There are times when a single grid scale factor is applicable to the entire line - depending upon the tolerance desired, maybe a mile or two.
For longer lines, an average grid scale factor (obtained as the mean of the grid scale factors at the endpoints) will suffice - again depending upon the tolerance desired, say up to about 4 miles in length.
For long lines (in excess of about 4 miles - again depending upon the tolerance) the equation given near the bottom of page 50 of NOAA Manual NOS NGS 5 is:
k (long line) = [ k(1) + 4 k(midpoint) + k(2) ] / 6
The issue of which to be aware is that k(midpoint) is not the same as the mean of k(1) and k(2). If the grid scale factor varied linearly, k(midpoint) would be the same as the mean of k(1) and k(2). But, the grid scale factor does not change linearly.
RIGHT!
I forgot that part...(k @ mid-point)
Thanks,
Loyal
What Distance Gets Scaled?
Thanks all for the most excellent responses.
Do you apply the Grid Scale Factor to distances on the Projection Grid to get Ground Surface distances, or is it the other way around? Where does the Combined Scale Factor come into play?
Dave
What Distance Gets Scaled?
Thanks for re-including the excellent figure (i somehow mised it the first time). It helps me answer (because i never remember either):
In regions where SF > 1 a distance on the ellipsoid must be stretched to match its projection on the grid.
In regions where SF < 1 a distance on the ellipsoid must be compressed to match its projection on the grid.
So,
grid distance = SF x ellipsoid distance
Using similar logic to ground distances, which are at an elevation above the ellipsoid, and assuming we have
EF = elevation factor
then
ellipsoid distance = EF x ground distance
So,
grid distance = SF x EF x ground distance
or for convenience
grid distance = CSF x ground distance
where
CSF = combined scale factor = SF x EF
Our ground distances must be "corrected" (ie, distorted) to fit the grid.
What Distance Gets Scaled?
Martin,
Thanks. With help from this forum and the great graphics in the SPCS PDF that I got from GeeOddMike, I'm slowly putting it together.
"Our ground distances must be "corrected" (ie, distorted) to fit the grid."
And then undistorted back to stake for construction.
I've been reading Shawn's post on State Plane Coords, and I'm starting to like Low Distortion Projections. With all the computing power we have now, why aren't we designing and staking projects on a 3D earth and eliminating flat projections entirely?
Dave
What Distance Gets Scaled?
> With all the computing power we have now, why aren't we designing and staking projects on a 3D earth and eliminating flat projections entirely?
Excellent question! It's worthy of a separate debate or two (or three).