What kind of medieval armour and weapons can you make using today's sciences?

[Brother Oni]

Checked the op again. Assuming modern metallurgy and engineering tolerances, not chemical knowledge though, and typical fantasy dark ages society otherwise.

Except you can't have modern metallurgy without the requite advanced chemical knowledge. Unless you know how to incorporate manganese, chromium and vanadium/uranium reliably into your metallurgy (rather than fluke it ala Damascus steel), you're not getting anywhere near the same quality as modern steels.

The weird part about ships is that, absent gunpowder, it seems entirely possible to build an essentially unsinkable warship. You wouldn't even need the ridiculous levels of belt armor seen on actual late 19th/early 20th century warships for this purpose; I have a hard time figuring you could use a torsion engine to shoot a projectile capable of punching through, say, 2 inches of Krupp cemented armor. Plus no explosives means no torpedoes, which is even more weight savings. So you could get a ship whose hull was completely resistant to literally every projectile weapon known to mankind.

You don't even need that - Korean turtle ships (거북선 or geobukseon) were pretty much immune to anything the invading Japanese forces had during the late 16th Century Imjin Wars. Admittedly they did use cannon, but they also had rams and sulphur based chemical weapons from the bow mounted dragon head.

In any event, cannons are great, if your gunners don't suck. Otherwise they are a giant pain that only work on mostly stationary targets.

Even then, you can substitute other loads - grapeshot would be useful for fast moving targets and what chainshot would to anything that's not an adult dragon doesn't really bear thinking about.