DCR vs. turns... linear correlation?

[FunkyKikuchiyo]

This feels like a really stupid question, but I have trouble making this assumption without good data. I feel like salvarsan's coil estimator should tell me if I use it properly, but I can't seem to find data to deal with this question.

For a given pickup design with a given wire (yes, I know DCR only tells a partial story) will the DCR vary directly (that is in a linear fashion) with the number of turns? I don't see why it wouldn't, except for the slight changing of the circumference of the coil and whatever extremes in tensioning may do as wire builds, but I am not sure. If it was a direct correlation, then in theory for every wire/bobbin combination there could a basic numeric constant to tell you roughly what a given DCR would be in turns. This could be done with just two sets of data; though it would obviously become more and more accurate the more data you introduced.

Again, it feels like a stupid question... but I love stupid questions. Feel free to give stupid answers.

[defaced]

will the DCR vary directly (that is in a linear fashion) with the number of turns?

No. This is a classical calculus/diff eq question. Calculating Length of Spiral
You can estimate, which I think is what the link lists, but you must consider the changing diameter and its effect on length. I can't seem to find the pages in my calc book to give a better explaination.

[salvarsan]

Here's some stupid for ya:

If every coil was wound with a "perfect lay" or "1:1 orthocyclic pitch", then the DCR and winds would correlate exactly. However, they aren't so they don't.

That's why the most recent Coil Estimator lists several fudge factors (cough!) ...er... fill factors for a particular DCR.

Magnet wire is variable, guaranteed to roughly +/-5% on any of its specs, enough to give a serious pickup builder fits when it comes to quality control.

A 5% change in resistance means a ~5% change in estimated winds but translates to a ~10% error in estimated inductance.

We can only estimate, and not very well when it comes to guitar pickups.

[Steve Conner]

Sure, but what about Mike's point? The outer turns have a larger circumference than the ones in by the magnets, because they're going on top of wire already laid down. So as you wind, 1 turn corresponds to a greater and greater length of wire. Therefore, the DCR does not correspond linearly to the winds. It's parabolic or something.

That assumes that you pile up the wire roughly in layers, but I don't see how it can be any other way to a first approximation. Random winding and scatter won't change the conclusion by a huge amount.

For small variations in turn count about some mean value, the linear approximation should be OK. The term "mean radius" or "mean turn length" is used in the coil winding industry, it's what the length of a turn would have to be to make the DCR work out, if the turns were all the same length.

[Mark Hammer]

It's also imortant to consider the coil form factor. The gradual change in circumference for a Jazzmaster pickup is different than that for a Tele neck pickup. But then that's why Salvarsan's coil estimater (Thanks!! Nice work!) asks what sort of pickup it is.

If one is truly "hand-winding", then scatter also changes with increasing number of turns and greater distance from the polepieces or slug/s.

[defaced]

The only way to practically get good answers is for a given winding technique, wire, bobbin, etc, is to develop the curve of DCR vs turns. Every 100 turns (or whatever increment you want), stop and take a reading. Do that for 30 coils and you'll have a statistically significant data set. Ain't no way I'd want to do this analytically. Too many factors with too much room for error.

[FunkyKikuchiyo]

For small variations in turn count about some mean value, the linear approximation should be OK. The term "mean radius" or "mean turn length" is used in the coil winding industry, it's what the length of a turn would have to be to make the DCR work out, if the turns were all the same length.

That is about what I was thinking. Of course it would change as it pudges out, but since no one is interested in a strat bobbin with 100 winds on it or 1000 winds on it, it should be a parabola that is darn close to being linear. For a given range of say, 6500 winds to 9000 winds, you could probably express it with a line, though the line wouldn't actually cross zero. That wouldn't be an issue if you're only using it within that given range as an approximation.

The type of wind of course would affect it, but I'm thinking more within one given style of winding. Let's say a manufacturer advertises two different pickups and says one is an "overwound" version of another, could you mathematically determine the change in windings based on the DC resistance? It could be assumed from the seller's description that all other variables are static.

[salvarsan]

The outer turns have a larger circumference than the ones in by the magnets, because they're going on top of wire already laid down. So as you wind, 1 turn corresponds to a greater and greater length of wire. Therefore, the DCR does not correspond linearly to the winds. It's parabolic or something.

The change in winding length is parabolic, you can treat it as linear without loss of accuracy since wire variability is so large. 5000 winds +/-5% is 250 winds either way.

It's also imortant to consider the coil form factor. The gradual change in circumference for a Jazzmaster pickup is different than that for a Tele neck pickup.

You can model the incremental change in winding length if you have the bobbin's inside dimensions.

I did the math and ended up with a parabolic equation that could be factored as a quadratic and tweaked for different fill/fudge factors.

The math write-up is here as a DOC file. Hopefully, someone else can improve it.

The Coil Estimator also lets you enter dimensions that aren't in the list.
The major code defect is that it doesn't set the wire gauge from the list.

Joe Gwinn posted a simpler estimation method a while back but I was too lazy to add in fill factor calculations.

@defaced
Yup.

Tracking your own work is the best way.

But when the pickup isn't your own, an estimation method is better than a guess.

[peskywinnets]

Of course it would change as it pudges out, but since no one is interested in a strat bobbin with 100 winds on it or 1000 winds on it

Erhmmm....I am!

You should wind yourself a low impedance pickup ....or even a transmitter/tester coil, sustainer driver etc! (not everyone wants to do or follow what everyone else is up to!).

Personally, I'd like a coil DCR predictor to add the diameter of the wire used onto the 'overall' circumference (with the initial circumference of the bobbin being derived from the bobbin dimensions as entered by the user) for each & every wind layer. ...but hey, beggars can't be choosers!

To date, I've used the Ziegler online pickup calculator to calculate DCRs .... I dunno if it does what I've just mentioned, but regardless, my resistances end up very close to its predictions.

[salvarsan]

... no one is interested in a strat bobbin with 100 winds on it or 1000 winds on it...

Sometimes, we izz.

If you want to make a low impedance strat pickup, your estimates run to ~700 winds of #32 or ~300 winds of #28.