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I am building a rail gun for a physics project, but I am confused on whether to use capacitors like 2.7V 500F capacitors or a 400V 3300uF capacitor. Most tutorials seem to use many 400V ones in parallel but I can't afford more than one. Initially I was planning to use 4 of the 2.7V caps in series to attain 10.8V at 125F.

The potential energy stored in a capacitor is 0.5 * C * V^2. The 400V capacitor would store around 264J while 4 2.7V caps in series would store around 7290J! Considering the railgun would at best be 20% efficient, the 2.7V caps seem to be a much better idea, but I haven't seen anyone using them, why? So which one would you guys recommend.

The only compromise I see with using the 2.7V caps is using a much longer barrel for as much of electrical energy to be converted to kinetic energy as the caps store a lot more charge and discharge slower because of the lower voltage.

I plan to use copper rails with a steel ball, 10mm used in ball bearings as the the projectile. I thought of giving it some initial velocity by pushing it with a spring to prevent it from welding itself to the rails. If you have any suggestions for these stuff also, that would be appreciated. Thank you.

Edit: Thank you guys, I will keep these things in mind. I do know that such high currents I dangerous, thank for the heads up anyways. I am wondering though whether I will actually attain such dangerous velocities with a very basic DIY design as I thought I would lose most of the energy to friction and heat. Also, I am worried about my capacitors blowing up, since I would be basically short the capacitors and they have a peak current rating of 180A. Should I add a huge resistor or even an old bulb to increase the resistance of my whole circuit? Or as Samuel weir mentioned scaling it down to safer levels. What do you guys think about 4 9V 1F capacitors in parallel?

Initially I was considering using something like these : https://www.mouser.in/ProductDetail/AVX/SCCY68B407SSB?qs=sGA

Here is the link for the 9V 1F I am thinking of now : https://www.mouser.in/ProductDetail/AVX/SCMR22L105SRBB0?qs=sGAEpiMZZMuDCPMZUZ%252BYl6pWnZvuEsiEPl7ldT8lrOU%3D

Any other capacitors you guys can suggest with lower potential energy levels that would work, I will use smaller projectiles if necessary also.

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    $\begingroup$ The energies that you're considering using are dangerous. I would suggest greatly scaling down your project idea. Also, the 2.7V, 500 Farad capacitors that you're considering (I see they have some on amazon) are probably some electrolytic type of capacitor which doesn't have very fast discharge/charge times. $\endgroup$ – Samuel Weir Apr 21 at 18:17
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The electrical resistance of the components in your rail gun will be very low, so voltage drop is not the limiting factor in your design. You want to use the ultra-capacitors to give you as much capacitance as possible. Then you want to connect your capacitors (if you have more than one) in parallel, as the equivalent capacitance of a capacitor bank is maximized in the parallel configuration but that capacitance is minimized in the series configuration.

The equation that applies to parallel capacitors is:

$C_{eq} = C_1 + C_2 + ... + C_n$

The equation that applies to series capacitors is:

$1/C_{eq} = 1/C_1 + 1/C_2 + ... + 1/C_n$

Thus, for the series configuration, it is seen that the equivalent capacitance is smaller than the smallest capacitance in the series ... you don't want to connect capacitors in this configuration.

Note - as has been pointed out in the comments by Samuel Weir, what you are doing is hazardous at best, and outright dangerous if you let inattention, immaturity, etc., get in the way of safety concerns. You will be dealing with large current flows, sparks, potential fires if flammable substances are close to your equipment, high kinetic energies from your projectiles, and possibly other issues that I haven't thought of. If your teacher lets you bring your rail gun to class, take ALL normal safety precautions (e.g., goggles, inspection of the rail gun range before firing, attention to where people are located, etc.), don't "show off" to impress friends, and don't let others commandeer your equipment in order to "show off" or "clown around". There is a REAL possibility of personnel injury, and YOU bear the responsibility to keep everyone safe.

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Here are some more design considerations.

The supercaps do store huge amounts of energy, but to dump that energy at 2.7 volts will produce truly gigantic instantaneous currents. Although the thing that drives the railgun is current, managing huge current means designing connectors and wires with extremely low parasitic resistances. Even a hundredth of an ohm in series with the current surge will dissipate so much I-squared-R power that the source of that resistance will turn into a bomb when the current comes on.

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