Laser curvature test on lake Balaton

[Strange]

 

I saw the "trembling laser" video. That's a bizarre effect indeed. It looks like it's mainly going left to right only, but the light that is hitting the board is "dancing" in on itself. There is a big bright area (around 30cm wide I'd say), but there is also a huge area hitting the board that is even bigger than the board itself. Very intriguing.

 

Did someone say that this is one of those laser projecters used for creating vector images through a series of mirrors? Could it be that it is always being reflected and that one of the mirrors is wobbling/vibrating?

[Sandor Szekely]

 

I saw the "trembling laser" video. That's a bizarre effect indeed. It looks like it's mainly going left to right only, but the light that is hitting the board is "dancing" in on itself. There is a big bright area (around 30cm wide I'd say), but there is also a huge area hitting the board that is even bigger than the board itself. Very intriguing. Do we have any optics nerd here in the forum?

 

Regarding the beam distortions, those are a huge risk to your data set.

 

If something like that happened during the night, there is no way to know what may have happened during the day. With this new information, I would say that you need to measure the beam spot every 100m or so. 500m may not be enough. It's too much refraction, reflection or whatever optic distortion is going on there, to guarantee the accuracy of the data.

 

Different doubt though: you mentioned reflection, but that would mean that the laser hit the water at one point, is that correct? If that's the case, the laser was either pointing downwards or the crazy refraction effects forced it downwards.

 

Are you taking notes of all Mordred's, Stu's, mine and others' suggestions? That's quite a lot

MrMaker,

as I pointed out that this 3rd measurement at dawn (4AM to 6AM app.) was a very unusual. Later we foulnd out at modelling that our laer hit the water around 1500 meters from the shore. So this is not refraction, but reflexion!

(I named the folder reflexion on the google drive not to make confusion with the other ones)

 

we went off the corse of the laser path and missed the point where it was hitting the water, as we got back on track the beam was very low. In a short distance it was rising upwards and passed above our heads. From the Canon camera it looked like a huge refraction, but from the laser position it was fine.

So the horizontal trembling laser was reflected on water surface and therefore did not have vertica movements (significant).

 

I absolutely agree that beam distorsion is the key of the measurement precision.

 

Scienceforum is my notepad I will discuss the subjects mentioned here from the forum directly with the Hungarian scientist too. Thank you for the very usefull and extensive information to all.

 

 

[studiot]

 

Sandor Szekely post#19

This was not the case here, the FE flat water model just fits perfectly with the 0.005 degree slope correction applied to the laser leveling. We had the laser beam height just as expected on the truly level water surface.

This is exactly the same outcome as the airborn LIDAR experiment.

 

The hypothesis of GE curved water surface model is 465 meters over the 77kms distance as we agree.

The measurements were taken upto 6kms distance and we found no curvature drop yet.

The LIDAR experiment had the same outcome: "the two data systems confirmed that standing water has a truly level surface" (page 8/15 in LIDAR pdf)

 

I think these extracts show the confusion between a flat surface and a level surface.

 

A level surface is most definitely curved, a flat surface is essentially planar.

 

So how can a flat water model be consistent with laser or any other leveling?

[snaphat]

 

I think these extracts show the confusion between a flat surface and a level surface.

 

A level surface is most definitely curved, a flat surface is essentially planar.

 

So how can a flat water model be consistent with laser or any other leveling?

 

It was noted by the author of the 2013 LIDAR experiment that their results are not consistent with a planar surface so I do not understand Sandor's statement either.

[DarkStar66]

I think these extracts show the confusion between a flat surface and a level surface.

 

It also makes it sound like they tested the whole 77km in their video but didn't, not even close. Yet still proclaimed it as "100% proof".

 

You guys are all talking about advanced calculations and measurements but have you watched their video to see just how badly this was done?

 

These guys believe that just because a camera on the boat can merely see the laser on the dock as a bright spot that this constitutes a valid measurement of the center of the beam height.

 

I've posted clear evidence that the beam spread was out of control but you can see in his responses that Sandor doesn't even understand that anything was wrong or take this seriously.

 

Please consider beginning by trying to convince Sandor that just because a camera on the boat can SEE the laser looking back at the dock that this doesn't constitute a valid measurement of the beam center.

 

I would think such fundamentals could be easily agreed upon.

 

Direct simple question: Sandor - based on what has been discussed about this data do you still consider your data point measurements to be valid and mostly reliable and accurate?

[Klaynos]

These guys believe that just because a camera on the boat can merely see the laser on the dock as a bright spot that this constitutes a valid measurement of the center of the beam height.

 

I've not watched the video. I did fear this might be the case. You can get "bright" spots off of thr beam path, and you'll be killed by any beam divergence or laser wobble. I don't really think this experiment is within the reach of a hobbyist. Although it looks simple as soon as you start actually thinking about it there are so many subtleties that will make your results meaningless.

 

That's a terrible way to measure. You could do something similar with a camera sensor but where you measure the intensity from each pixel. But you'd need a large area CMOS or ccd and some clever way of removing ambient light.

[Mordred]

I got about as far as the first ten minutes. Then I recalled a lesson. Systematic errors get increasingly worse at later measurement points and increased distance in this case.

After seeing the uncertainties in the first two points that was enough for me.

Hopefully the next attempt takes and applies the advice given.

 

Its a common mistake to overly trust a laser. One may be aware of atmospheric effects but not aware of how much a tiny variation increases over distance in angles. As well as other optical effects.

(simply calculate how much a 1% change in angle will change the height measured over 100 metres let alone 1 km.)

 

Most surveyer handbooks I've looked over including their equipment manuals recommend breaking down your total distance to increments of less than 100 metres. (coincidentally refraction is the primary reason). At least on the ones including level correction.

 

That a lot of measurement points and time over a 7 km lake let alone a 10 km survey.

Edited September 16, 2016 by Mordred

[imatfaal]

!

Moderator Note

 

I have hidden two posts concerning Member's affiliations with academic institutions and other matters. This is not the place to be discussing the person - there is a good thread going on the science and methodology; can we please stick to that? Could we also bear in mind a few logical fallacies;

 

- A poster being part of or not part of an academic body should not influence our response to their argument.

- The fact that a poster is wrong on an unrelated matter - or in a different place - does not affect the validity of this argument here. It may influence our readiness to give credence or point us in a particular direction to find factual/methodlogical flaws - but it does not disprove or void a contention.

 

Please let us avoid the easy distractions and continue this interesting discussion. Please do not respond to this moderation except through the reporting system

 

 

[imatfaal]

!

Moderator Note

 

Boxer

 

Which bit of "Please do not respond to this moderation except through the reporting system" was unclear? I have hidden your response.

 

Please do not respond to this moderation except through the reporting system.

 

Will everyone stick to the science please.

 

[MrMaker]

It also makes it sound like they tested the whole 77km in their video but didn't, not even close. Yet still proclaimed it as "100% proof".

 

You guys are all talking about advanced calculations and measurements but have you watched their video to see just how badly this was done?

 

These guys believe that just because a camera on the boat can merely see the laser on the dock as a bright spot that this constitutes a valid measurement of the center of the beam height.

 

 

Hi, Darkstar.

 

As I see it, the experiment was a POC and what Sandor is trying to do here, coming to this forum, is getting ideas and suggestions on how to get it right the next time.

 

If the intentions are not these, then we are just wasting our time here (oh well, isn't that what an internet forum is all about anyway? )

 

If he is currently presenting the POC as "100% proof" of anything, he is only hurting his credibility, causing the next experiment to be taken less seriously, and the uphill battle to be harder.

 

I see you bring a weight and lots of emotions from the 1000 posts in the other forum, but this forum is trying to be as fair as possible, given the information posted in this forum only. By saying that people here cannot see what are his beliefs, cannot see that the experiment was not accurate, cannot see that the data interpretation and presentation was biased, you are also saying that people here are clueless, what is kind of rude to be honest.

 

People here are showing Sandor that the amount of calculations and advanced math and physics needed to get it right is much more than what was used in the POC, and this point is well understood, at least it seems so.

 

You say: "Please consider beginning by trying to convince Sandor that just because a camera on the boat can SEE the laser looking back at the dock that this doesn't constitute a valid measurement of the beam center.". In this forum Sandor agreed a couple of times that the board needs to be improved for a second experiment, what seems to be an agreement that he understands that the estimation with the camera only is not enough.

 

The possible misrepresentation of the LIDAR paper, the title of the video, their belief, etc, I believe are not part of the discussion.

 

Worst case scenario, if people think he is not being honest, they will stop answering to the thread and it will be forgotten, right?

[Mordred]

excellent post MrMaker +1

[storrence]

 

So, it's like non-uniform-micro-refraction-artifacts that would cause the beam to change chaotically, making it impossible to predict the real direction of the beam?

 

I think this concept is being used to try to explain why the beam is apparently bending upwards.

 

It's interesting and would be a paper in itself. They should also explore that in the next experiment.

Another way to describe it but the beam was above this supposed zone. This zone would be in the 50cm range above the water which is why the bottom of the boat seems to disappear. That is why we were looking for a term to describe what we thought was going on in that area which was a chaotic density zone that would cause chaotic refraction. NUDTZ was just easier to say than NUMRA

Edited September 16, 2016 by storrence

[Sandor Szekely]

 

Hi, Darkstar.

 

As I see it, the experiment was a POC and what Sandor is trying to do here, coming to this forum, is getting ideas and suggestions on how to get it right the next time.

 

If the intentions are not these, then we are just wasting our time here (oh well, isn't that what an internet forum is all about anyway? )

 

If he is currently presenting the POC as "100% proof" of anything, he is only hurting his credibility, causing the next experiment to be taken less seriously, and the uphill battle to be harder.

 

I see you bring a weight and lots of emotions from the 1000 posts in the other forum, but this forum is trying to be as fair as possible, given the information posted in this forum only. By saying that people here cannot see what are his beliefs, cannot see that the experiment was not accurate, cannot see that the data interpretation and presentation was biased, you are also saying that people here are clueless, what is kind of rude to be honest.

 

People here are showing Sandor that the amount of calculations and advanced math and physics needed to get it right is much more than what was used in the POC, and this point is well understood, at least it seems so.

 

You say: "Please consider beginning by trying to convince Sandor that just because a camera on the boat can SEE the laser looking back at the dock that this doesn't constitute a valid measurement of the beam center.". In this forum Sandor agreed a couple of times that the board needs to be improved for a second experiment, what seems to be an agreement that he understands that the estimation with the camera only is not enough.

 

The possible misrepresentation of the LIDAR paper, the title of the video, their belief, etc, I believe are not part of the discussion.

 

Worst case scenario, if people think he is not being honest, they will stop answering to the thread and it will be forgotten, right?

Thank You MrMarker very well summarized.

 

"As I see it, the experiment was a POC and what Sandor is trying to do here, coming to this forum, is getting ideas and suggestions on how to get it right the next time."

Exactly I am here for this reason, and I am very pleased with the REAL scientific approach from most of You here!

 

I am reading through the comments (taking the notes ) and as well organizing the real scientific team and the new measurement.

Excuse me that I comment less now - I am listening carefully to the comments and I "try to catch up" with the terms and the explanations. (my profession is a cameraman)

 

Klaynos:

"I've not watched the video. I did fear this might be the case. You can get "bright" spots off of thr beam path, and you'll be killed by any beam divergence or laser wobble. I don't really think this experiment is within the reach of a hobbyist. Although it looks simple as soon as you start actually thinking about it there are so many subtleties that will make your results meaningless. "

 

Thanks for sharing your thoughts on refraction, I think this is the most important "uncertainity" factor of the experiment.

 

 

 

 

[Mordred]

Thanks for sharing your thoughts on refraction, I think this is the most important "uncertainity" factor of the experiment.

 

1) methodology

2) human error

3) instrument error

4) refraction

 

in order. Every experiment has the same sequence. The corrective measures not with standing

Edited September 16, 2016 by Mordred

[Sandor Szekely]

1) methodology

2) human error

3) instrument error

4) refraction

 

in order. Every experiment has the same sequence. The corrective measures not with standing

right

 

1. on the methodology I think it would be good to combine different techniques. I noted suggestion on various leveling equippments already, please advise how these different techniques can be used simultainosly to improve accuracy and exclude systematic errors from the measurement. Like how could a theodolite (possibly more in different positions) help to measure the laser beam height (maybe divergence too)? In this case of multiple theodolite laser height measurement we could make the measurements at the very same time (not like the boat 2.5 hours).

Please share suggestion on this or any other possible method.

 

What is your opinion on measureing on the frozen lake surface? (theodolites can be placed on the surface. refraction at night time or day time? is any posiible duct?)

 

2. human error will be best reduced with the help from professional geodezysts

 

3. instrument error may be reduced using multiple techniques?

 

 

 

[Sensei]

We will continue to make more measurments (improved with ideas from here as well) on the lake Balaton and over land also.

 

Then I hope so you will implement my ideas expressed in post #86

http://www.scienceforums.net/topic/98386-laser-curvature-test-on-lake-balaton/?p=943359

even though you didn't comment this post.

[MrMaker]

Another way to describe it but the beam was above this supposed zone. This zone would be in the 50cm range above the water which is why the bottom of the boat seems to disappear. That is why we were looking for a term to describe what we thought was going on in that area which was a chaotic density zone that would cause chaotic refraction. NUDTZ was just easier to say than NUMRA

 

How did you estimate this non-uniform area to be in the 50cm range? If this is only an idea to explain the "bottom of the boat seems to disappear" part, you need additional data to analyse that. The common conception would be that the bottom of the boat disappears due to the water curvature, and not refraction. I don't think that what Sandor wants to measure is the bottom of the boat, though, as that would lead to a rather different experiment, tools and planning. I would leave this "bottom of the boat" analysis to a different moment.

 

Additionally to the NUDTZ existance, and existing only below 50cm hypothesis, there is clearly something other than your NUDTZ taking place at 1.35m+. The trembling laser, the laser going down and reflecting back up, etc, needs to be explained and measured.

 

From everything that I read I though this NUDTZ idea was to explain all the erratic laser behavior during the whole experiment.

 

Anyway, add to my list of suggestion to forget about NUDTZ and think only about getting all the data the correct way. As someone mentioned here, try to formulate hypothesis after you get the data correct, not before.

 

I am reading through the comments (taking the notes ) and as well organizing the real scientific team and the new measurement.

Excuse me that I comment less now - I am listening carefully to the comments and I "try to catch up" with the terms and the explanations. (my profession is a cameraman)

 

 

 

That's great.

 

Don't forget any suggestions, I'd say.

 

If you are willing to share the next experiment setup, before or after you discuss with the university specialists, I think a lot of people will be happy to keep debating it.

 

I don't know about the others, but the amount of challenges (math, physics and resources) to get this "simple" experiment up and running are huge, and it's very interesting to debate what's the best way to do all of that.

[Sandor Szekely]

 

How did you estimate this non-uniform area to be in the 50cm range? If this is only an idea to explain the "bottom of the boat seems to disappear" part, you need additional data to analyse that. The common conception would be that the bottom of the boat disappears due to the water curvature, and not refraction. I don't think that what Sandor wants to measure is the bottom of the boat, though, as that would lead to a rather different experiment, tools and planning. I would leave this "bottom of the boat" analysis to a different moment.

 

Additionally to the NUDTZ existance, and existing only below 50cm hypothesis, there is clearly something other than your NUDTZ taking place at 1.35m+. The trembling laser, the laser going down and reflecting back up, etc, needs to be explained and measured.

 

From everything that I read I though this NUDTZ idea was to explain all the erratic laser behavior during the whole experiment.

 

Anyway, add to my list of suggestion to forget about NUDTZ and think only about getting all the data the correct way. As someone mentioned here, try to formulate hypothesis after you get the data correct, not before.

 

 

That's great.

 

Don't forget any suggestions, I'd say.

 

If you are willing to share the next experiment setup, before or after you discuss with the university specialists, I think a lot of people will be happy to keep debating it.

 

I don't know about the others, but the amount of challenges (math, physics and resources) to get this "simple" experiment up and running are huge, and it's very interesting to debate what's the best way to do all of that.

I will share - and cooperate - with scienceforum on the experiment setup and methodology as I think this is in the interest of my university partner as well.

We (Zack, Steve, me) would like to have an open source measurement and a cooperation in the evaluation too - that is the reason I have the post here on scienceforum (ONLY)

 

and let me share with you a PBS production : Genius with Stephen Hawking. The very first part of the film starts with a laser measurement and a boat. There is absolutely no scientific approach in this film - just a mainstream TV production - as they have not given any parameters or real measurements. You might like to check this film to understand better our motives to make a correct scientific approach to the question of curvature on water surface.

 

https://www.youtube.com/watch?v=oNZOh4SUWUc

[storrence]

 

How did you estimate this non-uniform area to be in the 50cm range? If this is only an idea to explain the "bottom of the boat seems to disappear" part, you need additional data to analyse that. The common conception would be that the bottom of the boat disappears due to the water curvature, and not refraction. I don't think that what Sandor wants to measure is the bottom of the boat, though, as that would lead to a rather different experiment, tools and planning. I would leave this "bottom of the boat" analysis to a different moment.

 

Additionally to the NUDTZ existance, and existing only below 50cm hypothesis, there is clearly something other than your NUDTZ taking place at 1.35m+. The trembling laser, the laser going down and reflecting back up, etc, needs to be explained and measured.

 

From everything that I read I though this NUDTZ idea was to explain all the erratic laser behavior during the whole experiment.

 

Anyway, add to my list of suggestion to forget about NUDTZ and think only about getting all the data the correct way. As someone mentioned here, try to formulate hypothesis after you get the data correct, not before.

 

 

That's great.

 

Don't forget any suggestions, I'd say.

 

If you are willing to share the next experiment setup, before or after you discuss with the university specialists, I think a lot of people will be happy to keep debating it.

 

I don't know about the others, but the amount of challenges (math, physics and resources) to get this "simple" experiment up and running are huge, and it's very interesting to debate what's the best way to do all of that.

It was just an estimate to explain the area closest to the water surface that I believe contains multiple refractions due to chaotic density variations . I think the effect doesn't get as high as 1.35m or at least is diminished. I'm not aware of another term describing it. I agree it's not very important to the test since it was describing the area obscuring the bottom of the boat and the laser should be higher than that.

[Mordred]

Most likely the evaperation duct. The average height for the temperature range was roughly 2 metres. Assuming I ran the calcs correct. The effect is that the light path curvature would be less than the curvature of the Earth. This causes signal entrapment and skipping.

 

Either way it indicated conditions not favorable to the test.

 

On the interest of the next test. It is difficult to guage how much those involved learned. Both from previous test and discussion.

 

I recommend we look first at methodology. Please describe how you plan to undertake the next test. Break it down to each stage.

 

From there we can look to improve this stage first. Then look at addressing human error corrections etc. As Studiot mentioned include your control points.

Edited September 17, 2016 by Mordred

[Boxer]

I will share - and cooperate - with scienceforum on the experiment setup and methodology as I think this is in the interest of my university partner as well.

We (Zack, Steve, me) would like to have an open source measurement and a cooperation in the evaluation too - that is the reason I have the post here on scienceforum (ONLY)

 

and let me share with you a PBS production : Genius with Stephen Hawking. The very first part of the film starts with a laser measurement and a boat. There is absolutely no scientific approach in this film - just a mainstream TV production - as they have not given any parameters or real measurements. You might like to check this film to understand better our motives to make a correct scientific approach to the question of curvature on water surface.

 

https://www.youtube.com/watch?v=oNZOh4SUWUc

Your outlandish claims about "scientific teams" just hurting the discussion. Don't plant smoke and mirrors, your experiment is not rocket science, its even below high school level, just don't do it in the middle of a blazing refraction.

 

To do it right you need a high enough laser and a board with reference grid, and don't matter how your leveling or refraction estimation was wrong, the data plot will show the shape of the earth, at least after 3 standard technical repetition.

 

You received very clear instruction about how you should do that, and its simple, and only your fault that you intentionally used a board that was prevented accurate measurements just at the right time where the academic model should start to diverge from your flat predictions.

 

So what is your base of confidence, considering that your video is still out there claiming absolute victory ? Exactly what part of your data shows any control or survive review questions, like how do you determined the beam center, or height, without the reference target ?

 

Also at the part in your video where the horizon started to obscure your boat, Why are you referenced a phenomena that is not even described in the history of naval transportation, science, and not even by you ? And why is that NUDTZ is conveniently at the right distance where the curvature of the earth should start to noticeably obscure that boat ? Please Answer !

[maximillian12]

From the given data, it looks the Balaton lake is not level. It flows like a river. It has a level +150.55 at inflow (left on the picture) and 149.65 at outflow, a difference of 90cm from level.

post-120902-0-23645600-1473549296.jpg

(I have added labeling on the maps provided in the OP)

 

The experiment was taken at a point after a bottleneck, transverse to the lake. From the color legend, the lake shows a slight level difference transverse also.

 

I don't have autocad but if anyone does - or some other similar way to plot an arc - here is a table showing the geoid height radius distances from the centre of the earth to points along the experimenters' route. As we can see, the radius increases about 1.667 meters for every 604 metres traveled.

 

 

Combined with the above data, this should give a more accurate image of the shape of the surface of the lake.

 

I'd attach them in a spreadsheet too but don't seem to have permission.

 

*Note: lake elevation was entered as 105m amsl.

Edited September 18, 2016 by maximillian12

[DarkStar66]

 

I don't have autocad but if anyone does - or some other similar way to plot an arc - here is a table showing the geoid height radius distances from the centre of the earth to points along the experimenters' route. As we can see, the radius increases about 1.667 meters for every 604 metres traveled.

 

Screen Shot 2016-09-17 at 11.48.32 PM.png

 

Combined with the above data, this should give a more accurate image of the shape of the surface of the lake.

 

I'd attach them in a spreadsheet too but don't seem to have permission.

 

*Note: lake elevation was entered as 105m amsl.

 

I made a chart using Excel based off the ellipsoidal equation for radius given latitude using the latitudes given in Sandor's provided Excel file.

 

r(θ) ~ a(1-f sin²(θ)) (see here)

 

I immediately ran into an issue because they stated the laser was at 46.94922N 17.88929E and their first data point is at 46.94923N 17.88927E and is given as 111 meters distance, but this point is only about 1.9 meters from the 'laser' coordinates. So the data is clearly wrong here. I used ESTIMATED coordinates for the laser of 46.950048N 17.888435E to make it 111 meters away.

 

The results are (with greatly exaggerated y axis) very similar to yours:

 

 

Or about 17m across the 6km of the lake.

 

Which is very interesting as that means that while the far side of the lake would be an ~2.87m 'drop' from a tangent (on a perfect sphere) due to curvature, there is a ~16.7m change due to ellipsoid? Did I get that right? That seems to be pretty significant in terms of this measurement.

 

I checked the WGS84 Geoid height and it was a pretty even 46.3 - 46.29m across the lake coordinates (as you would expect for a body of water) - so that should mean the Ellipsoid is roughly the correct shape.

 

I agree that marking this up in AutoCAD would be very interesting, instead of using spherical approximation.

 

 

But given the very large and evident spreading of the laser

 

 

Where I estimate these values:

 

at C1 = 111 meters, beam is 25 cm (diameter)

at C2 = 436 meters, beam is 35 cm (diameter)

at C3 = 631 meters, beam is 48 cm (diameter)

at C4 = 720 meters, beam is 72 cm (diameter)

 

Beyond that the beam is so spread out we can barely see it and cannot accurately estimate the diameter, other than to note that by C11 and C12 we can just barely make it out as covering a substantial portion of the whole board (enhanced contrast in the image below shows it more clearly).

 

This is showing beam spreading far greater than Gaussian beam divergence.

 

Combined with the unreliable methodology used to gather the height measurements as I show below where you can see they are marking the same few reflective spots on the boat at ever increasing heights, even when the reflection point moves to a lower point on the boat they marked it higher (see C19 case):

 

 

And since the calibration height at C4 was seemingly incorrectly marked, the 'leveling' height above the water is questionable as well.

 

 

So I don't think we can really get any data out of the prior experiment. I've been trying, you cannot get a reliable height estimate even at point C5 - see:

 

 

Even if I very conservatively model the beam spread past C5 I have a 12 meter wide beam on the far side of the lake. This swamps out any possible measurement because we repeatedly only see specular reflections from the bar, the reflector on the jacket, and camera lens glints.

 

 

So this is just a rough attempt to capture the ellipsoid into the data along with the estimated slope taken at C4. Now the interesting thing is that previously I was working with just the curvature estimate and the results did not align with observations -- this suddenly made everything snap into place up to about C11 which is really about as far as I can make sense of anything. This is using C4 as a true height of about 1.185m instead of their 1.3m and slope is calculated from there.

 

I'll try to put my spreadsheet online somewhere to share it as this is very interesting.

Edited September 19, 2016 by DarkStar66

[Mordred]

Some interesting work on examining the data presented.

 

I got curious on your comment "Gaussian beam divergence". Atmospheric optics isn't my strong suit. However I do recall collimation correlations with atmospheric turbulance via Gaussian Schell model beam.

 

Though never really studied it in detail.

Edited September 19, 2016 by Mordred

[DarkStar66]

 

I made a chart using Excel based off the ellipsoidal equation for radius given latitude using the latitudes given in Sandor's provided Excel file.

 

r(θ) ~ a(1-f sin²(θ)) (see here)

...

I'll try to put my spreadsheet online somewhere to share it as this is very interesting.

 

Here is my first stab at putting this into a spreadsheet:

 

https://drive.google.com/open?id=0B22sA7_PYGQvMFY5WWtIenU0ZVk

 

Assumptions: WGS84 ellilpsoid

 

f=1/298.257223560

a=6378137.000

Radius of Curvature at latitude θ ~ a(1-f sin²(θ))

That the top of the black tape mark is ~1.185m as estimated by Mick West's analysis.

The slope calculation is against a flat baseline calculated between the laser itself and measurement point C4, where they re-leveled the laser.

ΔGround[2.286] + laserHeight@C4[1.185] - laserHeight[1.25] / distance@C4[720] = ~0.003084 meters per meter

You can use column T to ignore the beam width or column U attempts to find where the bottom of the beam might be.

Beam divergence angle for C0, C1 is just set to same value as C2 as I don't have good values - the values in green are actual estimates, the values after that are extrapolated but conservative estimates from the green values only.

No refraction is taken into account.

Unfortunately the data is not clean enough to do a 'fit' analysis. But this does align well with the first few measurement points, accounts for the beam spread and later reflective hits.

Using simple curvature did NOT fit the observations well.

Some interesting work on examining the data presented.

 

I got curious on your comment "Gaussian beam divergence". Atmospheric optics isn't my strong suit. However I do recall collimation correlations with atmospheric turbulance via Gaussian Schell model beam.

 

Though never really studied it in detail.

 

Thank you.

 

By 'Gaussian beam divergence' I just mean the amount of divergence expected from a laser beam given some degree of collimation, even in a vacuum. This beam is spreading at an increasing rate of divergence rather than some fixed divergence angle. So I think that atmospheric effects are dominating. Some of that is diffraction, some is refraction - but end result is that the spot we see at C1 and C2 has grown considerably by C4 and by C11 it's so spread out we can barely see it on the board.

 

If you assume an ~100mm aperture (hands width) at the start and try computing the divergence angle at each of C2, C3, C4, & C5 you get different answers for each distance -- so it's not a constant rate of divergence (or maybe the distances are wrong but I think it's too great for this to be the only cause). These are the measurements that I'm referring to and I posted a montage showing these in my earlier post:

 

426m shows ~25cm diameter of spread

631m shows ~31cm diameter of spread

720m shows ~48cm diameter of spread

870m shows ~72cm diameter of spread