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.

Table L-2
Grid Scales
A1 1.00020 6404 software
Jerry-A1 midpoint 1.00020 9086 Equation H-4
Jerry 1.00021 177 datasheet
Jerry-B7 midpoint 1.00021 5856 Equation H-4
B7 1.00020 8953 software

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
Jerry's k 1.00021 177
Combined Factor
DH x CF 1.00016 082

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