Is there a theoretical limit to projectile velocity of a railgun if power and length of gun are stretched out to extremes, say 1,000 foot long rail.
C.
Sure - both the projectile’s ability to deal with compressive heating and the rail’s ability to maintain sufficiently high current densities that they don’t melt or expand and so reduce the exit velocity.
I’d think that if the electric field between the rails got too strong, the air between them would break down and you’d get arcing between them even without the projectile.
Well you could put an insulator between the rails to minimize that issue. Assuming it doesn’t impact the magnetic field to any noticeable degree and drop the gun’s efficiency.
or initiate nuclear fusion
As always, XKCD has it covered in detail
Relativistic Baseball
That would be an option if you just wanted to maintain a voltage on the rails, but there has got to be open space between the rails to send the projectile though.
Eventually as you get farther along the rail and the velocities get really insane, it becomes difficult to accelerate the projectile any more. The dwell time within any one coil segment gets so short that you can’t impart much energy without the power (=energy/time, where time is a very very small number) getting so high you can’t channel it without melting your equipment.
Because we’re dealing with a physical system, not just data, there’s also the problem that any slight variation in the projectiles and the temps and the atmosphere, etc., very slightly alter the acceleration profile. Eventually at high enough speeds, you start needing greater precision of control than can be done with simple timing; you need to actively track the projectile down the rail to trigger the next pulse on time. That’s going to be hard to do well enough and precisely enough.
IOW, the problem won’t be so much a physics barrier as an engineering and materials science barrier. After we’ve had production railguns for a few years we can certainly expect the max muzzle velocities to start creeping upwards as engineering progresses based on lessons learned with the production systems.
Could ride on top, all it needs to do is bridge the rails.