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This is a mix between a DIY question and an applied physics question, but I figure the folks here are more interested in these details.

My application is attaching a projection screen to a frame with tension to stretch the screen flat. One of the recommended products to do this is bungee balls. In my case, I am considering replacing the bungee balls with extension springs because I can affix them with a twist-tie on one side and it will be easier to attach/detach the screen on the other side. The specifications for extension springs are well detailed (e.g. spring rate measured in lbs/in, but I can't find any equivalent information on bungee balls. How can I find this information (my Google-fu failed)? Or is there a simple test I can do with a bungee ball to measure the spring rate?

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It is difficult to give a definitive answer. The spring constant refers to an ideal spring which obeys Hooke's Law (extension proportional to load). Real springs and especially elastic materials such as bungee cord do not necessarily follow this law. Usually they do initially for 'smallish' loads, but they depart from it gradually at large loads. What counts as 'large' differs between materials and structures (springs are structures rather than materials) and is very difficult to predict.

The bungee cord is more likely than the springs to deviate from ideal behaviour. Since you have these already, you will be familiar with the way they extend.

So as a tentative answer, as long at the load isn't 'too large' the test value of the spring constant should give a reliable comparison. Ultimately I think you can only be sure by getting hold of the springs and comparing performance in situ. Even if they are equally springy, you may discover some other reason to prefer one over the other.

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