Tuesday, December 9, 2014

Transit within Space Mega-Cities

This is intended to be the first post in a series on transport issues applicable to moving between one artificial gravity cylinder and another (not necessarily specific to a gravity balloon). The growing list of topics under this umbrella, new and old, have grown so much that a full series is needed. This post acts as a summary of those topics and establishes a central claim.

In particular, I want to talk about a billion person city. That is, a 3D city in space or inside an asteroid which has on the order of a billion people. For the purposes of this topic, I will use the term colony to denote a rotating artificial gravity cylinder in such a cluster, and the word city to refer to the entire cluster. In previous posts, I outlined how 1 billion people is just on the elbow of population constraints shifting from packing density to heat removal. Even that latter constraint isn't absolute, but it's not important because transportation times will put larger sizes in a different stratum anyway. The level of cultural connection is fundamentally different between occasional travel versus daily service.

Just that word "daily" introduces all kinds of qualifiers in the first place. Any concept of a day/night cycle would be artificial. My position is that this is only slightly different from modern cities on Earth since artificial light became rife, except that there's no natural suggestion from nature. The specifics of how a society manages the biological need for a day/night cycle is one thing I don't care to take a position on. The only kind of assumption I'm interested in here is how many trips per day someone takes between seperate colonies. Ideally this wouldn't include grocery trips or other relatively fungible activities. However, the entire draw of such a city is the connectedness, so I expect the relatively routine days of living in one colony and working in another would be balanced by extremely active collaborators. If you only go between your work and home colony that will obviously result in 2 trips. To balance things out, I'm saying 4 on average per person per day, for 4 billion A->B trips each day.

How you accomplish this volume, and the specifics of the physical manifestation is what I'm interested in here.

1. The Comparison

As an alternative hypothesis, this discussion will entertain the idea of lots of conventional artificial gravity habitats packed closely together. That conventional concept is an independently pressurized colony that rotates to create gravity. The problem I'm interested in here is inter-colony transport. Inter-city transport would be very different, the demand for it isn't well established, and there's not much I could say anyway. Comparing to the gravity balloon, the one obvious difference is that the space between the colonies is vacuum.

This still accomplishes the argument that a larger number of smaller colonies will have more surface area than a large single colony with the same volume. Transit is a lot easier with this system. Transportation within a colony is not much easier than transportation on Earth since it is a terrestrial-like environment. With no convenient fossil fuels you'll find public transportation more appealing too.

It should also be noted that these colonies would need to be tethered together in some way to avoid eventual collisions and resist destruction due to any perturbation. For instance, if a transport ship lost its pressure boundary, that air will then impart an impulse to the nearby colonies. It's obviously necessary to prevent those disturbances from causing millions of people's death by slow drift and collision of their colonies.

My reason for introducing this dichotomy is to identify very stark different between the gravity balloon and the conventional scenarios. Starting out, we don't want to prejudice ourselves to one or the other. Indeed, I think there are scenarios where the conventional approach might be better. It all comes down to what it is that you value. My predictable insinuation, however, is that if you desire a hyper-connected community of a billion people, the gravity balloon is almost certainly your best option... mostly because it doesn't need airlocks for intra-colony transportation.

But first, we need to formalize why airlocks matter.

2. Transport Network Topologies

Transportation can either be on-demand or mass transit. On-demand can entail either a personal or a shared vehicle. It also doesn't have to be the case that an on-demand vehicle is for a single person, but if it's not this will impose additional constraints which I don't want.

My perspective is that whether a trip is serviced by on-demand or mass transit depends on the volume of demand for the trip, measured in people per second. While the ideal volume for mass transit is disputable, I put it roughly in the range of 1.0 people per second. However, the minimum acceptable volume also depends on the number of transfers someone has to take during their trip. Doing 5 transfers at a cost of 1 minute each is taken to be equivalent to waiting 5 minutes for direct service.

Quantifying the difficulty of a transfer isn't precise but is still obvious. Going through an airlock is going to carry a higher time cost than stepping from one platform to another.

 2.1 Spoke-hub

On one extreme, the spoke-hub network topology is heavy on transfers. If all colonies only connected to one hub by their own dedicated route (or "spoke"), then even to get to your neighbor colony you'd have to travel to the very center of the city, transfer, and travel to the destination.

This complexity buys you a reduction in the total number of routes that have to be planned and maintained. Since the number of travelers is a constant, this increases the volume that each route sees. The 1 central hub is the extreme example, because there's only 1 route per colony.

Such extremism is not necessary. If you turn this into a hierarchy then the more central routes and hubs will have even higher volume than the local routes. As such, this method lends itself nicely to mass transit. The local routes will inevitably see usage rates 8 times the population of the colony per day. Since this will be in the 1,000s at least, any literal hub-and-spoke topology could be serviced entirely with mass transit.

Relaxing the extremism a little bit more, you would likely add cross-links either between colonies or regions. Since the volume is so high, this can be done while keeping mass transit viable, but still reducing the number of transfers.

Our tradeoff for extremely high volume is a larger number of transfers. I'll call the number of hierarchy levels I, and the number of regions/colonies serviced by a hub N. Then the total number of colonies is N^I. This established, the maximum number of transfers would be 2*I-1. If you used the smallest possible value of N, N=2, then you could be facing on the order of 30 transfers.

Such transfers would have to be virtually instant in order for the transportation system to be practical.

2.2 Point-to-Point

By putting people into colonies, we are dividing up our billion people into groups which are probably 10,000s to millions of people. Even the smallest realistic number of colonies is around 1,000. Even with this number of people, mass transit could only be minimal in a point-to-point system. This is because the number of routes in a full point-to-point system goes with the number of colonies squared. You'd be looking at 2-3 people for every route every minute.

This still forms a decent alternative hypothesis. By making the colonies large (although practically so), regular flights between colonies can be possible with the ridership being a handful of people.

2.3 Penalties for Distance and Transfers

A space city might find either one of these topologies favorable depending on the type of city and available transportation technologies.

Broadly, larger colonies are associated with conventional colonies because the task of reducing air drag in a gravity balloon becomes more onerous. Larger colonies are also associated with greater propensity to point-to-point transport topology.

More transfers are also disassociated with conventional colonies. The self-evident facts are that all colonies maintain their own atmosphere, and that colonies are stationary relative to each other. That means that you will use a minimum of 2 airlocks. If find it unlikely that any system designer would want to do any more than this. Any mid-range transfers would likely avoid merging the atmospheres of the vehicles if at all possible. Airlock cycling is slow and expensive.

3. Physical Mechanisms

Routes and transfers have been addressed in the abstract sense up until this point. That is, a route connects a hub or a colony to another hub or colony, while a hub is a point where one can exit one vehicle and enter another.

Even without any statements regarding the possible or likely network topology, a great deal can be inferred about the transportation system of a future space city from the underlying technologies. Popular illustrations of space colonies with artificial gravity sometimes add one or two details of ships entering and exiting... but if you start increasing the expected volume things start to get real weird real fast.

3.1 Means of Docking

By docking, I mean mean moving in and out of a colony or a transportation hub. Docking entails getting on a shuttle, getting off, and even the process of finding your next shuttle.

3.1.1 Conventional

Ports are most commonly depicted on the axis of a rotating space colony. For a cylinder, these are the two ends. For a sphere, these are the two poles on the axis. This rotates along with the space station, but the rotation rate is slow, and the accelerations mild.

But this is inherently one-lane. You could dock off-center but this will use propellant which I find to be incompatible with a large space city because the propellant demand for billions of trips would be huge. The only alternative would be to surround the city in a barrier and recover and recycle propellant. As such, I find the only valid solution to be sending larger ships through the airlock. This will likely be a ship that carries other ships in order to satisfy the point-to-point topology.

3.1.2 Gravity Balloon

A colony inside of a gravity balloon has open ends. This means that, hypothetically, someone could just walk off the edge. For our (more serious) purposes, we need some kind of architecture that gets them somewhere else after leaving. Since most of my reference designs have ends 30 m in diameter or more, this will entail collecting the people into a smaller space.

The solution I've been leaning toward is to have people's path through the colony mirror that which the air flow takes. Come in at the edge of the inlet end. Either take an escalator, shuttle, or a slide down to the terrestrial environment. Once they decide to leave, a building which spans the full diameter of the colony rises to the center-line. Here, they enter a tube where the low gravity and air flow move them out.

Individuals still need to make their own decision about what route to take, so you would essentially need a lot of handles and rails so they can move through the hub to their transport, which will be mass transport. Other than this, there's not much else to figure out. The atmosphere is continuous, so the only reason for doors in a transit shuttle is to keep people from falling out. A similar logic will apply for the transit hubs.

3.2 Means of Moving

The primary difference between the gravity balloon and conventional cities is the existence of an atmosphere in the former. This is a detriment to power consumption and speed limits in transit. However, it also can be a nice thing to have something to push against.

My position is that whether an atmosphere is a merit or a disadvantage is a function of the total size we're talking about. Since a gravity balloon can more easily host an extremely high density, these attributes somewhat make sense in conjunction. Alternatively, some methods might be available to get extremely high speeds in less dense clusters of conventional colonies.

3.2.1 Conventional

In the conventional space city concept, we are forced to move relatively small shuttles through the vacuum between colonies. I'll start out with the assumption that these shuttles are mostly free-flying and I'll classify the issues into 3 major parts, and only briefly touch on them here.

After departing the docking facilities of a colony, the shuttle obviously has to first accelerate. Since we're not very interested in multiple km/s speeds, this can almost certainly be accomplished mechanically. But we also must keep in mind Newton's law of motion. The transit volume almost certainly rules out reaction engines, so the shuttles are necessarily pushing against either the colony or some ancillary structure. I would favor the latter. A non-rotating envelope could surround the colony to provide easy access and also transfer momentum to and from the colony through axial bearings. So this non-rotating structure could launch shuttles through mechanical tracks or even mechanical arms. However, each shuttle is going in a different direction. The shuttle departure and arrival rate is also fairly high, so you would likely have many of these systems serving a single colony.

Once you get going, there will necessarily have to be some avoidance software, if we assume a mostly crude method of moving in the direction of the destination colony. If I assume a shuttle is about a square meter in cross-section, then random walks through my reference space city would result in roughly 1 collision every week. This is probably most surprising in illustrating the enormity of the 3D space. This is even after subtracting the volume of the colonies themselves. Avoidance might be one thing for which propulsive maneuvers makes sense because they are both infrequent and random.

Not only do you have to avoid other shuttles like yourself, but the lattice of colonies needs to be navigated around, but I classify this differently in the category of steering. Because you'll be going on movingly a preplanned route, it's thinkable that your redirects can be done by stationary infrastructure along your way. I would imagine that magnetic forces would be the most ideal for this because frequent catching and relaunching would make for a very uncomfortable ride.

Lacking a good vision of implementation of a system that handles these issues, I'm tempted to say that free flying shuttles won't exactly be the architecture that a conventional space city winds up with. I think something much more akin to roads are likely, but very different space roads. I would imagine these are steel guiding rails which the shuttle only makes contact with during acceleration, braking, and steering. This road network, thus, would still somewhat resemble a hierarchical network topology, although certainly not spoke-hub. I envision something much closer to an interstate system. For the large volume routes, the shuttles might even combine themselves in something resembling a mass transit system, but still while avoiding connecting via an airlock.

3.2.2 Gravity Balloon

Moving through a continuous microgravity atmosphere is the same as planes on Earth, except without the added complication of gravity. Thus, no novel technologies are needed and we can concern ourselves only with the economics of the system. If we use an extremely hierarchical transit system, the basic unit of transportation would likely be the individual and they would make decisions about where to go by grabbing onto guiding anchors as I argued before. Starting from that point, we only need to further identify the technology options for high-volume routes. These could use several mechanisms to minimize air drag, but the logistical implications of these approaches are also important.

One approach might be to just not worry about drag. You could even use a rope tow to transfer people relatively locally between colonies of the local hub. That is essentially a simple pulley in zero gravity. Many of these trips would be around 1 km in length, but they would need to be completed quite fast and very safely. The biggest problem with a person directly holding on to a fast rope tow would be the they can't breathe. If everyone wore aviator masks, the speed could potentially be rather high. That raises another complication - of how to grab on in the first place. This could likely be solved by a series of rope tows in steadily increasing speed, but all within arm's reach to the next stage. This also sounds somewhat dangerous, so a simple alternative might be a shuttle moving along a rope. It could accelerate with its own wheels, or it could just be on a pulley system. The only drawback is the relatively inflexibility since these approaches very strictly connect either two places or a loop.

The rope tow might be the most simple system I can think of. However, if we want to go in the extreme of maximizing logistical prowess while still not worrying about energetic efficiency, even a pneumatic tube starts to look like a valid option. If a traveler's destination was obvious (as in a true spoke-hub topology), the system planner can avoid a transit center where the person chooses where to go, and simply opt to suck the people up with a current of air. Yes, like the Jetsons. Actually, this could boost a much higher throughput with much greater simplicity than any other alternative. On the other hand, it can't be very fast (without killing people), and it would be highly inefficient.

Fixing the problems with the pneumatic tube by adding greater complexity would, in fact, be possible. You could actually invent a system that borrowed the physical principle from the friction buffers that I've discussed for the rotation of the colonies themselves. This concept was obvious to me a while ago, but I found it completely ridiculous. However, after studying the nature of hierarchical transit systems, it seems that the most central transportation routes can quite possibly get used by a large fraction of all the trips taken in a day. I mean, one route might service 2 billion trips per day. This is 1,000s of people per second. Even at 100 miles per hour, you could have 100s of people per meter. Any conventional system would involve massive docks or massive ships. The logistics of getting people in and out of a shuttle would be mind-boggling at these volumes. So a pneumatic tube isn't absolutely a terrible idea.

Considering these economic pressures, let me propose a ridiculous idea which would feasibly service the ridiculous populations of a space mega-city. Take a closed tube that goes in a large loop - a torus. Now surround this tube in another tube. Do this over many tubes. Have the inner tube rotate about its perpendicular axis at the desired speed. Each enveloping tube will move slightly slower. Let's say 5 mph over 20 tubes for a total of 100 mph travel speed. Then, of course, you would have doors in each level of tube so that someone could eventually make their way to the central tube. This could handle extremely large volumes, would be 100% continuous, and the power requirements wouldn't be all that high because the flow is controlled carefully. The main problem, I would imagine, would be training people to use it.

For people desiring methods which are more familiar, borrowing from planes, both jet and propeller craft are possible. You would only exchange the wing for another control surface or two. For the biggest legs of a mass transit system, air-breathing shuttles could reduce energy consumption and increase speed by increasing their scale. This is a coherent vision, but I doubt that the air-breathing engine would be the ideal choice for acceleration at the start of the trip since a simple mechanical boost at the start would be fairly trivial. Direction changes can be handled slowly over the course of the trip by control surfaces, so any launcher wouldn't need to aim either.

We don't necessarily have to consider on-demand transportation, but that is also relatively easy. It might also be a preference under certain circumstances, or just plain fun.

4. Gravity Balloon Connectivity Argument

Here's the point:
Why build a gravity balloon space city instead of the alternative?
I've been as general and generous as I can with the conventional type of space city. Indeed, I'm not trying to argue that any particular reference design is bad, just different. The attribute where a gravity balloon is appealing is transit connectivity. One real reason for pursuing a gravity balloon is desire for an interesting, vibrant, and interconnected city in space. I did not go into numbers here, although I hope to get to those in later posts, so you'll have to take my word on matters of degree. I wouldn't be saying any of this if I didn't have some empirical basis ready.

The desire to mingle among a billion person community daily might be somewhat difficult to reconcile with conventional space colonies. Even if one favored the extreme over-sized space habitat of a McKendree cylinder, it would take a heroic technology effort to make daily transit among the entire pseudo-terrestrial area viable.

As we try to get design convergence in the reference conventional I mention, several issues pop up. Smaller colonies result in greater transit network challenges and shorter average travel distances. However, larger colonies raise some serious safety concerns due to the speeds of the rotation. Even on the large side of ideal design range, I'm absolutely sure that the space between colonies would involve a large amount of clutter in order to make the formation of the movement of shuttles workable and comprehensible.

A gravity balloon, on the other hand, has really weird possibilities for the transportation routes, and considering the size that we're talking about these might even be relevant. Either way, having air to push against is a huge benefit. Also, no separate life support system is needed for every trip and people can live without constant airlock cycling. Those issues with conventional colonies are not deal-breakers, but the gravity balloon clearly has much greater desirability in this context.

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