Post by antigua on Aug 13, 2017 2:00:51 GMT -5
the first 3 terms imply:
Double the flux B, will double the voltage
Double string radius 'a' multiplies output x4 due the the a squared term
Coil size doubled also gives voltage x4
Time comes in due to the x and y terms with dots above them. These are 'rate of change' with respect time, ie velocity.
This raises some questions, which might even tie up some loose ends. In general, I would have thought these factors made smaller differences than the equation implies.
> Double the flux B, will double the voltage
We've seen that AlNiCo 3 pole pieces display around 550-650 gauss at the top, while AlNiCo 5 shows a fairly consistent 1050. Of course we know that pickups with AlNiCo 5 poles are not commensurately louder than pickups with AlNiCo 2 poles, due to everyday experience, and based on this experiment guitarnuts2.proboards.com/thread/7882/output-amplitudes-various-pickups?page=3 .
An obvious explanation, which I don't believe is factored into the McDonald equations, is that the higher permeability of the AlNiCo 3 amplifies the flux change in relation to the moving guitar string. This would mean that the higher permeability of the AlNiCo 3 must also effectively double the voltage, because lets suppose the AlNiCo 3 has a gauss of 500 and the A5 has a gauss of 1000, the A5 should be twice as loud, but if it turns out they are equal in output, the permeability of the AlNiCo 3 would have to also be doubling the voltage, so that you get the same voltage, despite the fact that the A3 is only hald the strength of the A5. Would you agree, or am I mistaken?
> Double string radius 'a' multiplies output x4 due the the a squared term
That's just surprising to me. I'd expect fretting the 9th fret of the of the G string to be a lot louder than an open E, having nearly double the radius, but it's only just a bit louder, and even that slight increase can possibly be attributed to greater fundamental movement of the shorter vibrating string, or reduced proximity between string and pickup.
Is there indication that McDonald might have made mistakes, or is his math and reasoning air tight?
> Coil size doubled also gives voltage x4
I'm especially confused here. I'd been led to believe it was the wind count that it important. For example, wind two pickups with 8,000 turns, one with 42AWG and another with 44AWG. They should have the same inductance and produce the same output. Lace Sensors have especially tiny coils, and low flux for that matter, but they produce a fairly strong output.
They way I've envisioned it is that a coil is like a lot of loops in series, and that the voltage is a sum of all those loops, with some loops seeing a larger flux change than others. So for example, there are loops at the top of the pickup, and there are loops towards the bottom. The loops at the top see greater flux change than the loops at the bottom, so you could make a coil larger and larger, but as more of those loops are further from the guitar string, they see less and less flux change, hence produce less voltage. That's why I understand a Lace Sensor to work well, because even though its coil might be very small, it's close to the action, it's near where the greatest amount of flux change occurs, essentially shedding the less productive bulk of a typical pickup's coil. Of course, all this is at odds with the idea that the voltage increased with sheer coil size. How would you relate the seemingly strong output of small coils to the McDonald equation?