Your math about sleep cycles is way wrong, and the idea that you'll still have half the free time you used to is laughable. Assuming a more or less 'normal' work schedule, most of the time they're sleeping, this guy will either be at work or will be sleeping himself.
My advice is to assume that for a few years you're going to have very little downtime unless you don't sleep much or don't feel the need to see your wife much.