The idea that humans are awake during the day and have one long sleep session of approximately 8 hours in the night time is a very modern concept.
The siesta system is phasing out but still common, especially in locations where the sun midday is strong enough, or the air hot enough, that you can't get much work done anyway. In this system you nap at midday then have one long stretch of sleep at night. Your total sleep per day is about the same.
A siesta is a short nap taken in the early afternoon, often after the
midday meal. Such a period of sleep is a common tradition in some
countries, particularly those where the weather is warm. The siesta is
historically common throughout the Mediterranean and Southern Europe.
It is the traditional daytime sleep of Spain and, through Spanish
influence, the Philippines, and many Hispanic American countries.
Factors explaining the geographical distribution of the modern siesta
are high temperatures and heavy intake of food at the midday meal.
Combined, these two factors contribute to the feeling of post-lunch
drowsiness. In many countries that practice the siesta, the heat can
be unbearable in the early afternoon, making a midday break at home
welcome. (ref)
Even with a nap during the day, we're still talking about a single stretch of sleep at night. And that's not how humans traditionally sleep. Bi-model sleeping was the norm in our past, and still is for some cultures.
While nighttime awakenings are distressing for most sufferers, there
is some evidence from our recent past that suggests this period of
wakefulness occurring between two separate sleep periods was the norm.
Throughout history, there have been numerous accounts of segmented
sleep, from medical texts, to court records and diaries, and even in
African and South American tribes, with a common reference to "first"
and "second" sleep.
Anthropologists have found evidence that during preindustrial Europe,
bi-modal sleeping was considered the norm. Sleep onset was determined
not by a set bedtime, but by whether there were things to
do...households at this time retired a couple of hours after dusk,
woke a few hours later for one to two hours, and then had a second
sleep until dawn. During this waking period, people would relax,
ponder their dreams, or have sex. Some would engage in activities like
sewing, chopping wood, or reading, relying on the light of the moon or
oil lamps.
…The first and second sleep started to disappear during the late 17th
century. This is thought to have started in the upper classes in
Northern Europe and filtered down to the rest of Western society over
the next 200 years. Interestingly, the appearance of sleep
maintenance insomnia in the literature in the late 19th century
coincides with the period where accounts of split sleep start to
disappear. Thus, modern society may place unnecessary pressure on
individuals that they must obtain a night of continuous consolidated
sleep every night, adding to the anxiety about sleep and perpetuating
the problem. (ref)
Studies show that humans adapt to differences in night-day timing.
...An experiment in which a group of people were plunged into darkness
for 14 hours every day for a month. It took some time for their sleep
to regulate but by the fourth week the subjects had settled into a
very distinct sleeping pattern. They slept first for four hours, then
woke for one or two hours before falling into a second four-hour
sleep. (ref)
Dividing sleep into 2 4-hour shifts was extremely common and occurred all over the world. In many places they refer to "first sleep" and "second sleep."
If your people have the human need to sleep 1/3 of their existence, in shifts of several hours at a time, then they would likely have 3 or 4 sleep shifts per 48 hour day. 1 sleep shift is not biologically reasonable and 2 sleep shifts would give way too much waking time for most people.
A reasonable schedule might be as follows:
(assume 0/48 is midnight, like on Earth, sunrise is 6, noon is 18, and sunset is 30)
32-36: First Sleep (late evening, people wind down as the sky gets completely dark).
36-2: Wake (midnight social time).
2-6: Second Sleep (completely dark).
6-12: Wake (the sun is rising and there is light, cool temps, and lots of productivity).
12-16: Third Sleep (late morning).
16-22: Wake (midday, time for the main daylight meal and primary socializing time).
22-26: Fourth Sleep (rest after the main meal).
26-32: Wake (productive work period, mostly at home, sunset and darkness partway through).
But it's unlikely that such a perfectly even schedule would work out over the long term. It's more likely that the culture would have some longer and shorter sleep periods and this would work around the weather and which times were the most productive for what activities.
If it's a hot climate, midday is a good time to sleep and the productive work times would be morning and evening, when there was daylight.
If it's a cool climate (assuming it's colder at night), more sleep hours might be bunched up at night and the most productive hours would be midday. The largest meal of the day might be at night (since cooking warms the house and sleeping after large meals is good).
A tri-model sleep cycle (or 3 main sleeps with one short nap) might work better than a quad-model one. It depends on your culture(s), your climate, the types of work they do, how much commuting they do to work, if you have indoor lighting, etc.
