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 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.
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...
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.
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'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?
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.
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)
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.
"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 ;)