The Pivot Point is the point that the ship turns around.

The position of the pivot point is the result of all forces inducing ship motion.

These forces are so numerous and so variable that the exact position of the pivot point cannot really be anticipated. At best it can be guessed.

When the ship is dead in the water the pivot point is generally in the center of the ship.

When initially ordering engines ahead, the pivot point shifts forward as the speed increases. Once the ship is steady state steaming, the pivot point settles back at about 1/3 from the bow.

When ordering engines astern the opposite takes place; the pivot point shifts aft and settles about 1/3 from the stern.