I was doing a recent project and was making a coil around a pipe and I was trying to find the length of wire required to make a coil of length $x$ cm. The wire has a thickness of 1cm and the pipe has an outer diametre of 3cm. I wanted to coil the wire around the pipe with no gaps between the coils so that they are all touching. This was my calculation, $$\pi\cdot\left(3+1\right)\cdot\left(\frac{x}{1}\right)=\operatorname{Length of wire}.$$ I believe this is flawed but can't figure out a better method.
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1"Unroll" the coil onto a (flat) plane, and the math becomes trivial. – David G. Stork Mar 17 '21 at 18:34
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I think adding wire thickness to diameter is too generous. Otherwise, your method is OK. – Vasili Mar 17 '21 at 18:53
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I have tried both ways and it never seems to turn out right with the calculation it is always less than the amount I actually used – lypsettt Mar 17 '21 at 18:55
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Is your wire really $1$ centimeter thick? I would call it a rod, rather than a wire... How can you bend it around a $3$ cm tube??? – CiaPan Mar 23 '21 at 17:09