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
- 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.
If you have any questions or comments regarding this technique, please contact us and mention the article title.
- Set the Active Datum to a datum that is applicable
to your geographical area. In the United States, we
suggest you use NAD 83.
- 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
- 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
- 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).
- 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
- 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.
- 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.
- 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
- Select the Save option from the File menu to save your current data
to a file for future use.
- 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).
- 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.
- 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.
- 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.
- 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.
- 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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