Railgun: Problems with reality check

[Elon]

So I was doing some calculations last night on railguns for fun, and I got some very surprising results which seams like they must be wrong. The calculations are simple and I must have overlooked something. So we all know that F = B * I * L when all are orthogonal, a capacitor discharge is I = V/R * exp(-t/(RC)) plugging in these into a(t)=F(t)/m and integrating to get velocity then plugging in reasonable numbers (found a 500F capacitor online so F=500, V = 2.7 V, R = 2.5* 10^-5 ohm (calculated from reasonable geometry on a projectile of aluminium that's 20mm*10mm*2mm and a 10cm long rail of copper that has a cross section of 1cm^2 and B = 0.5 T from two neodymium magnets close to each other creating a homogeneous field over the projectile and a mass of 8 grams (some added mass to the projectile instead of just the weight of aluminium alone). Plugging in 1 ms as the time of acceleration gave me something like 300m/s. Integrating the function again to get the length of the rail, again with 1ms) gave me a length of around 20 cm.

This seams completely unreasonable to me and I must have done something wrong (this is why I didn't write out all the integrals and such, if someone would want to double check it by doing the integrations themselves I would apprechiate it a lot :D ). The materials to test this device costs less than 10 dollars and it just seams unreasonable that you can build a pistol comparable to a 9mm pistol for less than 10 dollars. I do not want to try this in practice because of legal and social issues, but I am still interested in knowing if it would work.

Can anyone see any obvious flaws here? I considered eddy currents slowing down the projectile, but those can be removed by slicing the projectile into many glued together conductive slices, right? :s I am confused :s

 

[jedishrfu]

Here's one such implementation:

 

[Elon]

Here's one such implementation:

That seams to be a coilgun, operating on a different principle than a railgun, I am only interested in a railgun and more specifically if the calculations I proposed and evaluated are correct, not if railguns/coilguns have been implemented since we know the navy has one. I am basically asking "could you really build a deadly weapon equivalent and even better than a 9mm pistol for under 10 dollars without any powertools or machining required. It seams completely unrealistic to me but I can't find the error in my calculations and I do not wish to try it since if it works I would be breaking the law amd putting myself and others in mortal danger when I test it since I don't have any safe area to test it at.

 

[TeethWhitener]

You found a 500F capacitor online for under $10 ? Most commercially available supercapacitors are at least $50 a pop.

Edit: I didn't check all of your assumptions, but I ran through the numbers you gave and the current is roughly I = V/R = 2.7V/(2.5×10^-5Ω) = 108 kA. (The exponential turns out to be ≈1). I have to imagine there'd be some heating going on here that you're not accounting for.

 

[Elon]

You found a 500F capacitor online for under $10 ? Most commercially available supercapacitors are at least $50 a pop.

https://m.ebay.com/itm/1PC-Farad-Ca...%3A762d496315e0aa469485fe39ffe72858%7Ciid%3A1
There is is, it's available on many other sites too, here's someone testing one and getting around 435 F reading from it:


So it doesn't seam to be exactly 500F but close, and it probably varies from capacitor to capacitor, if someone would buy like 10 of them and test each one it would be greate, but still 430 F is still very good for a couple of dollars.

 

[nasu]

Supercapacitors have internal resistances of the order of at least mΩ. Some have even larger values. The current estimate based on the rail resistance only may be off by at least two orders of magnitude.

 

[Elon]

Supercapacitors have internal resistances of the order of at least mΩ. Some have even larger values. The current estimate based on the rail resistance only may be off by at least two orders of magnitude.

Thank you :) This is exactly what I was looking for, I will find out the internal resistance and update my calculations :D Anything else you can find that I have overlooked?

 

[Nugatory]

I am basically asking "could you really build a deadly weapon equivalent and even better than a 9mm pistol for under 10 dollars without any powertools or machining required.

It's possible to build a device that delivers a projectile with energy and momentum comparable to that of a 9mm pistol for ten dollars. That's not the same thing as "a weapon equivalent and even better than a 9mm pistol" once you consider accuracy, controllability, rate of fire, and other requirements for a weapon; a better comparison might be with a ten dollar zip gun.

(Whether a railgun can be built on that budget is another question)

 

[Elon]

It's possible to build a device that delivers a projectile with energy and momentum comparable to that of a 9mm pistol for ten dollars. That's not the same thing as "a weapon equivalent and even better than a 9mm pistol" once you consider accuracy, controllability, rate of fire, and other requirements for a weapon; a better comparison might be with a ten dollar zip gun.

(Whether a railgun can be built on that budget is another question)

The reason I said "equivalent or better" is because there are many properties of the railgun which could be considered better than a regular pistol, since the energy density of a lithium battery is higher than that of bullets you can put more bullets into the gun for the same weight, since you don't need a heavy barrel that could also reduce the weight of the gun since it can be built almost entierly out of light weight cheap aluminium. The rate of fire can be as high or even higher than a pistol, the recharge time of a the capacitor is approximatley 5 times it's RC constant, and this had an RC constant of 2.1 ms in (altho this has later turned out to be wrong by atleast a factor of two, so let's say 10 ms) meaning you can recharge the capacitor in 100 ms or 0.1 seconds, which is a fire rate comparable to that of a regular pistol. The thing which makes it surpass any modern pistol is the ammo, you do not need gunpowder or something equivalent, you just need a source of electricity (Which could even be generated by your own body through a human powered generator) and a piece of conductive metal, a sodacan could be used as ammunition after being either melted down or just hammered into a compact enough shape. This would be a huge advantage for rebell warefare, super cheap full auto guns, no need for large supply chains of amunitions and such. The accuracy I can't say much about, but considering that there are very accurate railguns out there it is physically possible to build accurate railguns, maybe not possible within 10 dollars, but still. This is why I felt this is completely unreasonable, if it were this simple it should have been done, so my question was, why hasn't it. Zip guns are not really comparable to that, they are just a worse way of using a bullet, and if you live in the majority of the world where bullets are heavily restricted a Zip gun is useless since you can't access the power of a bullet.