Orbital ring habitat structural collapse dynamics questions

[Telok]

In a game there is a planet, relatively Earth like once upon a time. It was strip mined and polluted to the point where it is functionally uninhabitable. The population moved into a series of space stations that eventually grew into the current orbital ring.

I have cause to believe that the PCs will cause a complete structural collapse, if not a total severance, of a section of the ring.

The ring is 8 to 12 km wide and about 3 km tall. Spaceships with sufficent anti-grav dock along either side (the PCs have such a ship) and shuttles land on top. Tethers/beanstalks are not used due to relatively affordable anti-grav & handwavium starship engines. Over the past 1200 years such a massive failure has become inconceivable (orbital defenses prevent incoming impactors at 100% success rates). Fail-safes, backups, emergency equipment, and evacutaion procedures have suffered from budget cuts and general neglect over the past 300 years.

I'm expecting either a salvo of orbital bombardment weaponry (torpedos with warheads that leave 500m radius craters &or energy weapons sufficent to punch through atmosphere and level about 4 sq.km) or a really spectacular intentional fusion reactor hiccup-explosion-total containment failure.

So how fast and in what manner/order is the rest of the ring likely to de-orbit? Any guesses?

[Palanan]

Originally Posted by Telok
The ring is 8 to 12 km wide and about 3 km tall.

By this do you mean the ring’s cross-section is approx. 10 km from inner to outer edge, with a thickness of 3 km?

Originally Posted by Telok
I'm expecting either a salvo of orbital bombardment weaponry (torpedos with warheads that leave 500m radius craters &or energy weapons sufficent to punch through atmosphere and level about 4 sq.km) or a really spectacular intentional fusion reactor hiccup-explosion-total containment failure.

This part has me confused. Are the PCs about to unleash one of these options, or someone else?

Originally Posted by Telok
So how fast and in what manner/order is the rest of the ring likely to de-orbit? Any guesses?

At what altitude is the ring orbiting? That is, what’s the radius of the ring as measured from the planet’s center of mass?

[monomer]

The time to de-orbit is most heavily influenced by the altitude and the surface area causing drag with the residual atmosphere. If the space station was already in a stable orbit it shouldn't fall out of the sky just because of the section collapse, though it would eventually if the orbit raising engines were damaged.

Orbital decay for current spacecraft in very low orbits (~200km) is measured in days, while for slightly higher orbits (~500 km like the ISS) it is measured in years, and for orbits above ~1000 km it is measured in hundreds to thousands of years. Now a huge space station will have a lot more drag than a current-day satellite or even the ISS, but if you are high enough to be out of most of the residual atmosphere, it could be a very long time before you de-orbit. So if you haven't explicitly stated the altitude yet, you can basically choose whatever timeline works for the adventure.

[Seppl]

The important thing to note here, despite the concept being really popular in science fiction, a ring around an object is not actually in orbit around that object in the first place. Thus, without constant active adjustment, the ring would crash into the object after a timespan of about the same magnitude as it would take any object to fall from that height.

If you want to read up on that, you can search for essays on the stability of Larry Niven's famous Ringworld. That's larger in scale, but the same physics apply.

[Lvl 2 Expert]

To be clear: the ring is a solid structure, but it's also actually in orbit, so without artificial gravity everything on board would be weightless?

[Palanan]

Originally Posted by Seppl
If you want to read up on that, you can search for essays on the stability of Larry Niven's famous Ringworld. That's larger in scale, but the same physics apply.

The OP mentioned starship engines, so it's simplest to assume that these are also used as attitude jets, essentially the reverse of Ringworld Engineers. (Starship engines adapted as attitude jets, rather than attitude jets being removed to power starships.)

[Seppl]

The OP mentioned starship engines, so it's simplest to assume that these are also used as attitude jets, essentially the reverse of Ringworld Engineers. (Starship engines adapted as attitude jets, rather than attitude jets being removed to power starships.)

Then the question comes down to how good those hold up in face of the mentioned negligence. As we do not have that information, OP can make up anything they want.

[Palanan]

Sure would be nice if we had some grenades answers from the OP.

In addition to the question about altitude, I'm also wondering whether the ring can be treated as a uniformly solid structure, or if the various components are only loosely held together. If the latter is the case, then damage on the scale the OP mentioned might break up the components into a ring of debris, in which some fragments de-orbit rapidly and individually, and others remain in a shattered swirl for a much longer time.

[Misery Esquire]

In addition to the question about altitude, I'm also wondering whether the ring can be treated as a uniformly solid structure, or if the various components are only loosely held together. If the latter is the case, then damage on the scale the OP mentioned might break up the components into a ring of debris, in which some fragments de-orbit rapidly and individually, and others remain in a shattered swirl for a much longer time.

That's a good thought; either way (linked or solid) a main concern for the rest of the ring is where any particular chunk goes. Because even if it can survive the new stress introduced or rebalance it's orbit, can it survive impact with another piece of itself or will a loosed section scythe through the rest when it goes off-kilter?

[gomipile]

The important thing to note here, despite the concept being really popular in science fiction, a ring around an object is not actually in orbit around that object in the first place. Thus, without constant active adjustment, the ring would crash into the object after a timespan of about the same magnitude as it would take any object to fall from that height.

If you want to read up on that, you can search for essays on the stability of Larry Niven's famous Ringworld. That's larger in scale, but the same physics apply.

What you're referring to is a result of calculations that are only simple because the Ringworld is impossibly rigid, and can be treated as a mostly rigid object with a meaningful single center of mass for its rigid body dynamics.

[factotum]

Yeah, the Ringworld stability relies on the Ringworld itself being a rigid structure. The real problem here is that the OP's "ring station" is functionally impossible to build--if it was actually rigid then it would require structural strength far beyond any known materials. There's also the question of why they would bother building it around their dead planet* when, with materials of the sort of strength we're talking here, you could make something like a Culture orbital instead, which would be far more practical. (In case you don't know what I mean--an orbital is a mini-Ringworld a few million miles across. Instead of enclosing the sun, like Niven's Ringworld does, this is more like a regular space station which orbits around the sun and spins for artificial gravity. Because it's in a regular orbit it doesn't have the stability problem inherent in Niven's idea, while still providing thousands of times the habitable surface area of a normal planet).

* From the description it sounds like the OP wants this to be a gimcrack affair that starts out as a bunch of separate space stations in the same orbit and gradually builds up until it forms a complete ring, and that just ain't gonna work no matter what.

[Telok]

Well. That was rather more interest, rather faster, than I thought there would be.

The ancient core of the ring started as a semi-rigid magnetic driver transportation system going through the most popular orbit around the equator of the planet. Eventually the free standing spinner habitats wore out and the new ones using gravity generators were built onto the ring structure itself. It's about 400 km above the surface and the '3km height' is measured from the inner edge of the orbit to the outer edge. I think we can assume that the ring is a bout 7000 km from the centre of mass.

It doesn't rotate at orbital speed any more. People patched it with antigrav every so often because that was easier than keeping the speed up. That has the benefits of making garbage disposal safer for the ring and reducing the power consumption to keep the habitats at a comfortable gravity. So un-corrected drag over the last centuries has reduced it to... 75% orbital speed (warning, number totally made up)?

How's that filk go?
"Oh the Ringworld is unstable.
Oh the Ringworld is unstable.
He did the best that he was able,
and that's good enough for me."

The ring is ideally a solid structure, and the inhabitants treat it that way because it's been almost completely perfectly stable for so long. You could treat it as an old bridge that sees 100,000 cars a day and looks fine from the roadway, but experienced engineers walking underneath occasionally get ulcers and yell at politicians until money is allocated to patch the cause of the ulcer until the engineer can be replaced with someone quieter.

Basically the PCs paid someone off with 2 kg of infectious living metal. That's fine if it's been properly processed so that it knows what it's current shape (2 kg ingot) should be. Being PCs they were of course explicitly warned, failed to do any sort of due diligence or quality control, have seen the warning signs of ingots trying to recombine, and don't want to mention it to anyone or do anything about it. It's previous shape, the one that it remembers, was a murder robot. Specifically a D&D modron quadrone combined with a WH40K necron demi-boss and sort of mated with StarTrek borg (except less cuddly and lovable). The guy they paid off with it just chucked it in an armored safe and went on a celebratory bender.

1) It will absorb the safe and revert to type before the owner of the safe gets back to it. When it will horribly murderize him and a number of other nearby people before moving around and beginning to convert other bits of the station in that local section.
2) Assuming the PCs ignore this too (very likely), a while later the section adjacent to where their ship is docked will suddenly be overrun with hundreds of assorted murder robots made from infectious living metal.
3) The PCs will leave (run away) and become persona non grata in this star system too. That's their usual reaction to these things. I'm fairly certain that they'll try blowing out the chunk of the ring with the infection in it. If they do choose to do that I am certain that they'll completely fail to consider any consequences to the rest of the ring.

Some loose guesstimates, googling, and fast math gives something like 360,000 tons per meter of length.

[factotum]

Well, if the ring is supported by anti-gravity--why is that going to suddenly stop working and cause it to come crashing down if part of the ring gets destroyed? 75% orbital velocity after centuries in a 400km orbit is definitely highball, too, the thing would probably be stationary by that time. Which actually means that they're using the anti-gravity to hold the ring off the planet's surface while presumably the planet's gravity is what's providing the gravity on the ring? (After all, if it's no longer orbiting then, assuming the dead planet is the same size as Earth, the actual gravitational attraction 400km up is going to be about 88% of what it is at the surface, which seems plenty).

I guess my biggest issue is still why they'd build it in this way. Since they're already having to build structures which are sealed against the vacuum outside, couldn't they do that on the planet's surface just as easily? That way they're not having to either boost the orbital speed or build anti-grav generators all over the place to keep the thing airborne.

I still believe just making it a giant spinning ring station like a Culture orbital would make most sense. That way, if you cut the ring, it isn't going to come crashing down to the surface, but it *is* going to uncoil (because its structural rigidity is what's keeping it in the ring shape) and everyone on it is going to die horribly pretty quickly as the air escapes from the cut ends and the rest of it loses the spin gravity that's holding them to the surface.

[gomipile]

Yeah, the Ringworld stability relies on the Ringworld itself being a rigid structure.

The Ringworld instability relies on it being a rigid structure.

[Lord Torath]

So how stable would it be if instead of a rigid ring, it was more like an 800-million-mile-long loop of railroad car-style stations in orbit around the star?

Or a 40,000 km long loop around Not Earth?

[factotum]

So how stable would it be if instead of a rigid ring, it was more like an 800-million-mile-long loop of railroad car-style stations in orbit around the star?

If it's not rigid then it implies a bunch of separately orbiting stations in the same orbit. Thing is, you still need some level of stationkeeping in order to keep a station in orbit at the same position, because the planet's gravitational field is not perfectly regular and that causes tiny perturbations in the orbit. Geostationary satellites, which obviously *have* to stay in exactly the same place, have a limited lifespan for this reason, because once their manoeuvring fuel expires they move off-station over time and are no longer useful.

If you have a whole bunch of stations all in the same orbit? Eventually some of them are going to crash into each other because there's no way that arrangement is stable over years.

[Manga Shoggoth]

So how stable would it be if instead of a rigid ring, it was more like an 800-million-mile-long loop of railroad car-style stations in orbit around the star?

Or a 40,000 km long loop around Not Earth?

Interestingly, that's a very good description of the Shadow Squares in Ringworld - literally the first part of the system they hit. They are a free-floating set of sheets held together by some form of cable that are used to provide the day/night cycle on the Ring.

[Telok]

As much fun as a free standing ring would be the narrative of the game already established it's position and general nature.

It uss a mix of orbital velicity and antigrav because that gave me more options in the original setup. However the precise ratio was never codified. Varying politics and funding levels over the centuries give me the fig leaf for that.

I should note that the original backbone of the ring, the magnetic accelerator transport tubes, are still in heavy and constant use. They move people and stuff around in... I think I put it at 2 hours to get to the opposite side of the ring. That should help make the disaster worse.

[Storm_Of_Snow]

The way I see it, if it's a rigid structure, every point on the ring is being pulled towards the planet it's orbiting (there'll also be a relatively small gravitational pull of the ring on the other side, and a minute lifting pull from the sections of the ring right next to the point we're looking at), and only being held in place by the strength of structure> However, the inside of the ring is in compression and the outside is in tension, with all those forces in balance.

If there's sufficient damage to fatally weaken the structure and break that balance, then those forces will now be able to act, and the whole ring will just tear open and unroll - essentially you've now got a massive drawn bow and you've just cut the string. When this happens, the side closest to the planet will rip itself open, while the original outside compartments will be crushed.

However, given the forces involved and the inertia they generate (plus thrust from compartments venting to space as they rupture), rather than deorbiting the ring, it may well throw what's left of it (or significant amounts of it at least) out of planetary orbit entirely.

[Tyndmyr]

Sure would be nice if we had some grenades answers from the OP.

In addition to the question about altitude, I'm also wondering whether the ring can be treated as a uniformly solid structure, or if the various components are only loosely held together. If the latter is the case, then damage on the scale the OP mentioned might break up the components into a ring of debris, in which some fragments de-orbit rapidly and individually, and others remain in a shattered swirl for a much longer time.

Given the size of the structure, if the materials are anything we know of today, "various components loosely held together" is going to be more accurate. A structure of that size simply could not support its own weight over that span. If it loses sufficient velocity to cease orbiting, it will not be capable of holding itself up.

If that outcome bothers you, some sort of unobtanium for solving it is traditional in sci fi.

[Palanan]

Originally Posted by Telok
It's about 400 km above the surface and the '3km height' is measured from the inner edge of the orbit to the outer edge. I think we can assume that the ring is a bout 7000 km from the centre of mass.

I can see the reasoning for that altitude, although I don’t know if LEO is the safest environment for a structure like this, given the amount of orbital debris that’s likely to have accumulated.

That said, if the ring is being held up primarily by the antigravs, then any disruption will destabilize the balance faster than they can compensate.

Originally Posted by Telok
The ring is ideally a solid structure, and the inhabitants treat it that way because it's been almost completely perfectly stable for so long.

Originally Posted by Tyndmyr
Given the size of the structure, if the materials are anything we know of today, "various components loosely held together" is going to be more accurate.

I agree that the ring can’t be treated as a uniform solid. If it’s only 10 km across its longest cross-sectional axis, then this is essentially a fine filament looped closely around the planet—a wisp of material compared to the diameter of its orbit.

Given this, it’s almost certain that the entire structure is constantly flexing to a small degree. The superstructure connecting the various elements should have been designed to account for that—this is an important aspect of engineering design for real-world on-orbit structures.

So the structure isn’t a uniform solid, it’s dependent on the antigravs and in a constant state of flex. It’s insubstantial in comparison to the planetary mass and it’s in a tight LEO that’s grazing the atmosphere.

If there’s a catastrophe that destroys even a small segment of the ring, then this will propagate waves around the ring, traveling outwards from both sides of the catastrophe. Those waves will meet at a point on the ring exactly opposite the site of the catastrophe, and it will almost certainly tear itself apart at that spot, with the remaining wave energy shaking components loose throughout the resulting segments. In short order the ring will have broken into dozens of fragments, along with a cloud of smaller debris.

Since the ring has been positioned in such a low orbit, atmospheric drag will immediately begin acting to bring the separate components into lower individual orbits, and they’ll burn up and impact on the planet in hours or days. Any components with engineers able to rapidly adjust the local antigrav units will have a better chance of staying on-orbit for the short term, but they’ll have to contend with collisions from other large components as well as an ever-intensifying debris cloud.

At best there will be a temporary ring of dense debris, but major components will continue to fall out until there’s nothing left but a cloud of fine fragments, which will be a permanent hazard for centuries to come.

[J-H]

This is a great thread that I have enjoyed reading.
Nothing to contribute... this is just fun stuff. :)

[Lord Torath]

I should note that the original backbone of the ring, the magnetic accelerator transport tubes, are still in heavy and constant use. They move people and stuff around in... I think I put it at 2 hours to get to the opposite side of the ring. That should help make the disaster worse.

Just as a fun little aside, your magnetic accelerator tubes have an average speed of about 11,000 km/hour, or 12.2 km/sec¹. Or 0.004% of the speed of light.

Regarding Palanan's analysis of the catastrophe, the waves spreading out through the station will probably propagate at the speed of sound through the base material, which, for steel, is about 21,500 km/hour. So approximately 1 hour after the PCs detonate a section of ring, the vibrations will converge on the far side of the ring, starting the catastrophe Palanan described.

That's assuming that waves traveling through a flexible string travel at the speed of sound of the string material, which I'm suddenly not at all certain of. If it was a rigid structure, that would be the case. As it's a flexible structure, the speed of the vibrations depends on the tension in the loop, which higher tension resulting in higher speeds.

In any case, it can't go faster than the speed of sound through the Mag Tube structure. So there is at least an hour, probably much longer, before the station starts breaking up. The PCs may be gone before they even know what happened, until they get a 'wave including a reward for anyone who can provide information on the destruction of Ring Station 53 of the Narlox System, or wherever they happen to be.

1: Positively slow compared the the first Jet Fire Transformer, whose tech spec proclaimed him able to reach any point on Earth in half-an-hour, about 25,000 mph, or 40,000 km/hour.

[Rakaydos]

I have cause to believe that the PCs will cause a complete structural collapse, if not a total severance, of a section of the ring.
(...)
Tethers/beanstalks are not used due to relatively affordable anti-grav & handwavium starship engines.

Even with saftey systems in decay, cheap antigrav can prevent complete structural collapse. There may be more martial law to implement it, but the capability exists.

[Palanan]

Originally Posted by Rakaydos
Even with saftey systems in decay, cheap antigrav can prevent complete structural collapse.

The problem is that the antigravs will be balanced against one another, all around the ring, and each one has been calibrated for the unique mass of its specific section. Once the initial detonation occurs, shockwaves will be propagating through the ring and each antigrav will be thrown out of alignment with all the rest.

Once that happens the antigravs will contribute to the destabilization, since each one will continue exerting its previous force--but the direction of that force will be skewed by the shockwaves, and the antigravs will add a shear force to the stresses on each component.

At best, the antigravs will help keep individual components on-orbit for slightly longer, but they can’t stop the shockwaves propagating in both directions around the ring. Once the antigravs are off-kilter, they’ll only magnify the stresses on the linkages between components, and they’ll help tear the ring apart.

[AMX]

The problem is that the antigravs will be balanced against one another, all around the ring, and each one has been calibrated for the unique mass of its specific section. Once the initial detonation occurs, shockwaves will be propagating through the ring and each antigrav will be thrown out of alignment with all the rest.

Once that happens the antigravs will contribute to the destabilization, since each one will continue exerting its previous force--but the direction of that force will be skewed by the shockwaves, and the antigravs will add a shear force to the stresses on each component.

At best, the antigravs will help keep individual components on-orbit for slightly longer, but they can’t stop the shockwaves propagating in both directions around the ring. Once the antigravs are off-kilter, they’ll only magnify the stresses on the linkages between components, and they’ll help tear the ring apart.

Wait, you're treating the antigravs like thrusters.
If they are actual anti-gravity devices, they can't produce shear force - any force they exert will be aligned with the gravity acting on the station, by definition.

[factotum]

Wait, you're treating the antigravs like thrusters.
If they are actual anti-gravity devices, they can't produce shear force - any force they exert will be aligned with the gravity acting on the station, by definition.

Let's say they do act as a repulsion force to regular gravity, like the name suggests. That would imply they're acting together to keep the ring system in tension, exactly as would happen if you just spun the whole thing fast enough for centrifugal force to overcome the gravitational attraction of the planet. What would happen in that case is that the entire ring would unravel quite rapidly once it was cut, just as it would if it was spinning. I'm not suggesting that it actually works that way, note, just that it's one possible interpretation.

[Rakaydos]

So it sounds like the problem is more a matter of incompetence than one of engineering. The stage has been set for disaster, and no engineers screaming that people are going to die will change upper managemen's policies, similar to the US shuttle program before the Challanger disaster.

The exact manner that incompetance ruins everything is of course a wide open field. Making something completely foolproof, after all, just breeds a more determined fool.

[Telok]

The exact manner that incompetance ruins everything is of course a wide open field. Making something completely foolproof, after all, just breeds a more determined fool.

Luckily I don't need a better fool. I have PCs with nukes.

So it looks like I've got rigid sections with limited flex linkages, surrounding the high speed transit core, partially supported by anti-grav and partially by not-quite-orbital rotational speed. Thus tension, but not full strength tension.

A section gets blown. The current & next couple high speed transit trains impact/transit the hot expanding debris field, adding their energy to the opposite ends as they become massive, slightly off-center shotgun blasts (mostly cargo, some people bits). Automatic emergency systems kick in as the shockwave begins to spread.

Antigrav systems will kick into high gear or turn off depending on their altitude sensors. Some may just fail from overloads and "value out of range" errors. Massive inter-section decompression doors will begin closing but the nearest ones may have been sufficently damaged that the adjacent sections will partially explosively decompress.

Some sections may rip free at either or both ends as the shockwave passes. When the shockwave hits the opposite end (between 1 & 2 hours?) that will rip free. The nearest sections will by flying outward into higher orbits from the release of tension. Faster if the antigrav didn't shut off, slower if it did. Likely spinning from uneven forces, possibly flupping over, maybe at full randomish tumbling. Larger strings of sections further from the center will... something. If they dip one end further into the atmosphere... something?

Sound ok so far?

[Palanan]

Originally Posted by Telok
A section gets blown. The current & next couple high speed transit trains impact/transit the hot expanding debris field, adding their energy to the opposite ends as they become massive, slightly off-center shotgun blasts (mostly cargo, some people bits). Automatic emergency systems kick in as the shockwave begins to spread.

On the rapid transit trains, I’m not sure how much their energy will affect the system as a whole. The blast from the nukes might actually serve to reduce the trains’ velocity, so they would add to the debris field but not significantly to the overall energy.

However, if they have dense cargo loads, then even at a reduced velocity they might well tear through adjacent components. It’s really difficult to say what effects that could have beyond additional physical damage.

Originally Posted by Telok
Antigrav systems will kick into high gear or turn off depending on their altitude sensors. Some may just fail from overloads and "value out of range" errors. Massive inter-section decompression doors will begin closing but the nearest ones may have been sufficently damaged that the adjacent sections will partially explosively decompress.

Unless there are carefully maintained redundant systems, I think it’s likely that warning comms and emergency systems will be lost almost immediately throughout the ring, since cables and fiber will be cut at the blast site, and the EMP will short out all unshielded systems on either side of the blast.

Any fiber that isn’t cut or melted will probably be overloaded with the intense visible radiation from the nukes, so that fiber will be propagating raw noise rather than useful signal. Again, it’s difficult to predict the fine details, but most sections will probably lose power, data and comms almost immediately, unless they have really good backup systems, and the inter-section doors may not receive the signals they need to close.

Originally Posted by Telok
Some sections may rip free at either or both ends as the shockwave passes. When the shockwave hits the opposite end (between 1 & 2 hours?) that will rip free. The nearest sections will by flying outward into higher orbits from the release of tension. Faster if the antigrav didn't shut off, slower if it did. Likely spinning from uneven forces, possibly flupping over, maybe at full randomish tumbling.

In the hour or two before the outbound shockwaves intersect on the opposite side of the ring, that portion may have the best chance of survival. They’ll have a planet between themselves and the detonations, so they won’t be directly affected, and any ships in polar orbit will have a direct visual on the damage and can relay that information to the opposite side.

If there are some smart engineers with access to the necessary systems, they can manually trigger the decompression doors for their sections, and they can try to manually configure the antigravs to compensate for the shockwaves. There’s also an hour or two for limited evacuations to begin, although they won’t have time to remove more than a tiny percentage of the overall population.

The result will be a BSG-style refugee fleet, with civilians crammed into any vessels that happened to be within range and that could find a place to dock and take on evacuees. It doesn’t sound like this planet has any remaining resources, so unless there are biodomes down on the surface, these refugees will need to find somewhere else to live.