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  1. DarkStar

    DarkStar Active Member

    Thanks Mick, really nice updates.

    Pretty full featured curve calculator now.
  2. Rory

    Rory Senior Member

    Nice work on the calculator, Mick: you've made what was already awesome even more awesome.

    I always thought for my dream calculator it would include the ability to enter latitude and longitude coordinates, which would then convert to the earth's radius using a geoid height calculator.

    A few things against this, I guess: number one, it needs a whole new set of equations, since we're no longer dealing with a sphere, but an ellipsoid; and number two, I seem to be the only one interested in this, which probably means I'm barking up a completely irrelevant tree. ;)

    Still not sure why, though. Take these three points on Lake Balaton, for example:
    According to the WGS-84 geoid data, Point C has a radius 48.2 feet greater than Point B, which has a radius 71.3 feet greater than Point A.

    (The mean radius, by the way, is about 3956.2 miles for these 3 points.)

    Can someone explain why the geoid height isn't a factor that needs to be accounted for?
  3. Mick West

    Mick West Administrator Staff Member

    I think the curvature is relatively unchanged. It's like a small shift in the position of the center of the Earth.
    Last edited: Aug 18, 2016
  4. Mick West

    Mick West Administrator Staff Member

    You're familiar with diagrams of the earth (viewed from the side) as a perfect circle. It's actually an ellipse, but an ellipse is simply a squashed circle. You can take any geometrical diagram you draw on a circle, and just squash it vertically to get the same relationships on the ellipse.

    Like this:

    Greatly exaggerated, becomes:

    So, you can take any math you did on the circle and just scale the horizontal and vertical to get the same math on an ellipse.

    Take the drop from the North Pole for example, that's a simple vertical (parallel to the axis of the earth) measurement, so the value would be scaled by the ratio between the horizontal and vertical diameters of the Earth, or 7899.84/7926.38 or about 0.9966, so any drop value calculated for a circle would need to be scaled by that amount to work on an ellipse.

    In general this means that the error for not using the geoid is <0.5%
    Last edited: Aug 18, 2016
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  5. Mick West

    Mick West Administrator Staff Member

    Or another way of thinking about it, those two points are at the surface of the lake, point B being 71.3 feet "higher" than point A. Now you might naturally think that them means that if you were to shine a level laser from point B, then point A would have an extra "drop" of 71.3 feet rather than just the 10 feet you'd expect from a perfect sphere.

    But that's conflating two things. The "level" here at point B is actually tilted down towards point A, you have to measure the drop from level on the geoid, and not level on the sphere.
  6. Mick West

    Mick West Administrator Staff Member

    When might "soon" be?
  7. DarkStar

    DarkStar Active Member

    Funny you should mention that since that's why I asked @Mick West to add the Earth radius as an input value :) It's only a tiny fraction more accurate of course.

    (I've been using but the link you gave has some really good info, thanks!)

    And just noticed Mick added 'tilt' angle and dynamic recalc, very nice -- where is dynamic URL permalink? :)

    To get it "perfect" is impossible, but if you really wanted to make it "better" you would probably want to input observer latitude, longitude, elevation, and either azimuth+distance or a second lat/long pair and use the WGS84 data to get the path integral (this is what Google Earth does for distance calculations). That seems a lot of work for what is probably a few inches over 100 miles :) If anyone takes a crack at it I'd love to see it. That Geoid library seems the way to go:

    But what I would like to see is something where you input your elevation and Field of View and it tells you what your horizon should look like. I haven't totally worked out all the math for that one yet but I built a GeoGebra calculator for it -- which I used here: But it still needs work, you have to move point Z manually still.

    Let's compare two different Earth radii with what we have:

    Distance = 100 Miles (528000 Feet), View Height = 10 Feet (120 Inches) Radius = 3949.9 Miles (20855486.59 Feet)
    Horizon = 3.87 Miles (20423.27 Feet)
    Bulge = 1670.99 Feet (20051.93 Inches)
    Drop = 1.27 Miles (6684.78 Feet)
    Hidden= 1.17 Miles (6175.74 Feet)

    Distance = 100 Miles (528000 Feet), View Height = 10 Feet (120 Inches) Radius = 3963.19 Miles (20925646.37 Feet)
    Horizon = 3.87 Miles (20457.59 Feet)
    Bulge = 1665.39 Feet (19984.69 Inches)
    Drop = 1.26 Miles (6662.36 Feet)
    Hidden= 1.17 Miles (6154.2 Feet)

    So that's just ~21.54 feet difference - only a small % but my brain likes it.

    Mick -- maybe we should move this part of the thread over somewhere else? Getting off topic :)

    But seriously, THANK YOU for all the work on the calculator.
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  8. Mick West

    Mick West Administrator Staff Member

    It's where it says "permalink", under the tilt angle
  9. DarkStar

    DarkStar Active Member

    LOL - nice, I missed it - I have shame
  10. Mick West

    Mick West Administrator Staff Member

    Yeah, there's really no point, as the error would be less than any reasonable measurement accuracy with atmospheric refraction (or even with just haze)
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  11. Rory

    Rory Senior Member

    Agreed. :)
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  12. DarkStar

    DarkStar Active Member

    Agreed, nobody is measuring anything over ~100 miles because of the curvature anyway :) so we're talking millimeters when our data isn't even 1 m accurate. But I'm not in this because I think flat earthers will be convinced by more accurate data. I'm doing it because it's fun to learn about the details of geodesy. :)

    I might grab that library just for grins - seems like it might just be a few lines of code using that.
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  13. snaphat

    snaphat Member

    I've been following this thread for awhile and waiting for the results. It looks like the reason they are taking so long is that they are making a youtube video to say they proved the earth is flat using the data they got. It also appears that there was curvature on the laser itself due to refraction that they claim to have compensated for. In addition, it seems as if they didn't follow Mick's instructions to take many measurements and plot the data to compensate for error in measurement. At least from what they have said. But, I guess we'll have to wait and see.

    Link to them publically discussing this:

    Last edited by a moderator: Aug 19, 2016
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  14. Mick West

    Mick West Administrator Staff Member

    This image claims to show the laser beam bending upwards in the distance. This could occur with warm water and cold air, the same as in inferior mirage.


    However, if the surface of the lake is flat, and the laser is level, then why would there be any refraction? Vertical refraction of a straight and level laser over water will only occur because the water surface, and hence the temperature gradient above it, is curved. Hence this demonstration suggests the surface of the lake is curved.
    Last edited: Aug 19, 2016
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  15. Mick West

    Mick West Administrator Staff Member

    Attached Files:

    Last edited: Aug 19, 2016
  16. Trailblazer

    Trailblazer Moderator Staff Member

    So the laser started getting increasingly high above the lake the further away they got? Excuse my ignorance but isn't that what you would expect on a globe?
  17. Mick West

    Mick West Administrator Staff Member

    Or from a laser that's tilted upwards slightly, however if they "leveled" it my making it the same height above the water at point B/C/E (0.4 miles out) then it would be tilted down a bit.

    The real key would to plot the measurements, and see what the shape of the curve is. I have low expectations here as to the accuracy, as there seems to be significant beam spread during the first mile.
  18. Trailblazer

    Trailblazer Moderator Staff Member

    They say "then the laser started to rise significantly in a short distance", which suggests an exponential curve, not just a tilt.
  19. Hama Neggs

    Hama Neggs Senior Member

    So they have ignored the advice that accurately leveling the laser is nearly impossible?

    PS: And unnecessary?
    Last edited: Aug 19, 2016
  20. Mick West

    Mick West Administrator Staff Member

    Last edited: Aug 19, 2016
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  21. Mick West

    Mick West Administrator Staff Member

    I suggested they try to get the laser as level as possible, then figure out the correction from the curve.

    Sandor wanted to "level" the laser by making it the same height on the boat at a certain distance. That's fine, as it should at least ensure the laser is not pointing upwards. But it's not clear what they actually did.

    Sandor has messaged me to say he's going to send me photos.
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  22. Ian Dalton

    Ian Dalton New Member

    Word spreads fast! It appears that I used the wrong image. Sandor said that the correct image is in a video, not a photo. I assume he's trying to find it now...
  23. Bass In Your Face

    Bass In Your Face Active Member

    I noticed the comments of that thread on FB are full of misinformation. One example is the comparison to the Hawking video, which we started discussing in detail here:

    Why is this TV show, which we've shown to be more of a TV show than a professional experiment, being compared with your experiment? The TV show's experiment is clearly not very controlled, and isn't done by the people who set it up.
    You should be comparing your "professional" laser experiment to experiments that are also more controlled and precise.

    Comparing your experiment to *only* the Hawking TV experiment seems ridiculous.

    Isn't this above statement from FB a demonstration of your LACK of knowledge about refraction?.......
  24. Ian Dalton

    Ian Dalton New Member

    I'm not sure what your criticism is exactly. The Stephen Hawking video was discussed here. I'm not allowed to discuss it as well? I think it is a perfectly valid comparison seeing as it is the same experiment that shows completely different results. I was merely asking for the same level of criticism to be applied to both experiments. My problem is that someone can put a poorly conducted experiment on TV and no one thinks twice about it, they just accept it as fact, then normal people do the experiment properly and show all their workings and get critised for it and accused of fakery.

    I feel like we're moving off topic though, I'm glad to be a part of the discussion on here. I applaud you all for conducting the debate in a structured and respectful manner that is usually impossible to maintain on Facebook and other forum sites, particularly in relation to flat earth theory.
  25. Mick West

    Mick West Administrator Staff Member

    Nobody here has accused Sandor of fakery that I'm aware of.

    However we have noted the problems with the Hawkins "experiments".

    It still remains to be seen what the results of Sandor's experiment are, but a the very least there some very interesting illustrations of refraction. Let's wait and see. I think you jumped the gun a bit with the 1.6m a 5.6 miles thing, as there's no actual evidence that happened.
  26. Ian Dalton

    Ian Dalton New Member

    I was referring more to the discussion we're having on Facebook, one member took your "this claim is dubious" comment and used it to infer fakery. As we are referring to the discussion on Facebook I would like to clarify that I made it clear in the original post that the results are forthcoming and that I was merely giving an unofficial summary of the preliminary findings. You are of course correct that the evidence hasn't been presented yet and I probably did jump the gun by taking Sandor's word for it but he's working hard to compile it ready for submission.
  27. Mick West

    Mick West Administrator Staff Member

    Well, all I've seen so far is the laser beam bending up with refraction in the far distance (closely following what you would expect, based on the observed inferior mirage), and the laser beam rising fairly rapidly as the boat moves away from the shore (indicating it's tilted up a bit). I shall wait and see what the actual evidence is.
  28. Hama Neggs

    Hama Neggs Senior Member

    You're simply describing the common reaction of the public to science. They mostly haven't a clue and don't really care because it would take too much effort. It's not some vast conspiracy to hide the truth. It's just how people are.
    Last edited: Aug 19, 2016
  29. DarkStar

    DarkStar Active Member

    I have a big problem with this statement from the FB page:

    This is just bizarrely inaccurate.

    #1 If they did what they said they were going to do they, ON PURPOSE, pointed the laser DOWN - we have no way to know how much so we cannot predict what you would see at 5.6 miles.

    #2 In the evening is EXACTLY when you have the most problems with refraction -- and we told them repeatedly to keep the laser well away from the water for exactly that reason.

    We said this days and days ago:

    and I know Mick has as well, going back further.

    There is no reason to believe that refraction would be uniform over a lake.

    Just watch Joshua Nowicki's video of what happens in one evening!

    Water presents a large thermal mass, so the higher air (generally) changes temperature more rapidly while the lower air stays closer to the water temperature - which creates a thermal gradient which CAUSES refraction.

    And I have no idea what we are supposed to be seeing in the image below. Is this lens barrel distortion, is it refraction, is it perspective? The horizon goes across near center of lens but the laser is askew so lens distortions would affect it more strongly.

    When you watch Joshua's video you MOSTLY see the water getting lower from your viewpoint because that is where the most refraction is happening and it's allowing the light to bend over the curvature - making it appear flatter.

    Is that also happening here? How far away is this? What is the EXACT size of the sensor and what focal length is that lens set at? What temperature was the water and what temperature was the air?

    Just because it LOOKS curved in the image doesn't mean it is following a sharply curved line in real space.


    They were warned well in advance not to place the laser near the water so this entire experiment is pretty much a bust and likely useless for anything except that is a great demonstrations of refraction if accurate.

    I'll re-evaluate once more information is released but judging by how horribly they handled their first attempt and seem to have completely ignored almost all that was said it doesn't look good.

    And the collimation on the laser wasn't ANYWHERE near what they promised (exactly as they were told it wouldn't be).

    Take a professional Theodolite up 25 meters or so above the water, Level it to the accuracy of the instrument. Then LOWER the angle to equal the margin of error and see if you hit the SAME level on the other side of the lake or not.

    For example, this is LEVEL from Apple Pie Hill to Philadelphia - WELL above any margin of error; about 3 arcseconds for this instrument, and this is 32.4 miles so that's +/-2.4 feet -- given by -- g = 2r*tan(α/2)


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  30. Hama Neggs

    Hama Neggs Senior Member

    From Sandor on the Facebook discussion:

    Can someone tell me if that makes any sense at all? It seems just.... silly.
  31. Ian Dalton

    Ian Dalton New Member

    I would like to be very clear (as I was on Facebook) that I started the thread on Facebook as a summary of initial findings and that the real data and evidence is to follow. I hope that the two discussions can be kept separate at this stage as this is the platform where the evidence will be submitted for review.
  32. Hama Neggs

    Hama Neggs Senior Member

    I wasn't clear that the person posting here was the same as the one on Facebook.
  33. Mick West

    Mick West Administrator Staff Member

    Yeah, I said this two weeks ago:
    But then I also said:
    I was thinking there of when the air is much warmer than the lake, however it seems from these videos that the lake s warmer than the morning air, so we get an inferior mirage effect (light bending upwards, creating a narrow mirror at the horizon, and bending the laser beam upwards)
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  34. Mick West

    Mick West Administrator Staff Member

    Sandor sent me this photo, camera time 5:00AM taken from a few feet west of the laser

    It shows the laser bending upwards, and it looks like it does actually hit something on the other side. What is fascinating is that the return light is then split in two, and we get a "reflection" underneath it, just just like with the lights on the right.

    Here it is with some reference lines. The red lines show better where it actually would be without refraction.

    From a different angle:
    Last edited: Aug 19, 2016
  35. Mick West

    Mick West Administrator Staff Member

    Name has been changed.
  36. Ian Dalton

    Ian Dalton New Member

  37. DarkStar

    DarkStar Active Member

    That 'reflection' below looks to me like the same inferior mirage that bounced the laser upwards (so it's not a return stroke, just a 'mirror' reflection) -- but at the point where it bounced the laser it's reflecting the night sky so it's less obvious than closer to the shoreline where it's reflecting the other lights as well. That would explain the 'gap' also.

    To me, this says the laser is pointed too far downwards.

    I would have to see whatever 'calibration' was done but I'm not hopeful. "Here we are pointing the laser that is 3-6 inches wide already at a bobbing boat and we're going to nail 20 arcsecond accuracy" -- I don't think so.

    20 arcseconds off is all it takes for this (that could put it 3 feet lower at 5.6 miles).

    Do we have GPS location for the 'target' end?
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  38. Rory

    Rory Senior Member

    In a lot of ways, I would agree with this. I think the level of accuracy demanded in the build up to the Balaton experiment has been of a vastly larger degree than that demanded of experiments that we happen to agree with.

    And, likewise, I've seen conclusions on here reached and accepted with nowhere near the level of scepticism and "fine-toothed combing" that this one has been.

    I guess in part that's human nature. But also given the extraordinary claims of the flat earth idea, necessary too. We've seen far too many shoddy experiments and demonstrations presented and subsequently accepted as proof of a flat earth, when there were clearly errors in the methodology and the conclusions reached.

    Let's say, if we want to flatter ourselves, we simply didn't want Sandor to go to all that trouble and have him come back with another flawed experiment full of useless data (such as Rob Skiba's recent trip to Chicago, which obviously cost him a few bucks, but returned nothing of merit simply because he didn't understand what he was doing).

    Props to Sandor for coming here, being open to suggestions and discussion, and taking on board what people were telling him.

    I for one will be waiting for the final presentation before wading in, as I think that's the right way to go - though I already suspect it's beyond my level of knowledge, not knowing much about refraction beyond the basics.

    Also, I already suspect that both sides will find evidence for what they already believe in, and carry on much as before.

    As for Stephen Hawking's "helicopter experiment", I think it's a brilliant and graphic demonstration of the effect of the earth's curvature, and hardly needs to be subjected to the rigours of a full scientific enquiry, being as it's an interesting, made-for-TV example of something that has been shown and explained many times over, rather than an isolated attempt to prove an incredibly extraordinary claim.

    Punning on his name to imply fakery, questioning whether the words he "says" actually come from him, calling the videos bs, and insinuating that "members of the public" are in fact "actors" is unlikely to convince anyone of one's analytical and scientific credentials.

    Then again, I'm sure we've all thrown a low blow or two in our time.

    In any case, I look forward to the next exciting instalment.

    Cheers! :)
    Last edited: Aug 19, 2016
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  39. Mick West

    Mick West Administrator Staff Member

    It's a bit of a mind bender. This mirage s not "reflecting" the light in the usual sense - it's bending the light very gradually over a long distance.

    Consider only the final spot at the end of the beam.
    It's seemingly illuminating the something on the far shore.

    Now compare that to the highest light on the right:

    Notice the laser sport has a mirage spot underneath, the light from those spots is coming from the same place on the far shore, but is taking two very different paths. The top path is higher so is bent very little, so the upper light appears only slightly lower than it should. The lower path has more significant curve and so appears a lot lower.

    It peters out because as the angle increases it beomes more than can be bent without hitting the water
  40. Bass In Your Face

    Bass In Your Face Active Member

    I never said you can't discuss it, I would encourage discussion on it (just pointing out the thread dedicated to it, and yes of course its been discussed here). What I was referring to was the way in which you are speaking about it and comparing it in that FB thread

    It just seemed that the overall tone of that post is that you've already made a conclusion about it's accuracy, and are ONLY comparing it to this ONE crappy experiment (in which the amount of disconnect between Hawking, others involved in writing up the experiment, and those who are producing/editing the show, is pretty big, and pretty common in TV/entertainment). Compare this new laser experiment with a legitimately controlled experiment, because the comparison solely to the Hawking video seems like a moot argument, and doesn't help anybody understand anything definitive.

    In sum, my criticism is that the tone of that thread seems anything but objective, however I do not mean to get off topic.

    Rory explained it better:

    I will wait for the final results, and hope they are discussed on this website in detail.
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