Quick Tips for Using COLUMBUS

Ad Hoc Calculations

• Calculating the curvature correction

• Calculating the effects of curvature and convergency (longer approach)

• Calculating the area of a polygon

Calculating the curvature correction

To calculate the curvature correction do the following:

1. Run COLUMBUS.

2. From the File menu, select New.

3. From the Tools menu, select Quick Calculations, then select the Curvature tab.

4. Enter the latitude (approx), elevation (approx), azimuth (approx) and horizontal distance (based on zenith of 90 degrees).

5. Click on the Compute button to compute the results based on your entered azimuth and other internally fixed azimuths.

Note: Computations are based on the active datum. Enter angular and linear quantities in the active units.

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Calculating the effects of curvature and convergency - a longer, common sense approach :>)

Have you ever wanted to calculate the effects of curvature and convergency accurately and in any direction, over just about any distance? Here is a way to do just that within COLUMBUS:

1. Run COLUMBUS.

2. From the File menu, select New.

3. From the Options menu, select Datums, and then select the datum to be active.

4. From the Data menu, select Stations.

5. Select the Geodetic grid and enter the geodetic coordinates for two stations.
   1. Assign the first station (Station 'A') the latitude and longitude of your area (approximate to nearest minute for latitude, if possible), then give it a height value of Zero.

   2. Assign the second station (Station 'B') a similar latitude and longitude (but not the same value). Don't worry about the actual coordinate value for Station 'B' yet. It is only needed right now so that it can be displayed on the screen (and not be on top of Station 'A').

   3. Click Keep and Close.

6. From the Data menu, select Observations.

7. Select the Azimuth Set grid and enter a set of observations (azimuth, zenith angle, and chord distance) from Station 'A' to Station 'B'.
   1. Estimate as best you can the azimuth you are interested in.

   2. Enter 90.0 degrees for your zenith angle, then enter the distance you are interested in to see the effects of curvature and convergency (perhaps 1000.0m or 5250.0 U.S. feet).

   3. Click the Keep and Exit button to add the observation set into memory. Both of the stations and the observation between them are now displayed on the screen.

8. Right click on the AT station ('A'), then right click on the TO station ('B'). A different colored line will appear between them.

9. From the Tools menu (or toolbar), select COGO | 3D Geodetic Traverse to compute the exact coordinate of Station 'B' relative to Station 'A'.

10. Keep the newly-computed coordinate for Station 'B' into memory.

11. Before closing the result dialog, examine the computed height value for Station 'B'. The difference between this height value and the height value of Station 'A' (set to Zero) is the effect due to curvature of the earth (based on the ellipsoid selected when choosing the Datum described above).

    For NAD 83, with Station 'A' at latitude 40 degrees north, an azimuth of 45 degrees, and a distance of 1000.0m, the curvature is 0.07844m (approx 0.26 U.S. feet).

12. To calculate the effect of convergency, enter a third station (Station 'C') as described above. Assign it the same latitude as Station 'A' and the same longitude as the newly-computed longitude for Station 'B'. Assign it a height of Zero.

13. Right click on the AT station ('A'), then right click on the TO station ('C'). A colored line will appear between them.

14. From the Tools menu, select COGO | 3D Local NEU Inverse to compute the inverse between these two stations.

15. Examine the Delta North value. This is the effect due to convergency. For this example, the value is 0.03285m (approx 0.11 U.S. feet).

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Calculating the area of a polygon

To calculate the area of a polygon based on either State Plane, UTM or Local NE coordinates, do the following:

1. Run COLUMBUS.

2. From the File menu, select New if you plan to enter the coordinates. Select Open if you plan to open an existing COLUMBUS-compatible file that contains the coordinates.
   (Note: Skip this step if you already have the coordinates in memory.)

3. Change the View to the context of the coordinates you are working with (State Plane, UTM, Local NE).

4. Using the right mouse button, form the polygon. To do this, click on the first station and each additional station until a closed polygon is defined. A colored line displays between each station pair. (To configure the color, select Colors from the Options menu.)

5. From the Tools menu select Compute Area or click the toolbar command to calculate the area of the polygon. The area displays in the active linear square units (square feet, square meters, and so on.)