The amount of sleep that a person needs varies from person to person as does the time they naturally feel sleepy. However the fundamentals of sleep are consistent from person to person and by understanding these you should able to calculate the time you should ideally be going to bed.
We all sleep in cycles and ideally we should be getting 5 of these every night. The length of a cycle varies from person to person, with a broad range being between 85 and 110 minutes. To calculate your cycle length write down the amount of sleep you have had over a few nights and divide by 5. By careful not to include any nights where you may have had only 4 cycles and if the cycle length is less than 80 minutes then this is probably the case.
Now that you know your cycle length write down on a piece of paper your ideal wake up time. Work back 5 cycles from that wake up time and add 15 minutes to get to sleep. That should be the time you go to bed.
Here is an example:
Night 1: 490 minutes divided by 5 equals 98 minutes
Night 2: 495 minutes divided by 5 equals 99 minutes
Night 3: 392 minutes divided by 5 equals 78 minutes
Night 4: 495 minutes divided by 5 equals 99 minutes
Night 3 looks like a 4 cycle night so exclude that night. I think a good estimate for this person is 5 cycles of 99 minutes.
If their wake up time is 7am then work back from that time 5 cycles of 99 minutes which would be 10.45pm. Add another 15 minutes to get to sleep and their go to bed time would be 10.30pm.
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