This is a specious argument.
https://www.theflatearthsociety.org/forum/index.php?topic=65704.msg1765362#msg1765362
Yes, the quote you linked is quite a specious argument.
The difference in the arc length and the straight line length is negligible.
This is because sin(x)~=x, for small x, with x in radians (which I shall use throughout)
If you take 41 mm as the arc length, then for a hypothetical smaller Earth (to exaggerate the point) with a radius of 6300 km, the angle spanned by that is 6.50794E-09 radians. Halving that to get a right angle triangle you can use sin with easily, that gives you 3.25397E-09 radians.
Finding the length of one half of the line connecting them gets you sin(x)=3.25397E-09, thus the length of one half of the line is 0.0205 m, thus the full length is 0.041 m=41 mm.
So the difference between the 2 is so small it isn't funny.
The difference between sin(x) and x, for small angles can be approximated as x^3/3!=x^3/6.
For our half angle, that difference works out to be 5.74234E-27. This gives a difference in length of one half of the straight line of 3.61767E-20 m, so the full line difference would be 7.23534E-20 m, which is far less than the size of a nucleus. The size of a proton is roughly 1 fm =1E-15 m.
So at that scale it doesn't matter if you use arc lengths or straight line lengths. They are effectively the same.
Also note that FEers are quite guilty of doing the exact same thing.
That whole 8 inches to a mile crap is based upon approximating trig functions as well.
Instead of using sin(x)~=x for small x, they instead use cos(x)~=1-x^2/2 for small x, and they treat the straight line distance between the points (or between one point and a point directly above or below the other point) as equal to the arc distance between the points.
It also isn't merely a hypothetical.
Yes, loading will change it as will wind passing through, but they are dynamic effects which can be averaged out.
The big question is if anyone has actually measured it.
However, also note what most of the FE responses to this indicate:
Contrary to what they often claim, where curvature is meant to play such a big role in projects meaning if the curvature wasn't taken into account it would fail, they now switch their claim to the curvature being so insignificant it wouldn't have any effect and that the curvature doesn't need to be taken into consideration at all even when constructing such a large object.
Don't you just love how they so happily change their mind when it suits them?
So which is it? Does curvature need to be factored in or is it irrelevant? You can't have it both ways. This is a pretty big bridge.