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### Messages - CriticalThinker

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121
##### Flat Earth Theory / Re: Using airline flight data.
« on: August 26, 2017, 05:43:14 PM »
Tau,

Furthermore, would the effects of Aether be mathematically reducible to 0 in the event that fight times and speeds were repeatable on different dates within the aforementioned margins of error?  As an example, if Speed = (Distance/Time) +/- acceleration due to Aether (A) we could postulate that the distance is a known value within a confidence interval provided that speeds and times were repeated.

On shorter distance flights within a single continent, distance is a known value measured by physical measuring devices that do not rely on a globed earth assumption so we could take 2 different non stop flights between cities within say Australia on different dates and solve for the variable Aether as such: +/- A = (Speed*Time)/Distance.  This would create both an upper and lower bound for margin of error due to the variable Aetherial Wind.

Would this be an acceptable methodology of accounting for the missing variable in my first series of equations?

Thank You

CriticalThinker

I would caution you against assuming that measuring devices like sonar and radar don't take the Earth's shape into account. These devices need to be calibrated, after all. If one calibrates them with the assumption that the Earth is round, but using data from a flat Earth, then one has effectively created a device which converts flat Earth data into round Earth data.

Tau,

You are very correct in your caution.  Doppler shift radar was specifically chosen because it does not assume a globed earth.  Electromagnetic waves at a known frequency are sent straight forwards from the device and some of them will be bounced back by the target.  The time difference between the echo of each successive wave is compared to the previous one which provides the variable distance traveled which is then divided by the constant time intervals created by the frequency of the wave.  Distance divided by time provides us with the data point speed.  They are calibrated using a metered track and stopwatch.  Before being employed by police and researchers, their accuracy/repeatability on a flat plane is measured against these flat earth compatible systems of measurement and only units capable of staying within a 1% margin of error are used.

This was covered in my very first post on this thread, along with a peer reviewed article that substantiates its accuracy and validity in measuring flight speed relative to ground speed.

I still have many unanswered questions re: Aether, that I hope you will find the time and inclination to answer.  In order for me to fully understand your philosophical world view, these are details which are very important.

Thank you,

Critical Thinker

122
##### Flat Earth Theory / Re: Using airline flight data.
« on: August 26, 2017, 05:15:41 PM »
Tau,

Furthermore, would the effects of Aether be mathematically reducible to 0 in the event that fight times and speeds were repeatable on different dates within the aforementioned margins of error?  As an example, if Speed = (Distance/Time) +/- acceleration due to Aether (A) we could postulate that the distance is a known value within a confidence interval provided that speeds and times were repeated.

On shorter distance flights within a single continent, distance is a known value measured by physical measuring devices that do not rely on a globed earth assumption so we could take 2 different non stop flights between cities within say Australia on different dates and solve for the variable Aether as such: +/- A = (Speed*Time)/Distance.  This would create both an upper and lower bound for margin of error due to the variable Aetherial Wind.

Would this be an acceptable methodology of accounting for the missing variable in my first series of equations?

Thank You

CriticalThinker

123
##### Flat Earth Theory / Re: Using airline flight data.
« on: August 26, 2017, 04:49:42 PM »

Certainly. In order to do so, I will need several millions dollars of funding and 4-8 years of engineering school. Should I start a GoFundMe?

Am I to understand then that no such instrument currently exists to prove the existence or effect of Aether on the physical world?  If so, I find that highly convenient to you and it leaves me at a distinct disadvantage.  I was required to prove the existence of devices that accurately measured the variables in question.  You're claiming the existence of another variable that I haven't taken into consideration, however, if it can't be measured, how can you provide evidence of its existence?

I'm not sure I understand what you mean. The speed of travel between Paris and New York would be affected by the Whirlpool similarly to how it is affected by the Jet Stream. Unless you mean latitudinally?

I am sorry for any confusion or miscommunication.  I will separate my question into smaller more well defined questions.
1. Is the Aether a constant or variable force?  (Like gravity vs wind)
2. Does Aether uniformly affect the world like your whirlpool example would affect my whole body and everything else in at the same time?
3. Using your whirlpool example as a size analogy, would there be a significant difference on the effects of aether between two very close points relative to the whole pool?  (If my body is representative of a flat earth, would the water in the whirlpool have a significantly different impact on two different fingers on the same hand?)

Thank you,

CriticalThinker

124
##### Flat Earth Theory / Re: Using airline flight data.
« on: August 26, 2017, 04:22:15 PM »
You sure about that? The GPS in my car likes to tell me I'm 400 feet from where I am and going in the opposite direction

http://www.gps.gov/technical/ps/2008-SPS-performance-standard.pdf

http://www.gps.gov/systems/gps/performance/accuracy/

They actually say that "the government commits to broadcasting the GPS signal in space with a global average user range error (URE) of ≤7.8 m (25.6 ft.), with 95% probability. Actual performance exceeds the specification. On May 11, 2016, the global average URE was ≤0.715 m (2.3 ft.), 95% of the time."

And..."GPS-enabled smartphones are typically accurate to within a 4.9 m (16 ft.) radius under open sky (VIEW SOURCE AT ION.ORG). However, their accuracy worsens near buildings, bridges, and trees."

So if you happen to be under heavy tree coverage (especially if it's been raining) - or inside a parking garage - then your position can be quite a bit off.   But when driving around in "normal" situations (and especially in an airplane) - these large errors should be brief.

As for the "facing the wrong direction" thing...here there is a misunderstanding.   GPS DOESN'T tell you which way your facing.   Navigation systems that use GPS do one of two things:

* Modern ones include a digital compass.
* Older ones rely on deducing your direction when you start moving - so they take positions every second or two and presume that you're facing in the direction you're moving.

Cellphone digital compasses have a hard time when you turn the phone upside down or sideways - and may need to be "recalibrated" once in a while (I know mine does)...but the digital compasses in cars generally don't get that kind of abuse.

So I'm not surprised you're seeing direction errors - that's not GPS.

But a 400' error is a hell of a lot.  I doubt you're seeing that when driving along an open road someplace.

Check out that second link I sent you - read the bit about "Why does GPS sometimes show me in the wrong place?"

You should get around 10' precision most of the time.

Hasn't been my experience. Maybe the people who wrote those documents are trying to sell you something?

This triangle etc. thing has beed discussed before with no response from TB.

You people are obsessed

I am obsessed with following the rules of the scientific method and adhering to polite standards of logical debate, thank you for noticing.

I believe that we keep bringing back up the point of geometry because it proves that the surface of the earth can't be planar through mathematics.  Tom has attempted to steer the attention away from this by using GPS accuracy as a red herring and so far refuses to debate on the rest of the proofs provided.

To briefly summarize my first post.

I established that:

1. That airline flight times are measured accurately with standardized timepieces that do not assume a globed or flat earth.
2. That flight speed can be measured accurately relative to ground speed using Doppler shift radar which also does not assume a globed or flat earth.
3. That speed is defined as Distance/Time and therefore using flight times and speeds we could algebraically solve for distance in under a 5% margin of error without assuming a flat or globed earth.
4. That the distances between the 4 cities used in the initial geometry proof are valid as aircraft speeds are tracked by both GPS and Radar which fits the initial stipulation that all data points had to be valid without the assumption of latitude and longitude accuracy.

Doppler shift radar is accurate within 1% margin of error in measuring flight speed over both short and long distance.

At this point, unless there is a way to disprove the existence of time, distance or speed then we have met all of Tom Bishop's demands and would like him to address it fully.  It is geometrically impossible for the earth to be flat.  It must be either concave or convex and based on my casual observance, it's not concave.

GPS accuracy, quite frankly, doesn't matter in this proof.  It doesn't invalidate the other device used to track flight speed.

Tom, Tsunami and any other flat earth believers are welcomed and encouraged to engage me in any portion of my hypothesis and research other than GPS accuracy.  I have politely and faithfully met all of the other demands placed upon this proof.  It is mathematically impossible for the earth to be flat.

Thank you,

CriticalThinker

Dear CriticalThinker,

Thank you for your kind response. I'd be happy to address your initial points if you'd like.

Imagine, if you will, a great whirlpool. This whirlpool has a diameter the same as, or perhaps even larger than, that of the our Plane. Within this whirlpool float the Sun, Moon, Stars, and Planets (alongside other cosmic phenomena). Now, such a large whirlpool does not work as simply as the one in your sink. You can think of it more like the storms and layers of Jupiter. At various places along its width, it can be faster or slower and even change direction. All of this stems from the unique properties of aether and the fact that the Earth is spinning relative to the whirlwind.

Now, imagine (for the sake of analogy) that you are a scuba diver deep beneath Charybdis. You would feel the pulling and pushing of the monstrous whirlpool above you, no matter how deep you went, correct? Similarly, on Earth we feel a shadow of the aethric whirlpool. In effect this works similarly to the theorized jet stream of RET, except that depending on one's position it can provide acceleration in either direction. This is what you fail to account for in your calculations.

Sincerely,
Tau

Tau,

Thank you for at least responding, I thought that perhaps I was being ignored by Tom other flat earth believers.

Please provide a standardized instrument capable of measuring Aether within a 5% margin of error so that I can account for it in my calculations. Based on the repeatability standards of the scientific method, I will accept any split half or repeated experiment published within the outer bounds of my own provided proofs which would be 1967.  I constrained myself to only studies after the establishment of a reliable methodology of measurement.

Based on your description, am I to assume that Aether is a constant, much like gravity or variable like casual wind?  If this whirlpool of Aether is so massive as to contain all of the stars, planets, moons etc, please explain how a short distance like that between Paris and New York can be dramatically impacted by it.  Imagine if you will, your underwater example.  If everything in the great whirlpool is impacted by it, would there be a statistically significant difference in the effects of the Aether on my right middle finger and right pinky finger?  The relative distances are similar to the ones that you are contesting in my calculations.

Thank you,

CriticalThinker

125
##### Flat Earth Theory / Re: Using airline flight data.
« on: August 26, 2017, 03:48:09 PM »
You sure about that? The GPS in my car likes to tell me I'm 400 feet from where I am and going in the opposite direction

http://www.gps.gov/technical/ps/2008-SPS-performance-standard.pdf

http://www.gps.gov/systems/gps/performance/accuracy/

They actually say that "the government commits to broadcasting the GPS signal in space with a global average user range error (URE) of ≤7.8 m (25.6 ft.), with 95% probability. Actual performance exceeds the specification. On May 11, 2016, the global average URE was ≤0.715 m (2.3 ft.), 95% of the time."

And..."GPS-enabled smartphones are typically accurate to within a 4.9 m (16 ft.) radius under open sky (VIEW SOURCE AT ION.ORG). However, their accuracy worsens near buildings, bridges, and trees."

So if you happen to be under heavy tree coverage (especially if it's been raining) - or inside a parking garage - then your position can be quite a bit off.   But when driving around in "normal" situations (and especially in an airplane) - these large errors should be brief.

As for the "facing the wrong direction" thing...here there is a misunderstanding.   GPS DOESN'T tell you which way your facing.   Navigation systems that use GPS do one of two things:

* Modern ones include a digital compass.
* Older ones rely on deducing your direction when you start moving - so they take positions every second or two and presume that you're facing in the direction you're moving.

Cellphone digital compasses have a hard time when you turn the phone upside down or sideways - and may need to be "recalibrated" once in a while (I know mine does)...but the digital compasses in cars generally don't get that kind of abuse.

So I'm not surprised you're seeing direction errors - that's not GPS.

But a 400' error is a hell of a lot.  I doubt you're seeing that when driving along an open road someplace.

Check out that second link I sent you - read the bit about "Why does GPS sometimes show me in the wrong place?"

You should get around 10' precision most of the time.

Hasn't been my experience. Maybe the people who wrote those documents are trying to sell you something?

This triangle etc. thing has beed discussed before with no response from TB.

You people are obsessed

I am obsessed with following the rules of the scientific method and adhering to polite standards of logical debate, thank you for noticing.

I believe that we keep bringing back up the point of geometry because it proves that the surface of the earth can't be planar through mathematics.  Tom has attempted to steer the attention away from this by using GPS accuracy as a red herring and so far refuses to debate on the rest of the proofs provided.

To briefly summarize my first post.

I established that:

1. That airline flight times are measured accurately with standardized timepieces that do not assume a globed or flat earth.
2. That flight speed can be measured accurately relative to ground speed using Doppler shift radar which also does not assume a globed or flat earth.
3. That speed is defined as Distance/Time and therefore using flight times and speeds we could algebraically solve for distance in under a 5% margin of error without assuming a flat or globed earth.
4. That the distances between the 4 cities used in the initial geometry proof are valid as aircraft speeds are tracked by both GPS and Radar which fits the initial stipulation that all data points had to be valid without the assumption of latitude and longitude accuracy.

Doppler shift radar is accurate within 1% margin of error in measuring flight speed over both short and long distance.

At this point, unless there is a way to disprove the existence of time, distance or speed then we have met all of Tom Bishop's demands and would like him to address it fully.  It is geometrically impossible for the earth to be flat.  It must be either concave or convex and based on my casual observance, it's not concave.

GPS accuracy, quite frankly, doesn't matter in this proof.  It doesn't invalidate the other device used to track flight speed.

Tom, Tsunami and any other flat earth believers are welcomed and encouraged to engage me in any portion of my hypothesis and research other than GPS accuracy.  I have politely and faithfully met all of the other demands placed upon this proof.  It is mathematically impossible for the earth to be flat.

Thank you,

CriticalThinker

126
##### Flat Earth Theory / Re: Using airline flight data.
« on: August 25, 2017, 08:48:16 PM »
As stated earlier in this thread, GPS accuracy compared to Doppler shift radar is not a requirement of my initial proofs.  All of my conclusions regarding the algebraic solutions for distance and the geometry calculations presented earlier in this thread are substantiated by the speed measurements as obtained by Doppler radar technology which has a tested margin of error of <1%.

Thank You

CriticalThinker

Your flight values are based on GPS being accurate.

No they are not.  Commercial airlines have both types of instrumentation.  Flight speeds are tracked using Doppler shift radar in addition to GPS, so the flight speeds remain valid under your constraints of a flat earth compatible system of measurement.

Please discuss any of the other points of my initial hypothesis, assumptions or conclusions.  The accuracy of speed data is no longer a valid dismissal as it is obtained using a flat earth compatible measurement system simultaneously with GPS.

Thank You

CriticalThinker

127
##### Flat Earth Theory / Re: Using airline flight data.
« on: August 25, 2017, 08:42:20 PM »
What is silly is that you enter these "debates" with no real information. You have no map, you don't know distances, you have no idea how long a mile is, why even debate distance??? It is ridiculous.

On a Flat Earth a mile is 5280 feet as it has always been defined. However, GPS will be in error when attempting to measure out exactly 5280 feet, because GPS is not accurate. We have already seen that multiple devices gave out wildly different values for the runners on a small track.

As stated earlier in this thread, GPS accuracy compared to Doppler shift radar is not a requirement of my initial proofs.  All of my conclusions regarding the algebraic solutions for distance and the geometry calculations presented earlier in this thread are substantiated by the speed measurements as obtained by Doppler radar technology which has a tested margin of error of <1%.

Thank You

CriticalThinker

128
##### Flat Earth Theory / Re: Using airline flight data.
« on: August 25, 2017, 08:33:14 PM »
Straight line travel margins of error were reported specifically as 1.9% and it was a direct quote from the researchers.

They were assuming that it was a Round Earth Radar Test, as opposed to a Flat Earth Radar Test. They were comparing the Round Earth coordinate devices (GPS) to Radar Test values, without knowing which shape of the earth they were on. The distance of a mile would measure differently on a Flat Earth vs using a Round Earth lat/lon coordinate system.

Since the GPS values were giving a wide range of answers we do not know which one is the most accurate, or how accurate they were, if the radar test was done on a Flat Earth.

Tom, please propose an accurate measurement system that you will accept. You do nothing but call the systems being used inaccurate because they aren't flat Earther approved. The reason everything takes into account the curvature of the Earth is because it is freaking round. If the curvature amount was inaccurate, all those systems that rely on precision location data would fail.

The problem is that you expect us to take your Round Earth coordinate system as face value accurate truth. That would be silly of us. If we assume that Round Earth lat/lon is true then we might as well just assume that the earth is round.

My car GPS successfully takes me to a location, based on coordinates, without me needing to know how much distance I actually traveled, or if the lat/lon distance prediction was correct. I do not see why you believe that airplanes would be any different.

The Radar system of speed measurement does not rely upon a latitude and longitude coordinate system and as such remains a valid method of establishing speed as per my post above.

Thank you,

CriticalThinker

129
##### Flat Earth Theory / Re: Using airline flight data.
« on: August 25, 2017, 08:31:13 PM »
Straight line travel margins of error were reported specifically as 1.9% and it was a direct quote from the researchers.

They were assuming that it was a Round Earth Radar Test, as opposed to a Flat Earth Radar Test. They were comparing the Round Earth coordinate devices (GPS) to the Radar Test values, without knowing which shape of the earth they were on. The distance of a mile would measure differently on a Flat Earth vs using a Round Earth lat/lon coordinate system.

Since the GPS values were giving a wide range of answers we do not know which one is the most accurate, or how accurate they were, if the radar test was done on a Flat Earth.

But the radar still gives an accurate speed and that is what counts in this discussion.

If a mile is different under the two systems, and is dependant on how it is measured, that means mph is in error.

Am I correct in assuming that you are calling into question the existence of the variable distance or the physical measuring devices used to establish it?

In my previous post, I established that a standardized system of measuring distance on a flat plane is in existence.  The 2 systems of measurement Metric and Imperial are valid on a variety of surfaces both planar and curvilinear.  That has been a requirement for all variations on science and manufacturing for all of industrialized human history.

Thank You

CriticalThinker

130
##### Flat Earth Theory / Re: Using airline flight data.
« on: August 25, 2017, 08:26:20 PM »
Straight line travel margins of error were reported specifically as 1.9% and it was a direct quote from the researchers.

They were assuming that it was a Round Earth Radar Test, as opposed to a Flat Earth Radar Test. They were comparing the Round Earth coordinate devices (GPS) to the Radar Test values, without knowing which shape of the earth they were on. The distance of a mile would measure differently on a Flat Earth vs using a Round Earth lat/lon coordinate system.

Since the GPS values were giving a wide range of answers we do not know which one is the most accurate, or how accurate they were, if the radar test was done on a Flat Earth.

They were not assuming any shape of the earth during the radar controlled GPS validation.  They were testing a new method of measuring speed under specific conditions against a long established valid control.  They were specifically testing if GPS trackers were accurate enough to calculate metabolic expenditures of athletes in sports.  In the above cited article, radar was the control measurement device which we have already established does not assume a globed earth model.  Radar measures the Doppler shift effect and is <1% margin of error to a measured track and stopwatch.  Airline speed as measured by the Doppler shift effect is still a valid method of establishing air speed relative to ground speed as was established by the first article that I referenced.  That the GPS speeds and radar speeds reported by aircraft match is irrelevant to the proofs that I have supplied.  We could communally agree to ignore airline speed as measured by GPS altogether and the rest of my argument can still stand on its own because flights are also tracked by Doppler shift radar.

At this point you can either attempt to invalidate the Doppler shift effect using physics and mathematics to prove its inaccuracy or contest one of my 3 assumptions.  I have listed out my assumptions above and none of them require a globed earth.  I can hang my hat on the accuracy of echolocation for determining the strait line speed of an object in flight relative to its speed on the ground and my final conclusions are not invalidated.

131
##### Flat Earth Theory / Re: Using airline flight data.
« on: August 25, 2017, 08:00:09 PM »
Fully agree with TomInAustin, a great post! Well laid out thank you. Although since we haven't seen a word from Tom in about 10 days, and I don't know that I've ever seen Junker respond in a strongly constructive manner, I'm doubtful of too much happening. CriticalThinker, would you mind if I posted this to the old(?) site and linked to this thread? There appear to be much more FE believers over there. Or perhaps you would be up for reposting it over there as a new thread. The site is here by the way. I've heard it referred to as the old site by Junker I believe, but it appears to have a bit larger population than this one from what I've been seeing perusing it recently.

I was unaware of the old site, so please by all means link to my post.

Thank you

CriticalThinker

132
##### Flat Earth Theory / Re: Using airline flight data.
« on: August 25, 2017, 07:58:21 PM »
Tom,

I supplied the Radar to GPS comparison primarily to show consistency between a flat earth compatible speed measurement system and globed earth speed measurement system.  As I am in healthcare, I would be happy to cover why the researchers in the sports medicine article saw varying degrees of accuracy.  They specifically discuss it within the article as it becomes a significant limitation with respect to what physiological data points they were trying to interpolate.  GPS monitoring devices for fitness have difficulty in accurately tracking speed outside of straight line measurements due to low refresh rates.  As most team sports require rapid changes in direction during the course of play, the speed data wasn't collected at a frequent enough interval to account for the physical exertion required by players.  It resulted in lower calculated cardiovascular efforts than were applicable.  This phenomenon can easily be witnessed in sports like football, soccer and all hockey variations where players have to stop, pivot and resume travel in a new direction frequently.  In long distance strait line travel, the refresh rate does not make a high statistical impact as was specifically quoted by researchers in the article itself.  You may find reference to it in the analysis section of the article.  Straight line travel margins of error were reported specifically as 1.9% and it was a direct quote from the researchers.  In their conclusion, the stated that GPS monitoring devices were not yet accurate enough to use for calculating metabolic demands on athletes due to the rapid changes in direction experienced during the course of normal play.

As flight speeds are measured with Radar in addition to GPS, statistically significant differences in speed data would have to be reported to FAA administrators and hardware vendors because the planes would not be allowed to fly.  Radar speed measurements do not require any assumption of a globed earth, so my analysis and conclusions still stand.

Thank you,

CriticalThinker

133
##### Flat Earth Theory / Re: Using airline flight data.
« on: August 25, 2017, 02:00:26 PM »
I will apologize in advance for the length of this post.

When a friend of mine told me about the flat earth society, I was curious and I came across this forum earlier today.  As I have a solid foundation in both science and mathematics, this particular thread piqued my interest enough to register and create a login.

As this is a logic model statement, I will have to state all of my assumptions before coming to my conclusion and I will support each part of my argument.  I will do my best to meet the demands of Tom Bishop and others on this forum.  In cases where the methodology of measurement assumes a globe map, I will corroborate that system of measurement’s accuracy with an alternative measurement system that does not rely on a globed earth assumption.

If there is not a significant difference in margin of error between the two systems of measurement, then we can confidently state that the methodology that assumes a globed earth is still valid for the measurements provided due to the fact that they can be corroborated using an alternative methodology.  Based on the standards and practices of physical sciences, for the purposes of this discussion, an acceptable margin of error in any two given measurements is 5%.  This stays in line with the scientific method as it applies to Chemistry, Biology and Physics which have formed the basis of peer reviewed scientific literature.

Assumption 1: time exists and is measurable.  The 24 hour daily clock is standardized by the breakdown of the cesium 133 atom as defined in 1967.  This has been the accepted standardization of time ever since.  All modern timepieces are standardized based on this assumption and it is not dependent upon a globed earth assumption.

Assumption 2: Distance exists and is measurable.  Both Imperial and Metric systems have been standardized for the purposes of measuring distance since prior to 1967 so that is still our outer bound for both of these units of measurement in peer reviewed literature.

Assumption 3: Speed is defined as Distance/time: Velocity = Meters/second for metric and Velocity = Feet/second for Imperial.

Without violating any of the rules for algebraic logic if V=M/s then M=V*s & if V=F/s then F=V*s.  As the three variables are inextricably linked, we only need only to prove the observable existence of 2 of the 3 variables and then solve for the 3rd.  In our case, we will use time and speed to solve for distance.

As time is defined by the observable physical phenomenon that does not rely upon a globed earth and corroborated by the life experiences of each person involved in this discussion, we can safely say that all commonly accepted methods of measuring time in studies are valid for the purposes of solving for distance.

This then leaves a requirement to identify a non-globed earth method for measuring speed or velocity relative to the ground that corroborates a globed earth methodology within the acceptable margin of error.

To that end:  I provide support that speed of flight can be measured relative to ground speed through the use of Doppler shift radar meets the criteria of a non-globed earth system of measuring speed.

EVANS, T. R. AND DRICKAMER, L. C. (1994). Flight speeds of birds determined using Doppler radar. Wilson Bull. 206, 155–156

During the above referenced article, the accuracy and validity of using Doppler shift radar gun technology to measure the ground speed of birds in flight was established.  Radar units determine straight line speed of a target by measuring the Doppler shift of each successive set of the electromagnetic waves sent out from the device towards the target.  These units are calibrated for frequency using a tuning fork and calibrated for speed accuracy by using a measured track and stopwatch before being placed into service.  The researchers verified their individual units by performing the internal circuitry test and using a tuning fork to verify correct EM wave frequency.  The reported margin of error between the Doppler shift calculations of the device and the physical measurements used to calibrate them must be less than 1% for manufacturer release.  This meets our criteria for a standardized measurement of flight speed that does not rely upon an assumption of a globed earth model.

Next I provide peer reviewed literature that corroborates GPS speed measurement accuracy using radar for comparison.

Rampinini E, Alberti G, Fiorenza M, Riggio M, Sassi R, Borges TO, Coutts AJ. Accuracy of GPS devices for measuring high-intensity running in field-based team sports. Int J Sports Med 2015; 36: 49-53

During the above mentioned article researchers specifically tested the accuracy and validity of using GPS based equipment to measure ground speed of athletes.  The standard for comparison was a Doppler shift radar gun.  The straight line speed differences between the 2 systems of measurement did not exceed our established margin of error.  The margin of error between the 2 systems was 1.9%.

This means that within a series of a few steps, I was able to corroborate speed as measured with GPS technology to speed measured using a physically measured track and stopwatch, as well as a Doppler shift radar gun.  A measured straight line track and stopwatch are both mechanical measurements of distance and time respectively that do not assume a globed earth.  The Doppler shift radar gun does not assume a globed earth and both corroborate the speeds as measured by GPS.  There was a maximum margin of error of 2.9% (summation of maximum margins of error of both systems) which does not meet the criteria for dismissal of GPS as a speed measurement device.

Now I have provided supporting evidence that both the GPS and Radar speed measurements employed by airlines are within an acceptable margin of error to physical measurements of speed that do not rely on any globed earth assumptions.  This means that the calculated distances based on time and speed of non-stop flights between airports can be used to calculate distance using Distance = Speed * Time as stated earlier.

Conclusions:
1: Speed as measured by GPS devices falls within an acceptable margin of error to speed as measured by systems that do not rely upon a globed earth assumption (1.9%).
2: Speed as measured by Doppler shift radar instruments which does not assume a globed earth model is a viable method of determining flight speed relative to ground speed.
3: Modern aircraft employ both technologies for measuring speed and, as such, reported speeds of flights are accurate for both a globed and planar earth models.
4: Ground speed can be determined using flight speed as reported by aircraft speed measuring devices within an acceptable margin of error to actual ground speed (< 1%).
5: Airline flight times are recorded using a measurement system that remains congruent with both globed earth and flat earth models.  These flight times are corroborated independently by all passengers equipped with standardized timepieces.
6: Using the distances derived from data produced by speed measurement systems that remain consistent with or without the assumption of a globed earth, we can calculate a distance D between 2 cities using the measured flight speed S and time T in a D=S*T equation without violating any of the imposed stipulations as both S and T can be produced without globed earth assumptions.
7: The stated distances between cities for nonstop flights used in the examples provided by both 3dGeek and Inquisitive can be accepted as true distance +/- 2.9% margin of error (largest summation value of the aforementioned margin of error rates) based on corroborating evidence as obtained from flat earth congruent speed measurement systems and algebra.
8: Due to the establishment of speed, time and distance in methodologies that do not rely upon a globed earth model for accuracy, the following example remains valid:

New York, Paris, Cape Town & Buenos Aries
NY - PA 8834
NY - BA 3346
NY - CT 7803
CT - PA 12844
CT - BA 6865
BA - PA 11043

NY angles are 123.6° or 100.9 + 61.5 = 162.4°

Even when accounting for a 2.9% margin of error, (the maximum summation of the 2 peer reviewed pieces of literature that I presented) a flat plane is still mathematically impossible.

Summary: Unless you desire to argue the validity of the existence of either time, distance or speed then I have met your demands specifically.  Time can be measured without assuming a globed earth model and Speed can be measured without assuming a globed earth model which allows us to solve for distance without assuming a globed earth model.  While the geometry proof provided by 3dGeek and Inquisitive does not have the ability to prove whether the earth is a convex or concave surface, the congruence of speed measurement systems that do not require a globed earth assumption and the ones that do, provide strong evidence that the earth is convex rather than concave.

Thank you.

CriticalThinker

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