Pivot pointed can be defined as the imaginary point about a vessel’s centerline about which the vessel is pivoted while turning and this point is not stationary and can change with the vessel’s speed and heading.

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**The pivot point is used to describe the ships turning circle maneuverability and handling at sea. It is not the actual center of rotation of a vessel but the apparent center of rotation.**

Geometrically pivot point can be defined as the point in a circular trajectory about which the vessel moves during a turning circle maneuver. It can be observed from the pivot point that the forward and aft of the vessel swing with the same angular velocity.

Pivot point also serves as a helpful tool for the vessel operators in determining the forces acting on the vessel and its equilibrium. Also, with regard to the area covered during a turning maneuver, we can also estimate the location of the pivot point.

If the pivot point is not located in the midship and is located in either the forward or aft of the vessel, the area will be four times larger during a turning circle maneuver than when compared to the pivot points being at the midship

Pivot points are generally located one-fourth of the ship’s overall length from the forward perpendiculars when moving ahead, at the midship when the vessel is stationary, and in close proximity to the stern when moving astern. The pivot points may be subjected to shift when an effective lateral force is applied.

## How To Find The Position Of The Pivot Point?

The pivot point doesn’t move instantly, but slowly depending on the hydrodynamical forces acting in the vessel. Let us consider the following cases,

- Ship at rest

Let us consider a ship at rest and on an even keel, condition subjected to calm weather conditions such that there are no external forces acting on the vessel, the pivot point coincides with the vessel’s center of gravity and can be located at half the length of the ship.

- Ship moving forward

Let us consider a vessel moving forward on an even keel condition subjected to calm weather conditions, two main forces acting on the ship which is the forward momentum of the vessel which builds up over a period of time as the vessel moves forward and the second force is the hydrodynamic resistance created by water against the hull trying to resist the forward motion.

In this scenario, the pivot point shifts forward from the midship and roughly can be assumed to be moved as 25% from the initial position which was midship or ¼ of the ship’s length measured from the bow of the vessel.

- Ship moving aft wards

Considering a vessel moving aft, the two main forces acting are aft ward momentum of the vessel along with hydrodynamic forces. The hydrodynamic forces will be predominant on the aft of the vessel.

The pivot point shifts aft from the midship about 25% or ¼ of the length of the ship measured from the aft of the vessel.

It should always be kept in mind that factors like acceleration, vessel geometry, and speed can play a vital role in determining the position of the pivot points. Also, the pivot point normally tends to shift away from the location of application of forces and moves towards the center of gravity of the vessel during applications such as bow thrusters deployment or when tugs are used to tow the vessel.

## Relation Between The Pivot Point And Turning Lever?

During a turning circle maneuver, there are multiple forces such as a rudder, centrifugal, and so on that act on a vessel that can shift the position of the pivot point.

- Case 1: Even lateral forces

Let us consider a 200 m long vessel in an even keel condition with calm water, being pulled against the starboard side both aft and forward of the vessel. Let us say both these tugs are able to generate a bollard pull of about 20 tons each. During the initial phase before the vessel is pulled the pivot point lies about the midship that is about 100m from the bow of the vessel.

Since the force applied from both the tugs are equal there are two equal turning levers which results in an even lateral motion and there is no shift in the position of the pivot point.

- Case 2: Vessel moving forward

Let us consider a vessel moving forward with an even keel condition with a calm environment, as discussed earlier the pivot point will be located ¼ from the bow of the vessel.

If we consider the same tugs pulling the vessel, the forward tug will provide a much lesser turning lever compared to the aft tug as the pivot point is shifted forward from the midship. Now, this is because the aft tug has a longer length of the vessel to work with compared to the forward tug.

- Case 3: Vessel moving aft ward

Let us consider a vessel moving aft ward with an even keel condition with a calm environment, as discussed earlier the pivot point will be located ¼ from the stern of the vessel.

If we consider the same tugs pulling the vessel, the aftward tug will provide a much lesser turning lever compared to the forward tug as the pivot point is shifted aftward from the midship leading to a much longer length for the forward tug to work with when compared to the aft tug. This results in the swing of the bow to the starboard side.

### What Motions Are Dependent On Pivot Point?

The pivot point depends on the two transversal motions sway and yaw but is independent of the longitudinal surge motion.

## Conclusion

The pivot point plays a huge role in determining a vessel’s maneuverability and handling characteristics.

To find the exact position of the pivot point we simply the forces which affect vessel handling to mechanical physics so that it becomes easier to work with and also consider that the hydrodynamical effects have primary importance when compared to other external forces.

Depending on the heading of the vessel, speed, geometry, trim, and heel, the application point of the pivot point will be in various points along the vessel, changing constantly during complex motions of the vessel.