What is the length of wire needed to create this spring?

So I model the spring:

I then create a helix that runs through it entirely. Figure it intersects any quadrant on the starting-bottom circular face and it will intersect the same quadrant on the finishing-top circular face; thing left to left, top to top, center to center. Measure that helix and you get:

Arc Length = **28.11"**

Another method might be to evaluate the volume of the modeled spring and reverse-solve for the length:

where the volume of the above model is π = 3.14..., r is the radius of the wire (0.0625") and h is the length

0.33720901=π(.0625)²h; h=0.33720901/(π(.0625)²) = **27.48"**

Another method might be:

where π = 3.14..., c= number of coils/turns, D = outer diameter (1") and d = wire diameter (.125") giving you:

10π(.875) = **27.49"**

It's interesting that the last two numbers differ, I imagine because of rounding error. What I don't understand is why does my perfectly-aligning helix not measure the same? It must be fundamental I don't understand about Arc-Length

Is there a method, maybe using surfaces or sheet-metal, to flatten this out to measure? The math gives me a different number. I could imagine a scenario where I'm making a million springs and end up a few hundred feet short of wire based on SolidWorks' measurement.

Abraham Azar

Shouldn't the radius be .46875 instead of .500 as you show in your 2nd image? And, formulas use an incorrect value also.