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I can make a flattish coil / ribbon cable using

Add > Curve > Add Curve Spirals: > Archemidian Then converting it to mesh then solidifying it.

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Is there a way to calculate the length of the ribbon or a way to calculate the values needed using a formula to get say 155mm of ribbon cable length at 0.3mm thickness when it's stretched out and 3D printed.

PS: I'm willing to model this differently if there is a better way.

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    $\begingroup$ There is an add-on in Mesh called 3D Print Tool Box. It will calculate the volume of a mesh. In simple terms, volume = length * width * height. You said the width is 0.3, length is 155, but did not give a height. You could also get a rough estimate from length ~ 2*$pi$*k*r where r is the average radius, k is number turns $\endgroup$
    – Ron Jensen
    Sep 23, 2021 at 16:45

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We want to create an Archimedes spiral curve 155mm long. The dialog to create Archimedes curves has three relevant parameters: (number of) Turns, Radius Growth, and Radius. This problem is under constrained, meaning there are an infinite number of values for these three parameters that will give us the spiral. We will need to pick two, then calculate the third.

Let:

  • $k$ be number of Turns
  • $\Delta r$ be Radius Growth
  • $r_0$ be initial Radius
  • $\theta$ (theta) be the parametric angle of the spiral. $\theta$ varies between 0 and $2\pi k$

Then the instantaneous radius of the spiral is given by:

  • $r(\theta) = r_0 + \frac{\theta} {2 \pi}\Delta r$

To find the length of the spiral we just integrate:

  • $L = \int_0^{2\pi k} r(\theta) d\theta $

This gives us the nice formula:

  • $L = \pi k (k \Delta r + 2 r_0)$

Fixing $r_0 = 1$, $ k = 5$ and $\Delta r 0.1 $ as in OP's screen shot gives a length of $L = 5\pi (5\cdot 0.1 + 2) \approx 39.27$ units are whatever units $\Delta r$ and $r_0$ are in.

Now lets look at ways to check our answer.

First we could use the 3D Print Tool on the finalized mesh object: Spiral as above with extrude set to 1/6 and a 0.03 solidify modifier we find a volume of 392900cm3 which is very close to what 0.333m × 0.03m × 39.27m predicts. Note that Curve->Geometry->Extrude is half of what's actually used! enter image description here

Another way is to create a cube that is 1/3 by 39.27 by 0.03 and subdivide the Y axis a few hundred cuts, then use a curve modifier to wrap the cube onto the curve. Before the modifier

You can see it fits well After the modifier

The second check technique can be used as visual way to create what you want. Make a new cube that is 1/3 x 155 x 0.03 and create a curve that will fully wrap that. 15 turns works.

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