Knowing the angle of the sail and the angle of the wind, how can you calculate the resulting angle of the boats movement?
How to calculate the angle at which a ship moves?
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trigonometry
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0I don't have time to make this a full answer, but break the velocity down into its components (do you know the velocity)? If not, break it into components using the velocity as a variable. Then, I am not sure how much you are supposed to read into the sail direction - what assumptions are you making? – 2012-01-01
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0If the sail of the boat is at a certain angle, surely the boat will go at a different angle? It's like light refractoriness. – 2012-01-01
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0It's effect should vary based on the shape of the sail... – 2012-01-01
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0It depends whether there is resistance against lateral movement - a keel or centreboard. Also whether the steering mechanism (rudder) can be ignored. And many other factors - e.g. sails are not flat. – 2012-01-01
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0This question is theoretical, I just want to know the basic equation for working out the direction, assuming that the sail angle effects the direction of the boat. – 2012-01-01
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5Actually, for a real sailboat, the (first-order) answer is that it moves through the water in the direction of its keel. The relation between wind and sail determines whether it is speeding up or slowing down. For a second order approximation, the wind can also push the keel _sideways_ through the water, but supposedly that effect is deliberately minimized by the hull design -- it needs to be minimal or the boat wouldn't be able to tack. – 2012-01-01
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0A better question would be: Given the wind and sail angle, which direction is the _force_ on the boat exerted by the mast and rigging? This is already a somewhat complex aerodynamical question depending on the precise shape of the sail. After we solve that, we can then treat the interaction between this force and keel, hull, current as a separate subproblem. – 2012-01-01
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0I second the previous comment! The direction of the boat's movement is mostly governed by the rudder, regardless of wind direction. The OP's question seems poorly formed. – 2012-03-02
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0Or rather, the direction of its keel as mentioned above. – 2012-03-02