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# Grid to Ground / Combined Scale Factor

All,

I recently saw a power point presentation that had some good diagrams in it on how scale factors, combined scale factors and the grid to ground conversions are done. I am not sure, but it may have been something that NGS produced. I can't seem to find it again. I would like to be able to provide the link for it or something else that has the process explained to a client. Anyone have something they can share?

Thanks in Advance,

JP

You're going to the the full gambit of instruction on this. I'll yield to whatever Kent, Loyal or Mighty Moe say for exact though.

However, my little diagram I used to keep till I memorized it said this.

CSF = GF * EF

Grid factor = where you are on the grid, no "Z" involved.

EF = mean radius of the earth/(mean radius of the earth + your orthometric height)

The hiccup is that NAD 27 uses 20,906,000 and NAD 83 uses something similar, but not exact (but I've NEVER seen enough to change me from using the NAD 27 version)

So, assuming for your project (this is where it's really going to get different) you have a grid factor of 0.999981 (Dave Doyle said no more than 6 digits was necessary) and you have an average elevation of 500', then your combined scale factor is

0.999981 * (20,906,000/[20,906,000+500]) = 0.999957

At least that's how I do it.

**Scale Factor and Convergence**

Three optional output fields for Interactive and Point Database Conversions are Scale Factor, Convergence, and Orthometric Height Scale. These fields only apply when a projected coordinate system is chosen as the output system. Orthometric height scale will only display when a Vertical Reference is selected. Points in a Geodetic systems do not have a scale or convergence.

**Grid Scale Factor**

Grid Scale Factor, often simply called "Scale Factor" is a measure of distortion at a given point on a projected map. The scale factor is not cartographic scale, but a factor used to calculate actual ellipsoidal distances rather than distances on the projected surface.

**Convergence **

Convergence is the angle of difference in direction from Grid North to True North. This will vary across a projected coordinate system and can be used as a measure of accuracy of angular measurements at a given point on the map.

Note: In Transverse Mercator projected coordinate systems, convention is to specify the convergence angle from True North to Grid North.

**Orthometric Height Scale**

Also known as Elevation factor, Orthometric Height scale represents a factor of elevation that can be used to calculate geodetic distances above or below the ellipsoid (also known as reducing to the ellipsoid). This scale is determined using a constant radius for the earth in the area of the calculation, but this is typically considered accurate enough for most applications.

**Combined Factor**

Combined Factor is simply Grid scale multiplied by the Orthometric Height Scale. This factor is used to calculate ellipsoid distance from a grid distance above or below the ellipsoid.

Example: The Grid Scale for two points is 0.999689, and the Orthometric Height scale for the points is 0.999999123, the combined factor is: 0.999689 x 0.999999123= 0.999688123272747

If the grid surface distance between the two points is 1000 meters, to calculate ellipsoid distance between the two: 0.999688123272747 x 1000meters = 999.69 meters

**Point of order**

When playing in NAD83, you should be using the “average ELLIPSOID Height” NOT the average orthometric height to do these calculations. Even at [only] 6 decimal places, this is a significant (non-trivial) difference in many parts of CONUS.

Kinda busy right now, but I'll get back to this a little later this morning.

Loyal

**Loyal**

I knew you'd kick in. I think you like geodesy more than beer and women sometimes. 🙂

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