Where am I?
Lecture 3
CONS 340
Learning Objectives
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Explain map scale
Define geodesy
Compare geographic and projected
coordinate systems
Define spheroids and datums
Datum transformations
Map Scale
 Linear (also called graphic)
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 Verbal
 20cm = 4.8km
 Representative fraction
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1:24,000
Conversion Example
20cm = 4.8km (original verbal scale)
20cm = 480,000cm (convert all units to a common metric)
1cm = 24,000cm (make the left side equal to one by dividing)
1 / 24,000 or 1:24,000 (remove the unit designation)
Large vs. small scale maps
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Because it is a ratio, scale is unitless and
large and small scale varies according to
project
1:1 is the largest scale
1:24,000 is large scale for Conservation
1:500,000 is a small scale for Conservation
Scale is inversely proportional to area given
the same size map (display)
Map Scale and You
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You will want to pay attention to map
scale, because there are always
questions on the exams dealing with
scale.
For example: Which of these is the
larger scale? 1:24,000 or 1:100,000
What is Geodesy?
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Geodesy is the study of:
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The size, shape and motion of the earth
The measurement of the position and motion of
points on the earth's surface, and
The study of the earth's gravity field and its
temporal variations
Types of Geodesy
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terrestrial or classical geodesy
space geodesy
theoretical geodesy
Basic Geodesy Facts
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Geographic/true directions determined by the
orientation of the graticule on the earths'
surface
Basic Geodesy Facts
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Magnetic directions must take into account
the compass variation (magnetic declination)
Basic Geodesy Facts
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Great circle – arc formed by the intersection
of the earth with a plane passing through any
two surface points and the center of the
earth
Basic Geodesy Facts
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Rhumb line, loxodrome
or constant azimuth –
line which makes a fixed
angle with all meridians;
spirals to pole
Conic projection
Mercator projection
The Earth is Not Round
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First the earth was flat
500 BC Pythagoras declared it was a sphere
In the late 1600’s Sir Issac Newton
hypothesized that the true shape of the earth
was really closer to an ellipse
More precisely an Oblate Ellipsoid (squashed
at the poles and fat around the equator)
And he was right!
Geoid, Ellipsoid & Sphere
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Geoid - estimates the earth's surface using mean sea level of the
ocean with all continents are removed
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It is an equipotential surface - potential gravity is the same at every
point on its surface
Ellipsoid - It is a mathematical approximation of the Geoid
Authalic Sphere - a sphere that has the same surface area as a
particular oblate ellipsoid of revolution representing the figure of
the Earth
Shape of the Earth
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Earth as sphere
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simplifies math
small- scale maps (less than 1:
5,000,000)
Earth as spheroid
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maintains accuracy for larger- scale
maps (greater than 1: 1,000,000)
Spheroid or Ellipsoid?
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What is a Spheroid anyway?
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An ellipsoid that approximates the shape of a sphere
Although the earth is an ellipsoid, its major and
minor axes do not vary greatly.
In fact, its shape is so close to a sphere that it is
often called a spheroid rather than an ellipsoid.
ESRI calls it a spheroid but the two can be used
interchangeably
For most spheroids, the difference between its
semi-major axis and its semi-minor axis is less
than 0.34 percent.
How About a Few Ellipsoids
Why Do We Need More Than
One Spheroid (Ellipsoid)?
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The earth's surface is not perfectly
symmetrical
the semi-major and semi-minor axes
that fit one geographical region do not
necessarily fit another one.
What is the best Ellipsoid for you?
After James R. Smith, page 98
Shape of the Earth
Relation of Geoid to Ellipsoid
From James R. Smith, page 34
Vertical Deflection
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Important to
surveyors
Deflection of the
Vertical =
difference between
the vertical and the
ellipsoidal normal
Described by the
component tilts in
the northerly and
easterly directions.
Measuring Height
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Traditionally measured as
height above sea level
(Geoid) but is changing
due to GPS
The distance between the
geoid and the spheroid is
referred to as the geoidspheroid separation or
geoidal undulation
Can convert but it is
mathematically complex
Coordinate Systems
Cartesian Coordinate System
 Used for locating positions on a flat
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map
Coordinates tell you how far away
from the origin of the axes you are
 Referenced as (X,Y) pairs
In cartography and surveying, the X
axis coordinates are known as
Eastings, and the Y axis coordinates
as Northings.
 False easting and northings are typically
added to coordinate values to keep
coordinates in the upper right hand
quadrant of the ‘graph’ – positive values
3D Cartesian Coordinates
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Cartesian Coordinates
can define a point in
space, that is, in three
dimensions.
To do this, the Z axis
must be introduced.
This axis will represent a
height above above or
below the surface
defined by the x and y
axes.
Local 3D Cartesian Coordinates
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This diagram shows the
earth with two local
coordinate systems
defined on either side of
the earth.
The Z axis points
directly up into the sky.
Instead of (X,Y) it is
(X,Y,Z)
Geographic Coordinate System
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The Equator and Prime
Meridian are the reference
points
Latitude/ longitude measure
angles
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Latitude (parallels) 0º - 90º
Longitude (meridians) 0º - 180º
Defines locations on 3- D
surface
Units are degrees (or grads)
Not a map projection!
Prime Meridians
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Origin of Longitude lines
Usually Greenwich, England
Others include Paris, Bogota, Ferro
City
Athens, Greece
Bern, Switzerland
Bogota, Colombia
Brussels, Belgium
Ferro (El Hierro)
Jakarta, Indonesia
Lisbon, Portugal
Madrid, Spain
Paris, France
Rome, Italy
Stockholm, Sweden
Meridian
23° 42' 58.815"
7° 26' 22".5
74° 04' 51".3
4° 22' 04".71
17° 40' 00"
106° 48' 27".79
9° 07' 54".862
3° 41' 16".58
2° 20' 14".025
12° 27' 08".4
18° 03' 29".8
E
E
W
E
W
E
W
W
E
E
E
Latitude/ Longitude
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Not uniform units of measure
Meridians converge near Poles
1° longitude at Equator = 111 km
at 60° lat. = 55.8 km
at 90° lat. = 0 km
Decimal Degrees (DD)
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Decimal degrees are similar to
degrees/minutes/seconds (DMS) except
that minutes and seconds are
expressed as decimal values.
Decimal degrees make digital storage of
coordinates easier and computations
faster.
Conversion from DMS to DD:
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Example coordinate is 37° 36' 30"
(DMS)
Divide each value by the number of
minutes or seconds in a degree:
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36 minutes = .60 degrees (36/60)
30 seconds = .00833 degrees (30/3600)
Add up the degrees to get the answer:
37° + .60° + .00833° = 37.60833 DD
Datums
Datums (simplified)
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Reference frame for locating points
on Earth’s surface
Defines origin & orientation of
latitude/ longitude lines
Defined by spheroid and spheroid’s
position relative to Earth’s center
Creating a Datum
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Pick a spheroid
Pick a point on the Earth’s surface
All other control points are located
relative to the origin point
The datum’s center may not coincide
with the Earth’s center
Datums, cont.
2 types of datums
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Earth- centered
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(WGS84, NAD83)
Local
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(NAD27, ED50)
Why so many datums?
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Many estimates of Earth’s size and
shape
Improved accuracy
Designed for local regions
North American Datums
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NAD27
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Clarke 1866 spheroid
Meades Ranch, KS
1880’s
NAD83
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GRS80 spheroid
Earth- centered datum
GPS- compatible
GPS
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Uses WGS84 datum
Other datums are transformed and
not as accurate
Know what transformation method is
being used
Relationship between 2
datums
Transformation method
accuracies
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NADCON
HARN/ HPGN
CNT (NTv1)
Seven parameter
Three parameter
15 cm
5 cm
10 cm
1- 2 m
4- 5 m
International datums
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Defined for countries, regions, or the
world
World: WGS84, WGS72
Regional:
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ED50 (European Datum 1950)
Arc 1950 (Africa)
Countries:
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GDA 1994 (Australia)
Tokyo