Interesting concept ! Tried to remember some mathematical formulas from the long gone schooldays.
This contraption may have a mass of about 200 kg , just as a very rough estimation ( Pilot, engine, cap,
fuel, emergency chute ...)? Then it has to produce a vertical lifting power of 200 kg, too, which would be
generated by accelerating air via the cap. Given the apparatus can accelarate air to the equivalent of
a gale with Beaufort 12 (about 33m/s) it would just have to pump downwards about 6 kg of air constantly,
roughly 7.3 cbm. Assuming a hemespherical shape of the cap, moment please ... a diameter of about
2.5 m would be enough ??? Can't believe it ! Ok, the thrust would be pulsating, so has to be much higher
to compensate for the interruptions and maybe 33 m/s is much more, than could be achieved. And it
probably would result in very severe vibrations and resemble not at all the swanning of a jellyfish !
And maybe I should have used my lunch break otherwise ... :-\