# Rainy Lake Experiment: In a Nutshell

This is a short version of the Rainy Lake Experiment Report, e.g. for presentations.

## Location

Img 2: Rainy Lake target locations

Rainy Lake is a relatively large freshwater lake (930 km2) straddling the border between the United States and Canada. Rainy Lake is part of an extremely large system of lakes forming the Hudson Bay drainage basin that stretches from west of Lake Superior north to the Arctic Ocean. ⇒more

## Choosing Target Heights

Img 3: Rainy Lake Experiment Design: Flat Earth side-view

The lower Bedford targets consist of a row of 6 targets, all 1.85 m above water level. ⇒more

Img 4: Rainy Lake Experiment Design: Globe-Earth side-view

The upper Tangent targets consist of a row of 4 targets, increasing in height with increasing distance.

## Size and Placement of the Targets

To optimize the visibility of the targets and to help better distinguish the targets, they are arranged in the following way: ⇒more

Img 5: Rainy Lake Experiment target design

## Predictions for Bedford Targets

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

Flat Earth: The Computer Model predicts that all Bedford targets appear exactly aligned with the horizon and eye level. ⇒more

Globe: 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

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
• Swap
• 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. ⇒more

## 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. The farther away a target is, the higher it will appear. ⇒more

Globe: The Computer Model predicts that the Tangent targets will appear about at eye level, variations due to how the heights were establised.

## Results for Tangent Targets

Img 13: Globe prediction for Tangent targets → Model
Img 14: Flat Earth prediction for Tangent targets → Model
• Swap
• 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. ⇒more

### 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

## Visualizing GPS Vectors

The GNSS Data Viewer displays the GPS Vectors as white markers and allows to make calculations between the data points. The software allows to import and overlay an image onto the display to see how observations match the measured GPS Vectors. ⇒more

Img 23: Overlay GPS Vectors with image of Bedford targets → App
Img 24: Overlay GPS Vectors with image of Tangent targets → App

The Bedford target, ice and water level GPS Vectors do not lie on a plane but curve down.

Due to Refraction the targets on the images appear as higher than the GPS Vectors, as farther away they are from the observer. This is due to refraction.

## Measuring the Radius of the Earth

Img 25: Measuring the radius of the earth from 3 data points → App

The calculated radius of the earth from 3 selected markers is 6025 km. That is only 363 km or 5.4% too less. ⇒more

The exact radius of the Ellipsoid at this location in the direction of the targets is 6388 km.

The surface of the earth is curved. If the earth were flat then all points with the same height would lie on a plane.

## Refraction

Refraction is a major factor when observing distant objects. Refraction changes the apparent vertical position with respect to a reference line like eye level. Because the Rainy Lake Experiment is about the relative vertical positions of targets, refraction has to be taken into account. ⇒more

### Refraction Coefficient

The refraction Coefficient k, often simply called refraction, is defined as the ratio of the mean radius of the earth R to the curvature radius of the bent light rays RR: ⇒more

(1)

per Definition

where'
 $k$ ' =' 'refraction Coefficient $R$ ' =' '6371 km = mean radius of the earth $R_\mathrm{R}$ ' =' 'radius of the curved light ray from the object to the observer in km

Standard Refraction: On average the atmosphere has a certain pressure, temperature and density gradient. This average is called International Standard Atmosphere. On standard atmospheric conditions refraction is called Standard Refraction and has a value of k = 0.13..0.17.

The refraction Coefficient can be calculated from air pressure, temperature and temperature gradient as follows:

(2)
where'
 $k$ ' =' 'refraction Coefficient $P$ ' =' 'air pressure at the observer in mbar or hPa or 1/100 Pa, Standard = 1013.25 mbar $T$ ' =' 'temperature at the observer in Kelvin, Standard = 288.15 K = 15°C $\mathrm{d} T/\mathrm{d} h$ ' =' 'temperature gradient at the observer in K/m or °C/m, Standard = −0.0065°C/m

### Apparent Lift due to Refraction

If we know the mean refraction Coefficient k we can calculate how much each target appears to be lifted: ⇒more

(3)
where'
 $l$ ' =' 'apparent lift due to refraction $\rho$ ' =' 'refraction angle $k$ ' =' 'refraction coefficient $d$ ' =' 'distance of target from observer $R$ ' =' '6371 km = radius of the earth

Note: This equations can be used for any shape of the earth.

### Horizon above Eye Level

If refraction causes the horizon to appear above eye level (concave earth), the ground will fade slowly into the sky and therefore the horizon is not a distinct line. ⇒more

At refractions k < 1 the Globe has a distinct horizon. The Flat Earth has only a distinct horizon when light is bent upwards due to negative refraction k < 0.

Below are 2 images from a Refraction Simulation that show how the horizon will appear at Standard refraction for the Globe and the Flat Earth model.

Distinct horizon on the Globe model
No distinct horizon on the Flat Earth model

## Measuring Refraction from GPS Vectors

The following screenshots show the overlay of photos of the Bedford and Tangent targets with the corresponding GPS Vectors in the GNSS Data Viewer. ⇒more

Img 23: Overlay GPS Vectors with image of Bedford targets → App
Img 24: Overlay GPS Vectors with image of Tangent targets → App

The apparent lift of the targets is due to refraction and can be measured from the image.

Bedford Target Refraction:

(4)

Tangent Target Refraction:

(5)

The markers in the Viewer were aligned exactly to the vertical positions of the first target centers, but in reality this targets were also affected by refraction and should appear slightly above this markers. Therefore this refraction calculations results in slightly too small values: 0.05 smaller than compared with Measuring Refraction with the Computer Model .

The GPS Vectors clearly show the earth is not flat.

## Measuring Refraction with the Computer Model

We can use the Computer Model to measure refraction from an image. ⇒more

Img 11: Overlay observation with Globe prediction → Model

Globe Model:

• Results for Bedford Targets: k = 0.270
• Result for Tangent Targets: k = 0.187

Flat Earth Model:

• Result for Bedford Targets: kFE = −0.730
• Result for Tangent Targets: kFE = −0.813
Img 22: Overlay observation width Globe prediction → Model

Such high negative refractions would cause very distorted images. We don't see distortions in the used images and this values are not consistent with the values obtained at Measuring Refraction from GPS Vectors.

This results show, the earth can not be flat.

### Refracted Light Rays on Globe and Flat Earth

We can see that the light rays bend exactly the same amount on Globe and Flat Earth model. The only difference is that we see the horizon at different vertical angles with respect to eye level. The apparent lift of the horizon or any object is practically identical in both models. The fact that the air layers are curved on the Globe but flat on the Flat Earth has no effect on distances much smaller than the radius of the earth, execpt on strong refraction conditions near the ground. ⇒more

## Strong Refraction

Distorted images are caused by turbulent air. Turbulent air is caused by temperature gradients that diverge from standard. So distorted images are always a sign of strong refraction. ⇒more

On the other hand, a clear image is a sign of a temperature gradient near standard which causes low refraction.

### Refraction Range of Clear Images

The following graph shows the correlation between the refraction Coefficient and the predicted horizon position with respect to eye level for the Flat Earth and Globe model. ⇒more

### Strong Refraction at Bedford Targets

If refraction gets greater than 1, even on the Globe the horizon raises above eye level and the earth appears concave shaped, but the image 28 looks very destorted. ⇒more

Img 27: Clear image, low refraction, watch video
Img 28: Distorted image, strong refraction, watch video

Globe Model: Image 27: clear = low refraction, horizon below eye level. Image 28: distorted = strong refraction, horizon above eye level.

Consistent with Globe model predictions

Flat Earth Model: Image 27: horizon way below eye level = strong negative refraction. This should cause a distorted image. But image 27 is clear.

Images of the Bedford targets with strong refraction are not consistent with the Flat Earth model.

Laser Tests

Image 28 shows why laser tests over water or ice are flawed due to strong refraction at dawn, when the air is still warm but the ground is cold. The earth appears concave - no horizon that hides the laser.

### Strong Refraction at Tangent Targets

• Time lapse at 13 s
• at 16 s
• at 20 s
• at 28 s
• at 38 s
• at 39 s

On the first images refraction is low, while on the last images it is high. ⇒more

Img 31: Clear image, low refraction
Img 32: Distorted image, strong refraction

Globe Model: Image 31: clear = low refraction, horizon below eye level. Image 32: distorted = strong refraction, horizon still below eye level.

Consistent with Globe model predictions

Flat Earth Model: Image 31: horizon way below eye level = strong negative refraction. This should cause a distorted image. But image 31 is clear. Image 32: horizon less below eye level = less negative refraction. This should look less distorted than image 31 but looks more distorted.

Images of the Tangent targets with strong refraction are not consistent with the Flat Earth model.

### Time lapse of Refraction

The camera was at a height of about 4 m above water level next to the auto level, which is at the level of the Tangent targets. ⇒more

## Night Observations

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

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. ⇒more

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.

## Drone Observations

• Next
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• h 4
• h 5
• h 6
• h 7
• h 8

The image sequence filmed from a 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. ⇒more

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 as predicted by the Globe model.

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

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

## Conclusion

All Observations match the Globe Model predictions very well, but contradicts the Flat Earth Model. ⇒more

The earth can't be flat. The data is consistent with a Globe with a radius of about 6371 km. The Rainy Lake Experiment shows this even better than the Bedford Level Experiment, because we also have GPS measurements, which are not affected by refraction or perspective.

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