I imagine Starfleet to be huge. If there are (conservatively) a trillion people in the Federation, and .5% of them are in Starfleet, that’s 5 Billion people. Thousands of planets, moons, asteroids, and space habitats. Maybe hundreds of thousands or millions of civilian ships.
I'm thinking 1% of UFP might be more likely to be part of SF given its an attractive option for exploring space with trained people who can keep you safe (such safeguards aren't always present on civilian ships who mostly DO rely on SF to keep them safe).
Having 1% of UFP citizens in SF would equate to 10 billion individuals.
But, even with only say 5 billion people in SF, those are quite the fun numbers to work with, so let's explore that:
This is why SF can EASILY have at least over 70 000 ships in active service in the late 24th century... and that's a fairly small number actually, considering the fact that even if you had 1200 SF officers [not including civilians] per starship, it would mean almost 90 million people working on starships alone leading up to USS VOY (and those are inflated numbers actually given the fact not every ship has the population of a Galaxy class [which in itself has a mixture of SF officers and families] - most starships would have half that population size I think in terms of SF officers).
74656 starships leading up to VOY seems fairly small too... given limitations of Warp drive and long journey times contrasted to 8000 ly's of space.
Starbases such as spacedock 1 could house a large contingent of people.
It was said by some sources that Spacedock 1 is capable of housing 60 000 SF officers and 40 000 civilians (but otherwise could house about 150 000 people in total).
We've seen that DS9 had a much smaller number of SF officers onboard - over 900 (but I'd round it up to 1000 for something that size).
Even if we assume one spacedock mushroop type starbase per UFP member planet... that's at least about 150 starbases and 9 million SF officers.
That's quite literally nothing (and don't think it would be good enough of a coverage for something the size of UFP which would in turn have a very large fleet).
Double up the number of starbases (at least 2 per UFP major solar system), and that number increases to 18 million SF officers.
And if we quadruple the number of starbases from say 150 to 600 - 3 per each UFP major species home system, and extra 3 in various nearby sectors equals 36 million SF officers on Mushroom type starbases throughout UFP space alone (we could even increase that 1000 mushroom type starbases for example and the numbers would only increase to 60 million SF officers on those bases).
In fairness, given how huge UFP is (stretches across 8000 Ly's and has over 150 member planets in late 24th century - aka, home systems of Warp capable species with fully developed infrastructure for ship building, etc - I would imagine that each UFP member planet home system like SOL would have similar SF presence and ship building capabilities around the main planet of origin after joining UFP, and possibly another planet like Mars that would have something akin to Utopia Planitia in the same star system).
We know that both Earth and Mars have a lot of ship construction facilities (aka drydocks) and support stations.
SF could easily assign 10 drydocks per UFP solar system to build a given class of ships... and they could easily build 1500 ships of the same class in a short span of time (say a month or less - it takes less time to build a ship than it would to design one [spend time on a drawing board]).
As such, UFP only building 12 Galaxy class ships never made sense to me. Given the size of UFP, the fact we're talking about fully developed member planets and SF presence having to be in each and every one of them with adequate starbases and ship construction facilities similar to SOL, not to mention highly advanced automation, replicators/transporters and a whole bunch of other technology that makes ship construction extremely easy (or at least vastly simplified).
So, even with UFP having lets say 74656 ships leading up to VOY and each ship having 1200 people (which is an inflated figure), it would give us about 90 million SF officers on Starships in 2371, with another 36 odd million on major starbases throughout UFP space.
That's only 126 million SF officers on all UFP ships and major starbases (not counting planets).
Lets say that UFP member planets have each about 1 million SF personnell... that would be at least 150 million SF personnell stationed on planets.
Even if we add 1000 outposts the size of DS9 that can each have about 1000 SF officers onboard, that would equate to only 1 million SF personnell right there. If you recall, DS9 at the start of the show was considered an outpost (it became a starbase later on after SF upgraded it heavily between S3 and 4).
So, now we have 150 million (stationed on planets), 90 million (on ships), 36 million (on starbases), 1 million (on outposts), totaling to about 277 million SF personnel (those are tiny numbers compared to the size of UFP).
If we add separate number of personnell stationed on drydocks (and presuming SF has at least 300 drydocks in each UFP member planet solar system), even with packing 300 people per drydock, you get an extra 13.5 million people assigned to ship construction across the entire UFP space (and lets be fair, with automation, you wouldn't be doing assembly of ships manually or welding stuff... thats what robots/automation would be doing).
So that's 295 million people - again, really tiny number compared to the size of UFP.
Side Note: SF could easily have 1.8664 million starships and SF personnell count would increase to 2.239 billion on starships alone... totaling to about 3.425 billion people (and we're still having just under 1.6 billion personnell to go to reach 5 billion people in SF).
If we increase the amount of SF personnell on planets from 1 million to 10 million per planet... that would give us at least 1.5 billion SF officers for all UFP member planets.
Ok... so with 74656 ships, 1000 large starbases, 1000 outposts, 150 member planets, and personnell for starship construction... would give us about 1.664 billion people in SF in 2371 (that might be a bit more sensible number - but its still nowhere near 5 billion mark).
Fun fact, if we actually allow SF to have 1.8664 million ships (with each vessel having 1200 officers - crewmen, ensigns, LT's, cmmdr's, etc), that would be 2.239 billion people on ships alone and the 'total' figure go up to 3.813 billion (that's a lot closer to 0.5% of people from UFP being in SF).
Would it be possible for SF to have 1.8664 million ships? Of course.
Going back to figures of having 300 drydocks per solar system, and taking a month or so to construct a ship (with automation it would likely be faster than this, but I'll make allowances for 1 month tops for something the size of galaxy class)... SF could build 45000 ships in 1 month throughout UFP.
If the shipyards are working for a full year, they would produce 540 000 ships. In 3 years, SF would be able to build 1.62 million ships (and 1.94 million ships in 3 years and 6 months).
Automation and technology can construct ships extremely fast (especially with transporters, replicators, tractor beams antigrav and forcefield tech) and with the process of technical efficiency (doing more with less), making new ships with less material (and maintaining them) would be perfectly doable (similarly SF would be able to upgrade older ship designs by disassembling their older hw and hull and recombining new materials/hw with replicators and put them into place).
Since most ships in UFP come with high levels of automation, would be capable of self-repair and self maintenance, servicing ships in drydocks every 4 years or so (if something can't be done in the field) would be doable.
I'd actually decrease the amount of SF officers on planets from say 10 million to say 6 million.
That way, you can have 600 million extra people on more starbases (about 8000 major mushroom type starbases each with 60 000 SF officers) and 120 000 outposts (each with 1000 SF officers).
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