GPS + Odometer + Speedometer + Cruise Control = Spherical Earth Affirmed (San Jose to Berkeley)



I recently got a very helpful suggestion from a person in Santiago, Chile, that expressing my work in metric units would be helpful to the international community, so this motivated me to travel metrically on a trip yesterday, as much as I was able, and to report the experimental results metrically as well.

In a nutshell, you track a car trip with your GPS and use cruise control to maintain intervals of constant speed as much as you can during the trip, noting the constant speeds you maintained as well as where on the trip you were able to do so. Once you get the GPS data you can analyze it and show that a spherical earth surface geometry interpretation of the data accurately gives the regions of constant speed and the overall trip distance in agreement with the car’s odometer and speedometer. On the other hand when you interpret the data according to flat circular disk geometry the intervals of constant speed do not show up as constant at all and the overall trip distance is much in error from the distance measured by the car’s odometer. I can already hear flat earth advocates saying something like the GPS data comes out right because it is based on spherical geometry, and indeed I agree that it is so based, but the car’s odometer and speedometer are independent of what theory of the earth’s surface you hold. The car should give accurate speeds and distances traveled whether you are on a flat earth or a spherical earth, or any other shape for that matter. The fact that the GPS data agrees with the independent data from the car’s odometer and speedometer is strong evidence that the spherical earth model is correct. The fact that the GPS data when interpreted according to flat circular disk geometry disagrees profoundly with the independent data from the car’s odometer and speedometer is strong evidence that the flat earth model is incorrect. I challenge all flat earth advocates and researchers to find a way to interpret the trip GPS data so as to show that it conforms to flat earth theory and also agrees with the independent data of the car’s odometer and speedometer.

The beauty of this experiment is that whenever someone does it they are going to get unique results that cannot possibly be predicted or planned for in advance. Where and at what speeds you are able to hold steady speeds with cruise control will vary with the road and traffic conditions. The path of the trip used will also impact the results in a unique way.

This type of experiment can easily be performed for a vast variety of trips all over the world and the data easily analyzed. I am going to share exactly how this can be done by showing how I did it for a trip from San Jose to Berkeley CA yesterday. All details are presented and the Excel files are made available to anyone through my Scribd account so they can see how it was done and use the spreadsheets to process the data from their own trips as well.


I used the GPS in my smartphone, a Samsung Galaxy S4. I used the App GPS Essentials, where at the start of your trip you start tracking, and when you arrive at your destination you stop tracking. The trip file can then be exported as a KML file. From there you can process the data in various ways. I like to use the website for some things and Excel spreadsheet for many other things.

Car speedometer and odometer

It was easy to push a button to get my speedometer to read in km/h instead of mph, so that way I could easily see what my speed was in km/h during the trip. I was not sure how or if I could get the odometer to read in km, so I took the readings in miles and converted to km.

Trip from San Jose to Berkeley

91.1 km (56.6 miles) by odometer

Duration by my watch 1:10

Duration Start to Stop GPS 1:09:28

90.6 km 78.3 km/h ave speed 131 km/h top speed reported directly by GPS

From my smartphone I exported the trip KML file via email to my PC. The KML filename was Track-171126-105544. I then went to the website, where I uploaded the KML file and choose output format plain text table. I then clicked the link to download this text file back to my PC. I accepted the default filename 20171126171339-38065-data. I then opened the Excel spreadsheet application. My version happens to be from 2010. From within the Excel application, find the text file and open it. Either select to look at All Files or just Text Files to make sure you can see the correct text file to open. Once you open it, the Text Import Wizard comes up. The default settings are fine, so just click on Next, Next, and then Finish. At this point I like to do a Save As on the file, and save it as an Excel Workbook file, and give it a name that is more meaningful to me. So I gave it the name 906783SanJoseToBerkeley. I got the 906 from 90.6 km for the trip and 783 from 78.3 ave speed for the trip in km/h and added SanJoseToBerkeley to further help me identify this data. I will use this name with additional things added to it as more files are produced based on processing this data. I do not intend to make any further modifications to the Excel Workbook file 906783SanJoseToBerkeley so this can be kept as a record of this stage of the data processing procedure that could easily be returned to as needed. So then I will again do a Save As to the file and give it the name 906783SanJoseToBerkeleySph. This will be the file where some modifications will be made so it will do calculations according to spherical earth geometry. One other change I like to make at this point is to rename the data tab. So go to the lower left and right click on the data tab, that currently has the really long name that came from the GPSVisualizer when it created the text file from the KML file, and select rename. I like to rename it 906783-data. Once you do this be sure to save the file again. And then do another Save As and save it with the name 906783SanJoseToBerkeleyFlt. This will be the file where some modifications will be made so it will do calculations according to flat circular disk shaped earth geometry.

So let’s start by working on the 906783SanJoseToBerkeleyFlt file. If you have followed the directions exactly as above that file should already be open. If not, open it now. Also open the Excel file FltGeomMetricUnitsTemplate. This is the file where we are going to copy the section with the equations for calculation and paste them into file 906783SanJoseToBerkeleyFlt.

In the 906783SanJoseToBerkeleyFlt file select across from Column E to Column J, so that Columns E, F, G, H, I, and J are all selected. Be sure to select across the column headings so that the entire columns will end up being selected. Then Right-Click anywhere inside the selection and choose Insert. This then creates 6 empty columns from E to J, and moves the other stuff to the right so nothing is lost. In these 6 columns is where we are going to do some calculations on the data. So we are now going to get the equations from the FltGeomMetricUnitsTemplate file and copy and then paste into the new spreadsheet. So from FltGeomMetricUnitsTemplate select from E1 upper left to J12 lower right so that a rectangle of 12 cells down and 6 cells across are selected. Then Copy (Ctrl-C). Then go to the 906783SanJoseToBerkeleyFlt spreadsheet file and select cell E1 to define the upper left of where to Paste. Then Paste (Ctrl-V). At this point the equations need to be filled down to the extent of the data. Select cell E12 which defines the upper left. Scroll down to the very bottom of the data, in this case row 3416. Shift-Click on cell J3416. This will result in all cells bounded by E12 on the upper left to J3416 on the lower right to be selected. Then do a Fill Down (Ctrl-D). This then results in the equations being pasted all the way down so we get the calculations done that we wanted for the entire extent of the data. Two values can be read off of the spreadsheet at this point. If you go to cell G3416 the total distance of the trip according to flat earth interpretation is 96.2 km and to cell I3416 the average speed is 83.1 km/h also according to flat earth theory. Next we will create a plot of speed versus time. Column J is speed smoothed over several data points and is what I will use because it minimizes the natural scatter in the data for a better looking plot. If you want to use the point to point speed just use column H for speed instead. So select from cell B12 to B3416. The way I like to do this is first select cell B12, then scroll all the way down and shift-click on cell B3416. Next we want to add to the selection cells J12 to J3416. The way I like to do this is first Ctrl-click on cell J12 and then scroll down and shift-click on cell J3416. Now that we have selected two separate columns, one defined by cells B12 to B3416, and the other defined by cells J12 to J3416, we can create a plot of this speed versus time data. So go to Insert, select Scatter, and then Scatter with straight lines is the one I like. This puts the plot in front of the spreadsheet table. I like to make it separate with its own tab. So right click in the right area of the plot and chose Move. Then click the button and accept the default name of Chart1 or give it your own name. I like to call it SpeedVsTimeSm, for speed versus time smoothed. This then is the speed versus time plot based on the flat earth interpretation of the data. This will eventually be compared with the equivalent plot based on the spherical earth interpretation of the data. What we will find is that the intervals where the speed was held constant with cruise control show up clearly and distinctly constant on the spherical earth interpretation, but with much variability on the flat earth interpretation.

So basically to get the equivalent calculations for the spherical earth surface model, repeat everything above, but instead using SphGeomMetricUnitsTemplate and working on file 906783SanJoseToBerkeleySph.

Once you do this you will get the results that I have summarized below.

Trip from San Jose to Berkeley

91.1 km (56.6 miles) by odometer

Duration by watch 1:10

Duration Start to Stop GPS 1:09:28

90.6 km 78.3 km/h ave speed 131 km/h top speed by GPS

90.67 km 78.32 km/h ave speed confirmed by calculations in Sph Excel spreadsheet

Speed versus Time plot for spherical model shows clear agreement with speedometer data

Speed versus Time plot for flat model shows large deviations from speedometer data

96.2 km 83.1 km/h ave speed by calculations in Flt Excel spreadsheet Inconsistent with odometer data

Spherical Earth model: Affirmed

Flat Earth model: Large deviations from reality

If I am able to display the Speed versus Time graphs I will show them here. If not they can be seen at the Scribd links.

Speed versus Time according to Flat theory

Speed versus Time according to Flat theory

Speed versus Time according to Spherical theory

Speed versus Time according to Spherical theory

I have made these files available to the public through my Scribd account.

20171126171339-38065-data    Text file

20171126171339-38065-data    Text file

906783SanJoseToBerkeley           Excel file

906783SanJoseToBerkeley           Excel file

906783SanJoseToBerkeleyFlt        Excel file

906783SanJoseToBerkeleyFlt        Excel file

906783SanJoseToBerkeleySph       Excel file

906783SanJoseToBerkeleySph       Excel file

FltGeomMetricUnitsTemplate         Excel file

FltGeomMetricUnitsTemplate         Excel file

SphGeomMetricUnitsTemplate         Excel file

SphGeomMetricUnitsTemplate        Excel file

Anybody should be able to see the files by just going to the links. The graphs of Speed versus Time for both the spherical and flat cases should be able to be seen this way. To download the files you need a Scribd account, and a regular account should be free to set up.

I was not able to make the KML file Track-171126-105544 available through Scribd because it is not a supported file type.

I encourage people all over the world to take their own data and process it in this manner and report their results. Let me know if you have any questions. Comments are welcome. Thank you.

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