Most people think that when they miss an hour of sleep they simply have to get an extra hour of sleep the next night. That seems like a logical assumption, but what they're not taking into account is that sleep and wakefulness are two parts of a balanced equation, and when you miss an hour of sleep, you also gain an hour of wakefulness. So, not only do you have to make up for the sleep that you've lost, you also have to make up for the wakefulness that you've gained.
Wait...what? Why do I need to make up for the time I was awake...?
Let's look at a typical 24hr day and see how the sleep/wakefulness equation is balanced. Conventional thought holds that healthy adults need around 8hrs of sleep each night. If you sleep for 8 of the 24 hours of a day, that leaves 16 hours when you're not sleeping (wakefulness). So in a 24hr day you have 16hrs of wakefulness and 8hrs of sleep. What that means is that for 16hrs of wakefulness, your body needs 8hrs of sleep to recover.
From this you can get a simple equation that shows how sleep and wakefulness are related.
16hrs of wakefulness = 8hrs of sleep
16 is twice as much as 8
therefore: 2hrs of wakefulness is worth 1hr of sleep -or-
1hr of sleep = 2hrs of wakefulness -likewise- 1/2hr of sleep = 1hr of wakefulness
and so the balanced equation looks like this:
8hrs of sleep x2(16hrs)=16hrs of wakefulness
So if you get 8hrs of sleep each night you'll have a balanced equation. For every hour you sleep, you can be awake for 2hrs, and for every hour you're awake, you'll need to sleep for a half-hour.
How do I get into SLEEP DEBT ..?
Let's say you've missed two hours of sleep. Knowing what we know now, let's create an equation for the lost sleep. If you miss 2hrs of sleep (from a normal 8hrs) that means you've slept 6hrs. Now we'll subtract that from 24hrs to see what the wakefulness/sleep equation looks like:
24-6=18hrs of wakefulness
(now remember every 1hr of sleep is equal to 2hrs of wakefulness so we need to multiply the "sleep" number by 2)
6hrs sleep x2(12hrs)=18hrs wakefulness (!!!!!)
We've got an imbalance equation, with a 6hr overplus on the wakefulness side (18-12=6). Thats 6hrs of wakefulness that went unaccounted for, and knowing that every 2hrs of wakefulness equals 1hr of sleep we can see that there is a 3hr sleep debt (6hrs/2=3hrs total sleep debt). So, instead of just needing 2hrs sleep to get out of debt, you really need 3hrs!
Still doesn't make any sense ..?
That's okay, that's why I built the SLEEP DEBT CALCULATOR, so you wouldn't have to do all of the math!
Enjoy, and good luck paying that sleep debt back!!