I am learning sailing on a 5m catamaran (Nacra 5). I am familiar with basic aerodynamics and the physics of the sail and keel.
We learned that when sailing closed hauled, too tight a mainsail tends to bring the boat up to the wind. And that the opposite is true for the jib. For example, one may steer up to the wind to come about, using the mainsail alone, by trimming it tight.
My question is why the trimmed mainsail in the above setup gives a larger torque.
This also seems opposed to the rule: "The more the mainsail is sheeted out the more the boat tends to come up.", as explained in http://www.sailtheory.com/mandf.html#sailsteering
To my understanding, there are several possible competing effects involved:
(1) Effects that tend to INCREASE the mainsail torque to head up:
(1A) The direction of the sail force becomes more perpendicular to the boat. This increases the heeling torque. Since heeling motion happens faster than turning, the boat will heel more. This moves the sail force out, which increases the lever arm and the torque to head up. see diagram in: http://www.sailtheory.com/mandf.html#hellingstuur
(1B) The sail force moves backwards since the sail is stretched backwards. This increases the lever arm and the torque.
(2) Effects that tend to DECREASE the mainsail torque to head up:
(2A) The direction of the sail force becomes more perpendicular to the boat. Assuming that the force is perpendicular to the sail, and that the center of rotation is between the mast and the center of force, one sees that pulling the sail in, reduces the torque to head up, as can be seen in the following diagram:
As Theta gets smaller, the torque Tau is reduced. This is opposed to what is stated in some of the answers below.
(2B) The sail force is reduced since the sail was pulled beyond its optimal angle of attack, thus losing lift and reducing torque.
(2C) Due to (2B) heeling torque is also decreased. With a similar reasoning to (1A) this decreases the lever arm and torque.
(2D) The sail force moves forward since the aft part of the sail is too flat and stalls. This shortens the lever arm and reduces torque. This is described in http://www.sailtheory.com/mandf.html#sailsteering
We know from reality that 1A+1B > 2A+2B+2C+2D. Considering heeling alone, we also know that 1A > 2C. It remains to be explained why in general this is the case.