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Registered Member #1525
Joined: Mon Jun 09 2008, 12:16AM
Location: America
Posts: 294
Yes! I love a good Physics discussion, most people I know just glaze over and shut down as soon as I mention anything science related.
Yandersen wrote ...
Sorry, Saz, but I must resist about shorter coils. The energy transfer efficiency of shorter coils is higher because short thick coils have higher gradient of a magnetic field - this gives higher acceleration.
I think you're mixing magnetic fields with electric fields. Electric fields accelerate a charge based on a potential gradient. Magnetic fields accelerate a charge based on field strength rather than field gradient. Take a look at the equation for magnetic force:
F=q*v X B
Force depends on the value of B, rather than it's derivative or gradient. If force depended on the gradient of the field, the equation would be:
F=q*v X del*B (incorrect)
wrote ...
Back to the simple principle of coilgun operation: every magnetic dipole of an iron bullet inside a magnetic field aligns in the direction of a magnetic lines, but PULLED in the direction where a magnetic field is higher.
First part: correct. Second part: see above. Force is not dependant on the gradient of B.
wrote ...
In the middle of your long coil bullet is pulled closer to the walls of a barrel, so this part of a coil just dessipates energy, while the pull is achieved only by the front end of a coil through which bullet enters. To prove and visualize it, energize one of your coils with a few Amps (AA battery, for example) and drag a little piece of iron through it via a plastic rod to check the difference in pull force in different parts of a coil. Mention how comparably low pull force is in the middle of a coil. Now take into account that your bullet is actually a mesh of such particles.
The effect your describing is due to a zero net force on the projectile. The front of the coil pulls the projectile forward, the end of the coil pushes it back. The effect must be integrated across the whole projectile to obtain net force (same effect you are describing of all the dipoles). When the projectile is at the cetner of the coil, the pushing and pulling balances out for a zero net force, this is precisely the point where you shut off the coil current to prevent suckback. Take a look at the magnetic field generated by the magnetized armature within the coil:
The axial component of the magnetic field is what produces the Lorenz Force with the charges circulating in the coil. Since F=q*v X B, the direction of the resulting force will always be along the coil axis, never normal to the coil walls.
wrote ...
If you want to wind The Best Coil, you must take this into account: every turn of each layer lowers the pull force, but extends it's effect length-wise; every layer highers the pull force, but each subsequent layer has less effect and contain more wire. So when you choosed the length of the coil (the shorter the better), you must add layers up until the effect of each next layer wound will become negligible. In practice such coil looks really thick - like triple of thickness of a barrel.
Take a look at the equation for the magnetic field of a solenoid (in scalar form).
B=u*N*i/l
Where u is the magnetic constant, N is the number of turns, i is the current, and l is the height of the loops. Notice that field strength is proportional to total number of turns N, and not on any effect of turns lowering the pull force and layers adding to it. Though it is true that as you add more layers, l for that layer increases, reducing that layers contribution to B.
wrote ...
In other words, many short coils is better than one long efficiency wise. The bullet may still be long one, but in this case single coil right in front of the bullet must be energized up until bullet enters the next one - one coil at a time, creating a concentrated magnetic field right in front of a bullet tip, pulling it inside via highest gradient possible.
The bit about more coils being better than fewer ones is probably true, since subsequent coils have a higher initial velocity, which improves induced voltage energy transfer to the projectile.
Yandersen wrote ...
And one question about IGBT you are using for energizing your coils: aren't they latch in ON state at such currents?!
Yes they are succeptable to latching since they are older IGBTs (circa 1995) but I've taken careful precaution to remain below the latching current of 300 amps.
"Force depends on the value of B, rather than it's derivative or gradient."
-Ha! Don't let yourself get blinded by pure formulas! Force is just proportional to the absolute value of the mag field at given point, but the direction of that force is determined by the gradient of a field. Example. Put an iron ball somewhere in the middle of long-long pipe laying horizontally and wound around with 1 layer of wire. No matter how much current you push through the wire the ball will stand still, being pushed harder and harder to the bottom part of that pipe. Then take that pipe and put it vertically. Ball will roll down (!) almost up till the END of a pipe. This way you will visualize, where the force you need is concentrated - at the end of a pipe. Now halve size of your pipe and compensate reduced number of turns by adding second layer to maintain the same B (sure, pipe is thick and wire is comparably much thinner). You will be surprized to see that with pipe standing up ball will be bouncing even higher showing you that force you need has increased. In the middle part of a pipe it is minimal. At least in the direction you need - along the pipe. Right in the center it is zero. The shorter the coil, the less dead space it has. That experiment proves that long pipe has huge amount of ballast wire that just dessipates energy while only few turns at the end of it are actually pull iron in the direction you need.
"Force is not dependant on the gradient of B."
Back to the simple experiment described above. You must agree that B has it's peak at the middle of a coil, but in that point ball is pushed not along the pipe but to the closest wall. Right in the geometrical center of a coil it will not be pulled anywhere AT ALL.
I have an interesting image in the attachment: it compares two coils - long thin coil and fat one. The image is generated by a program I wrote today getting interested in visualization of a mag fields and it's gradients. Both coils has the same amount of wire (but number of turns is different because of geometry), so the volume of copper is the same. On both images central cross section is shown. Strength of a magnetic field (B) at points around the coils is shown by green. For each point of the picture it was calculated as vector summ of mag field vectors and the intensity of green color represents relation of lengthes of those vectors. The fact that each subsequent layer has longer turns is not forgotten, heh. As you can see, the field inside a long coil is concentrated mostly inside, and it look quite constant along the coil. BTW I found interesting that field outside is so small - looks like external iron will not add any benefits, as I'm guessing (not sure it makes any sense...). Anyway. Compare that field with the one produced by thicker coil. It is easily mentionable that field of the fat oneis distributed more generously around the coil (good or bad?). If we summarize values of all pixels inside the barrel volume, then I'm sure (no proof!) that fat coil generates at least the same amount of mag cookies inside the barrel volume (and a lot all around in addition!). Let's go to the second picture. Here I visualized horizontal part of a gradient, which, according to the way of it's calculation, can be considered as a net pull force per volume - yellow is a pull force to the right, blue - to the left, intensity is a scalar part of that force, representing relation between forces at different points. How was it calculated? For each point I took it's left and right neighbours, calculated lengthes of their B vectors, and substracted those values one from another, this way achieving horizontal part of B-magnitude gradient right between them, at the central point of interest. Points close to the wire were ignored as seen by their black color, as well as those lying on the central symmetry axis. God forgive me for this! Anyway. If I was right considering this as a net pull force, the result clearly shows how much more efficient the fat coil is - just visually compare huge highlight far beyond the limits of a fat coil with a little sparks at the ends of a long coil. The only benefit I see in the long coil is that it lets much more iron inside before slowdown end will be reached, while the dead gap inside the fat coil is so short and slowdown starts so sharply, that precise triggering becoming a problem. Hmmm... I would say, that The Best Coil will be the one which would have equal acceleration and dead space lengthes. It will be something in the middle between those two coils, I think...
...And here are third coil shape in attachment to consider. Again, the amount of wire is the same, but the coil is somewhat between first two. Still would not have the same amount of pull force as fat coil, but bigger dead space gap allow more iron inside before pullback will become considerable:
Registered Member #1525
Joined: Mon Jun 09 2008, 12:16AM
Location: America
Posts: 294
Yandersen wrote ...
"Force depends on the value of B, rather than it's derivative or gradient."
-Ha! Don't let yourself get blinded by pure formulas!
Good sir, don't ignore foundational equations that have been cornerstones of electrodynamics for the past 130 years. If an assertation is inconsistent with a proven, foundational model, the assertation fails rather than the model. That's not narrow-mindedness, it's science.
wrote ...
Force is just proportional to the absolute value of the mag field at given point, but the direction of that force is determined by the gradient of a field.
This is also incorrect. The equation I gave you earlier(F=q*v X B) which actually is comprehensive in its description of the Lorenz force in all cases, shows that the force depends on the vector product of charge velocity and magnetic field. That means the direction of the resulting force is perpendicualr to both the field lines and direction of current flow- not in the direction of the gradient of the magnetic field, which would be indicated by the vector operator del.
wrote ...
Example. Put an iron ball somewhere in the middle of long-long pipe laying horizontally and wound around with 1 layer of wire. No matter how much current you push through the wire the ball will stand still, being pushed harder and harder to the bottom part of that pipe.
Again, a loop of wire will not exert a force on an armature within it that pulls the armature radially outwards towards the loop. Is this what you mean by pulling it "down"?
wrote ...
Then take that pipe and put it vertically. Ball will roll down (!) almost up till the END of a pipe. This way you will visualize, where the force you need is concentrated - at the end of a pipe. Now halve size of your pipe and compensate reduced number of turns by adding second layer to maintain the same B (sure, pipe is thick and wire is comparably much thinner). You will be surprized to see that with pipe standing up ball will be bouncing even higher showing you that force you need has increased. In the middle part of a pipe it is minimal. At least in the direction you need - along the pipe. Right in the center it is zero. The shorter the coil, the less dead space it has. That experiment proves that long pipe has huge amount of ballast wire that just dessipates energy while only few turns at the end of it are actually pull iron in the direction you need.
I admit I'm not able to fully understand what you're describing here (am I confusing pipe size with coil length?). But you are correct that the coil only dissipates energy (a ballast) when the armature is at it's center. However this isn't because the center part of the coil doesn't exert a magnetic force. The vector sum of forces on the armature from each loop sum to zero at the center, which is what your simulation is showing.
wrote ...
You must agree that B has it's peak at the middle of a coil
Not true. The magnitude and direction of B is approximately constant along the inside of a solenoid. See this image of the magnetic field, or any physics textbook. Furthermore the field generated by the coil does not produce the Lorenz Force that moves the projectile. The coil's field serves to magnetize the projectile, and it's the projectiles B field that interacts with the moving charges in the coil to produce the Lorenz Force.
Also, I like your simulation, you clearly have some remarkable programming and math skills. It's true that a short fat coil has a stronger B field than a long skinny one with the same turns and current, but the effect balances out once you integrate across the whole coil- the projectile will pass through the same amount of flux in either case. Either a lot of flux over a short distance, or less flux but over a longer distance. The area under the force vs. distance curve will be the same for both.
Lastly, external Iron is effective in that it routs more lines of flux emerging from the magnetized projectile through the coil where it can interact with the coil charges and produce more force. There's some great research, with experimental results, here.
Registered Member #30
Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706
I could be imagining it, but didn't we prove a long time ago that the optimal coil is the same length as the projectile?
Also, to prevent suckback, the current has to have decayed away by the time the projectile reaches the centre of the coil. The current in an inductor can't change instantaneously, so you have to switch off somewhat earlier. The diode-clamped circuit decays according to the LR time constant of the coil. A diagonal half-bridge gives a faster decay, because it can return energy to the storage caps. The result is more acceleration to the projectile, because you can leave the current on longer. The cost is twice as many IGBTs and diodes, and high-side gate drive.
Let's try to concentrate not on arguing but get closer to conclusion. You prefer to wind your wire forming a long coil, and I recommend to wire it over shorter distance forming a thicker coil stating that it will maximize efficency. And you are not agree with my point, saying it will not give any benefit. Am I understanding everything correctly?
Yeah, gradient theory without formulas is not the way to prove anything, I mast agree and sorry for that. Let me try the right way. Hope you will agree, that pulling force is perpendicular to both current flow direction and B vector. I also heard that fully saturated ferromagnetic armature can be considered as a coil too, so we can treat external coil as a source of a strong magnetic field and projectile as a coil, is it right? Summarizing both statements, the force experienced by each part of armature is proportional to the length of B vector at that point, the current through imaginary armature coil, and it is directed perpendicularly to both. And this is a key: inside a long coil flux lines aligned along the coil, producing zero vector force in that direction. And only at the ends of a coil those lines are separating apart finally making some angle with shot-direction axis. So there is no point to keep those lines parallel, as it is in a long coil - winds of wire in the middle do just this, and this is negative, because each turn dessipates energy. The total amount of force, as integrated over a barrel volume, will be directly proportional to the amount of those lines right at the center of a coil. So our goal is to wind our wire in a way to push as much flux lines inside that volume as possible, and let them separate apart as fast as possible, because this area gives acceleration to the iron inside it. Compare green color intensity at the centers of both coils on my picture - it represents the flux density, which is noticeably higher inside a thick coil, meaning that there are more flux lines inside, which is made with the same amount of wire (consider this as resistance) and the same current flowing through it. That is what I call "coil efficiency". What do you think about my theory? Oh, and by the way! The gradient of magnetic field is perpendicular to the flux lines, so all of my pictures are still correct if considered as shot-direction pull force per volume, visualizing the acceleration areas of a coil.
Registered Member #30
Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706
From conservation of magnetic energy, you can show that if a small movement of the projectile in some direction would increase the inductance of the coil system, then the projectile would experience acceleration in that direction.
For a short projectile inside a long coil, the inductance doesn't change over the range where the projectile is completely inside the coil. A similar argument can be applied to a long projectile passing through a short coil.
When the projectile is the same length as the coil, the inductance is always changing.
Registered Member #1525
Joined: Mon Jun 09 2008, 12:16AM
Location: America
Posts: 294
Steve- yes I understand that was decided on long before my time. Also thanks for the correction- I would want to quench current before the projectile reaches the center due to the finite time of current decay. As an alternative to the half-bridge, you can also use multiple commutation diodes in series. It's not as effective, but it speeds the decay without the bulk and cost of 2x IGBTs and also saves the need for high side drivers- that's the approach I've taken with my gun.
Yandersen wrote ...
Let's try to concentrate not on arguing but get closer to conclusion. You prefer to wind your wire forming a long coil, and I recommend to wire it over shorter distance forming a thicker coil stating that it will maximize efficency. And you are not agree with my point, saying it will not give any benefit. Am I understanding everything correctly?
Yes, the coil will not be more efficient simply because it's shorter. Length is important in that it should match the length of the projectile, as Steve Connor mentioned. Shorter coils matched with a shorter projectile can be more efficient because it allows for more stages to be fitted over a fixed barrel length. But as I mentioned earlier, this leads to a lighter projectile carrying less kinetic energy, and makes the gun more difficult to build.
wrote ...
Hope you will agree, that pulling force is perpendicular to both current flow direction and B vector.
Yes!
wrote ...
I also heard that fully saturated ferromagnetic armature can be considered as a coil too, so we can treat external coil as a source of a strong magnetic field and projectile as a coil, is it right?
The coil magnetizes the projectile. Then the magnetized projectile causes the force on the coil. So from that sense you could imagine the projectile as a coil although it isn't like an electromagnet.
wrote ...
Summarizing both statements, the force experienced by each part of armature is proportional to the length of B vector at that point, the current through imaginary armature coil, and it is directed perpendicularly to both. And this is a key: inside a long coil flux lines aligned along the coil, producing zero vector force in that direction.
The flux lines coming from the projectile which penetrate the coil always produce a force on the coil loops as long as the coil has current, but when the projectile is at the center of the coil the forces on all the loops cancel eachother out.
wrote ...
And only at the ends of a coil those lines are separating apart finally making some angle with shot-direction axis. So there is no point to keep those lines parallel, as it is in a long coil - winds of wire in the middle do just this, and this is negative, because each turn dessipates energy. The total amount of force, as integrated over a barrel volume, will be directly proportional to the amount of those lines right at the center of a coil. So our goal is to wind our wire in a way to push as much flux lines inside that volume as possible, and let them separate apart as fast as possible, because this area gives acceleration to the iron inside it. Compare green color intensity at the centers of both coils on my picture - it represents the flux density, which is noticeably higher inside a thick coil, meaning that there are more flux lines inside, which is made with the same amount of wire (consider this as resistance) and the same current flowing through it. That is what I call "coil efficiency". What do you think about my theory?
I see what you're getting at here. Yes it's only the axial component of the projectiles magnetic field that produces the force, and a longer projectile will have less of an axial component. But if the coil is also longer, the projectile will travel over more distance and prolong the interaction- the effect balances out. In mathematical terms, for the long projectile/coil, the force/displacement curve is low but long, and for the short projectile/coil the curve is high but brief- the area under each curve (energy) will be the same.
You definitely want as much flux inside the coil as possible- this is where external iron helps out in directing the field lines.
So we agreed that the more flux lines are inside the center of a coil, the higher the total pull force will be over the whole volume of a barrel, right? If so, than I have a direct proof that if the same wire is wound around a barrel to form a thicker coil, it will create higher flux density in the center - see the picture in attachment, where graph is shown generated by my program. In that version I have limited the area for which B vectors are calculated, and vertical lines on the graph represent the summs of values of those B vectors which lay on corresponding line. Obviously, peaks are at the centers of the coils, through which the whole bunch of magnetic lines goes through. All of those will emit out from the barrel at some points, generating pull force at there for bullet to grab it, that's why I assume that instead of integrating gradients over the barrel volume one can just count the total number of flux lines in the centers of the coils. Mention the difference between long and fat coils - almost 2 times more force per barrel volume fat coil can give! Howether, this force cookie is distributed differently over the barrel volume, but if all picked with the same projectile, than it will achieve higher speed faster, meaning it will get more kinetic energy and coil will consume less due to shorter energizing period. Think about this that way.
Oh, and here are the gradient graphs to help visualize where the pull and push areas are located for each of coil types . Yeah, it clearly shows that long projectile approaching superfat coil will have almost no room for acceleration.
Wonna tell secret to Steve: russians concluded that projectile just as long as the coil is less efficient than the one of half or 2/3 of the coil length. Practically, as they say. If my theory is right, than the clear explanation why it is so is shown on the graph above.
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