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[Nagidal]

I am about to build a minecart track but I have little experience with it. I have these questions:

1. Can a track stop be designated on a ramp?
2. Can a minecart be accessed, loaded, unloaded or pushed if it stops on a ramp?

I figure I will need to build several more or less evenly spaced track stops with a certain magnitude of friction on a long continuous downward ramp for a regulated cart descend. I have learned that a downward ramp adds 4890 (4900-10 for track friction) points of speed to a descending minecart.

3. When I designate a downward ramp as a track stop with high friction (diminishing the speed by 10000 points), how much will the minecart be actually affected? Will it be decelerated by 10000, 10010 (+10 for track friction), or by 5110 speed points (also taking into account the acceleration of the ramp and the track friction, 10000-4900+10)?

Or is this 4890 value only relevant for minecarts starting to accelerate in the middle of the ramp? This wiki article section suggests that a cart that rides a track ramp fully from one side to another will in fact be accelerated significantly more. I'm confused and don't know how to calculate this. Can you help me?

[Loci]

Ramps and track stops cannot share a tile.

While you can certainly calculate out the velocities in detail, it isn't really necessary. If you're careful with your track layout there's no need to worry about the speed of the carts. To enforce a turn at any speed make sure there is a wall backing the turn (so the cart cannot continue straight); to enforce a down ramp transition add an impulse ramp directly before it. If you're worried your cart won't stop at a track stop, you can loop the track so the cart passes through the stop however many times necessary. It's also a good idea to keep bystanders off the tracks with statues; even a relatively slow minecart can be deadly.   

[Nagidal]

I think I have finally understood how the speed of a minecart is calculated. This sub-tile positioning and calculating position and speed per tick rather than per tile stuff. It is written up in the wiki article in such a difficult way, though, so I still don't know what exactly happens with the sub-tile positioning on the transition from a leveled track tile to an up or down ramp track tile.

Anyway, since I cannot construct a track stop on a ramp, all these calculations are irrelevant. I must use guided minecarts. There is too little space between the cavern layers to install rollers or soften the descend angle of the ramp. I cannot use the "hug the wall" trick in corners because I want four parallel tracks. This would make the three inner tracks in the corner to derail.

[Fleeting Frames]

You could theoretically build a track stop on flat ground, then obsidian-cast it, then dig a ramp out of it and engrave it so that it accelerates.

In that case, it would be decelerated by (10000-4900+10) points every step it spends on ramp. The actual movement would be smaller due being on ramp, of course.

For preventing speed accumulating/building bidirectional ascending/descending single rampway, you could alternate EW and NSW tracks, with walls to the west, and alternating open spaces north and front of NSW tracks. Cart will checkpoint through all of them up or down, each z-level in 1 step.

NSW won't work for you due 4 parallel tracks, though, and just N/SW would only work if it is already derailing.

For the sub-tile position of a cart entering ramp from flat ground, the remaining distance into the tile gets multiplied by *0,70707. If this is less than 40k*0,70707 into said ramp tile, the minecart can't leave the ramp on the next step even if it has enough speed due "ramp-entering" checkpoint.

As for your track layout at corner, I imagine it is something like this:

╔===
||╔==
||||╔=
||||||╔

Could use this instead:
###╔
##╔╬
#╔╬╬
╔╬╬╬

It'd flip around the tracks, but that could be reversed by another corner, bit of planned diagonal movement or some other turns later.

There might be also some other freedom involved with the fact that cart always descends a ramp if there's a hole for it to enter, even if it's speed says it should jump.

[PatrikLundell]

Why not use a chute to drop the mine cart down and then use the (impulse ramp powered) tracks only to get the cart back up (that's what I do when I use mine carts)? A central drop hole with a spiral around it has a footprint of 5*5 (counting the walls to keep things in and critters out).

[Nagidal]

My goal was to have a minecart go down a track which descends 90 z-levels (with some insignificant straights and seven 90°-turns) without being guided and without the need of powered rollers. (And without killing dwarves or pets frequenting the ramp.) All with a single push. So I figured I'd need some high friction points here and there to slow the cart down. However, there are going to be three long ramp sections which descend almost 30 z-levels in one long 45° ramp. This is more than enough to accelerate the minecart to max speed and have it skipping tiles. But since I can't build track stops on a ramp conveniently (without obsidian casting), then I guess I'll let the dwarves guide the cart down.

For preventing speed accumulating/building bidirectional ascending/descending single rampway, you could alternate EW and NSW tracks, with walls to the west, and alternating open spaces north and front of NSW tracks. Cart will checkpoint through all of them up or down, each z-level in 1 step.

This is an interesting suggestion I cannot yet fathom. I'd be willing to exploit some bugs and trick the system even if it meant that I'd have to run a single track rather than four parallel tracks. Reading up on that I have stumbled upon this post linking a very promising design making a minecart descend 47 z-levels on a single push.

However, I think that this all comes at the price that I would have to thoroughly understand the mechanics of it to tailor it for my particular case. And I think I am not ready to delve much into this just yet. Maybe some other time in another fortress. I thought there would be an easy recipe for designing a long unpowered regulated minecart descends. If there isn't, so be it.

As for your track layout at corner, I imagine it is something like this:

╔===
||╔==
||||╔=
||||||╔

Could use this instead:
###╔
##╔╬
#╔╬╬
╔╬╬╬

It'd flip around the tracks, but that could be reversed by another corner, bit of planned diagonal movement or some other turns later.

Indeed, the former layout is what I'm going to dig. The latter one, however, is interesting. But since I'm giving up on fully understanding the minecart physics for now it does not matter that much anymore. I'll try to understand the minecarts again at some point later.

[Nagidal]

Why not use a chute to drop the mine cart down and then use the (impulse ramp powered) tracks only to get the cart back up (that's what I do when I use mine carts)? A central drop hole with a spiral around it has a footprint of 5*5 (counting the walls to keep things in and critters out).

Another very interesting suggestion. I have grossly underestimated how unusable the minecarts are without exploiting and tricking the system. Since I'm currently overwhelmed by the complexity of all the impulse ramps and checkpointing, I'll save it up for later. Thanks anyway. There is only so many things I am willing to experiment with in a single embark. Delving into minecart tricks with all the haunted stuff having fun with my fortress would make my head explode.

[Fleeting Frames]

Small physics note: Iirc, it takes 47 ramps to accelerate minecarts to max speed; though the difference is mostly academic for you.

If high friction track stops on turns are not enough, you could possibly use rollers instead, either as flat 100k friction or as a way to force a sideways movement into track corner, thus overwriting minecart's extreme speed with roller's. Ex:

Cart goes to south
↓
╔ Roller gives 50k westward velocity.
╔
╔ Cart tries to leave west, is turned around by non-derailing speed, thus overwriting it's speed to 50k -1k -floor friction
↓
Slower cart

This is probably trickier than any other possible (simpler) solutions for your corner setup, like perhaps making every second corner pass 1z below so that all turns happen nicely.

This is an interesting suggestion I cannot yet fathom. I'd be willing to exploit some bugs and trick the system even if it meant that I'd have to run a single track rather than four parallel tracks. Reading up on that I have stumbled upon this post linking a very promising design making a minecart descend 47 z-levels on a single push.

Heh, that thread is gold, if bit long, but that design uses a completely different behaviour from what I meant. Larix went into details about the bidirectional checkpoint elevator, but for in-game example, see this POI from my sig. Switch to front view to go to z85 to see how I give track turns pits to make sure carts can ascend them when going up. (Check Succession world z-19 for powerless magma loading.)
Often, it can be pretty much second or third thing I do on embark, going for magma for magma workshops.

And huh, thought you had bit better understanding of minecarts from the question in OP. Well, I know I don't have full and complete understanding of minecarts myself after ....10 months, at least.

Given that, I recommend you disregard entirely the ramp-entering checkpoint I mentioned in last post (outside of building cyclotrons I have never had to consider it) and just keep in mind that

carts always pass over different direction accelerating ramp or flat floor after an accelerating ramp in single step,
losing the acceleration of ramp they passed over on previous step.
(Though not the sideways displacement, which is why you have to alternate which direction the holes are in)


PS: Yes, I know, you said you're giving up understanding for the time being - but I expect you'll come back to it whenever a guiding dwarf drops a minecart into your shotgun cannon due exchanging places with a cat or something and scatters it's contents or kills someone.

[Skorpion]

My goal was to have a minecart go down a track which descends 90 z-levels (with some insignificant straights and seven 90°-turns) without being guided and without the need of powered rollers. (And without killing dwarves or pets frequenting the ramp.) All with a single push.

I've tried that, and the dwarves liked to use the track as a shortcut People ended up squashed, or cannoned into the forges by a runaway minecart.
Do not get clever with descending tracks. Just channel down through those 90 Z-levels, and make the room at the bottom a stockpile that loads into another minecart, with plenty of room to evade falling stuff, and no access to anywhere else other than the track leading out.
Dropping rocks and bars multiple Z-levels is actually safer than minecarting it. Quicker, too.

[Nagidal]

Well, I have carved the tracks and had my first successful haul downwards. When guiding the empty minecart upwards the dwarf decided that it's time to do something else and let the minecart go. My stonecrafter's foot and ankle are mangled beyond recognition. We have fun in Lancedbrains.

But all in all the Minecarts are a good thing, even when guided. Makes hauling so much easier. It's worth it.

[Fleeting Frames]

Yeah, guided dwarves tend to let go of the cart when thirsty or hungry or sleepy enough or when moved away by a pet or when activated by military or probably when pulled by "Do it now"....

That said, I don't use guided carts much :p Some timers, some temporary storage (carts guard against rot), always on flat ground.

E: I suppose if you replaced accelerating ramps with non-accelerating ramps, guiding wouldn't cause accidents, but I'm not sure your constricted tracks would keep carts moving swiftly like that.

@Skorpion: Well, you should build blocking projectile-passable buildings such as statues on ends of tracks so that you won't kill any cats. Or dwarves, but mostly cats; the dwarves are far more plentiful.

PS: What you described would be safer if you moved the entire minecart down, even if just by dropping onto ramp(it will not spill its' contents), so that it could put it's load down next to the smelters and be sent back up without chance to hit even a child playing make-believe. Probs less labour to make, too; not to mention high-speed minecarts traversing appropriate checkpoint elevators can traverse up or down faster than a falling cart, at 2z per step.