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I looked it up and this is real
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this post was submitted on 09 Mar 2025
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For those wondering why it did fly that way, it was a whole thing on Twitter: weather, fly zones, mostly.
https://www.thepoke.com/2025/02/26/elon-musk-said-planes-fly-straight-line-owned-into-economy-class/
Obviously the permanent main character on Twitter popped up to assert that planes must go straight despite flying in a private jet constantly that doesn't do that, and after a few hours the original guy said he asked the pilot when they landed (20 min ahead of schedule) and the pilot told him it was to avoid turbulence, which is likely what they say when a full answer seems like it'll just go over folks heads.
Elon Musk "rocket scientist"
There’s also the Great Circle flight paths. Essentially, because the earth is round, it’s actually a shorter distance to fly in an “arc” (when looking at a flat map). In the below picture, the upper curved line is actually shorter than the lower straight line:
Here’s another image which demonstrates why the curved line looks longer on a flat map:
And because of how map projections work, this applies to virtually any flight path that isn’t directly north/south… Just like the one in OP’s photo.
The path in the post has nothing to do with the great circle. The shortest path is very similar to how it appears on the Mercator projection (actually slightly bent in the other direction) because SF and Houston are fairly close and in a position where Mercator distortions are less pronounced.
Also, a line is the shortest path when the 2 points are both on the Equator (where the projection distortion is zero)
Worth pointing out too, that the air isn't "flat" either, you can have headwinds, tailwinds, and turbulence that will affect the shortest and most economical path.
It’s also good to mention that the projection shown in the tweet wasn’t Mercator either, it was a globe rendered via Apple Maps.
There's also the fact that the earth is an oblate spheroid and great circles are the shortest distance between two points on that shape. (Though this may not apply for short flights like this.)
And it doesn't apply because it would be curved upwards