Tuesday, October 29, 2013

More Designs for Space Stations with Artifical Gravity

Notable space station designs for permanent habitation all share the basic principle, which is to rotate a single rigid structure at a speed necessary to produce acceleration similar to Earth gravity.  As an adjustment to these designs, I argue in favor of "multiple moving parts", because real-world complexities of operational demands and material economics, combined with the flexibility of zero gravity leave a significant niche for less-intuitive designs.

This blog has proposed the use of "friction buffers" (as I call them) to reduce the fluid forces that drag on the cylinders rotating for artificial gravity.  Originally meant as a way to make the zero-gravity atmosphere of a gravity balloon useful, it has quantitative applicability for smaller designs, on the scale of the O'Neil Island One, Kalpana One, and others.  Both of these are proposed to have a diameter of approximately 500 meters.  This size comes from a necessity to minimize the false forces to make the place feel normal (to an Earthling).  Such a size and rotation rate would make it impractical to simply place the rotating ring inside a pressure boundary because of the energy needed to keep it spinning.  As I have argued before, there are ways around this.

Some proposals do, in fact, call for placing the rotating segment inside the pressure boundary.  In 2001: A Space Odyssey, the Discovery One ship had such a design.  This is evidenced by the way that the astronaut was able to climb up to the center of the ring, and then exit into the zero-gravity parts of the ship.  Adding a rotating segment onto some stationary space habitat creates an engineering dilemma, because it's completely impractical to maintain a pressure boundary at a rotating joint.  Your two possible solutions are:
• envelop the rotating part inside of the pressurized part
• keep the pressure boundaries of the stationary and rotating parts completely separate, and implement a go-between module which has an airlock that can engage both
The latter option is the exact solution that the Nautilus-X proposes, and has included in designs for the International Space Station.  In an obvious sense, this maintains modularity and doesn't disrupt other parts of the station, but it's important to think about the operational consequences.  The ISS is a large station that allows its occupants to float from one side to the other easily.  This would not be the same for the centrifuge module.  That module would be specially isolated.  To enter it, you will need to go into the cramped transfer chamber, close the airlock.  Wait.  Then experience the transfer chamber start rotating.  Then wait for the other airlock to engage.  Then you can crawl down into the module.

Anecdotal evidence has its limitations, so I want to take a solid technical approach to what these designs would mean for an extremely large station with a rotating ring diameter of 500 meters.  As I argued in the introduction post, the conventional artificial gravity cylinder needs a wall that can withstand the outward forces from air pressure, the load from humans and their stuff, and an additional load from the acceleration of the shielding material.  Because I was interested in specifically gravity balloons, I haven't gone into detail of the other options, so I will do that now.  To keep things simple, I will limit everything to the consideration of cylindrical artificial gravity tubes.  This confines it it to a 2D problem.

Different Cases of Interest
Labeled with Case Numbers 1 through 4

Case 1 represents the conventional notion of a space colony.  The benefits are simplicity.  The drawbacks (compared to other options) are greater structural material needs.  The entire matrix of advantages and drawbacks are tabulated below, and I will argue them in more detail.

1. Conventional- Simple- Structural material requirements
- Structural material self-support
2. Decoupled Shielding- Roughly halves the cylinder structural load- Greater bulk material requirements
- Sunlight access
3. Decoupled Shielding
with Pressure Support
- Lowered leak rate
- Can use "sandy" shielding rock
- Extra airlock and pressure boundary
- Can use lower strength materials
- Stationary docking
- Can combine with self-gravitation effects
- Friction buffers needed
- Larger total air volume

Decoupled Shielding Envelope (case 2 and 3)

The most simple approach to reduce the material burden would be to simply decouple the shielding material from the rest of the station.  The shielding material would be stationary, and there would be relative motion between it and the pressurized habitat.  Shielding blocks radiation by eliminating all direct lines between the station and sources of radiation, so this would necessarily have to cover the station completely and block all light.  It would still be possible to have paths for incoming space craft to use to drive in, via labyrinth entrance paths.  It would even be possible to have a series of mirrors that reflect visible light while blocking radiation, as others have argued.

Mechanically, the shielding only has to support itself from its own self-gravity (which is case 2).  We can assess this using the large-limit approximation for a gravity balloon wall.  This would be assuming that the shielding would be a large sphere surrounding the rotating habitat.  Due to the nature of gravity, it turns out that it doesn't even depend on the size of the sphere.  Thus, by assuming a given mass-thickness of 10 tons per square meter (the same shielding provided by Earth's gravity) we have our final answer.

The way to interpret this number is that it's either the internal pressure needed to support the shielding sphere (which is case 3), or its the strength that the sphere has to have to keep from self-collapse (case 2).  It's an extremely low number, but it's compressive, which complicates things.  Also, the entire point of a decoupled shielding sphere is to use simple and abundant materials, so it's not trivial that this (extremely light) requirement will be satisfied with little effort.

Kalpana One does an innovative type of calculation when they consider the maximum length to diameter ratio reasonable for stability of a rotating space habitat, and they seem to come up with the number of 1.1.  Taking the diagonal, this gives a largest dimension of 743.3 meters, and the shielding sphere's diameter would have to be equal to this or larger.  It also includes a radiator skirt which is 200 meters beyond the extent of the habitat itself.  That adds up to 500 + 200 + 200 = 900 meters, which turns out to be the limiting dimension.  This is for a rotating cylinder of 500 meters diameter, so that gives us very nice intuitive guidance for the size that a shielding sphere would have to be, as well as the general numbers we might expect for the ratio of habitat floor space to the surface area of the sphere.

For a spherical pressure vessel with an outward or inward pressure (inward in this case, compressive), you can easily calculate the mass needed to maintain that pressure under the thin wall assumption.  Here, I do that, but do it in terms of volume instead.  This is to establish the thickness of a structural material needed to hold all the shielding in place.

Structural Sphere Thickness Needed to Hold
Shielding against its own Self-gravity

So, if the shielding materials were supported by bricks (which have a strength of 80 MPa), and the sphere had a radius of 450 meters, then we find that the needed thickness of the sphere of bricks would be 0.2 microns thick.  Obviously this would not be difficult to satisfy.  Any accounting of the cost of those materials to hold the sphere up in its intended form would basically be negligible.

However, it's still possible to eliminate the stresses in those members, which I think is necessary to address for theoretical purposes (which is case 3 specifically).  After all, you could fill the sphere with a gas of 0.014 Pascals, and that would be higher than the pressure in space in general.  There would be some interesting dynamics to this gas, but it would certainly not contribute significantly to the slowing down of the rotating cylinder.  You would not need to add any friction buffers or anything of the sort, and it could be basically scaled up infinitely (in the absence of other cosmic forces).  Even if you wanted to accept the concept of superlarge rotating habitats that some science fiction writers propose - being made of carbon nanotubes, this could still exist within the envelope of a spherical radiation shield, and have that tiny pressure which holds it up from self-collapse.

I did look around for designs that are of the general nature of using a rarefied gas to support a large construction, and I found one example on NASA spaceflight forum.  It includes the detail that we raise the material from a 400 meter asteroid into a larger sphere by inflating a balloon place in its center, and that it would be done by using a rarefied gas.  Then there is also mention of creating a sphere to rotate in order to get artificial gravity.  However, I'm not sure if the exact same type of configuration is what the poster had in mind, and the entire thing is peppered with other details that seem irrelevant or jumps in the logic that I simply do not understand.

It's possible that the pressure support of the shielding material might be more detrimental than helpful.  After all, what if you had a leak in the station?  That would quickly blow away all of the shielding material!  But then again, this might actually be useful.  If you could build a thin but flexible pressure envelope, then you could adjust the size of the shielding envelope at will by letting slightly more or less gas into it, creating a "blow-fish" space station.  Exactly why anyone would need to do this - I don't really know, but it's an interesting addition to the toolkit.  The configuration would be quite stable, since the expansion of the gas itself limits the size it can grow to without introducing more gas.  Condensing it would probably require some cryogenic type machinery, but it would be workable.

Decoupled Pressure Envelope (case 4)

In a cursory mathematical look at the structural mechanics, decoupling the shielding material from the rotation is a clear win.  Less so for the strength needed to contain the air pressure, but it deserves a closer look.  A constant theme here is that carrying extra material along with the rotation carries with it a significant penalty.  So far, I have neglected the fact that structural material in the cylinder must also support itself.  This argues in favor of decoupling materials from the rotation, but I'm avoid inclusion in this post because it gets complicated.  If the pressure-retaining structural materials are a large part of the shell's mass in an O'Neil cylinder, then that material should be counted as shielding material as well.  That gets complicated with piecewise functions so I'm leaving that out.

The concept for my reference case (call 4) is to simply make a large spherical pressure vessel in space, fill it with air, and also put a rotating structure inside of it.  The energy loss due to air drag per floor space was also previously calculated in this blog, given assumptions about the number of friction reducing buffers you surrounding the rotating cylinder with.  This causes some amount of bloat of the space the cylinder takes up, but it is conveniently similar to the Kalpana One radiator size, so I will opt to use its numbers for the ratio of total volume number.  All the airlocks will be located on the non-rotating pressure boundary, and access to the rotating cylinder is entirely open.

It is a bit unfair to compare this design to that of a fully rotating space habitat, because this is two stations in one.  One with Earth gravity, and a microgravity volume.  Between the two there is some wasted space that is a requirement of the physics of the friction buffers.  The relative velocity between the two reference frames is about 110 mph, so it is no laughing matter.  You still need an elevator to get between the surface of the artificial gravity tube and its center, but once in the center, you can float out into the rest of the station.  You are not at risk of being smacked by a 110 mph wall, because the friction buffers exist to break up the relative velocity in multiple stages.

Recall in a previous post I looked at price for floor space given assumptions about what materials cost.  The source I used there argued in favor of materials pricing that was proportional to strength and mass.  Lumping all material densities together, this argues that a certain amount of tensile strength is roughly identical regardless of the strength potency.  If true, decoupling the pressure envelope offers no identifiable benefit in terms of structural materials (unless you count its self-support).

However, I think there's speculative reason to maintain that this will not be the case.  The entire principle behind space manufacturing will be that the materials we have access to will be limited.  At least early on, we will seek to use what we have, and the more variety of material we can use, the less material we have to bring into our processing facilities.  This is where the idea shines.  It can reduce the high-strength material needs by an order of magnitude, which may be a great boon to the viability of space colonies.  The pressure boundary can be made of material of any strength, as long as the structural engineering is sound.  Adding more material never hurts (aside from making the airlock more difficult).  In other words, this allows us to use a very thick pressure boundary.

Assume some cost for high strength material in space.  Then assume some cost of low-strength material.  If the high-strength material is a cost driver, then the case for this scheme is made.  Of course, there are other multipliers at work, particularly the usable volume.

Mass Requirements for
Spherical and Cylindrical Pressure vessels

Structural Mass Ratios for the two Cases

This is an example ratio of the increased material burden of this case.  Thus we conclude that if low-strength material is exactly 1.82 times cheaper than high strength material this will be cheaper in terms of the structural material.  However, there are other cost increases for case 4.  We have the energy costs to keep the cylinder spinning, which isn't necessary in the pure vacuum of space for case 1.  There is also the fact that case 4 uses more air in general, and procurement of air isn't free in the first place.  The premium for high-strength material would have to be sufficiently high to justify all these costs.

The dimensions for Kalpana One are certainly arbitrary, so I want to quickly cover a "capsule" case in general.  This is where a cylinder is capped on both ends by a half-sphere of the same radius.  This establishes the long dimension for the sphere, which is used to evaluate the ratio of structure material for both cases in the same way as above.

Structural Material Requirements of
Case 4 versus Case 1

Illustration of a Capsule Rotating Shape and
Relative Performance of the Cases

Here, we conclude that decoupling the pressure envelope will never reduce the total amount of material strength needed for a space habitat.  The best case is where the structural materials are in a 1-to-1 ratio for both cases, and this is actually unrealistic.  This is the scenario where the rotating structure is a sphere, and it's contained with another non-rotating sphere that holds the pressure in.  This doesn't afford space for the friction buffers so it couldn't actually be constructed.  Obviously you could take another route and envelope a cylindrical habitat in a cylindrical pressure vessel, but it seems this design route would be pointless as it would offer very little benefit.

The principle isn't entire new (refer to the 2001 reference), although I'm still looking for another reference that mentions anything like the friction buffers on this blog.  The idea of space colonization with similar methods has been thrown out there before.  For instance, someone on NASA spaceflight forum proposed a Demos station made of an inflated habitat with one atmosphere and a rotating ring inside of it to produce one Earth gravity.  The moon itself has so low gravity that the mechanical issues shouldn't really be a concern.  Aside from the friction buffers, everything else about the idea is in line with the case 4 I discussed.