Largest Plausible / Realistic Rotating Space Station

[whitelancer64]

Something I've been wondering about for some time - how BIG is it physically possible to make a rotating space station with currently existing building materials (not carbon nanotubes. We can talk about graphene sheets and nanotubes after we can build a bridge out of them)?

Some back of the envelope calculations based on a complete lack of materials engineering knowledge suggests to me that the tensile strength of modern high strength steel or titanium alloys should allow for the construction of rotating space stations well over 100 km in diameter.

A great deal is dependent upon the design, of course, but in broad sketch, I'm thinking something like the Elysium, which in the film was a 5 spoked hoop 60 km in diameter and 2 km wide. According to multiple web pages online (some of dubious quality), the overall design is realistic enough that, in theory, its structure could be built. My ideal concept would have a large habitation ring rotating at 1g and four smaller interior rings at 0.16 g, 0.37g, 0.5 g, and 0.75 g for research labs at those g levels. Perhaps also small mobile labs that can be raised or lowered between the rings to study any desired g level. But for the sake of simplicity we can assume just one ring at 1g with spokes that connect to a central hub.

Obviously, this would all have to be built in space with materials gathered, refined, and forged in space. I'd like to set that whole logistical process aside in this discussion, as well as the trillions to quadrillions of dollars it would cost to build.

To be clear: I'm not asking about impossible engineering like Ringworld, nor the (much, much smaller but still enormous and far beyond what could plausibly be built) Culture series' Orbitals. I'm wondering what is the largest we might be able to actually build with materials we have on-hand today.

[Coastal Ron]

Something I've been wondering about for some time - how big is it physically possible to make a rotating space station with currently existing building materials (not carbon nanotubes. We can talk about graphene sheets and nanotubes after we can build a bridge out of them)?

The challenge of answering this question is that until you have decided on what the overall design is, it is hard to imagine how it would scale. That is because we are obviously going to start out with much smaller rotating space stations, and no doubt we'll try out a number of different types of designs.

Also, where is the station going to be located, since if it is within the radiation protection of Earth that means less mass is required for radiation protection and mitigation.

But for the sake of simplicity, how about you simplify the calculation by just figuring out how large a simple hoop could be that is spun to produce one Earth gravity on the inside of the hoop? Didn't I see a hoop-stress calculator recently on the Rotating Space Station thread? Can that diameter be backed into?

That would likely give you the largest possible diameter, and then it is a matter of reducing the size based on the mass required for humans and all the things needed to allow them to live and work.

Would be an interesting piece of information to know...

[Nomadd]

 Has anybody ever put together serious comparisons for an outer shell suspended from a hub with something like aramid lines instead of requiring the ring to do all the work loadwise?
 A chart comparing mass both ways over varying station sizes would be interesting.

[whitelancer64]

For simplicity's sake, I would start with a simple Bishop Ring type design. Don't worry about radiation shielding at this point, we should figure out how big the forest is before we start counting trees.

There was a hoop strength calculator linked in the other thread, but I am unsure how to interpret the results. I tried a couple of other similar calculators but I found this one and I think it is better, as it gives the hoop stress in a flywheel.

https://www.calculatoratoz.com/en/hoop-stress-in-flywheel-calculator/Calc-1840

[Paul451]

Some back of the envelope calculations based on a complete lack of materials engineering knowledge suggests to me that the tensile strength of modern high strength steel or titanium alloys should allow for the construction of rotating space stations well over 100 km in diameter.

Can you post your calculations?

[Paul451]

Via the Engineering Toolbox...

Hoop stress in a rotating ring,

σ = ( 2 * pi * W / 60 )^2 * ρ * ( r1^2 + r1*r2 + r2^2) / 3   

where:
σ = hoop stress due to spin (Pa or N/m2)
W = angular velocity (RPM)
r1 = outer radius of disc (m)
r2 = inner radius of disc (m)
ρ = material density (kg/m3)


But since this is also a pressure vessel, you also need to add internal pressure:

σ = p * d / (2t)

where:
σ = hoop stress due to internal pressure (MPa, psi)
p = internal pressure (MPa, psi)
d = internal diameter of tube or cylinder (mm, in)
t = tube or cylinder wall thickness (mm, in)


and via wikipedia and googling manufacturer's websites...

Yield strengths (in mega-pascals), Density (in kg/m^3:

Common steel (ASTM A36) = 250 Mpa, ~7800 kg/m^3
High strength steel alloy (ASTM A514) = 690 MPa, ~7850 kg/m^3a
Stainless steel (AISI 302) = 520 MPa, ~7860 kg/m^3
Cast Iron (2-4.5% carbon) = 50-170MPa, ~7200 kg/m^3
Iron (no carbon) = ~100MPa, 7874 kg/m^3
Aluminium alloy (2014-T6) = ~400 Mpa, 2700 kg/m^3
Titanium Alloy (Ti6Al4V) = ~830 MPa, 4500 kg/m^3
Carbon fibre = ~5600 MPa, 1750 kg/m^3
Practical carbon composite, ie, yarn in epoxy resin = ~3500-4200 MPa, ~1600 kg/m^3
HDPE = ~30 MPa, 940 kg/m^3
Kevlar/Aramid thread = 3600 MPa, 1380 kg/m^3
Dyneema (UHMWPE) thread = ~3600 MPa, 970 kg/m^3

[Twark_Main]

Hoop stress in a rotating ring,

σ = ( 2 * pi * W / 60 )^2 * ρ * ( r1^2 + r1*r2 + r2^2) / 3
...


But since this is also a pressure vessel, you also need to add internal pressure:

σ = p * d / (2t)

It's an interesting design/algebra exercise for the reader to:

   A.) in the first equation, plug in some value for the assumed interior density ρ_interior (typical ISS value = 100 kg/m³).  And then...

   B.) set the hoop tension and the longitudinal tension in the ring to be equal (ie isotropic), and then figure out how the "solution" for r/R varies with the primary parameters, which in this case are ρ_interior and either R or ω (whichever you prefer). 

[Greg Hullender]

Perhaps a simpler task to start with would be to pretend you're building a suspension bridge. That is, it has a "roadway," maybe 40 meters wide, but it's not pressurized or anything. It has cables (titanium?) that connect to a large central hub (or wrap around it?). And the whole thing rotates fast enough to generate 1 g on the "roadway" surface.

Obviously this wouldn't be enormously useful by itself, but then you can look into what it'd take to scale it up.

[Twark_Main]

Perhaps a simpler task to start with would be to pretend you're building a suspension bridge. That is, it has a "roadway," maybe 40 meters wide, but it's not pressurized or anything. It has cables (titanium?) that connect to a large central hub (or wrap around it?). And the whole thing rotates fast enough to generate 1 g on the "roadway" surface.

Yes, I believe this is generally the way most newcomers picture structural stress operating within a rotating space station. The spokes "hold up" the "weight" of the torus.

It's quite natural. It appeals to our intuitions developed in a 1 g environment, and also one where every indoor built space doesn't need to resist huge internal forces due to pressure.

[Coastal Ron]

Via the Engineering Toolbox...
Hoop stress in a rotating ring,
...
But since this is also a pressure vessel, you also need to add internal pressure:

The structure of a rotating space station does not need to also be the pressure vessel. Certainly my rotating space stations have pressure vessels that are independent from the station structure - attached, sure, but the pressure vessel contributes nothing to the load a station structure can carry.

and via wikipedia and googling manufacturer's websites...

Yield strengths (in mega-pascals), Density (in kg/m^3:

Common steel (ASTM A36) = 250 Mpa, ~7800 kg/m^3
High strength steel alloy (ASTM A514) = 690 MPa, ~7850 kg/m^3a
Stainless steel (AISI 302) = 520 MPa, ~7860 kg/m^3
Cast Iron (2-4.5% carbon) = 50-170MPa, ~7200 kg/m^3
Iron (no carbon) = ~100MPa, 7874 kg/m^3
Aluminium alloy (2014-T6) = ~400 Mpa, 2700 kg/m^3
Titanium Alloy (Ti6Al4V) = ~830 MPa, 4500 kg/m^3
Carbon fibre = ~5600 MPa, 1750 kg/m^3
Practical carbon composite, ie, yarn in epoxy resin = ~3500-4200 MPa, ~1600 kg/m^3
HDPE = ~30 MPa, 940 kg/m^3
Kevlar/Aramid thread = 3600 MPa, 1380 kg/m^3
Dyneema (UHMWPE) thread = ~3600 MPa, 970 kg/m^3

Could someone run the numbers for the last two? I plan to use Dyneema for holding my stations in the shape of a hoop, with no suspension cable system. I've done some simple calculations in a spreadsheet, but I'm pretty sure my formulas are not as comprehensive as the one you identified.

[daveglo]

Please don't forget to allow a safety factor.  For a human-habitable structure, I'd suggest that the allowable hoop stress be no greater than 0.25X the assumed material yield strength.

You'd have to allow this, as the loads on the hoop will not be uniform at any time in it's life.

[Twark_Main]

Via the Engineering Toolbox...
Hoop stress in a rotating ring,
...
But since this is also a pressure vessel, you also need to add internal pressure:

The structure of a rotating space station does not need to also be the pressure vessel.

It doesn't need to be, but it's generally a good idea.

Certainly my rotating space stations have pressure vessels that are independent from the station structure - attached, sure, but the pressure vessel contributes nothing to the load a station structure can carry.

This would be like building a skyscraper and having one set of columns to support the weight of the building, and a completely separate set of columns to support the vertical component of wind loading on the building.

[snip]

Could someone run the numbers for the last two? I plan to use Dyneema for holding my stations in the shape of a hoop, with no suspension cable system. I've done some simple calculations in a spreadsheet, but I'm pretty sure my formulas are not as comprehensive as the one you identified.

If you're using Dyneema you need to watch out for creep. For a constant load application you can't just use any Dyneema, you need to use a low-creep grade such as DM20.




Math

For Dyneema I would assume a safety factor of no less than 8 for creep avoidance. For simplicity I'll split the problem into the two orthogonal components, but if you prefer diagonal filament winding you can use trig to find the optimal winding angle instead.

For the longeron direction, the total structure mass needed to resist the "weight" under rotation is:

m₁ = (safety factor) × (Dyneema density) / (Dyneema yield strength) × R × (torus section total mass) × (gravity)


For the longeron direction, the total structure mass needed to resist the internal air pressure is:

m₂ = (safety factor) × (Dyneema density) / (Dyneema yield strength) × (2 π R) × (π r²) × (internal air pressure)


For the hoop direction, the total mass needed to resist the internal air pressure is:

m₃ = (safety factor) × (Dyneema density) / (Dyneema yield strength) × (2 π R) × (2 π r) × r × (internal air pressure)


Total torus primary structure mass is m1 + m2 + m3.

By similar triangles, the optimal filament winding angle is—of course—simply atan((m1+m2)/m3). 

[JohnFornaro]

To the OP:

Here are some preliminary calcs about a possible structural armature designed to withstand the one-gee forces on an early version of my ring station.

Somebody check my math.

[Coastal Ron]

Via the Engineering Toolbox...
Hoop stress in a rotating ring,
...
But since this is also a pressure vessel, you also need to add internal pressure:

The structure of a rotating space station does not need to also be the pressure vessel.

It doesn't need to be, but it's generally a good idea.

So you think, but why? Elucidate.

Certainly my rotating space stations have pressure vessels that are independent from the station structure - attached, sure, but the pressure vessel contributes nothing to the load a station structure can carry.

This would be like building a skyscraper and having one set of columns to support the weight of the building, and a completely separate set of columns to support the vertical component of wind loading on the building.

Analogies are great if you pick the right one. Unfortunately you picked the wrong one... 

A container ship is a more apt analogy for what I'm doing.

[snip]

Could someone run the numbers for the last two? I plan to use Dyneema for holding my stations in the shape of a hoop, with no suspension cable system. I've done some simple calculations in a spreadsheet, but I'm pretty sure my formulas are not as comprehensive as the one you identified.

If you're using Dyneema you need to watch out for creep. For a constant load application you can't just use any Dyneema, you need to use a low-creep grade such as DM20.

That is a valid concern, and there are three things that I've done to address that, with one of them being that the station structure will be shaded, and kept cold - creep is generally not an issue if the material is kept at a cold temperature. The other two mitigation actions are something I'm not talking about yet, as they are something completely different than what I've seen others doing - in other words, not validated enough for me to spend time explaining and defending them, but they were conceived to address the longevity of using HMPE as a station structural element.

[Twark_Main]

To the OP:

Here are some preliminary calcs about a possible structural armature designed to withstand the one-gee forces on an early version of my ring station.

Somebody check my math.

Based on the drawing, you're relying on the secondary structures (the internal "floors") to transfer the enormous weight from the regolith shield to the armature. Unless those floors are made extremely strong (as in, strong enough that you need to also be calculating their weight), the armature won't "hold up" the shield, it will just buckle the floors.   


Also your floors are 30 feet high. For real ("cost is an object") applications, one would probably triple or quadruple the number of floors, and the associated dead/live weight.

Also why is the regolith radiation shield shaped like a square in cross-section? You could save (again enormous) mass by making it circular in cross-section, and locating it immediately outside the circular pressure vessel.

[Twark_Main]

Via the Engineering Toolbox...
Hoop stress in a rotating ring,
...
But since this is also a pressure vessel, you also need to add internal pressure:

The structure of a rotating space station does not need to also be the pressure vessel.

It doesn't need to be, but it's generally a good idea.

So you think, but why? Elucidate.

Lots of reasons.

One of the biggies is that structural members flex in response to loads. If your "air pressure" structure and your separate "spin gravity weight" structure flex by a different amount, You're Going To Have A Bad Time (unless you do a bunch of extra engineering to solve a problem you didn't need to make for yourself in the first place).

Also in general, "the best part is no part one part instead of two." This is why, for example, a rocket fuselage acts as both a tank and a load-bearing column. Same thing here.

Certainly my rotating space stations have pressure vessels that are independent from the station structure - attached, sure, but the pressure vessel contributes nothing to the load a station structure can carry.

This would be like building a skyscraper and having one set of columns to support the weight of the building, and a completely separate set of columns to support the vertical component of wind loading on the building.

... you picked the wrong [analogy]

No not really.

A container ship is a more apt analogy for what I'm doing.

In a container ship, the hull acts to both hold out water (hydrostatic/hydrodynamic force) and provide structure for the internal weight.

[snip]

Could someone run the numbers for the last two? I plan to use Dyneema for holding my stations in the shape of a hoop, with no suspension cable system. I've done some simple calculations in a spreadsheet, but I'm pretty sure my formulas are not as comprehensive as the one you identified.

If you're using Dyneema you need to watch out for creep. For a constant load application you can't just use any Dyneema, you need to use a low-creep grade such as DM20.

That is a valid concern, and there are three things that I've done to address that, with one of them being that the station structure will be shaded, and kept cold - creep is generally not an issue if the material is kept at a cold temperature. The other two mitigation actions are something I'm not talking about yet, as they are something completely different than what I've seen others doing - in other words, not validated enough for me to spend time explaining and defending them, but they were conceived to address the longevity of using HMPE as a station structural element.

As long as you also have ample safety margins, it should be fine.

You just have to engineer it such that the "creep life" of the Dyneema is beyond the lifespan of the space station.



^{(note that he's wrong in saying that old stain glass windows "creep"; the builders just put the thicker part of the glass on bottom)}

[Coastal Ron]

A container ship is a more apt analogy for what I'm doing.

In a container ship, the hull acts to both hold out water (hydrostatic/hydrodynamic force) and provide structure for the internal weight.

Ding, ding, ding, give the man a cigar! See, what did I tell you about making sure you use the right analogy, and container ships are maybe not perfect analogies, but pretty darn close. Think of the pressurized living spaces as the containers, which in real life they are, and they are connected together is ways that do account for flex, and also account for catastrophic failure of the support structure.

That is a valid concern, and there are three things that I've done to address that, with one of them being that the station structure will be shaded, and kept cold - creep is generally not an issue if the material is kept at a cold temperature. The other two mitigation actions are something I'm not talking about yet, as they are something completely different than what I've seen others doing - in other words, not validated enough for me to spend time explaining and defending them, but they were conceived to address the longevity of using HMPE as a station structural element.

As long as you also have ample safety margins, it should be fine.

You just have to engineer it such that the "creep life" of the Dyneema is beyond the lifespan of the space station.

Oh, not a problem. I've taken care of that with the other two mitigation actions that I'm not ready to talk about yet. I mainly took that into account because I thought that radiation would degrade the Dyneema, so degradation by temperature and creep would also be covered.

My Mars-gravity station will certainly not be optimized for weight, but it will be a 1st generation rotating space station, so I'm not worried about weight optimization as an end result of combining structures with pressurized spaces (which I think will take a couple tries to get right), I'm focused on what can be built quickly and for a "reasonable" price.

[JohnFornaro]

To the OP:

Here are some preliminary calcs... Somebody check my math.

Based on the drawing, you're relying on the secondary structures (the internal "floors") to transfer the enormous weight from the regolith shield to the armature. Unless those floors are made extremely strong (as in, strong enough that you need to also be calculating their weight), the armature won't "hold up" the shield, it will just buckle the floors.   

Kinda sorta.  The armature in that example is roughtly the same mass as the hull of the structure.  Since moment scales in a linear fashion, I wanted a BOTE on whether or not 'ordinary' steel could withstand the forces, and it appears that it can. I never did sketch out the structural relationship of the 'levels' [rather than 'floors']  to the armature.  That was a design exercise.

One of the current problems I'm working on is the hull sections which are not likely to be 3D printable as shown.  I'm thinking the hull might be a woven structure.

Also your floors are 30 feet high. For real ("cost is an object") applications, one would probably triple or quadruple the number of floors, and the associated dead/live weight.

Of course, "cost is an object" is not a scientific term, but still; it should be remembered that I propose selling 'condos' ['space-ohs'?]  as a means of financing the project.  In SK006, posted back in November, I suggested and illustrated that each 30' level could be filled with two 15' levels.  The structural calcs were predicated on these live/dead loads.

In this configuration, there are no extreme structural conditions.  Well, other than building the station itself.

Also why is the regolith radiation shield shaped like a square in cross-section? You could save (again enormous) mass by making it circular in cross-section, and locating it immediately outside the circular pressure vessel.

We had a discussion above about the squorus versus the torus.  Every level is the same width in the squorus.  This means that the level spans and thus the required structure is the same. My initial engineering opinion is that the minor 'weight' differences between the levels can be ignored as long as the outermost one is considered.   This is seen as an advantage.

Withstanding the air pressure need not be "optimized" in this configuration and the mass savings are seen to be less important.  An elephant of twenty tons is not that much smaller than an elephant of twenty-one tons, even tho bench pressing a ton is pretty difficult for me, what with my shoulder and all.

In that earlier scheme, I did propose a toroidal pressure volume to mitigate hull breeches, but later deleted it, after Michel's Kalpana concept was presented.  The entirety of the Kalpana environment is subject to a hull breech.  I still propose bulkheads every 200' or so as to mitigate hull breeches.

Just as an aside, how does this thread differ from the related thread?

[Paul451]

Via the Engineering Toolbox...
Hoop stress in a rotating ring,
...
But since this is also a pressure vessel, you also need to add internal pressure:

The structure of a rotating space station does not need to also be the pressure vessel. Certainly my rotating space stations have pressure vessels that are independent from the station structure - attached, sure, but the pressure vessel contributes nothing to the load a station structure can carry.

The size of the surface area of the pressure vessel will give you the required mass of the pressure vessel, which needs to be supported by the load-bearing structure. That load-bearing structure will have its own mass which it also needs to carry, etc. The "size" calculation thus affects both the mass of the load-bearing structure and the pressure vessel, both need to be simultaneously added to determine the required strength of the load-bearing structure. The two components are intimately linked.

This is particularly so if you are, as the OP requested, calculating the largest possible station.

[JohnFornaro]

The structure of my station, currently made up of various hollow segments, is the pressure vessel.