Video created 24 Jan 2010

# Coordinate Transformations: Defining a Custom Grid Projection

The video below demonstrates how to define a new Coordinate System in Civil 3D.

This particular demonstration shows how to set up a Low Distortion Projection for a small town in Colorado, using a Lambert Conformal Conic Single Parallel projection, and the NAD83 datum as the basis for our new coordinate system.

After watching this video, you may also wish to watch the next part on how to transform data between a State Plane Grid and our new Low Distortion Projection.  Also note that, at the bottom of this web page, there is further information on how the scale factor was determined for this Site.

The tasks illustrated in this demonstration may be performed in any version of Civil 3D, and do not require the Sincpac C3D.

(Run time: 6 min 30 sec)

## A Note on the Scale Factor

This section is an addendum for those who are confused about the choice of scale factor in this video.

Basically, my goal was to scale the NAD83 datum up, so that the ellipsoid for my new projection is running through ground level in my project.  We then use this "scaled-up ellipsoid" as the basis for a new grid, with its origin in the center of our "area of interest," aka our "Site".  (Note: in more-complicated usages, we may wish to have an origin that is some distance from our Site.  I won't go into that usage; I just wanted to mention it.)

In order to determine how much to scale up my ellipsoid, I first need to know the average ellipsoidal height for my project.  To get this value, we take the average NAVD88 elevation for our Site, and then add the average geoidal height for our Site.  We then come up with a scale factor using the following equation, where R is the radius of ellipsoid at our Site, and P is the average ellipsoidal height for our project:

scale factor  =  (R + P) / R

In this equation, it is almost always good enough to use an average curvature radius for R, such as R = 20,906,000 ft.  In this particular project, the average ellipsoidal height for our Site is 6000 ft, so that's the value we'll use for P.  Using these values to solve for our scale factor, we get 1.00028699989 and change.

However, when we did this, we scaled the ellipsoid all the way up to our project elevation.  This means that our grid scale factor is exactly 1 right at our grid origin, and it gets greater than 1 as we get further from the origin.  Instead, we may wish to drop the projection a little bit further, so that it is actually slightly below the surface of the Earth at the origin.  This makes our grid scale factor less than 1 at our project origin.  As long as we don't lower the projection too much, we can extend the range of our projection without harming its accuracy.

In this particular case, I decided to multiply the scale factor by 0.999999.  This value results in an "effective zone" of roughly 16 total miles north and south (8 miles in each direction) of the standard parallel for my projection.  This means that, anywhere within the "effective zone", we can completely ignore the grid scale factor, and we will introduce no more than 1 part-per-million of error.  We could relax this further.  For example, if we multiply by 0.99999 instead, we drop the surface even further.  In this case, we would have an "effective zone" of more than 70 miles, but our accuracy is down to 10ppm over that zone.  We also introduce another 1ppm for approximately every 21 feet of vertical difference from the Project elevation we identified earlier.  But as long as we choose appropriate values, we should have a rather large area where our Grid distances are essentially the same as our ground distances.

For this particular Site, we chose to multiply our calculated scale factor by 0.999999, which gives us 1.00028599866.  To make it a bit easier to deal with, I then rounded this number to 1.000286 exactly, which is the value you see me use in the video.

Note that if any of this is confusing to you, you may find it worthwhile to read the papers "Working with Grid Coordinates" (pdf, 0.5mb), "Solving Grid to Ground Problem" (pdf, 0.30mb) and Sinc's AU2010 PowerPoint presentation "Custom Coordinate Systems" (pptx, 6.20mb)