How much power can a discworld axle generate?

Factual Questions
1

Axles are rare artifacts of unknown origin that are composed a 2 cubes with six inch sides, connected by a rod. The cubes rotate with respect to each other. The rotation is unstoppable so we can assume infinite torque. They are also indestructible. The rotation speed is not specified other than to say they rotate slowly. So I am imagining 5 revs per minute.

https://wiki.lspace.org/Axle

If such a device were discovered, we could use it to generate power by attaching the cubes directly to a generator. It would be limited by the material strength of whatever can grab onto the cubes. Given that they turn so slowly, and are relatively small, how much power can reliably be extracted? In the books they are said to power entire cities. And that power is presumably purely mechanical. Is powering an entire city reasonable, even using modern materials?

2

The ‘axles’ could turn a large and heavy rotor, which would then generate electricity via a dynamo. I presume they have some sort of dynamo in the Discworld; or are you looking to import ‘axles’ from the Discworld into Earth? Axles+?= profit.

the limiting factor would be the stiffness and resistance to deformation of the junction between the ‘axle’ and the rotor - make the rotor too large and heavy, the metal at and near the junction will deform and shear, and eventually melt and stop turning the rotor at all.

What is the stiffest metal known that could resist deformation and melting in this situation? Would efficient cooling help?

3

[Moderating]
Yes, this question is prompted by a magical Device from a fictional world. But it’s ultimately a question about real-world materials. Hence, it is appropriate for FQ.

4

More specifically, regardless of what you ultimately hook it up to, power is torque times rotational speed. Rotational speed is a constant, here, and torque is limited by the coupling. So the question is, how much torque can you get from a real-world-material junction to a 6 inch cube?

5

There’s no rod, they just have two abutting faces.

6

Do we know this? They can’t be taken apart since they’re indestructible. And my impression is that the tolerances are fine enough that you couldn’t slip a shim in to check.

As for the OP, a rough answer. The compressive strength of diamond is somewhere around 60 GPa, which I’ll derate to 40 GPa. A 6-inch cube can apply force on the outer part of the non-axial faces, so perhaps a 150x50 mm strip across 4 faces.

The centers of this strip are ~90 mm from the centerline and so on average it goes through a distance of ~550 mm.

The OP says 5 rpm but I believe it’s stated in the books to rotate every 6.9 seconds, so I’ll use that number.

Also, the strips are angled at 45 degrees relative to the torque arm, so I’ll have to multiply by 70%.

All told, I get ~70 megawatts. Which indeed is in the ballpark for a small city. I don’t recall if they can create synthetic diamond (via magic) in the Discworld universe. If you have to use steel instead, the power goes down by about two orders of magnitude: ~700 kilowatts total.

7

I’d have guessed that the failure mode would be shearing a circumscribed cylinder out of whatever you embed the Axle in. Deformations, you can mitigate just by putting a bunch more material around the hole, but shearing, I don’t think there’s anything you can do.

8

It’s literally in the description in the link in the OP. N̈o rod is mentioned.

9

ISTM the limit is the biggest generator we can build. The axle can turn it no problem. You’d need some gearing to spin the generator at an ideal speed but that is no problem. We do that sort of thing all the time (see the slow spin of windmills versus the speed the generator runs at).

As long as the gears and shafts can hold up (and they probably can) it should be relatively simple to do.

Heck, you could probably string a bunch together. Not sure there would be a limit to that.

10

As mentioned by @Chronos, the limit is when you start to strip the thing you use to connect the cube to the generator. Think about trying to get out a rusted bolt from an engine block. Eventually the bolt will strip. In the case o the axle, eventually the axle will dig a circular cavity in whatever is trying to hold on to it.

11

Everything wears out in time and needs maintenance. This seems no different.

12

This seems like a good answer in my unqualified opinion. At least it is the kind of analysis I was looking for. No idea if it is right.

13

Yeah but for a high enough load, that time is basically instantaneously.

14

It just says they’re joined along one face, not how they’re joined. Could be a rod, a bearing, or just magic. Although the name “Axle” rather implies some kind of rod.

BTW, what’s with the umlaut? Channeling Spin̈al Tap?

I expect I’m within an order of magnitude. Maybe two :slight_smile: .

There might be a more efficient structure, but what I had in mind are four truncated pyramids. The top would be a flat 150x50 mm rectangle to interface with the cube. The bottom would be spread out, say to 1500x500 mm, so that it could interface with more conventional materials like steel. The details don’t matter as much past that point, but you probably would want some kind of gearing mechanism. The slow speed of the axle is the main obstacle to extracting lots of power.

15

Wait, you’re talking about internally? Not really knowable and certainly not known in-story. The two cubes are called an Axle, not their linkage. The archaic meaning of the word wasn’t ‘rod’ in any case.

Phone typing.

16

Well, yes. If someone hands me a Rubik’s cube, I’m not going to be satisfied if they tell me the subcubes are just attached at the faces and slide across each other in a peculiar way. I know there must be some internal axle or bearing system.

Well, I’ve only read a handful of Discworld books, though that does include Thud!. I’m not sure if they’re described in more detail elsewhere. Here is the actual book passage, which includes more detail than the link above:

“It spins once every 6.9 seconds but the torque is immense! It broke the clamp! What powers it?”

“No one seems to know,” said Carrot. “In Uberwald-”

“Excuse me, what is this about?” said Lord Vetinari, holding out a hand imperiously.

The man glanced at him and then turned to Carrot. “Who’s this?” he said.

“Lord Vetinari, ruler of the city, may I present Mr Pony of the Artificers” Guild?" said Carrot quickly. “Please let his lordship see the Axle, Mr Pony.”

“Thank you,” said Vetinari. He took the thing, which looked very like two cubes, each about six inches on a side, joined together on one face, like a pair of dice joined at the sixes. In relation to the other, one turned - very, very slowly.

“Oh,” he said flatly. “A mechanism. How nice.”

“Nice?” said Pony. “Don’t you understand? It won’t stop turning.” Carrot and Pony looked expectantly at the Patrician, who said:

“And that’s a good thing, is it?”

Carrot coughed. “Yes, sir. One of these drives one of the biggest mines in Uberwald. All the pumps, the fans that move the air, the trucks that haul the ore, the bellows for the forges, the elevators … everything. Just one of those. It’s another type of Device, like the cubes. We don’t know how they’re made, they’re very rare, but the other three I’ve heard of have not stopped working for hundreds of years. They don’t use fuel, they don’t need anything. They appear to be millions of years old. No one knows what made them. They just turn.”

It doesn’t really rule out there being a rod in there somehow. Vetinari assumes it’s a fairly ordinary mechanism to start with.

Relevant facts:

  • Spins every 6.9 seconds (8.7 rpm)
  • Two cubes about 6 inches on a side
  • Essentially infinite torque
  • Only 4 known Axles total
  • Already runs one of the biggest mines in Uberwald
17

This is a setting where photography is literally an imp in a box doing a painting. It’s magic. There doesn’t have to be any rational mechanism.

18

Just as an aside, the novel Pushing Ice by Alastair Reynolds contains a similar mechanism. It’s much larger–dozens of meters across, IIRC. And turns much more slowly (almost imperceptibly slowly). But it too has seemingly infinite torque and they’ve got sci-fi materials science, and adapt it to a generator system which indeed powers their city.

Thud! was published in September 2005; Pushing Ice in October 2005. So they couldn’t have influenced each other, unless the authors talked.

Though it would not surprise me if similar things had shown up in previous sci-fi/fantasy. The book Roadside Picnic has some artifacts along the same lines, such as a pair of discs that are connected to each other through empty space, with apparently infinite rigidity; also a ring that spins indefinitely.

19

Sure. It’s also possible there’s a rod between the two, just one made from their equivalent of scrith (like the cubes themselves). If the cubes are separated by a few hundredths of a millimeter, they could check with a thin piece of metal. The book doesn’t exclude that possibility. I already mentioned that “just magic” is a possibility, but it isn’t the only one.

20

Why?

Infinite torque doesn’t mean instant destruction. The torque on an escalator is huge but they rotate slowly and do not break.

It is turning around 10 RPM. Attach almost anything to it. Attach the biggest generator in the world to it. Clearly they are turned with no problem today with stuff we can make. You just need a gear box to increase RPM for the turbine…easily done.

Why would the axle break that?

Then line as many up in a series as you want. The axle will never slow down so there is no limit.