NavList:

Ten days ago, Bill Lionheart, you wrote:
"I am pretty sure moden aircraft navigation systems use geodesic distance on WGS84 standard ellipsoid."

Sure. That's quite possible. Hell, they may include the gravitational deflection of light in their computations because... [see below]. We just don't know. The avionics software is a blackbox as far as we are concerned. We can, however, legitimately assess whether the ellipsoidal code would make any difference. 

Let's consider what you wrote:
"It's only going to make a few km difference on a long flight"

Is that legitimately the case? If you fly from London to New York, would you get marginally better fuel consumption or flight-time efficiency if you use an ellipsoidal solution for distance instead of a great circle computation? Let's get this out of the way: NO, of course not. The distance is what it is. What I mean is that a slight improvement of a numerical value of distance cannot change the actual length of the trip. It is what it is. But there's much more to it...

Efficiency on a trans-oceanic flight is not going to be determined by the best geodesic given by the best model of the Earth's (approximately) ellipsoidal shape. It's driven by weather and by finding flight tracks that avoid practical limits on distance (political over-flight constraints as well as local air traffic control, regulatory issues, etc). But the really big problem with the idea that you might save a few km by using a mathematically clever geodesic over the ellipsoidal globe is that commercial air traffic almost never flies direct! The real distances that they fly  between known points are rarely more than 500 nautical miles. Commercial aircraft follow flight plans (which are usually generated by ATC with relatively little freedom to innovate) consisting of waypoints separated by dozens to hundreds of miles along standard tracks from departure to destination. These tracks, especially across oceans, are generally based on great circles, but only crudely. And they are modified based on weather, especially high-altitude winds (jetstreams). The ellipsoidal figure of the globe is a minor detail, lost in the noise. The only aspect that is not entirely lost in the noise is the modern definition of latitude, as I have discussed throughout this thread. The parallels of geodetic latitude (that's standard, modern latitude) are closer together by a fraction of a percent in lower latitudes (lower meaning closer to the equator). 

The unknown code in an aircraft's avionics may well be using the legendary "Vincenty" solution for each leg of a flight, but these legs between waypoints are so short that such code would be massive overkill. Most flight legs between those flight plan waypoints are so short that you could even use flat map geometry (also known as "plane sailing") to fly from point to point with negligible difference in efficiency. 

You added:
"but it's a computer not a human so they may as well"

One could argue that this is true because 'it's a computer', but the human reasons are more important: people get paid, so they may as well. All you have to do is convince the "suits" that the money paid to the coders today will benefit the airline's (or avionics company's) bottom line for the next thirty years, and things get done... --whether they are really needed or not. And no one is going to come back in thirty years and say, 'hey that didn't benefit our bottom line at all'.

Frank Reed