I'm in agreement with a number of the points raised here, although I tend to design in "Geek-land (FF&S) these days. If you are using FF&S, Bridge workstations are defined as being reconfigurable, so unless the ship is at general quarters ("Alert Status") the ranking engineer is generally monitoring from the bridge, not physically present in engineering. For "smaller" ships (with total engineering and maintenance crew less than 3) the engineers generally stay in engineering, but my bridge placement on small ships generally tucks the bridge right next to engineering anyway, so the engineering workstations are usually located on the flight deck (AKA "small bridge")
To Address KG's point (about mind-numbing boredom) most ships under about 400Dtons have the galley right next to the bridge as well, so it's a convenient "socialization" spot, and does double duty on survey ships as a conference room, in much the same way as the officers wardroom (Eating area) in subs will often convert into the captains office. and impromptu surgery when at action stations.
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Small ships generally have workstations for Pilot, Navigator, Sensor Ops. Depending on how far the Engineering spaces are from the bridge, Engineering may also be represented on the bridge. If the ship has serious fire control (master fire directors) these are generally also present on the bridge, unless the MFD's are built into the turret hardware.
Unless the ship is at "Action Stations" there is generally only a single crewmember on the bridge at any given time (the watch officer) although ships with large passenger capacities may require a minimum crew of 2 at all times as a precaution against hijacking.
If the ship does not carry passengers, the bridge is often largely unattended from 6 hours after jump to 12 hours before expected jump emergence (with *very* loud alarms in case any anomalies in the jump field are detected)
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For larger ships, the breakdown is a bit broader: in general "Watch" crew will be one officer, one electronics tech (Sensors and commo) and an engineer. If the ship is military, then there is often a gunner on watch as well.
If a doctor is carried, he has a sickbay, and will *never* be present on the bridge unless called there by a watch officer (Note 1) If there are bridge casualties then it is the job of the damage control parties to evac them *to* sickbay.
A large ships bridge at "Action Stations" (Now we're talking military vessels, since the civilian compliment doesn't change much) will have the following breakdown
-Captain (Relieves current watch officer, or stays put if he is the watch officer)
-1st officer (if the ship has a third officer)
-Pilot
-Navigator
-Watch Engineer (or Chief engineer)
-Chief Sensor Ops
-Additional sensor / electronics ops
-Flight Control Officer
-Watch Gunner (He doesn't leave)
If the ship carries more than 3 non-local (not in the turret) gunners, they are generally grouped onto a fire control bridge. Most of the engineers and maintenance staff, as well as the 3rd-5th officers (if the ship carries same) are tasked for damage control crews, with the understanding that part of the reason they are there is so that the chain of command doesn't disappear if the ship takes a bridge hit. This is also the reason that the *watch* engineer is on the bridge, not the chief engineer (who is usually also the 2nd or 3rd officer)
The reason that the 1st officer is only on the bridge if the ship is large enough to have a 3rd officer is because you want 2 "line" officers off the bridge at all times at "Action Stations". One of the "line" officers is almost always the chief engineer (Generally the Second or Third Officer) so you want to have another officer leading damage control: If you only have caprain, O-1 and O-2, then the engineer is in engineering, and the other line officer draws DamCon.
If the ship carries an Aux bridge, then the 1st officer is stationed there, and will generally split off the gunners workstations 50:50 between the bridge and aux con. In general, Aux Con handles "defensive" fire, while the main bridge handles the main guns. (Include "Missile Ops" as "Main Guns")
If the ship has a flag bridge then a similar grouping will occurr, with some of the gunners pushed onto the flag bridge. Captain and 1st officer are on the bridge, theh Second officer and flag officers are on the flag bridge. Gunners are "partitioned" from the flag bridge, and the flag bridge will often have a second set of dedicated sensors and sensor ops. In case the main bridge is rendered inoperational, the partition between the "flag" and "gunnery" section is removed, and the second officer will fight the ship from the flag bridge, while the Flag officers are forced to endure a bit more "battle chatter". The Flag bridge, like Aux Con will have a senior engineer present, if only to handle rerouting controls and sensor channels. The more "pragmatic" (cynical?) reason is to ensure that even with the loss of engineering and all other control sections, there is someone qualified to jury-rig repairs sufficient to limp the hull home for refit.
If the ship is large enough to have a bridge, Aux Con AND a flag bridge, then you get a truly prodigious amount of backup. In general, the Flag Bridge will not get more than 1-2 gunners stations, and they will only be manned (generally by flag officers) if the Bridge and Aux Con are already gone (at which point the Flag Bridge probably isn't effective for directing the battle anyway) There will generally be a seperate "fire control" bridge, which handles strictly defensive fire, The Main Bridge will handle direct fire, and Aux Con will handle missile ops. In this case you now have 4 "control" centers, with fire control split between 3 of them (Bridge, Aux Con and F.C. bridge) and Command and control spread across a slightly different 3 (Bridge, Aux Con, Flag Bridge)
Probably more detail than you were really asking for, but I thought that giving the reasons *why* the bridge crew breakdown was the way I described was at least as useful as giving you the raw list of "these people are here"
Scott Martin
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Note 1:
The number of times that the ships doctor would be called to the bridge would be vanishingly small. The only circumstances that I can think of would be to call the bluff of a free trader captain claining to have some bizzarre plague ("so please don't board and inspect me sir") or to discuss how to handle a particularly fragile VIP. I could anticipate most military ships doctors seeing the bridge precisely once during each tour, during the orientation session.
Of course there is always "Relieving the commander due to medical reasons" but I would expect this to be done in sickbay, even if the "medical reason" is a tidy hole through something vital.