[AATW]

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

Incorrect

https://www.ligo.caltech.edu/page/facts

LIGO’s arms are long enough that the curvature of the Earth was a factor in their construction. Over the 4 km length of each arm, the Earth curves away by nearly a meter! Precision concrete pouring of the path upon which the beam-tube is installed was required to counteract this curvature.

[Tom Bishop]

A further quote from the LIGO curvature compensation:

https://books.google.com/books?id=6mMlDwAAQBAJ&lpg=PA168&ots=fhaBCNVwoX&dq=ligo%20curvature&pg=PA168#v=onepage&q=ligo%20curvature&f=false

"The ends of each arm are actually situated several feet higher off the
ground than their starting point at the center station. That’s to compensate
for the Earth’s curvature."

It says that the ends of each arms are situated several feet off the ground than the center station to "account for the curvature of the earth."

Would it work if the earth was flat? Yes, it is possible to point a laser slightly downwards or upwards on a Flat Earth.

LIGO diagram:



They had to take steps to aim and align the components at some point. To hit the opposite marker they would have aimed the laser beam at the destination, or would have aligned the intermediate components so that the laser beam would hit the destination. The set up does not appear to be a physical obstacle on a FE.

[AATW]

That’s the second time recently you’ve posted a quote which says the earth is a globe. Have you finally seen the light?

I was simply responding to the point that they don’t ever need to compensate for the earth’s curve in engineering projects. They sometimes do in larger scale ones, thanks for backing up my point.

Were the earth flat they wouldn’t need to. Yes, they could have made a sloped tunnel and pointed the laser slightly upwards, but why would they?

[Zack Bimmel]

Comment 1 :
The pipes of the LIGO experiments are not only supported at either end, some 4 km apart, but at many intermediary support piers. Compensating for earth's curvature means that the height of theses piers would have to change quadratically with distance if measured with respect to the water level inside a 4 km long water trough running parallel to LIGO pipes. FE would result in a linear dependency.

Comment 2 :
Some of the more sophisticated GPS system measure to within a few centimeters the altitude with respect to an ellipsoid model of the earth. The value for the altitude can be positive or negative depending on whether the elevation you wish to measure is above or below the ellipsoid. Again, the elevation of various points along the length of the pipe should change quadratically. (P.S. Of course one could base a GPS system by approximating earth by a sphere. The principle is the same)

Comment 3 :
All GPS measurements ultimately lead back to having (preferably) four satellites above the horizon at the moment of measurement. All GPS related satellites orbit the round earth at an altitude of about 20,000 km (12,427 miles) and complete two full orbits every day.

Comment 4 :
In addition to millions of earthlings, NASA, NOAA and the entire military complex of NATO uses GPS rather successfully. Russia has its own GPS version (Glonass) and so do China (Beidou ?) and Europe (Galileo). All these systems are satellite based.
 

[somerled]

1. LEGO experiment link states vaguely that several feet of curvature is accounted for . Which model , pearshape or squashed ball or imaginary R= 6370km is used in this curvature correction?
Could just be allowance for topography .

2. Yes , as stated before WSG is a mathematical ellipsoid surface used to model a globe ,with all vertices converging at earth's supposed centre of gravity . Where is that in whichever  ellipsoid model used?

3. High altitude craft , balloon satellites , signals reflected of the dome, triangulation masts.

4. It's easy to brainwash young people . That's what schooling is about . Critical thinking is not part of the curriculum hence people cannot question what they are told they know .

i

[inquisitive]

1. LEGO experiment link states vaguely that several feet of curvature is accounted for . Which model , pearshape or squashed ball or imaginary R= 6370km is used in this curvature correction?
Could just be allowance for topography .

2. Yes , as stated before WSG is a mathematical ellipsoid surface used to model a globe ,with all vertices converging at earth's supposed centre of gravity . Where is that in whichever  ellipsoid model used?

3. High altitude craft , balloon satellites , signals reflected of the dome, triangulation masts.

4. It's easy to brainwash young people . That's what schooling is about . Critical thinking is not part of the curriculum hence people cannot question what they are told they know .

i

3. Not according to the documentation and information provided by receivers.  Do China and Russia have balloons over the USA?

4. It's not just about young people, engineers and scientists understand, design, build and operate GPNSS systems in many countries.

Conclusion - GPNSS operates exactly as it says on the tin.

[somerled]

Then which globe model does it say on the tin?

[inquisitive]

Then which globe model does it say on the tin?

WGS-84

[somerled]

But WGS-84 is a reference co-ordinate system system , not a globe models. Clearly explained here.
https://gisgeography.com/wgs84-world-geodetic-system/

OP's original post shows how surveyors who believe the earth is a sphere ( he kindly quotes this in his 2nd post) use a set of equations including a constant of refraction k calculated with a value of R = 6370km .  This is valid is on a perfect sphere only . We know this is not true whichever model we choose to believe .

WGS-84 is an ellipsoid reference co-ordinate system applied to one of many geoids which in the words of that site leads to Geodesists to " believe the error is less than 2cm which is better than NAD83."

The use of that word " believe " leads me to conclude that we are encouraged to have faith in whatever they tell us. Science now has the appearance of religion in which no one is allowed to question the high priests and the faithful have no need for truth .

[AATW]

1. LEGO experiment link states vaguely that several feet of curvature is accounted for . Which model , pearshape or squashed ball or imaginary R= 6370km is used in this curvature correction? Could just be allowance for topography .

Sigh.

And this is the problem with debating anything with someone like you. You said

Surveyors take no account of ( cannot find ) any curvature over any area of 100sq. miles - because we live on a plane

You provided no basis for that claim or no supporting evidence, you just asserted it.
So I found a link about a large scale project which I imagined would probably have had to take account of the earth's curve and, sure enough, found some information on their website where they said they did have to do that.
This is the people who build the sodding thing saying they did indeed have to take the earth's curve into account because of the scale of it.

This is the point where you're supposed to concede the point and see the error of your ways but instead you're just saying "well, maybe it's this, maybe it's that". Again, with no basis or supporting evidence. It's easy to prove yourself right if you ignore or dismiss all evidence showing you to be wrong...

[Zack Bimmel]

But WGS-84 is a reference co-ordinate system system , not a globe models. Clearly explained here.
https://gisgeography.com/wgs84-world-geodetic-system/

OP's original post shows how surveyors who believe the earth is a sphere ( he kindly quotes this in his 2nd post) use a set of equations including a constant of refraction k calculated with a value of R = 6370km .  This is valid is on a perfect sphere only . We know this is not true whichever model we choose to believe .

WGS-84 is an ellipsoid reference co-ordinate system applied to one of many geoids which in the words of that site leads to Geodesists to " believe the error is less than 2cm which is better than NAD83."

The use of that word " believe " leads me to conclude that we are encouraged to have faith in whatever they tell us. Science now has the appearance of religion in which no one is allowed to question the high priests and the faithful have no need for truth .

Dear somerled,

I find it amazing that you still think about R=6370km used by surveyors when displaying and communicating with each about refraction of light in the presence of thermal and humidity gradients. For a last time : they could have used as well the distance between Glasgow and London as a reference value or any other distance. The choice of a reference variable does NOT ever influence the calculations of the amount of refraction when expressed in terms of lengths and angles .

I realize that it is hard for you to accept that the line-of-sight experiments conducted in the past without taking thermal and humidity ' gradients into account are inconclusive. Therefore, true to the method Zeteticism, we have to strive for more up-to-date experiments, like a laser in a vaccum tube.

And for the record : I did not state that surveyors believe that the earth is a sphere. I used the term "round" which can be a sphere or an ellipsoid or a pear-shaped entity. But, as far as earth is concerned the naked eye is not good enough to discern the difference. The model ellipsoid of GPS is a pretty good approximation to earth with a semi-major and semi-minor axis of 6378137 meter and 6356752 meter, respectively. Choosing 6370 km as a reference length does seem to me a reasonable choice.

An ellipsoid, like the sphere, has no vertices. But you are correct in that the ellipsoid we are talking about is centered on the earth's center of gravity. You might want to study this web site https://www.state.nj.us/transportation/eng/documents/survey/Chapter4.shtm . I also encourage you to have somebody who has a GPS receiver with the required accuracy for vertical distance, verify the Bedford Level Experiment. Wouldn't it be worthwhile to find the truth ?

[somerled]

1. LEGO experiment link states vaguely that several feet of curvature is accounted for . Which model , pearshape or squashed ball or imaginary R= 6370km is used in this curvature correction? Could just be allowance for topography .

Sigh.

And this is the problem with debating anything with someone like you. You said

Surveyors take no account of ( cannot find ) any curvature over any area of 100sq. miles - because we live on a plane

You provided no basis for that claim or no supporting evidence, you just asserted it.
So I found a link about a large scale project which I imagined would probably have had to take account of the earth's curve and, sure enough, found some information on their website where they said they did have to do that.
This is the people who build the sodding thing saying they did indeed have to take the earth's curve into account because of the scale of it.

This is the point where you're supposed to concede the point and see the error of your ways but instead you're just saying "well, maybe it's this, maybe it's that". Again, with no basis or supporting evidence. It's easy to prove yourself right if you ignore or dismiss all evidence showing you to be wrong...

You could have wiki'd that - https://en.wikipedia.org/wiki/Surveying

Go down to the part about " plane and geodetic surveying " . 100 square miles .

Then you can check out some survey books  - the older real explanatory types are better . You will find  that plane survey is used in areas up to 100 square miles because no curvature is found that does not fall within error limits of precision survey equipment . That's alot of missing curvature over a circular area of 100 square miles - 80 feet or so .

So how much curvature over a few square miles did bob the ligo builder account for? , in exact terms . Vague statements mean nothing .

Zack - all the scientists have to do is measure , as exact as possible, the amount of curvature over the distance they use for their experiment . Measuring gradients of pressure , heat etc then applying imaginary values into their equations turns everything into mere ramblings.

[AATW]

You could have wiki'd that - https://en.wikipedia.org/wiki/Surveying

Go down to the part about " plane and geodetic surveying " . 100 square miles .

OK. It says this:

In geodetic surveying the curvature of the earth is taken into account while calculating reduced levels, angles, bearings and distances. This type of surveying is usually employed for large survey works. Survey works up to 100 square miles (260 square kilometers ) are treated as plane and beyond that are treated as geodetic

Right. So what this says that if the area being surveyed is less than 100 square miles - that's 10x10, not 100x100 - they treat the area as a plane. Not because it is a plane, simply because over this distance the error is so small that it makes no difference for their purposes. 10 miles is 0.04% of the earth's circumference. The curve of 0.04% of a circle is negligible. Have a go at this:

https://www.mathsisfun.com/geometry/polygons-interactive.html

You'll note that if you ramp up to a 20 sided polygon you're already getting to the point where it's starting to look a bit like a circle. Were the earth a regular polygon of 10 mile segments it would be a 2490 sided polygon. The angle between each side would be 0.145 degrees. It would be in all practical senses a sphere

Over lager distances it does start to make a difference so they use geodetic surveying. If the earth is flat then why is geodetic surveying a thing?

So how much curvature over a few square miles did bob the ligo builder account for? , in exact terms . Vague statements mean nothing.

1 meter over a length of 4km. Because the tunnel has to be straight but the earth curves. Again, were the earth flat then no accounting for this would have to be made.

TL;DR - it depends what you're doing. If you're making maps or whatever then over short spans you can think of the earth as flat, it doesn't make enough difference to cause errors. If you're drilling narrow tunnels and you need clear line of sight from one end to the other then you need to take the earth's curve into account.

It's weird that you provided the link that explains this and are pretending it says something else.

[somerled]

Only you mention an area of 10,000 square miles  - I take it you are not familiar with mathematical terms describing areas .

You can use simple maths to work out the diameter of a circle of area 100 square miles ( not 100 miles square - they are different ) . Then you can use any curvature calculator to see that's about 80 feet of curvature that can be ignored across that diameter of 11 miles .Such a small amount can be ignored in survey. Fantastic .

Of course the 100 square mile limit is arbitrary as far as I can find out . A vague limit matched in vagueness by the LIGO "allowance" for curvature , 1m or several feet . In such a scientific undertaking I think everything deserves measurement to as exact a degree as possible .

There again since earth is flat that is possible .

[AATW]

Only you mention an area of 10,000 square miles  - I take it you are not familiar with mathematical terms describing areas.

I was making sure that you are, I was just making explicit that 100 square miles is an area of 10 miles x 10 miles.
I explicitly said it was NOT 100x100 just in case you had confused "square miles" with "miles square".

You can use simple maths to work out the diameter of a circle of area 100 square miles ( not 100 miles square - they are different ) . Then you can use any curvature calculator to see that's about 80 feet of curvature that can be ignored across that diameter of 11 miles .Such a small amount can be ignored in survey. Fantastic.

Well, it depends what you're doing. If you're making a map then yes, the error is negligible and you can treat the earth as a plane on that scale.
For some engineering projects like LIGO then even over smaller distances the earth's curve has to be accounted for.
If the earth were flat then it wouldn't ever have to be considered and geodetic surveying wouldn't exist as it wouldn't need to.

[somerled]

Some good articles about the "true shape" of the earth and the problems of modelling this .

https://www.quora.com/What-is-the-exact-shape-of-the-earth?redirected_qid=26177289&share=1
https://zeilon.squarespace.com/well-grounded-blog/2016/6/28/the-shape-of-the-earth
https://techinabottle.wordpress.com/2017/01/23/what-is-the-real-shape-of-earth/

Plenty of PhD in there - that's Phoctor of Dilosophy to you and I .

Begs the question of which model did bob the builder make use of use when allowing for curvature in LIGO. Interesting . Will we ever know?

[stack]

Begs the question of which model did bob the builder make use of use when allowing for curvature in LIGO. Interesting . Will we ever know?

Here’s probably everything you need to know regarding the engineering, methodology, and ellipsoid reference points used in constructing LIGO:

Precision alignment of the LIGO 4 km arms using dual-frequency differential GPS

"The curvature of the Earth will cause the Earth's surface to deviate from the straight line propagated by light in vacuum by 1.25 meters over a 4 km path if the line starts out level with the surface. The alignment was, therefore, not the same as that for a level highway or pipeline.”

“The fundamental coordinate system for the alignment was the Earth ellipsoidal model WGS-84"

https://dcc.ligo.org/public/0072/P000006/000/P000006-A.pdf

[somerled]

Thanks for that link Stack . A lot to get through but it basically says the tubes are perfectly straight and level. Stand for correction though not read it all .

So far.
Uses GPS based ellipsoid model WSG-84 coordinate system - converts to plane survey along with plumb line and bubble level equipment , nice to see that in there. Computer software is always susceptible to error .

The 1.25 m allowance for curvature is based on the ellipsoid model WSG-84 coordinate system - which does not represent the true shape of earth as shown in previous links .

Will give a proper opinion when I've studied it - which may be some time ha .

[stack]

Thanks for that link Stack . A lot to get through but it basically says the tubes are perfectly straight and level. Stand for correction though not read it all .

So far.
Uses GPS based ellipsoid model WSG-84 coordinate system - converts to plane survey along with plumb line and bubble level equipment , nice to see that in there. Computer software is always susceptible to error .

The 1.25 m allowance for curvature is based on the ellipsoid model WSG-84 coordinate system - which does not represent the true shape of earth as shown in previous links .

Will give a proper opinion when I've studied it - which may be some time ha .

I'm not sure what you mean by, "...WSG-84 coordinate system - which does not represent the true shape of earth as shown in previous links." The point is, you were wondering what reference model was used by the LIGO engineers to account for the curvature of the earth. As stated in the paper, they relied on the WSG-84 coordinate system which is a Spherical/Global/Ellipsoidal model, hence the accounting for the curvature of the earth.

If you claim they shouldn't have accounted for the curve of the earth and that they were essentially wasting their time in doing so, well, then that's between you and the LIGO engineers. But fact of the matter, they chose to use a spherical earth model to measure and construct the installations. That alone certainly doesn't prove the 'true shape of the earth', but I'm pretty sure their intent wasn't to do so in the first place anyway.

[somerled]

Did LIGO account for curvature as expected from the pear shaped earth or the oblate spheroid sphere ? That is what I am trying to find out . Which shape did Bob the builder account for ? Apparently neither since he used a ellipsoid model constructed on a mythical centre of the earth. 
 
We know that WSG-84 is nothing but a mathematical construct in which earths centre of gravity is the starting reference point for the coordinate system .


I mean read this quote from the conclusion on this link https://gisgeography.com/wgs84-world-geodetic-system/
 
It states "Never before have we’ve been able to estimate the ellipsoid with such precision." Ho ho - estimate with precision .

Where is that centre of gravity on the pear shape /oblate model . Read the links I posted and you will see that is a big problem . There is no centre of gravity .

LIGO constructed its arms plane and level according to normal plane surveying techniques . That's my view .