The relation between fillister screw length and flux density

[antigua]

I saw a discussion recently about screw length in PAF humbuckers, and talk about how the tone changes when you snip the screws short. I found a lot of vague talk about the screw "changing the shape of the magnetic field".

So I got a screw that was about the right size to experiment with, in order to see what happens exactly. Long story short: and portion of the screw that sticks below the base plate subtracts from the magnetic strength at the guitar string (the only place where it ultimately matters).

Since the AlNiCo bar in the PAF is oriented on its side, with north out one side and south out the other, the magnetic field of the bar intersect the screws and pole pieces at a perfect right angle, complimenting the return path of the bar magnet. Since the slug only extends on it one direction, it has a proper north and south pole (south nearer the magnet, north further), but because the fillister screw goes off in both directions, like the top of a "T", the one length of metal becomes two opposing magnets, each side of the screw reading a south face.

Since the bottom half of the screw is opposite polarity from the top, from its distance, the bottom portion of the screw slightly decreases the flux density of the top half of the screw (and vice versa). For optimal magnetic strength at the top of the fillister screws, you would cut the screw right at the base plate, so that there is no permeable material on the other side of the bar magnet's return path that will serve to subtract from the side of the screw that magnetizes the strings.





Here are picture of the testing:

First, here is a demonstration of how the screw shows the same polarity on both ends.

275 gauss "south" facing on the top of the screw:




and 279 gauss "south" facing on the bottom side of that same screw.








Now to show that a shorter screw has a stronger field...

The test screw is the longer of the two. It's actually a mounting screw. I didn't want to ruin a proper fillister screw for the test.




Here is the long screw in place:




And the long screw shows a peak of 295 gauss:




Here with a piece trimmed off, the screws are all the same length...




and I get a slightly stronger reading of 298 gauss:




Now the screw if sheared at the base plate, so it's only as tall as the pickup itself:




Now the flux density shoots up to 361 gauss:




Trimming the screw at the base plate appears to be optimal. I tried clipping an extra millimeter off the screw in order to test whether having no permeable material on the opposite side of the bar magnet's flux path would yield a little more flux density, but it actually dropped from 360 max down to about 340.


In an abstract sense, a longer screws does constitute "changing the shape of the magnetic field", but what a lot of guitarists might not realize is that when the various steel pieces are magnetized, they become magnets in their own right. Magnetic fields follow the superposition principle , meaning that the magnetic fields of the magnetized steel add together with the magnet fields that created them, resulting in a net gain of magnetism overall. It's counter intuitive, because we're taught about the law of conservation, and that there is no free lunch, but when if comes to permeable materials such as steel, you do end up with more concentrated flux than you started with. Even though superposition means addition, if the fields that overlap are of opposite polarity, there will be a subtraction, and a net loss in magnetism, as can be seen with the two sides of the fillister screw. In magnetic diagrams, it might look like the magnetism is being pulled around like an oil slick, but what you really see is the sum of independent magnetic fields overlapping with one another, complimenting in some places, cancelling out in others.

[newey]

This is well put forth, and well tested. What I question is whether anyone could actually discern a tonal difference based on a roughly 50 gauss difference in flux or a slight difference in the shape of the resulting magnetic field.

A double-blind test would, I think, show that these slight variations would not be audibly detectable. If one is told that cutting the screws helps the tone, and the person then goes to the trouble of doing so, there will be a strong confirmation bias to hear a change in tone.

[antigua]

Whether something is happening or not, versus whether our sense or hearing can perceive a difference, are two different questions. Suppose you could hear a difference, that wouldn't necessarily tell what was causing the difference. This tells you what is liable to cause it, without telling you if you can hear it. Whether something can be heard or not is also more difficult to test. You need multiple participants and a test guitars set up in a quiet environment, among a lot of other things. 

I haven't seen a real strong correlation between flux density at the screw tops with AlNiCo 2, AlNiCo 5 and ceramic bars at the top. There should be, but I have examples of each that defy the rules. My best guess is that the flux density of the bar magnets themselves is inconsistent, and other such things. On the low side for rough cast AlNiCo 2, I measured 200G, but most AlNiCo 2 and 5 tend to land closer to 300, and ceramic bars tend to bring it closer to 400, but I can show you examples that deviate widely from that spread. If you supposed that the difference in sound you get with AlNiCo 2 versus AlNiCo 5 owes to flux density, my best guess would be that a difference of 60 gauss would be right at the edge of discernible difference. 

I think this also shows that there could be value in using alternative metals for screws and slugs to affect a difference. The combination of shorter or longer screws, along with a difference in permeability could make for a difference that exceeds 100 gauss, and is more likely to make an audible difference. 

[newey]

The combination of shorter or longer screws, along with a difference in permeability could make for a difference that exceeds 100 gauss, and is more likely to make an audible difference.

If that were to test out as true, I can foresee a new business. Instead of selling replacement pickups, sell replacement screws made of alternate materials. You could mark them up probably about 1000% and they'd still be cheaper than most boutique pickups, with no rewiring skills needed! Ideally, the new screws would be visually different so others would know that the player had the custom screws- maybe some sort of red or purple anodizing process?

So, antigua, once you've made your first million, just keep me in mind . . .

[antigua]

Yeah, I bet I could be tens of dollars selling special screws! But the only way it would work is if I could get a celebrity guitarist to endorse the idea. 

[ms]

I think that he proper length for the screws is that which gives best hum cancelation.  In general, since the screws have smaller diameters than the slugs, leaving a bit of extra length should help compensate for the missing permeable magnetic material.  I have not tested this, but have always thought that this is why the screws stick out a bit.

[antigua]

Feb 1, 2017 12:07:00 GMT -5 ms said:

I think that he proper length for the screws is that which gives best hum cancelation.  In general, since the screws have smaller diameters than the slugs, leaving a bit of extra length should help compensate for the missing permeable magnetic material.  I have not tested this, but have always thought that this is why the screws stick out a bit.

Knowing what I know about the design priorities of the first PAF, my guess would be that this happened to be the length of screws they had on hand, perhaps for the P-90's or something. 

[ms]

Feb 2, 2017 0:17:38 GMT -5 antigua said:

Feb 1, 2017 12:07:00 GMT -5 ms said:

I think that he proper length for the screws is that which gives best hum cancelation.  In general, since the screws have smaller diameters than the slugs, leaving a bit of extra length should help compensate for the missing permeable magnetic material.  I have not tested this, but have always thought that this is why the screws stick out a bit.

Knowing what I know about the design priorities of the first PAF, my guess would be that this happened to be the length of screws they had on hand, perhaps for the P-90's or something. 

I think Seth Lover wanted to use slugs for both coils.  When that was changed for marketing reasons, I think he would have made an effort to keep the hum cancelation as good as reasonable.  When you take the screws out one at a time while listening, you can hear the hum increase as each one is removed, and so at least a reasonable balance between the effects of slugs and screws is required to get good cancelation.  Of course opinions vary, and few bother to actually get the facts. For example,  the guy who ran the electronics sub forum on MMIF years ago insisted that a coil with no steel balanced one with steel just fine.  He knew because he tried it. Well, some reduction and good cancelation are two different things.

[antigua]

Feb 2, 2017 6:48:24 GMT -5 ms said:

Feb 2, 2017 0:17:38 GMT -5 antigua said:

Knowing what I know about the design priorities of the first PAF, my guess would be that this happened to be the length of screws they had on hand, perhaps for the P-90's or something. 

I think Seth Lover wanted to use slugs for both coils.  When that was changed for marketing reasons, I think he would have made an effort to keep the hum cancelation as good as reasonable.  When you take the screws out one at a time while listening, you can hear the hum increase as each one is removed, and so at least a reasonable balance between the effects of slugs and screws is required to get good cancelation.  Of course opinions vary, and few bother to actually get the facts. For example,  the guy who ran the electronics sub forum on MMIF years ago insisted that a coil with no steel balanced one with steel just fine.  He knew because he tried it. Well, some reduction and good cancelation are two different things.

I remember you had pointed out that Seth Lover's PAF patent contained some technical errors and/or dubious reasoning in the justification for the patent, so you're certainly well enough informed that I respect your educated guesses. Based on the errors in the patent though, I wonder how informed Seth Lover was about the importance of matched coils. 

I know that Seth Lover wanted all slugs, but Gibson added the row screws so that there would be visual continuity with the P-90 (otherwise why not have screws on both sides?), and so I wonder if Seth Lover was still involved in any design decisions by the time the screws were added. IIRC, the patent he filed shows all slugs, no screws. Since it appears that the PAF and P-90 use the same screws, it looks to me like someone else grabbed screws from the parts bin and added them to the construction. The question becomes, did that interloper at Gibson realize the longer screws might present an advantage?