Electrical – If I want to build a railgun, how to calculate the length of the rails


I want to build a railgun, but I find it difficult to calculate the length of the rails, since the acceleration is not uniform, due to the voltage's decreasing when the capacitors discharges. Neither do I know the way to calculate the curve of the capacitor's discharging. I plan to use 6 fully charged 1000uf 450v capacitors as the energy source, giving 1215 Joules of energy.
The projectile will be a 7mm steel ball weighting around 1.4g.
The rails will be copper cylinders, 10mm in diameter. The current in the rails will also create the magnetic field.
How long should the rails be?

Best Answer

The force available to accelerate the projectile decreases over time and distance. At the same time, the deceleration forces are increasing (friction with the rails, air resistance, etc.) You need to find the crossover point where the net force drops to zero, and have the rails end somewhat before that point. That's where you'll have the greatest "muzzle velocity".

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