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Knowing the angle of the sail and the angle of the wind, how can you calculate the resulting angle of the boats movement?

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    Or rather, the direction of its keel as mentioned above.2012-03-02

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In a simple model (of a boat in stationary, frictionless water), there are three components to the motion of a sailboat:

  • The direction of its keel, $k$
  • The direction of the wind, $w$
  • The normal direction of its sail, $s$

Speaking without precision about physical quantities, the force on the sail is the component of the wind normal to the sail. The force on the boat is the component of the force on the sail parallel to the direction of the keel. So the force on the boat is $\langle w,s\rangle \langle s, k\rangle k$.

In a more complicated model, one must take into account any currents pushing the boat and the interaction between the boat's hull and the water.

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    Yes, true. I have added a caveat to my answer.2012-01-02