JDtM (Just Do the Math): Let’s compute the ground distance between two grid projected points!

If you have not noticed, I still am not on the LDP bandwagon. I am the designated LDP Curmudgeon! 

In this second installment of JDtM, let’s compute the ground distance between two points with State Plane Coordinates:

Here are two points (East and West quarters that fall in the undeveloped area north of I-15/Washington City) shown in Carlson SurvCE:

Inversing between them we find:

The “HDist 5,314.116 sft” is the GRID distance.

Note that there is a 168 foot elevation distance between the two points. Is it Okay to just use a single scale factor (like the scale factor for point 10432)?

The LDP Curmudgeon says “Who cares? Just Do the Math!“

1. Reduce elevations to ellipsoid

2. Compute scale factors for two end points:

                (SF1)      10432    1.000,133,747,228

                (SF2)      10437    1.000,125,721,090

 You also need the scale factor for the midpoint of these points:

                 (SFC)     10023895.740 N, 1048125.982 E, 3059.909 Z           1.000,133,747,228

 The scale factor for line segment is: (If you don’t believe me Google “Grid Scale Factor(K) of a Line”)

                 SFLine   = (SF1 + 4 * SFC + SF2) / 6

                               = 1.000,132,409

 So the ‘correct’ ground distance is:

                 DistGround    = 5,314.116 * 1.000,132,409
                                         = 5,314.820 sFT

 If we wanted to just use a single scale factor (say the scale factor for the 10432 point:

                 DistGround    = 5,314.116 * 1.000,133,747
                                         = 5,314.826 sFT

You may ask, who cares about 6-thousandths? I say, it all adds up. 10 measurements and you have 6-hundredths. Next thing it is a tenth. Since you are not doing the math manually, (it is getting performed in the data collector) why not just do it and get the right answer.