How does a sailing boat sail at 45 degrees into the wind?

Question

I'm looking for the scientific explanations for how this works.

Answer 1

As said above, properly trimmed sails create a foil. The air has to move a grater distance on the outside of the sail to windward than it does on the leward side which creates a lower pressure on the windward side along the leading edge of the sail.   The result is the boat is sucked forward.  In addition to acting as a foil, the headsail funnels more wind over the mainsail, increasing the effect.

However, much of the pull is not straight in line with the boat.  This is where the center board or keel comes into play.  This makes it easy for the boat to move forward, but not so easy to move sideways, thus canceling much of the pull to the side.    This sideways pull is not completely canceled, so a boat sailing upwind will not travel exactly along the line at which it is pointing but will get pulled a little to down wind.  This difference is called leeway.