Wednesday, July 12, 2017

Robert Carter: A direct test of the flat earth model: flight times

More data supporting a spherical earth

Published: 6 December 2016 (GMT+10)
Flat Earth Society, with annotations by RC
flat-earth
Figure 1: “Flat earth” map obtained from the Flat Earth Society website. The locations of the cities used in this study are marked (blue dots), as are the straight-line distances from Johannesburg to each city (red lines). I also added a black flag at the approximate position of the north pole. Originally, the city locations were marked in pen on a printed copy of this map, using various geographic hints from the map itself, but the data are recreated here for the sake of the reader.
After receiving such a surprising number of negative comments on our flat-earth rebuttal, I decided to perform a numerical analysis of the flat-earth model compared to the traditional spherical-earth model.
Science is about testing hypotheses, so let us set up an experiment to test these alternative views. For this, I enlisted the help of two of my children, ages 13 and 11. It made for a fun homeschool project.
The basic problem is the distance between longitude lines in the flat-earth model. In a spherical earth, the longitude lines start from one pole and converge on the other pole, and the distances get wider the closer they are to the equator. But in the northern-hemisphere–biased flat-earth model, the longitude lines start from the north pole and radiate outwards to the supposed ‘encircling southern polar ring’ like spokes on a wheel.
This means that the distances become greater the further south they go. This suggests an easy test of the two models: compare distances to travel times for distant places in the southern hemisphere.
The normalized data revealed a tight correlation between the spherical earth model and flight time.
The goal of this simple study was to compare reported airline flight time data with two distance measures, the ‘great circle’ distance of spherical-earth theory and the ‘straight-line’ distance of flat-earth theory.
The driving hypothesis is that the flat-earth map is distorted and so the flight times will not match the calculated distances. This, of course, assumes there is no great conspiracy among the millions of people working for the airline industry or the tens of millions of people who fly on their airplanes annually, which seems reasonable. I am also assuming airplanes on a flat earth would use the rule we all learned in geometry that ‘the shortest distance between any two points on a [standard, Euclidean] plane is a straight line’.
This assumption was in favor of the flat earth model for, as we will see, any curved line would only exacerbate the noticeable distortion with increasing flight time and distance from the source.
Flat_Earth_Figure_2
Figure 2: Measured string length vs. great circle distances.
First, I obtained a map from the Flat Earth Society website (figure 1). With the help of one of my daughters, we located a suitable city that had many non-stop flights to different cities on other continents. In this case, we chose Johannesburg, South Africa.
We then looked up flights from this city and chose representative destinations on every continent (table 1). After carefully marking the city locations on a printed copy of the map, we painstakingly measured the distances between the cities using a ruler, to the nearest millimeter.
Table 1: Flight data from Johannesburg. Flight times and (great circle) distances were obtained from various online databases and calculators. Physical distances were measured on a globe using a taut string (to the nearest half-cm) and on the flat-earth map using a ruler (to the nearest mm). The globe was approximately 42 cm in diameter. The map was printed to the extents of an 8 ½ x 11 in. sheet of paper. Negative latitudes are south of the equator. Negative longitudes are west of the Prime Meridian.
CityAirport
Code
LatitudeLongitudeFlight Time
(hrs)
Distance
(km)
Measured Distances
String (cm)Flat (cm)
JohannesburgJNB-26.13428.242--------
AntananarivoTNR-18.79747.4793.22,1566.53.2
MahéSEZ-4.67455.5224.93,75212.04.2
DubaiDXB25.25355.3648.16,38920.54.9
DakarDKR14.740-17.4908.56,70521.55.6
Tel AvivTLV32.01134.8879.16,47320.54.4
PerthPER-31.940115.9679.28,32626.012.4
IstanbulIST40.97628.8149.57,43024.55.0
São PauloGRU-23.382-46.4699.87,45123.59.9
MadridMAD40.494-3.56710.38,07726.05.7
SingaporeSIN1.359103.98910.48,66127.59.7
FrankfurtFRA50.0338.57110.88,65827.55.9
ZurichZRH47.4658.54910.88,38727.55.6
AmsterdamAMS52.3094.76411.18,98629.06.1
LondonLGW51.148-0.19011.39,00429.06.2
SydneySYD-33.946151.17711.811,04435.015.8
Hong KongHKG22.309113.91512.810,67234.59.8
BeijingPEK40.067116.60014.111,69937.59.5
New YorkJFK40.640-73.77915.812,82441.09.9
AtlantaATL33.637-84.42816.413,58144.010.6
Next, with the help of my son, we went to the local library because we knew they had a medium-sized globe (approximately 42 cm diameter). We could have simply used the great-circle calculations from table 1, but I felt it was more fair to use my own measurements since I was manually measuring the flat-earth distances. Plus the more error we added, the more difficult it would be to conclude one method was less accurate than the other. It was highly likely that my rudimentary string-on-a-globe method would be wildly inaccurate.
Taking a string, he held the end on Johannesburg while I attempted to make a great-circle to each city. Together, we measured the length of the string from the end to the point where I had pinched it, to the nearest half-cm. This level of precision was chosen so that it did not exceed that of the flat-earth measurements. I wanted to make sure there was a higher level of precision in the theory I do not support. I did not expect much success, and was surprised after I plotted the distances obtained from my string method vs. the great circle distances in table 1 and obtained a line of best fit with an R2 (correlation coefficient) greater than 0.99 (figure 2). According to the string lengths, the scale of the globe was about 313 km/cm.
Flat_Earth_Figure_3
Figure 3: Reported great circle distances vs. reported flight times.
The final step was to compare the spherical-earth and flat-earth distances with flight times. First, I graphed the great circle flight distances vs. the flight times I obtained from the internet. Given that we are dealing with different airlines, airplane models, airport approaches, and taxiing times, I expected to see more variability in the data. However, a straight-line approximation was obtained, with an R2 greater than 0.97 (figure 3).
This set a high standard for the flat-earth model to meet. The average speed (the slope of the line of best fit) was 871 km/hr, which is a good approximation of the average speed of a modern airliner. The modern long-distance commercial airplane is designed to cruise efficiently at around mach 0.8, with speeds depending on altitude, airplane type, and the speed of local air traffic. Thus, the reported great circle distances are an excellent estimation of the expected flight time. This is another high bar for the flat-earth theory to hurdle.
The next step was to add a comparison of flight speed vs. distance in the flat-earth model, but the data are not in the same units. In fact I had three different units with which to contend: km/hr, cm/hr on the globe, and cm/hr on the flat map. Yet, the solution to this dilemma is simple. The measured distances had to be normalized by dividing by the shortest distance in each dataset.
Flat_Earth_Figure_4
Figure 4: Normalized distance data vs. reported flight times. The line of best fit is given for the string-length data and the flat-earth data. The string-length data are slightly below the corresponding great circle data, indicating that the shortest string-distance measurement was slightly off (+0.5 cm). Note the highly significant correlation between the string-length data and reported flight times (R2 = 0.9762). Note also the lack of correlation between the flat-earth distance data and flight time (R2 = 0.3388). The cities that were farthest off the line in the flat-earth model are the cities with the greatest longitudinal (spherical earth model) difference from Johannesburg.
The normalized data revealed a tight correlation between the spherical earth model and flight time, but no apparent correlation was seen between the flat-earth model and flight time (figure 4). The flat-earth data are so bad that no additional statistical measures were warranted. There is simply no correlation, and the data points that are closest to being true are also the ones closest to the same longitude (i.e. the distances are not distorted by the flattening of the truly spherical earth onto the flat projection).
One might think that, since the normalized flat-earth data are generally below the others in figure 4, that the distances between these cities are shorter in the flat-earth model. However, the normalization process is entirely dependent on the shortest measured distance (in this case, Johannesburg to Antananarivo) and any distortion within the map projection will affect all data points. Since Madagascar is due east of southern Africa, and since both are at a relatively high latitude, the flat-earth projection artificially inflates the true distance.
In other words, the flat map is distorting the true distances in a predictable manner.
Comparing the normalized flat-earth distance data to the city list in table 1 demonstrates that the cites with the greatest deviation from expected are the ones that are the farthest east and west of Johannesburg, namely Sydney, Perth, São Paulo, Singapore, and Hong Kong, in decreasing order.
Also, for any group of cities that are more or less along the same straight line from Johannesburg, the closer cities display less error than the farther ones. This is yet another example of the unreality of the flat-earth projection.
One additional measure is the string-length/flat-earth distance ratio. This will tell you proportionally how far apart the two distance measures are and it varies from 2.03 (Antananarivo) to 4.91 (Zurich). In this case, the ratio is highest for the cities in Europe and other places directly above southern Africa on the map, and lowest for cities farthest to the left and right. In fact, the angles of the lines in figure 1 are a direct estimate of this ratio. In other words, the flat map is distorting the true distances in a predictable manner.

Looking out the window

Unless we think all the flight times are wrong and the thousands of passengers are also lying about them, planes would have to be supersonic and have much greater fuel capacity than they do to make many of these routes. Also, the geography of the great circle routes on a global earth is very different from that of the straight-line routes on a flat disk. Passengers on multiple different flights would report seeing very different things out the window if the earth was flat.
For example, passengers on the Johannesburg to Sydney flight have fairly monotonous scenery for nearly the entire trip: the southern Indian Ocean. On a flat earth, the flight would go over the Himalayas (which would be hard to miss!) and other land.
Great Circle Mapper © 1996-2016 Karl L. Swartz, gcmap.com
Flat_Earth_Figure_5
Figure 5: The great circle route from Johannesburg to Sydney crosses the southern Indian Ocean, as reported by many eyewitnesses who have flown this route. It does NOT cross the Himalayas as it would in the flat-earth model (figure 1). 

Conclusions

I have set up a simple experiment to test two alternative models of reality. The spherical-earth model came through unscathed. The flat-earth model simply fails to reflect reality. I even made simplifying assumptions in favor of the flat-earth.
Anyone reading this has but two choices: either accept this experimental evidence or reject the reported flight times. However, if you are toying with the latter, please consider that these are backed up by the personal experiences of millions of people and the economic needs of billion-dollar companies in a cut-throat industry where the smallest profit margin might make or break a company.
If you conclude that the flight time data are inaccurate (and they have to be very much so), you are rejecting the type of data upon which your entire society is based. You could not use a computer, drive a car, or read this internet article if this logic upon which this study is based is not real.
If you still want to retreat into the flat-earth position, you are neither siding with the near-unanimous conclusions of 2,000 years of Christian scholarship, the biblical text when properly placed in its grammatical and historical perspective, abundant and simple experimental science, or logic.
Thus, you have not a leg to stand on. Please consider your answer carefully! Also consider that I have not just thrown up a list of facts that supposedly support my own pet theory. I took a lot of time to actually analyze real data. Have you ever seen a flat-earth document that even attempted this level of analysis? No, I didn’t think so.

Related Articles

Further Reading

SEDITION: U.S. Intelligence Community Conducting Soft Coup in Washington, D.C.

Deep State will not stop their stealthy
Purple Revolution until Trump is gone

C.I.A. using Mainstream Media to run propaganda campaign against Trump administration—24/7

“The C.I.A. always softens up the citizenry of a targeted country before a soft coup.  If that doesn’t work, they simply execute a covert but violent overthrow via assassination like they did with JFK.  Lastly, they will resort to an outright attack on the key organs of government authority and/or military power, but only when absolutely necessary.”

— Veteran Intelligence Analyst

Do you get it yet?

The NWO globalist entity known as Deep State, along with the Democratic Party, will — under no conditions — accept Donald Trump as the legitimate POTUS.  For that matter, neither will the many turncoat RINOs within the Republican Party.  You can add to this list of traitors most of the sultans of Silicon Valley, Hollywood moguls and actors, East Coast intelligentsia and Mainstream Media magnates.
Because of this unrelenting predicament, there’s no stopping the USS Donald Trump from hitting the Deep State iceberg.  By the way, no one said that Trump is at the helm of a 21st century Titanic.  He may just be the captain of a humongous icebreaker.   Only time will tell, however, and that time is fast approaching.
KEY POINT: Destiny cannot be thwarted when it is preordained in such a profound and fundamental way as it is right now for the United States of America.  Not only is the continuity of the American Republic at stake, the future of the planetary civilization hangs in the balance.  In other words the final outcome of “Trump versus Deep State” will ultimately determine the fate of humanity as it will for the world community of nations.

RUSSIA SCARE: C.I.A. Running PsyOp on the American People

For the uninitiated, ever since Election Day on November 8, 2016, The Company (aka the C.I.A.) has been very busy implementing “Plan B”, often referred to as the Purple Revolution.  Understanding the true purpose and key players behind this highly organized plot is crucial if it to be averted.  As follows: BEWARE: The Purple Revolution Comes To America…
This seditious revolution has several pillars that define both its strategy and MO (see the preceding graphic).  The whole world has been watching daily the “Russia scare” strategy— one of the main pillars.  Deep State knows that the Russian boogeyman was effective during the Cold War so why should they reinvent the wheel?
The following exposé details some of the subterfuge by Deep State and their agents within the Democratic Party which gave rise to the bogus “Russian hacking claim”.  In the face of so much MSM fake news about Russia, who will now believe the obvious truth in this post? CONFIRMED: DNC paid the ‘Russian’ founder of CrowdStrike to hack its server so it could be blamed on Russia!

C.I.A. and MSM: Fric & Frac of Deep State

Truly, no one has ever seen anything like it.  The C.I.A. uses their primary organs of propaganda — CNN, NBC, ABC and CBS — to run an unprecedented propaganda war against a sitting POTUS.  Likewise, the spook agency uses every major newspaper of record — especially The New York Times, The Washington Post, USA Today, and Los Angeles Times — to float patently false accusations and deliberately misleading headlines on their front pages.
KEY POINT: Even Nixon was not subjected to such a daily barrage of fake
news during the height of Watergate.  And, “Yes!”, much of that media hysteria
was also contrived fake news, produced to facilitate his premeditated removal
which was in actuality a soft coup.
The CIA knows full well how to execute a color revolution.  They’ve conducted many around the globe over several decades.  Their trademark MO is to sufficiently frighten the citizenry about ‘dangers’ associated with their current government and/or head of state.   This is why the American people are now treated to a nonstop campaign of Trump-bashing by the MSM.  The CIA is aware that eventually a critical mass of citizens will actively support an overthrow. And that those who don’t show up will at least lend their moral support to it.
The false story about ‘Russia election hacking’, of course, was the perfect pretext for the U.S. Intelligence Community to rally around.  Agents in all 17 agencies could be compelled to go with the flow — seditious flow — because the POTUS was said to be working with America’s historical enemy — R U S S I A!  Throw in a Democratic Party that is still beside itself with rage and madness about Hillary’s defeat and you have a full-blown Purple Revolution in the works. See the following link for valuable perspective: Former Democrat Insider Goes Rogue—Exposes Plot To Falsely Blame Russia
This transparent scam being run on the American people is not unprecedented.  Both World Wars of the last century saw similar inflammatory propaganda being thrown about here, there, and everywhere.  That’s just how it’s always done.  They did it against Germany prior to World War II after they demonized the Kaiser prior to World War I.
The salient point here is that it’s now Putin who is being vilified and Russia that is being represented as the mortal enemy of the West.  Nothing could be further from the truth, and yet a vast majority of Americans still believe the lies. Whenever a really big lie is repeated frequently, it starts to sink in.  That’s what CNN and NBC are all about today.  So are the NYT and WaPo.  Their CIA masters in Deep State know all of the best mind-control programs, as well as the magic formulas for effective war propaganda. Massive Conspiracy to Deceive the American People Exposed

The MSM and C.I.A. are guilty of sedition

There’s one major advantage that the President has at this pivotal stage of the Purple Revolution. The MSM now commits sedition on a weekly basis.  The C.I.A. likewise openly perpetrates treason against the nation.  These traitors to the American Republic expose themselves regularly because they think they can act with impunity.  This public display of arrogance and hubris has never happened before in the USA.
As a consequence, the MSM can legally be shut down with one executive order.  The C.I.A. can be dissolved with one stroke of the presidential pen.  Even the FCC can close down various MSM organs of propaganda for blatantly violating various rules and regulations. The law is squarely on the side of the FCC in this regard.
Hence, the longer that Trump permits the traitors to out themselves for all to see, the more of them he can get rid of when the time is right.  That moment is fast approaching as Deep State is getting closer to pressing the button on stage 2 of the 2017 revolution.  Their implementation plan has been designed according to a set schedule which sees this Fall as a crucial phase of the Purple Revolution.
What began with a clandestine partnership between George Soros and Hillary Clinton back in 2016 has evolved into a full-blown conspiracy to bring down the U.S. Federal Government under President Trump.  Clearly the growing insurrection against Trump has many ultra-liberal groups and faux progressives, far left-wingers and brainwashed Democrats, among them.  However, it’s the hardcore Obamabots, Clintonistas and Berniacs who are the most dangerous.  Rep. Steve Scalise found that out the hard way.
As always, George Soros is front and center in this treasonous plot.  Therefore, at the very least, he should be arrested post-haste for sponsoring seditious activity which has resulted in so much personal injury (including numerous deaths) and property damage.  One need look no further than the European Union to view the societal mayhem that Soros & Company has purposefully wrought.  Now they’re hellbent on doing it here in the USA. The Clintons And Soros Launch America’s Purple Revolution

Special Note:
The violent coup executed by the C.I.A. (and facilitated by the U.S. Department of State) in Kiev during February of 2014 is quite instructive.  Even President Putin was caught flat-footed while the Maidan Nezalezhnosti was turned into a war zone overnight.  That takeover was also preceded by a massive propaganda campaign aimed directly at Ukrainian President Viktor Yanukovych.  The country was split in two just like America is today.  With each passing day of naked lies and misrepresentations circulated by the MSM, enough insurgents eventually showed up at the city’s main square to effectuate a full-blown coup d’état.  Yes, it was deliberately staged while Putin was preoccupied with the Sochi Winter Olympics, but both he and Yanukovych were completely blindsided by the swiftness and severity of the manufactured violence.  Team Trump ought to be paying very close attention from this point forward as there are several plans afoot to depose the POTUS.  These are operating on parallel tracks, some of which are decoys and distractions. Then there are those covert operations which are mutually supporting each other in the event of a full-scale Purple Revolution.

Even Tim Kaine’s wife (far right) was dressed in purple during Clinton’s inflammatory concession speech that was actually a veiled call to insurrection.

Conclusion

Where is this all going?
God only knows.
If the American people do not demand an end to the violence and lawbreaking, the Bolshevik perps will only become more emboldened.  These Obama-led and Soros-backed agitators will eventually intensify their insurgency nationwide.  They will surely increase the number of rioters and protesters — from the ranks of so many disillusioned illegal aliens — who are quite willing to disrupt civil society.
The Bolshevik Left now demonstrates an unparalleled willingness to harm people and destroy property never seen within the body politic.  Their use of agents provocateur has become obvious to even the most naive and uninformed.  Hence, President Trump is completely within his power to immediately prosecute all of those culpable agents of Deep State.
These subversive mercenaries are all cut from the same RED bolt of cloth as those who incited and carried out the Bolshevik Revolution.  In fact, the Left is becoming more vicious and violent by the event.  Just as their ilk terrorized the major cities throughout Russia in 1917, they use the same brutal tactics in 2017 across the USA.
One thing is for sure: the C.I.A. will not stop this uprising until Trump is frogmarched out of the White House.  The question then remains: What will the patriots and nationalists do to prevent that from happening?
State of the NationJuly 11, 2017