Self-assessment for: Geometric and other reductions of observations

These self-assessment problems accompany the mini course Geometric and other reductions of observations.

Problem 1

Describe the reason we do each of the following:

a) Meterological reductions

b) Gravimetric reductions

c) Geometric reductions

Problem 2

Name an example of each of the above, along with an approximation or order of magnitude of the error that you would incur by ignoring the reductions in your examples.

Problem 3

a) If you measure a distance from an EDM to a reflector, what kind of distance do we call that?

b) Can that distance be used to approximate the distance between the marks you set up over? Why or why not?

Problem 4

a) Provide the equation(s) for reducing a slope distance to the ellipsoid.

b) Is this reduction greater for points A and B high above the reference surface or close to the reference surface? Roughly how much less / greater is it at orthometric heights of 10,000 m than 1,000 m?

c) Write an expression (in terms of the equations given above) for the following scale factor:

    \begin{equation*} k_e^s = \text{scale factor for converting a slope distance to the ellipsoid} \end{equation*}

d) Write an expression (in terms of the equations given above) for the following scale factor:

    \begin{equation*} k_e^{mm} = \text{scale factor for converting a mark-to-mark distance to the ellipsoid} \end{equation*}

Problem 5

a) For what region(s) of the UTM zone is the scale factor k_g^e = k_0k^{'}k^{"} greater than 1.0?

b) Given what you found in Problem 3c, and the relationship D_g = k_g^eD_e, what is the expression for the combined scale factor k_g^e:

    \begin{equation*} k_g^e = \text{scale factor for converting a slope distance to the mapping grid} \end{equation*}

Problem 6

Imagine you are going to do a traditional land survey (not GPS) to help put a new building on our campus around the following location:

    \begin{equation*} \begin{matrix} \phi=51^o04^{'}47.8128{"} N \\ \lambda=114^o07^{'}31.9224{"}W \\ h = 1111.0 m \end{matrix} \end{equation*}

And that you’ve been asked to do a network adjustment on the UTM mapping grid.

a) What is the scale factor at that location for reducing measured distances from the mark to the ellipsoid? You can assume that all measurements will be less than or equal to 500 m from the above position.

b) What is the scale factor at that location for reducing such a distance from the ellipsoid to the UTM mapping grid?

c) What is the combined scale factor that you would use survey-wide for getting from marks to mapping grid?

Tell me how you calculated these values, e.g. your own spreadsheet, an online calculator, etc…

Problem 7

Imagine your RTK DGPS receivers have been set such that they display grid distances (many do this for convenience):

a) By what scale factors and in what order would you multiply the scale factors if you wanted to convert a grid distance to a slope distance so it could be compared quickly in the field to distances measured by EDM?

b) What is the combined scale factor for doing this in the case of the example in Problem 6?


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