A fast sailboat, e.g. a boat that has a lot of sail and sits high on the water, can sail faster than the wind speed. Multihulls (catamarans and trimarans) sail faster than monohulls because a monohull must sit low in the water and/or have weighted ballast to offset the force of the wind on the sails. This creates drag and added weight for the monohull. A multihull is much wider (and lighter) than a monohull, and width itself offsets the force of the wind on the sails, eliminating the need for ballast and depth.
That said, a sailboat is like a bicycle. The faster it goes, the faster the wind hits the rider. And the faster the wind hits the sails, the faster the boat goes. It’s almost a perpetual motion machine! When there’s no wind, you can use a canoe paddle to make a catamaran go fast enough to fill the sails with wind and actually make your own wind, cheating the system! It’s amazing to see your boat sail along even when there’s no wind. Alas, the drag of the water slows the boat back down, so after a short while, you must start paddling again. You paddle back up to speed, relax for a minute, and sail along until the boat slows down again. Repeat until the wind picks back up, or until you get home.
The added wind speed your boat creates is called Apparent Wind, and if you’re going fast enough, the apparent wind always comes from the front, just like on a bicycle.
The reason the boat moves forward and/or even into the wind instead of sliding sideways (a problem with airplanes, actually) is because hull edges, foils and rudders stick down into the water and provide sideways resistance.
Example: Place an ice cube on a table, against a wall. Push on it just the right way, and it will scoot forward.
The sail shape forces the wind to rush across it in one direction from front to back, and the foils digging down into the water provide sideways resistance. The combination of the two creates forward motion.
Not a sailor, but I think that when a sailboat is rigged for sailing upwind, the wind blows across the sail and pushes it forward against the wind. So configured in that setting, paddling into the wind would be doing the same thing - putting wind across the sail and having that wind push the boat upwind.
It’s not really upwind as much as crossways, using the water to push the boat upwind, but the effect is the same.
Still trying to figure out the paddling making the wind which then pushes on the sail and gives you more push.
You can’t sail directly into the wind. Paddling or using a motor on a still day will create a wind coming from directly ahead, which will not assist your travel. In fact, having the sails up means you just have more drag.
I have recently experienced exactly what Davmor describes. It is counter-intuitive, but the effect is real, but it’s certainly not perpetual motion nor in violation of thermodynamics. My experience is anecdotal, but that’s all I’ve got.
I recently acquired a kayak with a sail and a pedal drive system. When sailing close hauled or on a beam reach (where the natural wind is coming from the 2 or 3 o’clock position, peddling the kayak forward increased the wind across the sail such that the kayak would actually heel over and gain additional speed, enough to stop peddling for a while.
I kept thinking that it was just coincidence that a gust of wind came along every time I started peddling, but then I realized that it was happening every single time without fail.
If the wind is coming from 3 o’clock, peddling forward simply shifts the apparent wind in the noon-ward direction, perhaps to 2 o’clock, and increases its speed over the sail, which may increase sailing efficiency depending on your particular hull and sail configuration.
Edit: And I agree that this effect cannot occur on a still day. You need some natural wind.
Do a google search for “ddfttw” or “directly sownwind faster than the wind” and there are lots of forum discussions. It’s counterintuitive, but absolutely possible without breaking any laws of thermodynamics.