[HN Gopher] Is this Duplo train track under too much tension? ___________________________________________________________________ Is this Duplo train track under too much tension? Author : robin_reala Score : 780 points Date : 2023-09-06 13:21 UTC (6 hours ago) (HTM) web link (puzzling.stackexchange.com) (TXT) w3m dump (puzzling.stackexchange.com) | custard42 wrote: | Look through a polarized filter to spot places under stress? At | least that might work if it was plastic. | happy-capybara wrote: | This 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 | bdavbdav wrote: | We have an incomplete toot toot garage track set. Over stressing | the parts is the only path to greatness. | modeless wrote: | I 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 | RandallBrown wrote: | The 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. | charcircuit wrote: | I am sure this could be calculated mathematically, but I | prefer a more quick, practical way. | | Jiggling is way more practical than having to do many | additions against a lookup table. | throwbadubadu wrote: | Yes, but he refines what he meant with practical, physical | approach is out, don't touch ;) | brewdad wrote: | As always, ChatGPT seems to be the answer. Quick, | practical, and possibly even correct. | modeless wrote: | Right, 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 wrote: | I 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. | 867-5309 wrote: | then what would an engineer use to solve the problem? | [deleted] | andruby wrote: | I 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 | zupa-hu wrote: | Exactly. 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. | [deleted] | bowsamic wrote: | The premise was obviously not serious. This seems like concern | trolling | denton-scratch wrote: | The "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. | ivanjermakov wrote: | Can'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. | logifail wrote: | > 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... | Kaibeezy wrote: | > _surface friction_ | | Assemble it on the air hockey table? | | Assemble it on a smooth, flat floor and sprinkle some | shuffleboard powder? | CamouflagedKiwi wrote: | With 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 wrote: | > 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. | SargeDebian wrote: | Yes, as the question states, you could. | | > I know I could just take one piece out, and put it back in to | feel it myself | f154hfds wrote: | I 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 wrote: | Look into the work of Soren Eilers | | https://arxiv.org/abs/math/0504039 | | 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/S0012365X1... | | https://arxiv.org/abs/1608.01562 | | as well as by Alexander M. Haupt: | | https://arxiv.org/abs/1810.10428 | thanatos519 wrote: | There 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. | robinhouston wrote: | Danny 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-trac... | lacrimacida wrote: | Not 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. | sircastor wrote: | I 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 wrote: | tangential 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 wrote: | I 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. | puzzledobserver wrote: | Does the answer to this question also depend on the order in | which the pieces are laid out? I suspect yes. | anthonypro123 wrote: | a | anthonypro123 wrote: | s | anthonypro123 wrote: | chhh | Not_John wrote: | I have the suspicion that this could be a future Advent of Code | Puzzle. | mikewarot wrote: | Are 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. | [deleted] | bowsamic wrote: | That'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 | bartread wrote: | This is what I love about the whole discussion. In some sense | this is so utterly trivial, but I imagine the kids would be | pretty upset if they broke a piece of the Duplo too. And I | love that we've all absolutely nerded out on it, and gone in | a dozen different directions with the discussion. It's just | fun and, what makes it even more entertaining, is that so | many people have engaged with it - as I write this it's | literally at the top of the front page, where it's already | been for at least a couple of hours, and closing in on 600 | points. It's a great and positive conversation, and it's | certainly added a bit of happiness to my day - I suspect lots | of other peoples' too. | lapetitejort wrote: | This 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. | xattt wrote: | Who's engineer that signed off on a track design that was | under too much tension? They need to be reprimanded | immediately! | dmd wrote: | Reprimanded is software "engineer" thinking. A P.E. who | signed off on that could go to jail. | ALittleLight wrote: | It 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. | mrighele wrote: | Duplo pieces are extremely durable so I wouldn't worry about | them getting broken (as my poor feet can attest). If else one | should be careful because with enough tension one piece may | detach from the track and fly around hitting somebody. | lqet wrote: | I found the linked site with an in-depth introduction to Duplo | rails even more interesting: | | 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. | zoomablemind wrote: | My 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. | bmmayer1 wrote: | My 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 ;) | hedora wrote: | My second favorite part is that it got me to install bsdgames | on my laptop so I could decode the rot13 quote. | rob74 wrote: | Well, it's Puzzling SE, so I guess people are more likely to | give (and upvote) theory-heavy answers. The "unloved" practical | answer would probably be more popular on Home Improvement SE. | But SE sites also tend to reward elaborate answers, even if | they're not 100% correct. For instance, the accepted answer on | this Aviation SE question | https://aviation.stackexchange.com/questions/94879/why-does-... | is not really correct, while my (very convincing, even if I say | so myself) answer only got 2 upvotes - Ok, the fact that I | posted it 2 weeks after the other answer also might have | something to do with it... | thih9 wrote: | I don't think it would work in practice. Duplo tracks are thick | and bendy enough that they would stay in place and hold the | tension. Maybe some excessive misalignment would cause the | track to be lifted, but the idea was to detect that at an | earlier stage, as indicated in the original question ("I know I | could just take one piece out, and put it back in to feel it | myself"). | nomel wrote: | > enough that they would stay in place and hold the tension | | Then, what's the issue? "Too much tension" is the question. A | reasonable definition of "too much" is possible damage or | that it affects performance. | | Having experience with these, if it's sitting on the ground | flat, and it's not being help there, then it's about an order | of magnitude away from "too much", for damage. | | "No tension" is a different question. | konschubert wrote: | The issue would be that you wouldn't have a nice problem to | think about on the puzzle stack exchange. :) | thih9 wrote: | Assembling and disassembling a track under tension requires | more force, it is easier to break it. | nomel wrote: | I'm sorry, but you must not be familiar with Duplo | tracks. This is an over engineered child's toy, | specifically designed with knowledge that they will be | abused. | | Again, if it's flat on the ground, it's far from the | point where something breaking is a concern. | krisoft wrote: | > very mathematical and accurate answer | | I'm afraid it is not accurate at all because it is not | answering the question as asked. It verifies that the track is | under tension, but it doesn't attempt to answer if that tension | is "too much". Which is what the question asks. | mahogany wrote: | > It verifies that the track is under tension, but it doesn't | attempt to answer if that tension is "too much". Which is | what the question asks. | | I think you (and many others in this thread) are confused | because you read the title but not the body of the OP. | Quoted: | | > 1. Is there any way to quickly see if there is any tension, | and why? (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, so I am able to reason it.) | | > 2. Suppose I want to update the track in the picture to | have less tension. If you have to take away exactly 1 rail | piece (straight or curved), which one is the best, and why? | If you have to add exactly 1 rail piece (straight or curved), | what is the optimal place to insert one? | | The accepted answer attempts to address these questions. | derefr wrote: | The OP, though, didn't mean "too much" as in "out of | tolerance", but rather "too much" as in "has progressed from | stress to strain and therefore is decreasing the useful | lifetime of the parts." | [deleted] | slingnow wrote: | OK, great. So can you explain how the mathematical answer | is a solution to your interpretation? | | Spoiler alert: it didn't. Nowhere does the mathematical | answer address the question of "too much". | | And what do you mean by "progressed from stress to strain?" | Stress doesn't turn into strain, they exist simultaneously. | You're probably trying to say progressed from elastic | deformation to plastic deformation. | tedunangst wrote: | The funny part is checking for flatness is also a mathematical | answer. Twisting into 3D is how ideal track pieces would | resolve an incorrect configuration. | mannykannot wrote: | The engineering approach determines that there will be stress | _and_ proposes a mitigation. That 's a win for engineering in | my book. | [deleted] | phreeza wrote: | Except in my experience as the father of a 2 year old it is not | correct. The tracks don't really buckle upwards appreciably. | neovive wrote: | Duplo'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. | TrueGeek wrote: | I'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 wrote: | I 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. | ZeWaka wrote: | Reminds me a lot of turning numbers. | dncornholio wrote: | How about letting your kids figure this out. I remember learning | to not stress duplo exactly with these pieces, trying to make a | loop.. | dclowd9901 wrote: | I don't think OP is genuinely concerned with tension. I think | they were just presenting an interesting trigonometry problem. | anigbrowl wrote: | Perhaps, but they should have just said 'I'm nerding out on | this' rather than dressing it up in a 'concerned parent' | onesie. | [deleted] | ascorbic wrote: | They posted it on the puzzling stackexchange, not the | parenting (or LEGO) one. | [deleted] | tylerneylon wrote: | I 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 wrote: | How is that different from the solution on the page? | lightbendover wrote: | For starters, the "solution" here doesn't ensure that the | ending piece meets the starting piece in the right direction. | :p | tylerneylon wrote: | To 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. | charlieboardman wrote: | To expand on the angles of a polygon idea. It looks like each | of these tracks has about a 30 degree bend. So you should have | 360/30 = 12 more right-handed than left-handed tracks, or vice | versa. It takes some counting, but you could probably get | pretty quick at going around the track and adding or | subtracting 1. If you end at 12, perfect. Your distance from 12 | is an estimator for tension. | yummypaint wrote: | I don't have a quantitative argument, but my intuition is that | it might still be possible to make a track that globally has no | net tension, yet still has "local" tension somewhere. This | might be done by creating a shape that slightly intersects | itself, pushing that section into tension, while a | complementary section sums to the negative of the first section | but without self-intersection. | [deleted] | jhwhite wrote: | 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. | phkahler wrote: | >> 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 wrote: | Or a 3D print: https://www.printables.com/model/126988-set- | lego-duplo-train... | RichieAHB wrote: | Simpsons aside: I wish this was titled "Is there a chance the | track could bend?". | teachrdan wrote: | Not on your life, my hacker friend. | the_af wrote: | I'm ashamed to admit I often wonder about this when | playing^H^H^H^H^H^H^H my daughter plays with my^H^H 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. | seabass-labrax wrote: | What material are the pieces made out of? Wooden pieces (when | properly dried) have a much larger ratio of elastic range to | plastic range, which is probably desirable for toys (as | you/your daughter would need lots of leverage to be able break | the pieces and could effectively never bend them). | the_af wrote: | Lego Duplo is the same plastic as regular Lego, I think. | Eduard wrote: | > I'm ashamed to admit I often wonder about this when | playing^H^H^H^H^H^H^H my daughter plays with my^H^H her Duplo | train. | | nice insider joke :) | | https://en.m.wikipedia.org/wiki/ASCII_control_characters | goldcd wrote: | No - 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. | [deleted] | mhb wrote: | It's a math problem. Read TFA. | slingnow wrote: | "Too much tension" is not a math problem. It's an engineering | problem (and a poorly defined one, at that). | | Try thinking for a few seconds before posting such a | meritless dismissal. | mhb wrote: | goldcd> It's not going to suddenly explode into shards of | plastic in the middle of the night. | | That gives you the impression that goldcd fully | comprehended the scope of the inquiry? | Retric wrote: | It's an engineering program masquerading as a math problem. | Long enough racks can have misalignment without noticeable | issues because each segment has some play. | mhb wrote: | No. 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. | lostlogin wrote: | I'd argue is a chemistry problem, or maybe material | science, as the type of plastic dictates the stress | tolerance. | Retric wrote: | The question opens with a question about the material | properties of a physical object and many of the replies | address that. | | As a pure math problem it's got a few constraints such as | the track not physically intersecting with itself which | go beyond the stated question. | | So yes it's a toy problem, but one constrained by real | world objects. | hgsgm wrote: | It's a real world problem, but one constrained by toy | objects. | mhb wrote: | Yeah, that's human interest to get you interested in the | problem and how it occurred to the author. Do you think | the trolley problem is about trolley cars on rails with | switches? | Retric wrote: | The most upvoted response was objectively wrong due to | real world constraints. | | The real world is irrelevant in the trolly problem or the | 4 color theorem etc. | | You may personally be interested in it as a purely | mathematical problem, but he's looking for a real world | answer so poor abstractions are useless. On the other | hand "I would first check for track flatness. When locked | in with extra effort, the loop will warp a little, | basically going into 3d instead of flat 2d." is a useful | shortcut. | mhb wrote: | > he's looking for a real world answer | | Based on his history in StackExchange, it is unlikely | Lezzup is looking for a real world answer. The top tags | of his posts are: mathematics, sudoku, geometry, logical- | deduction, sequence, and enigmatic-puzzle. | | https://puzzling.stackexchange.com/users/84683/lezzup | Retric wrote: | "I am sure this could be calculated mathematically, but | _I prefer a more quick, practical way."_ | notatoad wrote: | engineering 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 wrote: | The 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. | goldcd wrote: | and I quote "I am sure this could be calculated | mathematically, but I prefer a more quick, practical way." | rdberry wrote: | As 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. | travisgriggs wrote: | I 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. | h2odragon wrote: | My 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 wrote: | In 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/193... | | 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/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. | acquacow wrote: | Since we are discussing Lego strength here, this seems new and | relevant to post: https://www.youtube.com/watch?v=l10hJxV4SGo | firesteelrain wrote: | Why is this in the puzzling stackexchange? | the_af wrote: | I 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. | crazygringo wrote: | Serious 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. | modeless wrote: | I 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 | | Some amazing "illegal" Lego creations there. | _whiteCaps_ wrote: | Amazing creations! | | But the sound of those bending Lego bricks made my teeth | hurt, I had to mute the video. :-| | kfarr wrote: | FWIW 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 wrote: | One half of the duplo can be in tension and the other half in | compression. | aendruk wrote: | _Stress_ if you're looking for more precise language. | eesmith wrote: | They certainly do bend. You can stack Lego pieces into a | circle, like https://www.instructables.com/Lego-Circle/ . I've | done the same with (enough) Duplo. | po wrote: | My 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 | lostlogin wrote: | The idea that playing trains with the kids ended up this far | down the rabbit hole is very funny. | amenghra wrote: | https://blog.jgc.org/2010/01/more-fun-with-toys-ikea-lillabo... | looked into building different tracks with a single ikea train | set. | bombcar wrote: | I don't know if Bluebrick supports duplo, but it's a track | layout program for Lego track: https://mattzobricks.com/lego- | track-planning/bluebrick | xattt wrote: | There is indeed a Duplo package! | ScottWRobinson wrote: | > 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. | brnt wrote: | I managed to bend a Duplo track as a schild, the puzzle piece | connecting them specifically. | | A quick but incomplete algo is to ensure an even number of | curves and straights. With them even, a bent track needs to be | very bent so as to be immediately obvious. | Pulcinella wrote: | I 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... | ivanjermakov wrote: | Does lego piece strength vary throughout the day? | Pulcinella wrote: | It was a joke about stepping on one of my kids' legos in | the middle of the night while half asleep. | jodrellblank wrote: | "We can say there is at least one cow in Scotland, of which | at least one side appears to be brown." | | https://stepinmath.wordpress.com/2016/08/27/logic-with- | the-c... | adrianmonk wrote: | If we're getting technical, the weight of a human does vary | throughout the day. Generally, while asleep, your mass | decreases. You're always gradually losing mass as you | inhale O2 and exhale CO2. You're also losing mass as you | exhale moisture, and you may also sweat. | | Thus an adult human male (who sleeps, say, 10pm to 6am) is | less likely to break a lego brick at 2am than at midnight | and more likely than at 4am. | macintux wrote: | When I weigh myself, I make sure to do it in the morning. | Too depressing otherwise. | [deleted] | hef19898 wrote: | Strength I don't know. Pointiness does for sure. | giantg2 wrote: | Perhaps. Plastic structural rigidity varies with | twmperature. Temperatures fluctuate throughout the day. | This natural variation is probably insignificant in most | cases though. | [deleted] | MitPitt wrote: | Your logic is off, smaller pieces are generally harder to | break than larger ones | esprehn wrote: | Yup, the 2x2 can hold 950lbs: | 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. | xyzelement wrote: | In the picture in the story, the light gray pieces seem like | Duplo ones and dark is the "duple compatible" from amazon. | saiya-jin wrote: | Not really, I have similar or actually probably same sets | (and same 'topics' to think about with various bridges and | tunnels, track splits etc). I also have these straight or | curved stuff in light and darker gray. Cheap non-original | stuff is easy to spot - it simply doesn't fit nor hold as | well. It doesn't matter whether its bricks or different | stuff. | | Due to economy of scales, Lego can manufacture those at | consistently high quality and relatively reasonable prices. | Competition aiming for same quality would be at least | similarly priced. Also, its incredibly sturdy. So far I | haven't seen a single one crack or break in past 2 years. My | kids are not psychos but they for sure have no idea yet about | treating their toys with care. | [deleted] | syntaxing wrote: | Something 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 wrote: | Surely 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)? | tgv wrote: | Not 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 wrote: | Calculate 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? | jcrash wrote: | Gee, 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? | sentientslug wrote: | Yeah, 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. | bowsamic wrote: | Yeah 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 wrote: | Put 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. | jacobwilliamroy wrote: | Does 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? | Tade0 wrote: | I would suspect that yes, considering they're meant to be | compatible with regular Lego pieces: | | https://bricks.stackexchange.com/questions/38/are-duplo-bloc... | speedgoose wrote: | The 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. | po wrote: | Yes because they're made by the same company in the same way. | You can even fit them onto a Lego System plate. | rr60 wrote: | I 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 ___________________________________________________________________ (page generated 2023-09-06 20:00 UTC)