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.

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    $\begingroup$ 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. $\endgroup$ – AlexP Dec 13 '20 at 14:24
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    $\begingroup$ 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? $\endgroup$ – alephzero Dec 14 '20 at 0:32
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    $\begingroup$ “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. $\endgroup$ – Tim Dec 14 '20 at 16:00
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    $\begingroup$ Why six way? A flying car can enter the "intersection" at any angle. $\endgroup$ – DJClayworth Dec 14 '20 at 16:33
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    $\begingroup$ "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. $\endgroup$ – zovits Dec 15 '20 at 11:21

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.

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    $\begingroup$ 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. $\endgroup$ – Joe Bloggs Dec 13 '20 at 22:00
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    $\begingroup$ Blockchain is a solution looking for a problem, this isn't it either. $\endgroup$ – Separatrix Dec 14 '20 at 8:30
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    $\begingroup$ @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. $\endgroup$ – Separatrix Dec 14 '20 at 11:22
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    $\begingroup$ @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. $\endgroup$ – JanKanis Dec 14 '20 at 11:32
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    $\begingroup$ @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). $\endgroup$ – Separatrix Dec 14 '20 at 11:39

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.

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    $\begingroup$ This. Space is 3 dimensional - and our flatland brains aren't thinking 3 dimensionaly. $\endgroup$ – Criggie Dec 13 '20 at 23:22
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    $\begingroup$ There is no real problem designing "3D" junctions in normal gravity, if you need to. The 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. $\endgroup$ – alephzero Dec 14 '20 at 0:40
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    $\begingroup$ This would be the best answer if there was no space constraint - but there seems to be a massive space constraint. $\endgroup$ – Ash Dec 14 '20 at 3:04
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    $\begingroup$ There is no room for this as stated in the question. $\endgroup$ – User12321313 Dec 14 '20 at 17:04
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    $\begingroup$ @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. $\endgroup$ – Paŭlo Ebermann Dec 15 '20 at 1:23

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.

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    $\begingroup$ 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. $\endgroup$ – Separatrix Dec 14 '20 at 8:29
  • $\begingroup$ 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. $\endgroup$ – Kyyshak Dec 14 '20 at 13:24
  • $\begingroup$ 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. $\endgroup$ – User12321313 Dec 14 '20 at 17:09
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    $\begingroup$ If you pair up a roundabout with a spiral ramp, you could get up/down as well on a single structure $\endgroup$ – Journeyman Geek Dec 14 '20 at 18:41

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?

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    $\begingroup$ 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. $\endgroup$ – Rob Watts Dec 14 '20 at 23:24

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.

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    $\begingroup$ That looks like a way too sharp right-way curve in the inner roads of the intersection. $\endgroup$ – gerrit Dec 15 '20 at 8:30
  • $\begingroup$ @gerrit Traffic must slow to make the turn, naturally. $\endgroup$ – TylerH Dec 15 '20 at 21:32
  • $\begingroup$ What a cool looking, horrible intersection! This game, doesn't it know public transport? Thanks for this image, it made me laugh in the morning. Good start into my day. $\endgroup$ – Anderas Dec 16 '20 at 7:31
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    $\begingroup$ @Anderas oh it does know public transport. But shenanigans like this are more fun :) $\endgroup$ – Art Krenn Dec 16 '20 at 9:04
  • $\begingroup$ There's a junction round here called 5 ways, and it's a lot simpler than that. $\endgroup$ – Separatrix Dec 16 '20 at 9:47

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.


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.


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.


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