Star Trek
r/startrek: The Next Generation
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Impulse engines are probably too large and expensive to put on something like that, and you might need big starship-grade ones to be able to get something moving that quickly.
You would also want a tough deflector system, so that it isn't immediately obliterated by the first piece of space dust that it runs into, and a nice computer so that it doesn't just fly off into the first star 'til morning, and at that point, it might just be too expensive to bother with. You're basically building a small starship at that point.
At least in Trek, 24th century shields are extremely good at handling physical impacts. Even in a compromised state, with one of the shield processors having escaped and gone rogue, an ageing California class was able to take several hard impacts without so much as a scratch. They might have been able to resist indefinitely if their shields were performing optimally.
Earlier ones, like the ones fitted to the Kelvin-era Enterprise, are much weaker against physical impacts, such that the wreckage of a starship was able to still cause major damage to the outer hull, even with shields at full.
Shields are probably much weaker against energy fire, since they appear to be an outcropping of deflector screen technology, and as such, fare better against physical objects. A powerful energy weapon probably does a much better job at knocking down shields than just smacking them with the physical photon torpedo, even if the torpedo is fired at warp speeds.
If addressing kinetic impacts this isn't part of the handwavium, then there's frankly very little way to enjoy Star Trek. I am just an old English major, but various sources put the Enterprise-D at about 4 million metric tons of mass. If you accelerate that to even 5% of c with impulse drives, it would impact with a force of about 2/3 or more of the asteroid that wiped out the dinosaurs, and that's just one ship operating well within the accepted performance of the impulse drives.
@T156 this post makes me think of the “Infinite Mass Punch” in DC comics. https://vsbattles.fandom.com/wiki/User_blog:Matthew_Schroeder/Flash:_Explaining_the_Infinite_Mass_Punch
Wouldn’t a ship traveling at .25C firing a conventional missile effectively create the weapon that @kargarocP4 is describing?
I guess the rest of your points still stand regarding a deflector system for your conventional missile fired at sub-warp speeds.
I don't think system complexity is the issue.
They put impulse engines on 22nd century shuttlepods on the NX-01. They weren't even that big, probably about the size of a small room at most. And that's the 22nd century - they'd probably be a lot better by the TNG era.