When a vessel alters her course while turning, there are various forces that act on the vessel to causeher to turn. To understand the dynamics of the turning the ship, we have to understand the following:
a. Relation between ROT and Speed
b. Paths traversed by bow, stern and pivot point
c. Relation between Heading and COG
d. Lateral Traverse (Xr & Xm) of the stern due to Inertia of rest and motion
e. References to be monitored during turning
a. Relation between ROT and Speed
In restricted waters or in harbours, the navigator
has to follow a designed turning path. There is
not much room to deviate from the designed path. The designated path is proximate to
shallows and dangers. There is always a risk of running on to danger of getting aground and or collision.
For execution of a good turn
in restricted waters, vessel has to keep
right speed in proportion the right ROT.
Let’s assume,
r = Radius of the turn,
V = Speed in m/s
@ = Turn Angle,
t = Time taken to complete the turn,
d = Distance travelled on a circular path
ROT = Rate of turn of vessel in degrees / second
w= Distance from wheel over point to the point where vessel actually starts turning
Thus, ROT= @/t V= d/t, > V/d = ROT/@ > ROT= V@/d
Also, d=r@ > ROT = @/t= d/r*t = V/r > ROT=V/r
From above linear equations it is clear that the ROT is directly proportional to speed of vessel, V
If Vessel making a speed of V has to turn a angle of @ at a Rate of Turn - ROT, ROT has to be
directly proportional to speed V. If a vessel is making more speed,
her rate of turn has to be more and the vice versa.
When vessel moves from position-1 to position -2 the distance covered and angle turned by the vessel are the same in both the diagram. But the speed in one diagram is V1 and another is V2. So the ROT in one diagram should be different from other one.
V1 /V2 = ROT1 / ROT2 > ROT2 = (V2/V1)*ROT1
Thus to make a particular turning path,
the ship handler has to adjust her speed and ROT accordingly to get a designated turning path. If the vessel is making a lesser speed the rate of turn (or Swing) has to be slower and if the sped is more the rate of turn has to be higher for the vessel to follow the planned path.
b. Paths traversed by Bow, Stern and Pivot Point
While vessel is making a turn in open waters with abundant sea-room, the paths traverse by the bow stern and pivot point
matters a little to the ship handlers. But when
the sea room is very less, in a range of few metres, it is very important to understand the difference in the paths traversed by bow, stern and pivot point.
At the beginning of the turn, the path of the stern is of much interest to the handler as the stern moves away from the path towards the probable danger at the stern.
Bow is supposed to be in safe waters as the bow is turning towards the new course of the vessel.
However
towards the end the alteration, the path of the bow is important as the bow would move away from the new course once she overshoots the course. The stern is still coming and yet to come to the new course.
Regarding the paths traversed by the Stern, PP and Bow, the following observations are clear from above diagram:
1. The stern starts moving away from the original path in opposite direction of the alteration of course for some time and then the stern starts moving in the direction of alteration.
2. PP keeps on moving on the same course
for some time till the time the inertia of rest is overcome by the PP in her original course. After the inertia of the rest is overcome, the PP starts moving in the direction of alteration on a circular locus.
3. The bow immediately starts moving in the direction of the alteration away from the original course.
This helps the ship handler in minding where the bow or the stern exactly be landing while altering the course in a restricted waters.
This helps the ship handler in preventing the bow or stern to come closer to any navigational hazard in proximity.
c. Relation between Heading and COG
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Towards the end of alteration of course, once the vessel reaches her final course, there is still a
lag exists between the heading and the COG. The stern still moves away from the settled new course of the vessel due to the “inertia of motion” away from the newly attained course. The stern keeps on moving from the new course within the period of TLe till it reaches maximum. This is
“later altraverse of the stern due to inertia of Motion”(Xm). This would land the stern
off the centre line of the course. If there is not much sea room available at the stern on the opposite side of the turn,
this could cause a significant disaster if not controlled properly.
The classic example of a disaster due tothis is the accident of container vessel M.V. Milano Bridge in the Port of Busan in Apr 2020.
This “lateral traverse of the stern due to inertia of motion (Xm) during TLe is dangerous and pose serious threat to the vessel and environment in restricted waters, channels and harbours. This is due to following reasons:
1. The inertia of motion for large and loaded vessels is very high.
This is even higher when moving at a higher speed. To control this inertia of motion possibly the handler may
reduce speed in advance for loaded or larger vessels.
2. The time period of TLe is
relatively unknown to the handler. The time period may be longer or shorter varies from vessel to vessel. During this period
there is a degree of uncertainty in the position of the vessel as it continuously keeps on changing.
3. If there is effect of weather exists at the time of alteration, the amount of set generated by the external force e.g. current or wind etc. is unknown to the handler in the final course of the vessel. Though the direction of wind remains same relatively,
the current may be different in the new course. And with the changed course, the relative direction and strength of the combined external forces with respect to the heading of the vessel would be quite different. Thus the amount of set is unknown to the handler.
Though the pilot handles the vessels regularly and they can expect the amount of set on a new course. This varies with time in a diurnal range, month of the year, local disturbances in the weather system, strength and direction of tidal stream. There is a certain degree of uncertainty in this regard.
4. This set so generated due to external forces adds up the “
lateral traverse of the stern due to inertia of motion” would cause a great amount of uncertainty on the positioning of the vessel in the new course.
5.
The time to give correction is also very critical. If not acted swiftly vessel will land upon danger.
Due to above reasons it is very important to understand and take corrective action for this so as to keep the vessel in safe waters
all the time during large alteration of courses in restricted waters.
[...]
Conclusion
As pilots execute large alterations of fairly larger vessels within harbour limits at appreciable speed the momentum of vessel involved is fairly large. If not properly executed alterations within very narrow sea room, the potential risks to the vessel
as well as the harbour infrastructures are very high. Such improper alterations would damage the vessel as well as the port infrastructure with loss amounting to millions of dollars.
Off late it has been observed that many accidents are happening while such alterations of couse in harbour limits. Thus it is advisable the ship handlers and pilots must understand the theory behind the alteration of courses in harbour limits. I hope this would help the min execution of alterations with much ease and confidence with reduced risks to the property and life on board!