12 ms·
Is this Duplo train track under too much tension?
- denton-scratch 3y agoThe "answer" (which is rather good) doesn't answer the question about "too much" tension. It explains how to work out whether tension would be expected, and proposes ways to eliminate tension.
- h2odragon 3y agoMy first thought was summing the angles (each curve piece adds or subtracts 7deg of angle or whatever the actual angle is). However the question is false in its initial assumption, i think: if theres too much tension anywhere in the string that joint will separate. These pieces are designed to do that. Perhaps a better way of stating it would've involved the gaps between sections where there might be too much space and lead to derailment.
- jaclaz 3y agoIn the stackexchange thread they say that 12 pieces makes a circle, so each one is 30 degrees, but they also say that you can fit 13 pieces in a "circle", which means that each piece has 30-360/13=2.30 degrees tolerance. The maximum gap should then be in theory be around 2-3 mm, if this drawing is accurate: https://www.eurobricks.com/forum/index.php?/forums/topic/193856-duplo-train-track-accessories-printed-in-3d/&do=findComment&comment=3595907 https://www.eurobricks.com/forum/index.php?/forums/topic/193... https://i.servimg.com/u/f13/17/36/35/47/geom110.jpg https://i.servimg.com/u/f13/17/36/35/47/geom110.jpg But in practice due to the interlocking design, see here: https://www.onemetre.net/OtherTopics/Duplo/Track%20dims/DuploTrack.htm https://www.onemetre.net/OtherTopics/Duplo/Track%20dims/Dupl... there won't be any added gap (besides the ones due to the tolerance in the interlock), the pieces will deform along their length making no gaps capable of derailing at the juctions.
- dncornholio 3y agoHow about letting your kids figure this out. I remember learning to not stress duplo exactly with these pieces, trying to make a loop..
- dclowd9901 3y agoI don’t think OP is genuinely concerned with tension. I think they were just presenting an interesting trigonometry problem.
- deleted 3y ago[deleted]
- jhwhite 3y agoNo one knows the amount of thought I put into this same problem when building train tracks for my son but I had no idea how to solve the problem.
- phkahler 3y ago>> No one knows the amount of thought I put into this same problem when building train tracks for my son but I had no idea how to solve the problem. One piece of flex track bent and cut to length.
- bluescrn 3y agoOr a 3D print: https://www.printables.com/model/126988-set-lego-duplo-train-tracks-optimized https://www.printables.com/model/126988-set-lego-duplo-train...
- mcv 3y agoUnhook one piece, remove all the tension, and see how far the two ends you just created end up from each other. Not very scientific, but it works very well.
- po 3y agoMy friend and I used to discuss a similar question: given a fixed set of curved Duplo tracks, how many different looped track layouts can you generate? Straight sections are mostly ignorable since you can always add them in pairs on opposite sides of the loop if they are parallel. (although there are some interesting triangle-shapes that can be made that break that pattern) My friend even went so far as to code up a solver for it which mostly worked and generated some interesting layouts. We never got around to adding switches into it. It eventually led us to the math behind necklace problems because it was often hard to tell if 2 track layouts were identical: https://en.wikipedia.org/wiki/Necklace_problem https://en.wikipedia.org/wiki/Necklace_problem
- bombcar 3y agoI don't know if Bluebrick supports duplo, but it's a track layout program for Lego track: https://mattzobricks.com/lego-track-planning/bluebrick https://mattzobricks.com/lego-track-planning/bluebrick
- xattt 3y agoThere is indeed a Duplo package!
- po 3y agoYes, I've seen this as well! Thanks for the link. As my kids got older, we upgraded to Lego system track and I was initially very disappointed in it. The math for Lego track is quite different and there is something very satisfying about the Duplo system. The key difference is that switches in Duplo are equivalent to two oppositely curved tracks overlaid on each other. This means you can pop a switch in anywhere that there is a curve piece. In the Lego system track, it is a straight piece with a curve out and back in slightly. If you place two switches together you can connect two parallel tracks, but it has the disadvantage of being harder to place (you end up needing substantial straight sections to use switches)
- bombcar 3y agoThere are a number of third party companies that are filling the missing links (literally) for Lego track geometry. It can be worth investing in - I’ve always been annoyed that the Lego switches are clearly for sidings and yards and not for loops.
- ScottWRobinson 3y ago> However, as a father, I also don't want broken duplo pieces, so I wanted to make sure the track is not too much under tension. The asker severely underestimates the amount of force it takes to break a Duplo piece.
- Pulcinella 3y agoI can confirm that even a 1-by-1 Lego brick can withstand the full weight of an adult human male at 2 in the morning. ...my foot on the other-hand...
- MitPitt 3y agoYour logic is off, smaller pieces are generally harder to break than larger ones
- esprehn 3y agoYup, the 2x2 can hold 950lbs: https://news.ycombinator.com/item?id=4870283 https://news.ycombinator.com/item?id=4870283 We can also observe this (to a lesser degree) when they build two story Lego statues like at the Mall of America. I'll admit I've never seen a huge Duplo statue, but I assume the load limits are similar.
- ivanjermakov 3y agoDoes lego piece strength vary throughout the day?
- ivanjermakov 3y agoCan't you just check the tension by breaking the loop and seeing the offset between the start and end pieces (considering surface friction is low enough for pieces to move)? That would be my puzzle solution to: 1. Assign each piece type it's end offset and next piece connection angle 2. Start at 0,0 coordinate and iterate through pieces, advancing last piece position 3. Check the offset between the start and end pieces And the result would look like images in the answer. Updating the track to minimize offset is harder, though.
- CamouflagedKiwi 3y agoWith a track that size, I don't think surface friction will be low enough for the whole thing to realign itself. The ends of the track near the break will pull apart if there's tension but I can't imagine the whole thing moving.
- joeframbach 3y ago> I don't think surface friction will be low enough for the whole thing to realign itself. Then there's not enough tension to break any pieces either.
- Kaibeezy 3y ago> surface friction Assemble it on the air hockey table? Assemble it on a smooth, flat floor and sprinkle some shuffleboard powder?
- SargeDebian 3y agoYes, as the question states, you could. > I know I could just take one piece out, and put it back in to feel it myself
- logifail 3y ago> considering surface friction is low enough for pieces to move Our experience - which include track layouts that occupy a good proportion of the ground floor of our house, a la Wallace and Gromit's The Wrong Trousers Train Chase - is that if you open a section under tension, wiggle the entire track back and forth a bit, even on a solid wood floor it tends to settle into a "more relaxed" state, at which point you can adjust the relevant pieces to close the (often larger) gap...
- bmmayer1 3y agoMy favorite part about this thread is not the first, very thorough, very mathematical and accurate answer, but the answer below it that has 0 upvotes but is by far the most practical: "I would first check for track flatness" This thread is a great example of how engineering is often NOT a solution to problems, classic "hammer and nail" territory here. And how engineers often ofterthink things unnecessarily ;)
- phreeza 3y agoExcept in my experience as the father of a 2 year old it is not correct. The tracks don't really buckle upwards appreciably.
- TrueGeek 3y agoI'm really curious now. I haven't had 2 year olds for a while. Can you try this and see? Surely there is at least enough warping that you'll see a 1mm rise?
- ckozlowski 3y agoI also have a 2 year old here with these (imagine my surprise to see this on HN), and I've troubleshooted more than one track creation. I can confirm the findings of the above poster. They don't buckle upwards much. There's some margin for error in the connectors that allows for the tracks to pivot some. A degree or two off and you can still get the connector to fit, but you'll feel the tension in the track as one side is fitting much more tightly than the other due to the bend. So introducing another track segment somewhere in the loop (the link goes into the math behind this, but a little observation and intuition will also yield the correct result) will ease the pressure. In my experience this is almost always caused by trying to close the loop a little too tightly. Edit: Re-reading the rest of the "look for track flatness" comment; the second and third sentences about tolerances and bowed joints are spot on. For example, looking at the final track layout for the "mathematical" approach, I can tell you that I'd have no problem shifting that track down an inch and snapping it in place.
- neovive 3y agoDuplo's were the go-to toy in my house for years. The larger size makes it much easier to find pieces in "the big box of Lego" than standard Lego's. Duplo and Lego, in general, have amazing longevity — they were the best toy investment we made over the years. :-). As an aside, these articles are the gems that keep me coming back to HN.
- deleted 3y ago[deleted]
- goldcd 3y agoNo - it's Duplo and designed to be abused. It's not going to suddenly explode into shards of plastic in the middle of the night. Probably need to define "too much tension". Is a bit of tension that enables you to build the thing you want and couldn't otherwise, a good or a bad thing? (e.g. maybe I want a spiral) I'd have thought if overly tensioned, once tolerances were overcome, the track would develop a camber. Maybe build on a perfectly flat, frictionless surface and then if your track isn't perfectly level you know there's tension.
- mhb 3y agoIt's a math problem. Read TFA.
- Retric 3y agoIt’s an engineering program masquerading as a math problem. Long enough racks can have misalignment without noticeable issues because each segment has some play.
- notatoad 3y agoengineering takes into account material properties. the engineering solution is "no, that tension is way inside the design tolerances" the stack overflow answers are math.
- Retric 3y agoThe top rated answer was math, but it ignored the possibility that a section of track would be under tension to avoid intersecting with itself. For a mathematical curve that’s no issue, but physical objects add additional constraints to the problem.
- mhb 3y agoNo. It's the other way around. If someone did FEA on the track and showed you a stress map, it would be obvious how uninteresting framing it as an engineering problem is.
- jacobwilliamroy 3y agoDoes Duplo have the same level of quality control as Lego? Like I can go and buy 10,000 1 x 1 Lego pieces and be sure they'll all be exactly the same within about 10 micrometers. Are Duplo bricks also as insanely QC'd as Lego?
- po 3y agoYes because they're made by the same company in the same way. You can even fit them onto a Lego System plate.
- dolmen 3y agoNot just plate. LEGO builders use DUPLO bricks under as basic for building big landscapes, mountains.
- rr60 3y agoI am assuming they do. Duplo is a type of lego that are meant for younger audiences and thus have large brick sizes. https://en.wikipedia.org/wiki/Lego_Duplo https://en.wikipedia.org/wiki/Lego_Duplo
- Tade0 3y agoI would suspect that yes, considering they're meant to be compatible with regular Lego pieces: https://bricks.stackexchange.com/questions/38/are-duplo-blocks-compatible-with-lego-blocks-in-any-way https://bricks.stackexchange.com/questions/38/are-duplo-bloc...
- speedgoose 3y agoThe quality is very good, and I don’t know similar plastic toys for toddlers with the same quality. I have a lot of Duplo, some are new, some are 20 years old and went through a few toddlers. I can feel difference in tightness. The new ones are much better. Maybe Lego did improve the quality of the Duplo overtime, or they are simply less used. In my case, I also find the old transparent bricks to not hold so well. They don’t handle much load before detaching.
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- andruby 3y agoI prefer the parenting advice in the comments: > Not really an answer to the question as posted — but I think the premise needs some good parenting advice: let your kids break bricks. They are pretty darn durable anyway and fabulously cheap to replace. So when they break one they will begin to learn about over-stressing materials through their own experiences
- deleted 3y ago[deleted]
- zupa-hu 3y agoExactly. I’d much more prefer to explore the opposite direction: figuring out how much you can hack the rules of the game. That fosters creativity while the other fosters bluntly following rules.
- bowsamic 3y agoThe premise was obviously not serious. This seems like concern trolling
- zoomablemind 3y agoMy understanding is that the weak point in danger is the neck of a joint pin on either of the connected tracks. With duplo both links have a key pin and a hole. So when under severe misalignment, one side of the key would be pushed with extra lateral pressure and may deform or break. However, this sort of severe tension is likely to be in effect while attempting to link/lock the last joint. It's likely to be done by the child when the parent is not there to supervise the feasibility of such forced link. The parent will be alerted when it's either too late or when it succeeded and there's no need to fix it. Thus, if it were to snap a key neck, then it's just meant to be... No drama. The second key is still there to maintain the joint. Though caution, if no lesson is drawn, such section would become even weaker link! If it somehow coerced into a loop, then Yay! here comes the locomo. If the train cars don't tip over the forced link gaps or warped sections, then the ride goes on. Otherwise, a tuneup/rebuild is due.
- acquacow 3y agoSince we are discussing Lego strength here, this seems new and relevant to post: https://www.youtube.com/watch?v=l10hJxV4SGo https://www.youtube.com/watch?v=l10hJxV4SGo
- syntaxing 3y agoSomething very similar was my first programming project in college! The easiest method that most of us did was to brute force it and see if the ends were in the same location and angled correctly. Apparently there was a O(n) method that uses discrete mathematics but I didn’t really understand it at the time. It really is a great puzzle to solve.
- UltimateEdge 3y agoSurely following the path of the track (to see if the ends were in the same location and angled correctly, as you describe) is O(n)?
- syntaxing 3y agoProbably should have clarified, the goal of the project was to generate a valid track
- tgv 3y agoNot my first project, but an assignment in the first year. It was about minimizing coin change. I had a solution very different from the others, and the teacher wrote something along the lines of "I suppose that'll work too" on my solution. Can't remember what I came up with, though.
- Akronymus 3y agoCalculate smallest coinage (in terms of value of each coin) amount and progressively replacing them with the next higher amount? 2x1 cent -> 1x 2 cents, 2x2 cents +1x1 cent -> 1x5 cent and so on, maybe?
- lqet 3y agoI found the linked site with an in-depth introduction to Duplo rails even more interesting: https://www.cailliau.org/Alphabetical/L/Lego/Duplo/Train/Rails/Dimensions/%20Dimensions-en.html https://www.cailliau.org/Alphabetical/L/Lego/Duplo/Train/Rai... I owned both "new-type" and "old-type" (black) Duplo rails as a kid. I remember that even as a 4-year-old, I was annoyed with the old-type black rails and greatly preferred the new ones.
- ycombinete 3y agoIs that from the link by user Weathervane? Any idea why the rest of their comment it total gibberish? “gjryir frpgvbaf qb abg znxr na rknpg pvepyr, gurer vf n fznyy bireync, naq fb znxr n pv” etc.?
- robinhouston 3y agoThat's rot13. We used to use it a lot in the good old days, mainly as a way of obscuring spoilers in usenet posts, but sometimes just for fun. I bet I'm not the only person here who can read it – rather haltingly – without decoding it first.
- ycombinete 3y agoGunax lbh! V’z n lbhatre zvyyraavny, naq fgnegrq ba gur arg nsgre gur unlqnl bs Hfrarg. V’yy or hfvat guvf va gur shgher sbe fher.
- crazygringo 3y agoSerious question: is it even under actual "tension" at all? Don't the track pieces fit together loosely? And aren't most Lego/Duplo pieces made of such hard and rigid plastic that they don't effectively bend at all? So while it's still an interesting math problem about angles and lengths, I'm not sure the premise of "tension" is correct here.
- kfarr 3y agoFWIW you can get duplo track under enough tension that the tracks no longer have loose give and you can lift it up the entire track without it coming apart. It requires a bit of work to make a track like the one in OP
- mensetmanusman 3y agoOne half of the duplo can be in tension and the other half in compression.
- aendruk 3y agoStress if you’re looking for more precise language.
- eesmith 3y agoThey certainly do bend. You can stack Lego pieces into a circle, like https://www.instructables.com/Lego-Circle/ https://www.instructables.com/Lego-Circle/ . I've done the same with (enough) Duplo.
- modeless 3y agoI highly recommend anyone interested in the question of whether Legos can bend to watch some videos from this channel: https://youtu.be/lp7cFcnJCH4?si=eYMf8rcTpv_2DD-B https://youtu.be/lp7cFcnJCH4?si=eYMf8rcTpv_2DD-B Some amazing "illegal" Lego creations there.
- _whiteCaps_ 3y agoAmazing creations! But the sound of those bending Lego bricks made my teeth hurt, I had to mute the video. :-|
- jcrash 3y agoGee, based on these comments you'd think some of these HNers have never read a math word-problem. Or did you all think that guy really did need 98 oranges?
- bowsamic 3y agoYeah getting a similar feeling. Lots of moral grandstanding about it too. HNers can’t see a fun thing without finding a way that it’s “problematic” or “misleading”
- lostlogin 3y agoPut another way, they played trains with the kids, then argued about layout options with some other adult after bedtime, and came up with some novel solutions which were tested with the kids next day. However if I’m any guide, a basic game ends up with me fighting a broken soldering iron or a bug in some language I don’t understand while the kid asks if we are there yet.
- sentientslug 3y agoYeah, a perfect thread to demonstrate the lower than average social literacy of HN users. It makes this community come off as a bunch of fun haters. This kind of fun low stakes “engineering problem” is exactly the type of thing that should be shared here, but everyone’s a critic I guess.
- mcv 3y agoNot sure what the two of you are complaining about. It's really just this sub-thread that's all complaining. Everybody else is sharing fun stuff.
- jcrash 3y agoWhen I originally commented a high number of the posts were taking OPs question very literally. You can scroll to the bottom of the comments to see a few of them.
- modeless 3y agoI haven't seen anyone else say that the easiest way in practice is simply to jiggle the track. In a correct duplo track every piece will be loose and easily move a few millimeters when jiggled. If any pieces are snug then the track is under tension. No need to remove a piece. I suppose if the track is big enough then you would be able to insert a "wrong" piece without necessarily using up all the slack, so the pieces would still be somewhat loose. But in that case there would be no mechanical concern to worry about. Actually I suspect that it suffices to check one piece. If any piece is in tension then they all will be, assuming friction with the floor is not too large. Unless you have intersections in the track, then you have to check each loop separately, or maybe you could just check the switch pieces. Might be an interesting math problem there to minimize the number of pieces to check in complex tracks. I'll also point out that bending Lego pieces isn't always bad: https://youtube.com/@BrickBending https://youtube.com/@BrickBending
- RandallBrown 3y agoThe original asker of the question actually proposed that already. > I know I could just take one piece out, and put it back in to feel it myself, but I am looking for a more logical way Since that's the "puzzling" stack exchange, I think they were looking at this more as a logic problem than a real practical problem they needed to solve.
- modeless 3y agoRight, that's why I'm not posting this as an answer to the stack exchange question. Though I'm pointing out that it's not necessary to remove any pieces, and also suggesting that there may be an interesting math problem still there in this case.
- vanderZwan 3y agoI guess the obvious question is "given x amount of slack per piece, after how many pieces can I fit in on piece the wrong way without tension", but that feels more like an engineering problem than a math puzzle.
- firesteelrain 3y agoWhy is this in the puzzling stackexchange?
- the_af 3y agoI think you can consider the problem of optimally laying out the train tracks to reduce stress a kind of puzzle. Even less convoluted: the tracks must be assembled in a shape, and so are a sort of puzzle. The asker is asking a question about the geometry of the puzzle.
- mikewarot 3y agoAre the kids having fun? Does the train slide around the track easily enough? Duplo, while expensive, is a consumable, if you look at it through this old man's eyes. Now that that's out of the way, I love all the answers here.
- bowsamic 3y agoThat’s the joke. He’s taking something obviously not important and turning it into a puzzle pedantically. If it were an important thing like a train bridge it would be less interesting
- lapetitejort 3y agoThis track transports hundreds of Duplo citizens and various other toys daily. Damaged parts will not be able to be replaced until next birthday or Christmas, leading to significant delays. Furthermore, if the train were to snap mid play session, a citizen could be flung into the wall leading to loss of limb, which are not easily fixable like Lego minifigures. The train track is a critical part of playroom infrastructure and thus affords extra scrutiny.
- ALittleLight 3y agoIt would still be interesting as a train bridge, just for different reasons. The reason bridge you know that lives and material are on the line. For the child's train set you realize that there are deep and abstract principles underlying even childish things.
- ZeWaka 3y agoReminds me a lot of turning numbers.
- lacrimacida 3y agoNot sure if duplo has it but regular sized lego has a type of track that is flexible and very good at relieve the track coupling tension. This is available from lego as generic bricks lego and are good enough and much cheaper.
- RichieAHB 3y agoSimpsons aside: I wish this was titled "Is there a chance the track could bend?".
- teachrdan 3y agoNot on your life, my hacker friend.
- sircastor 3y agoI have a 5-year-old and we frequently assemble wooden BRIO train tracks in a variety of configurations. As he's building out track, I'm often a few steps behind him, silently reworking the track configuration so it's not over-constrained. It typically ends up being a fun, if not simple problem solving challenge that I get to spend time with kid my at.
- trgn 3y agotangential comment: What I like about brio tracks is that they don't trash up the house like plastic tracks from other sets. They just look nice, feel good to the touch. The slow speed but high torque of the trains also feel like it gives "mass" (not sure how to phrase it) to the experience, unlike a lot of remote controlled toys, which go way too fast for their size but struggle with carpets, edges, ...
- bick_nyers 3y agoI played with them a lot as a kid, and I distinctly remember enjoying the sound the wheels made turning against the wood, as well as the tactile sensation of moving the train across it with my hand. This makes me want to get a CNC machine and start spitting out train tracks! I already know when I retire in 30 years I'm gonna be one of those guys that has a train room.
- dolmen 3y agoMy retired father did that: my kids got track extensions he made himself. His wood processing tools were much simpler than a CNC machine though. However, it's quite easy to find second hand Brio tracks.
- bredren 3y agoI’m at the start of my brio journey. Haven’t picked up a set yet as we are immersed in magnatiles. Curious if anyone has milled their own brio tracks. (Maybe to allow some unusual shapes not afforded by standard types) I’ve made a single brio track compatible banana car but haven’t had a go at making any track yet.
- the_af 3y agoI'm ashamed to admit I often wonder about this when playingˆHˆHˆHˆHˆHˆHˆH my daughter plays with myˆHˆH her Duplo train. Except for the simplest of tracks, I often wonder if the misalignment of a complex track is not stressing the pieces. Of course, instead of asking in stackexchange I dismiss the thought and just play -- er, my daughter plays -- with the train.
- Eduard 3y ago> I'm ashamed to admit I often wonder about this when playingˆHˆHˆHˆHˆHˆHˆH my daughter plays with myˆHˆH her Duplo train. nice insider joke :) https://en.m.wikipedia.org/wiki/ASCII_control_characters https://en.m.wikipedia.org/wiki/ASCII_control_characters
- guitarlimeo 3y agoIndeed, I liked that as well
- zik 3y ago^H used to be a common idiom back in the usenet news days
- sytringy05 3y agoIt’s from the original borne / korn shell in Unix. Ctrl H was backspace, but the pc keyboards would send a different control character. you often had to map the backspace on the pc keyboard to make it work properly. Set -o or something like that.
- euroderf 3y agoAnd then it got even worse when you mixed in X Windows. "Delete" or something.
- okamiueru 3y agoThanks for explaining it.
- tylerneylon 3y agoI suspect the mathematical analysis could be even simpler. Here's one idea: View each track piece as a 2d vector. Add up the vectors. In a zero-tension setup, the sum is (0, 0). As a metric for tension, assume any mismatch in position is evenly distributed. Model this as the average of all the vectors. (Thus the same displacement is more meaningful when we have fewer pieces.) ___ That's the full idea. It might seem that it is ignoring rotation, because it doesn't explicitly mention rotations, but they are included because the effective vector that a track piece provides is both a current direction as well as the displacement contributed by that piece. If we wrote some code to model this, a cursor would consist of a direction (an angle) along with an (x, y) position. ___ Some related math concepts: * The exterior angles of a polygon sum to 360. So we could have another measure which is how far we are away from 360. * Not useful in this case, but this also reminds me of winding numbers from complex analysis, which is a way to locally walk along a curve to understand which side is the "inside" or how many times a curve goes around a given point.
- hgsgm 3y agoHow is that different from the solution on the page?
- tylerneylon 3y agoTo give the answer credit, that answer does suggest adding the vectors (the same). It is also much more thorough than what I said, and I like the images. I like the answer and I was attempting to iterate. I think these two things could be improved from that answer: * I'm suggesting a general approach to measuring track tension, which is the average of the vectors. I didn't see that idea in the answer. * I think the answer could be communicated a little more simply. For example, we don't need to think in terms of Q[sqrt(3)]; I see that as a distraction.
- aleph_minus_one 3y ago> For example, we don't need to think in terms of Q[sqrt(3)]; I see that as a distraction. Except for replacing Q[sqrt(3)] by a suitable ring extension of Z, I see no possibiliy to simplify the argument. So what kind of simplification do you have in mind?
- rdberry 3y agoAs a kid I would trace around the track. Starting with zero, I would add one if the track bent left and subtract one if it bent right. The answer needed to be +/- 12, 24, etc. because 12 make a circle.
- the__prestige 3y agoCan someone please ELI5 why this is true?
- silvester23 3y agoA full circle is 360° and a curved piece makes a turn of 30°, so you need 360° / 30° = 12 pieces turning in the same direction to make a full circle. Every time you use a piece turning the other way, you need to add an extra piece turning the way you want to complete the circle, so the difference between the directions has to be 12. Note, however, that not every track with exactly 12 more pieces turning one way than the other necessarily makes a complete circle, straight pieces can cause the ends not to match up.
- travisgriggs 3y agoI love the other .stackexchange forums. These types of questions and the answers they engender are great. I've seen some great discussions on aviation, ux, and math over the years. Long detailed answers with cool insights. A few hours ago, there was another HN post from the latin one. But (for me), the same is no longer true for stackoverflow. I used to participate on it both as an asker and an answerer. But something happened. It felt like it was a takeover by ever pedantic moderators. Now I participate there only rarely.
- custard42 3y agoLook through a polarized filter to spot places under stress? At least that might work if it was plastic.
- robinhouston 3y agoDanny Calegari posted a very interesting mathematical analysis of a similar question (but only considering curved pieces) to his blog in 2011: https://lamington.wordpress.com/2011/12/02/laying-train-tracks/ https://lamington.wordpress.com/2011/12/02/laying-train-trac...
- happy-capybara 3y agoThis reminds me of a problem on Project Euler [1] with a different turn angle. In the problem you can go through the same path several times though. [1] https://projecteuler.net/problem=208 https://projecteuler.net/problem=208
- f154hfds 3y agoI have a duplo/lego question - is there a name for the combinatorics problem of how many structures can be built with N 1XM legos? I have spent a fair bit of time thinking about this problem and I'm unaware if it's been posed elsewhere. Any piece able to freely rotate is considered the same structure. For example, for 2 1X2 legos the arrangement count is 2: top connected to bottom with both nubs, top connected to bottom with one nub because if you analyze legos you will find that such an arrangement can freely rotate over 270 degrees, and left vs right nubs result in the same structure when taking rotational symmetry into account. For the problem I assume an 'ideal' lego with 0 manufacturing tolerance, no illegal building techniques are allowed. Is there a name for the above combinatorics question? Is it well-posed? Is there a closed-form solution? If not is there a generator program? I should say that with a high enough N any generator would be very complex - imagine how degrees of rotational freedom give rise to the possibility of further structures hidden from other rotational orientations.
- orlp 3y agoLook into the work of Søren Eilers https://arxiv.org/abs/math/0504039 https://arxiv.org/abs/math/0504039 https://www.tandfonline.com/doi/abs/10.4169/amer.math.monthly.123.5.415 https://www.tandfonline.com/doi/abs/10.4169/amer.math.monthl... (for the latter: use sci-hub) Then there is also work for the 2D case by Tricia Muldoon Brown: https://www.sciencedirect.com/science/article/pii/S0012365X17300456 https://www.sciencedirect.com/science/article/pii/S0012365X1... https://arxiv.org/abs/1608.01562 https://arxiv.org/abs/1608.01562 as well as by Alexander M. Haupt: https://arxiv.org/abs/1810.10428 https://arxiv.org/abs/1810.10428
- thanatos519 3y agoThere is a display about the case of 6 1x4 bricks at Lego House in Billund. It's beside a machine molding 1x4 bricks and packing 6 of them into a bag which you can take for free.
- garblegarble 3y agoThat's quite neat! For anyone else who's interested, I found a video of this online[1] 1: https://www.youtube.com/shorts/iKs_zr6_qMg https://www.youtube.com/shorts/iKs_zr6_qMg
- anthonypro123 3y ago[flagged]
- anthonypro123 3y ago[flagged]
- anthonypro123 3y ago[flagged]
- Not_John 3y agoI have the suspicion that this could be a future Advent of Code Puzzle.
- bdavbdav 3y agoWe have an incomplete toot toot garage track set. Over stressing the parts is the only path to greatness.
- puzzledobserver 3y agoDoes the answer to this question also depend on the order in which the pieces are laid out? I suspect yes.
- userbinator 3y agoA great way to introduce young kids to Young's modulus.
- syntaxing 3y agoYoung’s modulus is the linear relationship between stress and strain in the elastic region, which does not exist for plastic parts (since the relationship is nonlinear and it’s mostly nonelastic aka plastic).
- jjk166 3y agoPlastic parts most certainly do have both an elastic region and a Young's modulus. Young's modulus is the slope of the curve during elastic deformation (the form of deformation where the part returns to its original shape after the force is removed) and is a measure of a material's inherent stiffness. All solids have a Young's modulus. Take a piece of plastic and bend it a little, then let go. It is elastic. Plastic deformation is the state passed the yielding where the part will not return to its original shape. Plastic the material and plastic the form of deformation are independently named from the greek plastikos: able to be shaped or molded.
- syntaxing 3y agoThere are undoubtedly elastic regions of plastic material but there are very few plastics with a linear relationship of stress strain (aka Young’s modulus). This is why for most FEA, the stress strain ratio is a lookup table rather a constant for plastic material. In addition, some plastic exhibit a non-Newtonian property. Long story short , Young’s modulus is not applicable for plastic parts. Also, it is not true all solids must have a one.
- jjk166 3y agoYou have absolutely no idea what you are talking about. The elastic region (there can only be one) is the range where a material has a linear relationship of tensile stress and strain. Every plastic and every solid has such a region, it is part of the definition of a solid. Again, the Young's modulus is just the slope of the curve at zero, it is mathematically impossible not to have one. All but the most brittle of materials have non linear stress strain relationships, and for FEA all materials use a look up table instead of using a constant value, because that's the point of FEA. Non-newtonian behavior is completely unrelated, instead dealing with a material's stress and time relationship, and again is not exclusive to plastics. Again, the terms plastic as in deformation and plastic as in the material are an etymological coincidence and don't have anything to do with one another.
- fudged71 3y agoOh great! Another simple item in my life ruined by esoteric factoids at the back of my brain
- deleted 3y ago[deleted]
- tabtab 3y agoUse 1950's logic: Until it puts an eye out, it's fine.
- PublicCoconut 3y ago[dead]
- euroderf 3y agoThis is a great discussion because... Märklin C-track is sectional too, but has rather tight tolerances for assembly. There is no flex C-track. A computational method for solving parts lists and connection plans would be fantastic. Currently people do it "by hand (virtually)" with a variety of apps, but that is labor-intensive. Where is the combinatorial algebra?
- counterpartyrsk 3y agoThere is a chance for humanity after all!
- plaidfuji 3y agoIt sounds like this problem may be simpler with Brios than Duplos as Brios only require 2 curves to turn 90 degrees vs 3 for Duplos, but.. my solution to this has always been to use the grain of the wood floor as a guide (which they have in this picture, but aren’t aligned with) - start your track aligned with a floorboard, and then every set of 2 (Brio) or 3 curves, check that you are either parallel or perpendicular to the grain.
- em0sh 3y agoHello hello! Licensed Mechanical Engineer here. Not to be pedantic, but the track wouldn't be in "tension". It would be in bending (a combination of tension and compression). Happy to elaborate further if it is valuable to the discourse!
- dave333 3y agoWhen creating a layout use of symmetry makes it easy to ensure the track will line up and fit in a zero-tension closed loop of whatever shape. So if you add a piece to the track with an initial direction, add the same piece to any point that is a net half turn, i.e. 180 degrees in the other direction.
- kisonecat 3y agohttps://lamington.wordpress.com/2011/12/02/laying-train-tracks/ https://lamington.wordpress.com/2011/12/02/laying-train-trac... is a blog post from the geometer Danny Calegari about this topic.
- coolspot 3y agoHow long until multi-modal LLM can solve this question to the level of top answer?
- euroderf 3y agoMy 3yo can sit endlessly, trying to transform a pile of track pieces into a pleasing layout. Try something, retry something, eyeball it, bend it, take it apart and try again. Does this indicate any sort of predilection for math or for engineering ? Or is it just a usual sort of kid behavior ?