Part 1: Reduction of distances to the ellipsoid

In class we reviewed the concept of reducing to the ellipsoid a distance measured between two points at or above the surface of the earth.

Step 1: Code the reduction

I would like you to create a C++ function or Google spreadsheet that implements this correction given the following as input:

1. For a first point, A:

  • Its orthometric height, H_A
  • The corresponding geoid undulation, N_A
  • The height of the instrument above the mark, \Delta h_A

2. For a second point, B:

  • Its orthometric height, H_B
  • The corresponding geoid undulation, N_B
  • The height of the instrument above the mark, \Delta h_B

3. The measurement of distance, or slope distance, S, between points A and B.

You can assume that all other reductions have been made, such as for meteorological effects and blunders.

Step 2: Check your implementation

Although you don’t need to hand anything in for this step, I would encourage you to check your implementation using the example to be made available to you by your TA in the lab session.

Step 3: Reduce some measured distances

I’d like you to use your solution to reduce the following slope distances:

Leg Measured slope distance (m)
AB 9273.142
BC 13615.575
CA 4360.905

Measured between the following points with these instrument heights, orthometric heights, geoid heights, and radii of curvature:

Point \Delta\textit{\textbf{h}} (m) \textit{\textbf{H}} (m) \textit{\textbf{N}} (m) \textit{\textbf{R}} (m)
A 1.245 1312.074 -11.87 6365236.896
B 1.552 2327.744 -12.15 6365253.472
C 2.443 1312.328 -11.77 6365228.783

Reduce each of these to provide:

1. The ellipsoidal or geodetic distance

2. The mark-to-mark distance

Step 4: Prepare and submit a suitable summary of your input and output

If you used Google Sheets this might just mean the link to your spreadsheet file. Be sure to share it so that it’s accessible to us as in previous labs.

In C++ this would mean submitting your input and output files.

Step 5: Draw some conclusions

I’d like you to comment in your submission on the magnitude of the reductions being made here. How big are they? On what do they seem to depend? When would you recommend doing them?

Step 6: Move to Part 2 of this lab when you’re ready

Once you’ve finished all of this you can proceed to Part 2.

The following schedules are for Alex’s in-class students:

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