Parallel coil-layers?
mogallin, Thu Jan 01 2009, 06:20PMHaving too much spare time atm and being too bored here comes another thing i've been thinking about;
Longer wire gives higher inductance, right?
Higher inductance gives longer discharge-time, right?
So connecting each layer in a coil in parallel would decrease the inductance and thereby the discharge time?
If so, what may be the problems with this?
Re: Parallel coil-layers?
Marauder709, Thu Jan 01 2009, 07:33PM
The discharge time would decrease but not because of any change in inductance. If you couple coils in parallel with the caps you can drastically reduce resistance of the circuit. If you reduce the resistance you increase your circuits frequency and thereby decrease the pulse length.
Theoretically you could hook up every single turn in parallel but you pulse would would me unbelievably short and the feild might not "grab" the projectile for long enough.
Self induction on the other hand is based on the coil's overall geometry, not how it is electrically hooked up.
Marauder709, Thu Jan 01 2009, 07:33PM
The discharge time would decrease but not because of any change in inductance. If you couple coils in parallel with the caps you can drastically reduce resistance of the circuit. If you reduce the resistance you increase your circuits frequency and thereby decrease the pulse length.
Theoretically you could hook up every single turn in parallel but you pulse would would me unbelievably short and the feild might not "grab" the projectile for long enough.
Self induction on the other hand is based on the coil's overall geometry, not how it is electrically hooked up.
Re: Parallel coil-layers?
mogallin, Thu Jan 01 2009, 07:43PM
ok. Thanks.
mogallin, Thu Jan 01 2009, 07:43PM
ok. Thanks.
Re: Parallel coil-layers?
badastronaut, Thu Jan 01 2009, 09:48PM
If you connected each layer in the coil in parallel, you'll end up with lower inductance. Two in parallel = half the inductance.
This is equivalent to using thicker wire. No free lunches lulz.
Inductors add in series and parallel just like resistors. It matters how they are connected.
badastronaut, Thu Jan 01 2009, 09:48PM
If you connected each layer in the coil in parallel, you'll end up with lower inductance. Two in parallel = half the inductance.
This is equivalent to using thicker wire. No free lunches lulz.
Inductors add in series and parallel just like resistors. It matters how they are connected.
Re: Parallel coil-layers?
Marauder709, Thu Jan 01 2009, 10:08PM
The quantitative definition of self inductance for a solenoid is: (N^2*u*A)/l (not exactly but close enough)
There is no I or B or R or any other quantity that is related to how the circuit is wired. You may be right though, I hadn't considered that inductors add in series. It would be interesting to see how the maths work out on that.
Marauder709, Thu Jan 01 2009, 10:08PM
The quantitative definition of self inductance for a solenoid is: (N^2*u*A)/l (not exactly but close enough)
There is no I or B or R or any other quantity that is related to how the circuit is wired. You may be right though, I hadn't considered that inductors add in series. It would be interesting to see how the maths work out on that.
Re: Parallel coil-layers?
uzzors2k, Thu Jan 01 2009, 11:19PM
Not quite. Resistance has no impact of the frequency of an LCR circuit, just the damping of it. Lower resistance will cause the current to swing at a higher amplitude and take longer to die out. This isn't necessarily good in a coil gun since the negative pulse will be clamped wasting all of that energy. Ideally you want a critically damped LCR circuit, consisting of one pulse.
uzzors2k, Thu Jan 01 2009, 11:19PM
Marauder709 wrote ...
If you reduce the resistance you increase your circuits frequency and thereby decrease the pulse length.
If you reduce the resistance you increase your circuits frequency and thereby decrease the pulse length.
Not quite. Resistance has no impact of the frequency of an LCR circuit, just the damping of it. Lower resistance will cause the current to swing at a higher amplitude and take longer to die out. This isn't necessarily good in a coil gun since the negative pulse will be clamped wasting all of that energy. Ideally you want a critically damped LCR circuit, consisting of one pulse.
Re: Parallel coil-layers?
badastronaut, Fri Jan 02 2009, 04:05AM
I think that is the ideal solenoid inductance equation and is a gross oversimplification of the problem. It is not the definition of inductance. The definition of inductance is the ratio of the voltage change to the rate of change of current through the inductor. It is also the ratio of flux to current.
In the case of the solenoid equation that you have posted, the number of turns is the effective number of turns that are in series. The ones in parallel won't count. It basically says how dense the number of turns are.
badastronaut, Fri Jan 02 2009, 04:05AM
I think that is the ideal solenoid inductance equation and is a gross oversimplification of the problem. It is not the definition of inductance. The definition of inductance is the ratio of the voltage change to the rate of change of current through the inductor. It is also the ratio of flux to current.
In the case of the solenoid equation that you have posted, the number of turns is the effective number of turns that are in series. The ones in parallel won't count. It basically says how dense the number of turns are.
Re: Parallel coil-layers?
Marauder709, Fri Jan 02 2009, 06:58AM
I don't think its a gross oversimplification. It's certainly the easiest way of calculating self inductance.
The maths, as far as I can tell work out like this:
-L(di/dt) = (cEMF). L is constant for a given circuit, no matter how you wire it. di/dt however does change quite drastically depending on the wiring.
When they say that inductance adds in series it assumes that the inductors have separate fluxes, separate magnetic fields. In mogallin's case however, the inductors share the same magnetic feild and thus must be treated as a single inductor. If you want quantitative proof: cEMF = -N(dphi/dt) where N is the number of turns through which the flux, phi, passes. Because the flux passes through all the turns they must all be counted as a single inductor.
Marauder709, Fri Jan 02 2009, 06:58AM
I don't think its a gross oversimplification. It's certainly the easiest way of calculating self inductance.
The maths, as far as I can tell work out like this:
-L(di/dt) = (cEMF). L is constant for a given circuit, no matter how you wire it. di/dt however does change quite drastically depending on the wiring.
When they say that inductance adds in series it assumes that the inductors have separate fluxes, separate magnetic fields. In mogallin's case however, the inductors share the same magnetic feild and thus must be treated as a single inductor. If you want quantitative proof: cEMF = -N(dphi/dt) where N is the number of turns through which the flux, phi, passes. Because the flux passes through all the turns they must all be counted as a single inductor.
Re: Parallel coil-layers?
blackgrunge, Fri Jan 02 2009, 06:49PM
Its not a gross simplification at all. It works with low voltage models such as 24v capacitor banks EXTREMELY well. I've done it my self to lower inductance and increase magnetic field strength. It also cuts back on resistance significantly (R= r^-1 + r^-1.....)
Its a great concept that hasn't been used all that often but I've experimented with it and it yields great results at lower voltages. It becomes uncontrollable at higher voltages because the discharge time plummets and you end up with a minuscule discharge time that become difficult to work with. In a way inductance is what helps people work with higher voltages and ultimately higher energy levels.
If anyone has the money or owns one, a car audio capacitor works excellent using this approach and if you build the coils as mentioned then you will see some great results working with those lover voltages. The bonus of using lower voltages with this method is that you can gain capacitance very fast. When I built this setup I put together a 6 stage in about 3 days because there was no need for high power SCRs, power MOSFETs did just fine. The one 1.2 Farad capacitor @24v served as a great central power supply for the coils.
blackgrunge, Fri Jan 02 2009, 06:49PM
Its not a gross simplification at all. It works with low voltage models such as 24v capacitor banks EXTREMELY well. I've done it my self to lower inductance and increase magnetic field strength. It also cuts back on resistance significantly (R= r^-1 + r^-1.....)
Its a great concept that hasn't been used all that often but I've experimented with it and it yields great results at lower voltages. It becomes uncontrollable at higher voltages because the discharge time plummets and you end up with a minuscule discharge time that become difficult to work with. In a way inductance is what helps people work with higher voltages and ultimately higher energy levels.
If anyone has the money or owns one, a car audio capacitor works excellent using this approach and if you build the coils as mentioned then you will see some great results working with those lover voltages. The bonus of using lower voltages with this method is that you can gain capacitance very fast. When I built this setup I put together a 6 stage in about 3 days because there was no need for high power SCRs, power MOSFETs did just fine. The one 1.2 Farad capacitor @24v served as a great central power supply for the coils.
Re: Parallel coil-layers?
badastronaut, Fri Jan 02 2009, 08:57PM
That's what I meant, putting the layers in parallel will reduce the inductance, just as you have said.
You're only increasing the magnetic field strength because you are increasing the peak current. Buy an LCR meter and measure it yourself. Or if you have a good voltmeter and a function generator, you can use phasor analysis to find the change in inductance.
badastronaut, Fri Jan 02 2009, 08:57PM
That's what I meant, putting the layers in parallel will reduce the inductance, just as you have said.
You're only increasing the magnetic field strength because you are increasing the peak current. Buy an LCR meter and measure it yourself. Or if you have a good voltmeter and a function generator, you can use phasor analysis to find the change in inductance.
Re: Parallel coil-layers?
ScotchTapeLord, Fri Jan 09 2009, 02:18AM
I was planning to parallel 3 strands of my 22 gauge wire in order to get a lower resistance coil without buying thicker wire, but also to help distribute current evenly over my SCR "bank." Each wire will be in series with the anode of each of my SCRs, with the cathodes to the bank ground.
Is this a good idea?
ScotchTapeLord, Fri Jan 09 2009, 02:18AM
I was planning to parallel 3 strands of my 22 gauge wire in order to get a lower resistance coil without buying thicker wire, but also to help distribute current evenly over my SCR "bank." Each wire will be in series with the anode of each of my SCRs, with the cathodes to the bank ground.
Is this a good idea?
Re: Parallel coil-layers?
rp181, Fri Jan 09 2009, 02:20AM
Just put all the wires in parallel, and wind it like a flat ribbon cable. But the SCR's in parallel and connect it to the coil.
rp181, Fri Jan 09 2009, 02:20AM
Just put all the wires in parallel, and wind it like a flat ribbon cable. But the SCR's in parallel and connect it to the coil.
Re: Parallel coil-layers?
Marauder709, Fri Jan 09 2009, 03:19AM
I quote from Halliday Resnick and Walker, a Physics book used to teach AP Physics C and introductory college level Physics courses: "Inductance depends on the geometry of the device (the inductor)"
Marauder709, Fri Jan 09 2009, 03:19AM
I've done it my self to lower inductance and increase magnetic field strength. It also cuts back on resistance significantly (R= r^-1 + r^-1.....)
That's what I meant, putting the layers in parallel will reduce the inductance, just as you have said.
You're only increasing the magnetic field strength because you are increasing the peak current. Buy an LCR meter and measure it yourself. Or if you have a good voltmeter and a function generator, you can use phasor analysis to find the change in inductance.
I quote from Halliday Resnick and Walker, a Physics book used to teach AP Physics C and introductory college level Physics courses: "Inductance depends on the geometry of the device (the inductor)"
Re: Parallel coil-layers?
badastronaut, Sat Jan 10 2009, 12:18AM
Yes, that is true, inductance depends on geometry.
It also depends on how it is wired, which is the topic of this thread.
The inductance formula stated earlier in the thread makes the assumptions that the coil is either a single layer or all the layers are wired in series with an average radius.
If you have a two layer solenoid and wire the two layers in parallel, you end up with something equivalent to using only one layer with thicker wire. If this is not true then everyone would be doing it. The inductance of this configuration would be lower than the one where the two layers are wired in series as in a normal inductor. People do in fact use parallel layers to handle high current where flexibility and ease of winding are desired. There's nothing wrong with using parallel layers in place of thicker wire.
Say you have a solenoid with 2 layers and each layer is composed of 100 turns for a total of 200 turns.
The magnetic flux density depends on the number of amp-turns you have in a given area. If you wire the two layers in series, then 1 amp through the solenoid will give you 200 amp-turns of MMF. If, however, you put the layers in parallel, you will get 100 amp-turns with 1 amp through the solenoid. This is because the current divides among the layers such that half an amp flows through one layer and the other half through the second layer. 0.5amps*100 turns + 0.5amps*100turns = 100amp-turns This is only true if you believe in conservation of charge.
Each solenoid configuration, parallel or series layers, has the same current through it, but the series configuration has the higher number of amp-turns. Since the geometry of each configuration is the same, you can say that the series configuration has the higher inductance because it gives the higher magnetic flux per current.
QED
Yes, you may be able to get the same magnetic flux by increasing the current which may be made possible by the lower resistance, but it is not the same as using higher inductance. You can even use a single chunk of copper, i.e. one turn, and have the same magnetic field as long as the current density is the same as the original multiturn solenoid. The reason to use multiple turns is to match impedance with the power supply and reduce the amount of current required by the power supply even though the losses are the same for the same magnetic field since the current densities have to be the same. Inductance and magnetic flux are related but not the same.
When you say you increased the magnetic field by doubling its inductance, that is assuming you were able to keep the current the same, which you may not be able to do because of the higher inductance, you would need a higher voltage to overcome the extra impedance assuming there are AC components to the current flowing through the inductance.
In a coilgun, reducing the inductance might give you higher magnetic flux density because the lower inductance allowed the peak current to be much higher.
Don't go around quoting random texts whether or not they are true unless you understand them enough to prove that they are true. Anyone can steal other peoples work. Yes of course inductance depends on geometry, but it depends on other things as well such as how the individual turns are wired.
In fact, if you wire one layer of the solenoid and then reverse the winding direction on the second layer, you will cancel out most of the inductance of the solenoid. One layer will have X number of amp-turns and the other layer will have -X number of amp-turns for 0 effective amp-turns. This is how they make low inductance wirewound resistors even though the absolute number of turns is the same.
You can't go around citing equations as gospel unless you understand them enough to derive them yourself and know what the assumptions were in deriving them.
Is there anyone else that can vouche for this post?
badastronaut, Sat Jan 10 2009, 12:18AM
Yes, that is true, inductance depends on geometry.
It also depends on how it is wired, which is the topic of this thread.
The inductance formula stated earlier in the thread makes the assumptions that the coil is either a single layer or all the layers are wired in series with an average radius.
If you have a two layer solenoid and wire the two layers in parallel, you end up with something equivalent to using only one layer with thicker wire. If this is not true then everyone would be doing it. The inductance of this configuration would be lower than the one where the two layers are wired in series as in a normal inductor. People do in fact use parallel layers to handle high current where flexibility and ease of winding are desired. There's nothing wrong with using parallel layers in place of thicker wire.
Say you have a solenoid with 2 layers and each layer is composed of 100 turns for a total of 200 turns.
The magnetic flux density depends on the number of amp-turns you have in a given area. If you wire the two layers in series, then 1 amp through the solenoid will give you 200 amp-turns of MMF. If, however, you put the layers in parallel, you will get 100 amp-turns with 1 amp through the solenoid. This is because the current divides among the layers such that half an amp flows through one layer and the other half through the second layer. 0.5amps*100 turns + 0.5amps*100turns = 100amp-turns This is only true if you believe in conservation of charge.
Each solenoid configuration, parallel or series layers, has the same current through it, but the series configuration has the higher number of amp-turns. Since the geometry of each configuration is the same, you can say that the series configuration has the higher inductance because it gives the higher magnetic flux per current.
QED
Yes, you may be able to get the same magnetic flux by increasing the current which may be made possible by the lower resistance, but it is not the same as using higher inductance. You can even use a single chunk of copper, i.e. one turn, and have the same magnetic field as long as the current density is the same as the original multiturn solenoid. The reason to use multiple turns is to match impedance with the power supply and reduce the amount of current required by the power supply even though the losses are the same for the same magnetic field since the current densities have to be the same. Inductance and magnetic flux are related but not the same.
When you say you increased the magnetic field by doubling its inductance, that is assuming you were able to keep the current the same, which you may not be able to do because of the higher inductance, you would need a higher voltage to overcome the extra impedance assuming there are AC components to the current flowing through the inductance.
In a coilgun, reducing the inductance might give you higher magnetic flux density because the lower inductance allowed the peak current to be much higher.
Don't go around quoting random texts whether or not they are true unless you understand them enough to prove that they are true. Anyone can steal other peoples work. Yes of course inductance depends on geometry, but it depends on other things as well such as how the individual turns are wired.
In fact, if you wire one layer of the solenoid and then reverse the winding direction on the second layer, you will cancel out most of the inductance of the solenoid. One layer will have X number of amp-turns and the other layer will have -X number of amp-turns for 0 effective amp-turns. This is how they make low inductance wirewound resistors even though the absolute number of turns is the same.
You can't go around citing equations as gospel unless you understand them enough to derive them yourself and know what the assumptions were in deriving them.
Is there anyone else that can vouche for this post?
Re: Parallel coil-layers?
Barry, Sat Jan 10 2009, 01:02AM
Well written badastronaut (aka goodengineer), I agree with everything you've said.
A good analysis includes consideration of all the operating conditions (e.g. is the power provided from a voltage source or a current source, etc) along with all relevant assumptions.
Also Uzzors correctly reminds us that the LC timing constant is independent of resistance. That is, the discharge time depends on inductance but not resistance. You can control the rate of damping with resistance but not the natural frequency. Thank you.
Barry
Barry tickles 2009 under the chin. She wiggles and giggles and begs him to stop.
Barry, Sat Jan 10 2009, 01:02AM
Well written badastronaut (aka goodengineer), I agree with everything you've said.
A good analysis includes consideration of all the operating conditions (e.g. is the power provided from a voltage source or a current source, etc) along with all relevant assumptions.
Also Uzzors correctly reminds us that the LC timing constant is independent of resistance. That is, the discharge time depends on inductance but not resistance. You can control the rate of damping with resistance but not the natural frequency. Thank you.
Barry
Barry tickles 2009 under the chin. She wiggles and giggles and begs him to stop.
Re: Parallel coil-layers?
SamS, Mon Feb 02 2009, 10:07PM
Just saw this thread and decided to drop by.
Would it be any good if a multilayer coil is made where each layer is a separate electromagnetic coil with it's own bank and switching. When all layers are fired:
a) Magnetic fields add up nicely?
b) If so, would this setup have any advantages compared to "traditional" multilayer coil wound from one wire if switching losses are ignored?
SamS, Mon Feb 02 2009, 10:07PM
Just saw this thread and decided to drop by.
Would it be any good if a multilayer coil is made where each layer is a separate electromagnetic coil with it's own bank and switching. When all layers are fired:
a) Magnetic fields add up nicely?
b) If so, would this setup have any advantages compared to "traditional" multilayer coil wound from one wire if switching losses are ignored?
Re: Parallel coil-layers?
j.azz, Tue Feb 03 2009, 12:59PM
I guess it's just more to do if every layer has it's own switching and bank. I see no improvements over single switching.
But seperating the layers has advantages as you can vary the number of layers of your coil and thus making prototyping more easy. IIrc Barry has done this with his MarkII.
Hope that helps.
j.azz, Tue Feb 03 2009, 12:59PM
I guess it's just more to do if every layer has it's own switching and bank. I see no improvements over single switching.
But seperating the layers has advantages as you can vary the number of layers of your coil and thus making prototyping more easy. IIrc Barry has done this with his MarkII.
Hope that helps.
Re: Parallel coil-layers?
Quantum Singularity, Sun Feb 15 2009, 05:59PM
Just thought I'd point out if your making flat coils like I use then paralleling layers I dont beleive changes the inductance within reason. I've built a few with parallel layers as well as others here too. The turns per inch stays the same as well as the diamter of coil so the inductance should remain the same right? Just less copper resistance. Basically just using wider wire, which now I have the rectangular wire to use instead... a lot easier than doing parallel layers.
Quantum Singularity, Sun Feb 15 2009, 05:59PM
Just thought I'd point out if your making flat coils like I use then paralleling layers I dont beleive changes the inductance within reason. I've built a few with parallel layers as well as others here too. The turns per inch stays the same as well as the diamter of coil so the inductance should remain the same right? Just less copper resistance. Basically just using wider wire, which now I have the rectangular wire to use instead... a lot easier than doing parallel layers.
Re: Parallel coil-layers?
Signification, Mon Feb 02 2015, 01:19AM
Suppose you had two identical large pancake coils placed against each other face-to-face wired in parallel. The parallel inductor's "rule" says that the total inductance of the two will be reduced to half of the inductance of one. If you try this, I think you will find that this is far from the case--the reason being that the mutual inductance or 'flux coupling' is significant--especially in this particular configuration and at coilgun currents. The rule assumes that there is NO mutual inductance. It may help to think of the definition of inductance as 'amount of flux per amp'--and a lot of flux from one goes through the other. However flux will largley cancel if the paralleled coils are wired out-of-phase. The ohmic resistance, on the other hand, is indeed halved.
Signification, Mon Feb 02 2015, 01:19AM
Suppose you had two identical large pancake coils placed against each other face-to-face wired in parallel. The parallel inductor's "rule" says that the total inductance of the two will be reduced to half of the inductance of one. If you try this, I think you will find that this is far from the case--the reason being that the mutual inductance or 'flux coupling' is significant--especially in this particular configuration and at coilgun currents. The rule assumes that there is NO mutual inductance. It may help to think of the definition of inductance as 'amount of flux per amp'--and a lot of flux from one goes through the other. However flux will largley cancel if the paralleled coils are wired out-of-phase. The ohmic resistance, on the other hand, is indeed halved.
Re: Parallel coil-layers?
BigBad, Tue Feb 03 2015, 03:25PM
Why don't you model it in LTSpice (easily done) and get back to us?
BigBad, Tue Feb 03 2015, 03:25PM
Why don't you model it in LTSpice (easily done) and get back to us?
Re: Parallel coil-layers?
Andy, Wed Feb 04 2015, 04:20AM
Why dont you test it in a sim, question but two coils on the same axis with at lest 90% coulping would make one coil with lower resistance, but the text books really dont teach you that, ie the book say half the inducane but its moe 0.05% the inductance but you get half the resisance, which if you didnt flood the projectile will equal more abilty to acceralate.
Andy, Wed Feb 04 2015, 04:20AM
Why dont you test it in a sim, question but two coils on the same axis with at lest 90% coulping would make one coil with lower resistance, but the text books really dont teach you that, ie the book say half the inducane but its moe 0.05% the inductance but you get half the resisance, which if you didnt flood the projectile will equal more abilty to acceralate.
Re: Parallel coil-layers?
Signification, Wed Feb 04 2015, 11:04PM
The textbooks can really mislead you when they don't specify: "this is NOT the exact answer". Especially when the true answer is not that much, if at all, more difficult to derive. A couple of which we can relate to are the true, or exact, B-fields along the central axis of a solenoid, and the exceptions of the rules of total inductance of series and parallel inductors--BOTH together when coilguns are involved.
I HAVE NEVER USED A SIMULATOR...would love to start...any suggestions?
When software such as DEBUG, Quick-Basic, GX-Graphics, faded out, it crippled me. I Loved creating computer-generated holograms, rotating anaglyphs, etc. In fact, I was making a living with it. It was a rough time when Windows took over and these things eventually totally crashed.
That held me back for about about 15 years!!!. Then, I discovered, quite recently, a programming language called "Processing". With it, I have recently plotted, on a hi-res computer screen the radial and axial B-Field everywhere inside any general solenoid at any cross sectional area--I was looking for some king of maxima forming in the interior of the coil, but could find none. All maxima went to the perimeter of the inside of the coil, independent of the number of turns, layers, current, etc. With thick layered coils the maxima would 'seep' inside some of the innermost coil volume. I was searching for a specific field in order to construct special coilgun projectiles that were most efficiently "latched" or 'bitten' into.
The program was solely based on the Biot-Savart law to ensure accuracy (no elliptical integrals yet). I used the colors of the spectrum. I always like to use 24-bit continuous color transition which takes advantage of the cone-receptor resolving limit of the eye of 8-bits (256 shades) per primary color--that's a total of 2^24 or 16,777,216 colors! Here, it beautifully indicated field strength: RED~strongest BLUE~weakest. When I needed a really accurate field due to much wire, the program could take days to run, but the resulting image was beautiful! Even though the coil interior was pretty much blue- and cyan-basd with the 'rest' of the rainbow hugging the coil wall.
Signification, Wed Feb 04 2015, 11:04PM
The textbooks can really mislead you when they don't specify: "this is NOT the exact answer". Especially when the true answer is not that much, if at all, more difficult to derive. A couple of which we can relate to are the true, or exact, B-fields along the central axis of a solenoid, and the exceptions of the rules of total inductance of series and parallel inductors--BOTH together when coilguns are involved.
I HAVE NEVER USED A SIMULATOR...would love to start...any suggestions?
When software such as DEBUG, Quick-Basic, GX-Graphics, faded out, it crippled me. I Loved creating computer-generated holograms, rotating anaglyphs, etc. In fact, I was making a living with it. It was a rough time when Windows took over and these things eventually totally crashed.
That held me back for about about 15 years!!!. Then, I discovered, quite recently, a programming language called "Processing". With it, I have recently plotted, on a hi-res computer screen the radial and axial B-Field everywhere inside any general solenoid at any cross sectional area--I was looking for some king of maxima forming in the interior of the coil, but could find none. All maxima went to the perimeter of the inside of the coil, independent of the number of turns, layers, current, etc. With thick layered coils the maxima would 'seep' inside some of the innermost coil volume. I was searching for a specific field in order to construct special coilgun projectiles that were most efficiently "latched" or 'bitten' into.
The program was solely based on the Biot-Savart law to ensure accuracy (no elliptical integrals yet). I used the colors of the spectrum. I always like to use 24-bit continuous color transition which takes advantage of the cone-receptor resolving limit of the eye of 8-bits (256 shades) per primary color--that's a total of 2^24 or 16,777,216 colors! Here, it beautifully indicated field strength: RED~strongest BLUE~weakest. When I needed a really accurate field due to much wire, the program could take days to run, but the resulting image was beautiful! Even though the coil interior was pretty much blue- and cyan-basd with the 'rest' of the rainbow hugging the coil wall.
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