Yep, claustrophobia. And really, considering the canon sizes of the ships, even the larger ones probably should have appeared smaller on screen. After all, most of us live in rooms that are about 10 feet high, maybe 15 feet diagonally or so (small bedrooms are often 9 feet by 9 feet). 3 feet is a little less than a meter.
Even the 2009 Enterprise
is 610 - 910 meters (http://en.wikipedia.org/wiki/Starship_Enterprise
), or around 1976 - 2948 feet. Even with standard small bedrooms, that's 220 - 327 of them on the entire ship (I can't recall how large that crew was, but there were more people than the 90 or so on the NX-01
), with no room whatsoever for engines, the bridge, sickbay, any recreational facilities, an armory, cargo storage, transporter room, etc. Doubling people up in such tiny spaces is possible but that would show even more claustrophobia.
It is possible to fit in everyone and everything, but even on a ship of that size, it should have seemed a helluva lot tighter. Enterprise
absolutely gets this feeling right, I feel.
Your math is... well, frankly, not math but random numbers hastily thrown into a calculator. Your calculation is 1 dimensional rather than accounting for a ship's width and multiple decks.
NX-01 has a beam of 135m (445.5ft) corresponding to the diameter of the saucer section and has crew quarters on 4 of its 5 decks (B through E). If that entire space were made up of your "small room" scenario which is actually close to the set design used, it would provide 7692 rooms (3.14 pi * 222.75 ft radius * 222.75 * 4 decks / 81 sq ft and some rounding). That's without windows, without sickbay, without engine space, etc. Just square 9'x9' rooms without even corridors to access them.
However, if Starfleet had some regulation that all crew quarters must have a window and much larger rooms of 20ft x anything were used, NX-01 could have supported 280 very large quarters (3.14 * 445.5 * 4 / 20). Assuming the quarters were 20 x 15, this would leave 82% of the ship's internal space for other purposes, even after accounting for the MASSIVE 6 ft wide corridors.
In other words, there was absolutely no reason a crew of ~80 people should have been cramped in a space that large. And it would be a very bad design to set that up as the norm on a long term ship of exploration.
As for other ships...
NCC-1701-D had a beam of 464 m or 1521 ft over 16 decks. It isn't perfectly circular, but close enough for this. With the small useless 9x9 rooms, it could hold 358,912 of them, not a few hundred. According to http://www.ussenterprise.co.uk/enter...d/entddeck.htm
normal crew quarters made partial use of 9 decks. Assuming mandatory windows, 20 ft rooms, and removing conference rooms and Ten Forward, the Ent-D could have held 2,142 decent quarters on those 9 decks.
CRUSHER: Jean-Luc, if I might ask, how many people are there on board?
PICARD: One thousand and fourteen, including your guest, Doctor Quaice.
LAFORGE: Is there something wrong with that count, Doctor?
CRUSHER: No. That's the exact number there should be.
The NX-74205 Defiant according to wikipedia is 170x134m with 5 decks. It's not a perfect rectangle, and I think I saw these dimensions somewhere, so I'll go with 120m/394ft by 100m/328ft. That's enough space for 7,977 9x9's, and it was supposedly built with only a few dozen double bunk coffins? That's ridiculous, even for a warship, unless that doubled up design is for potential tactical reasons other than space. That's less than 1% ship space for quarters. Sick bay is almost non-existent, the mess hall isn't overly impressive, and engineering isn't very big either going by the sets. IIRC, the only other spaces ever seen are a transporter room and hallways. So 75-90% of the ship is dedicated to torpedo storage, power conduits, and armor thickness?
Voyager's asymmetric shape makes it kind of a pain, but suffice it to say 344m x 130m x 63m should provide tons of room for 200 people even though the 344m includes the nacelles.
Basically everything on NX-01 was decided for TV reasons. The bedroom sets were built tiny to give the impression the ship was cramped even though they shouldn't have been, but hallways were made nearly as large as rooms to provide walking and talking scenes and to get camera angles. At least even the captain's quarters were tiny to portray a modicum of equality, but the doubling up of quarters for a "servant class" of crewmen (eg, Daniels) raises some questions of decency and ethics.
TUCKER: I know you don't think this chair is important, but you're wrong. What's the most critical component on this ship? The main computer? The warp reactor? Uh-uh, it's the crew.
I guess no one told the shipyard or the set designers.