With a RTL SDR type USB stick on its way, I turned my attention to
looking for an antenna with high gain that would give me good coverage
of ADS-B 1090 MHz broadcasts from aircraft, one that I could easily
and cheaply make for myself.

A quick google produced loads of hits for this type of antenna.

https://www.youtube.com/watch?v=TkUYdCPFXXs

as a random one. You get the idea.

They all consist of 'accurately' cut and calculated equal elements that
reverse the phase 180 degrees for each element so the theory goes.

Pondering over this, it struck me that although the websites do take
into account velocity factor of the coax, that is for the coax in
normal operation. Once the outer conductor, or screen becomes an
element in an array, exposed to the outside world it has a faster
velocity of propagation which, in turn means that the outer of the coax
must be longer than the inner which is there to maintain phase on each
segment. In other words an impossible antenna to make.

Those were my thoughts which have led me to have doubts about the
cheap, simple designs that abound.

Any thoughts, or have I missed something?

Steve G8IZY