In 2016 a young man published a video discussing the shape of the earth. He suggested that a physical demonstration of the earth’s curvature should be made. He proposed the building of a fence like structure with the top rail following a line which would continue straight in space and therefore independent of the earth’s shape. This would then demonstrate how the earth’s surface curved away from the straight line of the top rail. For reasons unknown this young man has disappeared from public forums but his idea is still active. It has great merit.

The project he proposed is an important opportunity to compare the physical surface of Earth with the WGS84 theoretical model of Earth. WGS84 stands for World Geodetic System 1984. Published in 1984 and revised in 2004 it is a set of mathematical values used as a reference in map making, studying the earth’s geometric shape, orientation in space and gravitational field.

The WGS84 model is constructed on a theoretical oblate spheroid referred to as the geoid. The geoid is the theoretical convex shape of the ocean by the action of gravitational potential upon water. In the WGS84 model this spheroid has a circumference of 24900 miles (40070 km) at the equator. A sphere of such dimensions must have a very subtle convex surface with a downward bend in all directions equal to 8 inches per mile squared.

Since WGS84 is the reference for such fundamental aspects of Earth science verifying the model is accurate by empirical data from the actual earth is of great importance.

In the summer of 2018 FECORE took on the challenge. As we discussed what was required to accomplish the task it became clear that it was an extremely expensive proposal in terms of building materials and the miles of land it would need. In addition to those obstacles the required structural features of the fence created an even greater barrier.

The WGS84 model states the geoid or average convex shape of the earth follows a line bending downward at a rate of 8 inches per mile squared. There is no physical material that be verified to remain ridged to less than 8 inches over a mile distance. Then having many pieces which are claimed to be straight would require a source of determining that straight line.

We discussed using a laser to determine the straight in space line. But a laser spreads and we need to have less than 1 inch over a mile. And no matter what we constructed the real question is how can we establish that a line is unbending over the distance of a mile or more?

We decided the method is through the science of surveying. We have a member of FECORE with many years of surveying experience who explained how it could be done.

Chris Van Matre lives in the US and has taken on the task of heading up the project we call Force the Level. We established what the margin of error would be using the best surveying equipment that can be found.

The surveying procedure is called **differential leveling**. It requires a high quality differential level. This is a precision optical instrument for measuring angles between designated visible points in the horizontal and vertical planes.

Our team will use the Trimble DiNi model. It can measure to within 1/10000^{th} of a foot over the distances we will take readings. The cost to buy this device is over $4000. Fortunately we found we could rent it by the day.

Four leveling rods will also be rented for the process. The following diagram shows the basic concept of differential leveling.

The Force the Level measurements differ from the standard surveying process since we are testing the reference data over an observably non convex surface.

This is description of the method used in the Force the Level project.

Prerequisite

The method described below assumes a previously surveyed stretch of straight and reasonably level land.

Equipment Required

1. One differential level that can be easily and accurately adjusted in height (plus surveyor to operate)

2. Four leveling rods (plus people to man them)

The Procedure

A series of positions are established with an equal distance between each. The first position is designated P0. This is the starting position of the differential level. Position 1 or P1 is the first leveling staff, P2 is the second staff and so on until the last position.

1. Let P0 to Pn represent positions at intervals of d over a distance of n * d. The distance between positions is proposed to be 40 meters or 131 feet. If that interval is followed then 40 positions will be required to span 1 statute mile. According to the WGS84 model from P0 to P40 about 8 inches of convexity should be observed.

The readings are made in this manner.

2. Position a leveling staff at P1, P2 and P3.

3. Using a leveled differential level positioned halfway between P0 and P1 make note of the readings at P1 and P2..

4. Move the differential level to a position halfway between P1 and P2.

5. Retake and record new readings from P1 and P2 and take a reading at P3.

6. Move the differential level to a position halfway between P2 and P3. Move the leveling staff at P1 to P4.

7. Retake and record new readings from P2 and P3 and take a reading at P4.

8. Let r be the next position to be read.

9. Move the differential level to a position halfway between Pr-2 and Pr-1. Move the leveling staff at Pr-3 to Pr.

10. Retake and record new readings from Pr-2 and Pr-1 and take a reading at Pr.

11. Repeat steps 9 and 10 until the desired distance is reached.

12. Repeat the whole process to return to the start position and to close the loop.

13. Once all iterations have been completed each position will have 3 readings associated with it; two readings taken from a distance of 20m (one foresight and one back-sight) and one reading taken at a distance of 60m.

By comparing the readings taken at 60m with those at 20m it is possible to calculate any refraction and then calculate the actual convexity of the earth’s surface.

Selection of an Appropriate Interval Distance

Unlike past projects this project was begun before the idea of the project was published. So the first test has already been completed.

On September 15th, 2018 several FECORE members gathered for the first test. The day was hot and sunny. Ideal conditions would have been overcast rather than bright sun light. But they were able to make reading of 1/4 mile. This is a time consuming process. The measurements themselves took 5 hours and the unseasonably warm day made it seem longer. Then Chris entered all the data into a spread sheet. This was only the first set of tests so making a conclusion with just one small data set is not a good idea.

After our experience in the first test the distance of 40 meters has been selected for the next test on March 9th and 10th.

FECORE is well versed in calculating any refraction effects from our experience with long distance laser observations. The 40 meters should be no problem to make any needed refraction calculations. And with a little luck we will finish all 40 readings in the two day period.

Surveying is based upon the WGS84 mathematical reference data. It is time that surveying tools should test it.