Your question relates to the effect of aerofoil shape on lift: https://www.grc.nasa.gov/www/k-12/VirtualAero/BottleRocket/airplane/shape.html

Please note that in aerodynamics, "lift" is any aerodynamic force that acts perpendicular to the relative wind on an object, so it's lift whether it pushes a plane up, down, left, right, or pushes a sailing boat across the wind.

Also the keel of the boat that keeps it sailing in a straight line is technically providing lift in the water, although that "lift" is sideways. Also it isn't aerodynamic lift, but hydrodynamic. The general field is called fluid dynamics, which covers both gasses and liquids.

You've got some good answers, but the problem with the air bouncing idea is that it ignores the air on top of the wing, or to the leeward side of the sail. The sail is pushed on by the windward air, and pulled on by the leeward air. (Edit: technically not pulled on, but you can model it that way if you take atmospheric pressure as 0 and anything lower than that as negative; it will give you correct results)

This is such a common misconception that NASA has listed it as a common incorrect theory of lift: https://www.grc.nasa.gov/www/k-12/VirtualAero/BottleRocket/airplane/wrong2.html

A better way to think about it is flow turning - as the wind moves past the sail, its flow is turned and the momentum change causes an equal and opposite change in momentum of the boat: https://www.grc.nasa.gov/www/k-12/VirtualAero/BottleRocket/airplane/right2.html

So ideally the leading edge of the sail should be parallel to the oncoming wind, and the trailing edge will be by definition parallel to the outgoing wind. The difference in velocity between these two winds multiplied by the mass of air passing over them over time will give you the force acting on the sail.

If the leading edge isn't parallel, the air's transition from free flow into contact with the sail will not be smooth, and will cause losses that reduce the efficiency of the sail.

In practice, the way to achieve this parallel flow is to let out the sail until you see "luffing", which is just the leading edge flapping a bit in the wind. Then you tighten it until the luffing disappears, at which point the sail should be correctly trimmed. As you carry on you can occasionally repeat this process to check that you've still got the right angle, as minor shifts in wind or boat direction can change the ideal angle of attack.

This is also called "setting" the sail. So when a ship "sets sail" it's referring to the fact a skipper would order the crew to "set sails", which would start them moving. Now the term also means to commence a voyage.

In some bigger boats you have strings called "telltales" on the surface of the sail. If you see them flapping you know the air flow is turbulent, and you can trim the sail until the telltales on both sides of the sail are blown into a smooth line along the sail. If you tighten the sail too much, the leeward telltales will flap. If you let it out it too much, the windward telltales will flap.

A flat surface is much less efficient as it will cause a lot more turbulence on the leeward side. A lot of work has been done to make sails form the most efficient shape, and they are always deliberately curved. The shape will change depending on the tightness of the sheet (the rope that sets the sail) and on its manufacture, but ultimately your sail shape was basically set when it was made. Different sail shapes will be optimised for different types of tack and different tasks, but I don't know enough about that to explain more. Mainly I know that spinnakers are made for running downwind and the other sails usually have to make do for the rest of the situations, but this article tells you a lot more: https://en.m.wikipedia.org/wiki/Sail_components

I only just found that article, so if it disagrees with anything I've said here I'd defer to it.

Very high performance sails and setups can do some cool things, like racing catamarans with their very sleek hulls and optimised sails allow you to sail in a close haul within 30-something degrees of the wind, whereas most normal sailboats can't get much closer than 45 degrees.

There is much more reading and interactive lessons on lift and other aerodynamics concepts on NASAs page here: https://www.grc.nasa.gov/www/k-12/VirtualAero/BottleRocket/airplane/short.html

Edit: This seems like a decent resource for first time sailors, and gives some more in depth explanation of how to set your sails correctly: https://www.cruisingworld.com/learn-to-sail-101/

This is also where I learned what telltales are called. I've never sailed bigger boats much tbh.

Okay, I think that's most of what I can info-dump on the basis of your question. You landed on an intersection of two of my special interests lol :)

According to my college physics 101 professor, a curved sail is generally superior in all situations. There are sails made out of rigid materials, and they generally are curved, even though they could be flat. Everybody who sails knows that you can adjust the slack in your sail, and that sometimes a tighter sail is better, for example when tacking. You can tell this just from the feel.

Now, then, it's been a LONG time since my physics 101 class, but the explanation was something like this: Although this is an oversimplification, you can imagine that a sail works when air particles bounce off of it. The momentum imparted to the sail depends not only on the direction that the wind is coming from, but also the direction that it ends up going when it bounces off the sail. A curved sail helps redirect the wind away from the sail in exactly the direction that the sail is pointing, which is better at pushing the vehicle in the correct direction.

Another way to look at this is if it is a pure matter of air pressure. A curved surface will be better at creating air pressure inside the curve. It's like if you're driving and you hold something out the window. When you hold a rigid board out of the window, it will be hard to hold in place, but the air pressure won't build up behind it as much as a sack, for example. If you hold a sack out the window, it will probably just be ripped out of your hands.

Sails don't really work like that. Sails are actually more like a wing. They create lift but pull sideways instead of lifting like airplane wings.

There are also crazy racing sailboats that use a ridged wing.

https://en.m.wikipedia.org/wiki/Wingsail

I'm thinking if the sail was flat and taught the air would push around the sail and you would lose a lot of energy through resistance or like wind moving laterally. Whereas the traditional sail kinda cups and holds the wind force and creates more pushing force towards the center rather than the edges.

Cause airflow is like fluid dynamics right? Imagine spraying a hose at a wall vs a sheet hanging from four corners.

But I'm high and kinda drunk so who TF even knows.

Isn't it loon?

think in the inverse: is a spatula better at serving liquid than a ladle? You’re trying to capture the kinetic energy of a fluid using a sail.

A lot depends on the angle you are heading relative to the wind and how strong and variable the wind is and how easily you want to be able to steer or hold your course.

The simplest case that I think you might be wrong is going down wind, especially in light air, you want the sail to catch the wind like a bag and direct it toward a central point to add all the vague forces into one direction instead of just twisting the sail one way or another. Like I didn't think you actually want the wind hitting the outer edges of the sail straight on as this would just move the sail, not the boat.

Stiff, even hard not cloth sails are useful to go into the wind at a slight angle, where they are optimized in shape like an airplane wing, and they even talk of the force generated as lift.