The Simple Principle Getting Sails Faster than the Wind

 Crosswind. 

 As long as some component of the wind is going across your bow instead of parallel to it, you can extract more energy from the wind. The limitation is that going faster perpendicularly makes the wind go faster relative to you, with some part of it a headwind, increasing your friction. But yes going faster than the wind isn't hard at all using a keel equivalent and the correct angles.

 What you can't do is go faster than a pure tailwind. Once you're going the speed of the tailwind, the air is relatively stationary to you. If you could extract energy from stationary air you would have a perpetual motion machine. Have to turn, get a crosswind, and accelerate that way.
 That is, you can't go faster than the wind while travelling in the exact same direction as the wind - if you get faster and then turn into alignment, you'll see a pure headwind, pure friction.

 There's an optimum angle between 0 and 90, and a true sailor would be able to tell you what it is.

 Without a keel, turning your sails isn't much use as the wind will mostly turn your vessel rather than accelerating it, unless the sails are exactly over your centre of mass, which they won't be because boats rock. (Hence all the oars on ye olde boats; they hadn't invented keels yet.) With a keel, the wind ends up trying to turn the water under your boat, but of course water isn't rigid so it becomes turbulence. A properly keeled vessel can not only go faster than the wind, it can head (painstakingly, tacking back and forth, never directly) upwind. 

 Exception: on land, using wheels on flat terrain, you can use a fan and gearing to extract energy from a headwind and go straight into it. However, this machine can only go into the wind - a tailwind would make the fan turn backwards, putting it in reverse; secondarily fan blades are concave, meaning they're convex (backwards) from the rear.
 I sincerely doubt you can get friction low enough that it goes faster than the wind, as friction usually goes with the fourth power of velocity, and you're starting at 1X[wind velocity] headwind. A larger fan gives you more power thus theoretically higher speed, but also increases your friction, limiting your speed at the same time. There must be some optimum fan size.