From NYMag (HT: ANM):
According to several studies summarized in the WSJ, naps are best optimized when based on an understanding of our natural circadian rhythms and REM cycles. Based on that, scientists (or professional nap analysts) have discovered the best time to nap is between 1 p.m. and 4 p.m. while sitting up slightly so you don’t fall into a deep sleep. The popular “I’m just gonna nap for 30 minutes” nap is actually the worst kind — it interrupts the REM cycle and leaves people groggy. Sixty-minute naps are best for “memory consolidation” and the 90-minute session is ideal because you’ve completed a total REM cycle.
Don’t have 90 minutes to nap? A study shows that a ten- to twenty-minute power nap is all you need to really recharge, and ten minutes is the sweet spot. People become “sharp right away” and the improved mental acuity lasts for about 2.5 hours.