# Rainy Lake Experiment: Predictions and Observations

## Predictions for Bedford Targets

The Computer Model of the Experiment uses pre-calculated and measured target positions in ECEF coordinates. The following images are screenshots from this Model. For image 6 and 12 the pre-calculated data is used. For the comparison with the real images, the measured GPS Vectors in ECEF Cartesian coordinates are used.

Img 6: Predicted views of the Bedford targets from the 1.85 m observer location for Flat Earth and Globe → Model

Flat Earth: From an observer height of 1.85 m the Computer Model predicts that all Bedford targets appear exactly aligned with the horizon and eye level.

Globe: From an observer height of 1.85 m the Computer Model predicts that the Bedford targets appear all below eye level. The farther away from the observer, the more below eye level.

## Results for Bedford Targets

The Rainy Lake Experiment shows that from an observer height of 1.85 m all Bedford targets appear below eye level as predicted by the Globe model. The farther away a target is, the lower it appears. The horizon is predicted at 5.68 km, so the target (5) pole should appear just at the horizon.

Img 7: Globe prediction → Model
Img 8: Flat Earth prediction → Model
• Swap
• Globe Prediction
• Flat Earth Prediction
Img 9: Bedford target observation → Model
Img 10: Globe prediction for Bedford targets → Model
Img 11: Overlay observation with Globe prediction → Model
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• Real Picture
• Globe Prediction
• Overlay

The Flat Earth model predicts that all Bedford targets appear aligned with the horizon and eye level, which does not match the observation.

In this observation, refraction was about k = 0.27, see Measuring Refraction with the Computer Model. This is slightly more than standard refraction of k = 0.17. The highly zoomed in image is clear. This indicates that refraction is near standard and constant for the whole distance. Strong refraction would cause a distorted image, see Refraction Range of Clear Images.

The black vertical and horizontal lines in the image is the crosshair of the auto level. The horizontal crosshair indicates eye level of the observer at 1.85 m height. In the Computer Model, eye level is indicated by a magenta horizontal line labeled Eye-Level.

The Computer Model uses for this predictions the measured heights of the Bedford target centers rather than the pre-calculated target center heights and the observation matches the Globe model very well.

## Predictions for Tangent Targets

Img 12: Predicted views from the 3.91 m observer location of the Tangent targets for Flat Earth and Globe → Model

Flat Earth: The Computer Model predicts that the Tangent targets will appear above eye level from an observer height of 3.91 m. The farther away a target is, the higher it will appear.

Globe: The Tangent target center heights are computed in such a manner, that on the Globe they will all appear at eye level from an observer height of 3.91 m with Standard refraction k = 0.17 applied, see Calculating Tangent Target Heights.

## Results for Tangent Targets

The Rainy Lake Experiment shows that from an observer height of 3.91 m the Tangent targets are aligned more or less with eye level, which is predicted for the Globe-Earth. The deviation from eye level is the result of aligning the Tangent targets optically at different days with different refractions, rather than setting them to the calculated target center heights.

Img 13: Globe prediction for Tangent targets → Model
Img 14: Flat Earth prediction for Tangent targets → Model
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• Globe Prediction
• Flat Earth Prediction
Img 15: Tangent target observation → Model
Img 16: Globe prediction for Tangent targets → Model
Img 17: Overlay observation width Globe prediction → Model
• Swap
• Real Picture
• Globe Prediction
• Overlay

The Computer Model shows the predicted image using the measured target center heights, which match the observations very well. The Flat Earth prediction does not match the observation at all.

The image is clear over the distance of 10 km, so refraction can be assumed to be near standard, see Refraction Range of Clear Images. With the Computer Model a refraction of k = 0.27 was measured from the image, which is slightly more than standard refraction k = 0.17, see Measuring Refraction with the Computer Model.

The last target appears about 1 m too high, compared to the pre-calculated height. A refraction variation of k = ±0.14 results in a height variation of ±1 m at a distance of 9.5 km. So the divergence of +1 m is due to a lower prevailing refraction at the day and time this target was setup.

Note: This image was shot with a P900 camera, not through a theodolite or auto level. That's the reason why the crosshair is missing. The camera was placed beside the auto level at the same height of 3.9 m.

## Another Day

The following observation was made earlier than the observation above, when the Tangent target (6) was not yet damaged by strong winds.

Img 18: Globe prediction for Tangent targets → Model
Img 19: Flat Earth prediction for Tangent targets → Model
• Swap
• Globe Prediction
• Flat Earth Prediction
Img 20: Tangent target observation → Model
Img 21: Globe prediction for Tangent targets → Model
Img 22: Overlay observation width Globe prediction → Model
• Swap
• Real Picture
• Globe Prediction
• Overlay

This image was shot through an auto level. Note that the magenta eye level line matches the horizontal eye level crosshair exactly.

The picture is clear with a small layer of inferior mirage above the surface. At the Tangent target heights refraction can be assumed to be near standard, see Refraction Range of Clear Images. With the Computer Model a refraction of k = 0.187 was measured from the image, which is slightly more than standard refraction k = 0.17. The targets in this observation are better aligned with eye level as the other observation above, which is due to less refraction.

## Night Observations

Img 33: Lantern through T2 theodolite
Img 34: Lantern through TOPCON theodolite

Part of the Rainy Lake Experiment was to show the Bedford targets at night. For this purpose lantern were mounted above the Bedford targets and observed through the two theodolites from a location more to the side of the line of targets. The heights of the theodolites were set exactly the same height over water level as the lantern.

Img 33: Magnified view through T2 theodolite shows the lantern drop with distance

It could be observed, that the lantern lights were all below the horizontal eye level crosshair. The farther away the target, the lower the lights appeared, which is expected on the Globe Earth.

Note: The drop of the targets shown here appears much less than in the images taken at daylight. But keep in mind that this images show a view more from the side with much less zoom, while the daylight images show a view along the targets with strong zoom. Looking along the targets causes the drop to appear much more pronounced due to zoom perspective compression.

Another reason may be refraction. Over cool water or ice at the evening refraction is commonly stronger than standard and lets the earth appear flatter than it is. But we can not derive any quantitative conclusions from this images.

## Drone Observations

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• h 6
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• h 8

The image sequence above was filmed from a Voyager 4 Drone from ground to about 100 m altitude. The drone uses a gymbal stabilized camera which keeps it pointing at eye level during the whole ascent. The yellow lines mark the horizon at the ground and at the highest altitude.

We can observe that the horizon drops with increasing altitude and that more and more of the landscape comes into view from behind the horizon. The Globe model predicts a horizon drop of 0.29° for an altitude of 100 m. The rate at which the horizon drops as a function of altitude is such, that it first drops fast and then slower and slower according to the following equation:

(1)
source
where'
 $\alpha$ ' =' 'drop angle in radian; multiply with 180°/π to get degrees $R$ ' =' '6371 km = radius of the earth. Use a radius of 7670 km to acount for standard refraction k = 0.17 $h$ ' =' 'observer altitude

The Flat Earth model predicts that the horizon will stay at the same position in the frame during the whole ascent.

In the center of the image is a corridor of 32 km length of ice. So the trees in the background of the coridor are 32 km far away. The distance to the Globe horizon from 100 m altitude with standard refraction is calculated as 39.2 km.

(2)
source
where'
 $d$ ' =' 'distance to the horizon $h$ ' =' 'observer altitude $R$ ' =' '6371 km = radius of the earth. Use a radius of 7670 km to acount for standard refraction k = 0.17

The Drone observation of a horizon drop matches the Globe model, but not the Flat Earth model.

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