Super-habitats

Ian,

Interesting post, I think I see what you are saying but I dont know if it
applies in this case. First before I put forward my counter-argument let me
demonstrate something that can happen when talking about a technical subject
and not backing it with maths. Not that I want you to do that, my maths is
not that strong and that would mean I would have to do a lot more research
than I have time for.

Okay, apologies to those who dont like long posts that include side issues,
so some of you may not like this, you are invited to skip this paragraph if
you wish.
I am going to show that you can say things in English that sound logical but
you can not say in maths, not that my maths is top class.
A little puzzle that illustrates my point.
Three guys are going to camp in the woods but it starts to rain so they find
a cheap hotel to stay at, the fellow at the desk tells them a single room
for all three will cost them $3.00, $1.00 each (this was along time ago or
else a very cheap hotel), they agree and pay the dollar each. After a while
the owner comes in and sees that they have been charged $3.00 for a $2.50
room. He gives the clerk 50 cents and tells him to give it back to them. On
the way up the stairs he thinks that 3 will not go into 50 even and why do
this work for nothing so he takes 20 cents and pockets it. At the room he
tells the 3 guys there has been a mistake and they have a refund so he gives
them 10 cents each back. Each man paid $1.00 and with 10 cents refunded they
have now each paid 90 cents, 3 x 90 cents is 270 cents or $2.70. the $2.70
plus the 20 cents the clerk had in his pocket makes $2.90. My question,
where did the other 10 cents go to?

Okay, above we have a simple problem with a simple solution especially when
written, it sounds logical but isnt logical at all. I have lost track of
the amount of time that I have spent trying to find a logic flaw in a
program, it can be frustrating, I hope this is not what we have here.

This is an example of something that can be said in English but not in
maths, you can not write down an equation that allows this problem to be
stated. I have to wonder, there are few possibilities.
I am talking about something that makes sense when spoken (written) but not
as maths, you are talking about something that makes sense when spoken but
not as maths, we are both talking about things that make sense when spoken
but not as maths and they are different things or some combination of the
above.

>On 08/09/06, Darren > wrote:

>> The size is an almost random number, as I said, so if it turns out that it
>> is too big to be practical I will not shed a huge amount of tears, though I
>> will admit to becoming attached to them.
>>
>> Now from what I understand from your post, you think that the large
>> circumference will make the rim speed so high it would not be practical.
>> From that I have to assume you think that normal materials will come apart
>> under the strain because of the speed. Why?
>
>Let me try and explain. If you take a chain, and hang it between your
>left hand and your right hand, you form a catenary. Now as you move
>your hands apart, the catenary flattens; but no matter how hard you
>pull, the chain never becomes straight; there's always a curve in the
>middle.

Okay, I understand this, in an earlier post I mentioned that Larry Niven had
to use unobtainium for his ring-world because of its size and because it was
in essence a single span that was supporting itself. I suggested that a
smaller ring and more supports might make things better. Your catenary will
have a given curve depending on the distance between supports, tension on
the material and the gravity pulling it down, question is why? If I have two
posts in space with no gravity pulling on it (okay, no effective gravity)
that are 1,000 metres apart and I put a single fibre of super wire X that is
1,000 metres long between them, then the fibre would be a straight line, no
sag (this is a thought experiment so things are perfect, sort of). Now I put
a large mass, say a small moon (got to love thought experiments, they let
you be god) under the set-up, the wire is going to sag a little, replace the
little moon with a bigger one and the sag gets bigger, replace it with a
small planet and the sag increases again, a giant planet and you have a much
bigger sag. The stronger the gravity the bigger the sag, this makes sense
but why does it do it? The wire is still 1,000 metres so where does the
extra length for the sag come from? Nothing is really perfect, the posts
will flex, the wire will stretch and from this you get your sag. You are
right about needing to pull harder to reduce the sag OR you could support
the wire, put more posts under it to lift it, hang lines down to support it.
This will turn one big sag into a lot of smaller sags, the more posts or
lines the more small sags, enough posts or lines and the sag will be so
small you can not measure it.

>It's a bit similar with a habitat, the curvature of a very big habitat
>is very small, so you need to put a lot of load on the hull to keep it
>flat against the psuedo gravity. Otherwise bits of it will try to fall
>away.

Okay, here I have to put in a bit of definition, by hull I assume you are
talking about the floor of the ring. If that is the case there are two
directions we could be talking about, the circumference of the ring, the
15,707 km length you get by multiplying Pi by the diameter (5,000) and the
other one is the 15,000 Km length of floor between the two end-caps (air
retention walls). Now here is where I have a bit of a problem, which one is
failing, the floor between the end-caps or the length around the
circumference?

Easy one first, lets reduce the length of the cylinder from 15,000Km to 1
metre a real impractical habitat. We now have two walls 5,000 Km wide with a
1 meter wide floor between them. To make it even easier lets get rid of the
floor and one wall so we are dealing with just one wall and to have a load
we will put a mass around the wall, a tube (made of unobtainium because it
is unimportant what it is made of so long as it acts as a load) filled with
water so each metre would weigh 100 kilograms under 1G. from the ring at the
centre of the end-cap (remember it was suppose to be an open habitat, the
size of the ring is an unknown variable) we have a number (the exact number
to be worked out later) of cables made from super wire (carbon nanotubes or
some other material, beside the point just now) hanging down to where it
attaches to the solid wall (made of woven super wire? Carbon nanotubes?
Genetically modified giant spider silk?) and this comes down to the rim, in
this case our tube of water. If we take two strands of the material of the
wall that are next to each other as our samples and measure the strains on
each, these can be either tension from the centre to the end and tension
pulling the two strands apart.
As we start to spin the wall we will see an increase in the tension pulling
down, as the speed of spin increases this tension is going to increase
until finally the downward pull exceeds the ability of the fibres making
up the wall to resist at which point it will fail. Now about the force
pulling the two sample fibres apart? Im not sure where this is coming from?
If the two fibres were not attached and were just hanging free they would
just form a circle made up of a large number of lines. If I then took a
strip of material (made of our woven super fibre) and attached it to our
sample fibres, loosely so as to not place tension on the hanging lines and
then spun up the wall, do you content that the material would come apart? If
the two sample lines were 1 metre apart (or 1 centimetre or 1 millimetre or
pick your distance) and the material I attached to them was 1.2 metres long,
where is the tension coming from? If the spin-gravity is 1G and the strip of
material is able to hold up to such a force, where is the problem? Sorry I
do not see it.

Okay, Im the fellow in charge and I have ignored your advice and maybe Im
being stupid, but now we have our two walls and its time to put in the
floor. Here I can see a real problem, we have two points 15,000 Km apart
that has to have a span placed between them, a single span bridge with a
15,000 Km span and for the sake of the discussion lets make it 10 Km wide!
Wow, that is one hell of a bridge! Now the thing is I dont see the
difference between this 15,000 x 10 Km wide span under 1G, spinning at 5 Km
per second (17,951 km/hr) and a long thin cylinder of 500 km wide and 15,000
Km long (the soda straw habitat, we go from 3:1 to 30:1) spinning once each
990 seconds at 1586 metres per second or 5712 Km/hr at 1G. The speed of
rotation should have little impact. I am more worried about how a 15,000Km
span is going to support itself. I would have to assume some kind of multi
arch system under the floor to give support and cables from the centre ring
to the floor to provide support, maybe one each 100 Km. it would depend on
the properties of the material it is made of.

>>

>> You can do the same with a rock and a string, a short string
>> fast and a rock at 5G will snap it, a long string going faster at 2G will
>> not.
>
>Now try it with a 200km long string and get back to me.

Okay, so I talk to my mate Bill and he gives me a few billion to try an
experiment. I hire a Russian spaceship and we head off to a trip around the
moon, two days in orbit (no worry about air resistance) and as we orbit it I
reel out 5 new fibres I have invented (super wire 1 through 5) with a 10 Kg
mass on the end of each of them. At the 1Km mark fibre #1 snaps, at 10 Km #2
goes, at 20Km #3 bites the dust, #4 goes at 100Km and #5 makes it all the
way to 5000 Km and then snaps, was it the speed of orbit or the weight of
the 10 Kg mass and the length of the fibre together that did them in?

Ian, I am not sure that the concept you describe is something to worry about
but rather than thinking about the rim of the habitat as a chain going
around the circumference, think of it as millions of fibres hanging down and
being linked at the rim. The tension is radial, from the middle to the edge,
not the edge being pulled lengthwise.
I do agree that if I have a given span between two posts and I want to
lessen the sag in the chain between the posts, I will have to put tension on
the chain but in this case the chain is not under tension, it is not that
kind of structure or if it is under tension we have to make sure the tension
is transferred from a longitudinal force to a radial force before anything
fails.

>For your own security, the Department of Homeland Security is watching you.

I am a first child with 4 younger brothers, does this mean that now I
finally have my very own Big Brother??

Darren