Flat Earth Proof? – Perfectly Flat Level Lake

YouTube video – “Flat Earth Proof? – Perfectly Flat Level Lake”

The smooth calm water of Cooper River Lake was used as a level reference to set 2 spikes at the same elevation. These two level points create an inter-visible line of sight 7,311 feet long across the water surface.

line_across_lake

img_3354Setting a spike 60 millimeters above the water surface on the eastern shore of the lake at the waterline.

img_3352Setting a second spike level with the first spike around 3 feet back from the water line.

img_3351Second spike is level with first spike 60 millimeters above the water surface on the eastern shore of the lake. The second spike 3 feet back from the water will be used as the survey point. This spike is called, “161101_COOPER_1“.

img_3367Quickly driving to the western shore to repeat the same process of setting a spike 60 millimeters above the water and then a second spike level with the first spike about 3 feet back from the water line. This survey point is called, “161101_COOPER_2“.

img_3373Measuring 1.458 meters to the notch at point “161101_COOPER_2“.

img_3374The dimension from the notch to the true target height is 0.158 meters.

img_3377The target is set on point “161101_COOPER_2” at a height of 1.613 meters above the spike facing point “161101_COOPER_1” across the water.

img_3384The Wild Heerbrugg T-2 theodolite is set up at point “161101_COOPER_1“. The measured slant height of 1.617 meters reduces to the straight height of 1.613 meters to be the same as the target height across the water.

img_3396The theodolite is precisely leveled occupying “161101_COOPER_1” before making observations to “161101_COOPER_2“.

img_3402The precisely leveled theodolite occupying “161101_COOPER_11.613 meters above the spike, viewing the target at “161101_COOPER_21.613 meters above the spike with the telescope set level, ie, the zenith angle is 90 degrees. Note that the horizontal cross hair is clearly visibly above the target 7,311 feet away. Both spikes were set at 60 millimeters above the water surface.

img_3402_close_upClose up view of the horizontal cross hair clearly over the target 7,311 feet away. The instrument cross hair and the target are both set at the same elevation using the water as the level reference. The heights of the theodolite and the target are both set at 1.613 meters above the spikes which were both set at 60 millimeters above the water.

Six sets of zenith angles were measured in F1 & F2 position.

The mean zenith angle of 6 sets measured from “161101_COOPER_1” to “161101_COOPER_2” = 90° 00′ 33.17″, SDV 0.75″ SEM 0.31″

img_3416Next the theodolite was moved to “161101_COOPER_2” and the target was placed on “161101_COOPER_1“, both set up at the same heights again, at 1.613 meters above the spike which was set at 0.060 meters above the water.

img_3419The theodolite set on “161101_COOPER_2” at 1.613 meters above the spike which was set at 0.060 meters above the water.

img_3431As before, the precisely leveled theodolite, now occupying “161101_COOPER_21.613 meters above the spike, viewing the target at “161101_COOPER_11.613 meters above the spike with the telescope set level, we see the horizontal cross hair is clearly visibly above the target 7,311 feet away. Both spikes are set at 60 millimeters above the water surface.

img_3431_closeupClose up view of the horizontal cross hair clearly visibly over the target 7,311 feet away. The instrument cross hair and the target are both set at the same elevation using the water as the level reference. The heights of the theodolite and the target are both set at 1.613 meters above the spikes which were both set at 60 millimeters above the water.

Six sets of zenith angles were measured in F1 & F2 position.

The mean zenith angle of 6 sets measured from “161101_COOPER_2” to “161101_COOPER_1” = 90° 00′ 33.50″, SDV 1.38″ SEM 0.56″

img_3434Next, a multi-frequency multi-constellation GNSS receiver was set up on “161101_COOPER_2” at a fixed height of 2 meters above the spike to collect carrier phase raw data at a 1-second rate.

img_3435Next, a multi-frequency multi-constellation GNSS receiver was set up on “161101_COOPER_1” at a fixed height of 2 meters above the spike to collect carrier phase raw data at a 1-second rate. These two GNSS receivers logged data simultaneously for 45 minutes in order to post-process the vector between the points later.

After the GNSS data collection ended, another set of zenith angles were measured from both ends of the line at a new independent height above the spikes and the water level.

img_3438Target set up and precisely leveled over point “161101_COOPER_2” for a second set of independent observations.

img_3439The new target height measured above the spike at point “161101_COOPER_2” is 1.430 meters to the notch. Adding the dimension from the notch to the true target height of 0.158 meters gives a true height above the spike at 1.588 meters.

img_3442The target at point “161101_COOPER_2” set up 1.588 meters above the spike facing point “161101_COOPER_1” ready for the second set of observations.

img_3447Unfortunately some dyslexia set in to allow for a whole set of observations to be recorded at the measured height of  1.340 meters instead of 1.430 meters above the spike at point “161101_COOPER_1“. But, fortunately taking pictures of each step helped to catch the mistake and take corrective actions while still on site.

img_3449This picture should have stopped everything, but wasn’t noticed until after recording 6 sets of zenith angles. The instrument height should be 1.588 meters. Oh well, so we have six sets of extra zenith angles measured at a height of 1.497 meters.

For what it’s worth and for completeness sake, the mean zenith angle of 6 sets measured from point “161101_COOPER_1” set up at 1.497 meters to point “161101_COOPER_2” set up at 1.588 meters = 90° 00′ 23.50″, SDV 1.52″ SEM 0.62″. 

As discouraging as this was, the theodolite was re-set at the correct height in order to continue recording a second set of independent observations at the new height of 1.588 meters.

img_3464Resetting the instrument on point “161101_COOPER_1” at the correct height of 1.430 meters above the spike to match the same height of the target at “161101_COOPER_2“. Adding the dimension from the notch to the true target height of 0.158 meters gives a true height above the spike at 1.588 meters.

img_3470Theodolite reset at 1.588 meters above the spike at point “161101_COOPER_1” ready for recording observations to “161101_COOPER_2“.

img_3473Just as before, the precisely leveled theodolite occupying “161101_COOPER_1” at a new height of 1.588 meters above the spike, viewing the target at “161101_COOPER_21.588 meters above the spike with the telescope set level, ie, the zenith angle is 90 degrees. Just as before, the horizontal cross hair is clearly above the target 7,311 feet away. Both spikes were set at 60 millimeters above the water surface.

img_3473_closeupClose up view of the horizontal cross hair above the target 7,311 feet away. The instrument cross hair and the target are both set at the same elevation using the water as the level reference. The heights of the theodolite and the target are both set at 1.588 meters above the spikes which were both set at 60 millimeters above the water. Six sets of zenith angles were measured in F1 & F2 position.

The mean zenith angle of 6 sets measured from “161101_COOPER_1” to “161101_COOPER_2” = 90° 00′ 29.00″, SDV 1.55″ SEM 0.63″. 

img_3480Setting the target on point “161101_COOPER_1” at the new height and moving the theodolite to point “161101_COOPER_2” at the same height to complete the second set of independent observations.

img_3481The target at point “161101_COOPER_1” set up 1.588 meters above the spike facing point “161101_COOPER_2” ready for the second set of observations.

img_3485Theodolite reset at 1.588 meters above the spike at point “161101_COOPER_2” ready for recording observations to “161101_COOPER_1“.

img_3494_closeup_2Close up view of the horizontal cross hair above the target 7,311 feet away. The instrument cross hair set at point “161101_COOPER_2” and the target on point “161101_COOPER_1” are both set at the same elevation using the water as the level reference. The heights of the theodolite and the target are both set at 1.588 meters above the spikes which were both set at 60 millimeters above the water. Six sets of zenith angles were measured in F1 & F2 position.

The mean zenith angle of 6 sets measured from “161101_COOPER_2” to “161101_COOPER_1” = 90° 00′ 26.67″, SDV 0.52″ SEM 0.21″. 

img_3498Next, a multi-frequency multi-constellation GNSS receiver was set up on “161101_COOPER_2” at a fixed height of 2 meters above the spike to collect carrier phase raw data at a 1-second rate for a second independent session.

img_3505Next, a multi-frequency multi-constellation GNSS receiver was set up on “161101_COOPER_1” at a fixed height of 2 meters above the spike to collect carrier phase raw data at a 1-second rate. These two GNSS receivers logged data simultaneously for 55 minutes for a second independent session in order to post-process the vector between the points later.

Post-processed GNSS vectors from point “161101_COOPER_1” to point “161101_COOPER_2vectors

Adjusted State Plane Grid Coordinates and Geodetic Latitude & Longitudeadjusted-values

Tabulated Results Of Observations And Computations Comparedcurvature-results

Advertisements