And by the way, on this post we can find thousands of measurements of the radius of the earth, see column |X,Y,Z| in the Data Points table.
Click on the data points to set the Reference Point (the airplane) to that point. Right click on a data point to set the Start Point. Data summed between Start and Reference Point is shown in the magenta info box. Click and drag the mouse to change the camera view and use the scroll wheel to zoom. To reset the view click on the button Nr. 1 in the lower right corner of the App Window below.
A short description of the elements in the App window can be found at Airplanes drop their Nose. For more informations how to control this App and what the values in the info boxes mean, please click on the Help button below the App window.
Data File: Flight QF6051/14 Brisbane-Buenos Aires-Darwin ⇐ click to select another file
Select another Flight Data File or Upload or Edit Flight Data (password required for upload and edit). Click here to reload the initial data set: Flight QF6051/14 Brisbane-Buenos Aires-Darwin.
Click on Zoom at the top left corner to reset Zoom. Click on top right corner to increment and bottom right corner to decrement Zoom, or use the mouse wheel.
Note: Speeds are calculated excluding GateTimes: Speed = Distance / Time, while Time = TotalTime − GateTimes.
In the table below is the data of each Data Point listed, displayed in the App above. The raw position data is given in Earth Centered Earth Fixed (ECEF) cartesian coordinates in the X, Y, Z columns in meters. In the column Time is the time stamp of each data point listed in UTC time. In the column |X,Y,Z| is the length of each (X,Y,Z) vector listed, which is the radius of the earth at the location of the data point plus its altitude. If there is additional flight data available, it is listed in the column Additional Data.
Click a line in the table above to copy the location as ECEF (Earth Centered Earth Fixed) X,Y,Z coordinates and as Latitude and Longitude into the fields above. You can copy the Lat/Long field into Google Earth to go to that location.
Click here to load the data set: Flight Wolfie Sydney Dallas displayed below.
The Attitude angle is the vertical angle, measured between the horizontal plane at a data point and the line of sight to the next data point. On a Flat Earth this angle is zero if the current data point and the next data point are at the same elevation. On the Globe Earth however, even if the elevation of the next data point is the same, the next data point drops below the horizontal plane of the current point, due to earths cuvature.
The connection between any two Data Points build a 3D vector, as depictied by the blue arrows in the figure. So we can use vector geometry to calculate the vertical angle between each vector and the horizontal plane at a Data Point, called the Attidude Angle.
Math: see Calculating Attitude Angle and dPitch.
If we have the Attitude angles of a Data Point to the previous and next Data Point we can calculate how much the airplane droped the nose at that point. In the App this change is labeled dPitch (for delta Pitch). It is the sum of the Attitude angle to the previous data point plus the Attitude angle to the next data point. This delta pitch is displayed in the green Leg Info Box at dPitch. A negative value means that the airplane has droped the nose between the previous and the next data point accordingly.
We can sum all pitch changes dPitch between Start Point and Reference Point to calculate, how much the airplane dropped the nose between this points.
What is the pitch rate calculated from the data in the example above?
The sum of all dPitch values between Start Point and Reference Point is displayed in the magenta Sum Info Box at the yellow highlighted dPitch field. It is also shown in the small window at the lower right corner of the App window in blue. The great circle distance between Start Point and Reference Point is displayed in the Sum Info Box at DistGC.
It turns out that the sum of all dPitch values, in the example −52.20°, is not zero as required by the Flat Earth model. The calculated PitchRate of -1° per 111.1 km is very close to the expected -1° per 111.195 km of the Globe model. Because (1) is the equation for a sphere, not an ellipsoid, there is this small difference. The value displayed in the App is more accurate for the flown track, because it is measured from real data.
Move the Reference Point (Airplane) by clicking a Data Point and watch how the total drop angle sum dPitch changes with the distance from the Start Point.
GPS flight data shows, that airplanes do drop their nose 1° per 111.2 km as predicted by the Globe model.
Note: The great circle distance GCDist is the sum of the great circle distances between each data point from Start Point to Reference Point. A great circle route contains the radius of the earth. If you want to calculate the PitchRate without assuming any earth model, simply use the line of sight distances Dist. If you use Dist instead GCDist, you still get a pitch rate of -1° per 111.3 km.
Some Flat Earthers claim that Globers only assume a Globe and GPS latitude/longitude can also be used on a Flat Earth and Navigation would work on the Flat Earth exactly the same as on the Globe. This is certainly not the case and I will prove it.
Flat Earthers use an Azimuthal equidistant projection centered at the North Pole as their map. This projection is also called the Gleason map. Because we know the latitude and longitude coordinates of every point on earth, we know that the Gleason map shows the locations of the continents and each point on it correctly, on this specific Globe projection. There can be no excuses like "we don't know the exact sizes of the continents yet". If we know the latitude and longitude of every point on earth, we can map all locations onto the Gleason map and we get the continents we see on this map. There is no ambiguity.
Navigation is not only a matter of having some locations with some latitude/longitude coordinates. It's also about the distances and directions between locations, the speeds and even accelerations.
Let's check how Flat Earth and Globe compare. For a mathematical description why Flat Earth projections don't work the same as the Globe, see Globe and Flat Earth Transformations and Mappings.
The longitude lines (north/south lines) on the Globe converge south of the equator and rejoin at the south pole, while the same longitude lines on the Flat Earth diverge. So mapping GPS latitude/longitude onto a Flat Earth stretches all distances between 2 locations that are not exactly in the north/south direction. Distances in the east/west directions are stretched on the Flat Earth with respect to the Globe by a factor k, depending on the latitude.
This is illustrated in the animation above. In the animation the Globe and the Flat Earth are scaled to have the same distances in the north/south directions. The numbered locations have exactly the same latitude/longitude on both models. We can clearly see that east/west distances are way longer on the Flat Earth than on the Globe and that the directions are not the same. The question is now, which distances are correct?
Lets say we have 2 GPS locations, A and B, with the following coordinates:
On the Globe this 2 points are 111.2 km apart. On the Flat earth they are k times farther apart, where at the equator k = 1.57. So the distance between A and B on the Flat Earth is 174.7 km. You can use the calculator below to calculate the stretching factor k for any latitude:
Math: For the math used in this calculator see Calculating East/West Stretch Factor k.
Extreme example: The stretch factor becomes infinite for latitude of −90°. It's a fact that if we are at a distance of 1 m from the geographic south pole (latitude = −89.999991°), we can circle it in a circle with circumference 6.3 m. The stretch factor at 1 m from the south pole is k = 20 × 106. On the Flat Earth the corresponding distance would be k · 6.3 m = 126,000 km.
I claim that the Globe distances are correct and I will prove it with measurements from GPS Flight Data recorded over Antarctica:
GPS locations can be expressed either in cartesian coordinates (X,Y,Z in the ECEF coordinate system) or in latitude, longitude and height above the reference ellipsoid. The fact that the recorded raw GPS (X,Y,Z) coordinates all lie on a sphere with a radius of about 6371 km, not on a flat disc, proves the earth is a Globe already. But lets pretend we don't know yet the shape of the earth on which the data was recorded.
I have a record of thousands of data points from a trip over Antarctica.  For each data point I have the (X,Y,Z) coordinates, as well as the latitude, longitude, altitude and time stamp. So we know the time that has elapsed between each location. We can map all locations using latitude/longitude either onto a Globe or onto a Flat Earth model. Although my App only shows the points in raw (X,Y,Z) coordinates, which lie on a sphere, it internally calculates the distances, speeds and accelerations for the Flat Earth model too.
The plane flew many turnes over Antarctica. So we can use my App to analyze the data and calculate, distances, speeds and accelerations at any data point for both models and compare them.
As I showed at GPS Latitude/Longitude on Flat Earth and Globe above, the resulting distances are very different on both models. And because speed is distance over time, the speed traveled is also different in both models accordingly. If the distance traveled in time t on the Flat Earth is 2 times longer than on the Globe, than the speed on the Flat Earth is 2 times faster than on the Globe.
As the image above shows, using the Flat Earth model, the data says that the airplane was seemingly flying in the east/west directions at 4200 km/h (red box SpeedFE), while in the north/south direction only 620 km/h. This is of course not realistic. No passenger airplane can fly such maneuvers. That means, the assumption that the data was recorded on a flat earth, is wrong, see Conclusion (Modus Tollens).
Using the Globe model however, the calculated speeds are always about 620 km/h in any direction (red box Speed), which is realistic.
Note: Due to the inherent uncertainty in non-precision GPS measurements like the recorded data, the accuracy of the calculated distances and speeds between neighboring data points is about 10% and fluctuating in this range. Summed over hundreds or thousands data points, the summed values are much more accurate than the individual values.
Math: See Calculating Speed and Acceleration from GPS data for how these speeds are calculated from the GPS data.
The situation gets even worse for the Flat Earth if we look at the accelerations.
If the data was recorded on a Flat Earth then the airplane would have flown turns which produced a G-Force load to the passengers and airplane of over 3.5 g. Of course this can not happen in reality. If we assume that the data was recorded on a Globe, then the data says that the G-Force load in all turns was less than 1.2 g, which is what we measure in reality in standard turns.
Math: The measured impossible accelerations match the predictions for the case that the data is recorded on a Globe and then mapped onto a Flat Earth, see Calculating Acceleration on the Flat Earth and Calculating G-Force Load on the Flat Earth. See Calculating Speed and Acceleration from GPS data for how these accelerations are calculated from the GPS data.
If however the locations and times were recorded on a Globe Earth and the data is mapped onto a Globe Earth, then the calculated speeds and accelerations must be realistic and independent on the direction. This is the case.
And if the locations were recorded on a Globe Earth and the data is mapped onto a Flat Earth, then the calculated speeds and accelerations must be unrealistic and dependent on the direction. This is also the case.
Conclusion: From the Modus Tollens it is inferred that the locations can not have been recorded on a Flat Earth. The claim that the locations were recorded on a Globe Earth are backed up by the calculations of speeds and accelerations for Globe and Flat Earth mapping.
The recorded GPS flight data and the derived calculations of speeds and accelerations disprove that the Earth is Flat. But the calculations yield exactly what is expeced if the data was recorded on a Globe Earth.