Following on from the last post . . . what would we expect of a Star Trek starship?
Well, the Constitution Class ship, if gingerly placed upon water and then released, would sink immediately. That's because the vessel's density is over four times greater than water, even including the hollows aboard. It would thus behave rather similarly to a dense rock, because, overall, that's the density she is.
I have no idea about the drag coefficient of the venerable Connie, and wouldn't be interested in hazarding a guess. I went and looked at this site where they do a wind tunnel test of a refit Constitution in the form of that crappy TMP-era toy that they re-released for Star Trek V. But, while I'm tickled pink at finally having a good excuse to link to that (had that one up my sleeve about ten years now), I'm sad to say they didn't provide any estimate of the drag coefficient.
An Intrepid Class ship would do about the same, but might sink somewhat less quickly, as her density is only somewhat above that of water. In any case, her frontal area is going to be significantly larger, and while her drag coefficient should be superior to the Constitution Class in some areas, they both suffer from the navigational deflector effect on drag.
I have no idea what would happen with the saucer section . . . would it hold up the saucer for a moment and make the ship sink tail first? Probably, especially if the nacelles are very dense.
But while writing this, something finally dawned on me. Klingon ships . . . at least the small Bird of Prey . . . may be rather on the light side of the spectrum.
See, though I've pondered the notion of a historical trend in regards to starship masses, it may simply be that the Intrepid Class was designed to land intentionally . . . after all, unless you make a big flat bottom, it's hard to land a Constitution Class weighing in at over 900,000 tonnes. Little landing legs just won't do. Even Voyager's legs shouldn't be able to work . . . the ground pressure would be enormous.
This brings me to Kirk's comment about the crashed Bird of Prey in ST4 . . . he says something about getting the whales out "before we sink", and had just ordered the bridge hatch blown upon finding out they were in the water. Kirk had no idea where the ship was . . . deep ocean, lake, river, et cetera . . . so unless he did some quick math about the fact that he didn't hear water all around the bridge yet, or didn't feel that the ship was turned ass-down, or if he felt the thud of the hind end hitting the bottom of the shallow San Francisco bay (whose depth is measured in low-double-digit feet), it might seem odd for him to order the hatch blown.
As noted in the last post, ships float because while the density of their parts is greater than water, the density of their parts all spread out along a large hull with lots of empty space inside isn't. But any ship whose total density is greater than that of water is going down pretty fast. That makes Kirk's comment odd, because if he was used to extremely sinkable ships, then the notion of a Bird of Prey lasting any length of time would be very odd, and ordering the hatch blown would have been a death sentence.
After all, if the Bird of Prey was as dense as his Enterprise, blowing the hatch would just fill the bridge with water. The crew would've had to live long enough for the water to fill the bridge and then escape . . . which is actually pretty plausible, except for the fact that by the time that happened they could be literally hundreds of meters below the surface of the ocean or whatever they were on (as far as Kirk presumably knew) assuming they dropped like a 50lb solid steel sphere.
This suggests that he had information of some kind . . . either that the tail end was down on something (at least temporarily) and the front end might drop down, or that the particular class of Klingon Bird of Prey he was riding on was actually less dense than he was used to, and maybe even less dense than water.
Another alternative, of course, is that Kirk is an idiot, and Spock too for not correcting him. Trek-haters would default to that, but that's not the style here.
In any case, the evidence for less dense Birds of Prey is somewhat flimsy, but there it is. Perhaps one could do a ground pressure estimate based on the landing in the park in ST4, but I don't know how well that would work. After all, Voyager's ground pressure figures don't work, either.
In any case, we have one other sinking event, that being the Jem'Hadar ship in "Rocks and Shoals"[DSN].
That ship lasted long enough to let everyone get out and get to shore with a little raft, which could suggest that it was a floater and thus that the bugs are less dense than water. However, that's less than clear, because the ship is, as seen in the picture, extremely close to shore. It might be like San Francisco Bay, a Great Lake, or any other such thing . . . the ship could be sinking only into water or it might be burrowing into murky muck at that angle, a la quicksand, or falling off of a shelf. There's no way to tell.