How do Aeronefs fly?

[Cat]

Phlogiston.

Phlogisticated air from the lift engine can also be captured, stored, and used for fire-fighting on board ship.

[Hammers]

Surely any sensible aeronef captain would man his or her ship with a acutely chtonophobic (greek: gound abhoring) crew which will resort to anything to keep the vessel from touching the ground.

[Hobby Services]

George Griffith's "Honeymoon In Space" hasn't been mentioned, which is a bit surprising.  Aeronefs in that setting used the proven gravity-repelling powers of R-Matter (R for Repulsive of course).  R-Matter is only found on Earth in meteor impact craters, which made holding such sites strategically important and further drove colonialism.  The general effect was a "pusher" ray that could be aimed to provide both lift and (by angling the ray against the ground below) propulsion.  It was quite capable of interplanetary travel as well as in-atmosphere maneuvering.  The Chinese forces occupying the ex-USA in Armageddon 2419AD (the original Buck Rogers novel) used a very similar system for their airships, although their rays were produced by weird science generators rather than a relatively rare natural resource.  They could also generate a tractor beam effect with a similar gadget, although the rebels quickly learned to use them against the Han by introducing bombs into the beam.