If a modern Day tank suddenly appears in 14th century Constantinople; in perfect condition, along with all the ammo, fuel, and components needed for it to run. How much of the technology in the tank could the Roman (Byzantine) Empire replicate, if not reproduce?
On a very fundamental level, the Romans would completely lack the means of replicating ceramic armor or complex alloys used in most modern MBTs even if you gave them a pamphlet explaining what they were and how they were made. Just reinventing the process that goes into the manufacture of modern materials would be a bigger task than assembling the tank itself.
Armor: If the tank had solid steel armor I'm sure the Romans could throw together something "functional" if they utilize effective casting methods. Unless they understand the chemistry of the hardening process, I can't imagine it being any more advanced than the steel they use in every day life.
Engine: This is the tough part. Separating the engine from the example tank and reverse-engineering it would be a colossal task for a civilization without heavy-lifting equipment or even the basic concept of what a combustion engine even was. Once they do remove it, they'll need to figure out what it even does. They could probably figure it out eventually if they had an old Soviet T-34 to look at or something comparable, but modern engines used in MBTs are just so complex they would be better off hitting the drawing board and inventing their own.
Gun: A tank's gun would be much easier to figure out than the engine, especially if they had the smaller machine guns to take apart and look at as well. The Romans would probably be smart enough to appreciate the mechanism that fires a bullet and recreate something similar if they had a way to cast the parts and could scale up the technology to make a cannon. Again, it would be a monumental task, but it could be done if they had an indefinite time frame, budget, and man hours.
Ammunition: Sabot? Maybe. Solid shot? Absolutely. High explosive? Probably not. They would need to figure out what gunpowder was and how to make it in addition to making shell casings capable of withstanding immense pressures. I'd say this would be difficult, but not impossible. Steel-cased ammunition would probably work and copper and bronze would be plentiful for the actual bullets and shells. Not sure how they would tackle the primer, however.
Turret: Electric? No. Mechanical? Sure.
Ultimately, the Romans would be catapulted into an industrial revolution using the techniques invented through the reverse-engineering process. They would probably use their newfound knowledge to better their civilization and not build another tank. So to answer your original question, the Romans could only reproduce solid components and parts they are capable of comprehending, like the armor, tracks, wheels, and maybe the guns if they have enough time to break them down and study them. When faced with a combustion engine, they would view it as alien technology. Without a basic understanding of how engines work, no pre-industrial civilization would understand what they were looking at without instruction.
The seat covers?
When you compare a 2017 tank with a 1917 tank, you will see many differences. These are not just because those silly people in 1917 didn't think of a turret with a big gun and a sloped glacis. They were unable to come up with good engines and transmissions that could haul armor plate to resist cannon shots, resistance against rifle shots was the best they could do.
Go back more centuries and you won't even get the screws to hold the engine in place, not to speak of the engine itself.
If they were to build an 1:1 scale replica with local materials and technologies, the engine would immediately grind to a halt (or more probably not start, because the starter fails), the turret wouldn't rotate, the gun would burst the first time it shoots full-power ammunition, etc.
What they could learn from the tank would revolutionize Rome
The ancient Romans could not duplicate a modern tank. But it's amazing what they could learn.
- Braided wire from a tow cable.
- Strong fabric from the safety belts (at least the weave)
- Clasps from the saftey belts, nuts and bolts, "attachment" tech. (Screws and bolts have been around since 400BC, the Romans would certainly understand how to dismantle the tank.)
- Gears and gear design (they could comprehend the transmision)
- The uses of grease, oil, gasoline(diesel)
- Bearings... Oh, what the Romans could have done if they had bearings...
Even the shapes of things (like the seats) would bring new innovation to the Romans. Crafty little honkers, those Romans.
There are things they wouldn't be able to comprehend. Microelectronics, for one. Laser optics for another. Microscopes weren't invented until 1590, but as @RadovanGarabik points out, they could learn telescopes from the tank's manual optics... which could lead to microscopes ... which could lead to looking at the small stuff. They still wouldn't figure out microelectronics, but they would suddenly learn about electricity and have the ability to examine nearly everything about it. Software would be beyond them, but who cares when you suddenly have electric lighting?
Could they duplciate that tank? Nope. I can't imagine how they could learn alloy lamination that quickly, for example. But I wouldn't sell the Romans short. They could and would learn a tremendous amount of stuff from a modern tank.
BTW, one assumes that nothing on the tank is locked, that they have access to the cabin and the motor compartments, etc. Perhaps not the ability to turn it on, but if the "key were in the ignition," so to speak, they'd eventually ask themselves, "what does that doohickey do?" and start the beast. The OP's question is sensless if they're locked out. But even then, they could learn stuff just from the outside.
They lack enough scientific understanding of the world to understand the basic principles behind the operations. Having said this, however, there is one piece of technology/science that can be grasped and replicated easily, and that is...
from the gunsight. Glassmaking was known, the lenses were likely known to the Romaioi, they had enough grasp of geometry to formulate decent foundations of optics, once they see and dismantle a working prototype. It might be easier with a WWII era tank, though.
Lots of great answers. I am going to say that one thing that would prevent anyone from before 1900 or so replicating most modern machinery is ball bearings.
Yep. Ball bearings.
Ball bearings are really, really hard to make. During WW II one of the things that absolutely crippled the Japanese war effort was the loss of the plants that made ball bearings. They had four or five, I think, and most were destroyed in the first bombing runs, the later ones took care of the rest.
That was WW II. Ball bearings require pretty precise tolerances (my dad used to work in a factory that made them. If you were off by 1/1000th of an inch they were thrown out). We forget that it is only in the last century that 1/1000 inch tolerances were possible. That's about what you need to build a modern engine, by the way -- at a minimum. Again, a generation ago my dad had a caliper that measured to the 1/10,000th of an inch and that was eyeballing it in a pretty standard machine shop. Before the advent of relatively advanced cutting and measuring tools that kind of stuff was just not possible.
Anyhow, ball bearings are absolutely essential for an internal combustion engine to work. They are also essential for a modern machine gun. So unless the ancients (or rather, medievals) were able to figure out how to cast 1/4 inch spheres with 1/1000 inch or better tolerances, they wouldn't be able to make much modern equipment.
They could, as others have said, figure out some basic things. Steel was a known quantity, and guns (though smokeless powder was four and a half centuries in the future, because chemistry). So the basic concept would be there (in fact the 14th century had a cannon of sorts, it wasn't very good).
But recall that you need the tools to make the tools. Many of the metals they wouldn't be equipped to even analyze, as the melting temperature of titanium or carbon steel is so high they would have a tough time getting a furnace that hot (maybe a glassmaker could do it?). Then they'd have to know what metals the alloys were made of. Aluminum wasn't discovered until the 19th century, and in fact all the elements in a modern battle tank's metal parts except the iron and carbon weren't discovered until the 1860s at least.
The fuel would be effectively unknown as they haven't got any way to refine it nor any concept of hydrocarbons. They had pitch and some oil, but recall that refining the stuff requires two centuries of chemical knowledge. So a good chunk of the tank would be effectively magic and require a lot of science they hadn't developed yet to reverse engineer. You can forget the electrical systems and electronics. Or plastics.
I suppose they could study the internal combustion engine and figure it out maybe, but there's a lot of basic principles that they'd have to work out first. Technology is built step by step. And sometimes there are new physical principles people find that make some technologies literally inconceivable to earlier generations. For example, a laser is utterly unimaginable without quantum mechanics, so a scientist from 1880 would be completely unable to reverse engineer it because QM hadn't been discovered yet. The very principle of a laser -- and semiconductors, for that matter - would have to wait another thirty or so years at least.
Also recall that getting metal in the preindustrial era was hard. If you lived in Iceland in 1400 iron was likely more valuable than gold to you. Gold is pretty useless, but iron? And there wasn't much of it around that could be mined easily. SO getting enough metal together to reproduce a tank would have been a pretty big project, even in iron-rich regions.
While the other answers cover the tank itself, a few other things that could have significant impact on 14th century.
Additional Equipment likely/possibly present:
Fire Extinguishers - likely compressed CO2. While unlikely they could reverse engineer either the gas or the compressed bottle, it would open them up to the world of modern extinguishing agents. Especially since the bottle itself has instructions on it. And with valves and hoses on the fuel systems, expecially creative individuals could arrive at similar firefighting methods as used in the 1800s
Medical Kit - Wide array of battlefield medications including instructions (designed to be used by the medical illiterate with pictures). All of which far exceeds the medical knowledge of the time. The chemicals would all be beyond the understanding of the times, but the methods of treatment (thanks to the illustrations and instructions), could translate.
Food - Food Supplies -> Food preservation. Tank operators spent most of the time in theater essentially living out of the tank. And military rations store for a long time. Modern rations are usually MREs or equivalent, though occasionally canned goods are used. Unsure which is more likely to be present in a tank. Though a British tank has a boiling unit for making tea.
14th century food preservation methods were limited to salting, drying, etc. Even canning was not discovered until the 19th century. Combined with the telescope as mentioned by Radovan Garabík, they could potentially discover bacteria substantially earlier (as opposed to 1670s).
Tools - Any equipment/tools left in tank for field repairs/jury rigging. Which could potentially aid is dismantling parts of the tank.
Any instructions in tank - Likely to include simple manuals/maintenance checklists. Unlikely to be detailed operating instructions, though it is potentially possible for repair manuals to be present. Not everything has shifted to digital yet.
14th century England spoke Middle English. Quite a bit different from modern English, but still mostly translatable (excepting modern terminology for which there was no concept for in 14th century e.g. electrical).
So while the tank itself could not be replicated, the amount of knowledge they could gain from it is difficult to calculate. Any 14th century society that had a 20th/21st century tank to study could potentially accelerate their technological level by several hundred years.
Not at all! Firstly, the Romans lack the metallurgy and the manufacturing process. Secondly, they wouldn't understand the basic mechanics of internal combustion engines.
Building a tank embodies many centuries of technical development and millennia of skills and knowledge to make them.
They could make a copycat tank out of wood, but it couldn't move or do anything useful. Also, the cost in terms of resources would be too great.
The concept is a non-starter. Sounds cute, but that's all.
What can be learned from it depends upon how effort they put into it. Which depends upon how the encounter it. If they see it wipe out an army, they will learn a lot because they will understand that it can be useful and powerful. If all they see is it sitting in a field, they aren't going to learn anything beyond there being a big metal object sitting in the middle of a field.
If they see it in action, that would indicate a person came along, and that person will be able to provide invaluable insight that could help them in their efforts to replicate it for as long as that person lived.
They won't be able to actually replicate it in any reasonable amount of time, what they will learn immediately is that there are possibilites that are worth pursuing.
So were talking about Rome in the 14th century. Prior to Leonardo DaVinci, but we have some things in place that could lead to advancements.
Let's set some assumptions early on. The Tank gets back in time or across dimensions, or whatever, with at least one person who can operate the tank and speaks a close enough language that he will be able to communicate in fairly short order. If you don't have this guy along for the ride, then a mysterious heavy thing will be in the landscape, ignored and feared, at least until someone gets curious enough to set something on fire and blow themselves up, or the dirt builds up around it and it gets buried as an unremarkable hillock.
Here is what 14th century Romans could cope with (after a brief demonstration):
A Cannon. A tank's main gun is a big cannon. It is a Tube that you set fire to the back of and a projectile comes flying out the other side to destroy the enemy. Yes, a tank's main gun is very complex, but that stuff surrounds the concept of loading and reloading. The core concept has not changed in hundreds of years.
A Cart for mobility. Cart mounted Ballistae were common even in ancient Roman times.
Though slow, oxen could pull a lot of weight.
Protecting your people. Ever hear of a shield turtle? 'Nuff said.
Your 14th century Romans might think this combination is a darn good idea.
What they aren't going to be able to deal with:
modern metallurgy and chemistry. They don't have the precision and tools to duplicate the metals and such required to duplicate the abilities of the tank's main gun or armor.
The internal combustion engine. The precision required is just plain beyond them not to mentioned the chemistry needed for lubrication and fuel. This goes double for the turbine powered modern tanks.
An Absolute Genius might be able to puzzle through the transmission and the Tread concept.
With a little guidance, they may even be able to get the concept of a breech loaded gun well enough to duplicate it.
So what I imagine is a large-ish cart that is pushed by two or three oxen. The cannon is mounted to a swivel at the front of the cart, probably right over the front axle. The whole thing is almost completely covered by interlocking roman infantry shields. Two ports are there for archers to stand up and shoot from relative safety.
The real key to this being awesome, though, is if they can duplicate a simple Breech Loading gun. That way the cannon crew could re-load faster and from relative safety. These guns were known that far back, and could be scaled up some.
You end up with something that will be nearly invincible to the common weapons of the day (bows, crossbows, normal infantry, and cavalry), so long as you had a buffer of infantry to move with the "tank". You will be able to move and shoot more quickly than anyone might expect (not real fast, but fast enough).
At least until someone figures out a well dug trench will make your life miserable.