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Built within an asteroid belt (near convenient resources) is a densely populated human settlement. While not a "planned city", the settlement has expanded in a organised, grid like fashion in all 6 cartesian directions. Up, Down, North, South, East, and West. Allocations of space within the city are basically rectangular prisms.

Tech is quite high - artificial gravity allows each dwelling owner to orient their space how they choose and the gravity field is confined to their dwelling. However not high tech enough that they can put their feet up. Most adults are employed, and most of them need to commute for work. People need to commute for supplies, or education, or social reasons, etc. Just like a modern city, except in 3D. Public transport is non existent. Everyone is using their own "flying car" - a personal transport rocket about 2-3m in size that is basically a car but in 3D. Can get up to 200kmhr on a straight and can do a 3G turn comfortably.

The city is overpopulated, very space constrained and densely packed. It can't afford the space to build a 6-way cloverleaf intersection every time 3 main "roads" (voids between allocated property in 3D) intersect. A 6 way stop sign definitely couldn't cope with the traffic, and waiting for 2 crossing traffics straights and 6 sets of turning groups would be a test on everyone's patience, especially if your commute requires crossing dozens of these intersections.

The largest "road" is 6 lanes high by 6 lanes wide, split in 2 directions like this diagram:

enter image description here

How do 3 roads like this intersect most efficiently?

enter image description here

What goes under the blue question mark to allow these 108 lanes to intersect as efficiently as possible?

Scaling up 2D intersection designs to 3D just don't seem to be an optimal solution, do we prioritise X, Y, and Z seperately using traffic lights? There are 18 turns which don't require crossing incomming traffic, 12 of those are going to have to wait at any one time even though their destination is "just there" - that's going to be very frustrating.

A 3-way roundabout (3 circles in X, Y and Z, or a sphere) could just fit if they go really slow, but I'm unable to work out the rules and it doesn't seem very space efficient when the traffic gets beyond a few dozen cars per minute, and I'm hoping to get something like 4000 cars per minute through this intersection.

User12321313
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    You don't need any "intersection design". This kind of vehicles will necessarily be under computer control. The computers will talk between them and optimize the flow by increasing or decreasing a little the speed of each vehicle so that they will pass through the intersection without stopping. – AlexP Dec 13 '20 at 14:24
  • @AlexP yup. I just finished writing an answer saying as much when I saw "1 new comment". – Ash Dec 13 '20 at 14:29
  • @Ash: And I upvoted the answer which I only saw after posting the comment... – AlexP Dec 13 '20 at 14:30
  • 108 cars simultaneously intersecting the space in 6 directions and at 200 kph... Computer control to avoid collisions would be the most common trope (Clarkean Magic) - but as an engineer, I have serious doubts that it could actually happen. Such a system would require whole-journey navigation from the moment it was logged (aka, "flight plan"). As the number of cars increases and the number of intersections increases the need to slow down does, too. This deserves thought. Maybe a cop, right in the center.... :-) – JBH Dec 13 '20 at 16:01
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    At 200 kph, a 3G turn requires a radius of about 375ft. Either your cars must slow to turn or you must permit more space for interchange ramps. Also, 4000 cars on 36 green-lighted lanes means one car roughly every 0.5 seconds and cars spaced about 25m apart. Every traffic control hiccup will have a tremendous death toll due to speed and inadequate braking distance. – user535733 Dec 13 '20 at 17:52
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    Frame challenge: if you want to get 4,000 vehicles/minute through this intersection, how many different vehicles are going to be travelling through this location in a reasonably short time (say 1 hour?) How how much volume of space do the owners of those vehicles require for living in? And putting those numbers together, why do they all need to go through this one "small" intersection? – alephzero Dec 14 '20 at 00:32
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    +1 Nice question. This is the kind of puzzle the guys on Silicon Valley (2014-2019 TV) would spend a weekend obsessing over, ultimately resulting in a new method for laying out microchips. – A. I. Breveleri Dec 14 '20 at 04:53
  • The distance between any vehicle and its following vehicle must be its stopping distance. If you want 4000 cars/min through there, they're going to be going quite slowly. In two dimensions peak traffic flow past a point falls at around 17mph. – Separatrix Dec 14 '20 at 08:34
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    These being flying cars, the chances are their stopping distance at any given speed is going to be considerably greater than that of a road going car. Hence even at 17mph their lane density is going to be lower than that of road cars. – Separatrix Dec 14 '20 at 08:49
  • Why wouldn't there be on and off ramps like with highways, instead of going through a huge intersection? In fact, you don't need an intersection at all. And seeing how we are much closer to autonomous vehicles before flying ones, it's likely it'd be 100% computer controlled, rather than a bunch of yahoos flying on their own. – Issel Dec 14 '20 at 15:12
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    “Public transport is non existent... The city is overpopulated, very space constrained and densely packed.” - this doesn’t make sense. Very densely populated regions necessarily have dense transport solutions. – Tim Dec 14 '20 at 16:00
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    Why six way? A flying car can enter the "intersection" at any angle. – DJClayworth Dec 14 '20 at 16:33
  • You say your highways are voids between rectangular prisms--how do you think the rectangular prisms fit around the intersection you showed? – David K Dec 14 '20 at 19:35
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    Very poorly, I would say. (Maybe it should be replaced by a "traffic sphere". – Hot Licks Dec 14 '20 at 22:58
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    "a personal transport rocket [...] Can get up to 200kmhr on a straight" That's not how rockets work, at least in space with no atmosphere. – zovits Dec 15 '20 at 11:21
  • Easy: computers are in control, resulting in something like this - https://www.youtube.com/watch?v=ufK2XRGUjuc – TylerH Dec 15 '20 at 21:30
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    I do hope this question and its answers somehow survive for hundreds to thousands of years, so our descendants can see how we imagined the future. Like those quaint old-timey postcards of flying cars and portable TVs that have been around. – Criggie Dec 15 '20 at 22:21
  • Really think 3d. Before you come to the intersection, cars would already switch lanes to have the right starting position: up or down, left or right, or center. The center lanes wouldn't intersect at all, they'd just flow around each other. The changers would have to brake and then let their computer control find a gap in the target lane. Plus, think the system, not one crossroad. People wanting to go right or up could do so some blocks in advance if a later intersection is full already. Certainly they have Google 3d maps. – Anderas Dec 16 '20 at 07:39

7 Answers7

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No intersections.

no intersections

You want your paths to be like interstate highway lanes. No direction changing or maneuvering - passing slow traffic at most. If you want to change direction you need to get off the interstate and change course out of the flow of traffic.

When rocket paths going different directions get close to each other, you want everyone to stay in their lanes and predictable. In 3d they do not need to cross. When the paths are close that is not where you want people maneuvering around to change directions.

Each of these various paths will have long on ramps and off ramps set well away from other paths. It will give the rockets time to maneuver, change course, decelerate and accelerate well away from traffic.

Willk
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    This. Space is 3 dimensional - and our flatland brains aren't thinking 3 dimensionaly. – Criggie Dec 13 '20 at 23:22
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    There is no real problem designing "3D" junctions in normal gravity, if you need to. The https://en.wikipedia.org/wiki/Gravelly_Hill_Interchange in Birmingham UK is about 50 years old, and deals with 18 different traffic routes on five different levels - including provision for horse-drawn barges to operate on a junction of four canals on the lowest level, without any obstruction to the towpaths and the boat tow ropes. – alephzero Dec 14 '20 at 00:40
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    This would be the best answer if there was no space constraint - but there seems to be a massive space constraint. – Ash Dec 14 '20 at 03:04
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    There is no room for this as stated in the question. – User12321313 Dec 14 '20 at 17:04
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    This is the 3D analog to the familiar clover leaf turnpikes, which have no intersections.It's also the correct answer. – Bohemian Dec 14 '20 at 22:28
  • From Hell's Heart, I stab at thee. – Hannover Fist Dec 15 '20 at 01:00
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    @User12321313 I don't really buy the "there is no room for this". This needs almost the same volume as your solution except for the tiny spot where all lanes cross – and by not stopping, you can get away with less lanes for the same amount of "cars" per time, so you save room. – Paŭlo Ebermann Dec 15 '20 at 01:23
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    @User12321313 That doesn't make any sense. If you don't have enough room for three roads that don't intersect, then you don't have enough room for three roads. Intersections don't save any space, because adding an intersection means you need to add lots more roads to make up for the vastly decreased throughput. – Tanner Swett Dec 15 '20 at 01:34
  • @PaŭloEbermann I wonder if the fundamental issue in regards to space is that this does not handle the last mile problem well. It seems to me that the "on-ramps" and "off-ramps" are going to need to be large, and everywhere--essentially adding several unnecessary lanes to each road on all 4 sides. – Eliza Wilson Dec 15 '20 at 07:58
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    What if you need to "turn"? Would you just make it with a bunch of on/off "ramps"? – mbomb007 Dec 15 '20 at 15:46
  • @mbomb007 - an interesting question. I was thinking about big turn around zones out of the way of traffic, like ramps. – Willk Dec 15 '20 at 20:21
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    @Willk Maybe like this, but 3D? https://en.wikipedia.org/wiki/Cloverleaf_interchange – mbomb007 Dec 15 '20 at 20:23
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Adjust each cars approach speed such that you always get a clear path.

You know those action movie cliche where a car runs a red light and, despite crossing traffic, the timing is so precise that the car gets through without hitting anything? You can use a central server to allocate slots in space and time for each car. The cars are high tech - so some autopilot system can request a clearence slot a few seconds in advance, and adjust the cars approach speed so that it gets through with an acceptable safety margin.

You have a natural 6 x 6 x 6 division of space, each about 3m x 3m x 3m or whatever your lane size is, 216 cubes in total. For a 200kmhr travel speed a straight travelling car with a 3m car length cars will cross through a cube within 50ms. With a safety margin of one car length each car would need to secure an allocation of a cube for about 150ms, and have 3 locked at any one instant.

Turning needs different allocations in time and space - many curves are possible, and it could depend on what lane the car enters in. By requesting multiple allocation sets in a priority order the car could do a fast wide 3-g turn that goes through lots of the lanes when traffic is low, but do a tight slow speed corner when traffic is busy by sticking to the edges.

By extending this to the entire city you don't need to allocate 18 lanes for each direction - you can flex it based on commute flows.

To explain flow here I'm going to introduce a unit called the "cubesecond", locking one cube for exclusive use for 1 second is 1 cubesecond. The intersection is fully swamped when all 216 cubes are locked, so you have 216 cubeseconds per second in budget.

Anyways this intersection design should allow a lot of traffic from our 216 cubesecond budget:

  • With 2-car-length safety margin (occupy a cube, reserve the one in front and behind you), each straight-through at 200km/hr locks 6 cubes for 150ms each - 0.9 cubeseconds per straight transit. This has an upper bound of 240 cars passing through the intersection per second. That's 15,000 cars per minute.
    • Lower the safety margin and you can get this higher. This is probably nail-biting enough already.
  • An "Up", "Down" or "not crossing the oncoming lane" turn1 occupies as little as 1 block for about 4 seconds each (tight, slow turn, but with time ), each of these uses 4 cubeseconds.
  • A "crossing the oncoming lane" turn needs to occupy as little as 4 blocks for about 3 seconds each (tight, slow turn). Each of these uses 12 cubeseconds.
  • A wide, fast, but greedy turn would occupy about 20 blocks for about 1 seconds each. This is 20 cubeseconds. You could theoretically do 10 concurrent wide greedy high speed turns.
  • You can mix and match these
    • If one person does a wide high speed turn in any right angle then ~195 cars could go through straight in any direction per second at 200km/hr.
    • If two people do wide high speed right angle turns then ~175 cars could go through straight.
    • 3 wide high speed turns then only 155 cars going straight per second.
    • 7 cars turning, and ~70 cars going straight, could get 420 high speed turns per minute and 4200 straights per minute. That should match your ~ 4000 cars per minute lower bound.

Footnote 1: Sorry, I'm Australian; I drive on the Left, Left turns are easy for me. I can't think in left and right here especially as your system seems to imply keep-right.

On further thoughts: No public transport kinda implies minimal or ineffective government, this may mean you can't run a central server. In this case - the cars can communicate among themselves on approach to each intersection. You'd basically use a networking protocol (eg blockchain) to build mutual consensus among a network of cars on which car has access to which cube of space at any one time.

Peter Cordes
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Ash
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    Blockchain isn’t the right tech here. A standardised traffic management protocol and some open source specs for how to build an intersection management unit would be better. If servers really can’t be used then mesh networking protocols and some distributed computation frameworks would work. – Joe Bloggs Dec 13 '20 at 22:00
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    Blockchain is a solution looking for a problem, this isn't it either. – Separatrix Dec 14 '20 at 08:30
  • If every citizen owns a car, there's no need for public transport. Or, coming form the other direction, public transport could consist of self-driving taxi pods. If those are cheap enough and space and energy/pollution are not a problem, no need to have buses/trains/etc. – JanKanis Dec 14 '20 at 11:10
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    @JanKanis, if every citizen owned a car and used it every day, most major cities would come to a complete standstill from system overload. There's neither the parking nor the road capacity to cope with it unless the city was built from the ground up and strictly restricted to make it possible. – Separatrix Dec 14 '20 at 11:22
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    @Separatrix For earthbound 2D cities and cars under direct human control, sure. But an extra dimension adds a lot of mobility, and computer controlled cars also give a lot of additional road capacity. (Why do we slow down when there is more traffic? We should be speeding up and decrease the space between cars so the road can handle more cars per unit of time!) Cars that are not in use don't need to be parked in the city center when they can self-drive, and you can reduce the total number of cars if they are shared taxi's. – JanKanis Dec 14 '20 at 11:32
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    @JanKanis, the distance between the cars is the stopping distance, if you speed up it increases by the square of the speed. You deduct the human reaction time and replace it with machine reaction time, but there still has to be space and time to act. Not all situations can be predicted, all situations have to be allowed for. Cars that aren't parked have to be allowed for in traffic capacity. A shared taxi has a name, it's called a bus (or sherut depending on country, but it's still mass transit). – Separatrix Dec 14 '20 at 11:39
  • @Separatrix I meant shared taxi in the sense of different people using the same vehicle at different times, like a taxi. Not as in unrelated people sharing the same vehicle at the same time. In reality the distance we keep between cars is mostly there for the reaction time. Cars at highway speed can't come to a full stop in one or two seconds. (Two seconds is the recommended distance to keep on the highway overhere, although many cars don't keep to it.) So these situations don't need to be handled in reality. – JanKanis Dec 14 '20 at 12:01
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    I don't have a way to do actual simulations, but I would think that doing a high speed turn across several lanes would work better in high traffic times than a slow/stop turn, which would have a tendency to make a bunch of other vehicles have to slow down or change lanes, causing more backup. If you do a fast turn from an inside lane across the lanes in the same direction, you're only slowing down the traffic to half speed, as the 2nd half of the turn is equivalent to cross traffic. This is where a sphere shape would save lots of space for such cornering, while easily keeping G forces "down". – computercarguy Dec 14 '20 at 21:20
  • So something like this, except with up/down also: https://www.youtube.com/watch?v=GhA917NnnCg – user1547672 Dec 14 '20 at 21:48
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    There's two amazing things about this answer: 1) it has upvotes, 2) is it's the accepted one. See Willk's answer for the obvious, logical and best solution. – Bohemian Dec 14 '20 at 22:31
  • @Bohemian Williks answer is explicitly forbidden by the question (3rd paragraph). I and the OP literally pointed that out in the comments. I haven't down voted his answer but it is wrong. – Ash Dec 15 '20 at 01:16
  • @Ash true, it is expressly forbidden. However, I don't think it's a valid restriction. The post starts with "Built within an asteroid belt...", which has an unimaginable volume - for all practical purposes 3D space there is unlimited. I don't believe a space faring population would not have the technology to make a clover leaf work, much less build their cities (which are literally in space) that can't have their parts moved apart slightly to fit in a clover leaf if one didn't fit initially. – Bohemian Dec 15 '20 at 02:48
  • If it is possible to cross vehicle streams without causing collisions, it is even easier to pack the streams more tightly, reduce number of lanes, and move the lanes without intersecting. – I'm with Monica Dec 15 '20 at 09:27
  • @Bohemian: I forgot the question said "belt". This answer would make sense if roads were tunnels carved into a single asteroid, so the outside borders of each lane were solid rock, and you can't just use more of the space between "buildings". That could create the problem this answer solves: an existing 3D "road network" that cars must travel along, which can't be easily / cheaply reshaped. – Peter Cordes Dec 16 '20 at 01:44
  • @peter good point about tunnels inside huge asteroids,, especially using tunnels because they could potentially be pressurised for easy living conditions – Bohemian Dec 16 '20 at 02:25
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Use a roundabout

Whilst Ash's answer is excellent when some form of automation is involved (as our current tech is leading towards already), I feel the question implies a lack of such technology.

Instead I will suggest something that every British driver is intimately familiar with, the roundabout.

In this case, all vehicles will drive in a circle until they reach their exit, at which time they leave. If you drive on the left, you go clockwise, on the right goes anti-clockwise.

"But wait," you say, "circles are 2D, what about the other two directions?" I'm glad you asked. The straight-on direction for the other two (say up and down) is straight through the middle of the roundabout.

If they want to join one of the other four directions (or someone from there wnats to join the Up/Down) they take a dedicated lane that splits off and puts them on it, much like those used in interstates/motorways.

If your city administration is on the ball, they probably know which direction pair is the "primary", and that one can be designated as the straight through route. Even if the primary route is Left/Up you can put a roundabout around the bend.

Unless you have a city of competent drivers, I suggest investing in space-buoys to mark lanes.

Kyyshak
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    The answer to competence is simple, you don't get flying cars until they're fully automated. Manual control just isn't ever going to be a thing for the average person. – Separatrix Dec 14 '20 at 08:29
  • Oh I agree, but we're not even science-based here, so we can use some willing suspension to get around the issue of putting the average person in charge of a literal rocket, especially as the OP says that is already the case. – Kyyshak Dec 14 '20 at 13:24
  • I think this will work for many of the intersections realistically - a "freeway" with a roundabout going around it is actually an interesting idea. I don't think it will work when there's too much "non primary" traffic though - the roundabout wont get the ideal radius due to space constraints so maximum speed will be something like 80km/hr. Still is an interesting visual. Thanks. – User12321313 Dec 14 '20 at 17:09
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    If you pair up a roundabout with a spiral ramp, you could get up/down as well on a single structure – Journeyman Geek Dec 14 '20 at 18:41
22

Do what city traffic engineers do today to solve super massive congestion problems.

One way streets

You solve half your problem by reducing the intersection to just three directions of traffic and using several other nearby intersections (between one and nine) for the complementary directions.

The use of one-way streets means traffic control (or, in your case, traffic scheduling) is substantially simplified — and that's really your goal.

Also, a quick frame-challenge alternative

You explain that your space is highly constricted and therefore huge cloverleafs can't exist. I'd like to challenge that. You have cloverleafs anyway. From any one direction there are only two of the five other directions that a traveling vehicle can turn into — and even then, at 200kph you can't simply turn on a dime. You need sizeable sweeping curves to get you into those new directions. And even larger sweeping curves to get you into the other three directions (including a U-turn). Cities today inevitably refer to this messy situation as a "mix master" or "spaghetti bowl."

Since you have that problem anyway (it really can't be avoided), you might find you actually save some space by off-setting the three paths at the intersection so that they don't directly intersect at all. You're invading the space you need anyway just to transition cars into the other directions. Granted, it will use more space than the mix-master itself would require, but in for a penny, in for a pound when it comes to safety. Right?

JBH
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    One problem with this answer - with 3 directions of traffic you have 3 pairs of interactions to worry about, but with 6 you have 15 pairs. Using one-way streets solve MORE than half your problems. – Rob Watts Dec 14 '20 at 23:24
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If you want the highest possible flow, you need to split lanes and merge them together afterwards.

You have 18 lanes. Split them in 5 possible directions thats 3,6 lanes per direction. Prioritizing the straight, thats 6 lanes straight and 3 lanes in every other direction. That could be splitted like so: enter image description here

As for the interchange design, there are a lot of examples for a 6-way-interchange, designed in the game "Cities Skylines".

enter image description here

From Reddit

All you have to do really, is change the directions of 2 ways and you are in the 3rd dimension.

You can alter and control the flow and prioritize connections if you alter the amount of lanes per direction.

Although this is the best solution for optimized traffic flow, it requires a lot of space.

Art Krenn
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Side Streets

It is a technique I see a lot in Texas, but rarely on the United States east coast. Put a low speed side streets next to the main thoroughfares, and do a classic intersection between them. This means that people who are turning must slow down, but people going straight just keep going.

3D roads

You've fallen for a classic trap. Your 6 lanes laid out side by side are a 2D design. For a 3D design, at the very least, stack them. What might be better is for each direction to have a two by two grid of lanes, for 8 total. This design also helps reduce the number of lane changes needed.

Rails

You might also consider a rail system. Like our railroads, it would be about keeping vehicles on the thoroughfare. Unlike our railroads, it would be more about guidance than support. It can make self-driving cars and computer management a much simpler proposition. If I were designing this, it would be a central hub that 3 to 6 streams of cars cluster around, using an extended rod to keep in contact with the hub. Supports for the hub would occur between lane changing zones. Local roads might just have one rail, one lane in each direction, and a stopping lane.

gerrit
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David G.
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    https://en.wikipedia.org/wiki/Frontage_road they exist outside of texas but texas has the most by far (in the USA) – crasic Dec 16 '20 at 02:36
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Allocations of space within the city are basically rectangular prisms

...

(voids between allocated property in 3D)

...

The largest "road" is 6 lanes high by 6 lanes wide

Would not result in 6 way supercollider intersection with "tunnels" leading to them. You would get gigantic (city wide) planes with 4-way (2D) intersection every block and much rarer 6 way intersections.

The largest roads would be 6 lanes wide and city size deep. So You would have much more room and much less traffic density than anticipated.

I would suggest that You use 4-car deep inner space for "express lanes" routed through the city, and reserve the outer-most (adjacent to structures) space for local traffic and the "cars" switching "express lanes".

For the express lanes You would have only option to flow the lane at high speed or switch to deceleration lane to join local traffic. For local traffic you would have low speed limit and more freedom to go where one please.

AGrzes
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