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One day, on the faraway world of not-medieval-Europe, someone discovered that a type of stone could be made to float. A decade or two later, there are flying castles, built out of and/or on a foundation of said floating stone.

Floating stone doesn't actually float everywhere. There are large lines (let's call them Ley lines) crisscrossing continents and oceans, where stone floats best on, separated by voids where it doesn't float much, or even at all. Altitude above ground also weaken the effect, so you won't see floating castles more than a few km up at most.

If a floating castle drifts away from a Line, it will (hopefully) gently float down and land - though "gently" at the scale of a castle can still be potentially fatal to anything both in or under the castle.

What propulsion would be used on a floating castle with medieval technology?

Standard airship techniques may not work, as flying castles are so incredibly denser and more massive. Ideally, it would allow for a fair bit of control, to avoid getting pushed out of a Line or into a mountain.

Available tech can be from late Roman to mid-late medieval era. There is no magic apart from floating rock, and it doesn't really scale down.

On the other hand, there have been a few decades with incentives to solve new problems, so new tech can be used if it could have reasonably been invented in those conditions. Likewise, flying castles themselves can help in engineering projects, for example to (slowly) move very large charges up.

The following numbers and assumptions are given as a baseline, but can be changed if it makes things more interesting:

  • The two main things moving a drifting floating castle are wind and natural currents from the Ley line. Generally, the Ley current is weaker though not negligible, and constant on one place. A castle can also very slowly gain and loose altitude. Assuming no ballast drop, a castle can accelerate at about 5 cm/s², with a max ascending speed of 2m/s, in good conditions (descending speed is limited only by lithobraking).

  • The largest flying foundations are roughly 30m radius circles, with 20m-thick foundation. The smallest ones are 8m radius and 6m-thick foundation. The foundation itself is at least 9/10 filled in stone, but there are often small chambres and tunnels for access below. There can be light structures hanging from under the foundation, though most of the mass must be over it.

  • Floating stone has a density of about 2.5 g/cm³. So the biggest castles have a foundation of about 150,000 tons, and the smallest of 3,000 tons. (If other properties are needed, we can use granite as placeholder)

  • Total non-floating-stone carrying capacity of a castle is about 1/3 of the stone mass, for the best-built (and most expensive) models - so 1,000 to 50,000 tons.

  • To save on capacity, walls can be partially built with floating stone, up to about 1/3 of the mass of the foundation. Those walls must be at least 1m thick, but don't count on carrying mass and can be used as support for other structures.

  • Flying castles typically have a smaller slab inside, in a long vertical shaft, capable of independent vertical movement. It is usable only when there is little to no horizontal acceleration, and with a max vertical speed of 10 cm/s. It can be used to raise about 1/30 of the mass of the foundation (so 100 to 5,000 tons). Some people are experimenting with cisterns at both ends, using hydraulic power from the upper cistern, then raising spent water from the lower to the upper one. Not sure how well this scheme would work - this would be the subject of another question, but consider that there is some power available from this, if it can help.

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    $\begingroup$ It seems to me that there's one more important detail we would need to attempt a coherent answer: what prevents a floating castle from "sliding" off the leyline it's riding? If the repulsive effect is weaker on one side of the castle than the other, wouldn't gravity just pull one side down, and the whole thing would start to slide sideways? (I guess, in my head, I'm modelling the repulsive force based on magnetism. It's a finicky thing to try to keep a magnet balanced "on top" of a magnetic field.) So, would you be able to describe the physics of the repulsive force, a bit? $\endgroup$ – Qami Jun 4 at 18:07
  • $\begingroup$ @Qami Let's assume it works like an airship whose center of buoyancy is much higher than its center of mass. The CoM is in the foundation slab, but the CoB is at least one radius higher, possibly more. So it is inherently stable, like the scale of a balance. Local variations of the Ley force are generally too small to unbalance the castle - though there may be particularly sharp discontinuities that cannot be averaged out and have to be avoided at all costs... $\endgroup$ – Eth Jun 4 at 22:51
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    $\begingroup$ definitely pull with ropes, as Starfish points out. $\endgroup$ – Fattie Jun 5 at 2:05
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    $\begingroup$ If a flying castle is intentionally or accidentally moved into a "void" where stone doesn't float, is it effectively stranded there permanently as it's now just regular stone instead of floating stone? $\endgroup$ – Nathan Griffiths Jun 5 at 2:12
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    $\begingroup$ When I started here, all there was was sky. Other kings said I was daft to build a castle on the sky, but I built it all the same, just to show 'em. It fell down from the sky. So, I built a second one. That fell down from the sky. So, I built a third one. That burned down, fell over, then fell down from the sky, but the fourth one... stayed up! And that's what you're gonna get, lad: the strongest castle in these islands. Sorry, I could not help it. $\endgroup$ – SJuan76 Jun 5 at 18:50
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You should work on the physics behind the floating rocks. What is the principle that makes them float?

We know that the force of the stones is parallel (but opposite in verse) to the gravity, so it alway points toward the sky.
This means that the rocks can only make the castle stay afloat. In order to move the castle, you need a force that can be addressed, with a parallel component with respect to the surface.

You said that, far from the Line, the floating power of the rocks gradually vanishes, as well as it is weaker the higher you are from the surface, so we can make some assumptions. Everything sounds as if there is a repulsive force from the ground (1), as well as a material that can dampen the force toward the sky that is generated by such stones (which should be plentiful far from the Line).
Now, let's say that I can shield my floating stones:

enter image description here
The mortals tremble in the presence of my superior Paint skills!

An unshielded stone, receives repulsive force from all directions, so that all the components parallel to surface cancel themselves. A shielded one, receive only the forces from one direction, so that it has a smaller component toward the sky, but also a component parallel to the surface, pointing in the opposite verse with respect to the opening in the shielding.

So, a castle could have some big unshielded stones, mainly used to keep everything afloat, and one or more partially shielded stones, mounted on joints that can be orientated, to propel and steer the castle itself.

(1) But let's be careful: the repulsive force from something that can be approximated as an infinite plane would be the same at every distance from the plane itself (in other words, it wouldn't fade with height). I suppose that the Line is thin enough that the ground under the castle can't be considered an infinite, repulsive, plane.

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    $\begingroup$ Careful use of massive keels may also be required to avoid embarassing incidents like the famous Fort I've Fallen And I Can't Get Up. $\endgroup$ – Starfish Prime Jun 4 at 19:56
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    $\begingroup$ @Starfish Prime Well, maybe the people in the castle would be prepared for such eventualities... for instance, in the living room, they would keep a set of forniture bolted to the floor and another one bolted to the ceiling :D $\endgroup$ – McTroopers Jun 4 at 21:46
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    $\begingroup$ Beating the RP FLIP to the sideways-bathroom design by centuries ;-) $\endgroup$ – Starfish Prime Jun 4 at 21:50
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    $\begingroup$ @Starfish Prime What's that feeling, when you think you've just said a really really absurd joke, and then discover that it is something that really exists? :D $\endgroup$ – McTroopers Jun 4 at 22:33
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    $\begingroup$ The mortals tremble in the presence of my superior Paint skills! - Awesome! $\endgroup$ – Tobias F. Jun 5 at 9:13
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Brute force. Lots of inertia in a castle, so you'll have problems making an engine sufficiently powerful to drive a propellor to move it along, even if you had substantially more advantaged technology than was generally available in the medieval period.

Therefore, brute force.

One means of brute force is to just get a lot of slaves on the end of ropes. This might be a good reason to get back to the good old loot'n'enslave warfare that was so popular back in the axial age. A slightly less ethically challenged option would be to use lots of draft animals... oxen would probably do, because you don't want to get up too much speed with a castle.

Another possibility is to use anchors and capstans, and use mechanical advantage to haul your castle up towards an anchor, and then (slightly less) brute force to move your anchor points in the direction you wish to go. You might have to use this method to make headway against very strong winds, and you'll definitely want to be anchoring your castle in place when you're not moving it around.

There's a minor additional benefit here in that you could perhaps fire a lightweight anchor via a siege weapon, and therefore be able to haul yourself along without actually putting troops or animals on the ground. This would be useful for navigating hostile or otherwise impassible terrain such as mountains, swamps or shallow lakes and rivers.

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  • $\begingroup$ Regarding "Firing" the anchor: the problem is not the anchor, it's the link. It's going to be one very thick, very heavy, link between anchor and castle; so firing the anchor would require a lot of energy to pull that heavy link. Maybe dangling the anchor and balancing, then releasing at its apex, would be easier? $\endgroup$ – Matthieu M. Jun 5 at 6:51
  • $\begingroup$ @MatthieuM. it seems like it should be possible to fire the anchor whilst it is attached to a loop of lighter cable, and when the anchor has purchase you can pull the lighter cable through to bring the heavier cable into position. Using multiple lighter cables with independant anchors may also be more desirable than one single massive one. $\endgroup$ – Starfish Prime Jun 5 at 7:10
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    $\begingroup$ I’d probably go with dropping the anchors at the front of the castle, repositioning the links to the back of the castle, then hauling. If your altitude isn’t too great compared to the length of the castle you should be able to provide enough motive power that way. $\endgroup$ – Joe Bloggs Jun 5 at 7:36
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    $\begingroup$ Moving a boat by setting out an anchor and pulling on the rope is known as 'Kedging'. When the rope is attached to some other fixed object, it's 'Warping'. (thus nautical warp drives are real but slow!) $\endgroup$ – Robin Bennett Jun 5 at 10:51
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    $\begingroup$ @Joe, anchors need to be pulled at a shallow angle or they won't dig into the ground. 4:1 is a typical maximum. Boats commonly use anchor chain that is heavier than required for pure strength, because the weight turns the upward pull from the boat into a horizontal pull, and helps the anchor dig in. Dropping the anchor from the front of the castle would limit your altitude to 1/8th of the castle diameter. $\endgroup$ – Robin Bennett Jun 5 at 10:56
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Ley-Line Canals

An image of the Segovia Aqueduct https://commons.wikimedia.org/wiki/File:Segovia_Aqueduct.JPG

Your castles may float along dedicated canals which are specifically built to allow for floating castles to navigate them. The Romans famously built aqueducts for transporting water, if you built something similar, it would allow for you to easily transport your castles around.

The canals would be constructed along the paths of the ley-lines, essentially acting as guides to prevent the castle from drifting away from the ley-line. This also means you will not accidentally drift into a “dead zone” where the stones do not float at all, which would cause a castle to crash.

Sails

Canals alone though wont cause you to move forward. Instead, as you are now floating along fixed lines, like a railroad track, you can now safely use sails to push you forwards. Before, without he canal, you risked being pushed out of the ley-line. Now though, as you are more firmly fixed into the line, there is significantly less of a chance for you to be pushed out, most momentum from the wind should push you forwards (assuming you angle your sails correctly and the wind is not blowing in the complete opposite direction you want to go).

Wheels

Alternatively, you might opt to use wheels to move your castles. Wheels would run along grooves in the canal and could be powered through a number of ways, such as by man power, using beasts of burden or even with falling water like a watermill. Don’t expect the castle to move particularly quickly though.

One problem with the concept of using canals though is they would take a very long time to build everywhere. Perhaps you only have canals on major routs, such as between cities (much like how highways only run between large cities and smaller towns build up along those routs). You could also take from the idea of shipping lanes where canals are only built on well-established and often used routs.

Magnetism

Essentially, your castles could work like levitating trains. Your stones would work like magnets, repelling away from the ley-line which causes them to float. If you can invert that signal, causing them to be pulled towards the ley-line rather than being pushed away, you could propel yourself through the power of magnetism (not really magnets per say but they function similarly enough).

The way magnetic trains work is by turning on and off magnets in a certain order, causing the train to be pulled forward. Your stones could be turned on and off, when they are on, they float on the ley-line, when they are off, they fall.

So how can we turn this into forward movement? Well if we start with all of the stones being turned on, the castle will be floating and relatively stationary (barring the flow of the ley-line and the wind pushing it). What we do next is turn off the stones at the front of the castle, only for a fraction of a second, which will cause the castle to tilt slightly forwards. The force of gravity will start pulling the castle downwards on that side, pulling it forward. To prevent us from crashing, we turn the stone back on, floating us back up, only now we are slightly further forward. If we keep repeating this process rapidly, we will soon start to build up significant speed, despite the castles high mass.

This concept is very similar to that of the rail gun which uses electromagnetic force to move a metallic object at high speed. Contrary to its name, it is not just intended for weaponry, NASA proposed to use a rail gun to accelerate small aircraft or spacecraft into orbit..

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    $\begingroup$ Interesting ideas, this make them more similar to hovercrafts than airships. $\endgroup$ – Eth Jun 5 at 21:55
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Tracks.

I wondered for how long people had been using rail-type tracks to move cargo overland. A long time: I found the Diolkos, used by the ancient Greeks to move ships overland.

https://en.wikipedia.org/wiki/Diolkos

The Diolkos was a trackway paved with hard limestone[26] with parallel grooves running about 1.60 metres (63 in) apart.[31] The roadway was 3.4 to 6 metres (11 to 20 ft) wide.[26] Since ancient sources tell little about how the ships were hauled across,[24] the mode of ship transport has largely to be reconstructed from the archaeological evidence. The tracks indicate that transport on the Diolkos was done with some sort of wheeled vehicle.

Your ley lines would have parallel tracks along them, probably of stone. Stays down within the tracks would prevent upward motion of the castle and having two would prevent lateral movement out of the influence of the ley lines supporting power.

The castle would be moved by sliding the stays along the tracks. A team of oxen could do this, in the same manner an ox team might pull a barge. Depending on the distance between the two stays you might need 2 teams working together.

You could do away with the stays and rails and just use the ox teams but you would need to have a cart heavy enough to oppose the lifting power of the castle which is more work to move.

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    $\begingroup$ If you've got wheels to resist sideways movement, sails would work for most directions, if not directly up wind. $\endgroup$ – Robin Bennett Jun 5 at 10:59
  • $\begingroup$ Giant sailing train wagons, this definitely has a ring to it! $\endgroup$ – Eth Jun 5 at 21:57
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What instantly comes to mind is: WATER

Water can be collected from rainfall in a cistern within the castle. You could then easily direct the flow of the captured water, and with water being relatively dense it would have the kind of propulsion you're looking for.

Since there is mechanical power available to these castles as the question stated, you could also manipulate the pressure at which water is propelled. Think of it like an ancient fire hose, which can output water with an immense amount of force.

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    $\begingroup$ I think that without the advent of steam to provide you with a means of developing a powerful, high velocity jet of water, you simply won't be able to get enough thrust to move your castle at anything more than a snail's pace (and very possibly not enough to move a larger castle at all), especially given the colossal weight of the reaction mass tankage. $\endgroup$ – Starfish Prime Jun 5 at 7:16
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    $\begingroup$ Throwing tons of waters out of your castle will also make you climb because you'll be lighter. So it isn't a true horizontal propulsion. $\endgroup$ – Echox Jun 5 at 10:00
  • $\begingroup$ According to the question, a small floating castle weighs as much as two Airbus A380s. Getting one up to a leisurely 5 meters per second requires ejecting 60 tons of water at supersonic velocities, or around a thousand tons at more reasonable firehose velocities. $\endgroup$ – Mark Jun 5 at 21:57
  • $\begingroup$ The castles can be equipped with a few hundred tons of water for internal hydraulic power, with the ability to raise it again at a few cm/s with an internal plate, as per the question. How would you use that power? And of course, some of the cargo mass can be used as ballast, though with the masses involved, that would probably be only for emergency use. $\endgroup$ – Eth Jun 5 at 22:01
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They have lifting stone in 'The Edge Chronicles' and ships all employ a Stone Pilot to carefully control the temperature of the ship's stone. Hot stone rises and cold stone falls, but differential heating can be used to angle the lift vector and push the ship along.

High performance stones have carefully bored holes, to allow fire (or cooling air) to reach the middle of the stone. Most people understand the concept, but only the stone pilots have the finesse to safely control a ship.

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Take a look at the work of Leonardo Da Vinci, he covered a couple of designs related to flight such as a man powered machine with mechanical wings, and a aerial screw. Either of these could potentially by modified and increased in power and size to assist in moving a floating castle. They would obviously need to be massively increased in size and efficiency to move something so massive though. Horse powered treadmills could provide the mechanical energy. As you said, they've had a few decades to improve on initial solutions so perhaps they may have increased to the point of developing a reasonable propeller. Remember too that the ancient Greeks developed the first steam engine, but saw it as a toy rather than as something that could be used as a tool.

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    $\begingroup$ Leonardo's work won't cut it -- his wing and screw designs are barely adequate for moving lightweight wood-and-fabric designs, and would have no effect on something as heavy as a castle. Even modern aircraft engines would be borderline. $\endgroup$ – Mark Jun 5 at 21:41
  • $\begingroup$ @Mark The castles do have some internal hydraulic power, as per the question, plus whatever crew or beasts of burden for muscle power. Being generous and giving them Renaissance-efficiency windmill propellers, how much (or little) would that help them? $\endgroup$ – Eth Jun 5 at 22:03
  • $\begingroup$ @Eth, going with some very generous assumptions about the efficiency of a windmill as a propeller, a single windmill 20 meters across could get a small castle up to a speed of 15 km/h in a few hours. It would take about 250 horsepower to turn the windmill, assuming no friction losses. $\endgroup$ – Mark Jun 5 at 22:26
  • $\begingroup$ @Mark So this is twice the power than what rising 100 tons of water at 10 cm/s with the inner plate would give. Probably not enough there, especially if wind disagrees. Maybe you could to expand on that and your other points in an answer? :) $\endgroup$ – Eth Jun 5 at 23:04
  • $\begingroup$ @Eth, I know lots of things that won't work, or at best, are just barely viable. Starfish Prime's already covered the one thing I'm certain will work well, with his ox teams. My personal preference would be to wait until the 19th century, when I can pull my castle around with a locomotive or two. $\endgroup$ – Mark Jun 5 at 23:29
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Fun fact about late Roman technology: They had all the tools to make a steam engine.

http://www.foresightguide.com/50CE-a-steam-engine-in-ancient-rome/

Steam engines are useful for a lot of things, and would help with several of the previous answers. Whether you're going on water or land having a steam engine would help enormously.

That may be a bit steampunk, and it assumes that the knowledge wasn't lost (they were called the dark ages for a reason), but steam turbines and propellers could definitely move your castle along the line.

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  • $\begingroup$ I see you've fallen into the aeolipile trap. Yes, technically speaking, it's a steam engine. It's also a horribly inefficient one, with negligible power output and near-zero torque. It's a dead-end for further development, because it's a distant ancestor of the steam turbine, not the steam piston, and the turbine doesn't become possible until the late 1800s with the development of high-strength alloys and precision machining. $\endgroup$ – Mark Jun 5 at 22:31
  • $\begingroup$ Even piston based steam engines require fairly accurate machining, which was a technology developed for the production of cannons. $\endgroup$ – Robin Bennett Jun 6 at 9:42
  • $\begingroup$ @RobinBennett, with a piston, you can substitute a flexible seal for a precision-fit machined surface, at the cost of greatly reduced efficiency (Newcomen's engine used a leather gasket and a layer of water on top of the piston head). A poorly-machined turbine shakes itself to pieces, or doesn't work at all. $\endgroup$ – Mark Jun 6 at 20:06

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