What are the aerodynamic design principles behind the "supersonic" propeller of Luigi Colani's C-309 racing plane?
Looks like the Colani Museum has picked up my question on Twitter and posted a response later with an archive photo of an advertising article:



The English part of the article says about the propellers:


  Since 1976 we have been investigating sharply cambered pusher and tractor propellers which maintain supersonic flow over part of their top surfaces.


In contrast, the German translation says:


  Since 1976 we have been investigating strongly forward-swept pusher and tractor propellers.


So this sounds to me like they were simply looking to develop strongly forward-swept propellers with a supercritical airfoil. Aesthetics almost certainly also played a role in the design.