Your attention please!Below is my original post on the subject, edited with most of my results. However, there's lots of newer, more accurate info (and written much more concisely) in eg. electrobadger's and expwnent's posts (#45 and #65, respectively). I didn't feel like rewriting everything to include their data, so go read those, or hopefully the same info will end up on the wiki pretty soon.Quantifying minecart physicsI've been thinking about doing some sort of SCIENCE before, but haven't really had any subject strike my fancy. Until now. I'd really want to have more numeric data for minecarts, similar to how we can plan a windmill farm or waterwheel power generation scheme beforehand (power is also visible in-game though), for better design of rail systems. Exactly how much roller power do you need to ramp up a level? How long can you make a flat track before the cart stops? Does is matter how strong the dwarf pushing off the cart is? What about the weight of the cart and/or its contents? Other factors?
So, the idea is to do some more quantifying of some aspects of minecarts and their physics. When I started thinking this out, I read some stuff, and while there had been some research, most of it seemed more engineering than physics - "how do I get this thing done/this setup to work", instead of "1 roller tile of lowest-speed rollers gives a standard iron minecart x Urists of kinetic energy." The significant exceptions I found on a read-through of the entire The "How Does Minecart?" Thread were Sadrice's testing, in posts
#200 and
#230, and xmoffitt's, in posts
#441 and
#488. At least Sadrice was using versions 34.08-34.09, I think. So some of this is verification of their results for 34.11 (even though I don’t think any of the numbers have changed since 34.08, and anything for minecarts in any way since 34.09), other stuff will be new SCIENCE.
If I've missed any other results like these, please point them out, I would be very interested to compare results.Assumptions/hypotheses and areas of research are listed below. I'll be using empty minecarts for now. Contents will weigh down the minecart, but the effects of that will have to be tested separately. I'll start off with pushing minecarts, since guiding doesn't really involve the physics at all, treating the minecart like a big, tracks-only wheelbarrow with more elaborate options, and riding is like pushing but with the dwarf as extra contents. I'll start with the speed gained from pushes, move onto the slowing effect of a flat track, then the friction of track stops, rollers of varying speed, then speed gained/lost from ramps,and finally fluids. This post will have a list of all the assumptions and their current status. Then, I'll post the actual descriptions/narrative of the experiments. I hope you'll forgive the multi-post, since my RTF of this is about 8 pages long. I
will put some stuff in spoiler tags, so you don't have to scroll as much. I was originally going to post this in
The "How Does Minecart" Thread, since that's where the previous results were posted, and it was my inspiration as well; however, it is already 39 pages long, and doesn't seem to collect much interest anymore, hence the new thread.
List of stuff to test:#1-6 (pushing, tracks and turns) -
mostly done:
#1: Minecart physics have no randomness. They are governed by a definable set of equations, probably some approximation of Newtonian mechanics. Exception: Some (small?) variability due to rounding to the tile grid and such may be observed. (Assumption, proof for some scenarios acquired)
#2: A push by the same dwarf will always give a specific minecart the same speed or possibly energy/momentum. (Assumption, verified; but see below)
#3: Factors affecting speed gained from push - which of the following matter: strength of the dwarf, weight of the minecart, other? How much energy/momentum/speed is imparted? First testing by Sadrice (post #200), but his track had turns. Sadrice did discover that a minecart always travels the same distance, regardless of contents, minecart material (=weight), or dwarf strength. (Measured/Verified; speed/distance traveled is always identical)
#4: 1 tile of track has some (small) amount of friction, and causes the cart to slow down. How large is this amount? (Measured; a cart stops on the 201th tile after the initial hauling stop on a straight track)
#5: My initial guess was that track turns wouldn't slow down the cart any more than any other track square. Sadrice had already found this to be false (post #230), though, stating that they have about 11 times the friction of a straight track tile. So 10 additional tiles worth of friction? (Measurements made indicate between 9-13 additional tiles worth of friction depending on the situation, no definitive answer)
#6: Carved and constructed tracks have the same friction, also regardless of material, ie. are always functionally identical. (Assumption, verified)
#7-8 (bridges and track stops) -
mostly done:
#7: Bridges have same friction as track tiles. They're not functionally identical, since dwarves guiding minecarts will not treat bridges like they do tracks, i.e. they will choose the shortest path if on a bridge.
(Assumption, verified)#8: Measuring the friction of track stops of varying settings. Also, does the dumping setting matter for friction? In a complex world, it'll matter only for non-empty minecarts; this will have to be tested at a later date, only empty carts for now. Fluids may be useful standard weights for testing this. xmoffitt came up with some data on this on
page 30 (Measured up to medium: lowest = no extra friction, low = 4 tiles of extra friction, medium about 40-50 (I measured 52) tiles of extra friction. High is at least, maybe exactly, 800. Highest might be infinite friction, but no certainty on that yet. Add the base 1 tile of friction from the track to these values.)#9-11 (ramps) -
testing done, no simple answers found:
#9: How much speed/energy does ramping 1 level down give? Does the ramp have regular track-tile friction? (subject to variation, but about 560 Urists, or as little as 470ish Urists if the cart has almost stopped before ramping down; regular track-tile friction probably applies)
#10: How does falling down 1 level compare to ramping down 1 level? This is related to whether ramps have regular track-tile friction, and to how falling/the parabolic paths work in general; probably only going to test a 1-z drop at this point. (Parabolic flight path, no track friction during it (of course). Depending on speed, the cart can go multiple tiles horizontally before it falls 1 z-level. Not testing flight paths more at this point.)
#11: How much speed/energy does ramping up 1 level take? Does the ramp have regular track-tile friction? I can't think of a way to test the latter at the moment, but it can probably be assumed that whatever holds for down-ramps is also true here. (Also variable, but results indicate that on average, somewhat less energy is required to ramp up than down, usually giving a net gain of energy; however net losses are also common; up-ramp friction not tested due to no ideas on how to do it)
#12-16 (rollers) -
partially/mostly done:
#12: Unpowered roller tiles are identical to regular track tiles, and powered roller tiles have regular track tile friction, but no other friction effects. (Assumption, verified)
#13: How much speed/energy do rollers of varying settings/length give? (1-tile rollers: Lowest 51 tiles, low 201 tiles = a dwarf’s push, medium 451, high 801, highest 1250)
#14: Does it matter if you have 5 one-tile rollers, or 1 five-tile roller? (To be measured)
#15: Is there a max speed that rollers accelerate to, as many have stated/the current consensus states? (To be measured)
#16: Can a track go over a roller in the opposite direction, if the rollers are low-strength, and the cart is going fast enough? What are the effects of this/is it possible to calculate the speed afterwards? (Might be possible, but at least low vs. lower isn’t enough. Hence it definitely isn't something simple like the "braking" roller subtracting it's speed from the cart's current speed)
#17-21 (derailing and fluids) -
abandoned/left for others to test:
#17: The physics of derailing (on turns): How much speed is needed, and how much friction do non-track tiles have, or is some other model used for bringing the cart to a halt? (To be measured)
#18: How much does 1 tile of water slow down a minecart, for different depths of water? (To be measured)
#20: Is ramping up/down affected by water; is a ramp down with water on it the same as a ramp down, plus a flat tile with the same amount of water on it? (To be measured)
#21: Is magma the same viscosity as water, i.e. does it slow down carts by the same amount? (To be measured)
Later research questions -
left for others, as planned originally:
- If a max speed from rollers exists, do carts going faster than this get set to this max speed if they go over a roller?
- Is there a max speed (set by the air friction) for regular tracks without rollers? (Lots of down ramps! !!SCIENCE!!)
- If so, does water/magma have a (lower) max speed that the cart slows down to immediately on contact?
- Inspired by
this post, is it possible to build a dwarf-powered long-distance minecart system using the possible behavior that a minecart colliding into another comes to a stop, and imparts all of its kinetic energy to the 2nd cart (totally elastic collision?)? In other words, does this happen and is the collision totally elastic, or is some energy lost in the collision? (Collisions do happen, and most, but not necessarily all, of the colliding cart's momentum is transferred to the collidee; see
this- I'm also leaving all parabolic trajectory research, as well as speed research, for others to do for now, although some results regarding speed can of course be deduced from the results I'll be getting.
Note on units: Throughout the text, I’ve mostly been using tiles of distance as units, sometimes calling them Urists. These are actually units of work/energy, as in, 1 Urist/tile of friction = The work done by the friction of a track over 1 tile. At least for track-related minecart physics, the mass of a cart doesn’t seem to have any effect on it’s behavior (not necessarily true for impacts, parabolic flight paths, or skipping on fluids, to mention some cases where the opposite might be true). If we take xmoffitt’s measurement of a dwarf push giving an initial speed of 0.2 tiles/tick and assume that for track physics, a minecart’s weight doesn’t affect it’s kinetic energy, but that the kinetic energy is rather just purely ½v2, the initial energy is 0.02 tiles2/tick2. The work 1 tile of track does as friction is then 0.1 milli(tiles2/2). Thus 1 tile2/tick2 = 10 000 Urists, and a dwarf pushes a cart off at 200 Urists (see discussion at end of #2 experiment). I have not done (almost) any measurements of speed (in tiles/tick) as a function of distance or time, unlike xmoffitt.
I'll be posting the more detailed descriptions of the results/setup in later posts, but will edit any knowledge into the list above. I've uploaded the
save folder to DFFD, if you want to do some testing with ready-made tracks (read the DFFD description and preferably the epilogue, which will come in the last of my initial experiment posts here, to get an idea what you're getting into with the fort). The version is 34.11, Phoebus tileset.
I'll be editing some results to the wiki, if they seem reliable. Feel free to test any/all of this yourself too, either for more verification, or new research into the stuff I haven't gotten into yet. It's very likely I won't have the attention span to test everything listed above in full detail; I will try to get at least some results for everything, though.
edit: my first post describing the experiments ended up as reply #5, so scroll down a bit.
3rd post describing results (questions #9-11) is
#21. Short versions of results also added above.
As of 25th July 2012, I'm not actively working on this anymore (will still try to check in on the thread, but not doing testing). See post #33.