Solenoids: Turns, Current, Voltage, and general confusion all around

solenoid envy

New Member
Hello! So I'm hopelessly lost on a few concepts here, and I'm putting myself at the mercy of the giant super-human brain they call the 'web' for answers.

I'm trying to make a linear solenoid electromagnet. Specifically, I want to shoot a nail through it. Like a railgun. Just for kicks. But I also want to shoot that nail as efficiently as super-humanly possible.

I've been experimenting with several different variables, and trying to maximize the force on the nail. From what I've deduced, force is proportional to the strength of magnetic field that my coil induces. (Assumption #1).

So if I can increase that magnetic field at the center of the coil (a quantity often called "B"), I can more effectively shoot the nail. I have come to understand that, for a solenoid, according to Amperes Law or somesuch,

B = [LATEX]\frac{\mu I}{4 \pi} \oint \frac{\vec{dl}\times \hat{r}}{r^{2}}[/LATEX]

With all the vectors, that gets messy, but it can really be simplified if you look at just one turn of wire, and solve for the magnetic field right there in the center of it, pointing only in the axial direction. My confusion isn't with the math so much as with the concept of it.

Here's where I'm getting stuck:

In the above equation, it would appear that more current "I" means more magnetism "B". And, the smaller the radius of the solenoid "r", the more magnetism also. I would assume that the more times you compound the effect by adding more turns of wire, you'd also increase the magnetism. HOWEVER, by increasing the turns of wire, would you not also increase the resistance in the wire? For a given input voltage "V", the current really depends on the length and area of the wire. So, in a gross yet practical over-simplification of the "B" equation,

B = (some constants) * I * N / r
I = (some constant) * V * Area-of-wire / length-of-wire

where N, the number of turns, is *linearly proportional* to length-of-wire. Notice how I also divided by length-of-wire just there. SO, why on earth does the number of turns of wire matter at all? Wouldn't the positive effect of more turns be canceled out by the negative effect of more resistance? It would seem, to the casual observer, that the only true way to improve a solenoid is to increase the voltage and wire-size, and decrease the radius of the loops. But a century of industry would beg to differ. What am I missing!?

Last edited:

MrAl

Well-Known Member
Hello! So I'm hopelessly lost on a few concepts here, and I'm putting myself at the mercy of the giant super-human brain they call the 'web' for answers.

I'm trying to make a linear solenoid electromagnet. Specifically, I want to shoot a nail through it. Like a railgun. Just for kicks. But I also want to shoot that nail as efficiently as super-humanly possible.

I've been experimenting with several different variables, and trying to maximize the force on the nail. From what I've deduced, force is proportional to the strength of magnetic field that my coil induces. (Assumption #1).

So if I can increase that magnetic field at the center of the coil (a quantity often called "B"), I can more effectively shoot the nail. I have come to understand that, for a solenoid, according to Amperes Law or somesuch,

B = [LATEX]\frac{\mu I}{4 \pi} \oint \frac{\vec{dl}\times \hat{r}}{r^{2}}[/LATEX]

With all the vectors, that gets messy, but it can really be simplified if you look at just one turn of wire, and solve for the magnetic field right there in the center of it, pointing only in the axial direction. My confusion isn't with the math so much as with the concept of it.

Here's where I'm getting stuck:

In the above equation, it would appear that more current "I" means more magnetism "B". And, the smaller the radius of the solenoid "r", the more magnetism also. I would assume that the more times you compound the effect by adding more turns of wire, you'd also increase the magnetism. HOWEVER, by increasing the turns of wire, would you not also increase the resistance in the wire? For a given input voltage "V", the current really depends on the length and area of the wire. So, in a gross yet practical over-simplification of the "B" equation,

B = (some constants) * I * N / r
I = (some constant) * V * Area-of-wire / length-of-wire

where N, the number of turns, is *linearly proportional* to length-of-wire. Notice how I also divided by length-of-wire just there. SO, why on earth does the number of turns of wire matter at all? Wouldn't the positive effect of more turns be canceled out by the negative effect of more resistance? It would seem, to the casual observer, that the only true way to improve a solenoid is to increase the voltage and wire-size, and decrease the radius of the loops. But a century of industry would beg to differ. What am I missing!?
Hi,

These questions always start out in a similar manner to yours. It's an optimization problem. The thing is though, when considering an optimum value for something that depends on other things, we can't overlook any of those other things or we'll either never find the right result or find a result that is not correct.

The thing that is missing here is quite common to these initial questions, and that is the internal resistance of the battery or other power source. Without considering that there is no way to optimize anything because after all if you increase the wire diameter with a given voltage even as low as 10 volts you can continue to decrease the wire size and draw more and more current until you have enough of a magnetic field to pull the moon closer to the earth In other words, without considering the battery internal resistance there is no limit to the magnetic field you can generate.

Considering the battery internal resistance it then becomes a genuine optimization problem where we try to find the best wire resistance to get the highest level of the magnetic field or the force itself.

We had talked about this a while back right here on this forum and came to a conclusion about the wire resistance. With several variables being eliminated through algebra and calculus the resistance found turned out to be the resistance that is exactly equal to the internal resistance of the battery. Thus, if the battery internal resistance was 1.2 ohms then the best wire resistance is 1.2 ohms.
If you care to follow the discussion and the optimization math you can do a search for that thread. We were talking about an electromagnet at the time.

But the bottom line is that the internal resistance of the voltage source has a lot to do with the maximization of the field, such that the wire resistance is the resistance that is equal to the resistance of the internal source. In many cases this wont be possible to achieve for practical reasons, so a lighter gauge wire is used with as many turns as fit on the desired coil form. The internal diameter is probably going to be dictated by the desired end use.
So if you cant get the optimum resistance then lighter wire with more turns or heavier wire with less turns. Obviously lighter wire with more turns means less current draw from the power source, and somewhat of a slower response to full current. The inductance increases as the square of the turns ratio, so the more turns the larger the inductance grows, and the inductance prevents the full current from appearing through the coil instantaneously. Less turns of heavier wire will mean lower inductance so the speed of response will be faster. The faster the full current (limited by the resistance) gets through the coil, the faster the force gets up to maximum. In this application that may be important too since something is going to be propelled.

Last edited:
• cachehiker

panic mode

Well-Known Member
total magnetic field is sum of all individual fields (created by each turn of the coil).
in other words field would be the same regardless if you run
100A through one turn, or
10A through 10 turns or
1 A through 100 turns or
0.1A through 1000 turns or
0.01A through 10000 turns or
4A through 25 turns or
3.333A through 30 turns or whatever

lookup amperes law, this is exactly how the field is calculated.

as you have noticed resistance of those coils is not the same.
also not all sources will be able to provide equal current.
finally there is power, and I^2R losses that produce heat...

solenoid envy

New Member
MrAl, thanks for the response - that makes sense. I was leaving out the resistance of the power supply, which means I thought I was getting hundreds of amps, when really I was probably getting Amps to milliAmps through my coil.

Thanks!

strantor

Active Member
well what kind of battery are you using? If you thought you were getting hundreds of amps, that makes me think you're using a car battery. If you're using a car battery, they you may have been getting hundreds of amps. car battery internal resistance is very low. depending on the size of wire though, I would think you would have blown your face off by now if you were dealing with hundreds of amps MrAl

Well-Known Member
MrAl, thanks for the response - that makes sense. I was leaving out the resistance of the power supply, which means I thought I was getting hundreds of amps, when really I was probably getting Amps to milliAmps through my coil.

Thanks!
Hi again,

You're welcome What this usually comes down to is we have to start with some limits on the size of the coil form because we cant build an infinitely large coil either. For this project say it is 12 inch outside diameter with 1/4 inch inside diameter and 12 inches long. The coil build would then be (roughly) 5 inches. The coil cross section is therefore a rectangle 12 by 5 inches. We want to fill this area completely with turns of wire so the wire cross section fills that rectangle as much as possible. Given a lighter wire gauge (small diameter wire) we would end up with a somewhat high total resistance, and given a heavy wire gauge (thick diameter wire) we would end up with a somewhat low total resistance, so the problem then becomes one of finding the best wire gauge to wind the coil form with. We then come up with a formula for the total resistance from the wire diameter, compute the optimum diameter, then look up the wire gauge. If the wire gauge comes out to be too heavy to wire by hand we might look into getting two lengths of wire that have an equivalent cross sectional area and wind them onto the form two in hand (bifilar), and drive the two windings in parallel.

Last edited:

cachehiker

New Member
Obviously lighter wire with more turns means less current draw from the power source, and somewhat of a slower response to full current.
And therein lies another variable for optimization, the response to full current should match the acceleration the nail to the center of the solenoid.

The kid (college frosh) at work who's building a backpack rail gun is discharging an array of 1500µF 200V capacitors chosen to minimize ESR at 48V (?) (not sure) through the solenoid to fire the nail and then charging them at a rate intended to optimize battery life for the impending zombie apocalypse. I haven't seen it. He'll bring it in eventually but my workplace has this thing about guns and ...

Last I heard it is working but he's winding a second solenoid and planning to use the secant method to design the final solenoid. He hopes his presentation will win him a scholarship.

(Now I'm stuck trying to mentally establish what the relationship between L, C, R, m, and a has to look like.)

Meat5000

New Member
Sorry to necro this thread but after a quick skim through I notice that most people are under the impression that magnetism has no bounds. You all seem to be ignoring the fact that Magnetic materials become saturated and so there is an absolute top end to the possible achievable magnet field strength from any coil.

"no limit to the magnetic field you can generate."

"draw more and more current until you have enough of a magnetic field to pull the moon closer to the earth"

"in other words field would be the same regardless if you run...~"

These statements are heavily inaccurate and slightly misleading (sorry dont mean to pick on anyone). Magnetic flux shows Diminishing Returns (less and less output for more and more input) as the material becomes saturated.

To achieve a fast response and hence fire a projectile it is required that you vastly overshoot the Voltage/current (system dependent) in order to achieve a much steeper 'ramp' but its is essential that V and I limiting/control is used so as to not burn out your equipment. You will not achieve Stronger Magnetism but you will achieve faster response. The classic example of where this is used is within Stepper Motors. This is often referred to as "Overdrive".

Here's a random page on Saturation.

https://www.duramag.com/techtalk/tech-briefs/magnetic-saturation-understanding-limitations-to-induced-magnetism-achieved-in-workpiece/

And this is a good little article on driving solenoids.

http://www.electronicdesign.com/analog/what-s-all-solenoid-driver-stuff-anyhow

Enjoy!

Last edited:

MrAl

Well-Known Member
Hi,

Yes even in the lab there is a limit, although i dont recall offhand what it currently is.

And yes, you can get the slope of the field to increase faster with a short higher voltage pulse. but that only gets up to the saturation point faster it wont go too much beyond that without a huge current increase.
It's not that the field does not increase after saturation, it is just that it increases so very little after that that it makes it very impractical do design something like that. The core material usually offers a 1000 to 1 or better increase in field over an air core, so after saturation we see a huge loss in that amplification factor and so it makes it kind of silly to rely on that behavior for anything practical. In other words, if you need 1000 times the current to see a significant increase, it's probably not worth doing it that way.
A more practical idea would be to try to take advantage of the area factor, where you can double the area and thus double the effective area the field has influence on. This would have applications in various areas. 