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Thursday, August 25, 2016

Flat Earth Follies: The Horizon Always Rises To Eye Level

Flat Earth Claim

The Horizon Always Rises To Eye Level

The Facts

What I want to know is, how exactly did you measure that?

It certainly does not look "eye-level" to me.

In fact, trivial observation shows that it drops by pretty much EXACTLY the amount we would expect on an Earth with a radius of approximately 3959 miles.

I have a Theodolite application on my iPhone 7 Plus which uses the accelerometers to position a reticle in the camera view marking out level & plumb and has indicators showing the angle of the camera in relationship to level.  In the image below I have purposefully tilted the camera along two axes so you can see that the reticle has turned red indicating that my view is very tilted but it has aligned itself to the horizon while the white cross-marks simply mark center of the camera view.

So it doesn't matter if my phone or the plane or anything else is tilted, the angles indicated by the Horizon Angle and Elevation Angle indicators are relative to LEVEL.

Figure 1

And yes, these are from a different flight so I'm on opposite sides of different planes, at different times.  I didn't think to take the above picture until my return flight but I wanted to show readers that the reticle finds LEVEL with our view regardless of what the camera is doing.

If the Earth is approximately a sphere with radius R = 3959 miles or 20903520 feet we would expect that a viewer at greater and greater heights would (using the left-side example here):

Figure 2

#1 see an increasingly distant horizon equal to equation (1) above where distance to the horizon (d):
  • d = √h √(h+2R)
#2 that the angle down to the horizon would thus be equal to:
  • horizon dip angle = arcsin(d/(R+h))
Armed with this information we can now look at two examples I captured.

Example #1

h=24854 feet
R=20903520 (Earth radius in feet)
d=1019651.849' (about 193 miles to the horizon) [wolfram|alpha]
horizon dip angle = ~2.79° [wolfram|alpha]

Figure 3 - Example 1
I'm only just now doing the math and that is a phenomenal agreement with my photo.  This was taken on the descent so technically was taken after the photo below.

There are a few sources of error here such as clouds, particulates in the atmosphere, and refraction affecting our true horizon so we cannot make an exact measurement.  Let's see if this holds...

Example #2

Now we're up much higher...

h=38805 feet
R=20903520 (Earth radius in feet)
d=1274295.105' (about 241 miles to the horizon) [wolfram|alpha]
horizon dip angle = ~3.49° [wolfram|alpha]

Figure 4 - Example 2
Again, every close agreement with my image.  The true horizon could well be at 3.5° in this image but it's at least 3.4° below our level reticle - that is very clear.  I tried to remove some of the haze in this image, resulting in the image below:

Figure 5

This is, IN NO WAY, "rising to eye level" - this is the exact opposite of that.

In fact, let's watch a movie showing this horizon drop in action aboard a drone:

Here is a video from the cockpit of a commercial flight showing the Horizon angle:

Here is another video on this subject:


Flat Earth is flat out busted - there is no excuse for such shoddy work.  Anyone claiming this is either knowingly a liar or lying in the sense that they haven't actually tested it but are making the assertion AS IF they know what they are talking about, when they very clearly do not.

They are already back-peddling and making excuses.

Funny that you have to make excuses as to why YOUR claims fail and end up looking exactly like an oblate spheroid Earth and, as I showed, the horizon getting lower as you climb up is exactly what we observe and it lowers an amount GREATER than a flat plane would because the curvature drops off at an exponential rate the higher we get.

The angle would be trivial to calculate on a flat plane Earth because RISE/RUN would give you the slope and the inverse tangent of a slope is an angle.  But Flat Earth can't even tell you why your distance increases with altitude (except by their false appeal to perspective) or by how much.

But let's try that with our second example:

rise = h = 38805'
run = d = 1274295.105' 

Gives us an angle of 1.744° [wolfram|alpha] from tan⁻¹(38805/1274295.105)

So toss this on the pile of Flat Earth Failures.


  1. It seems the plane is banking and the app was probably calibrated to level flight. Note the bright spot on the wing tip is isolated and if we were level the whole wing should be more consistent.

    1. First of all, as the 'calibration' image on the ground shows, the app doesn't care what angle the phone or plane is at, the reticle marks out level regardless. Secondly, those images are 36 minutes apart, the plane has moved a great distance, the Earth has rotated so the Sun is in a different part of the sky and the plane isn't even necessarily pointed in the same direction. You cannot look at some spot on the wing as an indicator of 'level'. I was very careful when I took the images to make sure the plane wasn't maneuvering. The first image WAS climbing, but the image at 38,805ft is level, steady flight.

      But the good news is YOU DON'T HAVE TO TAKE MY WORD FOR IT.

      As I mentioned in my earlier comment your objections are pointless because the POINT here is to give people the METHOD so they can make their own observations. If I'm lying about the method then PROVE it. What you are doing here is the same bullshit that conspiracy theorists pull - "well, MAYBE, blah blah blah". On the chance that your comment was pre-updated images I'll leave it with this as a warning.

      DO YOUR OWN EXPERIMENTS. This one is deadass simple -- buy one cheap smartphone app. There is no excuse for failure to execute here except being disingenuous.

      If I get a chance in the future to film a cup of water along with the observations I'll do that -- it's not necessarily easy to do that however. Meanwhile, do it yourself. That's the beauty of such simple observations, you can repeat them yourself.

      So, it's been 6 months since your comment -- have you made any such observations on your own?

  2. I captured new images with an updated version of the app and have updated and greatly expanded on this page now.

    I included an image to show the calibration accuracy on the ground. I actually didn't recalibrate at all because I didn't need to - it was already accurate, I just checked it on the ground.

    However, the point isn't to trust ME but to give readers METHODS where they can verify reality for themselves. Hundreds of millions of people have cameras and apps that can trivially replicate this.

    I also included Sly's analysis video on the flat earther David Ray showing his drone video and CLAIMING that the horizon is rising to Eye level when it very clearly is DROPPING off. Hoisted by his own petard.

    So... thank you for your feedback on the calibration question. However...

    >> "Note the bright spot on the wing tip is isolated and if we were level the whole wing should be more consistent."

    This is false and has zero basis in reality. The shape and relative angle to the wing would determine the pattern of spectacular reflections off the wing - the rotation of the plane would only change the relative angle from what it HAPPENED to be at that moment - which you have no information about so your assertion here is just making things up. Before you try making things up again you should be prepared to show your calculations supporting such assertions.

    In future criticism please don't make things up.

    Hope you like the updated page