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I mean the Academy doesn't seem much larger than an average university.

According to Wikipedia, the Federation has more than 150 member planets and thousands of colonies spread across 8,000 light years. These have to be guarded with a large number of ships each carrying dozens or hundreds of officers.

Yet, throughout all the series they kept mentioning the Academy, how hard it is to get in, how every officer has to successfully attend it (for example Nog in DS9, there seemed to be no other alternative for him to join Starfleet).

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    COs vs NCOs most likely. – Xantec Nov 12 '12 at 22:35
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    Enlisted personnel (NCOs) go to the Starfleet Technical Services Academy, on Mars. Still probably too incomplete for an answer, since only the Mars location is listed. – Izkata Nov 13 '12 at 1:23
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    Overhead in the Admissions Office: "Quick, remodulate the iso-enrollment array before it's too late! We've got less than 30 seconds before the dormitories implode, the sheer mass of cadets collapsing into a black hole!" "Captain, I can't! The positronic rejection letter emitter is jammed!" – John O Nov 13 '12 at 15:06
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I will lead this answer with my own extrapolations of how the Federation (and by proxy, all Alpha Quadrant species with similar structures) staff their military arm with my own experiences in the United States Navy.

There are several ways to answer this question. The simplest but not canonically supported is:

  • StarFleet Academy is much larger than it appears when we see it presented on film. We are never given a complete tour of the facility, no matter how many times we visit it, so to be honest we have no true idea of how large it is. For all we know, it could consume the entirety of the San Francisco area with its resources scattered throughout what we think of as the city proper.

  • To compare Star Fleet Academy to a modern university we can reference Arizona State University (ASU). ASU has a population of approximately 56,000 students in its program at any given time. It has four geographically local campuses which offer 250 different majors and 100 graduate programs. Its large population could be spread out over a wide array of locations with the San Francisco branch being the best known, largest and most central facility.

  • There is no reason SFA could not have satellite campuses on-site of other normal Terran Universities or Terran outposts, ala ROTC programs known in the United States today. Recruits could be found, recommended, remotely trained and eventually sent to the Academy for Officer's training. With the holodeck facilities available, every student could potentially receive quite a bit of standardized training before even being accepted. I can visual the equivalent being the current military entrance examination taken before being accepted as a candidate for boot camp as an enlisted man.

  • If the Federation is anything like the current military organizations of Earth, enlisted men's training programs are far shorter than officer's training. Their technical specialties can be completed in as little as a year. If you have a facility like NTC San Diego's Recruit Training Command, you can train as many as 40,000 troops in a year (as RTC did during the Korean War).

  • Star Fleet is not comprised only of officers, its enlisted ranks are likely trained in military training facilities where their technical skills could be learned and opportunities for rank development can take place. Candidates whose skills, training or aptitude do not allow them to attend the StarFleet Academy as an officer, may still have opportunities as enlisted personnel.

  • Such enlisted training could take place at any military facility with the troops, space and training facilities in the same fashion as Recruit Training Command at CNIC, Navel Base, San Diego. If the Federation matches the standard military ratios, there are an average of 5 enlisted men for every officer. This may vary from ship to ship but this means, the bulk of the average Federation ship is enlisted personnel.

The problem with media and science fiction shows is often insufficient effort is dedicated to the infrastructure required to explain how manpower, ships, and technology are developed, provided and maintained to explain the existence of vast fleets of ships and training of staff for those fleets. This lack of effort could be simply that stories do not revolve around such infrastructure issues, or it could be the writers simply have no idea of the resources required to run a military organization the size of the Federation.

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Taking some numbers from EU sources, I find a the Battle of Wolf 359 was "forty starships" - and that was over 10% of the fleet. Most of which had smaller crews than the Galaxy class. But even presuming 400 Galaxy Class Cruisers, that would only be 400,000 people. If we presume 1/2 are officers (unrealistically high, but until late in TNG we're not told of enlisted), and that half of those are ensigns... and that Ensigns remain so only 2 years... we're looking at 100K officers, 50K ensigns, and 25K ensigns per year...

We do know, however, that most of the ships are under half the crew size, most of the ensigns serve as such for 3-6 years (much slower than in the US military), and so we can trim those numbers. let's presume Starfleet has about 1/3 officers, about 250K total staffing, 4 years average as Ensign, and 1/3 of the officers are ensigns... we get 84K officers, 28K ensigns, 7K per year graduating, and a 4 year program at the academy, for a total enrollment of probably 40K cadets. It's a LARGE university, but note that the largest 10 in 2012 run 44-60K students enrolled. Assuming a 1:50 instructor-student ratio, I'd expect about 1000 instructors, and probably 1000 enlisted support staff as well, for a 2000 member staff. Plus probably another 1000-2000 support civilian staff.

Now, presuming technicians normally take a 2 year academy program, and have an average of 5 years service, and are half the service, that could push up Starfleet's academy enrollment quite highly. We hear Chief O'Brien speak of his time at the Academy in several episodes.

Let's assume a 50% Enlisted rate, with an average 60% of them being working technicians, and averaging 5 years until they move on or up, and 50% of officers are ensigns serving for an average of 5 years before promotion or leaving, this means 30% x 2/5 are in technician school; likewise, 25% x 4/5 are in Officer programs, and using a 400K personnel list, that means 80K officer cadets, and 48K are in technician training. 128K would be large for a single facility - about twice what we see for any campus (Miami-Dade University is about 80K on campus, but not all are enrolled; that includes some staff on campus, and a significant fraction of spouses of enrolled students, etc.)

If we instead presume a 1/3 officer, 1/3 of officers are ensign, and 2/3 of enlisted are working technicians, with 6 years for Ensigns and 6 for techs, and 4 years academy for ensigns, 1 for techs, and 400K persons in Starfleet, 44K ensigns, with a 2/3 replacement enrollment rate, about 30K Officer Cadets, and about 44K technician recruits... for about 70K.

One thing we do know - the Academy is a multiple campus system. There is a remote campus at one of the gas giants - not for classwork, but for field activities of various kinds, including the flight range. The Extended Universe includes a Martian campus, and one outside the Sol system, as well.

In the earlier TOS era, we know of 12 large starships. We can presume that there are 2-3 support vessels per large ship... and so probably 50 ships in the fleet, and maybe 3000-4000 members, and so graduating classes of a under 500 per year would be sufficient.

  • Minor quibble, Miles O'Brien was eventually established as an NCO in TNG 4x02, Family... Mostly. (+1, though) – Izkata Nov 16 '12 at 2:29
  • Yeah, I forgot that... but it's basically ignored until DS9 with the insignia change. – aramis Nov 16 '12 at 3:05
  • One thing - wee see a "crewman" with no pips in Picard's office in an episode, there are enlisted referenced in TNG, just without clear insignia. But, at the same time, Chief O'Brien attended the academy, too. Edit time. – aramis Mar 21 '14 at 9:53
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I am not sure how big the Academy is or whether what we have seen is just one campus and there are several other ones or whether there are starfleet acadmies colleges on various planets etc.

However, the fact that there is a finite space is probably a good thing for Starfleet as they can be more selective in who they accept. Rather like Sandhurst in the UK. It is also possible that not every student spends all of their time there, there could be field posts, remote studying etc.

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    Being "more selective" is NOT a good thing if it results in having too few people. – Michael Borgwardt Nov 13 '12 at 11:14
  • As in most things, it is a balancing act. Obviously there is a critical point at which you have too few people e.g. 1 man could not run all of Starfleet no matter how clever he was. However, if the situation were to happen where there was too little space to fill requirements then one of the other solutions I suggested would probably come into play e.g. remote study, off site locations etc. – Stefan Nov 13 '12 at 11:52
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    At least one example of the remote study was seen in Deep Space Nine with the Red Squad students doing the circumnavigation of Federation space. – Xantec Nov 13 '12 at 12:35
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This has always bugged me since Wesley has to try several times to get into the academy yet Nog gets in no problem and hes from a non-federation race.

I'd say all officers have final training at star fleet academy as its safe to assume remote training programs like Wesley used were also used by Nog. Also though it's never outright talked about its implied in both Voyager and DS9 that an rotc system is also used for per-training, so officers might only need a few years of specialized training before being shipped out as ensigns i.e. four years might be what an untrained but super smart cadet might need but most would have had a lot of training through rotc, remote training and satellite programs and only need a year or two of specialized training for the assignments they are going to start with. this would make Wesley less desirable because he was like 13 or 14 before he started training giving him only 2 or 3 years of training were as Nog had been taught engineering of Federation, Cardassian, Bajoran and Ferengi systems which probably made him more valued.

  • Welcome to scifi.stackexchange! Do you have any canon-evidence that such a training-programm exists? And how would such a program help with the space-problem at the acadamy? – Einer Sep 30 '14 at 9:37
  • Wesley has to try several times to get into the academy yet Nog gets in no problem - Wesley was trying to join at a time of relative peace. Nog was trying to join up after a war with the Borg, and Jem'Hadar. Entrance standards are often lowered a bit when you need to recruit more soldiers during a war. Wesley initially failed the psych exam. He seems to have grown out of that problem, so it may have just been something related to him being relatively young for a human. – Zoredache Jan 9 '15 at 21:42

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