Link to here:
To come to a Conclusion the following requirements have been set:
Although the whole Experiment was mainly George Hnatiuk's work, Jesse Kozlowski and Soundly joined him in early April 2018 to make GPS measurements (Jesse), images and videos (Soundly) of the Experiment. Later Walter Bislin created a Computer Model of the experiment, visualized the data in his GNSS Data Viewer and wrote this reported.
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.
During the winter months until May, the lake is covered by a meter-thick layer of ice. The lake was choosen for this experiment because George Hnatiuk lives right at the lake and is equipped with the tools and vehicles like a snowmobile necessary for the experiment. The lake provides an unobstructed path of about 10 km from George's home to a small island called Home Island, ideal for this experiment.
See Location Graph and Data for data assigned to the numbers.
The target center heights were chosen in such a way, that on each earth model one of two rows of targets will be at eye level of an observer while the other row curves up (Flat Earth) or down (Globe). The lower targets are called Bedford targets, the upper targets are called Tangent targets.
The lower Bedford targets consist of a row of 6 targets, all 1.85 m above water level. If the earth is flat, all this targets will appear at eye level for an observer at 1.85 m height. The upper Tangent targets will curve up for an observer at 3.91 m height.
The upper Tangent targets consist of a row of 4 targets, increasing in height with increasing distance. If the earth is a Globe, all Tangent targets will appear in line with eye level for an observer at 3.91 m height. The lower Bedford targets will curve down for an observer at 1.85 m height.
The height h of the Tangent targets is the sum of the observer height ho and the curvature drop xi at the i-th target. On distances as small as 10 km the leaning can be neglegted. The target center height can be computed as follows:
The Tangent targets were first placed roughly at the pre-calculated target center heights. Then they were adjusted to the eye level height as seen through the auto level at the observer. Because the targets were adjusted at different times and days, refraction was slightly different for each target so the targets did finally not align perfectly. But the height deviations are within the calculated variations of common low refraction.
|Target (2)||Target (4)||Target (6)||Target (7)|
|Distance||2168.50 m||4363.27 m||6428.94 m||9459.20 m|
|Refraction Lift k = 0.17||0.063 m||0.254 m||0.551 m||1.194 m|
|Calculated Height (1)||4.218 m||5.151 m||6.602 m||9.740 m|
|Measured Height||4.280 m||5.240 m||6.500 m||10.535 m|
|Difference||+0.062 m||+0.089 m||−0.102 m||+0.795 m|
|Refraction at Adjustment||k = 0.003||k = 0.110||k = 0.201||k = 0.057|
The Calculated Heights are calculated from the curvature drop of a sphere with radius R = 6371 km with a standard refraction coefficient of k = 0.17062 applied according to (1). The expected lift due to refraction for each target is shown in row Refraction Lift. The Lift depends on the Distance to the target.
In row Measured Height is the target center height with respect to water level at the observer, measured using GPS. I use the height with respect to water level at the observer rather than to water level at the target, because the targets were adjusted visually to the eye level at the observer. Measuring the Targets explains how the GPS Vectors to the target centers were measured.
Note: The water level elevation of the lake decreases about linearly with increasing distance from the observer. At the last target (7) the water level elevation is about 25 cm lower than at the observer with respect to the Reference Ellipsoid, due to variations in the gravitational field of the earth. This means that mean sea level is also 25 cm lower with respect to the Ellipsoid. The Geoid defines mean sea level with respect to the Reference Ellipsoid for each location on earth. See Obtaining Elevations for how the Geoid height is obtained.
The row Refraction at Adjustment shows the calculated prevailing refraction at the time each target was adjusted to eye level, using the measurements of the target center heights:
The different prevailing refractions at the adjustment times plus the current deviation from k = 0.17 at an observation results in the apparent height variations.
The Computer Model uses the measured GPS Vectors for the predictions after transforming them into a local coordinate system at the observer, see Target Positions and Sizes relative to the Observer. Therefore if the refraction in the Computer Model is set to the same refraction that was present when a photo was shot, the photo and the Computer Model image should match exactly.
To optimize the visibility of the targets and to help better distinguish the targets, they are arranged in the following way:
Targets of the same size appear smaller with increasing distance (left image). To counter this perspective effect, the targets were built in such a manner, that their angular size at the observer is about the same. This way they appear the same size no matter how far away from the observer they are (center image). The target (7) is about 4 times larger than target (2), see Calculating Target Size. Target (1) and (6) are different for better recognition.
The targets are not placed in a straight row, so that they do not overlap each other as viewed from the observer (right image).
The targets have two horizontal black or orange bars with a clearly visible gap between. A target is perfectly at eye level, if the crosshair of the theodolite or auto level is dead center in the gap.
Note: the slant of the orange target (6) is not intentional. It was damaged by strong winds.
To achieve that all targets appear the same size, they must have the same angular size
See Target Positions and Sizes relative to the Observer for the calculated and choosen target sizes.
Follow the links below for all data gathered and processed and the tools used:
See the following video documentations for the planing, execution and discussion of the Rainy Lake Experiment: