Real-World Applications of COLUMBUS

Using a Local Horizon XYZ (ENU) cartesian coordinates (usually from blueprints of a large structural design) on the geodetic model

• Assumptions
• Steps
• Questions or comments
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Assumptions

• The design coordinates for the structure you are building are based on a local X, Y, Z cartesian coordinate system.
• The design coordinate system is oriented to true North (Y) along one axis, true East (X) along a second axis and perpendicular to the XY plane along the third axis (Z or UP). In COLUMBUS, this is represented as a Local East, North, Up coordinate system. If the design coordinates are not aligned in this way, they must be rotated, translated and/or scaled to meet this requirement.
• There are no curvature or convergency corrections built into these design coordinates. They do not model the true shape of the Earth in any way.

Steps

1. Set the Active Datum to a datum that is applicable to your geographical area. In the United States, we suggest you use NAD 83.

2. From the Options menu in COLUMBUS, set the Global Settings 3D Geodetic Height to Ellipsoidal Height. This serves two purposes: First, all geodetic verticals on reports will be labeled Ellipsoidal Height (instead of Orthometric Height). Second, it will make COLUMBUS use the Ellipsoidal Height Field in the $GEO or $GEO_COMPACT record type.

3. Enter all design X,Y,Z coordinates into COLUMBUS using the Local NEU station type, where X is East, Y is North and Z is UP. Alternatively, create a COLUMBUS ASCII (Text) file using the $LOCAL_NEUE_COMPACT record OR import a comma-delimited file containing these coordinates.

4. For one of these points, create a geodetic station with the same name and assign it a latitude, longitude and ellipsoidal height that has been scaled from a map. The more accurate the ellipsoidal height the better (plus or minus a few meters, as this will effect measured spatial distances).

5. If you do not know the ellipsoidal height for this location, try to get a "good" orthometric height and convert it to ellipsoidal height by performing Geoid Modeling using the Tools menu (orthometric height + geoidal height = ellipsoidal height). In the United States, the geoidal height will always be negative and therefore, the ellipsoidal height will always be below the orthometric height.

   An exact ellipsoidal height is not important; one that is close to the correct height (plus or minus five meters) is sufficient.

   Note: EGM96 and Geoid03 models are included on the COLUMBUS Installation CD

6. Once all the data is in COLUMBUS (several Local NEU stations and one geodetic station), select Local NEE from the View menu. This tells COLUMBUS the context of what you will do next.

7. From the Tools menu, select Transformation | Local NEU <--> Geodetic to transform all your Local NEU points to the geodetic coordinate system. COLUMBUS knows you want to go from Local NEU to geodetic, because of the View context set in the previous step.

8. Click the Mean GEO button and select the geodetic station set up in Step 4. Click the Mean NEU button to select the Local NEU station with the same name as the Mean GEO station (the same point on the ground).

   Click Compute to transform all Local NEU stations to geodetic about this point of origin. Select the Keep option to save the coordinates into memory.

   At this point, all your design coordinates have been transformed to the 3D geodetic coordinate system.

   At any time, you can transform the geodetic positions back to Local NEU (Y, X, Z). This transformation will result in the exact Local NEU coordinates you started with, provided you use the same point of origin.

9. Select the Save option from the File menu to save your current data to a file for future use.

10. Relative to each other, you now have exact 3D geodetic coordinates for the original X, Y, Z coordinates (ENU). You will also notice that for any two points that have the same Z (UP) component, they will not have the same ellipsoidal height. For example, if all your XYZ coordinates had the same Z value (UP), the farther each point is from the point of origin (step 8), the higher it will be above the ellipsoidal surface.

    The geodetic coordinate system (latitude, longitude an ellipsoidal height) is a very accurate mathematical model, depending on the number of significant digits used in the calculations.

    However, when you put your instruments on the ground, they will be leveled in the direction of gravity and not the ellipsoidal normal. To use gravity-based observations on an ellipsoidal surface, you should determine the deflections of the vertical (N-S and E-W) for each geodetic station. Note: This is only required for surveys demanding the highest accuracy. Generally, these corrections will be minimal over short distances.

    If your project is within the United States, you can use DEFLEC99 to determine the deflection of the vertical for each geodetic station. This also requires that your originating geodetic station be accurate so that all projected geodetic coordinates are accurate (step 8).

11. From the View menu, change the view to 3D Geodetic. From the Tools menu, select Deflection Modeling. Enter the appropriate grid for your area. For the United States, the DEFLEC99 grid files are provided on your COLUMBUS Installation CD.

    To model the deflections of the vertical, simply click the Stations button to bring up a list of all geodetic stations in memory. Click Select all and COLUMBUS will compute the deflections in N-S and E-W for each station. Click the Keep button and COLUMBUS will save the deflections for each geodetic station to memory.

12. From the File menu, select the Save option to save the newly-added data so you will not need to calculate the deflections of the vertical for these stations again.

    Now, whenever you perform a Geodetic Inverse, COLUMBUS will correct the inverse results so they are based on the direction of gravity. When you perform a network adjustment, COLUMBUS will correct field observations so they will be based on the ellipsoidal model you established in Step 8.

13. From the View menu, change the view to 3D Geodetic and use the COLUMBUS Astro-Geodetic inverse routines to determine the angles and distances required to lay out each control station on the ground. Of course, you will need at least one station to start with (preferably your point of origin).

    The Astro-Geodetic inverse will give you the forward azimuth, zenith angle and slope distance from the AT station (current known station in your calculations) to each TO station. It already takes into account curvature, convergency, and deflections of the vertical (if step 11 is followed) so you don't have to. The inverse results are Mark-To-Mark.

    However, Mark-To-Mark may not help you much during layout, since you might not be able to set your instruments over the AT station at an Instrument height of zero. To achieve this within COLUMBUS, use this solution:

    If your Instrument height at the AT station is 1.50 meters and Target Height at the TO station is 1.2 meters, temporarily add these values to the AT station and TO station ellipsoidal heights, respectively. Then perform the inverse to compute the correct forward azimuth, zenith angle and slope distance from the AT station to the TO station as measured between the Instrument and Target Heights.

    The result is the required measurement that should be made from your AT station to lay out your TO station.

14. After you have established all your positions on the ground, you can begin doing 3D Geodetic adjustments to see how well all the redundant data fits together.

15. Periodically, you can transform your geodetic coordinates back to Local NEU to directly compare your adjusted coordinates with your original design coordinates. If your survey is of high quality, you should see very little difference between the adjusted coordinates (transformed to Local NEU) and the original design coordinates.

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