I haven't done engineering In a while but I remember shoving a resistor somewhere slows down the discharge

My first thought would be to program delay into the system using a microcontroller.

A resettable fuse or circuit breaker might work. They come with various trip delays, so you might find something that will open the circuit back up in the right amount of time. I believe larger gauss guns actually use sensors to turn off the circuit once the bullet passes a certain point. By doing that you can add multiple stages to further accelerate the bullet.

You can slap a resistor in the circuit and dial in the response time. Or rewire the capacitors to change the circuit capacitance, but that will sacrifice some current which is your driving force for the rod. https://en.m.wikipedia.org/wiki/RC_time_constant

True, this is what you're talking about: https://socratic.org/questions/how-do-resistors-affect-capacitors#:~:text=The%20larger%20the%20resistor%20%2C%20the,has%200%20Volts%20across%20it.

but they don't want to slow down the capacitor discharge, since that would decrease the force with which the projectile is propelled. They want to very slightly stagger the discharge of each capacitor, so that each capacitor discharges as the projectile is passing it down the barrel.

To do that, I would try using three solid state relays, and have each of them controlled by a microcontroller (e.g. an Arduino, or ESP32). Each relay would connect a different capacitor to ground (i.e. each relay would allow a single capacitor to discharge). That way the microcontroller could tell relay #1 to close, which would discharge capacitor #1, then tell relay #2 to close, which would discharge capacitor #2, etc.

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Edit:

Actually, sorry, I misunderstood. They're not trying to stagger the capacitor discharge. But it does seem like they're trying to accurately time the discharge of all 3 at the same time? If that's the case, a single relay + microcontroller would still be helpful. Maybe I'm still misunderstanding though.

Edit #2:

The reason I misunderstood is because many rail guns actually do use multiple staggered electromagnets along the barrel. If you do that, you would want multiple banks of capacitors to discharge at slightly delayed times as the projectile is passing their respective electromagnet.

First comment is to be very careful, the current those capacitor could put through a human body at 400 volts is very very far above lethal.

 

Second comment is, a resistor is going to drag down the cicruit and dissipate a lot of your energy. You know that the rate of change of current at the start, at time zero, is voltage divided by inductance, V/L. So at the beginning the graph of current over time looks like an increasing line of slope V/L. The total charge that has flowed is the integral of this which is 1/2 (V/L) t^2 if t is time. But then the voltage starts to decrease, the voltage is Q/C where Q is charge, and at the outset Q=Q_0 - 1/2 (V/L)t^2 where Q_0 is starting charge. The best way to continue is by differential equations because V is not really constant, but for small values of time, if we approximate the charge that has flowed as 1/2(V_0/L)t^2 where V_0 is initial voltage, then remaining charge is Q_0 - (1/2)(V_0/L) and voltage is V= (1/c) (Q_0 - (1/2)(V_0/L)t^2) so in this formula Q_0 is starting currentm V_0 is starting voltage and you see the voltage dropping off. It is clear that you need to increase L. As I say, this is just an approximation for small time.

 

By the way, you would also see if you write down the differential equation, an oscillation after the bullet has left. If you had an amazingly durable diode you could prevent reverse flow, but I do not know how expensive it would be to get a diode that can handle the very extreme currents you'd want to put through it.

 

You can see that you have a small coil --- that is the problem.

There's an entire EE degree to unpack here. The switch on time will be limited by the internal series resistance of the caps, best thing you can do is put them in parallel, which you've done, but when you do your calcs, don't forget to take this into account. For your switch off time, you want to use an IGBT - not a MOSFET. IGBT's are more or less the same but have better switching performance at high currents. I don't remember which ones specifically, but look at the IGBT's OneTesla uses in their Tesla coils. They sell replacements, look up that P/N and start from there. You may need to order a variant that can accommodate the currents your coil is drawing. Ballpark it by Vcap/(Rcoil + Rcaps).

Look up how to wire an IGBT as a switch and then use the gate as the on/off for your coil. Take a bottle of Adderall and watch very closely when the projectile gets to the middle of your coil and then quickly turn off the IGBT. Reaction time is key. When you realize you can't react that fast, think of a good way to use a sensor that will automatically switch off the IGBT when the projectile gets to a certain position. Perhaps an optical sensor, inductive feedback, or something. It will take some dialing in, but should get you there. There are a 1000 ways to optimize this, but this is a really great start and it's best to optimize one step at a time.

Keep it up! DIY projects and staying curious will get you much farther in your career than stereotypical "resume skills." When I interview people or look at resumes, this is one of the big things I look for - personal projects. To me, it means your curious, want to learn, and have a fundamental passion for engineering. Sure a coil gun may not be directly relevant to my company, but knowing that you understand the bigger picture - the product, the fabrication, iterating through failures, component costs - that is entirely relevant, and surprisingly a rare trait.

DM if you have some specific questions, I'll do my best to assist

I specifically look for hackers and inquisitive minds when I hire. I always tell people to bring in photos of DIY projects they have done and to not worry about how bad some of them are as I understand how ugly prototypes and junk building is.

Keep up the stupid shit! It will get you far and you don’t know why yet. But you’ll find out.

Putting a resistor in circuit will increase the response time, but that will reduce the force acting on the projectile in the beginning. You would get the same effect by reducing the charge voltage on the caps. What you, err... OP, ideally wants is maximum current going through the coil in 0 amount of time (maximum magnetic force) but turn it off right when the projectile gets to the center, otherwise the magnetic force will be pulling the projectile back to center after it gets to the other side, slowing it down. Since we have to deal with this pesky real world physics, there's a rise/fall time in current change that is dragged out due to resistance, so you ultimately have to switch off the coil before the projectile gets to center. There are a few ways to go about this, which is why engineering is so fun!

It's not reverse flow in this case, polarity shouldn't make a difference since it's just a magnetic pull. The problem OP is facing is that the coil is just a magnet pulling the projectile towards the center. At t=0, the projectile gains a ton of momentum rushing towards the coil, by the time it gets there the magnetic force has dropped a ton since the voltage of the caps has dropped. But there's still a little bit. Once the projectile gets past the coil, the magnetic field is now pulling back on the projectile, slowing it down. Since the voltage is much lower from when it started, it won't be an equal force, but it'll slow it down none the less.

There will certainly be a ringing after the coil dies down, but I don't think that's the source of OP's problem. Good point though, I recommended IGBT'S for switching the coil off and I didn't think of the flyback current on turn off. OP, look at guides to put a clamping/flyback diode across the IGBT. A 1N7007 should be fine. You can buy like 100 of them on Amazon for like $10. A great thing to keep in the electronics drawer too.

Use an H-Bridge.

The traditional solution to this is to have a multi-stage system, each stage being a capacitor, a coil, and a trigger circuit. Each stage is triggered as the projectile approaches it, using either a light gate or a hall effect sensor.

>polarity shouldn't make a difference since it's just a magnetic pull

 

Good point, the math for that isn't as simple as saying when the current reverses so does the force....it would if the projectile were permanently magnetized (and that were the significant effect) but it is just iron and its own magentization is caused by the coil and reverses too. If that did happen, one could try to tune the circuit to oscillate just once and pull the projectile partway then push. But as you say, by the time the projectile is at the midpoint one wants to have the current shut off.

or monostable 555