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