http://www.gizmag.com/the-archimedes-liam-f1-urban-wind-turbine/32263/
A recent development in wind turbines.
A recent development in water impellers.
https://en.wikipedia.org/wiki/Archimedes'_screw
The Archimedes screw, not a golden ratio but can be adapted as such.
http://www.google.ch/patents/US6702552
A ship impeller using the golden ratio.
Victor Shauberger inspired implosion propeller. Yes I know psuedoscience.. deal with it.
Egyptian impeller? You decide on that one guy.
I will turn this on it's head and attempt to use it to produce a low pressure zone over a wing and to provide propulsion.
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Water is an incompressible fluid (at our scales). Air is compressible.
But I think an even more striking difference is the scale of energy : a corkscrew pump that lifts water is around a few hundreds or thousands of Reynolds, while a VTOL vehicle is tens of millions Reynolds with extremely complex interactions.
I apologise in advance if knowledge sounds like arrogance.