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

by Tim Cummins, Harbour Pilot, Portsmouth International Port - published on 9 July 2020 4122 -

Tim Cummins, Harbour Pilot, Portsmouth International Port, UK

The ‘lever theory’ that we know so well in ship handling is still correct but the point where the lever rotates is not at the pivot point position that we may have been traditionally taught or even “see” when a ship is turning and moving ahead (or astern) at the same time. 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.

The question I asked myself was “So what? The ship is still rotating about a position somewhere about the ship even if it is not at the position that I understanding is the pivot point”. But then I realised (1) we as ship handlers have been operating ships on fundamentally incorrect principles (2) we can probably do more to a ship than we realise (3) it better explains why ships ‘do what they do’.

Archimedes ‘Lever theory’: A bar balanced on a pivot, the fulcrum. The fulcrum is the point where the lever turns or the rotation point. The effect of the lever depends on how much force is applied and where the force is in terms of distance from the ‘pivot point’. A lever can amplify force.

The ‘traditional’ pivot point theory of ships: The position of the pivot point on a moving ship should be right ahead or right astern depending on direction of motion but the friction of water causes a resistance therefore the pivot point settles in a position as indicated in the top diagram.

A tug pushing on a ship moving ahead using the ‘traditional’ pivot point theory: When pushing at a position away from the pivot point, such as right on the starboard quarter, it will cause the ship’s stern to swing to port and the bow to swing to starboard. The stern will swing with a rate of turn greater than that of the bow. This is still true even with the new pivot point theory.

A tug pushing at the position of the pivot point should have no turning effect because there is no lever, but instead may cause sideways movement of the ship if the force is big enough. This idea has been challenged by the new ‘pivot point’ theory.

Captain Hugues Cauvier started the argument against the ‘traditional’ pivot point concept and has since been supported by and Dr. Seong-Gi Seo (PhD) and Captain Paul Butusina. They argue that a ship rotates about its centre of lateral resistance (COLR), a position on the ship’s underwater hull form that will not rotate if force is applied in that position. Applying ‘lever theory’ as normal will mean that if lateral (sideways) forces are applied either forward of aft of the centre of lateral resistance then the ship will start to rotate about the centre of lateral resistance (assuming the force applied is greater than the water resistance acting against the hull). The position of the COLR will change depending on what the ship is doing as it moves through the water such as changes in direction, speed, trim, draft, experiencing heel in a turn. For example, when a ship moves astern from stationary the centre of lateral resistance also moves astern from a position that was approximately midships.

So, what about the pivot point that we “see”? A ship looks like it is rotating about a non-moving point on the centreline of the ship and not at the centre of gravity. Captain Hagues Cauvier, Dr S.G. Seo and Captain Paul Butusina provide a good answer.

Imagine a ship running dead slow ahead has a tugboat strapped to it port quarter and the pilot asks the tugboat to push on (or pull) with full power at right angles to the ship’s hull. This will cause two reactions in combination, rotation about the centre of gravity of the ship and sideways (lateral) or ‘sliding’ motion. As the momentum of the rotation builds it starts to appear that the ship is rotating about a central point but this central point is not at the centre of gravity of the ship but in a position that is away from the tugboat’s exertions, about a position that is 1/3rd of the ship’s length from the bow (if the ship was moving astern about a position that is 1/4th of the ship’s length from the stern). In fact, what is “seen” is concurrent sway, yaw and surge effect (aka drift, turn, forward motion) which appears to the ship handler as if the ship is swinging about a non-rotating point on the centreline of the ship if viewed against the water. This ‘visual’ position is mistakenly thought to be the ‘pivot point’ but in fact it is only the ‘apparent’ centre of leverage.

The trick of the eye: The six degrees of freedom of a ship; and a drawing demonstrating Captain H. Cauvier’s argument adapted from figures 4,5,6 and 7 from his article in UKHMA ‘The Pivot’. The ‘apparent’ pivot point is a combination of yaw and sway happening simultaneously and appears as if a part of the ship has not changed position in space. Dr Seo explains it as “the perception of two motions down to one motion”. Also, the diagram shows that the apparent pivot point will appear in a position away from the force being applied.

A verification experiment illustrated in Captain’s Hagues Cauvier’s article demonstrates the above.

If a lateral force is applied right at the bow (or stern) of the ship the pivot point ‘appears’ in a position away from the acting force and not in the position expected from the ‘traditional’ pivot point concept. This strengthens the argument that it is a ‘trick of the eye’ and that the ship is in fact pivoting on another point.

The diagram also shows that when lateral (sideways) forces are applied to the ‘traditional’ ‘pivot point’ position of a ship moving ahead this does have an effect because the ‘real’ pivot point is further aft than what is “seen” by the ship handler. There is a lever.

Doctor Seong-Gi Seo’s scientific papers supports the above arguments with mathematical equations and further demonstrates that the ‘traditional’ pivot point is not the centre of the ship’s rotation. The paper also addresses other common ‘mis-understandings’ about the pivot point. He says that the pivot point does not move instantly but gradually, and it does not move toward the bow and stern depending on whether the ship is going ahead or astern but is in fact independent of ship’s motion. He also demonstrates that the ‘apparent’ pivot point of a vessel can be ahead of the ship and outside of the ship’s profile for some manoeuvres.

The pivot point of a ship stopped and moving through the water. Adapted from figures 8,9,10 and 13 in Dr. Seo’s paper published in the International journal of Marine Navigation and Safety of Sea Transportation in December 2016 (Volume 10, Number 4)


Capt. H. Cauvier “The Pivot Point” – Article published in the United Kingdom Maritime Pilots’ Association “The Pilot”, October 2008, No.295

Capt. P. Butusina “The Pivot Point Revisited” – Article published in the United Kingdom Maritime Pilots’ Association “The Pilot”, Autumn 2011, No.306

Dr. Seong-Gi Seo “Safer and More Efficient Ship Handling with the Pivot Point Concept” - International journal of Marine Navigation and Safety of Sea Transportation in December 2016 (Volume 10, Number 4)

Dr. Seong-Gi Seo – “The Use of Pivot Point in Ship Handling for Safer and More Accurate Ship Manoeuvring” – Proceedings of IMLA, 1 October 2011, 1 (29), pp. 271-280 – available from https://ssudle.solent.ac.uk/id/eprint/2366/1/IMLA_Article(final).pdf
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. Opinion pieces might be deliberately formulated in a pronounced or even explicit tone and may contain biased arguments. They might be intended to polarise and stimulate discussion. In this, they deliberately differ from the factual articles you typically find on this platform, written to present facts and opinions in as balanced a manner as possible.

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Genick Bar-Meir U.S. Virgin Islands
on 1 April 2023, 15:43 UTC

The pivot point for ship and submerged body is in the mass centre of the combined of the added mass and body. Thus the understanding or the rotation point requires to understand what is added mass. The added mass is explain in book "stability of ship and other bodies" which can be obtained free here https://zenodo.org/record/6462156#.ZChQd8bMLeQ
The center of rotation or pivot point is not depends on the forces as claim in these comments. There is a proof that it simply wrong.
You also can read the article almost no math here
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Louis Vest Houston Pilots, USA
on 19 November 2020, 22:25 UTC

Kris De Decker suggests that the traditional method is ok to use in places where there is maneuvering room but that the demands of extremely confined spaces make use of this revised pivot point necessary because the location of the pivot point will be more accurate than the rough estimate provided by the traditional idea.

In all the occasions I have had in which the turning room was extremely limited (less than 15m forward and aft) the vessel was stopped. Longitudinal motion was limited to a "kick ahead" or a "kick astern". Using complex math in this situation was never considered. The pilot doing the maneuver had best be paying attention to spotters at the bow and stern of the vessel telling them their clearances. The pivot point was figured to be amidships and had no real opportunity to dance around.

The only possible practical use I can see for this information might be the refinement of mathematical models for ship simulators. I have had experience working with hydrodynamicists to validate simulators in the past. The simulators were to be used to model ships in extremely shallow water and narrow channels of harbors. I don't know if the math has gotten any better in the last 20 years, but at that time they were adjusting the common equations used for predicting ship motion by adding constants that ended up being numbers to the power of ten or more. Which is to say that the hydrodynamic behavior of ships in narrow channels and shallow water is very poorly understood. In that milieu the refinements offered by the new vision of pivot point will be a drop in the bucket.
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Jim Wright Southwest Alaska Pilots Association, USA
on 12 September 2020, 18:17 UTC

The line in the article catching my immediate attention is, “I was once a mystified practitioner”. That seemed to accurately reflect my 30 years as an Alaska pilot handling vessels of all types and sizes both with and without tug assist.
The question then becomes, “how can a pilot have a successful career in such a state of mystification?”.
Perhaps the answer was included in an earlier comment by another pilot to the effect that, “what sets Harbor Pilots apart from others is an observable understanding of relative motion”.
In my case, post retirement work as a facilitator in shiphandling sim exercises helped to combine observation with science. In my opinion, observation and experience still produces the best value.
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A community member on 13 July 2020, 19:33 UTC

This comment has been removed.

Ricardo Caballero Vega Panama Canal Pilots Association, Panama
on 13 July 2020, 17:57 UTC

I don't see any reason for being angry. On the contrary, I highly appreciate the fact that this open up new discussions on the matter. Especially during these days in which Pilotage, in some places, is being put on the spot and pilots questioned about their necessity.

We are not ship drivers, we are ship handlers, and there is science behind ship handling.

Tim Cummins Portsmouth International Port Portsmouth Pilots, United Kingdom
on 12 July 2020, 13:31 UTC

I appreciate the comments and please note this article is very brief and is only intended to reflect the work of Captain Hague Cauvier, Capt.Dr. Butusina and Dr. Seong-Gi Seo and to instigate continued discussion.
I suggest that the scientific paper by Dr. Seong-Gi Seo and the articles referenced above are read and then you can know more about the science that is not fully explained in my opinion piece. All of the references are free to download.
I have had a varied response and some mariners have been quite angry at me. I have also had many supportive replies. Apologies if I have caused a negative reaction and caused ‘frustration’. This is only an opinion piece.

Captain Wade Armstrong Hawaii Pilots' Association, USA
on 12 July 2020, 04:51 UTC

Having studied the science of ship-handling for decades, I am frustrated by the statement "Scientific Fact" without offering any actual evidence to support the claim. As Michael Nicholson commented, when you make a claim like this, be prepared to provide a real answer, which was not done.
The traditional concept still works well for better than 90% of pilotage maneuvers, and I am struggling to understand how this theory (not scientific fact) can be easily applied.
Captain Wade Armstrong
Pearl Harbor Pilots
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River Pilot Kris De Decker DAB Loodswezen, Belgium
on 10 July 2020, 10:02 UTC

This article is recommended reading for all pilots executing manoeuvers in confined waters. The "traditional pivot point concept" is a simplification of the academic "new theory of the pivot point". Like any simplification it has advantages (easy to understand, easy to apply, easy to explain) and has it disadvantages (not applicable in all situations). For manoeuvers with sufficient space the "traditional" method can be used. For manoeuvers with very limited space the more accurate "new theory" should be applied. For example, when turning a vessel with a forward tug and aft tug in a vey tight space the orchestration of the tugs will become critical as the pivoting point will be changing depending on the tug's pulling force and the motion of the vessel. Add some wind and some current and the prediction of the vessel's motions becomes even more difficult. Hopefully the simulator developers are reading this too because many simulators do not accurately simulate the manoeuver motions of large vessels in confined and undeep waters.

Ricardo Caballero Vega Panama Canal Pilots Association, Panama
on 10 July 2020, 01:55 UTC

I very much value the reevaluation of the "traditional pivot point", and find it fascinating that a concept largely used by ship handlers, turns out to be wrong.
However the idea or concept of the pivot point is paramount in piloting, and the fact that it hasn't gone out of fashion for such a long time makes me think that, even if wrong, has been usable.
New findings, supported by scientific data, experimentation, and mathematical equations are important in the sense that concepts are better understood. In the practical sense, at least in this case, they are of very little use. Are we going to ignore what our eyes, deceivingly sometimes, are telling our brains? It would be very difficult to do. Pilots normally take a curve earlier than they should even when the screen of their tablets is telling them that they can go deeper, precisely because they tend to trust their eyes.
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Mr Michael Nicholson Shipmove Ltd., United Kingdom
on 9 July 2020, 14:51 UTC

I don't think it's a good idea to start a hypothesis or a theory with the words "Scientific fact".
I did not find the explanation easy to follow, and the issue of the position of the applied force itself having an effect on the position of the pivot point (which it surely does) seems to have not been explained or taken into consideration. However my main criticism is that this alternative explanation does not assist the mariner as it is more about telling him where the pivot point isn't than where it may be. At the end of the day the ship performs as if the pivot point is in the forward 1/4 when going ahead and performs as if the pivot point is in the aft quarter when going astern. If the pilot or master acts on this assumption, he will not go wrong.
It's almost immaterial where it physically or theoretically is, if the current perceived wisdom leads to predictable movement and a succesful outcome.

Herman Broers Loodswezen Rotterdam - Rijnmond, Netherlands
on 9 July 2020, 12:53 UTC

Now that we accept the fact that the “apparent” Pivot point is outside the Ship When moving through te water, as a result of tugs, wind, current and rudder, and given the fact that this pivot point moves over an arc, the pivot point of the total movement is located outside the Center line of the ship.


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