Earlier quoted context omitted.
Other sources I've read suggest that around 15 minutes of sleep is optimal, and going over puts you into a different phase of sleep. Perhaps you have an easier time falling asleep than others. When I try to nap, I'm pretty sure it takes ~5 minutes to doze off usually, but sometimes even more than that.
I have not tried this, but have read about this technique: When you start your nap, hold something in your hand that will make a noise if you drop it. As your body relaxes and you start to sleep, you will eventually relax your grip enough that the object will fall to the floor and wake you up. This happens at just about the ideal wake time for a short power nap.
During meditation retreats, I often fell asleep during the first morning sessions. My teacher said that this was ok, but gave me comparable tip if I wanted to stay awake: meditate standing, when falling asleep, your body will always wake up in moments to stay balanced.