It is easier if you get the good seats and get at least some sleep on the way over. I usually save my $$, travel coach, and can't sleep worth a damn and end up getting a few low quality hours. Watching my wife and son sleep as if they were on a brand new posturepedic doesn't make it any better. BUT, even if you think you are tough, or actually are tough, lack of sleep or poor sleep relative to your usual means your performance is degraded whether you feel like it is or not. It may be good enough, but it isn't optimal. There are plenty of worthwhile and enjoyable things to do on the first day that don't involve a loaded firearm and it is probably not a bad idea to do them, settle in, get a good night's sleep and then get at it.
The particulars of the route can matter as well. Overnight US to Germany, layover all day, night flight with morning to Namibia can be rough if you don't sleep well on planes because it is two nights in a row on a plane. But there is plenty to do for the day in Frankfurt and if you really push it all day and stay awake, it is easier to sleep on the plane the next night. I find the return leg easier particularly because I am by nature a night person but my job starts early in the morning, so I try to stay on Africa time as long as possible which makes the first week back pretty easy for me- I can sleep in and still be up early!
US straight to Johannesburg is about 18 hours on a plane, which is enough to try the sanity of ordinary humans. But it is a night in a proper bed and then you are good to go more or less the next morning and more or less on Africa time.
