Instability of long cylinders

--- In spacesettlers@yahoogroups.com, "Combs, Mike" wrote:
>
> From: Bill
>
> > If I remember my physics correctly a cyclindrical gyroscope has a
> > magic length (I believe its 4.5 diameters but its been fifteen years
> > since I had to do that problem set) where the precision vector (the
> > thing that makes it want to go end-over end) is still has a component
> > pointing towards the axis (making the spin want to stay along the long
> > axis).
>
> If true, it means that this particular single-cylinder habitat design is
> probably OK:
> http://ssi.org/assets/images/Ch06p086.gif
> http://ssi.org/assets/images/Ch06p088.gif

Please remember that the people that are designing this stuff are
scientists and engineers with, I hope, a fairly indepth knowledge of
Newtonian Physics. Thus when asking about simple problems like overall
dynamic stability, one should at least believe that these people
solved the dynamic models especially when the numbers seem reasonable.

>
> > Actually the mirror design is completely impractical, but it is
> > possible to decouple the mirror completely and have a non-rotating
> > conical section instead. The mirror would still need to be strong
> > enough to allow the precision needed to track the sun, and the actual
> > mirror would have to be designed not to completely fry the interior
> > (for example having strips of mirror panels followed by non-reflecting
> > or empty strips) since such a cone would be focusing light in the
> > interior.
>
> I've had similar thoughts, but we would have to give up the appearance
> of a normal sun in the sky, especially as you moved closer to the
> sunward end of the cylinder. Another thing I've though about was a
> continuous mirror with a kind of bugle flare on it. Now we'd get a
> continuous, single sun, but it's shape would depart markedly from a disc
> shape. But that might be acceptable to many.

It should look like an ellipse with the long side of the ellpse
parallel to the axis of the cylinder.

>
> > Yes and no, the net angular moment is zero but the individual
> > cylinders have angular momentum and there is no reason why they can
> > fail individually.
>
> Yeah, but I was thinking that the linking structures (one tower under
> compression at one end, and one cable under tension at the other) would
> restrain the cylinders, preventing the spin axis from departing from the
> structural axis. In other words they would keep the wobble from getting
> started.

Yes you are right, that the tension and compression towers would
dampen the forces that would start the wobble, but that doesn't really
solve the problem. You are transfering the moment of the cylinders
forming a stress cycle in the towers. The wobble may actually cause
the towers to fail catastrophically if the stress the wobble produces
is higher than the yield strength of the metal in the towers. The
question then must be asked is the strength of the tension and
compression towers greater than the force the wobble will produce.
Also a wobble may induce fatigue cracking in the towers causing them
to fail.

All these kinds of failure modes would need to be analyzed and
appropriate safeties would need to be added during the design phase of
the project. On the bright side, this kind of structure need only be
designed once.

I doubt anyone would seriously promote an island 3 design prior to a
century after the construction of the first habitats.

Bill