Feature: The Pivot Point Revisited: Captain Paul Butusina

“OK Captain, she’ll pivot round the fender now: hard to port and slow ahead”.        Photo: JCB


Many of you will recall Hugues Cauvier’s excellent article on the pivot point in the October 2008 issue of The Pilot. Paul Butusina’s article covers much the same ground but due to the importance to pilots of understanding this elusive point I felt that it was well worth revisiting the topic. JCB

The aim of this paper is to add few corrections to the pivot point theory as it is presented in seafarers books, because  understanding the pivot point is such an important element of safe manoeuvring of the vessel.

Introduction

The pivot point of the ship turning is defined in seafarers publications more or less accurately as follows: The pivot point is the point which traces the turning curve of a ship. It is located in the fore section of the ship, abaft of the stem at 1/6-1/3 of ship’s length. However other factors such as acceleration, shape of hull and speed may all affect its position.

It should be noted that when at anchor the pivot point moves right forward and any forces acting on the hull, such as wind or current, cause the vessel to move about the anchor position or the point where the chain lies on the sea bed although a sudden change will initially cause the vessel to pivot around the hawse pipe.

The available literature on ship manoeuvring and handling does not cover all aspects of the pivot point in a systematic way since it is the point in the diametrical plan of the vessel or in the prolongation of this plan, around which the vessel swings on the trajectory which she describes. This trajectory can be a circle arch with its own centre of rotation on the traject (momentary centre of rotation) which can result in the pivot point being located outside of the ship’s shape.

The Queen Mary 2 turning at speed                      Photo: Cunard

At speed, a more accurate description of the pivot point is a Tactical Point of Turning (TPT) which is located at the point of intersection between the ship’s diametrical plan and the perpendicular from momentary centre of rotation.  This is important for ships’ operators because it gives some indications regarding the equilibrium of the forces acting on the vessel and consequently provides an indication regarding space swept during turning and the possibility to predict the ship’s orientation.

Movements of a vessel: Water Resistance and Pivot Point

It is important to remember the three degrees of freedom of a vessel (Fig 1):

1. Longitudinal, along axis X-X’

2. Transverse ,along axis Y-Y’

3. Swinging to starboard or to port.

To find PP position we will simplify the factors which affect ship’s handling to the mechanical physics although the hydrodynamic effects have a considerable importance.

During straightforward movement, water-resistance force is applied right on the stem, which creates high pressure in front and around the bow (fig.2).

 

The same effect occurs for astern movement but in both cases the shape of underwater hull is very important in determining the high pressure effect.

As soon as a controlled or uncontrolled horizontal force acts on the vessel the ship will start to turn and she will expose a larger section of the hull to the water flow. The peak of water-resistance and pressure will therefore shift from axe X-X’ to the geometrical centre of underwater hull section area perpendicular on the new direction of the movement and the direction of the water-resistance (R), could be anywhere between longitudinal axis, X-X’ and transversal axis,Y-Y’.

Depending of the direction of the movement, the vessel’s speed, hull shape, trim and heel, etc the application point of the water-resistance force will be in different points along the vessel, changing continuously during complex manoeuvres.

To analyse the influence of horizontal forces applied on the vessel (ie rudder & wind) we have to relate these forces to the water-resistance force where it acts. This force will be present as long as vessel is floating and moving. The arm lever of these forces is the distance between their supports and Water-Resistance Force.

The resultant effect of several forces acting on a stopped vessel can generate all three movements. For our purpose, the rotation and the sideway movement are considered. The rotation movement has a centre of rotation which is the pivot point where the fore and aft extremities of the vessel are turning with the same angular speed inside of ship’s shape in all situations.

Besides the pivot point, the vessel’s trajectory has its own centre of curvature called the Momentary Centre of Rotation. In fact all forces acting upon a vessel have, more or less, momentary effects in ship’s dynamic movement.

Water Resistance and Pivot Point of a vessel stopped

Considering a ship stopped in the water we can find a point situated near its mid length, from where if a tug pushed with a force F the fore and aft extremities of the ship will move with same speeds V1= V2 (Fig.3).

 

 

fig 3

The force F is applied on the same support as water-resistance force R. Its centre of application is the Centre of Water (Lateral) Resistance (CLR). The lever F -R is therefore zero and the ship will move from position 1 -2 without any rotation.

If equal but opposite forces are now applied equidistant from the CLR then the ship will pivot around that point (Fig 4).

fig 4

Returning to the situation in Fig.3, if the force (F) is moved slightly aft of the CLR then the resultant will be a sideways movement coupled with a slight ahead movement which will cause the ship to start rotating but in this condition the pivot point will be ahead and well outside the ship shape (fig 5).

 

 

fig 5

From position 2, if our force (F) is now applied further aft and on the starboard 1/4, the speed of rotation is increased but the forward movement is reduced and the pivot point moves closer to the bow of the ship (fig 6).

 

 

fig 6

Moving this force right aft onto the rudder area ( i.e. with a pod proplsion unit) the pivot point may move back within the ship shape (Fig 7).

fig 7

The bow thruster will have opposite effect of moving the effective pivot point to the stern of the vessel (Fig 8). Obviously these are very approximate locations but at least serve to help anticipate where the pivot point might be.

 

fig 8

 

Getting Underway

If the engine is now put ahead with the rudder amidships with two tugs pushing up with equal power equidistant from the CLR the vessel will start to move ahead and sideways (Fig 9).

 

fig 9

Due to lateral resistance RL and the longitudinal resistance RI a resultant water resistance force RT acts on the starboard bow. The pivot point moves forward in the direction of the movement and consequently the levers of F1 and F2 related to RT change and d2 > d1. In consequence V2 >> V1  resulting in an accelerating swing to port. Even with a short “kick ahead”, this increasing of rotation speed can be seen. The same effect of course occurs when a vessel in a tideway is stopped over the ground parallel to the berth and the stronger the tide the greater is the effect. It is important to note that in this scenario the pivot point may again move ahead of the ship shape.

Likewise, if a vessel is moored with a current from astern, the pivot point will be aft at the moment the lines are cast off and ship will start to want to pivot around the stern with the bow moving away from the jetty faster than the stern if 2 tugs are alongside pulling off with equal power.

Fig 10 helps to explain why bow thrusters become useless for turning a vessel as the speed ahead increases.

fig 10

As the thruster (T) tries to swing the vessel towards the jetty, the water resistance on the CLR increases and with such a small lever (d) there is virtually no turning moment.

If we take the same ship and berth it stern to tide ( or approach the jetty stern first) ( Fig 11) then the lever (d) is long and the vessel will swing readily.

fig 11

The “Donkey Effect”

One of the most spectacular examples of applying an external force upon a vessel and getting the opposite result to that expected (donkey-like) is the movement of the vessel when a tug is acting on the support of water resistance force against it (Fig12).

 

If the tug starts to push on a vessel moving  at speed in position M1 it cannot turn the vessel due to the short turning lever. She will drift to starboard but will maintain the heading as in position M2. As soon as the tug stops pushing in position M3, the vessel will start to turn towards the tug. She will continue to turn in that direction as is shown in position M4 until the forces stabilise and the heading stability is restored.

In real time trials with escort tugs this effect has also been observed when the tug stays pushing on the hull. This effect along with those explained  in Fig 9 are most important for pilots using tugs on a vessel making way through the water. The higher the speed the more pronounced the effect.

JCB

The following link is to Paul Butusina’s full research paper from which the above article was edited:

Pivot Point Paper

 


 

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