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Vortex Ring State is one of the hazardous states a helicopter can find itself into. VRS happens when a helicopter has low airspeed (and usually hovering OGE) and is descending. If the helicpoter is descending too fast (that might be around 300 fpm for some helos) the rotor will enter its own downwash. As this downwash is turbulent, the rotor will be unable to provide enough lift and the helo will start falling.

Would blade shaping (maybe like Airbus' Blue Edge or something similar to the scimitar shaped fan blades of the GE90) help with VRS? Or if not solve it, make it weak enough not to pose a threat.

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No. VRS isn't about the tip vortices you are thinking of.

VRS is a thing even if you had a pure actuator disk. I.e. it is a fundamental phenomena of powered lift. It has everything to do with disk loading and just about nothing to do with details of the blade design.

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Vortex ring state (VRS) is a blade root stall phenomenon that occurs in rapid descents. In a normal rapid descent, there is a small amount of airflow UP through the center of the rotor disc right at the blade roots.

When the conditions are right, the root stalled section expands out from the hub, and you get a very large upflow near the center of the rotor disc in addition to the up flow beyond the edges of the rotor disc.

This sets up an inner vortex that is more or less a mirror image to the vortex flowing around the blade tips. The two vortex fields meet over the mid span part of the blade and flow down through the disc.

All this downward flow, originating from both the hub area AND the blade tips is too much, and increasing sink rate just makes it worse. You could call it the "Double Donut Of Death" with an outer vortex and an inner vortex both combining their flows to hurtle you toward the ground.

The only way out is to disrupt the vortex somehow, usually by getting some lateral motion going, translating out of the vortex.

Wikipedia covers it pretty well, and once you see what is happening, it becomes apparent that trying to reduce the strength of the vortices at the blade tips with something like a droop tip or winglet (structurally problematic) has little effect, partly because the vortex field extends way beyond the tip, and mostly because the problem originates at the other end of the blade, near the hub.

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