Strangely enough, your boats aren't going to be THAT different from the boats we already have in terms of propulsion and wave handling. Balance is a completely different matter, but let's deal with each of these criteria one at a time.

Propulsion

You really have two options with your level of technology and they're the same options that everyone else had; oars and sails. Depending on how far above the water you sit though, oars are problematic because they have to be longer to get into the water meaning you need to be stronger to pull the oar. For open sea journeys this is an issue because putting the rowers close enough to the water to make oars effective is counter productive to being able to handle large waves, where you want high watertight 'walls' on the side of your boat (more on that later) so I'd stick with sails.

Sails could be managed by the people you describe technologically, especially as pre-industrial doesn't mean pre-science. There are plenty of examples in history of pre-industrial sailors who used sophisticated means to get their boats from one place to another in terms of both navigation and wind management so this is the best option. Just bear in mind, these kinds of large sailing vessels were a massive expenditure prior to industrialisation and they would be for your world as well.

Large Waves

Ultimately the best defence against high waves is high walls. On conventional ships, they sat very tall in the water (with massive ballast reserves in the hull to keep them upright) so as to survive high seas. Your floating boat will need the same walls, so your boat will still have a number of decks on it with walls on the side to stave off wave strike.

Balance (and Navigation because they're related)

These boats will have flat bottoms. It's that simple. You don't need to keep the boat from drifting in current because your boat floats above it in the first place, so there's no need for deep hulls. You'll need keels (and rudders) though, because the sails are only part of the propulsion equation in that boats actually rely on some resistance against the hull to change direction. Rudders for instance need contact with the water to reorient the boat. So, your boat probably has a large rectangular square bottom to maximise the repulsion area against the water, hence maximising the balance of the boat. BUT, it also has a series of long keels that dip into the water (not coated with the repulsive material) that help with steering, and at least some of these will be on swivels that can be controlled from within the boat for steering as a rudder. Ideally, these would be on the outer edges of the flat surface to preserve stability, like a catamaran.

As Aron points out in comments, this may not work. Certainly, the resistance that a keel can generate is minimal by comparison to a hull, so the idea that you could successfully do anything other than use a rudder like control surface is in doubt and as such, should be taken as speculative.

So, your boat would look like a very large floating bathtub, with keels and sails below and above it respectively. That will allow it to balance, survive high seas, and move & navigate on the open sea.

Alright I think a flat hull will be by far the most stable design. You want a constant repelling force and a flat wide hull gives you stability against waves. At the same time you do want a somewhat high front against waves.

A

A tall front to steer against waves. This also gives you a vantage point to engage your prey with if they're large enough. Obviously this comes equipped with a railing, in fact your whole boat will be.

B

Back/front view. A wide flat hull for stability with a high railing on the main deck.

C

I was considering using your water repellent for some sort of ingenious propulsion mechanic before I realized you need to push that down in the water with more force then the boat weights. But maybe it will inspire you or someone else to make it work with some force multipliers.

D

An upgrade could be extra hulls not unlike a catamaran. The idea being you place those far and wide to give addition stability against waves from the sides. This will require some very strong water repellent to work. Extra strength by joining them with the mast against the central line of the ship.

E

Sails will be your best propulsion system. With no contact with water you should be able to get some frightening speeds.

Now for more specific details I turn you to regular ship design. You might want more storage space then a single space between your hull and the main deck. You probably want regular rudders in the back to aid with steering your vessel, regular rudders should work, uncoated. You might want multiple sails, again regular sources on sail design should have you covered.

I'd think about it completely differently than a boat.

It's true that sailing would be impossible since it's been pointed out that sailing relies on the resistance of the hull in the water to navigate effectively. But that's not true for aviating like you might do in a balloon, which is essentially what you have. You have a flying craft that simply flies very close to the ground.

You haven't specified how far above the surface the craft would hover, but I'm assuming that it's at least a meter (~3ft) so that it can get over most of the mundane waves and swells. Your technology level doesn't really allow for using fans like a zeppelin or blimp would use to steer, but you could still navigate just like a hot-air balloonist or glider pilot would.

Like the Polynesians, your civilization would be familiar with ocean and wind currents, but with a bias towards the wind aspect as that's the strongest form of propulsion you'll use. Knowledge of the ocean currents would mostly only be useful for tracking prey.

As far as the design of the craft, it should definitely get wider as it goes down into a large flat base for the repelling material. Water would just stream off it down the sides. You can use sails or even kites, balloons or parachutes to grab the wind and pull you along. Control surfaces like wings and tails on airplanes help you steer. Remember, you're in the air not on the water. As long as you can keep your means of moving and navigating intact, your craft should survive just about anything.

As other answers suggest, the wider base will provide stability and since you have basically a sink proof material lining the bottom it won't really matter if the craft is totally swallowed by a wave. As long as the bottom is heavier than the top, the craft will rise back up from underwater. Maybe some kind of air bladder/attic area(s) sealed into the upper/highest parts of the ship. As long as your decks drained you could temporarily be fully submerged and probably come out ok.

Super surfboard.

In answers so far the water repulsion has been considered a sort of ultrafloatation. Really, though, this tech would be super useful for propulsion. Imagine a surfboard. Only the back is treated - possible at an angle, not parallel to the water surface. The treated back repels water and so rides higher. One would have exactly the same effect with a regular surfboard if the back were physically higher than the front which is the case where you are on a wave. The net effect of the vectors is to push the board forward.

With this water repulsion tech, the surfboards will move forward even on still water. Because the mid to front of the board is in the water, one can still use friction of the board against the water to steer just as with a regular board. A skeg or keel could still be on the board to improve maneuverability - just don't treat that with repulsion tech.

The main benefit of this application of the water repulsion tech is awesomeness. It will not be like a bunch of dudes hunched in a Teflon whaleboat. It will be more like Mongols on horseback - but faster. The party surfing out from shore at sunrise will be cool as can be. If there are waves (maybe created by the water creature?) they can do some regular surfing too. They will hang ten with their harpoon lassos. It might even be possible to surf right up onto the sea creatures.

For the sake of concision, I'm going to refer to the anti-water magnetic coating as AWMC. I'm assuming that AWMC is polar, that it can be turned off or directed, or that the repulsion is significantly stronger on one side, since otherwise the crew wouldn't be able to go near once it was applied (humans being mostly water). I'm also assuming that the AWMC resistance force is quite powerful.

The optimal hull design is to stick to regular hull designs just with a thin layer of AWMC that functions as frictionless coating + waterproofing.

The real genius is using AWMC for propulsion, since it's been shown by our resident sailors and kayakers that traditional forms of naval propulsion require friction/resistance. Introducing... the WHIFFLE MOTOR (patent pending)!! In its simplest form, the whiffle motor is a board with holes poked in it and AWMC applied to the back side. When it's first dropped into the water, the board generates thrust by resisting the water, but this creates a vacuum/pressure gradient in the water, most strongly right at the transition point where water comes in through the intake holes.
Water is pulled in by the gradient and then pushed backwards by the AWMC coating, and the cycle begins.
Better designs streamline the overall setup so that the most water possible is pushed backwards the most evenly, thus generating the most even and powerful thrust.
In my unprofessional opinion, the best designs probably would probably look like a jet engine or turbofan engine, making it so that water only comes in from the intake and all the water is ejected in a smooth stream.
Steering is now a question of having some lesser boards that can be angled more freely.

Basically, you now have spacecraft in a roughly 2D plane. Speed is limited by the direct resistance that water provides to being pushed apart, so you don't get to go stupidly fast just with a basic WHIFFLE MOTOR (patent pending).

Another way to use this magic substance for propulsion comes to mind, extrapolating on Willk's answer: A stone or piece of wood, with a hole bored through, and some of the substance smeared around the opening on one side would make a handy no-fuel water rocket, especially if it was put coaxially inside a tube of bamboo or something to direct the water flow.

You'd start the torpedo by sticking the front end into the water and pushing it down until a jet of water starts shooting out the back, and then lower the whole shebang into the water.

Basically I'm thinking of a ramjet-type operating principle, the water comes in pressurised to an extent by the intake shape and is vaporized by the cavitation effect after coming out of the stone nozzle, since under water the ring of well-placed magic substance (and it's toroid-shaped anti-water field) creates a no-water area right after the nozzle, leaving a small "hole" in the middle of the nozzle where the field is the weakest. There's more room in the exhaust section of the tube for the expanded vapor to escape, and less pressure, so the vapor escapes that way, creating suction for bringing in new water through the nozzle.

I don't know if this is really feasible give only a water-repelling magic substance, but sounds plausible enough for a magic-using world.

As a bonus, the question absolutely brings to mind the hydrophobe wizards of Krull from The Colour of Magic :)

Depending on the sea conditions, you might be able to do something interesting with waves. Ignoring wind and air resistance for a moment, a craft like this will tend to slide down a wave, so if you are going the same way as the waves then propulsion is very simple. If you combine this with a sail then you could, if you are clever enough, use the difference in wave and wind movement to control your direction.

The Wandering Albatross does something like this to glide without flapping its wings. Your islanders are not going to do exactly that, but they will probably have related techniques. The simplest thing would be to use a sail to move sideways along a wave, using the trough of the wave a bit like a keel, thereby going to the left or right of the wind and wave direction. I don't think you could tack like this though.

Being able to aim your craft while sailing relies on balancing the forces of the wind with the forces you apply on the water.

The boat is long and narrow, and has much much more resistance to movement perpendicular to its hull than parallel. When you add a force from the sails, it lets you "lever" that wind force into force going the direction you want. In extreme "tacking" cases you are even sailing into the wind using its force to pull you towards it!

This means that naive designs won't work. A flat-bottomed boat will act more like a balloon than a ship, and will be tossed around by the wind in the direction the wind goes.

While keels can help, that keel needs to be reinforced against the forces and large enough to provide the force you need all alone; in effect you end up with a hull.

But not all is lost. Under newton's law, all forces generate equal and opposite reactions.

Make the ship long and narrow. Have it force a line into the water, actually shaping the water and forming an impression.

Going forward a relatively narrow section needs to be moved, while going sideways a much larger section of water.

So you'll want the ship to be shaped much like a hull; or, more accurately, so that the "virtual" hull around it caused by the repulsion field is shaped like a conventional hull.

Defence against waves acts similarly, except the shape we care about is the virtual hull instead of the hull. Note that "holes" in the virtual hull may be harder than holes in a hull if the effect radiates out in all directions.

If the "virtual" hull can be shaped without shaping the hull things can get interesting. Does the effect end when you leave line of sight? Then you could do interesting things with "covers" to turn off/on the effect.

Imagine a tube picking up water. It fills a chamber. Then the entry tube is closed, the repulsion field is "turned on", firing the water out the rear. Then it is turned off, feeding more water into the chamber.

What more, the "hull" of the ship need not be solid. It could be a net of treated material held rigid in a frame. The virtual hull would be far smoother than the net, and would have no gaps.

Rowing could be done out holes in this "hull", extending through the virtual hull unopposed, and pushing against the water. The surface area of rowing would be larger than on a conventional ship, who is mostly limited by the water-air barrier around the ship.

The oars themselves could be treated with this substance and never themselves get wet. If you could cover up the effect, "oars" that permit that could be used for propulsion, generating an effect similar to the "jet" above.

A couple of notes on my approach to this before we begin the main design specs.

1. I'm assuming the coating only repels free water, not the water in the bodies of the people in the boat.




2. A mass of water equal to the mass of the vessel will be displaced from below the vessel. Whether the vessel is in contact with the water or not doesn't change this. In practice exactly the same rules of buoyancy apply as to a normal boat, if you fail to displace sufficient volume of water for the mass of your vessel, it will still sink. It will sink in a little bubble of repelled water, but it will sink.

Start with a dragonboat, they're beautifully designed fast boats which take a lot of people. We're going to run this like a normal boat, hull in the water. Lightly coat the gunwales and inside of the hull with your hydrophobic substance. The most important factor in any boat is keeping the people inside and the water outside, this use of your magic coating will serve particularly well for this. No need to worry about waves washing over the side or enemies squirting water at you risking swamping or sinking your boat. It'll also make it significantly more comfortable inside for your (dry) paddlers.

Add outriggers, these are going to make full use of your magic coating. Full length, wide enough for a warrior to stand on and fully coated in your magic substance. These are going to act both for stability and as a fighting/hunting platform. They'll have a stabilising effect significantly greater than their mass and volume would normally allow for. What's going to surprise you here is that the greatest risk is making the outriggers too buoyant. To a certain extent they need to be overwashed as they hit waves independently of the main hull, otherwise the forces on them transmit negatively back to the hull, making the whole thing a lot more uncomfortable than it needs to be along with risking high stresses on their struts and breaking the whole thing up.

Your magic substance is used for stability, improved versatility and comfort, but not as a critical element. Controlling a boat is already a fine art, having the hull in the water makes the boat controllable, whether you choose to sail it, row it, or paddle it like a big canoe, boat control is about balance of forces. Once you start taking some of those forces out of the system you get an unbalanced equation and control becomes particularly difficult.

Hull design isn't a simple game, whether you choose hard or soft chines, a "V" hull or flat bottom, carvel or clinker, daggerboard, centreboard or leeboard, fixed keel or lift keel, bilge keel or wing keel, all these things are significant, in most cases they're not compromises but deliberate design decisions fundamentally changing the boat for different purposes. If you fully coat the hull in your substance you take away all these options and leave yourself with at best a vague shapeless hull. Keep the boat in the water.

If this water propulsion is absolute (the substance cannot be made to come into contact with water at all), then wide craft would be the best bet to prevent tipping. If this substance is expensive, you can make a catamaran or trimaran hull.

For propulsion, you could use sail with keel and rudders in the water. Steering will still be a bit dicey (think putting a sail in a Frisbee (round plastic toy for those who aren't old enough to have seen one) on a flat icy lake. You'll spend almost as much time going sideways as going forward.

Another option is to dip a non-repulsing scoop into the water and have it fall into a tube with a sloghtly angled piece of the substance capping off the front end. that will drive the water out the back end of the tube. Add tubes until you have the propulsion you need. Note that you need to have some tubs of water on deck to start the ship moving. If you go this route, have the tubs created by some guy named Bussard.

I think that if your material is not a coating, but a kind of magnet (so that a ship is kept in suspension by an array of at least 4 of them), the hull of the ships should be studied much more like a building rather than a ship (think that it would have pillars where the magnets are located), and anyway it should be much lighter that a ship.

This is because a surface floating on the water could support much more weight than one suspended in the air (think a large raft with a heavy weight in the center: would it be more likely to break if it is floating on water or if it is kept raised by four pillars at its vertices?). So, it would be built so that all the weight is somehow distributed onto the magnets, because if the weight is loaded among them, they would risk to break down.

This would probably limit the size and total weight of the ship, even in consideration that the more massive the ship, the more difficult it will be to manoeuver it (because of the lack of lateral friction with water, you will need more force to counteract its inertia).

About the propulsion, as other answers point, in some conditions the magnets could be used to move and steer the ship. If it is possible to shield the water-repulsive effect, I think that placing a shielding on the sides of some of the magnets, and orienting them in diagonal, the resulting force would have components both normal and tangential with respect to the surface of water, allowing to move and not only to float.

Of course, I don't know how it could be explained in terms of energy conservation (maybe the magnets discharge with the use?)

Steam Propulsion

We normally think of steam as being an industrial age discovery. However the first "steam engine" was constructed in Roman times by Hero of Alexandra.

This should serve as the prototype of a simple steam based propulsion system, whereby a large steam boiler is vented directly into the water behind the vessel. Giving a good turn off speed, but limited range and manoeuvrability.

After a few centuries of trial, error and explosions, people will discover the...

Valveless Pulse Jet

This is much lighter than the Steam "rocket" engine and much smaller and cheaper to produce. This allows it to be mounted similar to an outboard engine.

The disadvantages of it include loud noise (all users of this tech would be deaf, 140dB range), being prone to exploding and an extremely bumpy ride.

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

I do have an idea, however it does not exactly fit the description of pre-inductrial tech, or at least I do not think it does.

The ship could be able to instead of using a sail using a wind turbine to harness the power of the wind at a much higher efficiency to work on a geared shaft that turns a propellor. The turbine itself would be a vertical axis wind turbine similar to this:

Now what this would do is create a vessel capable of sailing in any direction, because it can capture the wind from all angles. Simply because the blades face in all directions. It would also allow you to sail directly into the wind and in fact it would be strongest when sailing up or downwind because of it's omnidirectional (on a 2D plane) nature. It also would be able to better harness gusty winds than a horizontal bladed turbine. It has an advantage over saild in the fact that it isn't adversely affected by storm conditions and doesnt get damaged as easily since it's not a fabric that can tear, its most likely metal or wood.

You could use it to power some sort of catamaran for maximum speed and stability. And as the technology of your society advances you can create some forms of electric storage.