One Mile Level Line

YouTube Video – “One Mile Level Line”

 

1_mile_151109Observations made in November of 2015 between Mile Posts 27 and 28 on NJ Route 206.

first_vidMy first video, “Geodetic Surveyor Straightens Out The Flat Earth”.                                                             ….. Hooray !   Geodesy to the rescue !   Nope.

1_mile_151109_2Six sets of near real-time reciprocal zenith angles were measured and recorded. The tabulated reduced data is shown below.

151109_observations

1_mile_151109_3The 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.

ligoThe 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 –

img_3665High 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” .

gnss_observationsTabulation of post-processed vectors

gnss_adjustmentAdjusted  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.

level_line

img_3775Target 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.

img_3791Theodolite set at Mile Post 28

img_3788Setting 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.

img_3800_closeupView 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.

img_3806Setting 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.

img_3777Target 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.

img_3818View 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.

time_weather

 

img_3547No thank you …..

161117_set_a

161117_set_b

161117_set_c

161117_set_d

161117_set_e

161117_set_f

161117_reciprocal_sets_

final_results

 

 

 

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

Bench Marks – Geodetic Control

Surveyors reference their work to geodetic control points commonly referred to as “bench marks”.

aph_disc

NGS Data Sheet – APPLE PIE HILL RESET (PID = JU2986)

 

aph_llhBench Marks are referenced to the geodetic datum.

aph_spcs

The geodetic position is projected onto the State Plane Coordinate System mapping surface.

nos_5_spcs_stem

State Plane Coordinate System of 1983 Manual (PDF)

aph_nj_triang_diagram

The Geodetic Triangulation positions are computed as Latitudes and Longitudes for each control point.

spcs_zones

Every state has one or more state plane coordinate system zones that are used to flatten out the curved geodetic positions onto a mapping surface.

tm_projection

 

 

 

 

 

 

 

 

Flat Earth Proof? – Flat Level Lake Measurements

YouTube Video – “Flat Earth Proof? – Flat Level Lake Measurements”

On a calm day, Union Lake served as a level reference to set stakes at the same elevation on opposite sides creating an intervisible line of sight over the water surface. Repeated sets of near real-time reciprocal vertical angle measurements were made between the stakes. The results are presented here.

union_lakeUnion Lake in Millville, New Jersey

img_2995A 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.

img_3019The 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.

img_3037Target 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.

img_3039All the targets were consistently maintained at the same height for each set up over each stake for each new occupation.

img_3078Wild 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.

img_3128The axis of the Theodolite was consistently set up at the same height as the targets for each new occupation of each stake.

img_3035The targets were precisely leveled and centered over each stake for each new occupation made on each stake.

img_3077The Theodolite was precisely leveled and centered over each stake for each new occupation made on each stake.

img_3067Sighting 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.

img_3131Late afternoon sun glare avoided using Kern umbrella.

img_3136Using Kern umbrella to cast shade onto the Theodolite.

tbc_gnssGNSS data processing

tbc_t2T2 observation input

tbc_adjustmentGNSS & T2 observations combined least squares adjustment results reported at 2 sigma (95% confidence)

Final results produced from a least squares adjustment combining all the observations. results

Observing NYC From Washington Rock

YouTube Video – Observing NYC From Washington Rock

img_3233Recording survey observations of NYC from Washington Rock State Park.

vert_angle_deg=0.1 / horiz_angle_deg=-0.5View of my Wild Heerbrugg T2 Theodolite with NYC in the distance using the Theodolite app on my iPhone.

vert_angle_deg=0.1 / horiz_angle_deg=0.6View at 4.0X using the Theodolite app on my iPhone.

 

img_3229Precisely leveling the theodolite to establish the horizontal plane immediately prior to making observations.

level_vialThe Wild T2 level vial.

img_2942Making adjustments to the Wild T2 internal vertical circle compensator to assure high precision results from sets of repeated F1 & F2 observations.

161024_wrp_3Position of theodolite at point 161024_WRP_3N40°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.)

img_3222

Telescope elevation is 503.151 + 5.259 ft = 508.4 feet NAVD88.

img_3245Theodolite crosshair is level at elevation 508.4 feet NAVD88 intersecting the Empire State Building at around the 95th floor 143,383.83 feet away (27.2 miles).

Zenith Angle measured to top of spire = 89° 46′ 51″  +/- 12″

NGS Data Sheet for EMPIRE STATE BUILDING (PID = KU3602)

closeup_empire_state_buildingClose up estimating 95th floor of the Empire State Building.

 

one_world_za_89-36-36_light

Zenith angle measured to the blinking white light at the top of the spire on the One World Trade Center building = 89° 36′ 35.8″  sdev 2.5″, sem 1.25″ (4 sets of F1 & F2 pointings).

 

one_world_90za_light

Theodolite crosshair is level at elevation 508.4 feet NAVD88 intersecting the One World Trade Center Building  at someplace nearly halfway or more up the building 132,164.69 feet away (25.0 miles).

No NGS Data Sheet exists for this location currently. The horizontal position determined privately is – N40°42’46.09199″, W74°00’52.13634″ NAD83(2011).

tbc_screen_shotComputations and observation reductions combing measurements made from Fire Island Light House.

results*DROP OF CURVE COMPUTED USING 8 INCHES TIMES MILES SQUARED.

 

 

 

Fire Island Lighthouse – Observations

YouTube Video – Observations At Fire Island Lighthouse

img_2834On this return trip to the Fire Island Light House, zenith angle observations were recorded to the ocean surface from a point located on the front porch and from a point on the upper deck. This lighthouse is positioned in the NGS database as FIRE ISLAND LIGHTHOUSE 1865 and FIRE ISLAND LH EXT 3 1962 .

img_2840From 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 NYQN .

img_2850The trunnion axis of the Wild T2 telescope was determined to be at elevation 17.90 feet NAVD88.

ocean_surface_from_1_porch_za_90This is a picture taken through the telescope set to be horizontal at elevation 17.90 feet NAVD88 looking southward over the ocean.

ocean_surface_from_1_porch_za_90-05-28This 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″).

img_2887Next 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 NYQN .

img_2279The resulting elevation is in close agreement with the NGS station located on the opposite side of the deck called FIRE ISLAND LH EXT 3 1962 .

img_2891The elevation of the theodolite was determined to be 160.24 feet NAVD88 .

ocean_surface_from_lh_deck_za_90-12-46

This picture was taken through the telescope pointing at the ocean surface from the deck of the lighthouse. The elevation of the theodolite is 160.24 feet NAVD88. Four sets of F1 & F2 pointings were recorded. The mean zenith angle = 90° 12′ 46″ (std err = 1.2″).

empire_state_90zaThe Empire State Building was visible in the distance, which is also a Triangulation Station known as EMPIRE STATE BUILDING . This picture was taken through the telescope set horizontal at elevation 160.24 feet NAVD88 from the deck of the Fire Island Lighthouse at a distance of 216,874.9 Feet (41.07 Miles).

ft_light_za-90_1The blinking white light of the One World Trade Center building could be seen. This picture was taken through the telescope set horizontal 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).

ft_light_za-89-50-40This 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  One World Trade Center .  At the time of posting this blog entry, the elevation of the white light is estimated to be 1,785 +/- 12 Feet.