# Artificial gravity concept -- Rotating structure in space

artriant
Hello everyone, i m working on a full circle space centrifuge concept. I try to support it with some maths but i don't want to dive into crazy details. I used alrdy lot of countermeasures to dangerous effects.I have problems similar to bridge mechanics. The design is not solid so i need to be careful about many things.

The shape of my concept looks like a big cross (made our of wire ) on each end of the cross we have solid pieces metallic platforms, while 2 parallel circles of wire connecting the 4 platforms via "bridges". In the center we have a central hub. Hopefully this 4 bridges will be real solid bridges at some point.

The type of wires i picked is almost random, but I am trying to use some true characteristics like brake point.
My first problem was to understand how strong is my bridges.With help from forum i found the tensile force of a rotating full circle, and a second approach how much weight i can put per some x distance when the shape converts to an Ngon. So i produced some safety limits for example 300 Kg per meter of bridge at 0.1654 G.
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But in reality there are no full circles of wire, platforms getting in between every 45 deg isolating bridge wires into arcs<45 deg does that affect limits?.

Also at the start of p2 the bridges are almost empty, and i was thinking of 8 vehicles that could start using the wires as a railroad, to distribute, materials symmetrically, but if something heavy steps on a bridge the shape changes only i don't know how.For now, this is the main question that bothers me, how the shape of bridges will change with distribution of materials. Can somebody guide my how i can simplify this problem.

And btw since i want to end with a solid and rigid full circle i want to distribute space-frame materials. Any suggestions have you heard anything similar space frame based on wires? For space it should be something lightweight and strong right?

## Answers and Replies

Mentor
You're going to have vehicles driving around in space on your rotating structure? What is the diameter?

artriant
Yep i was thinking that this is like a railroad in the circumference definitely not a job for humans. The diameter is negotiable but for now it is 500(m) r=250(m), i heard that this is theoretically good enough even for 1G permanent, cause we need lower than 2rpm to provide that. But in the construction phase i chose to go with moon gravity that way it is possible to distribute heavier parts.

Mentor
It looks easier to build all the external stuff without rotation, and start spinning the thing once everything structural and everything heavy is in place.

phinds
Gold Member
If it's just holding vehicles, why does it need gravity? Just take a page out of roller coaster technology and put wheels on the top of the rails as well as the bottom.

artriant
Hey mfb, what makes this special is that you get in full extension, really quickly and you spin almost from start.
Similar to 2 probes connected with a tether. Only this is full circle. That allows you to benefit from AG early on. We could mount anything under these platforms even a manned mission, and then wait until robots solidify.

A full construction of a solid structure might take many years before we actually be able to spin. And is also hard to maintain in correct height while it does not have a center (still in construction). I think that postpones all those solid full circle designs into the future. Or actually ppl think that's like utopia.
So that works like a shortcut.

artriant
Hey Dave definitely I am going to use wheels on top and bottom for sure, cause i dont want my robotic vehicles to fall at any condition :) But i need gravity to preserve the shape from start and for the reasons i described above.

Mentor
A full construction of a solid structure might take many years before we actually be able to spin. And is also hard to maintain in correct height while it does not have a center (still in construction). I think that postpones all those solid full circle designs into the future. Or actually ppl think that's like utopia.
So that works like a shortcut.
There is no "height" and no need for a center with a non-spinning structure (although you would probably put docking ports there, so starting with the center is beneficial). You can still spin up and de-spin the station for multiple construction periods, if the whole assembly takes too long.

Even with a railway-like structure (which is hard to get stiff enough), you have the problem how to put additional modules on them while they are spinning.

Mentor
@artriant -- BTW, you will want to have two vehicle tracks running parallel. Quiz Question -- why?

artriant
There is no "height" and no need for a center with a non-spinning structure (although you would probably put docking ports there, so starting with the center is beneficial). You can still spin up and de-spin the station for multiple construction periods, if the whole assembly takes too long.

Even with a railway-like structure (which is hard to get stiff enough), you have the problem how to put additional modules on them while they are spinning.

In any case it will take many missions until something super rigid and safe is done in a full circle, could be decades, i think the construction will be most likely in low Earth orbit for the reason that LEO rockets are quite cheap compared to others so you need height corrections. You have a strong point that is hard to add modules (in one piece) on my design, while it spins. But you have the advantage that you already have 4 x platforms that can be loaded with some modules already possibly empty in the start. Plus you can also unload anything in parts and extend those modules, near the platforms. But i don't like that to be honest to complex i prefer to done with solidification faster insteed, maybe a basic solidification with super light materials that will allow me to decelerate.

In your case if you start a solid construction from center, even if you are building just a straight space frame and not a cross, it will take 500(m) of construction most likely assembly by humans, (or you need also a railroad system), till you be able to have the quality of that size, and that is a lot of missions.
It is an option. But ill stay with my design cause i calculated that you can have full deploy in the suggested size, with just a few missions. Its a matter of preference. I think its a head start. Both of them are doable. But i think space agencies avoid anything that is titled superstructure from start.

@artriant -- BTW, you will want to have two vehicle tracks running parallel. Quiz Question -- why?

I was thinking 8, 2 departing from each platform, mainly because after each "mission" of the robots i want two parts added on each bridge, better shape preservation, balanced tensions, or perfect symmetry, i don't know why 8 i think 8 can't cause any problems, you think i can i go with 4? That would complicate the distribution a litl bit could be doable with 4 not sure :P

Mentor
I was thinking 8 , 2 departing from each platform, mainly because after each "mission" of the robots i want to two parts added on each bridge, better shape preservation, balanced tensions, or perfect symmetry, i don't know why 8 i think 8 can't cause any problems, you think i can i go with 4? That would complicate the distribution a litl bit could be doable with 4 not sure :P
Not the physics answer I was looking for. You can go with higher even numbers of tracks, but you still need to understand how to schedule them...

Mentor
What is a "height correction"? Tidal gravity is not negligible, but you can (and have to) choose the spinning plane in such a way that your rotation is stable.

At least in the near future, space stations will be built similarly to the ISS: pre-manufactured modules get sent to space, brought into the right position, and connected to the existing modules. The modules might be inflatable, but their connection principle is still the same. You can't build a module inside another module - it does not fit. Even if you can do final assembly in space (in a special, larger module?), you have to move the module through vacuum towards its final place next to the existing structure, and connect it there. And that step is much more complicated if the structure is spinning.

artriant
Not the physics answer I was looking for. You can go with higher even numbers of tracks, but you still need to understand how to schedule them...

Heh, that's is why I am here, you guys know much better physics than me, in reality i don't know how to schedule the distribution, to maximize shape preservation. The only good advice i give to my self is keep some basic symmetry. I made a quick shape Here is why i think 8 is like minimum. after that i think of 16.

Red dots robotic vehicles, blue dots first materials distributed. Each robot steps on 2 wires, and can move back and fourth to get mats from platforms, and can run over obstacles. I am open to any suggestions. I understand that is hard to calculate the new shape after distribution.

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artriant
What is a "height correction".
We need to push ISS to stay in orbit

The ISS maintains an orbit with an altitude of between 330 and 435 km (205 and 270 mi) by means of reboost manoeuvres using the engines of theZvezda module or visiting spacecraft . It completes 15.54 orbits per day.[16]

you have to move the module through vacuum towards its final place next to the existing structure, and connect it there. And that step is much more complicated if the structure is spinning.
I agreed that unloading materials through an elevator system from central hub to the platforms, has limits, while spinning, you can't unload entire modules, but what if a basic solidification can be done really quickly to the point that we can decelerate completely, then is just classic assembly. Add modules and anything. Meanwhile you already had 4 modules to play with.

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Mentor
Ah, you mean the reboosts. If (!) the structure is spinning they are easier with a central hub in place, but that is not necessary. Actually, you can combine the reboosts with gaining the necessary angular momentum to keep the spinning rate while adding mass to the ring.

artriant
Ah, you mean the reboosts. If (!) the structure is spinning they are easier with a central hub in place, but that is not necessary. Actually, you can combine the reboosts with gaining the necessary angular momentum to keep the spinning rate while adding mass to the ring.
That is an interesting idea, could be useful, thank you.
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By the way guys just to let you know ill stick with that design and try to support since I am already writing lot of pages + i see some clear advantages that I am happy with, but all conversations / ideas are welcomed. I would like to remind that i have a few problems in that topic so far that i could get help with some equations or suggestions, cause in many topics i lack experience, so let's start with the one problem that bothers me the most. Ill try to simplify to a point that can be potentially solved, here is the problem:

The "Mass on an arc of wire" (part of the circle that spins).Lets isolate one "bridge", actually 1 wire only.

What is known:

• First we are in perfect conditions no gravity air and the center of rotation has zero accelerations towards all directions.
• Radius, G force(artificial gravity) or acceleration, linear speed, ω, RPM , (uniform circular motion characteristics).
• Mass of wire per meter, arc in degrees or length, and other kind of irrelevant stats like breaking point, rope diameter.(Wire rope characteristics).

So if i want to add a single mass in the arcs center.
What other characteristics do i need so i can calculate the new shape of the wire.
I guess the added mass, will extend and balance to a new radius Rnew,
Maybe also bend resistance could play a role here but if that complicates it too much we could skip.

Mentor
Maybe also bend resistance could play a role here but if that complicates it too much we could skip.
Probably negligible.

If you can neglect the mass of the wire, then you just get two straight sections, otherwise you get some radial equivalent to a catenary

artriant
artriant
radial equivalent to a catenary
That must be it! It sounds really advanced. I did some research on the web, but i can only find real bridge mechanics. Catenary maths alone melted my brain

I believe that the nature of Artificial Gravity will result to much different formulas.

Anybody happen to know a similar research, article or a paper?
Anybody can think of similar mechanics?
Maybe i just need to run a simulation, i don't know, I am officially lost

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artriant
Hello Everyone i did a simulation and want to show you an interesting visual, for discuss.
One "weird" aspect of the Artificial Gravity is that: it increases linear with the radius.
I call this "Weird Gravity" (WG). It sound not a big problem in the start.

Bellow is a snapshot from a simulation that i did, in a 3D app.

DOS: Direction of spinning, Green curve: original radius(perfect circle), Grey fat curve: Deformed shape of the actual cable. Deformed cable with a sense of red line in it : Sankd part(right), Cable with a sense of blue line in it raised part(left).

As you can see the image only focuses in a quarter of the construct. This in one cable actually between 2 platforms fixed in radius r, i call this bridge.

I find out earlier that even super gentle torque (towards DOS) in the entire construct via platforms, can cause same type of deformation only stronger.
However this snapshot is taken after long time in uniform circular motion after small increase in rpm. So the bridge cable had all the time to find equilibrium in a different shape. But it never came back completely to the original shape which is a perfect circle with radius r.

A serious candidate for what causes this permanent deformation is the "WG". There is also a small chance that the simulation involves an atmosphere by default that could make this effect more sustainable but i`m not sure if that is the case.

So i want to ask your opinion, can that deformation be sustainable, only by the nature of Artificial Gravity?
Or the cable has to come back in the green curve (perfect circle) when construct falls back to uniform circular motion?

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Mentor
This is equivalent to the question "is a circle a stable equilibrium?" I would expect so. Otherwise a freely rotating loop of string would not form a circle.

The effective potential is proportional to r2. For small deformations, we can approximate the total potential energy as
$$-E = \int_0^{\pi/2} r^2(\theta)\sqrt{r^2(\theta)+r'^2(\theta)} d \theta$$
The integration limits are always implied now. We have the constraints
$$\int \sqrt{r^2(\theta)+r'^2(\theta)} d \theta = \frac{\pi}{2} R = L, \quad r(0)=R, \quad r(\frac \pi 2) = R$$
where R is the radius of the anchors and the first long equation is the fixed overall rope length.

Euler-Lagrange looks too messy. Let's assume r' << r and keep only the first nontrivial order. Then ##\sqrt{r^2+r'^2} \approx r(1+\frac{r'^2}{2r^2})##.

Use it in the equations above and multiply by 2:
$$-2E = \int (2r^3 + r r'^2) d \theta$$
$$\int (2r + \frac{r'^2}{r}) d \theta = \pi R$$

Looks like calculus of variations could lead to something here but I just get a huge mess. Let's test a single variation: ##r=R(1+\alpha \sin(4\theta))## for very small ##\alpha##. This looks like the deformation shown in the picture, and it has the natural shape of a deviation. Then ##r'=4R\alpha \cos(4\theta))##.
$$-E = R^3 \int ((1+\alpha \sin(4\theta))^3 + 8(1+\alpha \sin(4\theta)) \alpha^2 \cos^2(4\theta))) d \theta = \frac \pi 2 R^3 (1+\frac{11}{2} \alpha^2)$$
Our rope length will change:
$$L = R \int (1+\alpha \sin(4\theta) + \frac{8\alpha^2 \cos^2(4\theta)}{(1+\alpha \sin(4\theta))}) d \theta \\ = \frac \pi 2 R + 8 \alpha^2 R \int \cos^2(4\theta) (1-\alpha \sin(4\theta) + \alpha^2 \sin^2(4\theta)-\alpha^3 \sin^3(4\theta) + O(\alpha^4)) d \theta \\ = \frac \pi 2 R (1+4\alpha^2 + \alpha^4 + O(\alpha^6)$$
To compare ropes of identical length, compare our new rope to a circular one with a modified radius ##R \to R_1 R (1+4\alpha^2 + \alpha^4)##. It has the energy ##-E= \frac \pi 2 R_1^3 = \frac \pi 2 R^3 (1+12 \alpha^2 + O(\alpha^4))##, a lower-energetic state (as 12 > 11/2) compared to the line with deviation. Including higher orders for the square root expansion above would not change this result, as it only leads to ##\alpha^4## terms.

The circle wins, and it should be the only equilibrium position. As all deviations are at least second order, the simulation program might have problems finding it precisely.

artriant
artriant
I still try to figure out what awesome answer you just posted right there sir! Thanks A LOT, you saved me, big time!

Since my construct is almost always in uniform circular motion, is good to know that the shape of circle will be preserved!

I was in the middle of a painful process to find counter measures, because something so expected didn't happen in the simulation. But now i can roll back to the original plan. Is good to know that shape is getting "automatically" fixed by nature after a small deformation from a gentle parallel to circumference acceleration (to sustain rpm). Awesome!

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