star trek - Could a shuttlecraft warp engine be used on a starship?

Several types of Starfleet shuttlecraft in the Star Trek universe are warp-capable (e.g. see this question).

I was thinking about the fact that a starship can be powered by dual, smaller warp cores with redundancy, just like modern multi-engine aircraft, and was wondering why no one ever thought to replace a damaged or missing warp core on a capital starship with a bank of shuttlecraft warp cores.

Is there a reason why a capital starship could not reach, say, a minimal warp (e.g. Warp 1 or 2) by gutting the warp cores out of a dozen or more Warp 5 shuttles and banking them together? Has this ever been explored?

Obviously, being able to use shuttlecraft engines as a makeshift warp drive would detract from the storytelling aspect of losing a warp core, but is there any in universe explanation of why this would or would not be possible (e.g. computer control not scaleable to more than N cores? fundamentally incompatible technology?)? Do warp-capable shuttlecraft even have standard (or at least standard-ish) warp cores (albeit small), or do they enter warp using some other method?

I would define "reaching warp" as attaining at least Warp 1 for a non-trivial length of time, even if the setup is not sustainable in the long term, is somewhat dangerous or risky (e.g. a 10% chance of a core breach might be OK), or is otherwise not ideal.

Answer

No (probably).

While in theory a shuttle's warp core (or rather multiple shuttle's warp cores) could be used to create power to help run the Enterprise-D's warp engines, in practice the sheer scale of the ship would make this a next-to-impossible feat of engineering.

Maintaining the Enterprise-D's warp field at Warp 1 (a bubble nearly a kilometer across) requires 20 gigajoules to create the field, and approximately 200 megajoules to maintain it. By comparison, a type 6 shuttlecraft is barely able to produce enough power to sustain a bubble ten metres across for more than a few tens of hours.

Although no specific figures are given in the TNG Technical Manual, we can presume that the power generation capacity of a shuttle's miniaturised Matter/Antimatter engine is going to be into the megajoule range (or maybe even below) rather than the gigajoule range. It would therefore take hundreds of these miniature cores working together to provide enough power for the Enterprise to create a stable warp bubble.

On top of all that there may be additional logistical details with trying to create a stable warp field when working with a power supply operating at a wide variety of differing energy frequencies.

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That all being said, Janeway (in VOY: The Void) feels that her shuttles can play a part in sustaining basic life support and other electrical systems even if they can't get the ship to warp.

NEELIX: I used to make a living scavenging for supplies. Let me take one of the shuttles. I might be able to find deuterium on one of those abandoned ships.

TUVOK: The shuttle would be too easy a target.

JANEWAY: I appreciate the offer, Neelix, but we're safer if we stay together.

SEVEN: The shuttles may be useful in another capacity.

JANEWAY: We could use their warp cores to augment power on Voyager.

_{^{VOY: The Void}}