2. Ground Distance to Grid

a. Ground to Ellipsoid

Figure L-2 Ground to Geodetic

We computed geodetic distances in Chapter K - those can be converted to meters to use here.
However, we'll do the computations from scratch using Equation H-2 to.

Equation H-2

Jerry's -33.902 meter geoid height will be used as a project average.

(1) Geodetic distance Jerry-A1

(2) Geodetic distance Jerry-B7

b. Ellipsoid to Grid

Figure L-3 Geodetic to Grid

 
We'll use and compare the same reductions for UTM as we did for SPC. Table L-2 shows the grid scale at each point and how they were obtained.

Jerry's CF from the datasheet is 1.00016 082.

Because the process is similar to SPC grid reduction, computations are not shown but results are summarized in Tables L-3 and L-4.

Table L-3 Line Jerry-A1 Grid Reduction Comparisons
DE x k	k	Grid Dist, m	Diff, m
Wtd Ave k	1.00020 9086	1305.3993	- -
Average k	1.00020 9087	1305.3993	0.0000
Jerry's k	1.00021 177	1305.4028	+0.0035
Combined Factor
DH x CF	1.00016 082	1305.4000	+0.0007

Table L-4 Line Jerry-B7 Grid Reduction Comparisons
DE x k	k	Grid Dist, m	Diff, m
Wtd Ave k	1.00021 4025	1568.8175	- -
Average k	1.00021 0362	1568.8175	0.0000
Jerry's k	1.00021 177	1568.8111	-0.0064
Combined Factor
DH x CF	1.00016 082	1568.8173	-0.0002

Unlike SPC reduction, using Jerry's scale as a project average resulted in the largest differences. Average line scale worked well. Jerry's CF reduction had small (inconsequential?) differences. Using CF reduction could be sufficient if the elevations of points A1 and B7 represent the range across the project.