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1 INTRODUCTION
As more ports are targeting to accommodate larger
ships at deeper drafts, there has been lots of pressure
on port planners to increase the port access channel
capacity through capital dredging. The main focus of
such capital dredging attempts is typically deepening
the channels as changing the horizontal profile of
navigation channel is considered to be the expensive
element. Consequently, ships are entering the port
waters with larger drafts, length and breadth while
the channel profile remains largely unchanged.
Resulting in higher risk in handling and
manoeuvering, especially when combined with
extreme weather events. Although in channel
development plans, minor modifications are made on
bend configuration, still there are lots of risk in
navigating big vessels through port waters. NCOS
ONLINE Manoeuvring Module [8] is a cloud based
online operational decision support tool that brings
the capabilities of real time manoeuvring simulation
of FORCE Technology’s SimFlex4 [10] to fast time
simulation, assisting the port operators to identify
risks in pilotage of big vessels under the
environmental forcing within shallow and confined
waterway.
Development and Validation of an Operational Fast
Time Ship Manoeuvring Solver to Increase Navigation
Efficiency in Horizontally Restricted Waterways
M
. Fathi Kazerooni
1
, M. Rahimian
2
, M. Tree
2
, T. Womersley
2
, S. Mortensen
2
& B. Jensen
3
1
DHI Water & Environment, Brisbane, Australia
2
DHI Water & Environment, Gold Coast, Australia
3
FORCE Technology, Brondby, Denmark
ABSTRACT: Growth of demand for containerized cargo shipping has put more ports into pressure to
accommodate larger vessels. Considering the limitations on dimensions of navigation channels, this is not
feasible unless aiming for significant capital dredging or alternatively creating high precision predictions of
vessel motions subjected to environmental forcing and interaction with shallow and restricted waterway. NCOS
ONLINE (Nonlinear Channel Optimisation Simulator) is a state of the art navigation support tool which
combines DHI’s high level forecast of environmental conditions with mathematical model of ship motions to
add an extra level of accuracy in predicting the under-keel clearance and vessel swept path to boost the
efficiency of navigation and pilotage within restricted channels. NCOS Manoeuvring Module utilizes an
autopilot scheme based on PID (Proportional / Integral / Derivative) controller and Line of Sight Algorithm to
FORCE Technology’s SimFlex4 manoeuvring solver for prediction of manoeuvring ship swept path and
response, which will effectively bring the accuracy of real time full bridge simulator to fast time operation
support tool. In this paper, the result of mathematical model is validated against fullscale measurements of
containership transits through Port of Auckland Navigation channel by comparing pilot commands, leeway
drift and swept path through output of portable pilotage unit. According to the results the model is found
promising to predict the behaviour of human pilots with precision required in operational use. Finally, the
swept path and manoeuvring performance of a sample transit is assessed on different environmental conditions
and tide stages to evaluate the safe transit windows in operation.
http://www.transnav.eu
the
International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 17
Number 1
March 2023
DOI: 10.12716/1001.17.01.
06
72
Both real time and fast time manoeuvring solvers
are generally based on the determined hydrodynamic
coefficients that come from captive model tests in a
towing tank or planar motion mechanisms [1]. Most
recently CFD application has been of interest as an
alternative for towing tank model tests [2]. However,
as it is difficult to take into the account the interaction
of propulsion and steering with vessel main hull,
these mathematical models should be validated before
using in manoeuvring solvers. Towing tank
experiments usually suffer from model scale effects,
and as the viscous effects in manoeuvring are not
fully understood, there would be a high level of
uncertainty when extending these results to fullscale
[3], There have been several attempts for validating
the manoeuvring mathematical models. Free-running
model tests can provide a higher level of accuracy as
the size of the model is not restricted by carriage
equipment in the tank and models are typically made
in larger scales [4]. Although the scale effects for hull,
rudder and propeller are still important in free
running model tests, the interaction of hull, propeller
and rudder are fully considered in free running model
tests. Validation of manoeuvring mathematical
models through this method shows more course-
stability than measurements [5,11].
Standard ship manoeuvering tests in fullscale are
considered as part of ship delivery sea trials [6], and
the results are made available through pilot cards or
wheelhouse posters. These results are often used for
validation of ship manoeuvering simulation models
[7]. Although sea trial results are good for developing
manoeuvering models, there are still several reasons
that they cannot be considered as a good measure for
validating fast or real time manoeuvring solvers. The
sea trial is typically handled in deep water as
executing the tests in shallow waters is risky, and in
most cases the vessels are in ballast or half-laden
condition, where the manoeuvering characteristics
can’t be easily scaled to deeper drafts.
NCOS ONLINE Manoeuvring Module is DHI’s
advanced manoeuvring simulation tool which
combines high level weather forecast systems with
FORCE Technology’s SimFlex4 manoeuvring solver to
identify risks in pilotage and handling of deep drafted
vessels in shallow and laterally restricted navigation
channels. NCOS ONLINE uses an autopilot algorithm
based on PID controller combined with line-of-sight
algorithm to navigate the ship through the channel in
fast time simulation [8]. The mathematical model
implemented in NCOS ONLINE is a fully coupled six
degrees of freedom dynamic model in which the
hydrodynamic effects are tabulated based on the
results of towing tank model tests, numerical
calculations, and experiences with similar fullscale
vessels [9]. NCOS ONLINE uses a detailed
representation of forcing on vessel dynamic through
databases coming from wind tunnel model tests.
Ideally, the forecast system, the mathematical model
of the ship hydrodynamics, confined waterway
interactions models and the autopilot algorithm itself
are considered as the sources of uncertainty in NCOS
ONLINE simulation. Making the test bed for
validating these various components individually
through model scale tests not only time and cost
consuming, but also fail to capture the interactions
between various elements. In previous attempts, the
performance of NCOS ONLINE autopilot has been
validated against human pilot performance through
real time full bridge simulation, by using the same
mathematical models and forcing condition, which
seemed promising in terms of autopilot following the
human pilot decisions with acceptable accuracy [8].
However, in order to provide a basis for full
validation of the model, in this paper the fullscale
measurement on a real transit is identified as the most
efficient way in terms of precision, time and cost.
Fullscale measurements on actual vessel transits will
enable the full validation of forecast models, vessel
dynamic mathematical model, and autopilot
algorithm performance all at a same time.
2 FULLSCALE MEASUREMENT
2.1 Vessel particulars and metocean condition
The measurements have been done on a Panamax
class containership approaching to Port of Auckland.
The outline of navigation channel is given in Figure 1.
Figure 1. Port of Auckland navigation channel and
significant waypoints
The main particulars of the vessel and loading
conditions are given in Table 1.
Table 1. Vessel particulars and loading condition
________________________________________________
Ship Type Panamax Containership
________________________________________________
LOA (m) 294.05
Beam (m) 32.2
Draft Mid (m) 11.9
Trim by Aft (m) 0.2
GM (m) 1.64 Free surface corrected
Lateral Windage Area (sq.m) 6761
Frontal Windage Area (sq.m) 1125
Engine MCR 41130 KW x 104.0 RPM
Rudder Type X-Twisted Leading Edge
Rudder Aspect Ratio 1.533%
Wetted Rudder Area (sq.m) 60.23
________________________________________________
The swell height during the approach was
insignificant and is not expected to affect the results.
The wind and current varied along the channel at
time of the transit as given in Figure 2. Wind speed
was moderate, between 14 to 20kn easterly, and the
transit started on a moderate flooding current slightly
exceeding 1kn, giving adequate under keel clearance
during the passage.
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Figure 2. Environmental forcing during the transit
2.2 Measurement methodology
The position of the vessel, heading and rate of turn
was extracted from high precision pilot portable units.
Three Leica DGPS units were also installed, with one
on each bridge wing and the third on the bow along
the vessel centreline. These were used to measure
vessel roll, pitch and heave during the transit and in
turn calculate the under-keel clearance.
The vertical error for each corrected DGPS signal
was typically below 25mm. Some satellite signal
reflection off the forward container stack was
expected and usually meant the bow DGPS
performed slightly worse than the unobstructed
receivers on the bridge wings.
A bridge voice recording was used to reconstruct
the pilot rudder, course and engine commands during
transit.
Figure 3. DGPS unit and PPU (Portable Pilot Unit) receiver
on bridge wing
2.3 Field measurement results
The vertical profile of the channel and vessel keel
position is plotted in Figure 4. At each location, as the
ship hull has curvatures, the lowest point of hull is
assumed here. According to the results simulation
output is in general conservative when compared to
measurements, especially on the bends, which will
result in lower rate of turns and turning ability when
compared to the measurements.
Figure 4. Measured maximum keel excursion compared to
NCOS safety 1% and high probability 99 % lowest keel
excursions. All depths to chart datum
The vessel forward speed, rate of turn and
executed rudder angle is given in Figure 5. According
to the results, the autopilot and simulation model was
successful in matching the transit speed with only
some differences in the last stage of the approach.
Measured rate of turns are slightly higher than
simulation, specifically on the bends, which confirms
that the mathematical model is conservative as it was
more difficult to initiate the turns on the bends
considering the reduced under keel clearance. Rudder
executions are in general higher than the
measurements. The human pilot sets the rudder
commands as step-wised function, however, in
simulation, the PID controller and line-of-sight
algorithm sets the input rudder angles smoothly
according to heading deviation at each simulation
time step.
Figure 5. Speed, rate of turn and rudder execution
comparison
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To evaluate the vessel position relative to channel
boundaries, two new parameters are introduced as
channel occupancy which is the ratio of vessel swept
path width to channel width at each time step, and
minimum distance to toelines as the least clearance of
vessel extremities to channel boundaries as illustrated
in Figure 6. From the Figure 6, when the vessel is
running with higher leeway angle, the channel
occupancy would be higher.
Figure 6. Channel occupancy and minimum distance to
toelines concept
Figure 7. Comparing transit geometric parameters to
measurements
The channel occupancy of actual transit is slightly
higher than the simulation on the straight sections of
the channel (Figure 7). This basically means that the
drift angles are higher in actual transits and vessel has
proceed with higher level of course-stability in
simulation. Most ship manoeuvering mathematical
models suffer from the same issue, which the reason
could be sought through the source of hull
hydrodynamic damping coefficients which basically
comes from towing tank model tests in model scale,
where the level of flow turbulence around ship hull is
not as high as fullscale and viscous damping effects
are exaggerated in model scale. Another reason for
lower simulation drift angles is the lower under keel
clearance and higher vertical motion in simulation. In
general drift angle would be less in lower under keel
clearance ratios. From the operational point of view,
those small differences in drift angle in simulation
will not impose any significant risks to transit
simulation, while the conservatism in under keel
clearance model is highly favoured with regard to
grounding risks.
The vessel swept path on fullscale measurement
and simulation are compared in Figure 8. On the
curved sections of the channel the swept path is wider
due to higher measured leeway angles. However, the
autopilot was able to finish the manoeuvre close to
areas swept by actual vessel.
3 OPERATIONAL APPLICATION
Combining the validated manoeuvring solver and
autopilot scheme with high level accurate weather
forecasts in NCOS ONLINE can provide port and
pilots with the ability to plan transit arrival times with
an anticipated level of risk, mitigated through safe
transit windows. The risks in navigation could be in
relation to vessel swept path geometry (channel
occupancy and clearance to channel boundaries,
leeway drift), under keel clearance and grounding
risks and pilot workload as steering and propulsion
variation during the manoeuvre or capacity to
respond to unforeseen circumstances.
In this section, the risks of excessive rudder usage
on transits of same containerships are evaluated for
different arrival times during a full 24-hour tide cycle.
On the straight sections of the channel the transit is
rated as low risk if average rudder usage is below 10
degrees, high risk if average rudder usage above 15
degrees and medium risk in between. Similarly, on
the parts that ship is turning through the curved
sections, thresholds of average rudder attempt are
increased to 15 and 20 degrees respectively. The
results of the fast time simulation are given in Figure
9. According to the results, at the flood stage, there are
some arrival times where the pilot rudder usage could
be relatively high. Considering the reduced speed
through water and flow velocity fed into the rudder, it
is expected that vessel steering would be less effective
at flood stage. However, the arrival on slack water on
peak of tide seems to be the best option for
accommodating this vessel, as it will provide higher
under keel clearance and with least adverse influence
on ship steering performance.
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Figure 8. Measured maximum keel excursion compared to
NCOS safety 1% and high probability 99 % lowest keel
excursions. All depths to chart datum
Figure 9. Manoeuvring risk on averaged rudder attempts
with respect to tide level at arrival time
4 CONCLUSIONS
The fullscale measurement of vessel manoeuvring
performance in actual transit conditions provided the
basis for full validation of the manoeuvring
mathematical model and autopilot performance.
According to the simulation results the agreement
between the measured vessel swept path, rate of turn
and rudder executions during the transit is within
acceptable range which provides a strong platform for
fast time manoeuvring simulation for operational
navigation support services. The simulation model is
proven to be more course-stable than the actual
vessel, finishing the manoeuvres with less swept path
width and leeway angle, which is slightly less
conservative on the curved sections of the channel,
however the differences are minimal. This is basically
due to lower under keel clearance predicted in the
simulation and model scaled based hydrodynamic
coefficients applied in manoeuvring mathematical
model which suffers from viscous scale effects. The
rudder use in simulation is generally higher than the
measurement due to a higher level of course-stability
in simulation method which is the result of using
model test based hydrodynamic coefficients in
simulation.
ACKNOWLEDGEMENTS
The authors would like to thank Ports of Auckland for
facilitating the fullscale measurements and their continuing
support in development of NCOS ONLINE.
REFERENCES
[1] Yoshimura T., Sakurai H., Mathematical model for the
manoeuvring ship motion in shallow water (3rd Report),
Journal of KSNAJ, Vol. 211, pp 115-126, 1988
[2] Du P., Cheng L., Tang Z., Ouhsine A., Hu H., Ship
manoeuvering prediction based on virtual captive
76
model test and system dynamic approach, Journal of
Hydrodynamics, Vol. 34, pp 259-276, 2022
[3] Jin Y., Chai S., Duffy J., Chin C., Scale effects on
hydrodynamic manoeuvring force prediction, 25th
International Ocean and Polar Engineering Conference,
2015, Hawaii, USA
[4] Im N., Sea J., Ship manoeuvring performance
experiments using a free running model ship,
International Journal on Marine Navigation and Safety
of Sea Transportation, Vol.4, No.1, 2010
[5] Eloot K., Delefortrie G., Vantorre M., Quadvlieg F.,
Validation of ship manoeuvring in shallow water
through free-running tests, OMAE 2015, Newfoundland,
Canada
[6] American Bureau of Shipping (ABS), Guide for vessel
manoeuverability, March 2006
[7] Gug S.G., Harshpriya H., Jeong H., Yun J., Kim D., Kim
Y., Analysis of manoeuvring through sea trials and
simulations, IOP conference Series, 2020
[8] Mortensen S., Kazerooni M., Harkin A., Womersley T.,
Jensen B., Dynamic assessment of safety in manoeuvring
through constricted navigational channels using online
operational system. Australasian Coasts & Ports 2021
Conference, Christchurch, New Zealand, 2021
[9] Kazerooni M., Womersley T., Harkin A., Jensen B.,
Turning induced heel of large containerships in shallow
water through a fully coupled 6DOF manoeuvering
solver, 6th MASHCON Proceedings, May 2022, Glasgow
UK
[10] Chislett M., A generalized mathematical model for
manoeuvring, marine simulation and manoeuvrability,
Proceedings of International Conference MARSIM, May
1995, Denmark
[11] ISO 13643-1 Ships and Marine Technology,
Manoeuvring of Ships, 2017, pp 2
