To put a number or ratio on this - x number of hours for y number of days - seems highly subjective to the point of not being practical. It seems that the threshold for minimum amount of sleep while retaining effectiveness is driven more by leadership and circumstances than in some physiological norm. I recall several occasions in Iraq when I was talking to someone and fell asleep in mid-sentence and then realized that I had been awake for several days (when you do most operations at night, spend most of the daylight in a building where the windows are sandbagged, and operations are driven by the situation, rather than a battle rhythm, it is extremely easy to miss out on sunrises/sunsets and lose track of days). On the other hand, at Fort Benning I could get a solid 8 hours of sleep every night and still not be able to stay awake for more than 45 minutes in building snore (4).