Two processes decide when you are sleepy

Pressure builds while you are awake. The clock does not care about pressure.

Borbély's two-process model is the frame the rest of this fits into, and it has held up for four decades. Two systems, largely independent of each other.

Process S is sleep pressure: adenosine building from the moment you wake and discharging while you sleep. Process C is the circadian clock: a rhythm that runs whether you slept or not, producing a strong push toward alertness in the early evening and a deep trough in the small hours.

You fall asleep easily when high pressure meets a falling clock. Miss the overlap and neither is enough on its own.

This explains the second wind. The circadian alerting signal peaks a couple of hours before habitual bedtime and can mask a great deal of accumulated pressure, which is why nine in the evening can feel wide awake after a genuinely bad night.

It also explains why a late-afternoon nap is expensive. Twenty minutes at five o'clock discharges pressure you were going to need at eleven, and the clock will not lend you any of its own.

The longer answer

Tired but can’t sleep applies the model to the evening it most often goes wrong: in the hours before your usual bedtime the body clock pushes hardest for wakefulness, however tired you are. How long should it take to fall asleep? gives the normal range, up to about 30 minutes, and how to fall asleep fast what the research supports when it takes longer.