1. Laser

    Laser Member

    WaterLevelDistantMountainAndHorizonCurvatureDrop.
    Here I show a simple water level set up at an altitude of about 470 feet showing a distant mountain of 512 feet altitude dropping below the level line due to earth curvature. It also shows the horizon failing to rise to eye level, but instead dropping by more than half a sun/moon diameter, an amount consistent with the globe theory.

    The level was set up at the Black Hill Lookout and trail head parking lot, in Morro Bay, California at an altitude a little above half way between the 440 and 480 foot lines on the topographic map. I estimate 470 feet including ladder height. It shows the level line towards Estero Point and the peak "Villa 2" which is marked 512 feet altitude on the topographic map. Despite Villa2 being higher than the location of the level, Villa2 falls well below the level line due to the downward curvature of the earth. This image also shows the horizon not rising to eye level, but falling .31 degrees, or more than half of the Sun/Moon diameter, below the level line. This is close to the predicted horizon dip of .36 degrees, from 470 feet altitude with refraction. The peak Villa2 is 12.32 miles from the level at bearing 307.9 degrees. The curvature drop without atmospheric refraction over 12.32 miles is 101 feet. Adjusted for standard refraction, the curvature drop should appear to be about 87 feet. The lattitude and longitude of the water level was 35.35825,-120.83359 Villa2 is in the Harmony Headlands state park near Estero Point, about halfway between San Francisco and Los Angeles at 35.467596,-121.006295. The camera was at maximum zoom of 36mm focal length for a 35mm equivalent focal length of about 200mm. At maximum zoom I previously measured the camera's pixel angular resolution at .0000336 radians per pixel. The ends of the water level were 70.1 inches between centers. The level tubing had an outer diameter of 15.5mm. The camera was about 13 yards behind the center of the level. This image was based on the file WaterLevelDistantMountainAndHorizonCurvatureDropDSCN0953.JPG of file size 8,276,946 bytes, taken 2017-10-23 10:28AM Pacific Daylight Time. It has been rotated slightly to level the horizon, a dotted line added, and cropped. This file, WaterLevelDistantMountainAndHorizonCurvatureDropDSCN0953.JPG, and WaterLevelApparatusDSCN0955.JPG have been placed in the public domain by me, the original photographer.

    This water level is cheap and easy to reproduce. Just a couple dollars of tubing. Due to the limited accuracy of such a level, you should probably pick a distant target at least 7 miles (10km) or so away, and preferably at least 10 miles (16km) away to ensure sufficient drop to be easily visible. Use a topographic map to find a mountain, large building, mountain pass, road, or something in the distance equal or just a little higher in elevation than where you set up your level. If you don't trust the map elevations, you can go to the distant location with your level and sight back to your first location to see if your results are consistent.

    If you are going to make a water level like this, be sure to keep the tube ends vertical in the front/back direction to prevent refraction shifting of the light if it passes through the clear tube walls at an angle. Being vertical in the side to side direction is not as important. The longer the tube is the more accurate it will be. When photographing the level, the camera should be 20 or 30 feet behind the level so the water level surfaces and the distant objects can both be nearly in focus. But being too far back reduces resolution in aligning the water surfaces. I think it is best to focus the camera on the water level rather than on the distant objects since the distant objects won't be very sharp anyway, and a sharp view of the level surfaces gives better accuracy. If your camera has a large diameter lens aperture like typical SLRs, then you probably should stop down the aperture to get a better depth of field so the level and distant objects will be in focus. I also recommend taking a picture with the near surface very slightly below the far surface so that the line of sight is actually very slightly down hill. That way if the distant mountain or horizon is still below even a slight down hill line, then you know it will be below a true level line.

    The following are my attempt to upload full resolution images, unaltered from the camera, of the apparatus and location and of the leveled and cropped image above. These images were taken at about the same time and daylight brightness, but one looks darker because I used a darker exposure in hopes of getting a little better horizon contrast. I think it would have been better at normal exposure. WaterLevelDistantMountainAndHorizonCurvatureDropDSCN0953.JPG

    WaterLevelApparatusDSCN0955.JPG
     
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  2. Mick West

    Mick West Administrator Staff Member

    Great experiment. It's such a clear demonstration of the drop of the horizon when done right.
     
  3. Laser

    Laser Member

    SunsetAndWaterLevelDSCN0995.
    Here is an image of the sunset and horizon dip with a water level from 120 feet (37m) altitude in Morro Bay, California. The horizon dip is almost a third of the sun width. 2017-11-04 Resolution is .0129 degrees per pixel. The width of the sun and the horizon dip are within a couple pixels of their predicted values according to the globe model. The water level is the same as the one above. The camera was about 13ft (4m) behind the level. The far end of the level has red water while the closer end has clear because I was rushed and I ran out of red colored water so I put some clear water in the close end. As the original photographer of this image, I release it into the public domain.
     
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  4. Laser

    Laser Member

    Here is a picture of the horizon with the horizon and the entire sun dropping below eye level.
    SunEntirelyBelowEyeLevelCroppedDSCN1068.
    And another picture of more than half the sun dropping below eye level.
    SunHalfBelowEyeLevelCroppedDSCN1062.
    There is a water level to establish accurately where eye level is at or is above. The sun is on the horizon to show that the true horizon is at or below the apparent horizon rather than the true horizon being at eye level and only obscured by haze. The horizon dip of .33 degrees in these images, is a close match to within 10% of the globe model predicted dip of .36 degrees, from the 470 feet (143m) altitude they were taken from.

    It might be argued that the sun and horizon in these pictures is dropping below eye level due to perspective. But if the horizon consistently doesn't rise to eye level due to perspective, then some flat earthers would have to admit that the claim they have been making for years, that the horizon rises to eye level as you increase altitude, has been a false claim that they didn't even check. They might alternatively argue that the horizon has dropped due to refraction. But again, if they claim that refraction _normally_ causes the horizon to dip by about this amount, then they would have to admit that their previous claims were false.

    There are occasionally exceptional atmospheric circumstances that could produce sufficient refraction to create this amount of horizon dip, but this was not a day of exceptional refraction. Nearly every day it is visible, I look out at the horizon, and it is almost always at a level where it appears to just touch the bottom of the crossbar of a certain power pole in the distance. The horizon was at the usual level on the day these pictures were taken. If flat earth believers want to argue that this is due to exceptional refraction, then they should first check with a good level at various altitudes to find out accurately what the horizon dip normally is.

    The horizon dip in these images not only matches the Metabunk curve calculator predictions, but also the table of horizon dip from the last page of the US Navy Air Almanac at http://aa.usno.navy.mil/publications/docs/aira.php
    If the Air Almanac horizon dip values did not match reality, aviators would have noticed the positions they measured with their sextants to be off quite noticably, especially when taking positions over or approaching a location with known coordinates.

    These pictures were taken from about 470ft (143m) altitude at the Black Hill parking lot at 35.35825,-120.83359 in Morro Bay, California.
    The camera was slightly above the level line, as evidenced by the nearer(apparently wider) water surface of the water level being slightly lower than the far surface of the level, and therefore eye level is slightly above the height in the images of both the near and far water level surfaces. If the camera had been precisely aligned with the water level surfaces, then the images would show even more horizon dip and be even less consistent with the flat earth model. In the image with two dotted lines, the top dotted line is the calculated height of eye level based on the difference of about five pixels in the near and far water level surface and the dimensions of the water level and the camera position. If you doubt the validity of the eye level calculation, you may simply reference the lower dotted line, which is lined up with the far water level surface, and is confirmed by the water level surfaces to be slightly below eye level. The horizon and more than half the sun is below even this lower dotted line of sight.

    In the uncropped pictures you can see a small machinists ruler clamped vertically on the left side with little tiny ears near the top. That ruler is precisely 6.25 inches (15.9cm) tall (6in from the end to the ears). It was perpendicular to the line of sight. There is a little square of scotch tape in the middle of the ruler that I forgot to remove, that's not a photoshop artifact. The water level was 70.25 inches (178cm) between centers of the water surfaces. The machinists ruler was 35.25 inches (90cm) farther from the camera than the closer water level surface. It was 216.25 inches (549cm) from the camera to the closer water level surface. The camera focus was at 6.6 m which is the infinity setting for this camera. At maximum zoom and focus, I calculate the camera vertical resolution at .00197 degrees per pixel. A picture of the water level from the side, along with some distant mountain drop photos, the location, and other good stuff, can be found in this thread:
    https://www.metabunk.org/water-level-showing-mountain-and-horizon-dip-due-to-curvature.t9203/
    Although the more recent photos of the level were of it clamped to a tri-pod instead of a ladder.
    The cropped pictures have also been rotated to level the horizon.

    The pictures were taken at about 5:24pm Pacific Standard Time(GMT-8) on 2018-01-26. Times in the Exif data are off by an hour because I just keep my camera on summer time all year. 12 days after taking these pictures I checked the time on my camera and found it 1 hour 1 minute and 55 seconds fast.

    If you want to observe the horizon and sunset dip angle, you should probably observe the moon instead of the sun. If you want to observe the sun, you should take great care not to look at the sun without proper eye protection. That means certified eclipse glasses, or maybe sufficiently dark welders lenses. Regular sun glasses or stacked sunglasses may let invisible Infrared and Ultra-Violet light into your eyes that may damage your eyesight without appearing bright or causing pain. Sometimes the sun seems dim enough to look at at sunset with the naked eye, but you still shouldn't look at it, because while the haze might scatter the visible light enough to be comfortable, the invisible infrared light doesn't scatter as much as the visible, and might still be dangerous. Even if you have looked at the sun before and didn't go blind, you may get minor damage that you don't immediately notice, like a little worse night vision that could impair your ability to drive at night.

    If you're going to take pictures of the sun, avoid pointing your camera steady at the sun for any longer than necessary, in order to prevent burning of the image sensor. Keep a lens cap on your lens during setup. You probably should use a camera with a small lens to keep pixel heating to a minimum.

    If you're going to make a water level, let the tubes stick up taller than on mine so you get fewer spills and less problem with clamps blocking the view of the surfaces. Or even use a complete circle to prevent leaks. You can probably get plenty good accuracy to verify these results with a level only two or three feet long, or even less. I was thinking of making a tiny circular water level to take on a plane to measure the horizon dip out opposite windows at the same time. I might use two little water levels with a mirror on one so that I could get levels pointing in opposite directions in the same shot at the same instant. You can't bring much liquid past security at airports these days, so the tube would have to be very small. Although you could probably get a little extra water in the restroom after passing security.

    As the original photographer of these images, I hereby release all four of them into the public domain.

    The following are the unedited full frame versions of the cropped and leveled images above.
    SunEntirelyBelowEyeLevelDSCN1068.JPG
    SunHalfBelowEyeLevelDSCN1062.JPG
     
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  5. JFDee

    JFDee Senior Member

    Atmospheric refraction makes the horizon rise, or doesn't it?

    So if we'd hypothetically subtract its influence, the distance from water level to horizon would even be larger.

    Furthermore, the effect of a rising horizon due to atmospheric refraction works only on a spherical (or cylindrical) planet, so I'd like to see a FE believer bring that up ...
     
    Last edited: Feb 12, 2018
  6. FlightMuj

    FlightMuj Active Member

    Do you doubt them?
     
  7. Mick West

    Mick West Administrator Staff Member

    It normally does, yes. Light bends towards the more dense medium, higher pressure air near the ground is denser than lower pressure air higher up. So light bends down, which makes the horizon appear to rise.

    However it seems some flat earthers are (understandably) confused as to why light bending down should make the horizon rise. If the light is bending down (they argue) should it not make the horizon seem lower (they ask)?

    It's a tricky on to explain to someone who is convinced they are correct. The apparent position depend on the incoming angle of the light at your eye/camera. But since most FE folk don't really understand light and optics then they have trouble grasping it. Normally you'd illustrate how it makes the sub rise up above the horizon - but that explanation obviously has some problems for them.
    fig_00493_1e.
     
  8. Laser

    Laser Member

    I've been informed that large uploaded images get downsampled, so I'm re-uploading the full unedited pictures here in zip files.
     

    Attached Files:

  9. JFDee

    JFDee Senior Member

    My question is - regardless of the direction - why sunlight would bend at all on a flat earth. As far as I understand the FE models, the sun is somehow supposed to be either inside the atmosphere or very close outside of it. In any case, when it's close to the horizon, its light should not have to pass any density changes - ergo no cause for bending.
     
  10. Mick West

    Mick West Administrator Staff Member

    I think the bigger problem there is how the sun gets "close to the horizon". That in itself is a far more fundamental violation of the laws of physics than a minor change in position due to refraction.
     
  11. Laser

    Laser Member

    I thought I'd post here this horizon dip table from the last page of the US Navy Air Almanac. http://aa.usno.navy.mil/publications/docs/aira.php

    It also occurred to me that every aviator's sextant has a bubble level to use when the horizon is not visible or is blurry due to high altitude. Therefore every aviator that uses a sextant has a precision angle measuring instrument and precision level reference in one, with which to observe and verify the Navy horizon dip table. The Navy could never get away with an inaccurate table.

    Note that in this table, the eye level altitude in feet is referred to as "Ht." whereas "sextant altitude" refers to the ANGLE from the horizon up to the astronomical object being measured. The "Dip" in this table is the number of arc-minutes the horizon is below the true eye level of the observer. One arc-minute is 1/60th of one degree. So at 2600 feet, the horizon appears about 50 arc-minutes, or a little less than one degree, below eye level.

    HorizonDipFromAirAlmanac.
     
    Last edited: Sep 11, 2018
  12. Mick West

    Mick West Administrator Staff Member

    A "bubble sextant", fascinating - in particular the "mechanical averager"
    https://www.airspacemag.com/flight-today/how-things-work-celestial-navigation-2640112/
    This solves a general problem with line-of-sight observations. Single measurement can be off for a variety of reasons. An average is often needed. With the water levels sometimes you see them being hand-held so individual frames from a video are not useful, but the average of multiple frames would give an accurate result.

    With @Laser's setup a single shot should be accurate (and certainly enough to demonstrate the basic principle), but multiple shots (like 3) should still be taken to demonstrate the level is not moving (water can slosh for a while)
     
  13. Laser

    Laser Member

    The tubing diameter of my water level was small enough that any movement was completely damped out in less than 15 seconds. By the time I got the camera ready for the shot, there was no visible movement at all. If there had been much wind, then the story would have been different.

    Still, I probably should have shot video just to add to the credibility for the flat earthers. My attitude was that there was no reason for me to try to prove that my experiment was true and correct, because it could be trivially faked, and they had no particular reason to trust me. I figured I was just doing a proof of concept for them to replicate. But since then I have realized that many of them won't or can't replicate the experiments, so making harder to fake video and answering as many objections as possible, may significantly enhance the impact of the demonstration. On the other hand, making video that is not embarrassing tends to require much more time than a few still shots. Also, my camera only does 720p video, whereas it does 20 megapixel stills. That's important when doing precision angle measurements based on water levels.

    Another difficulty I didn't fully appreciate at the time is how uncommon it is to have a sunset right on the water, not blocked by the marine layer of fog or clouds. On clear days, a lot of moisture evaporates from the ocean and then condenses into fog as the temperature cools before sunset. Growing up looking at sunsets on the ocean, I never really paid any attention to whether the sunset was all the way down on the water. It rarely is. I've been waiting for two or three months now here on the central coast of California without a single such day. It's worse in the summer. This may make it very hard for flat earthers the replicate a sunset on the ocean observation, especially if they have to travel from an inland location, without knowing till they get here if fog will form far out at sea. It looks like the only practical option may be to set up a timed camera on a mountain for several months to catch a shot.
     
  14. Laser

    Laser Member

    HorizonDropFrom2761FeetDSC_0061.
    Here is a location where you can verify horizon dip without even setting up a water level. This photo was taken from the un-named mountaintop of the north radio towers on Cuesta ridge near San Luis Obispo, California at 35.39327 Latitude, -120.70844 Longitude. The Mountain of the camera location is shown on the USGS topographic map to have an altitude of 2761 feet (842m). The picture shows the horizon being aligned with the top of Mt Buchon (aka Saddle Peak) which is shown on the topographic map to have an altitude of 1819 feet (554m), almost a thousand feet (300m) lower than from where the picture was taken. Thus the line of sight to the horizon is a slope down below eye level. Even if the topographic maps do not give exactly accurate heights for these two peaks, it is clear and easily verified that Buchon is much shorter than the north radio tower peak. If one had any doubt about the relative heights of the two mountains, one could just set up a water level at some location an equal distance from the two peaks and make an easy visual comparison of the heights. The horizon dip of .863deg in this picture is approaching twice the diameter of the sun, and is within 1% of both the dip from the Metabunk calculator(.862deg) and extrapolated from the Navy table(.859deg). That close of a match was probably rather lucky as one would normally expect a little variation from refraction along the light path to the horizon.

    The lattitude and longitude of Mt Buchon is 35.22234, -120.79307. Mt Buchon is 12.7 miles (20.5km) from the north radio tower peak at a bearing of 202.1 deg. If you look very closely you may notice that the horizon doesn't quite go all the way down to the top of Mt Buchon, but is 4 or 5 pixels above. Those 4 or 5 pixels amount to about two hundredths of one degree and are less than 1/40th of the full horizon drop, and so don't invalidate the conclusion that the horizon does drop considerably and in accordance with the globe model from this altitude. If you want perfect alignment, you could go to the camera location and walk 20 or 30 feet down the mountain to see perfect alignment of Buchon and the horizon.

    In the center left of the picture is the Camp San Luis Obispo National Guard base, and in the center right is Cuesta College.
    Based on the bearings to Cerro Romauldo and the street next to Cuesta College, I calculate the field of view of this image to be 25.17deg in width and 16.78deg in height. Although the version of the picutre you're seeing is probably resampled to a lower resolution, the original image had a width of 6000 pixels and a height of 4000 pixels, for an angular resolution of .00420deg/pixel. Obviously I edited the image to add labels to the mountains, and I also used the unsharp mask tool to increase the sharpness and contrast of the horizon and mountains. Unfortunately I hadn't expected to get a shot like this, so I didn't come prepared to get this shot with a level in it, in order to establish eye level. So I've calculated where eye level is in the image based on the calculated angle down to Mt Buchon. As the original photographer and editor of this image, I hereby release it to the public domain.
     
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