So, in this history, they just said "screw it, I'm giving railguns to the army", and they added a machine gun like rifle with big caliber, but low recoil, they carry a backpack with batteries and a lot of ammo.

But since I don't really know how much energy a railgun would require to shoot a bullet in the same speed of normal rifles, I don't know how big this backpack would need to be nor if it could be applied to tanks and armoured vehicles.

How much electricity I would require for such?

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    $\begingroup$ This looks like more of a physics question than a question about worldbuilding. $\endgroup$ – sphennings Apr 9 at 14:46
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    $\begingroup$ Interesting that a propellantless rifle will have quite a bit less recoil, for the same resultant projectile, than a normal firearm with chemical charge propellant. $\endgroup$ – PcMan Apr 9 at 15:13
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    $\begingroup$ @PcMan Correct -- the rocket effect of the escaping gas can account for up to about 1/3 of the recoil of a rifle round, as I recall. $\endgroup$ – Zeiss Ikon Apr 9 at 16:01
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    $\begingroup$ Why not just do the (very simple) math yourself? $\endgroup$ – jamesqf Apr 9 at 16:43
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    $\begingroup$ @PcMan thats both true and false right? Chemical propellant has a high peak force upon ignition that propells the bullet, a railgun can evenly accelerate the bullet along most of the length of the barrel if I recall correctly making it easier to handle the recoil as there is a lower peak force to deal with. Additionally your answer hasn't touched on the efficiency of chemical propellant, only on the energy imparted on the bullet. Also I read the article and the potential for 66% efficiency railguns is mentioned if materials and construction improve $\endgroup$ – Demigan Apr 9 at 17:56

According to this research paper, railguns can be about 47% energy efficient.

A 'normal' rifle bullet (Winchester .308 firing and 11 gram bullet) imparts some 3551Joule to the bullet.

One energy calculation later: Your railgun requires 3551/0.47 = 7555 Joule total energy per bullet.

Slightly more than half of this ends up as waste heat in the device.

I'm somewhat unclear as to how well railgun technology scales down to as small as a single 11 gram bullet, and speeds as low as only 800m/s

The typical railguns are more in the 50 MegaJoule class, firing a projectile of some 3kg

Battery size: A single Li-Ion AA battery stores some 11000 joules.
Given a suitable system to get the whole charge out of it, buffered and delivered in a suitable format for the gun without losses, you will need 7555/11000 = 0.687 of an AA Li-Ion battery to fire one bullet..

At 23g each, and ignoring packaging, wires, etc... A 1 kg battery pack will allow you to shoot off a 63 round magazine.

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    $\begingroup$ Thanks for your answer, but I can only chose one after 48h, but hey, do you know more or less how big a battery would need to be to provide energy for one shot? (nothing super specific, like "a car baterry" or anything like that) $\endgroup$ – Neto Ananias Apr 9 at 16:46
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    $\begingroup$ @NetoAnanias added to answer body. Bear in mind there is lots of room for variation, AA batteries are merely the most common format, not always the most efficient, and there's quite a bit of handwaving of packaging, wiring, conversion circuitry, control circuitry, cooling, and likely many other factors I miss. $\endgroup$ – PcMan Apr 9 at 16:56
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    $\begingroup$ Is the energy imparted the same as the energy the bullet has when exiting the barrel? Also a nice comparison would be the energy the explosives have total vs imparting on the bullet. If I remember correctly, explosives impart relatively little of their energy on the bullet. The advantage is that we can pack a lot of it in a tight space and have it impart the energy very quickly. $\endgroup$ – Trioxidane Apr 9 at 16:57
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    $\begingroup$ @Trioxidane out of my comfort zone, but let's wing it.. 308 reload for that round takes about 45 grains. 2.91 grams. at 6000joule/g, that's 17460 of chemical energy, producing bullet energy of 3551. So about 20.5% efficiency. Sounds about right for an "internal combustion engine" :) $\endgroup$ – PcMan Apr 9 at 17:07
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    $\begingroup$ Also bear in mind that a Railgun can DIAL the power. Shoot with less power to avoid overpenetration or shoot with more power to bypass armor. It will be really handy and could simplify a lot of logistics for the army. $\endgroup$ – Gustavo Apr 9 at 20:12

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