View Full Version : Tension in a ring

RoboSpy

2004-Sep-01, 02:34 AM

I was just fiddling with some numbers today, and I arrived at what I thought was a very disturbing conclusion about artificial ring structures used as space stations or the like - the tension created by spinning the ring for "artificial gravity" (it isn't really artificial, OR gravity, but I'm sure you all know what I mean) puts a very strict limit on its radius, assuming that it's constructed from alloys existing today. Any larger than this preexisting limit, and the ring rends itself apart by centrifugal inertia. I'm hoping - yes, hoping - that I'm having a misconception about the physics involved here and grossly overcalculating the tension in the ring. So my question is basically a Newtonian physics problem:

Am I correct in figuring that the tension in a ring spinning in space is equal to the total mass of the ring mulitplied by the centripetal acceleration of the rotation? (Assuming equal acceleration at the inner and outer rims of the ring - I know I should be integrating, but I'd rather not.)

The Bad Astronomer

2004-Sep-01, 03:41 AM

Hmmmm.....

www.weizmann.ac.il/wagner/COURSES/CLASS%252008/Lecture%25208.ppt+tension+spinning+ring+equation&h l=en]This (http://66.102.7.104/search?q=cache:jPvZWnXeL7AJ:[url) page might help[/url] (it doesn't appear to exist anymore, but is cached in Google).

Have you ever read Larry Niven's novel "Ringworld"? He discusses this problem, though does not do the math. My friend Erik Max Francis has a page listing Ringworld parameters (http://www.alcyone.com/max/reference/scifi/ringworld.html), including the tension. I assume therefore he knows how to calculate it. Email him, and tell him I sent you!

eburacum45

2004-Sep-01, 06:03 AM

In Orion's Arm we use much smaller Bishop rings, 2000 km in diameter, which are near the limit for size using Carbon buckyfibre tubes;

these were suggested by Forrest Bishop in 1997

http://www.iase.cc/openair.htm

we do have some maths available somewhere to determine the limits of size in such structures, but I can't find it at the moment.

But if there are any other relevant equations I would be interested.

Here is my page about such artificial worlds- many of the largest structures use artificially strengthened atomic bonds and advanced (read imaginary) technology...

http://eburacum45.5u.com/artificial_worlds.html

daver

2004-Sep-01, 06:28 PM

I believe this is called hoop stress; you ought to be able to google the formula if you want to check your derivation.

You're assuming that all the support comes from tension along the outside "floor", aren't you? You should be able put in some radial spokes to help with that--there are still size limits, but they get more manageable.

John Dlugosz

2004-Sep-01, 06:40 PM

Am I correct in figuring that the tension in a ring spinning in space is equal to the total mass of the ring mulitplied by the centripetal acceleration of the rotation? (Assuming equal acceleration at the inner and outer rims of the ring - I know I should be integrating, but I'd rather not.)

Picture a discrete approximation, such as a railroad train made up of many cars connected by links. Curve the train into a circle.

Imagine two adjecent cars. Draw the centripital force vectors of each: they are nealy paralell, with a small angle between them. The force pulling the cars apart is the projection of one of those vectors onto the other (dot product I think?). I don't care about the "total tension" of the entire mass of the ring; just "is this one link strong enough?". It implies that the larger the ring, the lower the tension.

Now, extend the railcars into trapezoid shapes, so they touch at a mitered angle rather than being hooked together. Now the edges are in compression, not under tension. That is, you can pre-stress the ring to compensate for the tension.

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