So, if I go to bed right now, I’ll get maybe an hour of sleep before I have to get up, get dressed, and start my day. Am I better off grabbing that little bit of sleep, or just staying up and making one long go of it? I tried doing a search on the topic, but oddly just came up with a bunch of threads talking about airliners.
I vote for the nap. YMMV
If I tried sleeping for an hour then getting up, I wouldn’t get up. I’d bull through it. Prepare to collapse at some point during the day, though, and don’t attempt anything remotely complicated. (You’re not a surgeon, are you?)
No, but I am learning (or trying to learn) Chinese. 
Take a nap
From a sleep management course I once took (related to a job where one would end up being woken up at all manner of odd intervals, and then being required to be on the ball) it was suggested that naps where you stayed in shallow sleep were good and one could be awoken with minimal problems for alertness, and still feel rested. However if you dropped off into deep sleep, which occurs roughly after 40 minutes, then it was very difficult to get back quickly to a full state of alertness. It was better to stay asleep for 4 hours, when the body would typically come back to a period of REM or less deep sleep, before plunging off into the abyss again.
So in summary - take a max 40min (YCRMV) nap or don’t bother at all.
Maybe it depends on the person. I was a champion all-nighter person in college and once went over three days without a wink of sleep during finals (aced them all). I have stayed up more than 24 hours many times since then. For me, laying down to sleep at all is the kiss of death and must be avoided at all costs. I wake up confused and groggy the time or two that I tried it. I vote for staying up.
I also vote for nap. Why were you up all night anyway?
This is a real YMMV topic. Me, I cannot nap without feeling like crap. I am a coffee person.
I’ve been in the Navy for over twenty years. Our adage is “some sleep is better thatn no sleep” and I think it’s 100% correct.
Basically stayed up late stressing over how I had the quiz and homework to do and how I hadn’t done it all weekend (yeah, I know, I know). Mostly I ended up posting to LJ all night.
In the end, I stayed up until 5AM, then took a series of 15-20 minute catnaps, sleeping in a position that traditionally doesn’t afford me deep sleep (on my belly, arms tucked up against my chest, as opposed to rolled up on my side when I want to sleep for hours), and basically kept doign that until about half an hour before I had to be at formation, and I got dressed and headed out for the day. Managed to stay awake all day except for one part where I dozed for a few seconds and caught myself, and again right towards the end of my last class where the guys on either side of me decided to help me out by slamming their hands on my desk (a source of endless amusement in an academic environment, I assure you)
I swear, when you haven’t slept, 5AM to 6AM is the longest hour of the day, aside from 1PM to 2PM for some weird reason.
That’s me. I would have to suffer through the day. If I went to bed, I would sleep through eight screaming alarm clocks, home phones, cell phones, and answering machine messages asking where in the hell I was, and wake up at 2pm.
I need my sleep, and it’s not a getting old thing. I’ve been like this since I was a young kid…
One night my SIL and BIL made a surprise visit and we stayed up until 5:30am talking.
I had to get up at 6:30am.
I was fine in the morning, fine at work all day, but the drive home finally did me in. I stumbled in, handed the kids off to Ivylad, and crashed.
Next time, do your homework. 
Naps are good. It is best of they are around “siesta-time” and for only 20-45 minutes. Don’t allow yourself to fall into deep sleep or you’ll just be groggy. A hour is about the max for a nap.
YMMV, but what I do in that situation is to take a nap, but try not to get too comfortable. That way I could get up fairly easily, and not be too groggy when I do. E.g. sleep on the floor (carpet) instead of the bed. Or sleep on the bed, but at right angle to it so my legs are dangling from the side of the bed.
This is good advice if you are continually in a sleep deprived state. However, if it’s a one off thing with a decent amount of time to recover, I think the all-nighter is better.
Taking some good advice tonight and going to bed early (where “early” = 11:30PM)
no weird reason at all, you have two points in each day where your core temperature drops, for most people its around the times you just posted, its why the afternoon nap is so tempting and why early morning is the worst hour of an all nighter.
I work the overnight shift in a hospital lab. It is my third year at this particular hospital. The full-timers as well as mostly everyone else have grown into a special night routine, that while is technically against HR policy all of us night owls kinda wink it off.
They all take a one hour nap in the middle of the shift. Not all at once of course., but Mary will take her break from 2AM-3AM and then Jeff will go from 3:30 AM to 4:30 AM. Everybody except me, I simply prefer no break at all, and to work straight through the night. Taking the nap in the middle of my shift causes me tremendous grogginess, and although I only sleep for an hour I am a zombie for three.
Just MHO.
Related question. It’s almost 1:00 AM here. I have a paper due at 9:30 AM, which I have spent a good portion of tonight doing research for. I don’t want to start writing now because my writing will sound like nonsense, and I expect to get an A on this paper; also, I have a speech and a small reflection paper due tomorrow as well, which I plan to write tomorrow, so I don’t want to write those on no sleep. My research for the paper will be done by the time 1:00 rolls around. I want to wake up at about 6:00.
What’s my best option? Should I wait til 2 and sleep for exactly four hours?
when I took Chinese in University in the US, I became the king of 15-20 minute power naps. As pointed out earlier, there is a threshold before you hit REM sleep. You can take the short power nap, get up and go get a drink of water, and I found could then concentrate again on memorizing characters.