wouldn't the sheer mass prevent the ship from traveling beyond a certain speed or possibly not even able to move at all?
Even an itty-bitty ion thruster imparting a fraction of a Newton will
eventually get it moving to relativistic speeds, it's just a matter of how long you're willing to wait and how much propellant you have available. Munging the Tsiolkovsky equation a bit, you can compute the propellant mass as
)
So if the
Enterprise masses, say, 1.9 x 10^8 kg per one online estimate (
mdry), and we want it to go 0.5
c (
delta v), and our itty-bitty ion thruster has an exhaust velocity of 50,000 m/s (
ve), then we'd need on the order of
e2998 kg of propellant.
That's ... a lot (my calculator overflows on it). So, yeah, practically speaking, getting something as big as the
Enterprise moving would be a challenge.
I am not fully clear how the impulse engines would work, but it seems that they would have to put out quite a bit of energy to move the ship with any significant speed
It's never really explained exactly how impulse engines work. Given the name, it's strongly implied it's some kind of reaction drive, but God knows what the actual mechanism is. It could be a fusion drive sort of like what's used in
The Expanse (at least the TV version); a pellet of deuterium wrapped in a lithium (I think) shell, blasted by lasers to induce fusion, reaction products are directed out of the engine at near light speed. Low mass, but super-high velocity, providing a pretty good push.
But again, it's never really explained, and like with the itty-bitty ion thruster the fuel necessary would likely out-mass the rest of the ship by a lot.
The genius of warp drive (at least as commonly envisioned) is that you aren't moving very fast at all relative to local space; you're warping spacetime to bring your destination closer to you and push your departure point away from you. The mass of your vessel is almost irrelevant. And, what many people seem to miss is that if you can warp spacetime, then you get artificial gravity and inertial damping for free
1.
It's a big "if", though. The math works, sure, but the energy requirements are on the far side of feasible. I know people have been refining Alcubierre's work to bring that energy requirement down, but it's still more than we can realistically generate or harness with any near-term technology. There's a reason
Trek hand-waved it away with anti-matter.
- Although the Enterprise wouldn't be shaped like that; the images I've seen from Alcubierre's work shows something that looks like an elongated football with a ring around it, and I imagine the force of gravity would be oriented in the direction of travel; IOW, you'd be flying feet-first.