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.

Comments

Post a Comment

Popular posts from this blog

Pic Gaspard (3880m)/Grand Ferrand (2758m) from Pic de Finestrelles (2826m) in the Pyrénées

Image
I have some new toys to share in this installment of 'Yes, the Earth really is Curved even though you can see one distant mountain peak from another', so this should be fun! This time we're going to look at a view of two distant mountains from Pic de Finestrelles (2826m) in the Pyrénées , taken by Marc Bret of Beyond Horizons (see also the Flickr album ). Pic Gaspard (3880m) in the Massif des Écrins range at a distance of 443 km. Grand Ferrand (2758m) at a distance of 392.48 km. Our view is right around 42.414466°N, 2.132839°E at about 2826 meters elevation, looking right along the coast. Pic Gaspard/Grand Ferrand from Pic de Finestrelles in the Pyrénées, image by Marc Bret The EXIF metadata shows this image was taken by a Panasonic DMC-FZ72 with a focal length of 215mm -- given the 5.62 crop factor of the 1/2.3" sensor in this camera, this gives you a 35mm equivalent focal length of 1200mm giving a full frame view of 1.644° wide and 1.215° high. Since 1521 x 101...
Read more

Flat Earth Follies: Planes would have to constantly pitch down to fly!

Image
Flat Earth Claim Planes would have to constantly pitch down to fly! Short Version In the Globe model "LEVEL" follows a sphere of uniform gravity potential. Feel free to disprove that is the case if you can but that is the model. In an airplane, Elevator Trim simply controls the RATE of pitch of an aircraft - not the actual pitch of the plane. A 747 flying at 35,000' would have a flight circumference of  about 2π*(3959+(35000/5280)) ≈ 24916 miles Flying at 570 miles per hour, this plane would fly a fraction of the 360° around given by 360*570/24916 Since that's 1 hour we can divide by 60 to get the degrees per hour: 360*570/24916/60 ≈ 0.137°/minute That is down in the noise since pitch rate is affected by temperature, density, power, and control settings on the plane you simply trim the plane for as close to ZERO vertical speed as you can and you've automatically compensated for all of them at once.  Of course, on a 747 computers do that.  In a small plane the pitc...
Read more

Fort Myers to Naples - Flat Earth failures continue

Image
No amount of curvature is enough for a Flat Earther.  We can SEE the shoreline disappear, and then the bottoms of buildings.  But since they don't understand the geometry of what they see they cannot properly evaluate it. Flat Earth once again fails to understand WHAT the horizon even is. @captscorch @ColdDimSum @nicholaspitts @CobraElDiablo @UnCastellsMes @twatterfull @sciencegecko @skeptropolis @FlatEarthReal Still waiting on my curve pic.twitter.com/zh2zFXmMVi — JACK (@Adidas68Jack) April 24, 2017 And a copy of the image from Jack just in case (which Jack now deleted). I'm going to admit right here at the start that I do not know the EXACT location from which this photo was taken.  Neither does 'Jack'.  However, we both know the APPROXIMATE location to within a few miles because we can see the nearby buildings and at least their rough orientation. But without a higher resolution image I cannot positively identify the distant buildings, and neither can Ja...
Read more