Test the Earth's shape: Measure a mountain!

This is lifted from another thread with minimal editing, so it'll look familiar to some of you!

For this you need an accurate map. Now, right away, I know you'll be thinking "but the maps will have been doctored to give you the results you find". Well, if they were, this method would actually show it up with inconsistent results, but it doesn't, so you can put that thought out of your mind.

Equipment: 1 spirit level, 1 set square, and 1 ruler. You might also want something to set the spirit level up on, and some packing to level it.

Method: pick a mountain that is easily identifiable from a distance (I have a few to pick from where I am). Find a point on the map 30km away, 40km away, and 50km away (or any other largish distances, as long as you can measure them accurately. This is part of what negates any doctoring of the maps: picking arbitrary points to measure from). Set up your spirit level so that it points toward the mountain you picked, ensuring it is level. Set your ruler at a specific distance along the top of the level, standing up at right angles to it (that's what the set square is for). Sight from the edge of the level furthest from the mountain to the mountain top, and note where your line of sight crosses the ruler. The ratio of the measurement on the ruler to it's distance along the top of the level would be equal to the ratio of the mountain's height above your observation point to your distance to it (simple triangular geometry).

The height of the location the measurement is taken from is important, as you will get different results from different elevations at a given distance. Another reason why this cannot be faked or doctored.

In the below diagram, the ratio of h/d should be equal to r/s if the earth is flat, and should always be that way, no matter how far away from the mountain you are.



When I did this experiment though, there was a difference between h/d and r/s, and it got bigger and bigger the further away I got from the mountain. I did some extra maths to work out where the mountain top would be for a round earth:

apparent height on a round earth = square root of ((earth's radius + h)² - d²) - (earth's radius + altitude of your position)

When I tested the results against those calculations, they matched perfectly. Remember: maths and geometry don't care what shape the earth is; they will always tell you the truth.

Results:

Mountain (Castle Top, in the Nandewar Ranges): 1075m AMSL
Point 1 (my back yard): 30.44km from peak, 215m AMSL
Point 2 (Kamilaroi Hwy): 40.46km from peak, 205m ASMSL
Point 3 (Wee Waa levee): 55.57km from peak, 192m AMSL

Using a 1100mm baseline on the spirit level, the following apparent heights were recorded:
Point 1: 28mm
Point 2: 18mm
Point 3: 11mm
Let's be pessimistic and say they're only within 1mm either way.

Here's what they should have been for a flat earth:
Point 1: 31mm
Point 2: 21mm
Point 3: 16mm
Note the increasing difference. This is due to the mountain 'going over the edge'.

Conclusion: The data collected disagrees with FE predictions*, and almost exactly matches RE predictions. The experiment is easy to conduct, and not prone to significant error, so the results can be considered reliable.

* Rowbotham's 'perspective' has been cited as a possible cause of the results. However, a passing familiarity with geometry should be sufficient to show that this 'effect' is not responsible for the rate at which the actual measurements diverge from what they should be for a flat earth.

Interesting Note: if you use the following equation, you can work out the difference between the apparent height for a round earth and a flat earth (with respect to the diagram):

rf - rr = s * tan((d / ce) * 360 / 2)

where rf is the apparent height on a flat earth, rr is the apparent height on a round earth, and ce is the circumference of the round earth. d and ce need to be in the same units as each other, and rf - rr will be in the same units as s.


Sorry for the long post! I thought it would be best to give plenty of detail, so that others can reproduce this experiment and obtain accurate results.

Interesting!

While I'm a RE supporter, I'm guessing a lot of FE'ers will cite "Bendy Light," AKA Electromagnetic Acceleration (long story) as an explanation for this. Has this been considered?

Interesting!

While I'm a RE supporter, I'm guessing a lot of FE'ers will cite "Bendy Light," AKA Electromagnetic Acceleration (long story) as an explanation for this. Has this been considered?

If light bent away from the surface of the earth at a consistent 1° per 60 nautical miles traveled, then yes, "bendy light" could possibly explain this. It could also explain the curvature measured by all other properly conducted experiments. However, there are a number of unresolved issues with "bendy light", mostly covered in this thread: Another hitch with bendy light?
Given those problems, I don't think that "bendy light" can be pulled out as an explanation for anything just yet.

Thanks for the comment! 

Are you actually experimenting? Data? What is this? Are you lost? This is the Flat Earth Society, you utterly foolish noob! Do you not know that data is not welcome here?

Be GONE!!!

Darknavyseal, please keep your low content replies out of the upper fora.  This is not your playground.   Consider this a warning.

has anyone tried this yet? Particularly flat earth advocates? If you don't have a spirit level, you can jury rig a very accurate one using a long straight-edge and a length of water filled plastic tube.

has anyone tried this yet? Particularly flat earth advocates? If you don't have a spirit level, you can jury rig a very accurate one using a long straight-edge and a length of water filled plastic tube.

I'm going to try this on Mt. Hood (er, against Mt. Hood?) from various places near my home. Might do Mt. St. Helens and Mt. Adams as well.

Quote from: Scintific Method on July 30, 2013, 04:19:25 PM

has anyone tried this yet? Particularly flat earth advocates? If you don't have a spirit level, you can jury rig a very accurate one using a long straight-edge and a length of water filled plastic tube.

I'm going to try this on Mt. Hood (er, against Mt. Hood?) from various places near my home. Might do Mt. St. Helens and Mt. Adams as well.

That should give some pretty outstanding results! Remember, the further away you get, the greater the difference between FE and RE predicted heights.

Mt. Adams:
Measurement: 0.875" at 36" (1.39 degrees)

Distance (me to mountain): 114.2 km (70.96 mi)
Summit (height of mountain): 3743 m (12,280 feet)
Elevation (me ASL: 84 m (276 feet)

FE Prediction: 1.15" (1.84 degrees)
RP Prediction: 1.14" (1.81 degrees) (that's Rowbotham's Perspective Prediction)
RE Prediction: 0.83" (1.32 degrees)

My measurement differed from FE predictions by .28", or 31% error.
My measurement differed from RP predictions by .27", or 30% error
My measurement differed from RE predictions by .05", or 6% error.

EQUATIONS (see below for list of givens):

FE Predictions:
RP Prediction: Amount of mountain 'merged' with horizon (due to <1 arcminute diameter):

Predicted measurement:

RE Predictions: A bit more complicated. First, the angle of the Earth over which I was viewing:

Next, the drop height over 114.2 km:

Next, the apparent height of the mountain (tilted at A=1.03 degrees away from what I see as vertical):

Then, how high the mountain was above my horizontal:

Finally, how high that should appear:

PROCEDURE:

Tools: Spirit Level, yard stick, carpenter's square, friend.

Using the apex of the roof and a metal protrusion, we used the spirit level to make the carpenter's square perfectly horizontal (and stable), pointing toward Mt. Adams. Then, my friend used the spirit level to make sue the upper leg of the square was perfectly vertical. Using the yardstick, I placed my eye exactly 36 inches from the close edge of the square's vertical leg. I then used the yardstick to indicate where on the square's vertical leg I saw the summit of Mt. Adams. My friend placed a fingernail there, and we read the measurement together: 7/8 inch.

I took and recorded the measurement before calculating the RE and FE predictions.

Givens

Radius of the Earth: 6371 km (3959 mi)
Circumference of the Earth: 40,009 km (24,860 mi)
Distance (me to mountain): 114.2 km (70.96 mi)
Summit (height of mountain): 3743 m (12,280 feet)
Elevation (me ASL: 84 m (276 feet)

Nice writeup Alex! Wonder if any FE'ers will follow your fine example? 

Thanks! Sadly, only Adams was visible from my roof. I'll have to drive a bit to get a view of Hood or Helens.

And using my awesome psychic powers of prediction, I foresee that not only will no flat-earth advocate attempt this, but they will refuse to acknowledge that this experiment even exists.

I found it quite enjoyable, however. When I post my observations of Hood and Helens, I'll skip the whole equation section. Just the cold, hard facts.

Nice writeup Alex! Wonder if any FE'ers will follow your fine example? 

I'm afraid that they may be too preoccupied with looking at clouds from an airplane rather than taking part in a cleverly designed experiment.

Quote from: Scintific Method on July 31, 2013, 12:36:43 AM

Nice writeup Alex! Wonder if any FE'ers will follow your fine example? 

I'm afraid that they may be too preoccupied with looking at clouds from an airplane rather than taking part in a cleverly designed experiment.

Astutely noticed! FYI, I wouldn't worry about low-content posting here. This thread doesn't exist, apparently.

We already know about the Sinking Ship Effect.

We already know about the Sinking Ship Effect.

And how is that relevant to the thread? This is about geometry and the major difference between apparent heights on flat surfaces, and those on curved surfaces, not the visual merging of the lower portion of a distant object with the surface upon which it rests (which, btw, does not explain objects being obscured by the horizon, but that's not the topic of this thread).

I would suggest reading the chapter to see how it is relevant.

I would suggest reading the chapter to see how it is relevant.

I'm sorry but this does not help and is extremely obtuse.

It's like me suggesting you read a geometry book to see how that theory is wrong.

I would suggest reading the chapter to see how it is relevant.

Like I said, this is about geometry and the reduction of apparent height of objects as distance increases over flat vs. curved surfaces, NOT the reduction of visual features to less than one arc minute of angle at the viewer's eye as distance increases. Seriously Tom, try to keep your comments relevant to the topic at hand.

Quote from: Tom Bishop on August 03, 2013, 01:06:01 AM

I would suggest reading the chapter to see how it is relevant.

Like I said, this is about geometry and the reduction of apparent height of objects as distance increases over flat vs. curved surfaces, NOT the reduction of visual features to less than one arc minute of angle at the viewer's eye as distance increases. Seriously Tom, try to keep your comments relevant to the topic at hand.

Tom, if you look at my data, I have given you how tall Mt. Adams was in degrees. The summit was well above the vanishing point, and even if the base of the mountain became indistinguishable from the horizon, this wouldn't magically pull the summit lower.

Tom is exactly correct that you are misinterpreting perspective. The experiment would prove nothing to me. I have no doubt that the mountains' height as calculated by simple art-school perspective will differ.

The experiment would prove nothing to me.

No surprises there, the rest of your comment makes it pretty clear that you do not understand the basis of this experiment: geometry. If you can tell me how something looks half a degree (that's the visual size of the sun or moon, btw) lower than it should be, I'll be very interested.

Slightly off-topic: if you can also tell me how something can appear ~50 times it's own width lower than it should be (the sun at sunrise or sunset), that would also be quite interesting.

If you had read any of the material provided, you would see that Dr. Rowbotham meets your objection and that art-school perspective is not rooted in reality, but merely approximates it.   

If you had read any of the material provided, you would see that Dr. Rowbotham meets your objection and that art-school perspective is not rooted in reality, but merely approximates it.   

I have read the material provided, and there's a good reason why art school perspective does not account for what is seen: art school perspective is based on planar geometry. In other words, it is what we should see if the earth were flat.

Tom is exactly correct that you are misinterpreting perspective. The experiment would prove nothing to me. I have no doubt that the mountains' height as calculated by simple art-school perspective will differ.

Okay, so the bottom arcminute of Mt. Adams merged with the horizon. Do you know how much that is? 33 meters. So let's assume this somehow magically pulls the summit of Mt. Adams 33 meters closer to the ground--shortened my measurement by a whole arcminute.

My measurement was off from FE predictions by 30 arcminutes. Where are those extra 29 arcminutes coming from, Ski? Why was my measurement a whole half-degree shorter than what FE predicts?

If you had read any of the material provided, you would see that Dr. Rowbotham meets your objection and that art-school perspective is not rooted in reality, but merely approximates it.   

Art school perspective is based on observation. Brunelleschi would trace reflections on mirrors to derive a 2D image of a 3D subject. Rowbotham's perspective is based on wishful thinking and was created to suit his needs.

I'm glad that the two "FE supporters" who bothered to respond displayed complete lack of understanding of the experiment. I consider their logical and mathematical ignorance as further support for RE.

Quote from: Ski on August 13, 2013, 04:05:20 PM

Tom is exactly correct that you are misinterpreting perspective. The experiment would prove nothing to me. I have no doubt that the mountains' height as calculated by simple art-school perspective will differ.

Okay, so the bottom arcminute of Mt. Adams merged with the horizon. Do you know how much that is? 33 meters. So let's assume this somehow magically pulls the summit of Mt. Adams 33 meters closer to the ground--shortened my measurement by a whole arcminute.

My measurement was off from FE predictions by 30 arcminutes. Where are those extra 29 arcminutes coming from, Ski? Why was my measurement a whole half-degree shorter than what FE predicts?

You obviously didn't read the chapter Tom provided you. I'm not sure how else to help you.   

I did read the chapter. It says: "when any object or any part thereof is so far removed that its greatest diameter subtends at the eye of the observer, an angle of one minute or less of a degree, it is no longer visible."

The two examples with the disks show that while the portions of a larger objects vanish, the object itself remains unchanged--The disk with a 1-inch stripe on the bottom is still perfectly round even when the white segment disappears.

He then proceeds to give many examples--all of which can be misinterpretations of viewing things disappearing over the curve of a round Earth, but that's for another time.

The important thing is that Rowbotham says that a) only objects, or parts of an object, less than one arcminute in diameter, cannot be seen and b) if a smaller part of a larger object is unable to be seen, the larger object remains wholly unchanged in size.

Let's take this to Mt. Adams, shall we? I measured 1.38 degrees--nearly 83 times larger than the size required for it to vanish. Even if a length of 33 meters did indeed vanish from the mountain, Rowbotham clearly states that the whole of the mountain would remain unchanged.

Your insistence that this can explain why I saw Adams a whole half-degree smaller than I should have for a flat Earth makes me wonder if any FEer has actually read Rowbotham's Chapter 14.

Quote from: Ski on August 13, 2013, 05:03:16 PM

If you had read any of the material provided, you would see that Dr. Rowbotham meets your objection and that art-school perspective is not rooted in reality, but merely approximates it.   

Art school perspective is based on observation. Brunelleschi would trace reflections on mirrors to derive a 2D image of a 3D subject. Rowbotham's perspective is based on wishful thinking and was created to suit his needs.

Brunelleschi used a mirror to demonstrate how closely his painting matched the actual baptistry he painted. It was across a plaza and not near the horizon. If Brunelleschi had actually traced the reflection of a distant object, he may have realized how his take on linear perspective was flawed wherein lines dissimilarly distant from the eye-line recede at the same rate.

I did read the chapter. It says: "when any object or any part thereof is so far removed that its greatest diameter subtends at the eye of the observer, an angle of one minute or less of a degree, it is no longer visible."

...

Your insistence that this can explain why I saw Adams a whole half-degree smaller than I should have for a flat Earth makes me wonder if any FEer has actually read Rowbotham's Chapter 14.

If Alex had read the chapter, ...

he may have realized how his take on linear perspective was flawed wherein lines dissimilarly distant from the eye-line recede at the same rate.

I would suggest reading the chapter to see how it is relevant.