A few notes regarding Airborne Wind Energy from bottom-up direction. Some repetition of key points in other posts and topics will occur.
A kite anchored to Earth expresses Newton's First Law, of an opposite and equal reaction between Atmospheric Motion and Planetary Motion. Newton himself was an avid kiter, and the history of kite physics is a rich topic. Etzler foresaw the world could be kite powered almost 200 years ago.
In our time the Power Kite emerged as a steerable decelerator technology in NASA Gemini and Apollo Programs, and aerospace engineers soon applied it to new sports like paragliding and kitesurfing. These in fact have already displaced some portion of fueled sports (ski-lifts and water-ski boats).
Power Kites scale beyond any other aviation class, and have the highest power-to-mass, without fuel. The practical single soft-kite scaling limit is about 1000m2. Such a unit-kite can produce about 10MW of wind power. Topologically ordered unit-kite networks will reach GW-rated scale.
Aggregated Kite Power can directly drive by cableway the largest GW-rated utility generators. Existing Power Plants can in principle be converted to Kite Hybrids, with no fuel needed when wind is blowing.
There is a lot of interesting mathematical engineering science to a kite. A power kite is a thermodynamic heat-engine, when considered as such. The compression side of a wing is a hotter gas volume than the low pressure cooler side. In a "steady state", one may consider a working wing as a frozen wave system (surfer POV). Kite Chaos Physics identification started with [van Veem, 1997].
The Mass Scaling Exponent of a single-skin kite is Quadratic, but high L/D kiteplanes resembling gliders have a Cubic Mass Scaling Exponent. Therefore, while a kiteplane may have a far higher L/D, it does not scale as well as a soft kite. Superior figures-of-merit for soft kites are higher-power-to-mass and lower-Levelized-Cost-of-Energy (LCOE).
The current hot frontier of kite tech is Network Topologies (if anyone wants to join the global scholar email circle). A kite network is a sort of topological Boojum. Kite Network Operations are studied for their topological stabilities, and dependencies like Topological Surgeries. Subscale prototypes are designed and flown. Exascale Multi-Physics Multi-Solver Sims are being architected by a US DOE (NREL) affiliated circle. The combined CFD and structural-dynamics super-computing challenge is obviously math-intensive. The atmospheric dynamics alone is a vast aspect.
AWE is an emergent Green Math Wonderland.