The 10,000 ly jump was longer than the 17 second ones, it lasted longer because there was the Delta Flyer acting as a pilot boat.
The Delta Flyer never sent any successful corrections, so its role here is moot.
Chaos theory; there may not be a margin for errror. it might just blow up when you push the start button next time
While that's technically a possibility, it contradicts on-screen evidence. In both the simulation and actual use, Voyager was able to enter Slipstream and use it for several seconds before the phase variance became a problem. We'll never know if "hopping" would work because they never tried it, but balance of probabilities suggests that it should (provided they had enough special crystals).
What you're saying, is the US Military should do away with parachutes because there was that time where a guy managed to land in a haystack and walk away when his parachute didn't work. After all, troops would be deployed quicker. And if it happened once, there's got to be a way to replicate it, right?
I'm not saying that at all. Based on the on-screen evidence, there was never any real risk that Voyager would blow up the moment they pressed the button. The crew may be morons, but even they wouldn't have designed, built, and tested the drive without taking
that into consideration. The phase variance was only discovered at the last minute by Tom Paris, and from what we've seen it only started to take effect after Voyager had been in the slipstream for several seconds. They attempted to compensate by using the Delta Flyer, but Voyager just wasn't up to the task of going all the way to the AQ in one jump. While it's mere speculation on my part, it seems more likely than not that the main reason why they didn't try "hopping" was because of the crystals, which were specifically mentioned to be degrading and becoming unusable.
It should also be noted that Voyager built
two Slipstream drives. The first one was built in time to chase the "USS Dauntless", and they were able to whip that one up very quickly. Apparently all it required was some modifications to the warp core. We don't know exactly what the modifications were, but as there was no mention of things like the special crystals or Borg tech being used it's more likely than not that exotic parts weren't necessary. They were able to get a full hour of use out of it, so navigation wasn't an issue. The problem with their first drive was that it was considerably slower than the second one (IIRC it would still take days/weeks to get back to the AQ using it) and Voyager's hull wasn't capable of withstanding that kind of stresses for that long.
Apparently their solution was to build a 2nd Slipstream drive that was many times faster, and hope that Voyager wouldn't be in Slipstream long enough for the hull integrity issue to matter. Obviously that didn't work out as intended.
It's not explicitly stated in the episode; but I'd presume it's stuff they've nicked, as she says borg technology, not borg knowledge. If you get the know-how to build something from France, you're likely to call it french knowledge, or science, not French technology, that makes me think of physical goods from France. Hardly hard and fast, but I'd say balance of probability is she's talking about actual equipment. In various other episodes they explicitly go about nicking things, such as the slightly later Dark Frontier. Voyager's deflector itself - the thing used to generate the slipstream remember - was altered by the Collective in Scorpion
It's just as possible that at least some of the parts they nicked had equivalents in the AQ, but they weren't able to build / replicate them themselves. To use the French analogy, if you take your car to France and a part breaks, the fact that you used a French mechanic with a French part doesn't necessarily mean that your country is incapable of producing cars, it could just mean that you don't have the tools and parts in your car to fix it yourself. I would imagine that a place like Utopia Planitia would have more options when designing and building things than a small starship trapped across the galaxy without support.
Also, IIRC while the Borg used the deflector to open a singularity to S8472 realm, that was done within a couple of minutes and there wasn't any mention of the dish being
physically altered by Borg tech. There is no evidence to suggest that the Borg had permanently modified the deflector beyond the capabilities of Starfleet to reproduce, nor was Borg tech mentioned being used when they built their first Slipstream Drive in "Hope and Fear".
Of the two drives that were built I agree that the 2nd drive would probably be a lot more difficult for Starfleet to successfully reproduce given the navigational issues, special crystals and explicit use of Borg tech. IMO it's probable that Starfleet would eventually be able to reproduce the first drive, and their only real issue would be designing a vessel that's capable of withstanding the stress over long periods. Sure, it may be slower than the second drive, but it's still much quicker than their conventional warp engines.
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