BALANCE
(Picture from "The Annapolis Book of Seamanship", Rousmaniere, 1999.)
A sailboat has large forces acting on its sail which cause the boat to have a tendency to roll in the direction that the wind is blowing on the sail. This must be counteracted by a keel that has the appropriate surface area and ballast to keep it upright. When the rudder, keel, and sails are all applying forces on the boat they can influence horizontal rotation. The physics of sailboat balance can be treated like a static equilibrium problem. If the sum of the torques acting around the center of balance and the sum of forces acting on the centerline are zero then the boat is in equilibrium. An appropriate force diagram for the forces that influence the yaw (horizontal rotation) on a boat would look smething like the following diagram. If these four forces sum up to zero; the boat's yaw will be in equilibrium (the boat will not experience any horizontal rotation).
A diagram for the forces that can cause roll (vertical rotation with the center of bouyancy acting as a moment) is shown here:
(Picture from "The Science of Yachts,Wind, and Water." Kay, 1971.)
It is appropriate to calculate the torques around the center of rotation in order to calculate what forces could be generated in order to acheive equilibrium at this angle. Since Torque = (Force) x (distance from center of rotation) x (sin (the angle of the component of the force vector perpendicular to the axis being torqued)), This quantity would have to be calculated for every force that exerts a torque on the axis of roll. If the sum of the torques equals zero then the boat is in equalibrium. For the above example
torques would be calculated for "W", the drag force the water exerts on the keel, the windforce on the sail, and the water sideforce.
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