Comment by pizza

I strongly suspect that you don't need to actually get into a sleeping state for an attempted nap to be beneficial. It loosens the bolts of the mind a bit. As long as you can stop attending to the signals of the outside world, you free up a little brain power to do a little relaxation/mental de-fragmentation. The problem is that sometimes people feel if they didn't drift off that it was a waste of their time (usually it's people who are always busy who feel the loss of 15 minutes as the most damaging), and feel worse off after. The key idea is to be able to up-regulate or down-regulate your mental energy expenditure per unit time (or 'power') as you feel necessary. If napping affects your sleep schedule negatively, it's because you feel it gives you too high an energy level at an inappropriate time, i.e. that it negatively affects your ability to manage your energy level better at will.