Analysis: Apple Pie Hill to Philadelphia

This is a review of the view from Apple Pie Hill to Philadelphia done by professional surveyor Jesse Kozlowski, executed using a Wild Heerbrugg theodolite (Video).

Technical Data

Observation Point (Apple Pie Hill):

Ground: 204'
Tower: 46'
Total: 250'

Target (Comcast Center Tower):

Ground: 42'
Height: 973'
Top: 1015'
Zenith Angle: 89.95389° [89° 57' 14"] // ~166 arcseconds
Distance: 171281' (~32.44 miles)

Instrument (Wild Heerbrugg theodolite):

I do not know exactly which model of this theodolite was being used but looking at several that looked similar I'll estimate that we have a level accuracy of 30" which gives us about +/- 25 feet at this distance.  But the specifications for these theodolites indicate that they are good for viewing objects about 12 miles away, so this would introduce additional error in our measurements as the angular size of objects over 32 miles away would be reduced, so roughly we might expect 24.912*(32/12) = +/- 66.432'

With better information here we might be able to tighten up our errors bars a little bit but I think I show below that this doesn't matter and greater accuracy would make the Flat Earth hypotheses even LESS likely.

Analysis Flat Earth

On a Flat Earth model would have expected the distant level point to be even with our observation point at 250', with error bars that means we should see 765'+/-66.432' of the tower sticking out above our level mark.  This is well outside the range of even our very generous error bars.

Analysis Curved Earth

Using the Metabunk Curve Calculator we find that the curvature drop over this distance is between 701.74' and 601.49' if we assume standard atmospheric refraction (HOWEVER the hidden height is only 114.03', and 75.93' with standard refraction, because we are substantially higher up than the city, so this view is completely consistent with curvature as we clearly do not see the lower parts of the city which should be clearly visible on a Flat Earth).

Therefore, on a globe, we would expect that extending out a line that is level from our viewpoint on Apple Pie Hill, the elevation in Philadelphia would be the amount of curvature 'drop' (701.74' / 601.49') plus our elevation (250'), or somewhere between 851.49' to 951.74' at the Comcast Center Tower in Philadelphia.  That would leave 163.51'+/- 66.432' to 63.26'+/-66.432' above our level mark at the tower.

Based on the zenith angle measurement of 166 arcseconds we calculate the top is an estimated [g = 2r*tan(α/2)] = 138.8' above the level mark - this agrees with the visual mark on the tower so that seems more accurate (indeed the angle measurement accuracy on this theodolite is cited as being 1" so a higher accuracy in this measurement makes sense).

That's a pretty big error bar but our 138.8' is entirely consistent with the view we see with only moderate refraction and accuracy considerable better than worst case.

Conclusion

So, this shows that this view is entirely compatible with a curved Earth of 3959 miles radius and is completely incompatible with a Flat Earth model.