Re: booster propeller

> I haven't found any references to this idea. :)
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You would want to search rotary rocket
Here's one reference:
http://www.spaceandtech.com/spacedata/rlvs/rotary_sum.shtml

Scaling that up you may want to research Hiller's work on flying
cranes:
http://avia.russian.ee/helicopters_eng/hiller_crane-r.html
There were problems with using gas turbines at the tip, so research
was going towards a resonant pulse-jet (valveless) design that would
allow even bigger flying crane designs.

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