"it is not too difficult to have a desalinization plant on board". But that takes a lot of energy. Only sustainable with nuclear power.

@ronjohn, solar desalination is a thing, will eat up a lot of your deck space however.

@John solar desalination is slow and inefficient. And it will be -- by design -- h-o-t hot under that plastic sheet, so no moving around on deck.

@RonJohn the power needed is about 1 Kwh for m3. Let's say 2 for not state of the art plants, but it nothing that a ship engine (or other methods) cannot generate

Small evaporative water purifiers can run directly on solar power. Since you already need to choose a good latitude for trade winds if you rely on sail power, you can choose one with warm weather as well. A super-earth would have more choice of latitudes than we do.

@RonJohn please note that actually there are some small wind turbine that can generate about 400 Watt each (some say up to 1 or 2 Kw) and you have a ship to install dozen if not more of them

Navy ships have small desalination plants, but even they are restricted.

"and you have a ship to install dozen if not more of them" There's no free lunch. Those wind turbines are a big drag on the ship.

@RonJohn If you install them to wrok in parelel with the sails it is a free lunch. It actualy increaeses your power forward. You just need the space.

@PCSgtL This answer assumes an engine driven ship, not a sailing boat. While those are still affected by the wind, quite a bit of the point is to no longer be entirely dependent on it. Adding a bunch of fairly static surface is going to significantly increase drag under non-ideal conditions, which will both make the trip longer and cost additional fuel.

@Cubic A ship is not aerodynamic by default, the drag produced by the wind turbines is trivial compared to the drag of the hull itself

I would worry a hell of a lot more about the size of storms & waves that will show up on a massive ocean of the size described.

The ship would have to be a tanker (or similar) to carry the needed fuel. Some of the tank capacity can be used for fresh water and plenty of food. I'd say late second half of 1900's.

Build an Ekranoplan with a Nuclear Ramjet!

A ship under sail is moving slower than the wind that is driving it. Thus a turbine is guaranteed power so long as the ship is moving and it's better than free--the turbines add a little bit to the sail area. On an engine-driven ship, might as well get your energy directly from the engine, no reason to use turbines.

@LorenPechtel not always, most fast sail boats can sail faster than the wind - boatsafe.com/kids/bramp1099.htm

"Now the problem is that they don't know how long the trip is" - the circumference of the planet gives them an upper bound. And yes, they can estimate it without leaving their continent. Eratosthenes did it 2000 years ago and was just off by 10%.

If your wind turbines are efficient enough, you're better off getting rid of the sails altogether and use an electric engine powered by the turbines. We are barely at the required tech level today, though.

If it's a super-earth, then it's a big planet, so has high gravity. That means your ship has to be bigger to displace enough water to overcome sinking. Whilst Polynesians and others did some amazing trips in small boats in Earth's history, they'd have had to build much larger boats to do it on a super-earth. That naturally pushes the lower bounds of technology up quite a bit as you now need to make much bigger structures to keep your boat from breaking up.

@Eth my ship has not sails, the wind turbines are only to power the desalinization implant (but they can also probably power other systems)

@RalphBolton The OP stated that for some magical reason, the gravity is the same of the Earth, so no, my ship does not need to be bigger just to not sink