Ringworld Parameters

logan_mcgrath89.RemoveThis@hotmail.com wrote:

> How do mass, thickness, and width of the ring play into all this? I'm
> thinking that the heavier the ring, the more energy to get it spinning.

The total mass m and its radius r determine its moment of inertia, I,
which in turn determine its total angular momentum L and rotational
kinetic energy:

I = m r^2,

L = I omega,

K = (1/2) I omega^2.

To get the Niven ring up to speed, you have to provide the amount of
kinetic energy K yourself.

The thickness doesn't contribute per se to a Niven ring's angular
momentum or kinetic energy, but it does affect the tension stress
induced in the Ringworld by its own rotation.

> For aesthetics, I tried designing a model with the inside surface
> curved like a sphere so every flat surface was perpendicular to the
> center. Thing is, because of the way the ring generates the gravity
> effect, it should ideally have the inner surfaces parallel to the axis
> of rotation. Otherwise, you would have a gentle slope coming up to the
> sides. I don't really like the thought of an orbiting soup can... I
> hope I'm just paranoid, lol.

What you're describing is a cylinder. Which is exactly what a Niven
ring is -- albeit a very squat one.

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Erik Max Francis wrote:
>
> What you're describing is a cylinder. Which is exactly what a Niven
> ring is -- albeit a very squat one.

Actually, I think the curved inner surface might work better with the
whole "flup" thing... assuming that Larry Niven would've wanted some
way to get a general movement of sludge from the rims into the seas at
the ring's middle. Would it also be possible that the curved insides
could contribute to the ring's structural integrity?
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logan_mcgrath89.RemoveThis@hotmail.com wrote:

> Actually, I think the curved inner surface might work better with the
> whole "flup" thing... assuming that Larry Niven would've wanted some
> way to get a general movement of sludge from the rims into the seas at
> the ring's middle.

Why?

> Would it also be possible that the curved insides
> could contribute to the ring's structural integrity?

No. Why would you think that?

--
Erik Max Francis && max.RemoveThis@alcyone.com && http://www.alcyone.com/max/
San Jose, CA, USA && 37 20 N 121 53 W && AIM erikmaxfrancis
War can only be abolished through war, and in order to get rid of the
gun it is necessary to take up the gun. -- Mao Zedong, 1898-1976
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logan_mcgrath89 RemoveThis @hotmail.com wrote:
> How do mass, thickness, and width of the ring play into all this? I'm
> thinking that the heavier the ring, the more energy to get it spinning.
>
> For aesthetics, I tried designing a model with the inside surface
> curved like a sphere so every flat surface was perpendicular to the
> center.

That would be a very bad design. If the inner surfaces were spherical,
then at the rim of the Ringworld they would be more than 1000 miles
closer to the axis of rotation than at the middle. That would mean that
all the water would accumulate on the centerline of the Ring, with the
air right on top of it, while the Rims would be in a near-perfect
vacuum. There'd be no need for the rimwalls to hold the air in, which
could be considered an advantage of this design, but rendering most of
the Ring uninhabitable would easily cancel out that advantage.
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Erik Max Francis wrote:
> logan_mcgrath89.RemoveThis@hotmail.com wrote:
>
> > Actually, I think the curved inner surface might work better with the
> > whole "flup" thing... assuming that Larry Niven would've wanted some
> > way to get a general movement of sludge from the rims into the seas at
> > the ring's middle.
>
> Why?

I'm thinking that because the seas would be the "lowest" points on the
ring, and also that the inside is contoured like the land above it,
then the additional curving would just happen on it's own just because
of the formed surface. Even if it wasn't intended, I could definitely
see it happening that way.

> > Would it also be possible that the curved insides
> > could contribute to the ring's structural integrity?
>
> No. Why would you think that?

I was thinking that the additional arching would contribute to the
strength... Thinking that a more rigid ring floor would be better than
Niven's contoured and relatively paper-thin ring, then I could see
something like a hyperbolic cross section for the foundation. None of
our materials could handle the tension stresses with the way Ringworld
floor is contoured. I geuss a rigid/arched floor would be better... I
dunno.
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kuyper.DeleteThis@wizard.net wrote:
> logan_mcgrath89.DeleteThis@hotmail.com wrote:
> > How do mass, thickness, and width of the ring play into all this? I'm
> > thinking that the heavier the ring, the more energy to get it spinning.
> >
> > For aesthetics, I tried designing a model with the inside surface
> > curved like a sphere so every flat surface was perpendicular to the
> > center.
>
> That would be a very bad design. If the inner surfaces were spherical,
> then at the rim of the Ringworld they would be more than 1000 miles
> closer to the axis of rotation than at the middle. That would mean that
> all the water would accumulate on the centerline of the Ring, with the
> air right on top of it, while the Rims would be in a near-perfect
> vacuum. There'd be no need for the rimwalls to hold the air in, which
> could be considered an advantage of this design, but rendering most of
> the Ring uninhabitable would easily cancel out that advantage.

You have effectively killed my art... lol, just kidding. Actually, you
have a very good point, thanks!
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I think kuyper.DeleteThis@wizard.net has also effectively killed the Dyson sphere
with his argument on the "curvy ring" because there is no way to
generate ANY gravity inside of the sphere without all the air draining
into the equator. *high-five* You rock!
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logan_mcgrath89 DeleteThis @hotmail.com wrote:
> I think kuyper DeleteThis @wizard.net has also effectively killed the Dyson sphere
> with his argument on the "curvy ring" because there is no way to
> generate ANY gravity inside of the sphere without all the air draining
> into the equator. *high-five* You rock!

Dynson spheres have never been intended to rotate, and people were
never intended to inhabit the inner surface.

A Dyson sphere has a surface gravity which is equal to the surface
gravity of the enclosed star, divided by the square of the ratio of the
radius of the sphere and and the radius of the star:

Gdyson = Gstar*(Rstar/Rdyson)^2

Therefore, if you make the sphere small enough, it could have a surface
gravity equal to that of Earth; it could therefore sustain an
atmosphere like earth's.

Unfortunately, the sphere must radiate energy at the same rate as the
enclosed star; otherwise it will keep heating up until it does radiate
that much energy. Blackbody radiation is proportional to the surface
area and the fourth power of the surface temperature. This means that

<Tsphere^4> = Tsun^4*(Rstar/Rdyson)^2

Where <Tsphere^4> means the average, over the surface, of the fourth
power of the temperature at each point on that surface.

A sphere surrounding a star like our Sun that was small enough to have
a surface gravity equal to that of Earth would have a surface
temperature much greater than Earth's rending the surface
uninhabitable. The T^4 law helps here; a small portion of the surface
(a radiator) that is much hotter than the rest of the surface would
disproportionally contribute to radiating away the heat, allowing the
rest of the sphere to be much cooler. It might be feasible, using
radiators, to live on the surface of aphere enclosing a star much
cooler than the Sun. However, normally a Dyson sphere would actually be
built like a space station, with amosphere contained in pressurized
containers, rather than sitting freely on the surface.
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logan_mcgrath89.RemoveThis@hotmail.com wrote:
> Erik Max Francis wrote:
>
>>What you're describing is a cylinder. Which is exactly what a Niven
>>ring is -- albeit a very squat one.
>
>
> Actually, I think the curved inner surface might work better with the
> whole "flup" thing... assuming that Larry Niven would've wanted some
> way to get a general movement of sludge from the rims into the seas at
> the ring's middle. Would it also be possible that the curved insides
> could contribute to the ring's structural integrity?
>

But your air and water form cylinders. With a curved inner surface they
would pool around the center, leaving dry frozen flup at the edges.

Jim Lillie
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logan_mcgrath89 RemoveThis @hotmail.com wrote:
> I think kuyper RemoveThis @wizard.net has also effectively killed the Dyson sphere
> with his argument on the "curvy ring" because there is no way to
> generate ANY gravity inside of the sphere without all the air draining
> into the equator. *high-five* You rock!
>

I thought the Dyson sphere depended on 'artificial gravity fields'
rather than spin.

Jim Lillie
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kuyper.RemoveThis@wizard.net wrote:
> Dynson spheres have never been intended to rotate, and people were
> never intended to inhabit the inner surface.

And now the whole concept makes sense, lol. Thanks!
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kuyper.DeleteThis@wizard.net wrote:

> A sphere surrounding a star like our Sun that was small enough to have
> a surface gravity equal to that of Earth would have a surface
> temperature much greater than Earth's rending the surface
> uninhabitable. The T^4 law helps here; a small portion of the surface
> (a radiator) that is much hotter than the rest of the surface would
> disproportionally contribute to radiating away the heat, allowing the
> rest of the sphere to be much cooler. It might be feasible, using
> radiators, to live on the surface of aphere enclosing a star much
> cooler than the Sun. However, normally a Dyson sphere would actually be
> built like a space station, with amosphere contained in pressurized
> containers, rather than sitting freely on the surface.

It would require a star at the very limit of the main sequence:

http://www.alcyone.com/max/writing/essays/outside-dyson-shells.html

--
Erik Max Francis && max.DeleteThis@alcyone.com && http://www.alcyone.com/max/
San Jose, CA, USA && 37 20 N 121 53 W && AIM erikmaxfrancis
Come not between the dragon and his wrath.
-- King Lear (Act I, Scene I)
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Jim Lillie wrote:

> I thought the Dyson sphere depended on 'artificial gravity fields'
> rather than spin.

The original conception of a Dyson sphere doesn't physically living on
it at all. It just involves collecting all (or a very large percentage)
of the enclosed star's sunlight for energy use.

Science fiction authors then came along and thought about making it
solid and habitable. If you want to live on the outside, then you need
to make it very small and around a very small red dwarf. If you want to
live on the inside, you need some sort of nonphysical gravity
generators, since the gravitational field inside a uniform, spherical
shell is zero.

If you want to spin it centrifugally for gravity, then the air and
everything will collect at the equator. So instead you should make it a
cylinder ... which is precisely the line of argument that leads you to a
Niven ring. Except for the slightly inconvenient fact that you need
unreasonably strong materials as your tensile strength to get one gee of
artificial gravity for a Niven ring the size of Earth's orbit.

--
Erik Max Francis && max.RemoveThis@alcyone.com && http://www.alcyone.com/max/
San Jose, CA, USA && 37 20 N 121 53 W && AIM erikmaxfrancis
Come not between the dragon and his wrath.
-- King Lear (Act I, Scene I)
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