Horseshoe pickups: what do they do that's "different"?

[Mike Sulzer]

I forgot to add what you might do if you did not have FEMM and wanted to do an approximate solution where you can look up the answer you need. You might approximate the magnetized bit of string by a sphere in a constant magnetic field. Now, approximations do not always work
(Q: How does a physicist milk a cow?

A: Well, first let us consider a spherical cow...),

but in this case it should not be too bad.

The solution is described here: farside.ph.utexas.edu/teaching/em/lectures/node77.html

The second equation gives the simple scalar potential. To get B, you multiply by mu0, differentiate wrt r, and then subtract B0 to get the field of the "string bit" without the permanent field. As expected, it varies with 1/r^3, and scales with B0 and the radius of the sphere, and so you have to assume a reasonable size. Now you easily get the field down the center of the coil and approximate the flux, and see how that much changes over a typical string excursion.

[rjb]

Note to self: Flux equals product of magnetic field and area.

Are you thinking that your proposition implies that the changes in permanent B field with distance from the pickup have less effect than expected

Maybe not "less", but "different".
I'm thinking the difference in B field has most effect at the voltage signal's zero crossings.

...the voltage produced is zero at the extremes and maximum in between, both when the string is headed towards and away from the pickup?

Yup.
And |maximum voltage| will be produced when the product of the string's velocity and its field seen by the coil are maximum.
That condition should be met at a single point in space, whether the string is traveling up or down...
unless the force of the permanent magnet "tugs" on the string and alters its velocity...
which could account for Joseph's observed ~20% asymmetry.

Hey, wow, I just thought of the "unless" part right now.

[Mike Sulzer]

This file (www.physics.princeton.edu/~mcdonald/.../guitar.pdf) was discussed sometime ago, I do not remember who introduced it. It is a solution such as I have described. The exact string shape is considered, but the permanent field is spatially constant, and the coil is essentially air core, no eddy currents or permeability. (This is an important simplification since a complicated vector potential can be replaced with a simple scalar potential (as in the file I link to below).)

He discusses the non linearities that result. (I suspect that these are more significant than the one that Joseph has described resulting from the non uniform permanent B field.) The use of steel or alnico pole pieces would significantly alter the equation he derives and thus affect the nonlinearity, and so his results should be considered very approximate. However, it is a very useful description of the characteristics of the voltage resulting from the time varying flux of the vibrating string.

[Joe Gwinn]

I forgot to add what you might do if you did not have FEMM and wanted to do an approximate solution where you can look up the answer you need. You might approximate the magnetized bit of string by a sphere in a constant magnetic field. Now, approximations do not always work
(Q: How does a physicist milk a cow?

A: Well, first let us consider a spherical cow...),

but in this case it should not be too bad.

The solution is described here: Boundary value problems with ferromagnets

The second equation gives the simple scalar potential. To get B, you multiply by mu0, differentiate wrt r, and then subtract B0 to get the field of the "string bit" without the permanent field. As expected, it varies with 1/r^3, and scales with B0 and the radius of the sphere, and so you have to assume a reasonable size. Now you easily get the field down the center of the coil and approximate the flux, and see how that much changes over a typical string excursion.

The infinite cylinder cow may be a better approximation.

[Joe Gwinn]

Not only is it perfectly valid, but it is essentially fundamental, at least at the level of classical physics, and thus is to be preferred, unless there is some real advantage to the variable reluctance view. There is not in the case of a pickup.

The variable reluctance view has strength in simplicity when an analogy with electrical circuits (resistors, batteries, wires) is valid. The high permeability portions of a magnetic circuit are like wires, and small gaps are like resistors. There is a simple equation for the reluctance (resistance of the "resistor") because the problem can be reduced in dimensionality (edge effects are small, etc.) when the gap is small.

Pickups have a short (usually) high permeability pole piece, a very small high permeability bit of string and a huge air space. The "flow" of flux is limited by this space. Solving for its multi dimensional "reluctance" requires solving a three dimensional partial differential equation, the same equation that would have to be solved in the electrical case where we have three dimensional flow (current density) driven by an electric field which must be solved for in a self-consistent way. The problems are the same, and so if one is not simple, then neither is the other.

The pickup is much simpler when analyzed in a two step process where an applied field magnetizes a bit of string. Even determining the magnetization of the string is not such a simple problem, but because it is small, you can approximate and even get an answer with a two dimensional solver such as FEMM. Once that is done, you use linearity to eliminate the permanent field from the problem and look at the flux through the coil for difference positions of the vibrating string. You can even vary the magnetization of the string as a function of position (the effect that Joseph mentioned) if you like.

We've been around this before. There are many methods, and they all give the same answer is applied correctly, so the choice of method is primarily a matter of convenience and current purpose.

To be precise, variable reluctance is a subset of quasi-static.

[Mike Sulzer]

...the choice of method is primarily a matter of convenience and current purpose.

Those seem like excellent criteria. Let's consider the simple case of a spatially constant permanent B field and an air core coil, the case considered in the file I most recently referred to. How is it convenient to analyze by variable reluctance, and how does an initial intuitive analysis lead to a simple calculation? In particular, how would it be more convenient and more helpful than the calculation method adopted in that analysis that I referred to?

[David Schwab]

OK, I thought you meant just the flux from the permanent magnet.

Yes, magnetizung the string. Now it is possible to say that without starting an argument with a certain former moderator who insisted that it did not happen.

Are you talking about me? I'm not a former anything.

I said it doesn't work very well. Try it and see. You don't get a lot of output. I tried this 40 years ago.

Also once you change strings you have a problem. Just hope you don't break one while playing!

What I said is the permanent magnet is much stronger than the magnetized strings. They make poor magnets. So when you have a permanent magnet in a pickup it's doing all the work and over shadows magnetized strings. Similar to how the patch cord capacitance is way more than any capacitance in the pickup coil. So the smaller of the two is inconsequential.

So now we are getting into variable reluctance more than a moving magnet type of situation.

Agree or not, the pickup still functions. And they don't work well at all without the magnets.

[Mike Sulzer]

Please try to understand. Magnetization refers to lining up the magnetic domains, partially or completely, temporarily or permanently. It is happens when you put a ferromagnetic material in a magnetic field. Therefore it happens when you put a pickup with a magnet on a guitar and install strings over it. It is not open to question, and there is no other physical effect that allows a vibrating string to induce a time varying field through a coil. It is essential to the operation of the pickup, whether the magnet is part of the pickup or located somewhere else.

Variable reluctance does not offer a different physical effect to explain the operation of a pickup. It is a method of explaining some magnetic phenomena by making an analogy to voltage and resistance. Just a different way of explaining what happens. And it is a terrible way except in certain simple cases. Guitar pickups are not one of them. In my previous message I asked Joe to attempt a similar analysis to what the Princeton researcher did but using variable reluctance. He has not responded. There is no simple way to do it. The standard way is the right way. This researcher put the string in a magnetic field, computed the resulting field, and then computed how much flux changed through the coil when the string was moved relative to the coil. The analysis has some significant approximations, and so it is not completely realistic, but it is pretty good, and it is much easier than trying to do it by variable reluctance, which would require computing the field everywhere and defining some complicated 3D path. In fact in attempting the reluctance solution, you would already have solved the problem the easier way and could stop.

You have some fundamental misconceptions about electromagnetism. Please drop them and learn how it really works.

Are you talking about me? I'm not a former anything.

I said it doesn't work very well. Try it and see. You don't get a lot of output. I tried this 40 years ago.

Also once you change strings you have a problem. Just hope you don't break one while playing!

What I said is the permanent magnet is much stronger than the magnetized strings. They make poor magnets. So when you have a permanent magnet in a pickup it's doing all the work and over shadows magnetized strings. Similar to how the patch cord capacitance is way more than any capacitance in the pickup coil. So the smaller of the two is inconsequential.

So now we are getting into variable reluctance more than a moving magnet type of situation.

Agree or not, the pickup still functions. And they don't work well at all without the magnets.

[David King]

Non-magnetic strings, gut strings for instance, do not work regardless of how large your permanent magnet is. Steel, nickel or cobalt strings do work because they alter the permanent magnetic field as the move through it. The only thing they can do to alter that field is to gain and lose some magnetic charge. Is that a fair assessment that we can all agree on?

[rjb]

Meanwhile, Back at the OP...

OK, we've had our fun arguing "variable reluctance" vs "moving magnetized string", and exploring the non-linearities of magnetic pickups (which, as far as I can see, only affect the timbre of the signal). May I suggest we return to the original query?

Does anyone concur or dispute that the through-string pickup design affects the signal envelope (i.e., increases sensitivity & sustain over that of an under-string pickup)?

FWIW, Jason Lollar sez

The steel plate that goes over the strings spreads the magnetic field to surround the strings. This increases the pickup's sensitivity and reduces magnetic pull on the strings which increases sustain.

Supro Steel Guitar Pickup

Here's some more info on the design under discussion
Lollar Supro Steel Guitar Pickup Now Available | Lollar Pickups Blog

[Mike Sulzer]

Non-magnetic strings, gut strings for instance, do not work regardless of how large your permanent magnet is. Steel, nickel or cobalt strings do work because they alter the permanent magnetic field as the move through it. The only thing they can do to alter that field is to gain and lose some magnetic charge. Is that a fair assessment that we can all agree on?

No, the variation of magnetization of the string as it moves is a secondary matter. The pickup works fine if it remains constant as assumed in the Princeton analysis. The field produced by the string magnetizatino varies in space, falling off with distance from the string. This is true with constant magnetization and it causes the flux through the coil to vary as the string moves.

[Mike Sulzer]

Unproven. It might be true or it might not. It is reasonable, but unless it is proven, it remains in question. To me it seems likely that the effects known as "string pull", or whatever, in their strongest form, are a result of the gradient in the permanent field and that there is some effect on the string even at the normally used field strengths. But that is very different from knowing that it is true.

I think one way to prove it would be to make two pickups the same, including the field strength at the string, except for the gradient of the field at the string. Perhaps this could be done by making one of them with very strong magnets located farther than normal from the string. This would require some careful design and effort.

Does anyone concur or dispute that the through-string pickup design affects the signal envelope (i.e., increases sensitivity & sustain over that of an under-string pickup)?

FWIW, Jason Lollar sez

Supro Steel Guitar Pickup

Here's some more info on the design under discussion
Lollar Supro Steel Guitar Pickup Now Available | Lollar Pickups Blog

[Joe Gwinn]

Unproven. It might be true or it might not. It is reasonable, but unless it is proven, it remains in question. To me it seems likely that the effects known as "string pull", or whatever, in their strongest form, are a result of the gradient in the permanent field and that there is some effect on the string even at the normally used field strengths. But that is very different from knowing that it is true.

I think one way to prove it would be to make two pickups the same, including the field strength at the string, except for the gradient of the field at the string. Perhaps this could be done by making one of them with very strong magnets located farther than normal from the string. This would require some careful design and effort.

Careful, Mike. Jason doesn't do theory. Jason will have built test articles and tried this.

[Mike Sulzer]

Careful, Mike. Jason doesn't do theory. Jason will have built test articles and tried this.

From the description for the pickup:

This is an exact copy of the Supro/ Valco/ National string through steel guitar pickup as used on the "Coodercaster." The pickup is humbucking yet it sounds exactly like a single coil. Output is remarkably high yet it has all of the clarity of a low output pickup. The steel plate that goes over the strings spreads the magnetic field to surround the strings. This increases the pickup's sensitivity and reduces magnetic pull on the strings which increases sustain. Chrome plated to look as good as it sounds.

The usual practice is to allow considerable leeway in advertising, and I consider the claims just that, not necessarily the result of extensive research into the matter. It is advertised as an exact copy, and but that does not imply that the reason for building an exact copy of this original is because his research showed that it is technically the right thing to do. Usually you build exact copies because guitarists want them. You have to have a market for what you make.

The bolded statement could be interpreted as meaning "It makes the field close to constant in region where the strings are", but but is that really is what he means?

I am sure it is a great pickup, but not at all sure about what makes it so. It would be interesting to know. One way would be to use a different method of making the field nearly constant in the region of the strings (as I suggested) and see how that compares.

[Mark Hammer]

Well, I asked the question because that Lollar pickup is what's on the "Coodercaster" that Blake MIlls is playing here: https://www.youtube.com/watch?v=g1i8dnAi3X4

I don't know how else to describe it but that it feels like being able to get 30 more points out of your Scrabble letters when you only have 4 or 5 tiles left. There's more expression left far along in the note, when you would normally feel it going limp.