What diameter would a rotating space ring need to have 1G and a 24 hour rotation period?

Thanks man :) also that's so fucking huge

[eqn]F=m\cdot g\\F={{m\cdot v^2}\over{r}}\\v={{2\cdot r\cdot \pi} \over {T}}\\m\cdot g={{m\cdot 2^2\cdot r^2\cdot \pi^2}\over{r\cdot T^2}}\\g={{4\cdot r\cdot \pi^2}\over{T^2}}\\r={{g\cdot T^2}\over{4\cdot \pi^2}}[/eqn]

Now insert your values

the second line was supposed to read
angular velocity*

2,305,287 miles in diametre.
What... the... fuck.
O'Neill's 5 miles is much more realistic.

>Freshman physics
I'm pretty sure that's high school physics or even lower.

8th grade I would assume.

I TA for freshman physics at a University of California campus. You would be surprised.

But you're right. I learned it in 11th grade. It's still technically freshman physics though.

Why would you want it to rotate once every 24 hours? You don't want any windows in there, most realistic designs have an inner steel cylinder that's sealed off and enclosed in an outer non-rotating shell made out of residual materials left over after you've smelted the asteroid. Windows are a huge structural weakness and your main concern in there is getting rid of heat, so you want as little sunlight as possible.

There's one thing I could never understand about angular velocity. Why does it equal to 2 pi / T? I dont get the 2 pi part. Angular velocity means angle in time. 2 pi is not an angle but a number. So why do we write it as 2 pi at the top?

>2 pi is not an angle but a number
user, I...
en.wikipedia.org/wiki/Radian

A radian is defined as the angle at which the subtended arc length is equal to the radius. Therefore there are [math]2\pi[/math] radians in a circle. Angular velocity is the number of radians an angle changes by in a given time. So one rotation every 24 hours is equal to the expression in my original post.

Furthermore, a radian has no physical unit interpretation (like distance), and it's standard to use radians, not degrees, in math and science. As a result, the word "radians" after the multiple of pi is intentionally omitted.

2ND QUESTION:

What would it look like if we LOOKED up from this inner cylinder. Would we perfectly see a circular tubing, or would light from that distance be hard to see?

> You don't want any windows in there
okay, I'm not going

Lemme see. You're asking what you'd see if you looked parallel to the axis of this spinning cylinder? Assume the cylinder was of a reasonable diameter,say 5 miles.

If the air was clear enough to see to the far end, something like this...

since lighting would be most likely done by an luminous central axis you'd likely see blue sky with a bright line in it parallel to the cylinder.
On your side you'd see the city going up until it would be too far and the scattering would block your view

This

Maybe.
O'Neill's designs called for windows, with chevrons to keep out cosmic rays.
Rama had luminescent panels on the "ground".
The glowing-tube-along-the-axis is usually confined to stories with cheap fusion power.

Remember though that toroidal colonies require much less mass than a cylinder of comparable radius. In which case you'd see skylights and/or a roof.

>Yeah, at his radius, it rotates many times per day. If you read my fucking post you'd know I want it to rotate once per day, and I'm wondering what radius that requires.

Well the one is 5miles by 20miles and rotates 28 times an hour, so to rotate once per day it needs to be 3360 miles by 13,440 miles in size.

Considering this thing would be exerting 1G and would encircle the entire Earth-Moon system with millions of kilometers to spare on either side, the atmosphere inside would probably be confined near the walls (it may be taller than Earth's actual atmosphere due to the reduced force further inwards, but not by much). That means you'd be able to look up out of the atmosphere on your side, across the vacuum in the center, and down through the atmosphere on the other side to the 'ground'. However, land masses the size of Eurasia here on Earth would be indistinguishable specks from that distance. Assuming a random assortment of land masses ranging from Australia to Eurasia in size, making up 30% of the surface, with oceans up to as large as the Pacific making up the other 70%, from that distance it'd all blend together into a mottled blue-green surface, with tiny little white spots of clouds. Travelling to those land forms through the atmosphere in a sub-sonic jet would take years, requiring you to travel many millions of kilometers. Going above the atmosphere, slowing down relative to the rotation and thus feeling no outwards force, then drifting to the other side through 'space' would be much faster. However, since this huge cylinder would be rotating at 134.9 km/s at the inner 'surface', this method would be impossible with chemical rocket technology. The best you could do is long-distance hops sideways from your position, but no chance of actually crossing the diameter unless you had an Orion pulse drive handy.

That's not how that works.
As the radius gets bigger the cylinder has to speed up in order for the same force to be exerted, so for every 2x increase in size the rotation rate slows down by less than 2x.

The real answer was already calculated in this thread, but for 1G of force at the 'surface' and a 24 hour rotation period you need a cylinder with a radius of 1.855 million kilometers, rotating at 134.9 km/s.

>want it to rotate once per day
why?
>other measures to simulate day-night
O'Neil specified mirrors, pic related, to simulate this, independent of rotation rate. No need for anything more complex

>As the radius gets bigger the cylinder has to speed up in order for the same force to be exerted
what? The opposite is true
see [math]a=\omega^2 r[/math]

What's better? Ringworld or O'Neill Cylinder?

In the USA, in the 1980s flyover state, we never had anything like that even in High School. It was hinted at and we were told "college".

O'Neill Cylinder because it is actually within the realm of the real world. Ringworld is 110% sci-fi fantasy. Though, other shapes are a bit better, like a torus, just not at Ringworld scales.

The absolute speed increases, but the rotational rate in degrees slows down. That is to say, the cylinder spins faster, but takes longer to complete one rotation, because of the proportionately increased circumference of the cylinder.

Besides, all I did to get the 134.9 km/s figure was take the radius of 1.855 million kilometers, get the circumference in kilometers, then since the rotation rate was known to be 1 revolution per 24 hours, divided by 24, then 60, then 60 to get the velocity in kilometers per second. If somehow you think a rotating cylinder 100m across needs to spin faster than 134.9 km/s to generate 1G of centripetal force, I'd implore you to reconsider.

Lol.

All of these things are set up for catastrophic failure from very regular events. Five generations? You won’t get close in one of these spaceships.

You have to have a huge array of colonies on many worlds, eventually beyond this system.

Something that could not be borked by a few meteors the size of OP's cock is a start.

whats causing it to spin? is there any chance it fucks up and spins too fast or too slow or break down?

It spins up by spinning a counter weight in the opposite direction, ideally something very big and heavy. The spinning mechanism would be a simple electric motor, granted it'd be a very large one.

ok, how big of an electric motor? how reliable of an electric motor? what im getting at is if 1g is affected in any way what damage would that do to a growing fetus, say if the spin stops for a week or two, would they be born deformed or what

>say if the spin stops for a week or two
?
user, you only need the motor for the initial spin up. Afterwards it's just needed for slight corrections, if at all.
If something causes your habitat to stop spinning then you have bigger problems than just a few mishappen fetuses (if at all)

Once the station is spinning it lets go of the counterweight and keeps spinning. There's literally nothing to break down or fail, the entire station just rotates in space.

As for how big, assuming the station weighs several hundred million tons and is a few hundred meters across, you'd need a pretty big motor to accelerate that cylinder up to the required speed. Probably definitely bigger than any electric motor built on Earth so far. It'd look kinda flattened, since for better leverage you'd want the rotor and winding to be as far from the axis as possible, resulting in a motor in the shape of a large, flat disk. The counterweight would probably be the asteroid you built this habitat out of, since it's likely to weigh several thousand times more than your structure.

Bout tree fiddy

No point building a huge motor and rotor that's only going to be used once. (Incidentally, only the rotor would have to have a massive moment-of-inertia. The motor could be quite small if you're in no hurry.)

Gyros and momentum wheels are used only in very small satellites which need precise pointing, like Hubble or Kepler. For a one-time spin-up rockets are more practical. Once begun, rotation continues forever and you don't have bearings to worry about.

The motor would not stay with the station, it would stay with the counterweight/asteroid. After the first station is built and released, they start working on a second and spin it up using the same motor once it's finished. Rinse and repeat.
Rockets would work but would require a surprising amount of propellant for a station as large as one of these cylinder habitats. It's far more efficient to use an electric motor instead of reaction engines.

No. The rotor would remain spinning. If you don't want the rotation to build indefinitely, you de-spin it to turn the 2nd habitat in the opposite direction. So the rotor is really just a temporary angular momentum bank.
Might as well counter-rotate two habitats at the same time. See image. The habitats are the cylinders centered in the cones (which are mirrors)

Surprising amount of propellant? Don't make me laugh. Compared to moving the construction materials into position adding spin is trivial.

You don't move the construction materials, you go to an asteroid and build your habitats on-site and give them enough of a nudge that they escape that asteroid's gravity.

The rotor, attached to the asteroid, would indeed remain spinning, but the station would separate from it. All parts of the motor assembly are permanently attached to the very large mass of the asteroid, and can spin up dozens of habitats before causing a noticeable spin in the asteroid itself. The habitats are attached to the motor shaft by a coupler, which decouples once the appropriate spin rate is achieved. Obviously the rotation doesn't build up forever, you turn the motor off and release the station after it's spun up.

You could have two habitats counter rotate against one another, but if they remain attached you're looking at a constant source of friction. A single habitat floating alone would never have that rotational bearing wear out, because there are no bearings.

Yes, a surprising amount of propellant. You're accelerating hundreds of millions of tons up to a pretty good clip. With pure rocket propulsion you're need several million tons of propellant. Compare that to zero for an electrically spun up system that lets you go after getting you rotating; you use zero propellant and end up in the same situation as you would have if you'd used rocket engines, except you have a lot more water than you would otherwise.

Thats about 5 times the distance to the moon, to put things in perspective.

Two linked, but counter-rotating, habitats have a major advantage over one.
Zero net angular momentum. Most designs require one end of the cylinder to follow the sun over the course of its yearly orbit. How are you going to turn your humongous single-cylinder gyroscope?
If you look at you'll see there are TWO colonies cabled together. Likewise . You can't build and spin them up separately.

Two colonies also provide safety and redundancy. And it's easy to get from one to the other without expending any mass or energy; just let go at the right time and you're flung across. If aimed at the same radius, you meet it tangentially with zero relative velocity.

>What diameter would a rotating space ring need to have 1G and a 24 hour rotation period?

Or have the space colony rotate on two axes: one for artificial gravity and the other for a day-night cycle.

>can't convert km to miles
It's barely over 1 million miles dumb-shit.

how did it take this long?
and how did I not think of this?

Why would there be a specific diameter, brainlet? Huh? Huh? Why do you create this false equivalency instead of actually looking at the problem in front of you.

Just read Ian M. Banks' Culture series
en.wikipedia.org/wiki/Orbital_(The_Culture)

>The Culture's Orbitals are approximately 10 million kilometres in circumference, which, together with their rotational speed, creates gravity and day-night cycles to normal Culture standard.

>What diameter would a rotating space ring need to have 1G and a 24 hour rotation period?

3,709,146.7 kilometers.

>The Culture's Orbitals
pretty sure the tensile strength required to hold the ring together exceeds the strongest covalent bond, and I treat the talk of "fields" the same was as "magic". You'd need continuously firing rocket engines "pushing" the ring together to stop it snapping. What is feasible is separately orbiting platforms in a swarm.
part agree with but it's also over pessimistic about what humans could tolerate. Fact is we have near zero data on health in fractional gravity - a centrifuge was planned for the ISS to study just this (half G, third G for Mars, sixth G for Moon) but scrapped due to budget limits.
Political will is the bottleneck of course, and not tech, but simpler systems will always be chosen over these flights of fancy, such as small asteroid with small centrifuge habitat, tethered habitat providing what G you want and all without extoic unobtanium materials.
pic related but replace one module with small asteroid.

user, read his post
>2,305,287 miles in diametre.
>diametre

>8th grade
This is 5th grade stuff, what backwater school did you go to? Kek you literally are a brainlet.

Have fun working at Mcdonalds, though it will be a challenge at your level but I think you will manage.

>You could have two habitats counter rotate against one another, but if they remain attached you're looking at a constant source of friction. A single habitat floating alone would never have that rotational bearing wear out, because there are no bearings.
You use magnetic bearings for that. You can't have a single rotating habitat because it will eventually start to tumble due to tennis racket theorem.

I argued against the single habitat.
But does the tennis racket theorem apply to a cylinder with radial symmetry around its long axis? i.e. two moments of inertia are equal.

If you can keep mass distribution perfectly symmetrical, sure, but even a tiny difference will mean that eventually you will start tumbling.

Point taken. So you're better off with a torus so the spin-axis has the minimum MoI?
Still ought to be two of them so they can turn to follow the Sun.

Incidentally, the illustration in was written well before the TRT, but the cylinders have pumps to re-distribute mass and keep them balanced. The author (or whatever technical papers he cribbed from) gave a good deal of thought to the engineering

>torus
Are you planning to build elysium OP?
Can I come?

Not OP. Was the movie any good?

>Are you planning to build elysium OP?

No, Elysium was bullshit. Building a space colony that large from resources from the Earth and not something with a much lower gravity well like an asteroid or the moon.

I kinda liked it
Cyberpunky
Nice special effects
And it's first of its kind

all you need is 1g and no Coriolis effect felt by people and animals.

day/night cycle would be controlled by the mirrors reflecting sunlight into the cylinder.

>day/night cycle would be controlled by the mirrors reflecting sunlight into the cylinder.
Or, you know, by walls

Have you autistic idiot never taken basic physics classes? Literal middle schoolers should be able to solve this

Found the brainlets. lol

>that finger asmr

269794 meters.

a=(v^2)/r
T=24hrs = 86400s
a=9.81ms^-2

T=C/v
C=Pi*d = Pi*2r

v=((Pi*r)^2)/86400
a=((((Pi*r)^2)/86400)^2)/r

a=9.81
9.81r*86400=2Pi*r
423792=Pi*r
r=134897
d=2r=269794

Will there be Flat Earthers there?