Here's an image of some airship in the John Carter movie.
The way they fly doesn't seam to be explainable on the basis of any know aeronautic principle.
So, how do they fly?
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Any flying Barsoomian technology does so by manipulating the forces of the Eight Ray. The Eight Ray is emitted by planets and other massive objects, so it can be assumed to the Barsoomian equivalent of gravity. The flying technology of the Red People is able to control and manipulate the Eight Ray for flight.
Their vehicles have less of a need for aerodynamic principles like fully functioning wings when they are manipulating the fundamental force of gravity. They would still need a thrust mechanism and some means of dealing with changing direction, which explains the sails on each wing which may help with tacking and direction changing as well as adding or becoming potential thrust.