It turns out that the computed distance (18743 km) is merely 0.05% off from what you experience in the real world (18752 km). Not bad I must say, as the model didn't even factor in ellipsoidal shape. Here's what it looks like on a globe. The plotted distance and angles are quite consistent with real world experience:
It looks pretty much like a half-circle. So we could estimate that it is roughly π
Now, looking at the angles and distances on both plots, please tell me which plot you would prefer if you were sitting in a boat and trying to navigate from Valparaíso to Shanghai.
It is my understanding that one of the two is absolute bollocks for very simple mathematical reasons. (as described in the blog #34,35,43).
The two following links can be a good starting point for your own research: