Environmental Monitoring
& Technology Series
Navigation &
Mapping
For Technicians
Study module 4
cffet.net/env
Navigation & mapping for technicians
Study Module 4
Assessment details
Purpose
Upon successful completion of this study module you will have an understanding of the
different types of reference systems, datum’s, coordinate systems and specific notations
used in navigation as well as being able to perform simple unit conversions.
Instructions
◗ Read the theory section to understand the topic.
◗ Complete the Student Declaration below prior to starting.
◗ Attempt to answer the questions and perform any associated tasks.
◗ Email, phone, book appointment or otherwise ask your teacher for help if required.
◗ When completed, submit task by email using rules found on last page.
Student declaration
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Details
Student name
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Assessor
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Class code
N&M
Assessment name
Study module 4
Due Date
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Total Marks Available
29
Marks Gained
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Final Mark (%)
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Marker’s Initials
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Date Marked
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Weighting
This is one of twelve formative assessments that make up 40% of
the overall mark for this subject
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Navigation & mapping for technicians
Study Module 4
Projected Coordinate Systems (PCS)
A Projected Coordinate System (PCS) is a transformation system that allows for the
construction of a 2D map from 3D reality. A PCS is defined on a flat, two-dimensional
surface. Unlike a GCS, a PCS is different because it exhibits;
◗ constant lengths, angles, and areas across the two dimensions
◗ is always based on a GCS which itself is based on a sphere or spheroid
◗ a map projection
◗ a set of definitions called projection parameters
The projection parameters customize the map projection for a particular location, and a
linear unit of measure. A projected coordinate system such as universal transverse Mercator
(UTM), Albers Equal Area, or Robinson, all (along with numerous other map projection
models) provide various mechanisms to project maps of the earth's spherical surface onto a
two-dimensional Cartesian coordinate plane.
Map projections
Whether you treat the earth as a geoid or a spheroid, you must transform its threedimensional surface to create a flat map sheet. This mathematical transformation is
commonly referred to as a map projection.
Figure 2.7 - Mercator map projection of the Earth showing how the projection distorts the projected
image (How? Greenland is actually 3.5 times smaller than Australia, but not in the image). Each grid
represents the same area. Sutton et al (2009).
One easy way to understand how map projections alter spatial properties is to visualize
shining a light through the earth onto a surface, called the projection surface. Imagine the
earth's surface is clear with the graticule (criss-cross lines) drawn on it. Wrap a piece of
paper around the earth. A light at the center of the earth will cast the shadows of the
graticule onto the piece of paper. You can now ‘unwrap’ the paper and lay it flat. The shape
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Navigation & mapping for technicians
Study Module 4
of the graticule on the flat paper is different from that on the earth. The map projection has
distorted the graticule, as seen in the Mercator projection from Figure 2.7 above.
Three common map projection types or methods are;
◗ Cylindrical (sometimes transverse)
◗ Conical, and,
◗ Polar/planar/azimuthal
Each of these is explained in brief in Table 2.1 below.
Table 2.1 – Projection types, processes and results. Sutton et al (2009).
A spheroid cannot be flattened to a plane any more easily than a piece of orange peel can
be flattened because it will tear. Representing the earth's surface in two dimensions causes
distortion in the shape, area, distance, or direction of the data.
A map projection uses mathematical formulas to relate spherical coordinates on the globe
to flat, planar coordinates.
Projections can also be described by the projection technique (distortion or ‘quality’
aspects) of the area representation. Projections can be;
◗ Equal area (or shape conformal)
◗ Equal distance
◗ Equal angles (or direction)
Different projections cause different types of distortions. Some projections are designed to
minimize the distortion of one or two of the data's characteristics. A projection could
maintain the area of a feature but alter its shape.
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Navigation & mapping for technicians
Study Module 4
Table 2.2 – Different types of map projection used in the industry. There are hundreds more, some
good, some bad. From http://www.radicalcartography.net/?projectionref (accessed 10/04/2011)
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Navigation & mapping for technicians
Study Module 4
Map projection parameters
A map projection by itself is not enough to define a PCS. You can state that a dataset is in
Transverse Mercator, but that's not enough information. Where is the center of the
projection? Was a scale factor used? Without knowing the exact values for the projection
parameters, the dataset cannot be reprojected.
Each map projection has a set of parameters that you must define. The parameters specify
the origin and customize a projection for your area of interest. Angular parameters use the
GCS units, while linear parameters use the PCS units.
Linear parameters
The Linear Parameters of a map projection allow for the units of measure and are typically
in the form of Easting and Northing values, which are similar to the grid concept of latitude
and longitude, but are not the same.
False easting is a linear value applied to the origin of the x-coordinates. False northing is a
linear value applied to the origin of the y-coordinates. False easting and northing values are
usually applied to ensure that all x- and y- values are positive which simplifies calculations.
This is explained in more detail when we discuss maps in Chapter 3.
Angular parameters
Angular parameters relate the map projection properties back to the GCS. The key
parameters include;
◗ Azimuth
◗ Longitude of origin defines the origin of the x-coordinates.
◗ Latitude of origin defines the origin of the y-coordinates.
◗ Standard parallel 1 and standard parallel 2
Unitless parameters
Scale factor is a unitless value applied to the center point or centerline of a map projection.
The scale factor is usually slightly less than one. The UTM coordinate system, which uses the
Transverse Mercator projection, has a scale factor of 0.9996. Rather than 1.0, the scale
along the central meridian of the projection is 0.9996. This creates two almost parallel lines
approximately 180 kilometers, or about 1°, away where the scale is 1.0. The scale factor
reduces the overall distortion of the projection in the area of interest.
From global maps to topographic
So far, so good! We have defined the datum as a source of reference points, we have
wrapped the globe in a geographic coordinate system, and we have projected that system
onto a flat map of the world, so surely going from a ‘large’ flat map to a ‘small’ flat map is
the easy part? Well no…we need a further intermediary; something universal.
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Navigation & mapping for technicians
Study Module 4
Assessment task
After reading the theory above, answer the questions below. Note that;

Marks are allocated to each question.

Keep answers to short paragraphs only, no essays.

Make sure you have access to the references (last page)

If a question is not referenced, use the supplied notes for answers
a) Use general internet sources to establish a definition of ‘azimuth’. Also look up a synonym
for ‘azimuth’ (hint: should start with ‘b’). 2 mk
Type your answer here
Leave blank for assessor feedback
b) Using reference 4, define True Azimuth. 1 mk
Type your answer here
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c) What does a Projected Coordinate System produce? 1 mk
Type you answer here
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d) What is a map projection (notes and Ref 2)? 4 mk
Type your answer here
Leave blank for assessor feedback
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Navigation & mapping for technicians
Study Module 4
e) List the three common projection methods, and briefly explain the difference between
each (notes & Ref 2/3). 6 mk
Type your answer here
Leave blank for assessor feedback
f) What are the three common projection techniques. 3 mk
Type your answer here
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g) What do the linear parameters of a map projection allow for? 2 mk
Type your answer here
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h) What is the specific purpose of the angular parameters? 1 mk
Type your answer here
Leave blank for assessor feedback
i) The unitless scale factor reduces what specific problem associated with map projections?.
1 mk
Type your answer here
j) What is the scale factor used for the central meridian in the UTM system? (you study UTM
in the next module) 1 mk
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Navigation & mapping for technicians
Study Module 4
k) Using reference 3, explain five (5) key features of the Mercator projection. In your
answer, explain which sections of the map are the most distorted. 7 mk
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Study Module 4
Assessment & submission rules
Answers
◗ Attempt all questions and tasks
◗ Write answers in the text-fields provided
Submission
◗ Use the documents ‘Save As…’ function to save the document to your computer using
the file name format of;
name-classcode-assessmentname
Note that class code and assessment code are on Page 1 of this document.
◗ email the document back to your teacher
Penalties
◗ If this assessment task is received greater than seven (7) days after the due date (located
on the cover page), it may not be considered for marking without justification.
Results
◗ Your submitted work will be returned to you within 3 weeks of submission by email fully
graded with feedback.
◗ You have the right to appeal your results within 3 weeks of receipt of the marked work.
Problems?
If you are having study related or technical problems with this document, make sure you
contact your assessor at the earliest convenience to get the problem resolved. The name of
your assessor is located on Page 1, and the contact details can be found at;
www.cffet.net/env/contacts
Resources & references
References
1.
2.
3.
4.
5.
These notes
http://www.icsm.gov.au/mapping/about_projections.html
http://www.icsm.gov.au/mapping/map_projections.html
http://www.lpi.nsw.gov.au/surveying/geodesy/projections
http://www.ga.gov.au/earth-monitoring/astronomical-information/astronomicaldefinitions.html#azim
If you are keen to learn more about the mathematics of map projections (joke), check
out this scary document.
6. http://user.gs.rmit.edu.au/rod/files/publications/A%20GUIDE%20TO%20MAP%20PROJE
CTIONS%20V3.pdf
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Navigation & mapping for technicians
Study Module 4
Resources
Check out this short video from National Geographic
http://education.nationalgeographic.com.au/education/media/selecting-mapprojection/?ar_a=1
A more comprehensive video from ArcGIS ESRI can be found here. Note that some aspects
of the notes are clarified, but some information is also introduced and some contradicted,
so go easy on this. All in all, I like this video, but YOU ONLY NEED TO LISTEN TO THE FIRST
10:00 MINUTES!
http://www.youtube.com/watch?v=eFhsBHgGMI0
This presentation covers a few concepts all in one.
http://www.slideserve.com/seven/geodesy-map-projections-and-coordinate-systems
And one last one for you;
http://www.slideserve.com/andrew/map-projections-and-coordinate-systems-1234589
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