## Introduction

A ship in the harbor is safe, but that’s not what ships are for. – John A. Shedd, *Salt from My Atti*c, 1928

We all know that a ship is stable in a port, but that’s not the case when it sails out beyond the coastal waters. When at sea, a ship experiences continuous movement in six different ways. These are known as the six degrees of freedom:

- Pitching
- Rolling
- Yawing
- Swaying
- Heaving
- Surging

These movements may occur separately or sometimes be a combination of two or three. It is really uncomfortable to sail in these conditions. But the question is “Even though a ship experiences such terrible movements, what keeps her upright?"

## Gravity, Buoyancy, and Metacenter

The Center of Gravity is the point upon which the entire weight of the ship is assumed to act. The more the weight of the ship, the closer it will be to the keel. It is represented as “G" in the diagram. The fact is the point “G" follows the movement of masses on board a ship. For example: If a cargo of 50 tons is added to the lower most deck, the point “G" also climbs down. If a cargo of 100 tons is removed from the lower most deck, then the point “G" raises up respectively. This is illustrated in the picture (click to enlarge).

Center of Buoyancy: Buoyancy is an up-thrust or upward force exerted by water. Any object when dropped in water experiences this upward force. It is the density of the object which decides whether the object will float or sink. In simple terms, the center of buoyancy is the center of gravity of the underwater area of a ship or the collection of all individual buoyant forces assumed to act at one particular point. This point is referred as “B" and it is always acting equal but opposite to “G," and is assumed to act on the same vertical line.

Metacenter: As the ship tilts sideways, the underwater area changes. The water line changes from WL to W’L’. Thus the buoyancy also moves out on the direction of heel from “B" to “B1." However we have previously discussed that the point “G" and “B" are equal but exactly opposite and fall in the same vertical line. As the ship heels, the points “G" and “B1" are no longer in the same vertical line. Thus a line from “B1" is drawn to meet the vertical center line and the point of intersection is called the metacenter, “M." The distance between the points “G" and “M" is known as the metacentric height.

## What Happens when the Ship Rolls?

To understand this, please closely refer to the attached picture. Let us assume that the ship rolls over to the starboard side. As mentioned earlier, the center of buoyancy “B" shifts to “B1." This is because of the change in the water line or the underwater area. As the new center of Buoyancy “B1" is not in line with the center of gravity “G", let us draw a vertical line from “B1" to the original center line and call the point of intersection the metacenter “M."

The force of Buoyancy and Gravity are equal in magnitude, but opposite in direction. At this position of heel, they are not acting in the same line, but parallel to each other. Thus two equal forces acting opposite to each other constitute a “Couple." This couple tends to produce a rotational force, which brings the ship back upright.

Once the ship becomes upright, the force of Gravity and the force of Buoyancy, which are equal in magnitude and opposite to each other act on the same straight line and thus “B1" comes back to “B."

GM is called the Metacentric Height of the ship and GZ is called the Righting Moment.

Here are some typical values for metacentric height for some various types of ships:

The same effect happens when the ship inclines to the port side, too. These effects happen when the ship inclines for small angles of approximately 7 to 10 degrees. The Metacenter “M" does not change for these small angles, and the righting arm is considered to be straight. At higher angles, the position of “B1" will tend to be on an arc. Also the above explanation is valid when the metacentric height is positive. The effects when the metacentric height is negative will be discussed in future articles.