543 lines
28 KiB
Plaintext
543 lines
28 KiB
Plaintext
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LASER LEVEL EXPERIMENTS
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MEASURING CURVATURE OVER WATER
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SURFACE
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Terrestrial Laser Targeting (TLT) Method to Measure Curvature of Water Surface on Lake Balaton, Hungary and Lake Ijssel, Netherlands.
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Authors: Sandor Szekely, Mike Cavanaugh
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EXPERIMENT GOALS
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FECORE Inc. intends to achieve the greatest distance laser optical measurement over water surfaces in Hungary and The Netherlands connected to our series of refraction experiments.
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The main principles of the experiments are:
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• To study the effects of terrestrial refraction in different ambient conditions at very small incidence angles close to the Non-Uniform Density Transition Zone (NUDTZ) above water surfaces.
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• To determine the shape of the surface of large bodies of water.
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MOTIVATION
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Through our previous experiments, we’ve found inconsistencies with the curvature of the geoid model over water surfaces, and we hypothesize the theoretical calculation of curvature on the surface of Lake Balaton and Lake Ijssel is nonexistent.
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We are researching whether these lakes have a geopotential surface anomaly, or are all water surfaces non-uniform with the geoid surface.
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ABSTRACT
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The Terrestrial Laser Targeting (TLT) method was used in order to achieve long-distance curvature measurements over water surfaces. A Super Accurate Laser Aiming Device (SALAD) and a high-precision laser device with a collimation of 0.08mRad were developed. Through the analysis of the error source models of curvature testing, the optical configuration of the testing devices was optimized. Several target distances in different ambient conditions in different locations were tested. Environment readings are referenced and calculated to reduce measurement errors caused by ambient conditions. Through the above processes, the relative accuracy of the measurements meet the experiment design requirements. The TLT method used in the experiments has high accuracy and practical advantages.
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INTRODUCTION
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The geoid is defined as a more smoothed representation of the Earth and is described as the surface that would be assumed by the undisturbed surface of the sea. Therefore, the water surface follows the geopotential surface, and by that we have the common understanding water surfaces follow the curvature of Earth. The topographic surface is measured with different surveying methods all based on the assumption of the WGS84 model.
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INTRODUCTION
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The required accuracy depends on the needed deliverable output. Accuracy refers to how closely a measurement or observation compares to a true or established value, since measurements and observations are subject to errors. By analyzing the error-source models of curvature testing, the optical configuration design of the testing device was optimized. The precision of the TLT measurement is expected to be within 1% of the volume compared to the target hidden height calculated on each measurement distance to arrive at a definitive result. The accuracy of the Terrestrial Laser Targeting method is affected by the angle of sight, distance from the object, and weather conditions. Considering those limitations, the research will evaluate and compare accuracy with the volume of expected target hidden height calculation.
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INTRODUCTION
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The Terrestrial Laser Targeting (TLT) survey method can be used with sufficient accuracy on large distance curvature measurements. Compared with other curvature test methods, the method used in this paper has proper accuracy and practical advantages.
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In this document, we are introducing TLT
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measurements up to 40 km (25 miles) conducted by our research team as late as the 23rd of April, 2018.
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OBJECTIVE OF RESEARCH
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The general objective of this research is to evaluate and compare the results of TLT measurements over surfaces of lakes with the calculation of the geoid curvature to determine the shape of the lake surface.
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Our secondary objective is to study the effects of terrestrial refraction in different ambient conditions at very small incidence angles close to the Non-Uniform Density Transition Zone (NUDTZ) above the surface of the lakes.
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SCOPE AND LIMITATION OF
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THIS STUDY
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The scope of this study is limited within evaluating and comparing the curvature of the surface on Lake Balaton and Lake Ijssel and the effects of small incidence angle refraction. Determining and evaluating the accuracy of the measurements requires favorable weather conditions. During measurements taken on Lake Balaton, there were many limitations, especially adverse weather conditions (cold, humidity, snow, and wind). Due to the unstable weather, all goals set forth were not accomplished in the timeframe allowed, so our measurements were continued on Lake Ijssel in favorable weather conditions.
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SIGNIFICANCE OF THE STUDY
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This document can be used as a spring board for further studies for those who are interested in the research of water surface model measurements.
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IN THIS DOCUMENT
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We will provide our measurements and guide you through:
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• The experimental process • Environmental conditions • Curvature calculations • Optical and geodesic correction factors • The references and the terms used, as well as
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an explanation of results.
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MEASUREMENT PROCEDURE LAKE BALATON
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The initial aiming of the SALAD occurred during daytime to the direction of the target by visual observation with a precision of ±1 degree using a Nikon P900 camera and a Celestron Powerseeker 70EQ telescope. The laser beam was difficult to see from a side view as it was well collimated, therefore it had to be within a few degrees facing the observer to be detectable. After sunset, the laser beam was adjusted parallel to the water surface using the horizon line and visible city lights on the opposite shore as a reference. An observation team was placed on the opposite shore spread along the coast line to locate the laser beam while maintaining communication with the laser operators in order to fine tune the beam’s direction.
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MEASUREMENT PROCEDURE LAKE IJSSEL
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Based on our experience with aiming difficulties at Lake Balaton, Mike Cavanaugh made changes in the software of the SALAD and developed an automatic GPS targeting system. The new aiming precision of the SALAD is ±0.01 degrees. We used a closer distance reference target with GPS coordinates to calibrate the laser heading, and the software was then capable of automatic laser targeting to any position based on GPS coordinates. The observation team placed on the opposite shore shared their GPS coordinates with the laser team, and the laser was automatically pointed to that location. The laser beam then was fine tuned by the teams through GSM communication.
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MEASUREMENT PROCEDURE
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Once the beam was directly on the target, we took the measurement readings. We used optical visualization with cameras and a measurement board.
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LASER BEAM HEIGHT
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CALCULATION
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We determined the lowest minimum altitude of the laser beam on the curved surface model at the target location using Autocad with 14 digits precision and compared the results with generally accepted curvature calculators.
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We then calculated the corrections for the height above MSL (Mean Sea Level), the WGS84 ellipsoid model, and the difference in geoid undulation.
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REFRACTION
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Laser light travels in a straight line through a homogeneous medium. Light angles due to different refraction indexes in a non-homogeneous atmosphere. We calculated the direction and amount of refraction to show how much laser-beam deviation affects the measurement outcome. In a non-homogeneous atmosphere where the index of refraction increases with height, rays of sufficiently small initial elevation angles are refracted upward. This curvature is proportional to the rate of increase of the bi-directional index of refraction with height.
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Lake Balaton, Hungary measurement 21st to 27th of February, 2018
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Map of Lake Balaton showing the measuring position and laser position.
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LASER POSITION Lake Balaton
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GEOID UNDULATION – LAKE BALATON
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Geoid undulation is the term used to describe the distance of the geoid above (positive) or below (negative) the mathematical reference ellipsoid (WGS84).
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Geoid undulation was at the same level in both positions.
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[1]
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EFFECT OF TIDES - LAKE BALATON
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“Lake tides are known to have amplitudes of up to 10 cm (0.33 feet) in larger lakes (Trebitz, 2006). In case of Lake Balaton, the shallow depth and the relatively low water volume of the lake suggests this effect would be smaller. During long-term investigations of water movement conducted in the 1970’s, no evidence of lake tides were observed (Muszkalay, 1973), therefore we do not expect tides to have influenced the lake level.”
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[1]
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REFRACTION CONDITIONS
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The lake was partly frozen, therefore walking along the beam on the ice or using a boat was not possible. As no data on the ambient conditions along the laser beam was available, we measured the conditions at the measuring position and laser position. The data showed there were no significant differences in temperature and humidity between the start and end points of the laser beam.
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MEASUREMENT 1
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- LAKE BALATON
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On the 22nd of February at 22:44 PM, the blue laser pointer was at the opposite shore (Siofok) to help the targeting of the SALAD at the laser position. The pointer was held in hand at 1.5 meters (4.92 feet) above the lake surface level at Siofok. The team at the laser position was able to see the beam and record it from 12 km (7.46 miles) at 1.6 meters (5.25 feet) above the water level.
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MEASUREMENT 1 22nd February 2018 at 22:44 PM
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Balatonvilagos observation position
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MEASUREMENT 1 22nd February 2018 at 22:44 PM
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Siofok Laser position
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LASER BEAM HIDDEN HEIGHT
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CALCULATION
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The 12km (7.46 miles) distance calculations based on a spherical model results in a target hidden height of the measurement position of 4.56 meters (14.96 feet)
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CURVATURE CORRECTION WGS84 AND
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MSL
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The radius of Earth is 6366.776 km (3956.131 miles) at the 46.911702° latitude (Siofok) on the WGS84 ellipsoid model, and 6366.75 km (3956.115 miles) at the 46.982097° latitude (Balatonvilagos Target). The measurement direction heading is 131.09°
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R = √ [ (r1² * cos(B))² + (r2² * sin(B))² ] / [ (r1 * cos(B))² + (r2 * sin(B))²]
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The calculated difference of curvature drop on WGS84 to the spherical model from Siofok to Target: +0.046 mm (+0.0018 inches) The height of Lake Balaton above Mean Sea Level is +105 meters (+344.49 feet) that gives a calculated difference of -0.187 mm (+0.0074 inches) of curvature drop.
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MEASUREMENT 1
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ambient conditions 22nd February 2018 at 22:44 PM
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Balatonvilagos Hum. 90% Temp. +2°C (35.6°F) Wind 32km/h (19.9 mph) waves 50cm high (1.64 feet)
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Siofok Hum. 92% Temp. +3°C (37.4°F) Wind 32km/h Waves 50cm high
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REFRACTION CALCULATION
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OF 1ST MEASUREMENT
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The lake temperature was 2°C (35.6°F) and the air at night was around 3°C (37.4°F) above the lake.
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The humidity is always higher the closer you are to the lake surface, which indicates a lower refractive index.
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The ambient conditions showed that the refractive indexes were about the same at the two sides of the lake. The difference in temperature was marginal. The level of humidity decreases as you rise in altitude above lake surface.
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We concluded the gradients above the lake surface did not cause any significant refraction of the laser beam.
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POSITIONS AND HEIGHT DATA AT
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LAKE BALATON
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Balatonvilagos (laser position): Latitude = 46.9820972222222° N = 46° 58' 55.55" N Longitude = 18.162325° E = 18° 9' 44.37" E GPS ellipsoidal height = 149.85 meters (491.6 feet) Geoid height = 44.918 meters (147.367 feet)
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Siofok (measurement position): Latitude = 46.9117027777778° N = 46° 54' 42.13" N Longitude = 18.0444944444444° E = 18° 2' 40.18" E GPS ellipsoidal height = 149.85 meters (491.6 feet) Geoid height = 45.047 meters (147.790 feet)
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Difference of geoid height: -129 mm (-5.08 inches)
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Laser beam was recorded at 1.6 meters (2.79 feet)
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Measurement 1 Target hidden height spherical model: 4.570 meters (14.993 feet)
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WGS84 laser to target correction: +0.029 mm (0.0011 inch)
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MSL correction: -0.119 mm (-0,0047 inch)
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Refraction correction +0 mm (+0 inch)
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EXPECTED target hidden height 4.5699 meters (14.9929 feet)
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Difference of geoid height: 129 mm (-5.08 inches)
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SIOFOK POSITION Lake Balaton
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MEASUREMENT 2
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LAKE BALATON
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On the 26th of February at 20:00, the blue laser pointer was placed at Balatonvilagos on the SALAD at 2.2 meters (7.2 feet) above the lake surface. The source of the beam was seen on the opposite shore at 12km (7.46 miles) distance (Siofok) at 1.6 meters (5.25 feet) above the lake surface.
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MEASUREMENT 2
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26th of February 2018 at 20:00
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Balatonvilagos Laser location
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Siofok observation location
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The blue laser at 2.2 meters.
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The green laser at 13 meters.
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CURVATURE CORRECTION WGS84 AND
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MSL
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The radius of Earth is 6366.776 km (3956.131 miles) at the 46.911702° latitude (Siofok) on the WGS84 ellipsoid model, and 6366.75 km (3956.115 miles) at the 46.982097° latitude (laser). The measurement direction heading is 228.91°
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R = √ [ (r1² * cos(B))² + (r2² * sin(B))² ] / [ (r1 * cos(B))² + (r2 * sin(B))²]
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The calculated difference of curvature drop on WGS84 to the spherical model from Laser to Siofok is: -0.046 mm (-0.0018 inches) The height of Lake Balaton above Mean Sea Level is +105 meters (+344.49 feet) that gives a calculated difference of -0.187 mm (+0.0074 inches) of curvature drop.
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MEASUREMENT 2
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26th of February 2018 at 20:00
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Balatonvilagos Hum. 58% Temp. -6°C (21.2°F) Wind 22km/h (13.7 mph) waves 1m high (3.3 feet)
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Siofok Hum. 60% Temp. -5°C (23°F) Wind 28km/h (17.4 mph) waves 1m high (3.3 feet)
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REFRACTION CALCULATION
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OF 2ND MEASUREMENT
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The lake temperature was 0°C (32°F) and the air at night was down to a minimum of -11°C (12.2°F) above the lake. Air temperature at the time of the measurement was -6°C (21.2°F).
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The ambient conditions showed the refractive indexes were about the same at the two sides of the lake. The change in temperature was decreasing and humidity was increasing above the lake surface versus the air above – resulting in a slight upward refraction.
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REFRACTION CALCULATION
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OF 2ND MEASUREMENT
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Angle of incidence (θ1): 0.0029°
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Refractive index calculation (based on Modified Edlén Equation)
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n1 = 1.000302762 (445nm, -6°C, 60%)
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n2 = 1.000296015 (445nm, 0°C, 70%)
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Angle of refraction is calculated with Snell’s law: sin θ2 = (n1 * sinθ1) / n2 = 0.00290002 degrees Angle of deviation = 0.000000020°
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We conclude the ambient conditions refracted the laser beam upward by a maximum of 0.235 mm (0.00924 inches)
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Laser beam was recorded at 1.6 meters (2.79 feet)
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Measurement 2 Target hidden height spherical model: 3.52 meters ( 11.5484 feet)
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WGS84 laser to target correction: +0.026 mm (0.001 inches)
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MSL correction is -0.119 mm (-0.0047 inches)
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Refraction correction (max) +0.235 mm (+0.00924 inches)
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EXPECTED target hidden height 3.52009 meters (11.5487 feet)
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Difference of geoid height: -129 mm (-5.08 inches)
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Lake Ijssel, Netherlands measurement April 2018
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Map of Lake Ijssel between the four measurement positions and laser position
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LASER POSITION Lake Ijssel
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Differences between gravimetric and geometric height anomalies at height markers in The Netherlands
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GEOID UNDULATION AT
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LAKE IJSSEL
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Geoid undulation is at the same level in all positions. [2]
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EFFECT OF TIDES AT LAKE IJSSEL
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Lake tides are known to have amplitudes of up to 10 cm (0.33 feet) in larger lakes (Trebitz, 2006). In case of Lake Ijssel, the average shallow depth of 5.5 meters (18 feet) and the relatively low water volume of the lake suggests this effect would be even smaller and within our measurement error margin.
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REFRACTION CONDITIONS
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The lake temperature ranged from 7 - 14 Celsius (45F - 57F).
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As no data on the ambient conditions along the laser beam was available, we used data at the two end positions. The data showed there were no significant differences in temperature and humidity between the start and end points of the measurements.
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TARGET 1 POSITION Lake Ijssel
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(Measurement 3)
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MEASUREMENT 3
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LAKE IJSSEL TARGET 1
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On the 8th of April at 1:00 AM, the blue laser pointer was placed on the SALAD at 2.85 meters (9.35 feet) above the lake surface.
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It was seen on the opposite shore at 21.26 km (13.21 miles) to Target 1 at 1.2 meters (3.94 feet) above the lake surface.
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MEASUREMENT 3
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Lake Ijssel 8th April 2018 at 1:00 AM
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Enkhuizen Laser location
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MEASUREMENT 3
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Lake Ijssel 8th April 2018 at 1:00 AM
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Target 1 observation location
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MEASUREMENT 3
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Lake Ijssel 8th April 2018 at 1:00 AM
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Target 1 at 21.26km observation location
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LASER BEAM HIDDEN HEIGHT
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CALCULATION MEASUREMENT
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3 TARGET 1
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The 21.26km (13.21 Miles) calculations based on a spherical model results in a target hidden height of the Measurement 3 Target 1 position of 18.18 meters (59.6 feet)
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CURVATURE CORRECTION WGS84 AND
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MSL
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The radius of Earth is 6364.598 km (3954.778 miles) at the 52.836208° latitude (Target 1) on the WGS84 ellipsoid model, and 6364.643 km (3954.806 miles) at the 52.710094° latitude (laser). The measurement direction heading is 48.51°
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R = √ [ (r1² * cos(B))² + (r2² * sin(B))² ] / [ (r1 * cos(B))² + (r2 * sin(B))²]
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The calculated difference of curvature drop on WGS84 to the spherical model from Laser to Target 1: +0.251 mm (+0.0099 inches)
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The height of Lake Ijssel above sea level is 0 meters.
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MEASUREMENT 3
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8th April 2018 at 1:00 AM
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Lake Ijssel water temperature chart, April 2018
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REFRACTION CALCULATION
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|
|
OF 3RD MEASUREMENT
|
|||
|
|
|
|||
|
|
The lake temperature was 7.6 Celsius (45.7 F) and the air was 10.8 Celsius (46.4 F) above the lake.
|
|||
|
|
The ambient conditions showed the refractive indexes were about the same at the two sides of the lake. The difference in temperature was marginal. The level of humidity decreases as you rise in altitude above lake surface.
|
|||
|
|
|
|||
|
|
REFRACTION CALCULATION
|
|||
|
|
OF 3RD MEASUREMENT
|
|||
|
|
|
|||
|
|
Angle of incidence (θ1): 0.0047°
|
|||
|
|
Refractive index calculation (based on Modified Edlén Equation)
|
|||
|
|
n1 = 1.000284523 (445nm, 10.8°C, 76%)
|
|||
|
|
n2 = 1.000287811 (445nm, 7.6°C, 85%)
|
|||
|
|
Angle of refraction is calculated with Snell’s law: sin θ2 = (n1 * sinθ1) / n2 = 0.004699985 degrees Angle of deviation = 0.000000015°
|
|||
|
|
We concluded the ambient conditions refracted the laser beam downward by maximum of 0.329 mm (0.01295 inches)
|
|||
|
|
|
|||
|
|
POSITIONS AND HEIGHT DATA AT
|
|||
|
|
TARGET 1 POSITION
|
|||
|
|
|
|||
|
|
Enkhuizen (laser position): Latitude = 52.7100944444445° N = 52° 42' 36.34" N Longitude = 5.29597222222222° E = 5° 17' 45.5" E GPS ellipsoidal height = 0 meters (0 feet) Geoid height = 42.409 meters (139.137 feet)
|
|||
|
|
Target 1 (measurement position): Latitude = 52.8362027777778° N = 52° 50' 10.33" N Longitude = 5.53254166666667° E = 5° 31' 57.15"E GPS ellipsoidal height = 0 meters (0 feet) Geoid height = 42.176 meters (138.373 feet)
|
|||
|
|
Difference of geoid height: +233 mm (9.17 inches)
|
|||
|
|
|
|||
|
|
Laser beam recorded at 1.1 meters (3.6 feet)
|
|||
|
|
|
|||
|
|
Measurement 3 Target hidden height spherical model: 18.18 meters (59.6449 feet)
|
|||
|
|
WGS84 laser to target correction: +0.18 mm (0.007 inches)
|
|||
|
|
MSL correction is 0mm
|
|||
|
|
Refraction correction (max) -0.329 mm (-0.01295 inches)
|
|||
|
|
EXPECTED target hidden height 18.17985 meters (59.64445 feet)
|
|||
|
|
Difference of geoid height: +233 mm (+9.17 inches)
|
|||
|
|
|
|||
|
|
TARGET 2 POSITION Lake Ijssel
|
|||
|
|
(Measurement 4)
|
|||
|
|
|
|||
|
|
MEASUREMENT 4
|
|||
|
|
LAKE IJSSEL TARGET 2
|
|||
|
|
|
|||
|
|
On the 8th of April at 3:00 AM, the blue laser pointer was placed on the SALAD at 2.85 meters (9.35 feet) above the lake surface. It was seen on the opposite shore at 28.68 km (17.82 miles) to Target 2 at 0.85 meters (2.79 feet) above the lake surface.
|
|||
|
|
|
|||
|
|
MEASUREMENT 4
|
|||
|
|
Lake Ijssel 8th April 2018 at 3:00 AM
|
|||
|
|
Enkhuizen Laser location
|
|||
|
|
|
|||
|
|
MEASUREMENT 4
|
|||
|
|
Lake Ijssel 8th April 2018 at 3:00 AM
|
|||
|
|
Target 2 observation location
|
|||
|
|
|
|||
|
|
MEASUREMENT 4
|
|||
|
|
Lake Ijssel 8th April 2018 at 3:00 AM
|
|||
|
|
Target 2 observation location
|
|||
|
|
|
|||
|
|
LASER BEAM HIDDEN HEIGHT
|
|||
|
|
CALCULATION MEASUREMENT
|
|||
|
|
4 TARGET 2
|
|||
|
|
|
|||
|
|
The 28.68km (17.82 miles) distance calculations based on a spherical model results in a target hidden height of the Measurement 4 Target 2 position of 40.21 meters (131.9 feet).
|
|||
|
|
|
|||
|
|
CURVATURE CORRECTION WGS84 AND
|
|||
|
|
MSL
|
|||
|
|
|
|||
|
|
The radius of Earth is 6364.589 km (3954.772 miles) at the 52.860294° latitude (Target 2) on the WGS84 ellipsoid model, and 6364.643 km (3954.806 miles) at the 52.710094° latitude (laser). The measurement direction heading is 54.15°
|
|||
|
|
R = √ [ (r1² * cos(B))² + (r2² * sin(B))² ] / [ (r1 * cos(B))² + (r2 * sin(B))²]
|
|||
|
|
The calculated difference of curvature drop on WGS84 to the spherical model from Laser to Target 2: +0.458 mm (+0.018 inches)
|
|||
|
|
The height of Lake Ijssel above sea level is 0 meters.
|
|||
|
|
|
|||
|
|
MEASUREMENT 4
|
|||
|
|
8th April 2018 at 3:00 AM
|
|||
|
|
|
|||
|
|
REFRACTION CALCULATION
|
|||
|
|
OF 4TH MEASUREMENT
|
|||
|
|
|
|||
|
|
Angle of incidence (θ1): 0.0040° Refractive index calculation (based on Modified Edlén Equation)
|
|||
|
|
n1 = 1.000283508 (445nm, 11.8° C, 74%)
|
|||
|
|
n2 = 1.000287811 (445nm, 7.6° C, 85%)
|
|||
|
|
Angle of refraction is calculated with Snell’s law: sin θ2 = (n1 * sinθ1) / n2 = 0.003999983 degrees
|
|||
|
|
Angle of deviation = 0.000000017°
|
|||
|
|
We concluded the ambient conditions refracted the laser beam downward by maximum of 0.494 mm (0.0194 inches)
|
|||
|
|
|
|||
|
|
POSITIONS AND HEIGHT DATA AT
|
|||
|
|
TARGET 2 POSITION LAKE IJSSEL
|
|||
|
|
|
|||
|
|
Enkhuizen (laser position): Latitude = 52.7100944444445° N = 52° 42' 36.34" N Longitude = 5.29597222222222° E = 5° 17' 45.5" E GPS ellipsoidal height = 0 meters Geoid height = 42.409 meters (139.137 feet)
|
|||
|
|
Target 2 (measurement position): Latitude = 52.8602638888889° N = 52° 51' 36.95" N Longitude = 5.64140555555556° E = 5° 38' 29.06"E GPS ellipsoidal height = 0 meters Geoid height = 42.103 meters (138.13 feet)
|
|||
|
|
Difference of geoid height: +306 mm (12.05 inches)
|
|||
|
|
|
|||
|
|
Laser beam recorded at 0.85 meters (2.79 feet)
|
|||
|
|
|
|||
|
|
Measurement 4 Target hidden height spherical model: 40.21 meters ( 131.921 feet)
|
|||
|
|
WGS84 laser to target correction: +0.439 mm (0.0173 inches)
|
|||
|
|
MSL correction is 0mm
|
|||
|
|
Refraction correction (max) -0.494 mm (-0.0194 inches)
|
|||
|
|
EXPECTED target hidden height 40.20995 meter (131.9208 feet)
|
|||
|
|
Difference of geoid height: +306 mm (+12.05 inches)
|
|||
|
|
|
|||
|
|
TARGET 3 POSITION Lake Ijssel
|
|||
|
|
(Measurement 5)
|
|||
|
|
|
|||
|
|
MEASUREMENT 5
|
|||
|
|
LAKE IJSSEL TARGET 3
|
|||
|
|
|
|||
|
|
On the 22nd of April at 0:00 AM, the blue laser pointer was placed on the SALAD at 2.92 meters (9.58 feet) above the lake surface. It was seen on the opposite shore at 18.73 km (11.64 miles) to Target 3 at 1.6 meters (5.25 feet) above the lake surface.
|
|||
|
|
|
|||
|
|
MEASUREMENT 5
|
|||
|
|
Lake Ijssel 22nd April 2018 0:00 AM
|
|||
|
|
|
|||
|
|
Temperature & humidity
|
|||
|
|
|
|||
|
|
At water level 11.4°C (52.5°F) 89%
|
|||
|
|
At 2 meters above (6.56 feet) 13.3°C (56°F) 77%
|
|||
|
|
|
|||
|
|
Enkhuizen Laser location
|
|||
|
|
|
|||
|
|
MEASUREMENT 5
|
|||
|
|
Lake Ijssel 22nd April 2018 at 0:00 AM
|
|||
|
|
|
|||
|
|
Target 3 observation location
|
|||
|
|
|
|||
|
|
LASER BEAM HIDDEN HEIGHT
|
|||
|
|
CALCULATION MEASUREMENT
|
|||
|
|
5 TARGET 3
|
|||
|
|
|
|||
|
|
The calculations based on a spherical model results in a target hidden height of the Measurement 5 Target 3 position of 12.504 meters (41.024 feet)
|
|||
|
|
|
|||
|
|
CURVATURE CORRECTION WGS84 and MSL
|
|||
|
|
|
|||
|
|
The radius of Earth is 6364.585 km (3954.770 miles) at the 52.872386° latitude (Target 3) on the WGS84 ellipsoid model, and 6364.643 km (3954.806 miles) at the 52.710094° latitude (laser). The measurement direction heading is 15.25°
|
|||
|
|
R = √ [ (r1² * cos(B))² + (r2² * sin(B))² ] / [ (r1 * cos(B))² + (r2 * sin(B))²]
|
|||
|
|
The calculated difference of curvature drop on WGS84 to the spherical model from Laser to Target 3: +0.237 mm (+0.0093 inches)
|
|||
|
|
The height of Lake Ijssel above sea level is 0 meters.
|
|||
|
|
|
|||
|
|
MEASUREMENT 5
|
|||
|
|
Lake Ijssel 22nd April 2018 at 0:00 AM
|
|||
|
|
|
|||
|
|
REFRACTION CALCULATION
|
|||
|
|
OF 5TH MEASUREMENT
|
|||
|
|
|
|||
|
|
Angle of incidence (θ1): 0.0040°
|
|||
|
|
Refractive index calculation (based on Modified Edlén Equation)
|
|||
|
|
n1 = 1.000287426 (445nm, 9.8°C, 1.0198Bars, 71%)
|
|||
|
|
n2 = 1.000287582 (445nm, 9.7°C, 1.0200Bars, 72%)
|
|||
|
|
Angle of refraction is calculated with Snell’s law: sin θ2 = (n1 * sinθ1) / n2 = 0.003999999 degrees Angle of deviation = 0.000000001°
|
|||
|
|
We concluded the ambient conditions refracted the laser beam downward by a maximum of 0.0117 mm (0.00046 inches)
|
|||
|
|
|
|||
|
|
POSITIONS AND HEIGHT DATA AT
|
|||
|
|
TARGET 3 POSITION LAKE IJSSEL
|
|||
|
|
|
|||
|
|
Enkhuizen (laser position): Latitude = 52.7100944444445° N = 52° 42' 36.34" N Longitude = 5.29597222222222° E = 5° 17' 45.5" E GPS ellipsoidal height = 0 meters Geoid height = 42.409 meters (139.14 feet)
|
|||
|
|
Target 3 (measurement position): Latitude = 52.8724444444444° N = 52° 52' 20.8" N Longitude = 5.36933055555556° E = 5° 22' 9.59" E GPS ellipsoidal height = 0 meters Geoid height = 42.149 meters (138.28 feet)
|
|||
|
|
Difference geoid height: 260 mm (10.24 inches)
|
|||
|
|
|
|||
|
|
Laser beam recorded at 0.85 meters (2.79 feet)
|
|||
|
|
|
|||
|
|
Measurement 5 Target hidden height spherical model: 12.504 meters (41.0231 feet)
|
|||
|
|
WGS84 laser to target correction: +0.16 mm (0.0063 inches)
|
|||
|
|
MSL correction is 0mm
|
|||
|
|
Refraction correction (max) -0.0117 mm (-0.00046 inch)
|
|||
|
|
EXPECTED target hidden height 12.50415 meters (41.0236 feet)
|
|||
|
|
Difference of geoid height: +260 mm (+12.05 inches)
|
|||
|
|
|
|||
|
|
TARGET 4 POSITION Lake Ijssel
|
|||
|
|
(Measurement 6)
|
|||
|
|
|
|||
|
|
MEASUREMENT 6
|
|||
|
|
LAKE IJSSEL TARGET 4
|
|||
|
|
|
|||
|
|
On the 22nd of April at 2:19 AM, the blue laser pointer was placed on the SALAD at 2.92 meters (9.58 feet) above the lake surface heading to 3.66°.
|
|||
|
|
It was seen on the opposite shore at 40.14km (24.94 miles) to Target 4 at 1.5 meters (4.92 feet) above the lake surface.
|
|||
|
|
|
|||
|
|
MEASUREMENT 6
|
|||
|
|
Lake Ijssel 22nd April 2018 at 2:19 AM
|
|||
|
|
|
|||
|
|
Laser location
|
|||
|
|
|
|||
|
|
Target 4 observation location
|
|||
|
|
|
|||
|
|
MEASUREMENT 6
|
|||
|
|
Lake Ijssel 22nd April 2018 at 2:19 AM
|
|||
|
|
|
|||
|
|
Target 4 observation location
|
|||
|
|
|
|||
|
|
Target 4 observation location
|
|||
|
|
|
|||
|
|
MEASUREMENT 6
|
|||
|
|
Lake Ijssel 22nd April 2018 at 2:19 AM
|
|||
|
|
|
|||
|
|
Temperature & humidity
|
|||
|
|
|
|||
|
|
Water level 9.6°C (49.3°F) 94%
|
|||
|
|
|
|||
|
|
At 2 meters (6.56 feet) 11.6°C (52.9°F) 85%
|
|||
|
|
|
|||
|
|
Enkhuizen Laser location
|
|||
|
|
|
|||
|
|
LASER BEAM HIDDEN HEIGHT
|
|||
|
|
CALCULATION MEASUREMENT
|
|||
|
|
6 TARGET 4
|
|||
|
|
|
|||
|
|
The calculations based on a spherical model results in a target hidden height of the Measurement 6 Target 4 position of 90.81 meters (297.33 feet)
|
|||
|
|
|
|||
|
|
CURVATURE CORRECTION WGS84 AND
|
|||
|
|
MSL
|
|||
|
|
|
|||
|
|
The radius of Earth is 6364.514 km (3954.726 miles) at the 53.070055° N latitude (Target 4) on the WGS84 ellipsoid model, and 6364.643 km (3954.806 miles) at the 52.710094° N latitude (laser). The measurement direction heading is 3.66°
|
|||
|
|
R = √ [ (r1² * cos(B))² + (r2² * sin(B))² ] / [ (r1 * cos(B))² + (r2 * sin(B))²]
|
|||
|
|
The calculated difference of curvature drop on WGS84 to the spherical model from Laser to Target 4: +2.56 mm (+0.101 inches)
|
|||
|
|
The height of Lake Ijssel above sea level is 0 meters.
|
|||
|
|
|
|||
|
|
MEASUREMENT 6
|
|||
|
|
Lake Ijssel 22nd April 2018 at 2:19 AM
|
|||
|
|
|
|||
|
|
REFRACTION CALCULATION
|
|||
|
|
OF 6TH MEASUREMENT
|
|||
|
|
|
|||
|
|
Angle of incidence (θ1): 0.0020°
|
|||
|
|
Refractive index calculation (based on Modified Edlén Equation)
|
|||
|
|
n1 = 1.000287887 (445nm, 9°C, 1.0186Bars, 79%)
|
|||
|
|
n2 = 1.000288697 (445nm, 8.3°C, 1.0189Bars, 81%)
|
|||
|
|
Angle of refraction is calculated with Snell’s law: sin θ2 = (n1 * sinθ1) / n2 = 0.001999998 degrees Angle of deviation = 0.000000002°
|
|||
|
|
We concluded the ambient conditions refracted the laser beam downward by a maximum of 0.064 mm (0.0025 inches)
|
|||
|
|
|
|||
|
|
POSITIONS AND HEIGHT DATA AT
|
|||
|
|
TARGET 4 POSITION LAKE IJSSEL
|
|||
|
|
|
|||
|
|
Enkhuizen (laser position): Latitude = 52.7100944444445° N = 52° 42' 36.34" N Longitude = 5.29597222222222° E = 5° 17' 45.5" E GPS ellipsoidal height = 0 meters Geoid height = 42.409 meters (139.135 feet)
|
|||
|
|
Target 4 (measurement position): Latitude = 53.0700555555556° N = 53° 4' 12.2" N Longitude = 5.33469166666667° E = 5° 20' 4.89" E GPS ellipsoidal height = 0 meters Geoid height = 41.847 meters (137.292 feet)
|
|||
|
|
Difference geoid height: 562 mm (22.126 inches)
|
|||
|
|
|
|||
|
|
Laser beam recorded at 1.5 meters (4.92 feet)
|
|||
|
|
|
|||
|
|
Measurement 6 Target hidden height spherical model: 90.81 meters (297.92945 feet)
|
|||
|
|
WGS84 laser to target correction: +2.17 mm (0.086 inch)
|
|||
|
|
MSL correction is 0mm
|
|||
|
|
Refraction correction (max) -0.065 mm (-0.00257 inches)
|
|||
|
|
EXPECTED target hidden height 90.81211 meters (297.93637 feet)
|
|||
|
|
Difference of geoid height: +562 mm (+22.126 inches)
|
|||
|
|
|
|||
|
|
TARGET 4 POSITION Lake Ijssel
|
|||
|
|
(Measurement 7)
|
|||
|
|
|
|||
|
|
MEASUREMENT 7
|
|||
|
|
LAKE IJSEL TARGET 4
|
|||
|
|
|
|||
|
|
On the 22nd of April at 23:20, the blue laser pointer was placed on the SALAD at 2.92 meters (9.58 feet) above the lake surface heading to 3.66°.
|
|||
|
|
It was seen on the opposite shore at 40.14km (24.94 miles) to Target 4 at 1.5 meters (4.92 feet) above the lake surface.
|
|||
|
|
|
|||
|
|
MEASUREMENT 7
|
|||
|
|
Lake Ijssel 22nd April 2018 at 23:20 PM
|
|||
|
|
Temperature & humidity
|
|||
|
|
|
|||
|
|
At 2 meters (6.56 feet) 13.9°C (57.0°F) 71%
|
|||
|
|
Water level 13.0°C (55,4°F) 79%
|
|||
|
|
|
|||
|
|
Enkhuizen Laser location
|
|||
|
|
|
|||
|
|
MEASUREMENT 7
|
|||
|
|
Lake Ijssel 22nd April 2018 at 23:20 PM
|
|||
|
|
Target 4 observation location
|
|||
|
|
|
|||
|
|
LASER BEAM HIDDEN HEIGHT
|
|||
|
|
CALCULATION MEASUREMENT
|
|||
|
|
7 TARGET 4
|
|||
|
|
|
|||
|
|
The calculations based on a spherical model results in a target hidden height of the Measurement 7 Target 4 position of 90.81 meters (297.33 feet)
|
|||
|
|
|
|||
|
|
CURVATURE CORRECTION WGS84 and MSL
|
|||
|
|
|
|||
|
|
The radius of Earth is 6364.514 km (3954.726 miles) at the 53.070055° N latitude (Target 4) on the WGS84 ellipsoid model, and 6364.643 km (3954.806 miles) at the 52.710094° N latitude (laser). The measurement direction heading is 3.66°
|
|||
|
|
R = √ [ (r1² * cos(B))² + (r2² * sin(B))² ] / [ (r1 * cos(B))² + (r2 * sin(B))²]
|
|||
|
|
The calculated difference of curvature drop on WGS84 to the spherical model from Laser to Target 4: +2.56 mm (+0.101 inches)
|
|||
|
|
The height of Lake Ijssel above sea level is 0 meters.
|
|||
|
|
|