Hello! Capt. Erica, here, making my debut with a brief overview of stability. For my off-season job, I teach high school physics, so I thought this would be a good place to start.

First, some definitions:

Center of Gravity (aka. Center of Mass)

Every object has a point that is in the middle of the way its mass is arranged, called the Center of Gravity (COG), around which the object will rotate. For humans, it is near our belly buttons. Relocating your mass in any way, such as by raising a hand or bending over, moves the location of your COG. It is sometimes called the balance point, because if the COG is located above the support, the object will balance. Although gravity pulls down on every part of an object, the COG is often the point we use to model what gravity will do to the object as a whole.

For a boat with a symmetrical hull, the COG will be on the centerline, in the average location of the mass. If you add mass to the boat, such as cargo, fuel, rigging, or by raising a dinghy, the operating Center of Gravity moves to the new center of all masses. Each object has its own COG so you can estimate the location of the overall COG. 

Figure 1: Point G shows the location of the Center of Gravity of the hull.

Figure 2: The operating location of the Center of Gravity of the boat has moved as a result of the addition of the cargo and dinghy.

Buoyancy

When a boat is placed in water, it pushes some amount of water out of its way. The amount of water that is displaced results in the force that pushes the boat upward, called buoyancy. To estimate its location, look at the part of the hull that is under the water line. The center of that area is the place we will consider the buoyancy force to act. Like gravity, it acts along each part of the hull, but we are simplifying in order to model it.

Figure 3: The blue shaded area shows where the hull is submerged in water. Point B is the center of the submerged section, which is the location of the buoyancy point. 

If the boat tips or heels and a different part of the hull is underwater, the location of the buoyancy point will change.

Figure 4: The location of the buoyancy point (B) moves depending on which part of the hull is submerged. 

How Gravity and Buoyancy Work Together….Or Not….

If a boat is simply sitting on the water, the Center of Gravity will be above the buoyancy point. The force of gravity pulls down while the buoyancy force pushes up. They counteract each other and the boat floats and balances.

Figure 5: The boat is stable when the center of gravity (G) is directly above the buoyancy point (B). The force of gravity acts downward while the buoyancy force acts upward and they counteract each other.

If the boat heels, then the location of the buoyancy point moves out from directly underneath the COG. The buoyancy force then pushes the boat up some distance away from the COG, and causes the boat to rotate around the COG, righting. 

Figure 6: When the buoyancy point (B) is outboard by a distance called the righting arm (r) from the center of gravity (G), then the buoyancy force will cause the boat to right using the torque shown in pink.

The distance directly outward from the COG, level with the horizon, to the path of the buoyancy force, is called the righting arm. The larger the righting arm, the better the boat will right itself. The desire for the boat to rotate around its COG and right itself is also called torque.

If the boat heels further over, the buoyancy point moves closer to the COG. This makes the righting arm shorter and gives the boat less strength to right. Assuming no mass relocates or water comes onboard, it still will right, but more slowly to start.

Figure 7: When the boat heels further, the buoyancy point (B) becomes closer to the center of gravity (G), shortening the righting arm (r), and creating a weaker righting effort or torque. Assuming no water gets into the boat, it will still right, but more slowly to start.

There is a point at which the boat will heel too far. Once the buoyancy point moves to the keel side of the COG, the upward force it exerts will cause the boat to rotate the opposite way around the COG, causing the boat to capsize. Again, this starts slowly, but the farther the buoyancy point gets from the COG, the longer the righting arm and the stronger the rotation will be.

Figure 8: When the buoyancy point (B) moves to the keel side of the center of gravity (G), the buoyancy force will no longer cause the boat to right, but will reverse it’s acting direction and will cause the boat to capsize.

Figure 9: The farther away the buoyancy point (B) moves from the center of gravity (G), the greater the resulting torque will be. In this case, it helps the boat capsize faster.

Messing Around in Boats and Using These Forces to Your Advantage

You can feel these forces at work especially well in a small boat. If you press on the gunnel of a canoe, you can feel it push back up at you. There is a tipping point when you will feel that force is the strongest. Be careful here, push too far past this point and you’ll be overboard! 

Figure 10: Messing around in a small boat can give you a good feel for how rearranging your mass will move both the center of gravity and cause the boat to tip, moving the buoyancy point. You can find a balance point with most boats where the central COG (G) is above the buoyancy point (B).

You can also move the locations of each point easily in a small boat. Moving yourself moves the COG; tipping the boat moves the buoyancy point. You can find a balanced point where the boat is tipped but stable, as in Figure 10. This is also part of how hiking out helps in a small sailboat, why a crew will sit on the rail of a 12m, or why some fishing boats have outriggers.