The experiment given by Rab is obviously crap. They give them the expected result, and then are surprised when it matches up. Its called confirmation bias. Then they use only 23 points of data. They have it spread out over a few days. He also is trying to prove against a strawman - picking a random point and using it to determine the height of the sun is ludicrous.

There are just so many things that make this laughable. It's not even "children's science tv show" level of valid.

The main point that makes it laughable is that it is discussing FE as if it might be real.

Would you care to provide more points of data? Most people would accept 23 points, as it would be quite conclusive.

See just using 2 points isn't enough (or points where the symmetry reduces it to 2) as that would be unconstrained as the radius of Earth could be changed to produce any height. But using 3 points allows one to start determining the both the radius of Earth and the height of the sun, both to some degree of error, with the possibility of one value having no upper bound.

Or explain how these data match the FE?

Or do the experiment yourself.

Really, the only valid objection would be to say that the distances between the points of longitude are completely wrong.

That if the distance between the equator and 45 degrees north is 5000 km; then instead of the distance between each 10 degrees of latitude, going from the equator, being a constant ~1111 km, it would instead be:

~880, ~940, ~1070, ~1310, ~1760, ~2700, ~5080, ~14620, ~infinite.

But to avoid this issue I would recommend limiting the measurements to the northern hemisphere (in fact, if Earth was flat you should be able to continue this in the southern hemisphere, but the observations require that to be more than infinitely far away from Polaris, making it quite difficult), and then as well as observing the sun on the equinox also observe Polaris. Because it is well known that for every degree of latitude you move south away from Polaris, its angle of elevation would drop by 1 degree.

This now produces the same kind of series, but now instead of having the distance between the equator and 45 degrees north being 5000 km, you have the distance between the north pole and 45 degrees north being 5000 km, and you have the distances between each 10 degrees increasing as you go south, not north.

Now, you might try and say that that relies upon the assumed height and distance, but it doesn't.

See, it doesn't matter what the actual distances are. The important part is that for a FE the distance between the degrees of latitude must increase as you go north if you use the sun, so the distance between 70 and 80 must be larger than between 10 and 20; while if you use Polaris, they must decrease, so between 10 and 20 must be larger than between 70 and 80.

i.e. a>b, while also b>a.

It doesn't take a math genius to figure out that is impossible.

So as you dismiss the experiments by REers, perhaps you can get a bunch of FEers together (in the metaphorical sense) to take measurements this equinox?

The angle of elevation of the sun at solar noon and the angle of elevation of Polaris at night.