Gravity pulls on every part of the boat. Wind pushes on the entire sail. Water's buoyant force pushes up on all submerged surfaces. These distributed forces are equivalent to forces acting at a single point. Knowing the positions of these special points simplifies the calculations of the torques.
The most familiar "center" is the center of mass. Simple experiments (in principle) can determine the center of mass of any object, including a sailboat. Suspend a sailboat from a single point. A line drawn directly down from the suspension point passes through the center of mass. It doesn't matter if you lift the boat by the bow, the stern, or the mast. All lines descending from the suspension points pass through the same center of mass. Sailboat symmetry means the center of mass lies in the plane that separates port from starboard.
Although gravity pulls down on every piece of a sailboat, all the forces act as if they were pulling on the center of mass with a force Mg, where M is the total mass and g = 9.8 m/s2 is the acceleration of gravity.
Just as gravity pulls down, buoyancy keeps a boat from sinking by pushing up with a force that is equal but opposite to gravity. Buoyancy pushes up on all submerged parts of a boat, but these forces act as if they were pushing at a single point. That point is the center of buoyancy.
When a boat is placed in water, it sinks down and moves water away. The mass of this displaced water equals the boat's mass. That is Archimedes principle. The center of buoyancy is the center of mass of this displaced water. Although the boat's center of mass is fixed, the center of buoyancy moves as a boat tips. A sailboat is stable when tipping causes the center of buoyancy to move in a direction that stops the tipping.
Wind pushes on a sail. The total wind force can be represented as if it acted on a single point. That point is the center of effort. A simple example is a mainsail shaped like a right triangle. If the pressure is uniform over a sail's surface, the center of effort is one-third of the way up from the boom to the top of the sail (the "head"), and one-third of the way back from the mast to the end of the boom. If the pressure is nonuniform, the total force can still be represented by a center of effort, but its position will be different.
There is also a center of effort for the water's horizontal force on a centerboard (or keel). This center of effort is centrally located on the centerboard.
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