YouTube Video – “One Mile Level Line”
Observations made in November of 2015 between Mile Posts 27 and 28 on NJ Route 206.
My first video, “Geodetic Surveyor Straightens Out The Flat Earth”. ….. Hooray ! Geodesy to the rescue ! Nope.
Six sets of near real-time reciprocal zenith angles were measured and recorded. The tabulated reduced data is shown below.
The raw measurements uncorrected for deflection of the vertical are referenced to the geoid. These measurements reveal the tilt that exists between the vertical plumb directions at the ends of the line. At this latitude, the tilt is found to be approximately 1 arc minute in one mile rounding off. If need be, for various specific applications that require very precise determinations of the curvature and the tilt, high precision measurement procedures can be applied to account for these differences at very exacting positional tolerances. One such example among numerous that can be examined is the case of the construction of the LIGO facilities.
The closest LIGO will ever come to detecting gravity was during the construction when the tubes were being built STRAIGHT rather than following the natural curved level path linear structures such as pipelines, highways, and railroads normally follow. In the case of LIGO, the long tubes had to be constructed straight to within very exacting tolerances.
……. back to New Jersey Route 206 –
High precision GNSS receivers were used to record repeated static sessions in November 2015 and again in November 2016. Carrier phase multi-constellation, multi-frequency GNSS data was logged to produce high precision 3D vectors between Mile Posts 27 & 28. Geodetic latitude, longitude and ellipsoid heights were produced by adjusting the repeated vectors from NGS CORS (Continuously Operating Reference Stations) “NJTW” and “NJGC” .
Tabulation of post-processed vectors
Adjusted Latitude, Longitude, Ellipsoid Height, State Plane Coordinates and Elevations.
Returning One Year Later To Repeat The Test ….
By setting the target and the theodolite up at these calculated heights, a level line of sight was established at elevation 59.30 feet NAVD88.
Target at Mile Post 27 over the point at elevation 53.79 at a measured height of 5.51 feet places the target at elevation 59.30 feet.
Theodolite set at Mile Post 28
Setting the theodolite at a measured height of 4.78 feet over Point 28 at elevation 54.52 places the telescope at elevation 59.30 feet.
View of horizontal cross hair through the telescope set level at elevation 59.30 feet on Point 28 looking at the target set up at elevation 59.30 feet on Point 27. Note the distance the cross hair is over top of the target. Six independent sets of 4 zenith angle repetitions in F1 & F2 positions were observed and recorded for a total of 24 near real-time reciprocal zenith angles over a 4 hour period from both ends of this level line. The results are tabulated down below.
Setting the theodolite at a measured height of 5.51 feet over Point 27 at elevation 53.79 places the telescope at elevation 59.30 feet.
Target at Mile Post 28 over the point at elevation 54.52 at a measured height of 4.78 feet places the target at elevation 59.30 feet.
View of horizontal cross hair through the telescope set level at elevation 59.30 feet on Point 27 looking at the target set up at elevation 59.30 feet on Point 28. Note the distance the cross hair is over top of the target. Six independent sets of 4 zenith angle repetitions in F1 & F2 positions were observed and recorded for a total of 24 near real-time reciprocal zenith angles over a 4 hour period from both ends of this level line. The results are tabulated down below.
Time and weather were recorded at the start and the end of each independent set of zenith angle repetitions.
No thank you …..
Setting a spike 60 millimeters above the water surface on the eastern shore of the lake at the waterline.
Setting a second spike level with the first spike around 3 feet back from the water line.
Second 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“.
Quickly 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“.
Measuring 1.458 meters to the notch at point “161101_COOPER_2“.
The dimension from the notch to the true target height is 0.158 meters.
The 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.
The 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.
The theodolite is precisely leveled occupying “161101_COOPER_1” before making observations to “161101_COOPER_2“.
The precisely leveled theodolite occupying “161101_COOPER_1” 1.613 meters above the spike, viewing the target at “161101_COOPER_2” 1.613 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.
Close 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.
Next 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.
The theodolite set on “161101_COOPER_2” at 1.613 meters above the spike which was set at 0.060 meters above the water.
As before, the precisely leveled theodolite, now occupying “161101_COOPER_2” 1.613 meters above the spike, viewing the target at “161101_COOPER_1” 1.613 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.
Close 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.
Next, 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.
Next, 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.
Target set up and precisely leveled over point “161101_COOPER_2” for a second set of independent observations.
The 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.
The 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.
Unfortunately 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.
This 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.
Resetting 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.
Theodolite reset at 1.588 meters above the spike at point “161101_COOPER_1” ready for recording observations to “161101_COOPER_2“.
Just 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_2” 1.588 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.
Close 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.
Setting 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.
The 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.
Theodolite reset at 1.588 meters above the spike at point “161101_COOPER_2” ready for recording observations to “161101_COOPER_1“.
Close 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.
Next, 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.
Next, 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.
Bench Marks are referenced to the geodetic datum.
A three-foot carpenters level was used to set 2 stakes close together on each side, for a total of four stakes numbered 1 & 2 on the southwestern edge and 3 & 4 of the northeastern edge.
The distance above the water surface was measured at 0.175 meters. All 4 stakes were set at the same distance above the water surface as closely and carefully as could be achieved. The least squares adjustment of all the observations reveals that the tops of all 4 stakes were set to be within the worst case range of 1/2 inch at elevation 26.03 feet NAVD88.
Target set on Stake 4 and GNSS receiver set on Stake 3 logging carrier phase multi-frequency, multi-constellation data at a 1-second rate at 2 meters over the stake.
All the targets were consistently maintained at the same height for each set up over each stake for each new occupation.
Wild T2 1-second Theodolite set on Stake 2 and GNSS receiver set on Stake 1 logging carrier phase multi-frequency, multi-constellation data at a 1-second rate at 2 meters over the stake.
The axis of the Theodolite was consistently set up at the same height as the targets for each new occupation of each stake.
The targets were precisely leveled and centered over each stake for each new occupation made on each stake.
The Theodolite was precisely leveled and centered over each stake for each new occupation made on each stake.
Sighting conditions were good. Sets of F1 & F2 observations were repeated for horizontal and for vertical angles to the targets and also to the tops of the 2 meter poles holding the GNSS receiver as shown in this picture. The target is on Stake 2 and the GNSS receiver is on Stake 1.
Late afternoon sun glare avoided using Kern umbrella.
Using Kern umbrella to cast shade onto the Theodolite.
GNSS data processing
T2 observation input
GNSS & T2 observations combined least squares adjustment results reported at 2 sigma (95% confidence)
Recording survey observations of NYC from 
View of my 
View at 4.0X using the 
The Wild T2 level vial.
Making adjustments to the Wild T2 internal 
Position of theodolite at point 161024_WRP_3 = N40°36’45.62613″, W74°28’20.39403″ (NAD83 2011), 503.151 feet orthometric height NAVD88 (2 Sigma error = +/- 0.02 feet N, +/- 0.01 feet E, +/-0.04 feet Elev.)
Theodolite crosshair is level at elevation 508.4 feet NAVD88 intersecting the 
Close up estimating 95th floor of the Empire State Building.
Computations and observation reductions combing measurements made from 
*DROP OF CURVE COMPUTED USING 8 INCHES TIMES MILES SQUARED.
From a location on the front porch the elevation was determined to be 12.44 feet NAVD88 by recording carrier phase dual frequency multi-constellation GNSS data for over one hour and post processed to the closest NGS CORS called 
The 
This is a picture taken through the telescope set to be horizontal at elevation 17.90 feet NAVD88 looking southward over the ocean.
This is a picture taken through the telescope at elevation 17.90 feet NAVD88 looking southward pointing to the ocean surface. Six sets of F1 and F2 points were recorded. The mean zenith angle = 90° 05′ 28″ (std err = 2″).
Next the theodolite was moved up to a location on the deck of the lighthouse. The elevation of the deck was determined to be 154.82 feet NAVD88 by recording carrier phase dual frequency multi-constellation GNSS data for over one hour and post processed to the closest NGS CORS called 
The resulting elevation is in close agreement with the NGS station located on the opposite side of the deck called 
The elevation of the theodolite was determined to be 160.24 feet NAVD88 .
The 
The blinking white light of the 
This picture was taken through the telescope at elevation 160.24 feet NAVD88 from the deck of the Fire Island Lighthouse at a distance of 222,361.3 Feet (42.11 Miles). Four sets of F1 & F2 pointings were recorded to the white blinking light located on the spire. The mean zenith angle = 89° 50′ 39.8″ (std err = 2″). No published position for this location exists at this time. Additional research is required to obtain the precise elevation of the white blinking light on top of 