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.
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:
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.
Unhook 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.
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.
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)
There 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.
Perhaps. Plastic structural rigidity varies with twmperature. Temperatures fluctuate throughout the day. This natural variation is probably insignificant in most cases though.
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.
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.
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.
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.
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.
> 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...
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 ;)
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?
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.
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.
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").
> 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.
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.
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.
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."
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.
> 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.
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...
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.
The comment reminds of a story I heard as a kid where some famous eexperimental physicist wanted to test a new theoretical member of his lab by giving him an extremely complicated shape and asked him to determine the volume.
Several days and derivations later, the theorist reports the volume, after which the experimentalist tosses the shape into a volumetric flask and determines the volume by looking at the difference in flask volume levels. (I am unable to track this story down to its original)
In the real world there are tolerances, so at my job I rarely have to get the correct answer which can be really hard, I just have to get close to the correct answer which can still be hard, but compared to actually solving the problem, it's a lot easier.
Now because I work in a textile mill, the tolerance I usually get is 0.125 inches which is huge. I usually go all the way down to 0.0001 inches because I think it's funny, and also I do have aspirations beyond just working with textiles.
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.
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.
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.
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.
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?
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.
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.
As it seems that English is not his first language, and that quote you offered appears to contradict "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", and based on the provenance of his other postings, these appeals to contort the question into some kind of uninteresting material science one are not credible.
There’s no contradiction to “logical methods” including things like noticing the pieces curve into 3D space because they don’t fit together. Saying you don’t want to rely on taking it apart doesn’t invalidate simple inspection.
The fastest solution is going to be a combination of heuristics and multiple forms of mathematical modeling. Something like 1 does it look reasonable, 2 do the internal angles add up correctly, then 3 a more precise assessment based on actual curves and piece lengths. Doing 3 when it already failed 2 is redundant.
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?
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.
I would hope so. Imagine only focusing on making really good plastic bricks for 53 years. There have probably been a lot of technological advancements over time that have let them make more bricks more precisely.
> 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
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.
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.
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.
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.
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?
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.
Is 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.?
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
The proper term is stress? Since there is also compression.
My 3yo son usually ends up with really "tense" tracks if he manages to build a circle. The lever torque of the track length makes them bend a tiny bit, so there should be tension in the outer rail. The fittings are quite close fits.
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?
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”
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.
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.
Introductory math word problems often involve unrealistic quantities of things. "Alice had 100 oranges and Bob took two. How many does Alice have?" That sort of thing.
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.
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.
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.
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.
In this case not-so-brute force of fitting actual pieces, since it won't take that many. And otherwise estimates based on highly simplified approximations.
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.
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
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.
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.
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.
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.
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.
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.
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.
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, ...
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.
Custom router bits do exist for the track groove profiles, which suggests that SOME folks are doing it. I've always wanted to create some custom pieces--my siblings and I growing up played with Brio far later than the expected ages, as we were all railway nerds, and frequently mis-used the degrees of freedom of track components for wildly more complicated layouts spanning rooms.
Nowadays one of my nephews ended up with lots of generic track (gifts from uncle: me) and some very specialized custom switches cast out of resin by his maternal grandfather. There are multiple ways to solve the problem!
Lidl and Ikea wooden tracks are pretty cheap and mostly compatible (you might have to file the joints a little, otherwise they can be hard to attach and detach).
Lidl & Ikea tracks give a feel of cheepnis. I haven't stopped to properly contemplate why it is so. Maybe some sanding of edges would help - Brio are much more pleasing to the touch.
We’ve 3D printed a lot of special tracks. Crossovers and splits, bridges, etc. It was really fun, and my kid pretty much always incorporates all of them into whatever layout we’re working on.
A friend has 3D-printed custom duplo and lego tracks. Not sure if she's also done it for wooden railroads. I haven't but I could really use some track pieces to adjust between common length and width differences. We've got several pieces that have two sets of track next to each other, and they all have a different spacing between the two tracks. Very frustrating.
I do that too. My son and his friends love building big train circuits. I love that too, but I've got a bit more eye than them for where things are under tension, and I try to correct for it.
Brio tracks are nicely designed in that altho you can combine them in myriad ways (with switches etc.), in general one of the shorter lengths of straight track does properly satisfy any gap you get.
That is to say, in the overall system, only a _small_ integer number of different straight track lengths are required.
257 comments
[ 3.4 ms ] story [ 316 ms ] threadHowever 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.
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.
One piece of flex track bent and cut to length.
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
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)
And: https://techcrunch.com/wp-content/uploads/2010/01/picture-29...
No idea what the 3rd picture was.
Processing code is here: https://blog.jgc.org/2010/01/ikea-lillabo-processing-code.ht...
Relevant: https://m.youtube.com/watch?v=NTJQTc-TqpU
I mention that to people more often than most would think.
The asker severely underestimates the amount of force it takes to break a Duplo piece.
...my foot on the other-hand...
https://stepinmath.wordpress.com/2016/08/27/logic-with-the-c...
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.
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.
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.
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.
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.
Then there's not enough tension to break any pieces either.
Assemble it on the air hockey table?
Assemble it on a smooth, flat floor and sprinkle some shuffleboard powder?
> I know I could just take one piece out, and put it back in to feel it myself
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...
"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 ;)
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.
As an aside, these articles are the gems that keep me coming back to HN.
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.
Again, if it's flat on the ground, it's far from the point where something breaking is a concern.
Far from a concern, as long as it’s stationary.
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.
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.
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.
Several days and derivations later, the theorist reports the volume, after which the experimentalist tosses the shape into a volumetric flask and determines the volume by looking at the difference in flask volume levels. (I am unable to track this story down to its original)
Now because I work in a textile mill, the tolerance I usually get is 0.125 inches which is huge. I usually go all the way down to 0.0001 inches because I think it's funny, and also I do have aspirations beyond just working with textiles.
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.
the stack overflow answers are math.
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.
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.
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
The fastest solution is going to be a combination of heuristics and multiple forms of mathematical modeling. Something like 1 does it look reasonable, 2 do the internal angles add up correctly, then 3 a more precise assessment based on actual curves and piece lengths. Doing 3 when it already failed 2 is redundant.
Try thinking for a few seconds before posting such a meritless dismissal.
That gives you the impression that goldcd fully comprehended the scope of the inquiry?
https://en.wikipedia.org/wiki/Lego_Duplo
https://bricks.stackexchange.com/questions/38/are-duplo-bloc...
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.
Interestingly you can build things that incorporate Primo, Duplo and regular Lego bricks!
Same manufacturing quality. Or even stronger design and QA checks as it is expected that toddlers will play with them.
> 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
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.
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.
I bet I'm not the only person here who can read it – rather haltingly – without decoding it first.
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.
Some amazing "illegal" Lego creations there.
But the sound of those bending Lego bricks made my teeth hurt, I had to mute the video. :-|
My 3yo son usually ends up with really "tense" tracks if he manages to build a circle. The lever torque of the track length makes them bend a tiny bit, so there should be tension in the outer rail. The fittings are quite close fits.
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.
You can scroll to the bottom of the comments to see a few of them.
What is this in reference to?
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
> 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.
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.
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.
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, ...
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.
However, it's quite easy to find second hand Brio tracks.
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.
Nowadays one of my nephews ended up with lots of generic track (gifts from uncle: me) and some very specialized custom switches cast out of resin by his maternal grandfather. There are multiple ways to solve the problem!
That is to say, in the overall system, only a _small_ integer number of different straight track lengths are required.
In comparison, TrackMaster requires many more.