For top speeds, that's easy. Hull speed is a practical limitation of how fast a given displacement hull can move through flat water, and depends solely on waterline length (note that this is the sailing waterline, which may be greater than the displacement waterline as heeling places more of the hull in the water).
In particular, the hull speed in knots is approximately 1.34 times the square root of the waterline length in feet.
For a generic tall ship of, say, 150 feet, this formula gives a practical speed limit of 16.4 knots. 18,000 miles is about 15,600 nm, which corresponds to about 40 days of travel if maintaining top speed continuously. This is our lower bound - in reality, varying conditions, storms, high pressure systems with no wind (doldrums), and inefficiencies in the necessary route will cause the actual velocity made good (closing speed to the destination) to be lower.
Here's a good record for you.
In 1851, the 225 foot long clipper ship Flying Cloud set the record for the fastest journey from New York to San Francisco, 16,000 nautical miles in 89 days. As Wikipedia mentions, the average ship during that era took on average around 200 days.
Hull speed has nothing to do with wind direction.
It just gives the maximum speed for displacement hulls independent of what drives them.
Of course there are ways to go faster, like planing and "cutting through" the bow wave (like most catamaran designs and other semi-displacement hulls do), but both of those are out of the question for tall ships.
And even for smaller hulls, those rules are interdependent of wind direction.
Small cats will enter the semi-displacement regime going upwind, and performance skiffs will easily plane upwind.
If you've got a motor, I would use it to idle into the wind, and either tie your rudder down or move it down into the feet well to keep it from moving too much.
Remember though, it's only a matter of time (depending on wind conditions) before the boat will start to move away from the wind. So you've got to be fast.
In order to do that, while back at the dock before leaving, I would have all of the slides in the track and ready to go, with the rope cleated off ready to be pulled. Then I would just use one piece of rope to reef knot the main down to the boom, to keep the sail from flapping around. Leave a loop in the knot though, because this allows you to remove the knot in one motion in just a split second.
You pull the string and poof, it's off.
So then you just idle into the wind, run up to the mast, pull your rope loose, uncleat the halyard, and start pulling.
Once the main is raised and winched, you scamper back down to your cockpit to correct whatever-the-hell-direction your boat is now trying to go. Run a halyard back to you if you can.
You might need to pick up another block to act as a turning point. That way you can hoist most, if not all of the way from the cockpit then, if you need to, you can quickly go forward when you're head to wind and secure it.
Another way, which would be a bigger pain in the ass would be to anchor, hoist, then raise anchor and sail off.
The third way takes some skill and a small boat like the Catalina 22.
It would be using your body weight to keep your boat head to wind while hoisting. As a dinghy sailor first, this makes sense to me but learning to control your boat with your body weight can be challenging, especially if the boat is moving backwards.
Then if your jib is a roller furling, you just get it going from the cockpit, and now you are ready to go.
So to recap: Motor out and pick up a mooring, or anchor somewhere shallow on the windward side of the river/harbor. Then you can hoist the sails with no rush, and slip the mooring or pull up a couple of yards of chain and sail away.
While I am largely in support of DIY, there's something to be said for paying a premium for a solution to a problem that comes out of a box, pre-engineered, and ready to go. I too have spent some time thinking about this project.
I love the idea of saving money on an autopilot system that is custom designed for my boat, but I'm not prepared to spend the time and money to go through an R/D cycle that would result in a system equal or superior to what's already on the market. Maybe if I thought I could get it right on the first try...
Anyway, if you're already ordering parts, it sounds like you're serious about this or have at least put started thinking about your design. Mind if I ask a few critical questions in the spirit of collaboration?
Without some serious engineering calculations involving rudder/tiller forces on your boat, the best I can do is look to industry standards.
Base displacement weight of your boat is 23,500 lbs.
Loaded for cruising, add another 2,500, bringing us to 26,000, which is close, but 2000lbs over the Maximum displacement recommended on the chart for the Type 1 unit. Whether you'd bounce up and pick the next size is a personal choice, but even so, let's compare the Raymarine Type 1 drive unit to the actuator you picked.
There doesn't seem to be a lot of raw data on the Raymarine chart, but working with what we have, we can compare peak thrust, stroke length, hard over times, and power consumption. While the stroke length and amperage seem to be identical, the servo you selected has a "dynamic load" of 180lbs, versus the Raymarine unit, which has a "peak thrust" of 650lbs, or 1050lbs, for the next size up. Can't say for sure whether these ratings are comparable, but it's worth considering that they might be. The other issue I found which may be more problematic is the hard-over time, or speed of actuation.
The Raymarine unit has a "hard over time" of 11 seconds, or approximately .9 sec/in travel. The ServoCity servo has a listed speed of .3 sec/in travel, or .2 sec/in under max load, which is 3-4 times slower.
In the end, it's hard to quantify comparisons without exact technical specifications and a discrete set of requirements to satisfy, but I hope I have helped clarify some issues that you may encounter if you proceed.
When we first got our 420 it felt like I had this overwhelming fear of the thing capsizing. Granted we hadn't done any sailing before that. What I came to learn is that with our sailing being done on a lake, what's your worry?
You're on a lake, the shore is in view.
Keep your lifejacket on (and we always do) we got over it by jumping for the fun of it! Swimming around! Freak ourself out from the fish biting your toes, and realize there's really nothing to fear from being in the water. And as for the boat? It's built to be righted and not to sink. And if it capsizes, so what? It won't be the first or last time for that boat.
When you move on to bigger sailboats, meaning fixed keelboats with lead ballasts, you will NEVER capsize from wind. The boat is built with science to ensure that. Remember these principles of boats:
- They are designed to lean. The boat is happy in this position even if you are uncomfortable. Even if the rail is in the water, you are not in danger of capsizing (though you may be putting stress on the rigging) because the more the boat leans, the less the sail catches the wind. And the thousand(s) of pounds below the water are counteracting the force above it. You are always in equilibrium when heeling and cannot roll from the wind.
- Boats are designed to head up into the wind and depower themselves in a big gust. There is nothing short of a white squall that could simply push over a bigger boat. While you freak out, the boat just will round up and stop. I'm assuming a simple sloop rig and no spinnaker, which is a big sail that should be handled with care
- If somehow, some way, you do capsize a bigger boat, say from a rogue wave on open ocean, the boat will most likely right itself. It's like those sock-em blow up toys you can't knock over: they're designed to right themselves.
All that is for your future dreams and to remind you that there is nothing to fear from capsizing. Most boats are built much stronger than their captains. You will roll over long before the boat does.