# Coordinate and Mapping Systems:Transformations and Calculations… 1 answer below »

Need to use the GDAy software:

The software is basically an interpolation routine, which needs a “gridfile” to interpolate from. The gridfiles contain shifts (in easting/northing or latitude/longitude) to convert between coordinates in the old and new Australian systems. Two gridfiles are provided. You will need to choose whichever one you think is most appropriate for each question. It is strongly recommended that you read the GDAy user guide before first use.

Task 1 [5 marks] The first task required is to convert the coordinates of the points on the baseline from AMG84 coordinates into MGA94 coordinates using the GDAy software and the correct gridfile. a) Using only the GDAy software and the correct grid file, what is the MGA94 coordinates of the points BL1 and BL2? (3 marks) b) What is the total horizontal shift in coordinates (metres) from AMG84 to MGA94, and with what bearing? (2 marks) Task 2 [15 marks] The second task is to perform a 7-parameter transformation of the points on the baseline, to convert from AMG84 to MGA94 coordinates. By following the steps below, you will do the same transformation in Task 1, but using a 7-parameter transform. For this task, you will need the Geoscience Australia Excel spreadsheets redfearn.xls and transxyz.xls. Do not use the gridfile transformation software. a) What are the AGD84 latitude and longitude of the points BL1 and BL2 in Task 1(a)? (2 marks) b) What are the ANS geocentric Cartesian coordinates of the points BL1 and BL2? (2 marks) c) What are the GRS80 geocentric Cartesian coordinates of the points BL1 and BL2? (2 marks) d) What are the GDA94 geodetic coordinates (include ellipsoidal height) of the points BL1 and BL2? (2 marks) e) What are the MGA94 coordinates of the points BL1 and BL2? (2 marks) f) What is the total horizontal shift in coordinates (metres) from AMG84 to MGA94, and with what bearing? (2 marks) g) Comment on the difference between the MGA94 coordinates derived from this method in Task 2, and the gridfile transformation method in Task 1. Which do you think is more accurate, and why? (3 marks) SPAT2002 Coordinate and Mapping Systems Assignment 2018 5 Task 3 [15 marks] The third task is to perform a 7-parameter transformation of reference station point CORS from MGA2020 to MGA94 coordinates. This will be done by following the steps below. For this task, you will need the Geoscience Australia Excel spreadsheets redfearn.xls and transxyz.xls. Do not use the gridfile transformation software. Remember to take care in which direction you are doing the transformation. a) What is the ellipsoid height in GDA2020 for the point CORS? (3 marks) b) What are the GDA2020 latitude and longitude for the point CORS? (2 marks) c) What are the GDA2020 GRS80 geocentric Cartesian coordinates for the point CORS? (2 marks) d) What are the GDA94 GRS80 geocentric Cartesian coordinates for the point CORS? (2 marks) e) What are its GDA94 geodetic coordinates (include ellipsoidal height) for the point CORS? (2 marks) f) What are its MGA94 coordinates for the point CORS? (2 marks) g) What is the total horizontal shift in coordinates (metres) from MGA94 to MGA2020, and with what bearing? What does this shift represent? (2 marks) SPAT2002 Coordinate and Mapping Systems Assignment 2018 6 Task 4 [35 marks] For task 4, you will be required to calculate several measurements between the points BL1, BL2, and CORS for a surveyor to compare to their field measurements. To do this, you will need the Geoscience Australia Excel spreadsheets gridcalc.xls and vincenty.xls. Please use the MGA94 and GDA94 coordinates you have calculated for the points in Task 2 and Task 3. It may be easiest to summarise the solutions to each as a table. a) For points BL1, BL2 and CORS, what are the point scale factors and grid convergence at each point? (6 marks) b) For the lines BL1 to BL2, BL1 to CORS, and BL2 to CORS, what are the arc (ellipsoid) distances, plane (chord) distances, and line scale factor for each line? What is the relationship between these values with respect to the line scale factor and point scale factor (and show that your values agree with the relationship)? (10 marks) c) For the lines BL1 to BL2, BL1 to CORS, and BL2 to CORS, what are the azimuths, grid bearings, plane bearings in both the forward (e.g. BL1 to BL2) and reverse (e.g. BL2 to BL1) directions, as well as the arc to chord corrections along these lines? What is the relationship between the azimuth, grid bearing and plane bearing with respect to grid convergence and arc to chord corrections (and show that your values agree with the relationship)? (14 marks) d) For the triangle formed by points BL1, BL2 and CORS, based on the information from the previous parts of this task, would you calculate the angles observed in the field based on azimuth, grid bearings, and/or plane bearings? What would the values of these observed angles be, what would the total sum of the angles be? Would you expect the value to be equal, less than, or greater than 180o . (5 marks) SPAT2002 Coordinate and Mapping Systems Assignment 2018 7 Task 5 [30 marks] For task 5, you will be required to convert the local plane grid (LPG) coordinates of the ventilation shaft point VS into MGA94 coordinates. To do this, you will need to follow the steps below. Note that you will need the Geoscience Australia Excel spreadsheet redfearn.xls and some of the values you calculated in previous tasks. The full procedure is outlined in Chapter 9 of the lecture notes. a) Modify the spreadsheet redfearn.xls to generate a Local Transverse Mercator (LTM) grid, with the central meridian centred on point BL1, a central scale factor of 1, and the false easting and northing being 500,000m and 10,000,000m respectively. What are the LTM coordinates of points BL1 and BL2? (7 marks) b) Using the LTM and LPG coordinates of the points, what are the 2D Helmert Transformation parameters from LPG to LTM (scale, rotation and translation)? (10 marks) c) Using the 2D Helmert Transformation parameters from part b) on the LPG coordinates for point VS, what is LTM grid coordinates for the point VS? (5 marks) d) Using the modified spreadsheet redfearn.xls, what are the GDA94 coordinates of point VS? (4 marks) e) Using the spreadsheet redfearn.xls, what are the MGA94 coordinates of point VS? (4 marks)

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