Distances at altitude

MyMatesBrainwashed

Active Member
So my line of reasoning is along the lines of, from a fixed point a on the ground and a fixed point b somewhere else on the ground, travelling from point a to point b along the ground should be shorter than travelling from an altitude plumb to point a to the same altitude plumb to point b, while maintaining the altitude during travel, IF the earth is a globe.

If the earth is flat then the distances should be exactly the same.

I'm sure a diagram would help but I'm reluctant to get mspaint out and hopefully my explanation is good enough to illustrate what I'm getting at.

If my reasoning is correct then I'm imagining a drone could do this. It could fly directly up from a point, altitude should be able to be maintained from air pressure. Not entirely sure how a drone can determine distance travelled though without gps help or something else that could be used against the test. The idea is that drone travels x distance but comes down way before point b which is x distance away from point a.

If my reasoning is correct then I'd imagine it all falls apart in the numbers. How far apart would point a and point b need to show a significant result? How high would it have to be to show a significant result? (I do appreciate there should be a relationship such that the higher you do it the less distance you need). How accurate would instruments need to be to maintain altitude? I'm really not good enough with numbers to be able to work any of that out myself.

If my reasoning is incorrect (most likely) then no doubt Mick'll come along to poopoo my idea in seconds :( But jokes aside I do learn from having my mistakes pointed out to me. Honest!
 
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Mendel

Senior Member.
This is usually suggested with bridge pylons, e.g. Firth of Forth, and the claim that they're a few cms further apart at the top than at the bottom.

Article:
The towers of the Humber Bridge rest on pylons in the estuary bed. The towers are 1410 metres apart, and 155.5 metres high. If the Earth were flat, the towers would be parallel. But they’re not. The cross-sectional centre lines at the tops of the two towers are 36 millimetres further apart than at the bases.
019-HumberBridge.jpg
Unfortunately, in all my searching I couldn’t find any citations for anyone actually [measuring] this.

Measuring distance in the air while flying is impossible for a drone.

There's a relativity experiment that involved clocks in aircraft, but the people who can understand that don't generally doubt the globe.
 

FatPhil

Senior Member.
There's a relativity experiment that involved clocks in aircraft, but the people who can understand that don't generally doubt the globe.

The aircraft one was an pretty old one, and was a SR test, IIRC (moving slows your clock down). There's been a more recent one in a lab just with altitude differences, no additional movement, and that's a GR one. Of course, both tests had lower=slower because GR and higher=slower because SR, but the relative magnitudes of those two influences was very different. And, as you say, if you understand any of that, you'll not be in the FE camp.
 

Ann K

Senior Member.
Back of the envelope calculations - I get 131 feet difference if you have a generous hundred mile course at the surface and if the plane is one mile high, or 0.025 % difference. All you'd need would be a little gentle breeze at altitude to throw that off, so it seems to me to be theoretical but not practical.

(assuming my computation to be accurate, since I've just had two phone calls and a doorbell ring to distract me! :) )
 

Rory

Senior Member.
theoretical but not practical

Theoretical but not practical hits the nail on the head. Even if you could carry it out perfectly I'd say there's zero chance it would impress a committed flat earther; and for those who aren't fully committed there are much more obvious ways to show the Earth is a globe.
 

FatPhil

Senior Member.
This is usually suggested with bridge pylons, e.g. Firth of Forth, and the claim that they're a few cms further apart at the top than at the bottom.
...
Unfortunately, in all my searching I couldn’t find any citations for anyone actually [measuring] this.

There's a new one to test it out on: 1915 Çanakkale Bridge
Height 334 m (1,096 ft)
Longest span 2,023 m (6,637 ft)
https://en.wikipedia.org/wiki/1915_Çanakkale_Bridge

2.023/6370 ~= 0.00032, so a maximum difference of 10cm tip-to-tip, almost 3 times that of the humber bridge
Alas, that's not easily measurable with commodity equipment.
 

Ann K

Senior Member.
There's a new one to test it out on: 1915 Çanakkale Bridge
Height 334 m (1,096 ft)
Longest span 2,023 m (6,637 ft)
https://en.wikipedia.org/wiki/1915_Çanakkale_Bridge

2.023/6370 ~= 0.00032, so a maximum difference of 10cm tip-to-tip, almost 3 times that of the humber bridge
Alas, that's not easily measurable with commodity equipment.
At the distances such as these for bridges, it seems likely to me that the piers would bend enough to change those values considerably under a wind load, or when the sun strikes them on one side, or perhaps when one pier is in the sun and another is under cloud. If my assumption is correct, then the accuracy of measurement wouldn't be the critical thing anyway. (Nope, I'm not an engineer, so I don't know how much they'd be expected to change.)
 

Mendel

Senior Member.
At the distances such as these for bridges, it seems likely to me that the piers would bend enough to change those values considerably under a wind load,
From the article on the Humber bridge:
Article:
Interestingly, I did find a paper about measuring the deflection of the north tower of the Humber Bridge caused by wind loading and other dynamic stresses in the structure. The paper is primarily concerned with measuring the motion of the road deck, but they also mounted a kinematic GPS sensor at the top of the northern tower[1].

[graph omitted]

From the graph, we can see that the tower wobbles a bit, with deflections of up to about ±10 mm from the mean position. The authors report that the kinematic GPS sensors are capable of measuring deflections as small as a millimetre or two. So from this result we can say that the typical amount of flexing in the Humber Bridge towers is smaller than the supposed 36 mm difference that we should be trying to measure. So, in principle, we could measure the fact that the towers are not parallel, even despite motion of the structure in environmental conditions.
 

Rory

Senior Member.
Indeed. So if you took the GPS down to the base you'd be able to measure the difference between top and bottom.

Problem is, it wouldn't mean anything to a flat earther - any number on a screen can be fabricated - and to everyone else it's just an interesting factoid.
 

Mendel

Senior Member.
Indeed. So if you took the GPS down to the base you'd be able to measure the difference between top and bottom.
GPS sensors measure positions, not distances.

You can measure the relevant distances with surveyor's tools, or with laser ranging. Put your laser in the middle of the bridge, use a drone to fly laser reflectors up there.
 

FatPhil

Senior Member.
Indeed. So if you took the GPS down to the base you'd be able to measure the difference between top and bottom.

Problem is, it wouldn't mean anything to a flat earther - any number on a screen can be fabricated - and to everyone else it's just an interesting factoid.

I suspect that's dead-reckonning using an accellerometer (thus double integration, one to get velocity, twice to get position), and that might be accurate for 10mm of movement, but isn't for 200+m of movement.
 
Flat-earthers often ask questions about tilting of buildings caused by the curvature of the Earth.

The angle between two tall buildings can be easily calculated using the approximate formula derived below:
α = 0.009s. When you put the distance s between the buildings in kilometers into this formula, you get the angle α in degrees. At this angle, the plumb lines would cross if you could directly compare them. Some examples:

s (km) ––– α (degree)
1 ––––––– 0.009
10 –––––– 0.090
100 ––––– 0.900
150 ––––– 1,350
270 ––––– 2,430
444 ––––– 3.996
500 ––––– 4,500
1000 –––– 9,000

For example, at a distance of 100 km, the angle is 0.9 degrees. A good rule of thumb is also that the north-south distance between the latitudes is approx. 111.1 km. Finland is located roughly between latitudes 60 and 70, so the north-south length of Finland is approx. 1110 km. The skyscrapers built in Helsinki and Nuorgam would be at an angle of approx. 10 degrees to each other.

Suppose the skyscrapers are at distance of 100 km from each other and tall enough that you could see the other from the top of the other. Could you detect the angle between them? They are in the same line of sight, so the tilt would be away from you. You should go very far to get an orthographic side view. Still 0.9 degree angle could be impossible to measure.

The picture shows the Leaning Tower of Pisa, whose current inclination is approx. 4 degrees. If a completely vertical tower were built 444 km away in the direction of the tilt, it would be parallel to the Pisa Tower.
Pisan torni.jpg
 
Some more thought of 1915 Çanakkale Bridge in Turkey. It is the longest suspension bridge in the world. Its total length is 3,563 m and the length of the main span 2,023 m. The height of the bridge's two towers is 318 m.

With the formula α = 0.009s, the angle between the pillars is 0.018207 degrees. From this it can be calculated that the tops of the pillars are approx. 10 cm further apart than the bottoms (see picture). As FatPhil said: "Alas, that's not easily measurable with commodity equipment." What kind of devices would be accurate enough (assuming there was no wind at all)?

Flat-earthers may ask some more direct method to detect the angle. Go to the tip of the promontory marked on the map (point O). From there you can see the bridge roughly perpendicular. If you look with binoculars (or Nikon P1000), you can see the bridge's pillars A and E. If your eyes are sharp enough, you may see that the angle between the pillars is approx. 0.018 degrees, or approx. 65 arc seconds. However, if you don't, you can only blame your eyes. ;)


1915 Canakkale Bridge.jpg


When building long suspension bridges, is it necessary to consider the "wider at top" value? Here is a discussion on Official Flat Earth & Globe Discussion site:

Source: https://www.facebook.com/groups/FlatEarthGlobeDiscussion/permalink/1435374913571069
.

There Gary A Brown says:
"Mino Re, It has to be accounted for in structural drawings to assure mating of the cables at the correct point on the tower, otherwise, stresses and compression of the cables would be off."
If this is correct, then the curvature of the Earth must be accounted for during construction?
 
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Rory

Senior Member.
If your eyes are sharp enough, you may see that the angle between the pillars is approx. 0.018 degrees, or approx. 65 arc seconds. However, if you don't, you can only blame your eyes. ;)

Or take a high resolution photo and zoom in on your computer.
 

Mendel

Senior Member.
Or take a high resolution photo and zoom in on your computer.
0.018⁰ tilt comes to 3 pixels per 10000. If your camera can capture the bridge side-on with 10,000 pixels height, the image width needs to be about 100,000 pixels.
 

Rory

Senior Member.
Yes, if you know the shape of the Earth. See the problem?

Not really; I know the shape of the Earth. ;)

You're still thinking of using it as a flat earth debunk? Thought we'd ruled that out.

0.018⁰ tilt comes to 3 pixels per 10000. If your camera can capture the bridge side-on with 10,000 pixels height, the image width needs to be about 100,000 pixels.

Yeah, figured it would be pretty minimal pixel-wise, though a little surprised it's that extreme. Thanks for doing the maths. :)

I guess another few years till we get our hands on billion pixel cameras - a quick check says 400 million is about the highest commercially available right now.

They'll be in dumb phones by the end of the decade though. ;)

PS just quickly checked the maths and I made it about 600,000x94,000 to show a 3 pixel difference. Wonder where we differed?
 
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MyMatesBrainwashed

Active Member
Back of the envelope calculations - I get 131 feet difference if you have a generous hundred mile course at the surface and if the plane is one mile high, or 0.025 % difference. All you'd need would be a little gentle breeze at altitude to throw that off, so it seems to me to be theoretical but not practical.

(assuming my computation to be accurate, since I've just had two phone calls and a doorbell ring to distract me! :) )
Thanks for that. I did think it'd fall apart with the numbers. A lot of impracticalities seem ok until you see the numbers (like breeze, just do it indoors, oh, I need a building a mile high and 100 miles wide).

I've never considered measuring bridges to be particularly practical either. Just getting to one is hardly practical for most people. Nevermind standing at the bottom with your tape measure wondering how to climb it.
 
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