So, did I get everything wrong?

This story takes place in February of 2102, and Anzu James is
writing a journal of her adventures, as if it were to be read
by people living in the year 2000 (it's a joint English/Modern
Earth History assignment). Anzu is sixteen years old and a
junior at Gerard O'Neill High School.

Oh, and for those of you who have already met Anzu James: don't
worry, she's dressed in this part. This is the day before her
Program week begins.

Looking back, I see that I've made several references to
"weightlessness" and "variable gravity" and even "where I
live," so maybe it's time to go into that. I live in Space.
Yep, out in HEO, or High Earth Orbit. That's why my high
school is named after Gerard O'Neill. It seems like half the
high schools in Space are named after him, with Konstantin
Tsiolkovsky, Arthur C. Clarke and Robert H. Goddard sharing
most of the rest. O'Neill gets the lion's share because he
was the first to describe in detail a plan for inhabiting
Space on a large scale. You can look him up. He was already
dead by your time. Actually, it's cool to think that some of
you could have met him. I've had kind of a crush. So that's
where I live, where less than a thousand of you have ever
been. But there are more than a thousand out here now! At
last count, a few hundred million people lived away from
Earth.

We don't live out in the vacuum, of course. And we don't
live in anything you would have called "space stations." No,
we live in enormous rotating tori, spheres, or cylinders.
The one I live in, I2 B11, is called a "Bernal Sphere," but
it's actually not quite spherical. The main body is two
thousand metres in diameter but two thousand one hundred
metres long. The extra hundred metres is right at the
equator, and there we have our beach. Our rotation is one
RPM, or rotation per minute. This means that we're actually
a little bit over one G right at the equator, but as it's in
the water, you don't notice it.

The water is a single ring-shaped pool, circling the
circumference and one hundred fifty metres wide, covering the
entire one hundred metre wide equator and an extra twenty-
five to either side. Sandy beaches rise from the sides of
the pool and extend another seventy-five metres to either
side. Thus, the whole water-and-sand thing encircles the
equator and is three hundred metres wide. The rise here is
so gentle you don't notice it. If you jog along the beach,
you can jog forever, or at least until you wear out. Waves
are generated in the middle of the sea (we call it that, and
it is salt water, with tropical fish), every fifteen seconds,
and every fifth wave is just big enough for surfing. I'm a
passable surfer, but would never win any contests or anything
like that.

Along both sides of the beach are the six villages which make
up the greater community. There are three to the north, and
three to the south. This is where most of the housing is for
the one hundred thousand people who live here. The villages
are each five hundred metres wide and two thousand metres
long. Since the circumference of I2 B11 is six thousand two
hundred eighty-three point two-is-close-enough metres,
there's just enough room between villages for a ninety-five
metre wide strip of parkland, with bridges crossing the
water. Each village houses sixteen to seventeen thousand
people, as well as local markets, schools, and a few local
businesses.

The villages are each named after an Earth community which
runs on the same time zone. For instance, I live in
Mendocino, which runs on Pacific Standard Time, the same as
Mendocino, California, USA. Tijuana runs on the same time,
but Dublin and Monrovia run eight hours ahead (the same as
Greenwich, England) and Beijing and Perth run eight hours
ahead of that (and thus eight hours behind me). Now you
might wonder why in the world or beyond it we would do such a
thing, but the reason is because this lets us run everything
from restaurants to factories around the clock without
anybody having to work early morning or graveyard shifts. It
also allows me to get out of school at 4:40 PM, cross the
park strip and be in another time zone, enjoying the past-
midnight nightlife in Dublin or perhaps watch the kids in
Perth start their school day. Actually, I have too many
after-school activities for the one, and the other seems
somehow cruel.

The rest of the sphere is mostly parkland, and is shared by
everybody, sort of like a county on Earth, perhaps. This is
a pretty standard set-up.

When you leave the equator you find yourself climbing a
hill, where your weight decreases (but not your mass!
Remember I said that was important here?) the closer you get
to the center. Right at the center, you weigh nothing at
all and can float like a cloud. I can't imagine living on a
planet, with the same gravity value all the time all the
time all the time. I'd go nuts if I couldn't cycle between
full-G, low-G, and zero-G every day.

Outside the main not-quite-a-sphere, there are the twelve
ag-rings. Six of them are on the "north" side, and six on
the "south." These are tubes, fifty metres in diameter,
bent into rings with the same two thousand metre diameter as
the main sphere. These are, or rather were, used for
growing food. With so many of the old I1's being converted
to dedicated food production, we only use half of our
ag-rings for food production and import the rest. The
others have been turned into parks, with one even holding
a small zoo.

On Dec 15, 2008, at 11:59 AM, sailor.barsoom wrote:

> The one I live in, I2 B11, is called a "Bernal Sphere," but
> it's actually not quite spherical. The main body is two
> thousand metres in diameter but two thousand one hundred
> metres long. The extra hundred metres is right at the
> equator, and there we have our beach.
>

This shape is not stable when rotating about its long axis. It
"wants" to rotate around a short axis, to get more of its mass away
from the axis of spin. (By which I mean that the latter spin axis is
a lower-energy state for the same angular momentum than spinning about
its long axis, so it's to that state it will naturally tend, given any
perturbations.)

In short, such a space station will want to tumble, and all that water
(as well as the people and vehicles and most of the buildings) will
end up stuck to the endcaps. Consider the shape of a top... have you
ever seen one tall and thin, like a pencil?

There are only a few ways around this (AFAIK):

1. Place a bunch of extra mass around (and attached to) the equator.
Maybe the hab's radiators are there? If it's enough mass, that'll
make it stable.

2. Make it shorter than it is long.

3. Have two of your elongated habs, side by side, connected together
at both poles by very strong struts, and spinning in opposite
directions.

> This is where most of the housing is for
>
> the one hundred thousand people who live here.
>

100K people seems like a bit of a stretch, though it's not too
outrageous. I usually figure 150 m^2 per person. A cylinder with
spherical endcaps, with 100 m flat section, has a total area of
13,194,689 m^2 if my math is right. So I'd say that could comfortably
house about 88 thousand people. And that's with no sea circling the
equator -- you've essentially removed the entire flat section from
use, so it would be more like 80 thousand. But I'm sure you could
cram in an extra 25% if you tried hard enough.

> The villages are each named after an Earth community which
> runs on the same time zone. For instance, I live in
> Mendocino, which runs on Pacific Standard Time, the same as
> Mendocino, California, USA. Tijuana runs on the same time,
> but Dublin and Monrovia run eight hours ahead (the same as
> Greenwich, England) and Beijing and Perth run eight hours
> ahead of that (and thus eight hours behind me). Now you
> might wonder why in the world or beyond it we would do such a
> thing, but the reason is because this lets us run everything
> from restaurants to factories around the clock without
> anybody having to work early morning or graveyard shifts.
>

I've got the same plan for my Disney-esque orbital theme park, but
that's because you're trying to pump money out of tourists 24/7. In a
general-purpose hab, it seems a bit far fetched. Restaurants wouldn't
need to run around the clock if people would all sleep at the same
time, and factories should be able to mostly run themselves. 100
thousand people isn't a big city -- about the same size as my town
(Fort Collins). As it is, we have to go to Denver for a lot of stuff
that the town just isn't big enough to support. If you divide into
three time zones, you're effectively reducing your city size by a
third (at least with regards to "things to do" like museums and plays
and so on).

> Outside the main not-quite-a-sphere, there are the twelve
> ag-rings. Six of them are on the "north" side, and six on
> the "south." These are tubes, fifty metres in diameter,
> bent into rings with the same two thousand metre diameter as
> the main sphere. These are, or rather were, used for
> growing food.
>
If they're significantly toward the poles, then these are contributing
to the instability problem. But if you moved them in towards the
equator, they could help. Of course then they'd be under more than a
G, which seems a little pointless for ag rings (and no fun for parks).

> With so many of the old I1's being converted
> to dedicated food production, we only use half of our
> ag-rings for food production and import the rest. The
> others have been turned into parks, with one even holding
> a small zoo.
>

I'd be surprised by this -- I'd expect the ag rings to have less
shielding than the main habitat, just because they don't need it as
much. But that would make them unsuitable for parks or zoos. You
might want to add something about how the conversion involved
importing extra dirt for shielding.

Cheers,
- Joe

I'm going to snip a bit of my own stuff here, for space.

--- In spacesettlers, Joe Strout wrote:

> On Dec 15, 2008, at 11:59 AM, sailor.barsoom (as Anzu James)
> wrote:

>> two thousand metres in diameter but two thousand one hundred
>> metres long. The extra hundred metres is right at the
>> equator, and there we have our beach.

> This shape is not stable when rotating about its long axis.
> It "wants" to rotate around a short axis, to get more of its
> mass away from the axis of spin.

ACK! I've thrown myself smack into the "cylinder problem"
Great.

> In short, such a space station will want to tumble, and all
> that water (as well as the people and vehicles and most of
> the buildings) will end up stuck to the endcaps. Consider

I suppose one could be build that way to begin with, but that
isn't what I'm going for, so...

> the shape of a top... have you ever seen one tall and thin,
> like a pencil?

Nope. Guess there's a reason for that, huh?

> There are only a few ways around this (AFAIK):
>
> 1. Place a bunch of extra mass around (and attached to) the
> equator. Maybe the hab's radiators are there? If it's
> enough mass, that'll make it stable.

Well, there is a lot of water and sand. That might be enough.
If not, then adding the radiators might do it. Except of
course for the ag-rings.

> 2. Make it shorter than it is long.

Maybe, but I'll be happy if I can find another way.

> 3. Have two of your elongated habs, side by side, connected
> together at both poles by very strong struts, and spinning
> in opposite directions.

The Island 3 solution. Dr. O'Neill was a very smart guys,
wasn't he?

>> the one hundred thousand people who live here.

> 100K people seems like a bit of a stretch, though it's not
> too outrageous. I usually figure 150 m^2 per person. A
> cylinder with spherical endcaps, with 100 m flat section,
> has a total area of 13,194,689 m^2 if my math is right. So
> I'd say that could comfortably house about 88 thousand
> people. And that's with no sea circling the equator --
> you've essentially removed the entire flat section from use,
> so it would be more like 80 thousand. But I'm sure you
> could cram in an extra 25% if you tried hard enough.

It would be more room per person than the 1976 Stanford
Torus design, but still crowded compared to most places
Anzu's ancestors from the early 21st Century cared to live.

> I've got the same plan for my Disney-esque orbital theme
> park, but that's because you're trying to pump money out of
> tourists 24/7. In a general-purpose hab, it seems a bit
> far fetched. Restaurants wouldn't need to run around the
> clock if people would all sleep at the same time, and
> factories should be able to mostly run themselves. 100
> thousand people isn't a big city -- about the same size as
> my town (Fort Collins). As it is, we have to go to Denver
> for a lot of stuff that the town just isn't big enough to
> support. If you divide into three time zones, you're
> effectively reducing your city size by a third (at least
> with regards to "things to do" like museums and plays and so
> on).

I had considered having three habs as a "community," each hab
with its own time zone. Thus, the entire hab Anzu lives in
would be "Mendocino," with "Perth" and "Shunyi" (changed from
Beijing) being other, nearby habs. Each could have, say,
seventy-five thousand. This would solve three problems:
it would reduce the per-hab population density, it would
increase the over-all community population from 100,000 to
225,000, and it would solve the problem of trying to do all
three time zones in the same hab (how do you keep it from
being to bright in a village at "night?").

>> Outside the main not-quite-a-sphere, there are the twelve
>> ag-rings. Six of them are on the "north" side, and six on
>> the "south." These are tubes, fifty metres in diameter,
>> bent into rings with the same two thousand metre diameter as
>> the main sphere. These are, or rather were, used forgrowing
>> food.

> If they're significantly toward the poles, then these are
> contributing to the instability problem. But if you moved
> them in towards the equator, they could help. Of course
> then they'd be under more than a G, which seems a little
> pointless for ag rings (and no fun for parks).

A look at my diagram shows that the ag-rings are near to,
though not at, the equator, and at one G. They should be
helping. I'll sick the diagram over in FILES.

>> With so many of the old I1's being converted to dedicated
>> food production, we only use half of our ag-rings for food
>> production and import the rest. The others have been turned
>> into parks, with one even holding a small zoo.

> I'd be surprised by this -- I'd expect the ag rings to have
> less shielding than the main habitat, just because they
> don't need it as much. But that would make them unsuitable
> for parks or zoos. You might want to add something about
> how the conversion involved importing extra dirt for shielding.

Which makes them even more useful for stabilizing the hab?

Thanks, I can see that running this over here was a good idea.

I've got it! The habitat is, of course, surrounded by a
radiation shield considerably more massive than the hab
itself. Suppose that the shield is connected to the hab
at either end with strong (magnetic?) bearings. Then it
can be slowly counter-rotated and that will solve the
tumble problem. Rotating the shield at a full one G
would require a very strong support structure, but since
that isn't necessary anyway, we won't do that.

Next, I do have the population density too high. I was
figuring a hundred thousand divided by the TOTAL hab
area, when it should have just been divided by those
villages. Doing that gives me almost twice the density
of Stanford Torus. Also, this is late enough in the
Breakout period (Island Four is being constructed, many
of the old Island Ones are being converted to
specialized food production, and so on) that Island Twos
wouldn't be as jammed full of people as possible.

So those are the changes I'll be making:

a) one time zone per hab (there are scores in the
vicinity, so there can still be three overall)

b) the entire hab is named Mendocino

c) the population of Mendocino is 36,000 (much more than
the real, Twentieth-Century, Earthside Mendocino).

d) if you guys don't think that the sea, beach, and
radiators at the equator are enough (and/or that the ag-
rings aren't helping), then I'll mention the counter-
rotating radiation shield in the chapter Thursday, School.

Thanks. I've got some re-writing to do, but I think I'll
try to finish Wednesday, Evening first.

On Dec 16, 2008, at 1:29 PM, sailor.barsoom wrote:

> I've got it! The habitat is, of course, surrounded by a
> radiation shield considerably more massive than the hab
> itself. Suppose that the shield is connected to the hab
> at either end with strong (magnetic?) bearings. Then it
> can be slowly counter-rotated and that will solve the
> tumble problem.
>

Sounds about right to me.

> Rotating the shield at a full one G
> would require a very strong support structure, but since
> that isn't necessary anyway, we won't do that.
>

Seems like we should do the math, though. The momentum of the shield
needs to equal the momentum of the hab. I find it hard to believe
that it's going to be all that much more massive than the hab. You're
talking about a shield a couple meters thick... but the hab contains
pressure shell, dirt, several-story buildings, water, wave machines,
and so on. If they're comparable in mass, then you really would need
to rotate the shield at a G or so.

> Next, I do have the population density too high. I was
> figuring a hundred thousand divided by the TOTAL hab
> area, when it should have just been divided by those
> villages. Doing that gives me almost twice the density
> of Stanford Torus.
>

Sounds about right too.

> a) one time zone per hab (there are scores in the
> vicinity, so there can still be three overall)
>
> b) the entire hab is named Mendocino
>
> c) the population of Mendocino is 36,000 (much more than
> the real, Twentieth-Century, Earthside Mendocino).
>

Sounds great.

> d) if you guys don't think that the sea, beach, and
> radiators at the equator are enough (and/or that the ag-
> rings aren't helping), then I'll mention the counter-
> rotating radiation shield in the chapter Thursday, School.
>

I'm just a software engineer, but my hunch is that the counter-
rotating radiation shield is going to be hard to make work. I'd go
with the radiator story. And you might even dangle some additional
weights out from the radiator, which can be reeled in and out under
computer control, to stop any wobbling in its tracks.

Best,
- Joe

From: Joe Strout

> Seems like we should do the math, though. The momentum of the shield
> needs to equal the momentum of the hab. I find it hard to believe
> that it's going to be all that much more massive than the hab. You're
> talking about a shield a couple meters thick... but the hab contains
> pressure shell, dirt, several-story buildings, water, wave machines,
> and so on. If they're comparable in mass, then you really would need
> to rotate the shield at a G or so.

I think at the lower scales, the shielding mass generally outweighs the rest of the habitat by 10x. At least I know that's the correct ratio for the Stanford Torus.

I know that the Bernal Sphere uses this notion of canceling momentums by counter-rotating the shield. So I suspect the equator of the shield is looking at around 1/10 G of centrifugal force (and considerably less in most other areas).

But then it just occurred to me that the Bernal Sphere will be more efficient of shielding mass than a torus. So I'll bet the Bernal Sphere's radiation shield is less than 10x as massive as the structure, but it's probably still some multiple over.

> I'm just a software engineer, but my hunch is that the counter-
> rotating radiation shield is going to be hard to make work. I'd go
> with the radiator story.

I think the radiators are deceptively low in mass in comparison to their surface area. But like I said, I'm pretty sure the counter-rotating shield notion is in at least one of the peer-reviewed designs, so I'd be fairly confident in it.

Regards,

Mike Combs

On 16/12/2008, Combs, Mike wrote:
> I think at the lower scales, the shielding mass generally outweighs the rest
> of the habitat by 10x. At least I know that's the correct ratio for the
> Stanford Torus.
>
> I know that the Bernal Sphere uses this notion of canceling momentums by
> counter-rotating the shield. So I suspect the equator of the shield is
> looking at around 1/10 G of centrifugal force (and considerably less in most
> other areas).

No, 0.01g. The equation is a= v^2/r, and it's going 1/10 the speed if
it's 10x the mass.

Allowing for the extra mass that's spinning, you'll need about 1/10
the bracing mass that the main living area needs.

> Regards,
>
> Mike Combs

--
-Ian Woollard

We live in an imperfectly imperfect world. Life in a perfectly
imperfect world would be much better.

Ian's right. The "gravity" scales linearly with radius, but NOT linearly with speed.

Regards,

Mike Combs

OK, here's how I'm dealing with the instability:

Right at the equator, and for fifty metres north and
south (the entire one hundred metre flat section) you
have salt water to a depth of five metres, with tropical
fish, some coral, and wave machines (hidden). For
another twenty-five metres to either side you have salt
water gradually decreasing in depth from five to zero
metres. Then for seventy-five metres to either side you
have sand (half of it wet with salt water) to a depth of
one metre. Then for five hundred metres to either side
of THAT you have the village of Mendocino, with
buildings, roads, and so forth. The rest is parkland,
though there are occasional buildings (the Lagrange Dojo
is located at the 0.5 G level).

The whole sea/beach/village band encircles the hab and
is one thousand three hundred fifty metres wide.
However, this does not mean that it takes up 1.35 Km of
the hab length. A hundred metres (the sea) is direct
length, because it's the flat section, but the remainder
is curving up the inside of a sphere. So it is somewhat
less than that. How much less? This is where my math
breaks down. I can't just divide by pi, right? This
band is where all of the heaviest stuff is located.

The two groups of ag-rings, one group to the north and
another to the south, begin at about four hundred
twenty, maybe four hundred fifty metres (direct length)
from the equator and extend another three hundred metres
(both north and south, because there are two groups).
They stop short of the poles.

Again, I have put some diagrams here:

What this all boils down to is this: there is enough
extra mass near the equator that the thing isn't going
to tumble. I'm willing to assume that if the water, and
the sand, and the buildings, and and and isn't enough,
then the engineers just slapped some extra thickness on
right at that flat section.

Anzu addresses the stability question in the chapter I
am writing now.