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Why was the Ent-D sickbay so small? And why only one doctor?

How many medical staff would a ship need?

Here in the Netherlands as well as in the UK, the average general practitioner has between 2,000 and 2,100 patients. A Galaxy-class starship has a complement of around 1,100.

Of course, injuries are more likely aboard a starship than in a small Dutch or English town, so it makes sense to have more medical staff relative to crew complement.

If there are 4 medical staff on duty at any time, and the ship runs on a 3-shift rotation, that means a Galaxy-class starship would have a minimum of 12 medical personnel. Since Crusher talks about "my" staff, I assume that number doesn't include her, so let's make that 13.

I would assume that at least two sickbays, one in the saucer, one in the stardrive section, are open at any time. The third ward mentioned in "Tapestry" would be a back-up. Maybe, for symmetry, we can assume one regular and one back-up ward in the saucer section, and one regular and one back-up ward in the stardrive? With at least two medical staff present in each regular ward at any time. That would kinda correspond with what we see on the show, where there are usually Dr Crusher and one or two nurses in sickbay.

We know there are also recovery rooms, an isolation ward, etc. but those wouldn't need to be permanently manned.

If we size this down to an Intrepid-class starship, which has a complement of ~140, it makes sense for such a ship to carry just one doctor and one or two nurses.
 
If nothing else, having a second doctor on board (even a junior doctor) gives the other one a day off!
 
A ship in the middle of federation space would be fine having 1 doctor on board because if there's a crisis, there are other ships/planets nearby.
 
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