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tintor

Is there a geometrical shape, that will always settle in the same orientation?

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In fact there is! It's called a Gomboc:

https://en.wikipedia.org/wiki/G%C3%B6mb%C3%B6c

My d20 needs this

You could create a d1 with this shape! Much better are more stable than Jorge Luis Borges': https://biblioklept.org/2019/04/02/the-disk-a-very-short-sto...

Wow, that's unintuitive, but cool.

Doesn't help on the moon, though, where the surface is soft, and may contain boulders.

With a lunar lander you can play with the weight distribution. You can make it more dense on one side. This, together with a self-righting shape, could increase the chances of settling in the desired orientation.

While it was settling it would destroy all/most of the external fixtures including antennae, engine nozzles, and sensor housings. Bonus the rocking action during settling could puncture the hull or break a windows on a sharp boulder.

All of that could happen.

What if airbags inflated around the lander? The external shape of the lander-with-inflated-airbags and the internal weight distribution could make it self-righting, while shielding the external fixtures and the hull.

Just throwing ideas around and role-playing spacecraft designer.

Air bags are ok if you don't have humans inside being pulverized as the craft bounces and rolls. If you have people inside bouncing isn't the best.

Prior art:

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

That shape must be patented or copyright protected, because all the Amazon listings are several hundred dollars each. The usual knockoffs are conspicuous in their absence.

AFAIK the required precision for it to work is quite high.

Indeed. The Wikipedia article says: "The gömböc, as the first physical example, is less sensitive; yet it has a shape tolerance of 10−3, that is 0.1 mm for a 10 cm size."

Well, it's an example of a convex homogeneous body that does this. It's much easier if these are not requirements, just have a sphere with an off-center mass.

https://en.wikipedia.org/wiki/Weebles#Design_principle

(Darn; I was two hours late to post this...)

I'd try a sphere, with some weight at the bottom.

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