Crew Compliment and their functions.

The original Gene Roddenberry guide (a 16 page booklet produced prior to 'The Cage') says the Crew Complement was 203 persons.

My 'unofficial and uncensored Trek Encyclopedia' says 432 crewmembers.

My 'official' Encyclopedia doesn't say, neither does the 'Chronology'. If it was mentioned in the series, I believe it would be in one of those two books.

So take your pick!
 
This guy also wonders what everyone does...

http://www.computercrowsnest.com/sfnews2/04_feb/news0204_4.shtml

Starfleet In Motion

There's rather a lot of crew on a Federation starship. So apart from jogging around a lot during a red alert, what the heck do they all do? Uncle Geoff muses on the unlucky blue shirts who draw the Enterprise's toilet duty.

Let's face it, everything is automated! You only need someone to operate the machines and cook meals (replicated food tastes bad because it is replicated at a molecular rather than a quantum level.)
 
Remember that the 20 odd crew that has been found would have to be at least trebled up for shifts. They don't just stop at some cosey starbase every night, so somebody has to drive and stoke the engines when Trip and co aren't manning things with gritted heroic teeth.
 
Talking to a Merchant Navy friend earlier and it looks as if Enterprise might be shorthanded!

If we just take the Bridge and Engine Room, there should always be a senior watch officer in command. Thus no deep blue vessel can sail without at least a Third Mate and Third Engineer, all of them have to be certified by maritime law (Passenger liners go down to a fifth and sixth, but the cargo has a habit of moving around so requires more care).

The only time you will find them on the bridge together is when the ship is entering or leaving harbour, or when it is sinking.
All this excludes the Captain, who does not have a standing watch at all. Captain's have very little to do with the running of a ship. Third Mate handles cargo, Second crew, First the ship.

Then you need a bridge crew. On Enterprise this appears to be a minimum of 3: Driver, Comms and Lookout (or whatever the T'Pot is supposed to be). If we assume standard 8 hour watches that gives us 12 crew to man the bridge. Plus the Captain.

In Engineering there should also be a full operational crew, plus the shift engineer. There seems to be a lot of people in Enterprise's engineering section, so we will say half dozen on the watch. That is 21.

Enterprise has a combat role. So it requires the plebs to handle that. Again it has to be trebled up. There should always be a crew in the magazines and weapons platforms. Say two for each torpedo and two for the ion cannon stations. Plus Senior Weapons Officer to control them and somebody to handle fire control. 30

Enterprise appears to have a galley. At least 2 for each shift, plus the Captain's own chef and steward. Say 9 in total.

That gives us 72.

On top of that there is the general ship upkeep, damage control, science and provost branches, the sawbones.
 
I think that's a fair estimation (except that you didn't mention Sickbay.)

Even though everything is automated you would still need that number of people to oversee the various programs.

If something as small as an artificial gravity generator failed, you could have a catastrophic movement of cargo.

On the other hand, we saw Saavik pilot the Enterprise-A out of spacedock without any electronic help, so maybe it is not that hard to pilot the ships, and we never see any bumps between ships (maybe some kind of magnetic fenders operate?)

Most flight time is spent at Warp. Can ships crash while at Warp? Surely if they do not occupy space they cannot hit each other. I saw a comedy sketch last week on TV with Picard having nothing to do but ask "Are we nearly there yet?"
 
Don't need many bodies to simply drive. It is when you want to do it safely that a crew becomes necessary.

As for floating around in Warp. Warp has to be somewhere, they do appear to be able to see other ships when in it and there does appear to be a lot of ships floating around, so there must be a possibility of ramming somebody.

I could perhaps draw a parralel with aeroplanes?
The chances of two aircraft realistically being in the same place at the same height and at the same time is statisticaly quite remote. But flying London to Paris, you could well meet somebody going Paris/London, but that has nothing to do with mathematics, as it is all the pilots fault.
 

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