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I've had this question on my mind for quite a while and looking at the web, I couldn't find an answer to this question.

I've had a lot of physics experiments involving springs, unintentionally dismantled a hair clipper once, helped my dad repair his car, and all of them have very identical springs.

Here's an image of a variety of springs that are used for multiple purposes:

enter image description here

So, what's with the spiral/helical shape? And why are they "curled" in circle-like shapes. Why not triangle, square or any other geometric shape? What exactly is the physics behind this.

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  • $\begingroup$ ":spiral shape" Helical shape? $\endgroup$ – DJohnM Jun 26 '19 at 8:55
  • $\begingroup$ Although I am sure, my intuition says that the gap between two turns has to do with the spring constant. $k=Y\frac{A}{L}$, where $Y$ is Young's Modulus, $A$ is cross-sectional area and $L$ is the length of spring. You can also visit this page springhouston.com/spring-information/spring-engineering.html $\endgroup$ – Jitendra Jun 26 '19 at 9:07
  • $\begingroup$ Not all springs are based on a spiral, many vehicles have flat springs, some door locks have flat springs... $\endgroup$ – user207455 Jun 26 '19 at 10:22
  • $\begingroup$ @ GiorgioP Yes, it's indeed a very similar question, but the user didn't ask regarding the shape of the spring. So a separate question is needed. $\endgroup$ – user226894 Jun 26 '19 at 11:06
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    $\begingroup$ There is another aspect of this that should be mentioned. If you have a straight rod of the same diameter as the spring metal, you can stretch it very little before it exceeds its elastic limit, and the force would be very large, while the elongation would be tiny. The mode of deformation here is uniaxial extension. But, if the same metal rod is wound in a helical coil, the resulting spring can be extended a large amount without exceeding the elastic limit of the metal, and the force will be much more reasonable. The mode of deformation here is shear between adjacent metal cross sections. $\endgroup$ – Chet Miller Jun 26 '19 at 23:26
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I think you should be more specific in your question, indeed if the question is why the section of the springs is often circular, I think that this has just to do with the fabrication process. To build a spring with a circular shape is faster and cheaper that building a spring with, for example, a triangular section at industrial level. However I'm pretty sure that also a spring with a triangular section would work. While if your question is why the springs have an helical (stretched) shape, my answer is that there are a lot of variety of springs and not all have this shape. Maybe these are the most common, but there are some other. For example this is the spring of a mechanical watch, it is flat: enter image description here This is a leaf spring, used in automotive: enter image description here I mean you can project the shape of a spring according to what you need to do,and the helical shape is good just for some applications, not for all.

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  • $\begingroup$ A triangular spring compared to a circular spring would likely have issues with stress concentration at the least. The smooth curvature of helical and coil springs allows for approximately even stress across the spring; thus things like thickness and strength don't have to account for areas where they experience different stresses. $\endgroup$ – JMac Jun 26 '19 at 14:49
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The answer is that to fit a long length of spring into a small physical space you need somehow to curl the spring up, and a spiral is a good way of doing that. The reason that the spirals are round is twofold: first of all making round things is much easier than making things which are odd shapes, and secondly the stresses in materials are higher for smaller radii of curvature (this is why, for instance, cracks propagate, and why the square windows in the original Comet were so catastrophic). So if you want to make something strong you want to make the smallest radius of curvature as large as possible, and the way to do that is to make it circular.

Note that springs which don't require to fit in tiny spaces often are not spirals: leaf springs for vehicles are a good example of this.

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  • $\begingroup$ If you made a spring straight... it also wouldn't really behave like a spring. The helical shape of a helical spring for example actually allows you to convert the torsion of twisting a long thin bar into an axial elasticity. A coil spring allows you to convert the bending of a long thin bar into a torsion. $\endgroup$ – JMac Jun 26 '19 at 14:56
  • $\begingroup$ @JMac: sure it would: that's what a torsion bar is! $\endgroup$ – user107153 Jun 26 '19 at 16:28
  • $\begingroup$ It wouldn't behave like the spring it is emulating, sorry for being unclear. For example, without the helical pattern, a traditional helical spring would just be a torsion bar; but a usual helical spring is not meant to withstand torsion at all; so the helical shape actually has a direct impact on the relationship between the loads it is designed to carry, and the actual loading on the material; not just space constraints. $\endgroup$ – JMac Jun 26 '19 at 16:30
  • $\begingroup$ @JMac: you can use torsion bars to work as a linear spring with suitable levers on the ends, and they were (maybe are?) so used in vehicle suspensions, so by simply unwrapping a coil spring you can turn it into a torsion bar, but it is then physically much larger than it was (which was an advantage for car suspensions at the time as it meant the stress ended up on strong points of the chassis, far from the wheel). Without lots of pictures I think we are just arguing at cross purposes here. $\endgroup$ – user107153 Jun 27 '19 at 10:07