[RonJ]

Your experiment has already been done: check out the 'LIGO Experiment'.
It's a laser in a vacuum.  The arms are long enough so the concrete supports for the
pipes had to be adjusted to compensate for the earth's curvature. 

Maybe they should have consulted the wiki on here and saved themselves a bunch of money!

[Zack Bimmel]

Hi someled

Here is my last attempt to convey to you that indeed, in the references I provided the occurrence of the radius of the earth, R, does not indicate that anybody suggests that the mechanism of the refraction of light is influenced by R. It also should become clear to you why it pops up in the equations in the references. If that seems to you a contradiction in terms than please study the following with care to see the contradiction vanish in thin air (pun intended).


For the following see my attached image, I have it available only on my home computer and didn't know how to imbed into this post.
This image is a my counterpart to Fig. 1 in Ref.[3]. As in that figure we have the cord-length S stretching from point 1 to 2 with point 3 in the middle. The circular arc going from point 1 to 2 represents a beam of light under influence of refraction with point 2 being the target and point 1 the observer. Line 1-4 is tangential to the circular arc at point 1 and points in the direction the observer at point 1 perceives the target to be. Again, Delta_beta is the angle of refraction. Perpendicular to this tagent is the radius line 1-0. By way of similarily of right triangles you can prove that the angle Delta-beta occurs again between the lines 0-1 an 0-3.

Some trigonometry :Or with extremely small errors (less than 1%) according to the info in my previous post :

Delta_beta = S/(2*r)

Now use this relationship to eliminate Delta_beta from Eq.(7) in Ref.[3]. The resulting equation is :

S/(2*r) = -S/2 * (dN/dh) * 1.e-6

I assumed that the cord-length, line 1-3, is running horizontally. Hence cos(beta) = 1

The factor S/2 appears on both sides of the equation and therefore cancels out.

1/r = - (dN/dh) * 1.e-6

This equation still does not contain R=6370km which is what you rightfully demand to be. So, how does R=6370km come into being in eq.(10) in Ref.[3] you might ask.

Well, here is what scientist often do. In order to converse easily among each other it is better to present r with respect to some reference length, let's call that L. One can argue endlessly as to how big the value of L might be. If all the involved scientists were to live in the UK one (usually it is the one who publishes first on the subject at hand) might suggest the distance between London and Glasgow. If subsequent publishers in the field like that choice because they think that distance is relevant to the refraction of light in the context of surveying the landscape or the building of large structures the original suggestion for L will pervail, otherwise somebody else comes up with a different idea.

I suggest that L = distance between London and Glasgow is really not a good idea but maybe using the radius of the earth might not be a bad choice for two reasons. a) Everybody knows at least a good approximate value of that ( 6370km or the equivalent in miles or whatever units one prefers). b) r in above equation often comes out to be in the neighborhood of thousands of kilometers under common atmospheric conditions.

Last step to get to Eq.(10) in Ref.[3].

Multiply my last equation by R on both sides :

R/r = - R*(dN/dh) * 1.e-6

and abbreviate : k = R/r to obtain eq.(10) in Ref.[3]. Bingo.

And this is my last post trying to explain to you that in all the references I provided the radius of earth is simply used as a convenient way to display and communicate the effect of refraction of light due to temperature gradient in the atmosphere. Thank you for your time. Zack

sin(Delta_beta) = S/(2*r)

[Zack Bimmel]

Your experiment has already been done: check out the 'LIGO Experiment'.
It's a laser in a vacuum.  The arms are long enough so the concrete supports for the
pipes had to be adjusted to compensate for the earth's curvature. 

Maybe they should have consulted the wiki on here and saved themselves a bunch of money!

Congratulations, but you really took away my punch line.

[Zack Bimmel]

Hi,
Don’t mean to hijack this conversation, but I do have two comments.
I agree with somerleds position that if you have a flat earth model, refraction doesn’t make sense as the line of sight is always perpendicular with the thermal gradient, so refraction would always be zero.

But you do have two problems otherwise.
1.   In the Wiki, it is stated that one of the reasons that ships vanish below the horizon, which is basically the same thing as this Bedford experiment, is refraction.  You can have it both ways, either refraction interferes with the path of light in the flat earth model or it doesn’t.

2.   Whenever I have seen these “Rowbotham effecst” demonstrated, it is pretty clear that the experimenter always puts the observation point and the target very close to the ground. (including Rowbotham).  The reason seem pretty obvious, when you are close to the ground, the thermal gradient is the highest and therefore the refraction is the highest and you get the illusion that the earth is curved more than it actually is.  If you see others perform the experiment, they always make sure to do it well above the surface which minimizes refraction and shows that the earth is curved.

DaveP : sorry to contradict you a little bit. Refraction of light takes place of cause when light enters a medium with a n index of refraction different from that medium the light beam comes from. In addition to that, light is also refracted when light beam and temperature gradient are perpendicular to each other. Or for that matter by gradients of absolute humidity.

But, you are correct with you last paragraph, you can use refraction to make points in favor or against the flat earth model. Unless, of course, you measure the temperature gradient exactly along the line of sight during your experiment and then correct accordingly. I am not aware of anybody in the FE community or otherwise has done that nor published about his/her/their experimental evidence.

There is at least one experiment (conducted for totally unrelated purposes) called LIGO of which we have two examples in the US and one in Italy. It is based on a laser beam traveling down a long straight tube ( 4km) and being reflected back to where it came from. No air or other gases on the inside, just a plain, high-quality vacuum. They had to take earth's curvature into account increasing the cost of a rather expensive experiment (hundreds of millions of dollars). LIGO is doing well continuously listening to the "sounds" of the universe.

It seems to me there might be other such instance where creating large structures might have to consider earth's curvature. Maybe underground subway system where two tubes cross each other; one on top of the other with little clearance in between. I am thinking of those instances where these tunnels were "dug" by those huge machine which grind their way for miles on end never to see the light of day why doing so.

[RonJ]

When you construct a microwave link, it's essential that you consider the curvature of the earth. 

The engineering plan must consider the height of the antenna at each end, the height of the terrain in between,
and the curvature of the earth.  The height of any object or a rise of terrain near the middle of the path could be
a game changer causing the costly construction of taller towers at one or both ends.

If it weren't for the curvature of the earth than a microwave transmitter on top of the Sears Tower in Chicago could easily
communicate with a tower in Omaha.  In the real world, that's impossible all because of the nasty curvature of the earth.

The same goes for TV towers.  If it weren't for the earth's curvature you wouldn't be able to put a TV transmitter on any of
the same channels as are used for the ones in Chicago anywhere in the USA.  Mutual interference would be the result. 

That doesn't happen for the vast majority of the time.  Yes, I used to sometimes watch TV from a distant city usually on the
lower TV channels 60 years ago.  Quirky weather conditions would allow the TV signals to bounce back to the earth, but those
kind of things only happened less than 1% of the time.  All that means is that, yes, you can indeed receive those signals from a
longer distance but for the most part it's the earth's curvature that keeps that distant TV signal from interfering with your local
TV station and keeping all the viewers happy.

[somerled]

In the LIGO experiment which model of earth curvature (oblate spheroid or pearoid) did the building bods account for ? Did they just account for the fictional R = 6370km in such a delicate experiment ?

[Bikini Polaris]

In the LIGO experiment which model of earth curvature (oblate spheroid or pearoid) did the building bods account for ? Did they just account for the fictional R = 6370km in such a delicate experiment ?

The LIGO setup is not floating on water, so I don't think it would prove anything. Maybe the closest thing to a visual proof (that REs would take as a disproof of their theory blablabla) would be to check the Bedford Canal supposed flatness at an increased height, where the temperature gradient wouldn't affect light so much.

[DaveP]

Funny you should mention that......

Rowbotham repeated his experiments several times over the years but his claims received little attention until, in 1870, a supporter by the name of John Hampden offered a wager that he could show, by repeating Rowbotham's experiment, that the earth was flat. The noted naturalist and qualified surveyor Alfred Russel Wallace accepted the wager. Wallace, by virtue of his surveyor's training and knowledge of physics, avoided the errors of the preceding experiments and won the bet.[5][6] The crucial steps were to

Set a sight line 13 feet (4 m) above the water, and thereby reduce the effects of atmospheric refraction, and
Add a pole in the middle that could be used to see the "bump" caused by the curvature of the earth between the two end points.[1]

Despite Hampden initially refusing to accept the demonstration, Wallace was awarded the bet by the referee, editor of The Field sports magazine. Hampden subsequently published a pamphlet alleging that Wallace had cheated and sued for his money. Several protracted court cases ensued, with the result that Hampden was imprisoned for threatening to kill Wallace[7] and for libel.[8][9] The same court ruled that the wager had been invalid because Hampden retracted the bet and required that Wallace return the money to Hampden. Wallace, who had been unaware of Rowbotham's earlier experiments, was criticized by his peers for "his 'injudicious' involvement in a bet to 'decide' the most fundamental and established of scientific facts".[1]

https://en.wikipedia.org/wiki/Bedford_Level_experiment

[AATW]

Had a quick look on YouTube as I figured someone must have reproduced the experiment. Couldn't find anything but I did find this



It's a similar experiment over a 9 mile stretch of water with no significant waves.
I'll be fair and say they picked some of the crazier flat earthers but it was unsurprising to see results which you'd expect on a globe being declared by Mark Sargent as exactly what he'd expect on a flat earth.

[Zack Bimmel]

AllAroundTheWorld (also mentioning RonJ's post)
thanks for posting that video. But, it really doesn't help the discussion about flatness or not because the experiment again does not address the impact of refraction in a satisfactory manner. One of the FE persons tries to talk about it ( naming it mirage effect or something like that) and the "science" guy just smiles condescendingly. At the end, everybody, on both side of the debate, felt confirmed in their opinion. Come to think of it, that was utterly foreseeable and one has to blame the "science" guy.

As I said before, line-of-sight experiments like the Bedford level and Lady Bount experiments are only really useful when the atmospheric conditions including temperature and humidity gradients have been measured accurately or when the atmospheric conditions do not come into play in the first place like with LIGO with its vacuum tubes. Also, the post by RonJ about establishing microwave links must be taken into account. We have those links all over the world and they are working and they take earth's curvature into account.

Does anybody know of more things being built which have to take earth's curvature into account ?

Interestingly enough, comments from the FE side have not been definite in this thread although they should be shaking to their core. Guess I am rattling the cage here hoping that something constructive falls out.

[inquisitive]

AllAroundTheWorld (also mentioning RonJ's post)
thanks for posting that video. But, it really doesn't help the discussion about flatness or not because the experiment again does not address the impact of refraction in a satisfactory manner. One of the FE persons tries to talk about it ( naming it mirage effect or something like that) and the "science" guy just smiles condescendingly. At the end, everybody, on both side of the debate, felt confirmed in their opinion. Come to think of it, that was utterly foreseeable and one has to blame the "science" guy.

As I said before, line-of-sight experiments like the Bedford level and Lady Bount experiments are only really useful when the atmospheric conditions including temperature and humidity gradients have been measured accurately or when the atmospheric conditions do not come into play in the first place like with LIGO with its vacuum tubes. Also, the post by RonJ about establishing microwave links must be taken into account. We have those links all over the world and they are working and they take earth's curvature into account.

Does anybody know of more things being built which have to take earth's curvature into account ?

Interestingly enough, comments from the FE side have not been definite in this thread although they should be shaking to their core. Guess I am rattling the cage here hoping that something constructive falls out.

The WGS-84 model is the proven shape.

[somerled]

As King Arthur's horse once said - It's only a model . https://www.esri.com/news/arcuser/0703/geoid1of3.html

[Tom Bishop]

The WGS-84 model is the proven shape.

Your WGS84 geographic syestem is a flat map management system:

http://www.boshamlife.co.uk/wp-content/uploads/2013/11/PrimeMeridian.pdf

  “ By 1911, the Greenwich meridian had been accepted as the prime meridian for the whole world. However, relating the maps of an individual country or region to a standard system of latitude and longitude is not only difficult, it is nearly impossible. The earth is approximately spherical, but maps are flat. They are fitted as closely as possible to the surface of the earth in one region, but when fitting them to a standard system of latitude and longitude, there are bound to be slight discrepancies. The differences between the coordinate systems used by different maps really didn’t matter until recently. When the GPS system was introduced in the 1980s, it was realised that having dozens of ‘local’ systems of latitude and longitude for different countries wasn’t going to work. A single coordinate system had to be devised, which would give the best results for every part of the world. It is known as WGS 84 (World Geodetic System 1984). ”

[inquisitive]

The WGS-84 model is the proven shape.

Your WGS84 geographic syestem is a flat map management system:

http://www.boshamlife.co.uk/wp-content/uploads/2013/11/PrimeMeridian.pdf

  “ By 1911, the Greenwich meridian had been accepted as the prime meridian for the whole world. However, relating the maps of an individual country or region to a standard system of latitude and longitude is not only difficult, it is nearly impossible. The earth is approximately spherical, but maps are flat. They are fitted as closely as possible to the surface of the earth in one region, but when fitting them to a standard system of latitude and longitude, there are bound to be slight discrepancies. The differences between the coordinate systems used by different maps really didn’t matter until recently. When the GPS system was introduced in the 1980s, it was realised that having dozens of ‘local’ systems of latitude and longitude for different countries wasn’t going to work. A single coordinate system had to be devised, which would give the best results for every part of the world. It is known as WGS 84 (World Geodetic System 1984). ”

And:

WGS 84 is an Earth-centered, Earth-fixed terrestrial reference system and geodetic datum. WGS 84 is based on a consistent set of constants and model parameters that describe the Earth's size, shape, and gravity and geomagnetic fields. WGS 84 is the standard U.S. Department of Defense definition of a global reference system for geospatial information and is the reference system for the Global Positioning System (GPS).

https://gisgeography.com/wgs84-world-geodetic-system/

The Global Positioning System uses the World Geodetic System (WGS84) as its reference coordinate system. It comprises of a reference ellipsoid, a standard coordinate system, altitude data and a geoid.

Do you understand how the various GPNSS systems work - GPS, Glonass, Beidou, Galileo? 

Very strange you think WGS84 is a flat map management system. We look forward to your reply.

[ChrisTP]

Tom bishop is just a black belt in cherry picking. Maps are flat, based on a globe map still. There’s no use picking words out of an article that has already stated the earths shape being spherical in an attempt to prove they’re saying the earth is flat... Surely you can see that the overall paragraph Isn’t saying the war is flat, Tom?

[robinofloxley]

Tom bishop is just a black belt in cherry picking. Maps are flat, based on a globe map still. There’s no use picking words out of an article that has already stated the earths shape being spherical in an attempt to prove they’re saying the earth is flat... Surely you can see that the overall paragraph Isn’t saying the war is flat, Tom?

I've read WGS84 related posts from Tom before and really don't understand his reasoning.

If you want to map the Earth using modern technology then you need some sort of mathematical reference shape to base your coordinates on. This needs to be an approximation since it would be impractical to model every single pile of rock or lake bed in a usable mathematical model.

If you start with the assumption the Earth is a globe you could pick a sphere as your reference shape, but an ellipsoid (spheroid) is a better approximation. There is no such thing as a best reference ellipsoid, all of them are compromises, they fit better in some places than others and you choose the reference ellipsoid which best fits your location. In North America you might decide to use NAD83, but in Australia maybe AGD84 (Australian Geodetic Datum 1984).

Of course if you are using GPS/GNSS then you don't have a location as such, it's a global system, so you need a really generic, best fit everywhere ellipsoid and that's what WGS84 gives you. It's a bit like choosing an off the peg suit designed for an average person of a certain size (WGS84) vs an expensive tailor made suit just for you (NAD83 - if you live in North America).

Once you have recorded all your features in your WGS84 or NAD83 (or whatever) coordinate system, you need to display the results. If you happen to have a computer to hand you can do this more or less directly, but if you want a 2-D map, you have to mathematically project your 3-D ellipsoidal model onto a 2-D surface and you have to accept a compromise here. If you want accurate distances for example, then your directions and areas and shapes are compromised. There are many different projections, and you choose one which best fits your need and location, so a GA pilot in North America needs a different projection to an Australian trucker for example.

Every description you'll ever read about WGS84 or NAD83 will talk about a reference ellipsoid, so I just don't get why Tom keeps saying WGS84 is a flat map system.

[Bikini Polaris]

Trying to getting back to the OP:

1 - Refraction does exist for FEs and it may cause the sinking ship effect, see https://wiki.tfes.org/Sinking_Ship_Effect_Caused_by_Refraction

2 - Rowbotham acknowledges the existence of the Sinking Ship effect, but adding that it's unpredictable and it doesn't prove RE.

3 - Rowbotham shows he doesn't understand air refraction and that, by the same token as 2, also the Bedford Level Experiment wouldn't necessarily prove FE.

4 - FET is still unable to provide formulas for that, and maybe it could be a totally unpredictable effect for FEs. Even though I'd be curious to know how in the mentioned link in 1 it's boldly stated:

Firstly, the reader should note that, if that curvature seen the photograph were actually the curvature of the earth, the image would suggest that earth is very small.

without any reference to any formula. The same sentence somehow shows that FET does indeed acknowledge that seeing that the earth is round is really difficult because it's so big.

[somerled]

Wgs84 is a mathematical defined surface that approximates the geoid which itself is a model based on the assumption that earth is some sort of pear shape or oblate spheroid.It's use is to map the earth as some sort of globe . Tom is correct imo .
This globe is then flattened to produce workable maps and to allow gps to function.
The flat earth geocentric model is used in all endeavors that involve navigation or survey . Geodesy is system of measure of earth based on the assumption of it's shape.

The shape of earth is easily measured by survey that doesn't have to include any atmospheric refraction or assumption of shape . Surveyors take no account of ( cannot find ) any curvature over any area of 100sq. miles - because we live on a plane .

Refractive distortion provides a smoke screen for the non existence of the globe . That is why science uses a coefficient of atmospheric refraction based on figures that cannot be accurate.

[inquisitive]

Wgs84 is a mathematical defined surface that approximates the geoid which itself is a model based on the assumption that earth is some sort of pear shape or oblate spheroid.It's use is to map the earth as some sort of globe . Tom is correct imo .
This globe is then flattened to produce workable maps and to allow gps to function.
The flat earth geocentric model is used in all endeavors that involve navigation or survey . Geodesy is system of measure of earth based on the assumption of it's shape.

The shape of earth is easily measured by survey that doesn't have to include any atmospheric refraction or assumption of shape . Surveyors take no account of ( cannot find ) any curvature over any area of 100sq. miles - because we live on a plane .

Refractive distortion provides a smoke screen for the non existence of the globe . That is why science uses a coefficient of atmospheric refraction based on figures that cannot be accurate.

There is no assumption of shape, we accurately know it. A sphere.

[robinofloxley]

Wgs84 is a mathematical defined surface that approximates the geoid which itself is a model based on the assumption that earth is some sort of pear shape or oblate spheroid.It's use is to map the earth as some sort of globe . Tom is correct imo .

Tom says WGS84 is "a flat map management system". You say "it's use is to map the earth as some sort of globe". These two statements sound to me like more or less opposite views. Yet you say Tom is right? I'm very confused.

This globe is then flattened to produce workable maps and to allow gps to function.
The flat earth geocentric model is used in all endeavors that involve navigation or survey . Geodesy is system of measure of earth based on the assumption of it's shape.

Surely geodetic surveying does not use a flat earth model and heliocentrism is irrelevant to any kind of map or survey. Navigation involving ocean voyages and long distance flights are both based on following great circle routes which only make sense if you assume you are on a globe. If all navigation is based on a flat earth, why are the routes curved?

The shape of earth is easily measured by survey that doesn't have to include any atmospheric refraction or assumption of shape . Surveyors take no account of ( cannot find ) any curvature over any area of 100sq. miles - because we live on a plane .

Refractive distortion provides a smoke screen for the non existence of the globe . That is why science uses a coefficient of atmospheric refraction based on figures that cannot be accurate.