I've heard that a beam reach (perpendicular to the wind) is the fastest point of sail on modern sailboats, but I haven't heard a satisfying explanation of the physics behind the claim.
Triangular sails propel the boat by forming an airfoil and generating lift. With a rigid airfoil, such as an airplane wing, my understanding is that the lift should be proportional to the speed of the air over the foil. That would imply that sailing upwind should be faster, since the apparent wind is greater when sailing against the true wind. At the same time, if one sails into the eye of the wind, the sail loses its shape, and stops acting like an airfoil.
The tension between these two processes would indicate an optimum somewhere in between sailing close-hauled (as close to the wind direction as possible while maintaining sail shape; usually about 45˚ away from the wind) and a broad reach.
We can rule out running before the wind (sailing directly away from it), because then the sail acts like a parachute rather than an airfoil, so the boat can never go faster than the wind (whereas, in an infinite sea of frictionless water with no air resistance, sailing upwind would cause the boat to accelerate forever–much better!)
Also, I suppose one has to consider the direction of the force from the wind. If we can assume that the force of the wind on the sail is perpendicular to the boom (which I'm not quite sure we can), then on a beam reach the forward component of the wind force vector is greater than when sailing close-hauled, where the boom is more closely aligned with the centerline of the boat. Maybe that's actually the most important factor.
Then there's drag from the wind and water, but I'm not sure how much that matters for this particular question… there's also waves to consider, which travel in the same direction as the wind and would thus also favor a beam reach, but let's assume they're not significant.
So, as a layman I'm not sure if my line of thought really holds water (so to speak). Is my thinking correct, and if so, which of the phenomena is mostly responsible for the beam reach being the fastest?