What basic maths ? I don't see any, except that the diagram that you click on shows it as being 2m high. Even at a 10m radius, that's only 40 m2, or about the same as a 7m diameter prop. The Bergey XL, which is 7m diameter, is rated at 10 kW for the grid-tie version, 7.5kW for the battery version, and that's about 30-40m up in the air, not on the ground.
The article states that the temperature differential between the ground and 1m above it starts a "self-sustaining vortex" that then drives a horizontal prop. Well, if energy is going to be extracted on a continual basis, then it has to be removed. The only sources of energy are wind and solar.
Solar-based ones, i.e., props that work on a temperature differential, with a greenhouse on the bottom funneled up through a vertical tower, have been done; they take a lot more than 10m diameter for 50 kW, and they do not use a similar design. They have actual working prototypes.
Wind-based ones have also been done; they're called VAWTs; none are being built for commercial-scale electricity. I'm sure this is because the basic technology is being suppressed, and simple devices that have heretofore been overlooked can extract zero point energy directly. (I hope you are awash in the dripping sarcasm from what I just said.)
Quite simply, if there is a new method for extracting energy, tell us where the energy is coming from, and explain in a simple diagram how it actually works, don't use words like "self-sustaining" and "vortex", which have no meaning, and are meant to fool those who don't understand physics. To say the ARPA-E and Stephen Chu are interested doesn't impress me. Explaining how it really works without using buzzwords (and including the actual math) does impress me.