It is NOT impossible. In fact, I already designed one with a perfect spherical pattern. It's called the Caltrop antenna which is circularly polarized too. Unfortunately it's large and unweildy so it is best used in ground applications.
This antenna was designed as a substiute for diversity. If you turn your TX antenna to the side rather than upright, this will match the polarization fairly well even when banking. Horizontal polarization of the TX antenna actuall gives longer transmission range. It's also nice to know you have no nulls to worry about either
-Alex



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