How many millions of intercontinental flights based on RET would it take to convince you?
You need to learn how flights work. Airliners use filed flight plans and radar communication with air traffic control. The filed flight plans are based off of years of historic data collection. Nothing here proves the shape of the earth.
I don't know about "proving" the shape of the earth, but flight systems and navigational protocols rely on Globe earth calculations, maps, and geodesy. For example, see this from the FAA:
Maximum Course Length between Required Navigation Performance (RNP) Waypoints
It is the purpose of this analysis to determine a maximum distance between RNP waypoints, which ensure that overall risk to navigation remains at or below an acceptable level...
Manufacturers of FMS systems were contacted regarding the computational course solution used in their FMS systems, including satellite navigation. Each indicated that the computations used in each of their respective systems are based upon great circles of the volumetric sphere. The paper cited in the references from Smiths Industries also examines the differences between spherical great circle and geodesic WGS-84 ellipsoid solutions. The results shown are consistent with the analysis contained herein...
Similarly, for routes with designed primary widths of 8 NM constructed using Lambert projections and flown with either great circle or WGS-84 geodetic computations, it is recommended that maximum route length between waypoints be set at 100 NM. [/font][/size]
http://www.tc.faa.gov/its/worldpac/techrpt/afs420-92.pdfI'm sure you're aware what Great Circles are and how they conform to a spherical earth. As well, I'm sure you're familiar with the WGS-84 ellipsoid model. Well, that's what Airliners use.
Here's what Lambert Conformal flight chart looks like:
It, like many others, is a projection from a globe. Here's how a Lambert conical projection is rendered:
In short, Airliners correctly or incorrectly rely on a spherical earth for all things navigation all the way down to calculating required fuel amounts for a given leg. So I'm not sure where you are getting your information from that they don't. But if you have a source, feel free to present it.