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.
> 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...
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.
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.