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Tuesday, July 19, 2016

Chicago skyline 'looming' from MI - explained

The Chicago skyline stretched with lower parts sunken below the horizon makes for another beautiful image.

This is a snip from a an image by Joshua Nowicki (*) that shows the Chicago skyline from across Lake Michigan at Grand Mere State Park.  Take note of the very tall Willis Tower (Sears Tower) in the red box, we will revisit this image towards the end (and note, RADAR, being photons just like light, experiences refraction too!)

But what you really need to do first is watch Joshua's other video first because it shows the dynamics of what is going on during these events:

I grabbed some of the frames (in order) and put a strip side-by-side so you can see what is going on (click to enlarge).

Asking why we see what see is a good question to ask and understand, but to reach understanding you must also study all the relevant aspects.  How can you watch the Chicago skyline 'rise up' from behind the horizon, constantly shimmering and flickering through all kinds of different refraction and mirage effects and deny that you seeing the effects of atmospheric refraction?  You can literally see the buildings moving up and down in some cases and, in other cases, the horizon visibly drops.

Even Rowbotham cites from Britannica on how refraction curves the light in exactly this manner, he just then proceeds to dishonestly ignore it.  But this shows that the greatly varied effects of refraction were clearly known in his time and that he was very clearly aware of this.

The response, however, has been everything from claims that this is NASA tricking us to just completely ignoring the evidence and claiming 'Flat Earth PROVEN!' with this picture.  How can they ignore the missing half of the Chicago skyline that remains below the horizon?  Well, they aren't famous for allowing facts to get in their way :)  But I digress...

Once again, I refer the reader to my page with the details for the relevant mathematics I will be using here:  Derivation for Height of Distant Objects Obscured by Earth Curvature

And for quick reference, I remind the reader that what we want to know is how much of the distant Chicago buildings should be obscured by the Earth's curvature on a spherical model. This is measure (B) from the following image, not distance (D) since the camera here is clearly not submerged half-way under the water of Lake Michigan at "0" elevation.

Note: D should actually point towards center of Earth as shown in my post on [8"×d²]

From my page above we know that:

Height of Distant Objects Obscured by Earth Curvature = h₁ = √[(d₀ - [√h₀ √[h₀ + 2 R]])² + R²] - R (when √h₀ √[h₀ + 2 R] is LESS THAN d₀)

This fairly simple geometry - I didn't even use trig functions, just basic algebra - so hopefully this is fairly accessible to readers.

Grand Mere State Park, Michigan

Joshua has many (awesome) pictures and videos of Chicago from various locations along the Michigan shoreline, Warren Dunes State Park, Grand Mere State Park, and Michigan City Pier just to name a few.  He is a very good photographer and you should definitely check out some of his work (facebook) (smugmug).

The image in question here was from Grand Mere State Park (source), so we will use the details for that location.  The first thing we need to do is locate Grand Mere and get the geographic details for that location.  Using Google Earth we find a plausible viewing location on the Dunes overlooking Lake Michigan and we get our viewing altitude (190m) and latitude 42.003712.

(aside, I welcome corrections on anything throughout this post, especially from Joshua who might have better information than my estimate of elevation and location, however, I attempted to be fairly conservative)

From here we draw a path from this location at Grand Mere to the base of the Willis Tower (I measured all the way to the base of the actual building, not just shoreline) - the upper line here is to Grand Mere, for comparison the lower (and only slightly shorter) line is to Warren Dunes.

NOTE: Google Earth gives you GREAT CIRCLE distances along the oblate spheroid of the Earth, so these are NOT straight-line distances.  But at under 60 miles the difference is negligible so I'll just stick with these values - but if you were working with hundreds of miles you would need to take that into account.

So we're at about 90,933 meters (~56.5 miles) distance.  CAUTION: there is a danger here of thinking we are "exactly 90,933 meters away", that is not true, we don't know this value exactly because we don't know exactly where Joshua was standing, so we need to keep in mind that we could be somewhat closer or further away.  But we are in the ballpark sufficiently to get a good estimate of what we would expect to see, given an oblate spheroid Earth model.

Next we need to check our elevation profile to #1 verify nothing would be blocking our view (it isn't) and #2 to find the lowest-point between us, this is our elevation bias (or 'ground level').  We can't use sea-level because we have 175 meters of water and Earth between the surface of the Lake and sea-level that we can't see through.  NOTE: if you use sea-level, even with zero refraction, you find only 136m hidden so we would think we could see almost all of Chicago if you use the wrong values.  You really must understand what these values mean so you can measure properly and get proper results.

So we find that Lake Michigan is at about 175 meters elevation which is our elevation bias - this is the amount we need to add to the Earth's Radius to get our 'ground level' for this observation ('ground level' meaning the lowest point we could possibly 'see over').  It helps that we are viewing over a lake that is at a fairly constant level so we don't have to worry about hills in between.

We also note that we are at about ~15.5 meters over the water, plus ~2 meters for tripod, so 17.5m overall for the elevation of our observer, over 'ground level'.

Now we come to the most difficult part, estimating the refraction.  We know for a fact from the video above that there are very strong refraction effects that bring Chicago all the way from being 100% obscured to being somewhat visible over the horizon.  But we don't know the exact values for the moment that first picture was taken (which was ), so what we're going to do is calculate an estimate based on 0% refraction, 10% refraction, and 20% refraction and that will give us a range of values so we can compare them against our observation.

Remember that we already know from the video, that one possible observation is that Chicago skyline is completely obscured (indeed, this is the normal observed condition).  We see that very clearly in the video, and then we see it 'rise up' and fluctuate quite a bit.  But we never see the bottom half of the city!  So this already dis-confirms the Flat Earth model, where we should be able to see all the way to the shoreline of Chicago.

Some attempt to appeal to some mythical version of perspective to explain this observation away, but perspective changes the angular size of distant objects - it simply does not shift one object behind another.

And perspective also cannot only make the bottom half of the city microscopic while leaving the top half stretched out and distorted. If you want to make such a claim you'll need to show your math and your model of physics which accounts for it.  Basically this is just a non sequitur appeal to a phenomena they do not understand.  Meanwhile, the science behind refraction is well-documented (if complex).

Perspective makes things appear smaller, it doesn't hide one thing behind another.

And refraction explains why we can see a little further than we think we should.  I've also seen appeals to how 'perfect' this view of the Chicago skyline but I show below that it is far from perfect, there are many severe distortions.  But first, let's get our best estimate of what we might expect to see under varying atmospheric conditions...

Next we use the Earth Radius by Latitude Calculator and our Latitude (42.003712) giving us our Earth radius (close estimate) at this location for ground level of 6368.78km (6368780 m).

Latitude: 42.003712
Earth radius, R = 6368780m
h₀ = elevation of observer = 17.5m
d₀ = total distance to distant object = 90933m

So we have everything we need here to estimate how much of distant Chicago skyline should be hidden behind the Earth. I've provided Wolfram|Alpha links which solve the exact equation I gave above with the following values (only changing refraction %):

0% refraction: d=90933, h=17.5, R=6368780 = 453m
10% refraction: d=90933, h=17.5, R=6368780*1.10 = 404m
20% refraction: d=90933, h=17.5, R=6368780*1.20 = 364m

So this gives us some estimates, under different atmospheric conditions, that estimate how much of Chicago we might expect to see at this distance and observer elevation.  It varies from 364m hidden with a pretty significant (but not maximal) value for refraction, and 453m hidden at the most extreme (no refraction).  I would say this pretty much matches what we see in the video and it looks like the photograph is showing just about 20% net refraction to the top of the building, with a significant amount of distortion.

Now let's consider our subject...

Chicago Skyline

The ground floor for Willis Tower is ~6 m above the water level (at 181m elevation), the tower itself is 442 meters tall up to the spires on top, and then those extend another 85 meters up.  So here is a diagram showing the heights, the image is from Google Earth because it allowed me to get a straight-on shot of the building, I show an actual photo for comparison.

And a little closer up with the spire moved side-by-side showing they are approximately the same size (81 meters for the thinner segment of the building and 85 meters for the spires):

Here is an actual photo for comparison:

In the above picture, note the proportion of the Spires to the narrower top part of the building and compare those proportions again with Willis Tower in the distant image, annotated below.  It is obvious on this examination that the narrow part of the building, just below the spires before the building widens, has been stretched significantly.

It isn't really possibly to be certain here because the image acuity is insufficient to identify fine details in the middle area of the buildings but it is perfectly likely that some portion of that layer is inverted and causing some of the stretching.  Especially if you look at the row of buildings to the right of Willis Tower (the top line of the buildings between the green arrows), those are NOT all at a constant elevation, so you are certainly seeing extreme distortion in that layer that appears to be an inversion (and you can see it VERY clearly here).

I would say, based on this shot, that the refractive effects we are seeing vary from Superior mirage with ducting, to looming, and towering - along our different sight-lines with a narrow superior mirage just above the horizon sight-line and distortion from looming/towering above that.

This nothing even close to a clean shot of a distant skyline.

Another shot taken by Joshua Nowicki of Chicago, showing clear Superior Mirage effects:

Researching this topic I also found in the 'Chicago Skyline' thread on Flat Earth Debunked someone had done a building-by-building match-up between several of the 'distant Chicago' images and a skyline shot.

You can see here that all but the tallest buildings are often obscured by the horizon and that the amount changes between this comparison image, some of the other images above, and especially in the video - where you see it change right in front of your eyes.

In the middle image (which I believe was from 30 miles away in this case) you can see the lighted Spires clearly inverted over the top of the building.  and just as clearly, we can see that most of Chicago is hidden behind the horizon (due to curvature of the Earth).

Finally, here is a video with ~360 meters of Chicago gone missing:

Another objection raised is they think the buildings should be leaning WAY BACK or something.

Ok -- BASIC MATH here.  360° in a circle, 40075017m all the way around, 90933m to our target.

So 360 * (90933 / 40075017) ~ 0.8°

How are you going to detect less than 1° lean at 90km when you can't even make out any details in the HUGE buildings and they are all blurry and wavy and distorted from refraction?  You've compressed an ENTIRE CITY BLOCK of width down to a dozen pixels but think you can detect a 0.8° difference that is AWAY from you.  Utterly imperceptible.

No excuse for this one, someone is grasping at straws.


  1. Excellent presentation. I did double check your math. No problems there, right on the money.
    I work in land surveying and cartography.

    1. Thank you sir. Always good to have more eyes on the math!

      Another good video from Joshua Nowicki I just saw is:

      at 0:32 you can see some amazing Fata Morganas

  2. This is stupid, as usual people disregard atmospheric density. There is no "mirage" its just dense air. Because of buoyancy, low altitude air is much more dense. You can see an air gradient even in your photo. The white line of air followed by a light blue batch of air which blocks the lower half of the sky line. At no point does the skyline "magically bend back to the observer". If that was true we would see those light bends in all 3 dimensions including in crepuscular rays that travel 100s of miles through air and horizontally when we can see 100s of miles of horizon there isn't any bend of light at all.

    1. I see that, true to Flat Earther form, you have ignored everything written which DOSES talk about refraction and shows VERY CLEARLY where there are OBVIOUS mirage effects in the images.

      And you ignored the video which CLEARLY shows how extreme the mirage & refraction effects developed over time.

      DENSITY changes is what CAUSES refraction (which is what causes mirage effects).

      And no you would NOT expect to see nearly the same effects side-to-side because the density gradient which is what causes changes in the refractive index is caused MAINLY by pressure & temperature gradients WHICH ARE MOSTLY VERTICAL AND NOT HORIZONTAL GRADIENTS.

      So yes -- "THIS" being YOUR POST is stupid, as usual.

  3. what you see you get - you can see the buildings with you eyes on a clear day when they should be out of sight down the curvature. The Earth is Flat.

    1. The first video debunks your claim because we see the HUGE fluctuations caused by atmospheric refraction: and we can NEVER see the bottom few hundred meters of the city. The view matches what is expected on a Globe. Nice try at gaslighting and using assertion fallacies however.

    2. This comment has been removed by the author.

    3. This comment has been removed by the author......LMFAO
      gee I wonder why?

  4. It is amazing how people try to have their own facts. As a geographer and cartographer I am absolutely dumbfounded by flat earther's assertions on the subject. Willful ignorance at its best.

    Good work, Dark Star ;)

    1. Hey thanks! You wouldn't know anything about working with/converting NAD 83 XYZ coordinates would you? E.g., I have XYZ data for DP0739, BJ1342, & AA5493 and I want to plot them out in 3D.

      Are they strictly Cartesian coordinates (if so, where is 0,0,0?)

      BJ1342 NAD 83(2011) X - -10,884.151 so X=0 must be pretty close to there

      Or just need a good reference link :)

  5. This comment has been removed by a blog administrator.


    1. Your link is dead and your argument is invalid.

    2. I didn't make anything 'rise' -- you ignored observer height like a typical lying Flat Earther.

  7. Thanks for the research. I'm trying to wrap my head around this. So based on your refraction formula, a 20% refraction should still hide 364m of the Chicago skyline. Is that correct? Just curious because Josh's original photo seems to show much more than 20% refraction would allow. Help me out though, I'm just trying to understand the math for myself. How much refraction is possible under regular atmospheric conditions?

  8. Thanks for the research. I'm trying to wrap my head around this. So based on your refraction formula, a 20% refraction should still hide 364m of the Chicago skyline. Is that correct? Just curious because Josh's original photo seems to show much more than 20% refraction would allow. Help me out though, I'm just trying to understand the math for myself. How much refraction is possible under regular atmospheric conditions?

    1. You'll need to be more specific -- exactly which image, how many pixels, did you account for the obvious and clear distortion I pointed out, etc?

    2. As to 'how much refraction is possible' -- greater than 100% is possible but not likely that extreme over that distance. But I showed in the video analysis how much the refraction changes with the side-by-side.

  9. These are just mathematical formulas and nothing to do with reality. All mathematical formulas are derived to match with the results that one is looking for. And the base of these formulas are based on wrong hypothesis that earth is a globe so it all false.

    1. Math is just PRECISE wording about what you are saying. This is used to build a MODEL against which we can test if reality matches model A or does NOT match model A. If your model is FALSIFIED by the evidence against it then you can discard it.

      The 'Flat Earth' model is 100% falsified by the observations. Flat Earth is a very simple model so it is very easy to describe -- unfortunately (for you) the observations conclusively disprove the Flat Earth model.

      But your Flat Earth tears are much appreciated.


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