[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
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