wendy wrote:The difference between a 3d driver and a 4d driver, is that the up direction is part of the wheel in 3d, but in 4d, the 'up' direction is not one steers to. Turning a steering wheel in 4d does not make the car go upwards. In 4d, a wheel is still a fat circle, but the steering device is a disk (ie a N-1 sphere that one might grip). Let's call it a steering-disk to remind us that it is not a fat circle.
Basically, think of both the steering wheel and the road ahead as a diameter of a circle in 4d. So where we have left vs right, and move the wheel accordingly, in 4d, you have a 360 degree circle, perpendicular to the height-forward space, and a corresponding 360 circle on your steering disk. So when you push 12-oclock to 1-oclock, you turn right, at 2-oclock, it's still right, but harder. Likewise, when you poke the NP at 1-oclock on c40, you turn to c40, at 2-oclock to c-40, you turn to c-40 harder.
The reason it's important that the wheels rotate in the height/forward space only, is because any other rotation will spin the cab around. You might want to do this, which is why i have the turn the steering-disk left-right.
Klitzing wrote:The 4D steering wheel is not at all complicated and unusual. They would have 4 directions to drive away from straight on, just as we have only 2 directions within our driving contexts within 3D. Thus our cars use a real steering wheel (using its tangential directions) to drive on streets. But aeroplanes also have 4 sideward directions: right, left, up, and down. They do use a joy stick for steering wheel. Either direction serves for any of the directions of deviation. And undeflected it will guide straight ahead. Thus, cars of 4D world most probably would just use a joy stick as well.
--- rk
gonegahgah wrote:Hi quickfur. It is certainly thinking outside the box which is what we need to do (well, even literally I guess because a box is only part of a tesseract).
Can you imagine if we used the same principle in our world: lines to follow rather than lane dividers?
The challenge is what happens when the two vehicles stray and scrape. Who gets to claim that the other was invading their space?
The benefit of lane dividers is that we can more clearly delineate the zones for the separate vehicles...
gonegahgah wrote:A bit of paint can be saved by painting in cage pattern instead of full dividers.
They could start with the corners of the hexagon to delineate the lanes then add in a few inter-extra lines along the edges of the hexagon dividers.
They would probably just need enough lines so that lane changing must involve intersecting those lines with some part of the vehicle.
That would possibly work and reduce the amount of paint necessary?
Keiji wrote:<plug>Of course, you could always avoid all this trouble with planar rail</plug>
Keiji wrote:Actually there are 2 rails so it is not monorailbut they are 2 parallel planes, hence planar rail.
And yes, lane changing is the idea - You steer left or right on the plane to select your lane, just like you do in 3D. Whereas for actual curves in the road, the plane banks for them so you would steer straight ahead. So the only time you ever need to steer, is in order to change lane.
Keiji wrote:You wouldn't even have to steer for a cross road! Unless space was extremely limited that you couldn't build a banked turn.
Keiji wrote:Does the Planar rail wiki page help?
Keiji wrote:I wonder if the need for both planar rail vehicles, and spaceship-steering vehicles, will lead to bi-modal ones being developed?
I'm not sure how that'd work with the controls, though. Or the wheels. But it's a thought
gonegahgah wrote:The idea is beginning to conceive as very excellent Keiji.
Just as a consideration I am wondering if two tracks are sufficient for vehicles to remain upright; and not fall over sideways when the vehicles are stationary or moving.
Of course we already have mono-rails in 3D; but they are big and require careful balancing.
Generally our trains run on two tracks. If our trains tried to balance on a single track they would fall over sideways.
Would trains in 4D on only two tracks likewise tend to fall over; even tracks at 180° to each other?
Is it possible that we would need three tracks as a minimum (probably 120° to each other) to allow vehicles to remain upright while travelling; even on these excellent planar rails?
quickfur wrote:gonegahgah wrote:Of course we already have mono-rails in 3D; but they are big and require careful balancing.
Generally our trains run on two tracks. If our trains tried to balance on a single track they would fall over sideways.
Would trains in 4D on only two tracks likewise tend to fall over; even tracks at 180° to each other?
Is it possible that we would need three tracks as a minimum (probably 120° to each other) to allow vehicles to remain upright while travelling; even on these excellent planar rails?
The vehicle doesn't need to be completely supported by the tracks. The tracks can just act as guide rails, constraining motion to a single lateral direction, but the vehicle itself can easily be supported by other wheels (outside the track) that rest on support surfaces beside/between the tracks.
Keiji wrote:Actually, neither is necessary! Two parallel planar rails, with eight wheels on the vehicle, four on each rail, are sufficient to keep the vehicle stable.
Keiji wrote:If you were using linear rails, like our 3D railways, then yes, you'd need a minimum of three rails for stability. However, since the rails are planar, you can imagine the shadow of the vehicle being "wedged" mostly between the two planes, attached to it by the wheels. Gravity then does the rest of the work, keeping the vehicle directly on top of its shadow.
quickfur wrote:So for the main traffic corridors in the city, you'd want to have the planar rails confined to a narrow strip (this also saves on the cost of materials for building the rails!)
gonegahgah wrote:Keiji wrote:Actually, neither is necessary! Two parallel planar rails, with eight wheels on the vehicle, four on each rail, are sufficient to keep the vehicle stable.
Hi Keiji, I'm not so sure about that. If we put 8 wheels in-line on our trains (or any number) and send them along a single rail they are still likely to fall over sideways.Keiji wrote:If you were using linear rails, like our 3D railways, then yes, you'd need a minimum of three rails for stability. However, since the rails are planar, you can imagine the shadow of the vehicle being "wedged" mostly between the two planes, attached to it by the wheels. Gravity then does the rest of the work, keeping the vehicle directly on top of its shadow.
Again, I'm not so sure about this yet. The planar rails I would have thought would allow complete freedom of movement in the 'yaw' (or 'pitch'?) of the rail? So, wouldn't the vehicle still be very wobbly and fall over sideways?
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