How much power can a discworld axle generate?

What is the conversion rate between kilowatts and spherical-cow-power?

Not an engineering/physics guy, but if the device was rigged so both sides spun would that double the potential output? I’ve been assuming that the weak point was the 6” diamond receiver hole, so would splitting the load between two diamond receivers (one on each side) help matters?

Unfortunately not. You need two diamond receivers either way, since the forces are the same. But splitting the load just means each side is rotating half as fast. Energy is force times distance, and half the speed means you’re covering distance at half the rate. So the power output is also halved (but there’s two sides, so it comes out equal overall).

Depends… are we discussing horse-power equivalent or methane output?

For the purposes of getting a, say, ten-foot diameter drive wheel slipped over the 6-inch cube, I’d be inclined to call it slow.

And the merry-go-round idea illustrates this nicely. If the axle is already turning when the carousel is installed, you only have to worry about matching the speed of the hub to that of the axle. I certainly wouldn’t try stepping onto a twenty-five foot diameter carousel rotating at 8.7rpm, but a 12-inch diameter axle rotating at that rate would seem more doable.

Spherical cows are a result of NOT having an output for methane.

That’s not my spherical cow!

To be clear, I meant that a clutch that would slip above some torque (presumably a little less than the ultimate torque of the interface yoke) would be a good idea to prevent accidents. Making both sides turn might have some practical purpose, but if so, I’m not sure what it would be.

It’d also be fairly easy to make that clutch, since you could do that at a much larger radius, so you wouldn’t need extreme forces there.

Oh, and…

Not exactly synthetic, but they might be able to get the same effect. Troll teeth are diamonds, their teeth grow somehow, and they can be very large. You’d just need to get a troll’s tooth to grow around the Device.

This is, for all practical purposes, currently the case. As the OP properly says “the two halves rotate with respect to each other”. Without some third reference point on the device to declare stationary, you cannot declare that only one side is the one actually moving - all you can say is that the two pieces are moving relative to each other.

As already stated, the forces on each half (whether against a generator or stationary anchor) are necessarily equal.

Isn’t this essentially the purpoe of a key in an axle, to shear before catastrophic damage is done to more imprtant parts of the mechanism?

I suspect that in this case, those more important parts correspond to the indestructible device so such a protection mechanism is not required.

What material would be used on Earth Prime?

From wiki’s article on Young’s modulus (" the slope of the linear part of the stress–strain curve for a material under tension or compression." GPa is a gigipascal, if anyone is wondering.), diamond tops the list followed by Graphene, a Single-walled carbon nanotube, and Carbon nitride (CN2) if you can settle for less than 80% of the strength of diamond. Are any of these available to governments, industry, or mail order in a way that could be fashioned into a useful grip-grommet? Or do we have to settle for Tungsten carbide, about 65% the strength of diamond at most?

Gonna be tough to match covalent carbon bonds. Tungsten carbide is likely your best bet for conventional materials.

If a government really wanted to throw a billion or ten into a project, though, I think solid diamond blocks are achievable. Synthetic diamond is already cheap as chips. Making a large block of it is harder, but doable with a refinement of current tech.

I’d forgotten about that. A large tooth is actually perfect for what I had in mind, depending on the orientation of the crystalline structure. Cleave off the tip to leave a flat spot. Arrange four teeth around the circumferential sides of the cube on the forward-moving half. Being vaguely conical, the tooth spreads that high load to a much larger area on the other side, where a conventional wheel structure is built (out of steel or the like).

If you were evil, you could probably also capture a young troll and surgically modify the jaw to produce teeth in whatever arrangement you needed. Maybe even have it produce diamond cylinders of indefinite length if you can keep the teeth growing via some medical means.

I have never heard of this device but is it even established that you have to anchor one cube while the other spins? Or does it just spin unstoppably by itself. I mean it is fantasy so…

The information about it is limited, but it gets moved around easily and handled as if it were an ordinary mechanical device. It doesn’t seem like one side of it is locked in space, rotationally or otherwise.

Maybe there’s a hidden button that enables the anchoring system, like the immovable rod in D&D.

Young’s modulus is a measure of stiffness, not strength.

Noted. I am neither a physicist nor a material engineer. I found this webpage at Cornell to be helpful:

The words ‘stiffness’ and ‘strength’ both imply a sense of resistance and are both determined by geometry and material properties. However, a strong object may not necessarily be stiff, and vice versa! …

Strength [N/m2] is the maximum stress that the material can resist before deformation or fracture.
Stiffness [N/m] is the rigidity or resistance to bending.

So strength is resistance to damage, while stiffness is merely resistance to bending.

Rotation is not relative in that way. Attach a disc to both rotating parts and place ball bearings on both discs - the rotating one will fling them off and no declaration of different reference frames will change that.