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, Matlab function, or Excel spreadsheet that implements this correction given the following as input:

1. For a first point, :

• Its orthometric height,
• The corresponding geoid undulation,
• The height of the instrument above the mark,

2. For a second point, :

• Its orthometric height,
• The corresponding geoid undulation,
• The height of the instrument above the mark,

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

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 I handed out in class.

## 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)
9273.142
13615.575
4360.905

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

Point (m) (m) (m) (m)
1.245 1312.074 -11.87 6365236.896
1.552 2327.744 -12.15 6365253.472
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 Excel this might just mean your Excel file.

In C++ this would mean submitting your input and output files. I’d also like to see your full C++ project files again so we can provide you with feedback.

In Matlab I’d like to see your functions and some capture of the input and output.

## 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. You can do this at any time. Just press “Unlock the next lesson”.