A Corrected Version on Positioning of Pivot Point

by Capt. Santosha K Naya - published -

A Corrected Version on Positioning of Pivot Point

Text and pictures by Capt. Santosha K. Nayak, Marine Pilot, Krishnapatnam Port  from his book "Theory and Practices of Marine Pilotage"

Understanding the fundamentals of the pivot point is highly required for understanding the alteration of the courses. Pivot point is an imaginary point on the vessel which turns on a circular path on the perimeter of vessel’s turning circle when the vessel makes a turn. The knowledge about the position of the pivot point in a manoeuvring situation provides the ship handler with the information on the geometry of motion of the ship. When sway and yaw occur simultaneously, a ship handler can only perceive the combined effect of drift and turn, which gives him a false impression that only a rotational motion happened about a certain point on the ship’s centreline. This apparent centre is called the Pivot Point of the ship. This is a simplified perception of two motions down to one motion.

It is at the same point as the longitudinal centre of gravity of the vessel when vessel is stopped and making no movement. It starts moving towards the bow when the vessel increases her speed. The distance of the PP from the longitudinal COG varies with the speed of the vessel.

We can understand the existence of pivot point mathematically as an imaginary point. Among all the points in the ship in planar motion, there is only one point on the centreline at which the sway and yaw completely cancel each other, thus making this point seem to be stationary. All other points appear to be turning about this point. This point is the Pivot Point.

Sway means the linear transverse (port to starboard) motion. This motion is generated directly either by the water and wind or currents exerting forces against the hull or by the ship’s own propulsion or indirectly by the inertia of the ship while turning. Yaw is the rotational motion of the vessel about the vertical axis. If the sway speed and yaw speed are known, the position of the pivot point can be obtained as the distance from the centre of mass (GP) using equation:

V + (GP x ROT) = 0

Where,   V(m/s) = Sway Speed;

                       G = Centre of Gravity;

                        P = Pivot Point;

               GP(m) = distance between P and G;

       ROT (rad/s) = Yaw Speed.

There are some traditional views held by ship handlers of the Pivot Point and also mostly found in the literature of books on ship manoeuvring. These views about pivot point are:

  • It moves towards the bow or stern depending on the direction of the longitudinal motion of the vessel
  • When making sternway, the pivot point moves aft and establishes itself approximately 1/4L from the stern
  • It is the centre of rotation of the vessel
  • It has instantaneous movement from the COG to its position

There have been many experiments carried out to understand the existence of Pivot Point and how it moves with the motion of the vessel. There are some new findings related to Pivot Point and the some of the traditionally held views about PP are incorrect. All the above mentioned views are incorrect. The corrected facts about PP are:

  • It is independent of direction of motion,
  • It is only an imaginary point
  • It moves gradually towards or away from the COG depending on the application of forces on the vessel.

However, ship handling professionals, particularly the seasoned practitioners, find it very difficult to accept these findings.


Verification Experiment to establish the location of Pivot Point

A verification experiment was done in for a panamax vessel. The ship’s turning force was provided by setting the engine half astern. The propeller is right handed with fixed pitch. For the purpose of analysis, the whole experiment was divided into 8 time intervals. In each interval, the result was analysed calculating the position of the pivot point as the average in the interval. The positions are given as percentage lengths between the bow and the pivot point, to the length of the ship. The experiment shows plainly that the pivot point was at around 17% of the ship length from the bow. Near the end of the experiment, it is obvious that the pier is interfering with the water flow being created by the propeller.

This experiment conclusively proves that the traditional teachings and leanings about the pivot point for centuries are incorrect

Position of Pivot Point as deducted from the experiment                           

The exact position of the pivot point may be deducted from the following formulae. GP is the distance of the Pivot Point (P) from the longitudinal Centre of Gravity (G).

GP = - (L2 +B2)/ 12GFr, is a simple equation for a box shaped vessel

Where, GP – Distance between the GOG and PP,

              Fr – Position of Resultant force on the vessel,

               L – Length and B- Breadth of vessel

The interpretations of above findings are essential knowledge for the ship handlers. Above equation correlates some practical points which can be used by ship handlers during manoeuvring of ships are as follows:

  • The minus (‐) sign indicates that the pivot point appears on the other side of G from Fr.
  • A bigger GFr yields a smaller GP, which means that an external force farther away from G causes the pivot point to be closer to G.
  • A bigger block coefficient will cause the pivot point to be closer to the bow.
  • The direction of the longitudinal motion is irrelevant with the pivot point location.
  • If the propeller and rudder combination at the stern is used as the only propulsion system, the pivot point will always appear near the bow


A-Vessel moving ahead,
B-Vessel moving astern, 
C-Vessel experiencing external force 
D- Vessel being pushed by one tug (In case 2 tugs, the tug applying more force decides)

A-Vessel moving ahead,
B-Vessel moving astern, 
C-Vessel experiencing external force 
D- Vessel being pushed by one tug (In case 2 tugs, the tug applying more force decides)

A-Vessel moving ahead,
B-Vessel moving astern, 
C-Vessel experiencing external force 
D- Vessel being pushed by one tug (In case 2 tugs, the tug applying more force decides)

A-Vessel moving ahead,
B-Vessel moving astern, 
C-Vessel experiencing external force 
D- Vessel being pushed by one tug (In case 2 tugs, the tug applying more force decides)

The pivot point settles down at one point when the motion of a vessel becomes steady. All above observations are confirmed by pilots carrying out manoeuvring regularly on day to day basis. The understanding of above facts can be understood very well when vessel is making a astern movement at a certain speed aided by the tugs while keeping in a restricted and narrow channel.
Editor's note:
Opinion pieces reflect the personal opinion of individual authors. They do not allow any conclusions to be drawn about a prevailing opinion in the respective editorial department. Opinions are usually deliberately formulated in a pronounced or even explicit tone and may contain biased arguments. They are intended to polarise and stimulate discussion. In this, they deliberately differ from factual articles you typically find on this platform, written to present facts and opinions in as balanced a manner as possible.

Join the conversation...

There are five comments to this.
Login or register to view comments and join the discussion!

Opinion Scientific Fact: The ‘traditional’ understanding of the ship’s pivot point is wrong!

by Tim Cummins, Harbour Pilot, Portsmouth International Port - published

In fact, the pivot point that we “see” is a trick of the eye, it looks like the ship is rotating about this point but in fact it is elsewhere, a point that you cannot see.


Article A review of the ship’s pivot point: Science, Maths and Observation’ Where is the centre of a ship’s rotation?

by Tim Cummins, Harbour Pilot, Portsmouth International Port - published

This my attempt to do just that. This is a summary of all scientific papers and articles that I could find about the ship’s pivot point. I have added links to any videos associated with the publications and have also included any useful diagrams or equations that the authors published to help explain their research.


Video Pivot Point Demo - HS Wismar

Found on YouTube. Created by "ISSIMS GmbH - Marine Prediction Technology".
SAMMON Lecturing Video describing
"Pivot Point Demonstration"

SAMMON - the IDEAL tool to identify manoeuvring capabilities of a ship - SAMMON - learning the EFFECTIVE way


Video Recorded Webinar: Pilot Ladder safety and Pilot Transfer procedures

Found on YouTube. Created by "HIMT".
Recorded presentation by All India Marine Pilots Association (AIMPA) on the topic "Pilot Ladder safety and Pilot Transfer procedures"


Video First women boat pilot for Mozambique

Found on YouTube. Created by "Marine Pilot Ana Goetsa".


Video Successful overtaking of another ship in a canal - Port Revel Shiphandling

Found on YouTube. Created by "Port Revel". From 2014...

Manoeuvring large ships at close quarters and on shallow water is one of the most difficult aspects of shiphandling because of the complex hydraulic interactions depending on the ships' speeds, on the water depth and on lateral restrictions like in canals. Training is conducted both on meeting and on overtaking ships in shallow waters. This video shows how overtaking in a canal should be conducted: come in close to the stern and then move away from the bow that will be sucked towards your ship.

More information: http://www.portrevel.com/3781-shiphan...


Video How AIS Works - Operation of AIS

Found on YouTube. Create by "Marine Online"
This section should give a short introduction to:
Operational aspects of AIS
Functions and features
Human aspects

Key Points
The AIS transponder unit.
Automatic communication.
SOLAS requirements.
AIS Information sent by ships.
Static information update. MMSI
Dynamic information update.
Voyage related information update.
Checking AIS data. BIIT
Display Of AIS data.
Recommended AIS symbols.
Sleeping target symbol.
Activated target symbol.
Selected target symbol.
Dangerous target symbol.
Lost target symbol.
AIS information displayed on ARPA and ECDIS.
Minimum graphical information.
Symbol harmonization.
Priority of AIS target symbols.
Common reference.
AIS information on radar .
Suppressing dangerous targets.
Course Over Ground (COG) Vector.
Speed Over Ground (SOG) Vector.
Automatic target acquisition.
Warning limits. CPA, TCPA
Automatic display selection.
Human interface.
The human factor.


Video OMC International DUKC® - Port of Melbourne

Footage of deep tanker Felicity navigating through the treacherous waters of the Port Philip Heads channel entrance.


Opinion Rituals around shipping. The „Titanic“ never got its name in a christening...

by Bianca Reineke, lutheran Pastor, Germany - published

Do you ever leave the harbour to get on a vessel you will guide along without a ritual? Whatever we trust in, whatever the rituals or traditions you Marine Pilots have - when you board your pilot boats, climb the ladders, get the vessels through the harbour - keep them and cherish them, they are good and they are important.


Article Harbour Master Naresh Sewnath navigates his way to success


Two decades ago, candidates were selected for TNPA's accelerated training programme in Rotterdam, which aimed to train a new generation of ship pilots, managers and other maritime professionals.