What are some of the longest flights without modern navigation systems? Context: As a private pilot, I enjoy preparing my flights with a mix of paper charts and iPad apps. In flight, my navigation is now often very assisted by the G1000 or iPad, relegating the paper maps to backup. But I remember that, when I was only using paper maps during training, the workload could quickly rise and that I was sometimes exhausted after a short navigation because of that. 



What are the longest (either by time or distance) known flights ever flown without any "modern" navigation system ?  

I'm interested by flights that comply to the following criteria:


Did not use any GPS or inertial navigation system (maps and stars are ok)
Radio navigation is ok (but bonus point if the aircraft is not equipped for that)
Have only one leg
Take off and landing fields can be the same if the flight was long enough to require actual navigation (recon missions, circumnavigation...)
Can be historical stories (war heroes, military experiment, pioneers...) as well as modern ones (record attempts...)
May have a flight crew as large as Pilot + Co-Pilot + Navigator + Engineer, but...
...don't have any rest period for the crew (no backup crew on board)
This list of flight endurance record on Wikipedia lists as number 3 an endurance record of 84 hours 32 minutes between May 25th and 28th 1931. It seems reasonable to assume that no modern navigation means were used in 1931. 
However, the flight was mostly local, so navigation was not really required.

The all time record is from Dick Rutan and Jeanna Yeager in 1986. The Rutan Voyager had state-of-the-art navigation on board, including an Omega Navigation System and a GPS receiver. The latter was only functioning for approximately 4 hours per day, because the GPS constellation was not yet complete and many satellites were missing. 

The Double Sunrise flights seem to qualify, with times in the air between 27 and 33 hours.