
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10. Berthing maneuver
Port M
Port Y
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11. Berthing maneuver
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12. Berthing maneuver
Port M
Port Y
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13. Conclusion in Berthing velocity measureing
• Berthing velocity distribution is peculiar to each berth.
• In these ports, there seems to be no correlation between
vessel sizes and berthing velocities against Brolsma chart.
• In these ports, wind effect doesn’t have significant influence.
Wind doesn’t make the difference of berthing velocity
distribution.
• Tug boat and thruster seems to have equivalent ability to
control berthing.
• The main cause of difference of berthing velocity
distributions shall depend on berthing principle of each port.
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14. Berthing velocity and fender performance
1990’s Trellex element fender swept fender market. But their
fenders broke very early.
Reason 1
The recess for fixing bolt had the strong stress concentration.
Reason 2
Trellex gave the big speed factor to element fender.
Higher berthing velocity generated higher reaction force and
bigger energy absorption.
But speed factor and temperature factor are same characteristics
in visco-elastic materials.
Which has bigger reaction force, higher berthing velocity in
tropical or lower berthing velocity in the winter in Norway ?
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15. Fender performance
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16. Fender size
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17. Strain rate
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18. Temperature and speed
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19. Experiment result and combined method result
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20. Temperature-frequency reducibility
William Landel and Ferry formula
2
T n aT k Ts
G1 ( , T ) Gk Ts 2
s Ts k 1 1 aT k Ts
T
G1 ( aT , Ts )
s Ts
T
G2 ( , T ) G2 ( aT , Ts )
s Ts
WLF formula
T s c1 T Ts
log10 aT log
s T c2 T Ts
Ts Tg 50
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21. 3.5 -30 degrees
3.0 -１ degrees
0
Reaction Force Rate
Temperature vs. 23 degrees
2.5
deflection velocity
50 degrees
on experiment and 2.0
multiple combined at 70 degrees
25% compression 1.5
deflection
1.0
0.5
0.0
1.E-08 1.E-06 1.E-04 1.E-02 1.E+00 1.E+02
aT*strain rate
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22. Comparison with Japanese manufactures’ TF & VF
Company Company Company Company Company
A B C D E
Circular
Sample Shape Circular Rectangle Circular
Cylinder -
Corn Type Type Corn Type
Type
Sample Height
(Nominal Height) 100mm 125mm 100mm 100mm -
Preliminary Compression 10times 3times 10times 5times -
Compression Interval
in measuring TF 6 hours 3.5hours - 6 hours -
-30℃ -20℃ 50℃
↓ ↓ ↓ 50℃
Order of measurement 50℃ 50℃ -30℃ ↓ -
↓ ↓ -30℃
-30℃ 50℃
Performance
Hard Soft - - Hard Mid Soft -
(Rubber) Grade
Max Difference between
0.03 0.06 0.09 0.02 0.04 0.03 0.06 0.02
TF and VF
Glass Transition
-41.9 -41.9 -45 -35 -32 -36 -38 -34
Temperature (℃)
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23. TF & VF for each manufactures -1
(After convert to WLF formula)
2 2
Company A - Hard: aT converted to TF Company A - Soft: aT converted to TF
Company A - Hard: VF Company A - Soft: VF
1.5 1.5
Reaction Force Rate
Reaction Force Rate
1 1
0.5 0.5
1.E-03 1.E-01 1.E+01 1.E+03 1.E+05 1.E-03 1.E-01 1.E+01 1.E+03 1.E+05
aT×Strain Rate (%/sec) aT×Strain Rate(%/sec)
2 2
Company B: aT converted to TF
Company C: aT converted to TF
Company B: VF
Company C: VF
Reaction Force Rate
1.5 1.5
Reaction Force Rate
1 1
0.5 0.5
1.E-03 1.E-01 1.E+01 1.E+03 1.E+05 1.E-03 1.E-01 1.E+01 1.E+03 1.E+05 1.E+07
aT×Strain Rate(%/sec) aT×Strain Rate(%/sec) 23

24. TF & VF for each manufactures -2
(After convert to WLF formula)
2 2
Company D - Hard: aT converted Company D - Mid: aT converted
to TF to TF
Reaction Force Rate
Reaction Force Rate
1.5 1.5
1 1
0.5 0.5
1.E-03 1.E-01 1.E+01 1.E+03 1.E+05 1.E-03 1.E-01 1.E+01 1.E+03 1.E+05
aT×Strain Rate (%/sec) aT×Strain Rate (%/sec)
2 2
Company D - Soft: aT converted to TF Company E: aT converted to TF
Company D - Soft: VF Company E: VF
Reaction Force Rate
1.5 Reaction Force Rate 1.5
1 1
0.5 0.5
1.E-03 1.E-01 1.E+01 1.E+03 1.E+05 1.E-03 1.E-01 1.E+01 1.E+03 1.E+05
aT×Strain Rate (%/sec) aT×Strain Rate (%/sec) 24

25. 2.0
1.5
Reaction Force Rate
1.0
Bridgestone Hard rubber compound TCF
Bridgestone Soft rubber compound VCF
Company Z TCF
Company Z VCF
0.5
1.E-03 1.E-01 1.E+01 1.E+03 1.E+05 1.E+07 1.E+09 1.E+11 1.E+13
aT×v (%/sec)
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26. Temperature and Strain rate
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27. Conclusion of the relation between velocity and temperature
• The velocity factor and temperature factor of fender reaction
force are expressed as unity by WLF formula. Temperature-
frequency reducibility can be applied to fender reaction force.
• Temperature and speed factors of some companies can not be
applied to WLF formula. They might make some mistakes in
experiment or data handling. PIANC WG145 will define test
procedure for temperature and speed factor in detail to avoid
making wrong data.
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28. Measured Berthing Angle in 4 ports
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29. Berthing angle vs. Berthing velocity
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30. Berthing angle vs. DWT
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31. Container vessel shape and flare angle
Upper Column:Dimension
Maersk Post
Lower Column:Divided by Panamax
E class Panamax
dimension of No.3
No. 1 2 3
Length m 397.71 333.60 276.00
Length i /Length 3 1.44 1.21 1.00
Lpp m 376.00 316.30 260.80
Lpp i /Lpp 3 1.44 1.21 1.00
Width m 56.70 45.60 32.20
Width i /Width 3 1.76 1.42 1.00
Depth (from themain deck) m 30.00 27.20 21.00
Depth i /depth 3 1.43 1.30 1.00
Draught m 15.50 14.50 11.50
Draughti /Draught 3 1.35 1.26 1.00
DWT 156907.00 102351.00 63265.00 Figure 3 Fender elevation
DWTi /DWT3 2.48 1.62 1.00
TEU 15500.00 9200.00 4100.00
TEUi /TEU3 3.78 2.24 1.00
Table 1 Container vessel dimensions
No.1; Maersk E class No. 2; Post Panamax No.3; Panamax
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Figure 2: Cross sectional views of No.1, No. 2 and No.3 vessels

32. How to obtain flare angle
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33. Flare angle vs. Berthing Angle
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34. Hull radius in horizontal plane
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35. Ratio of Parallel Hull at Fender elevation in Port Y
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36. Conclusion in berthing angle
• Actual berthing angles are rather small than design
conditions.
• In this study, flare angles are bigger three times than berthing
angles in minimum.
• In horizontal plane, the contact point of vessel hull to fender
has big hull radius. Many fenders were installed on every 15
to 20m in container berth. Multiple fenders could absorb
berthing energy.
• Container vessel upsize rapidly and container vessel shape
change greatly. The shape of the latest container vessel
cannot be obtained. There may be a big difference in the
present status with this study.
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37. THANK YOU
FOR YOUR ATTENTION!
TAKK FOR DIN STØTTE TIL
JAPAN JORDSKJELV OG
TSUNAMI 2011.
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