Where am I?
Lecture 3CONS 340
Learning Objectives Explain map scale Define geodesy Compare geographic and projected
coordinate systems Define spheroids and datums Datum transformations
Linear (also called graphic)
Verbal 20cm = 4.8km
Representative fraction 1:24,000
Conversion Example20cm = 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)
Map Scale
Large vs. small scale maps 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)
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
Map Scale and You
What is Geodesy? Geodesy is the study of:
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
terrestrial or classical geodesy space geodesy theoretical geodesy
Basic Geodesy Facts Geographic/true directions determined
by the orientation of the graticule on the earths' surface
Basic Geodesy Facts Magnetic directions must take into
account the compass variation (magnetic declination)
Basic Geodesy Facts 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 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 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
Geoid - estimates the earth's surface using mean sea level of the ocean with all continents are removed
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 Earth as sphere
simplifies math small- scale maps (less than 1:
5,000,000) Earth as spheroid
maintains accuracy for larger- scale maps (greater than 1: 1,000,000)
Spheroid or Ellipsoid? What is a Spheroid anyway?
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)? 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.
After James R. Smith, page 98
What is the best Ellipsoid for you?
Shape of the Earth
From James R. Smith, page 34
Relation of Geoid to Ellipsoid
Vertical Deflection 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 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 geoid-spheroid separation or geoidal undulation
Can convert but it is mathematically complex
Coordinate Systems
Cartesian Coordinate System
Used for locating positions on a flat 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 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 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
The Equator and Prime Meridian are the reference points
Latitude/ longitude measure angles
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 Origin of Longitude lines Usually Greenwich, England Others include Paris, Bogota, Ferro
City MeridianAthens, Greece
23° 42' 58.815"
EBern, Switzerland 7° 26' 22".5 EBogota, Colombia 74° 04' 51".3 WBrussels, Belgium 4° 22' 04".71 EFerro (El Hierro) 17° 40' 00" WJakarta, Indonesia
106° 48' 27".79
ELisbon, Portugal
9° 07' 54".862
WMadrid, Spain 3° 41' 16".58 WParis, France
2° 20' 14".025
ERome, Italy 12° 27' 08".4 EStockholm, Sweden
18° 03' 29".8 E
Latitude/ Longitude Not uniform units of measure Meridians converge near Poles 1° longitude at Equator = 111
km at 60° lat. = 55.8 kmat 90° lat. = 0 km
Decimal Degrees (DD) 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: Example coordinate is 37° 36' 30"
(DMS) Divide each value by the number of
minutes or seconds in a degree: 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) 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 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
Earth- centered (WGS84, NAD83)
Local (NAD27, ED50)
Why so many datums? Many estimates of Earth’s size and
shape Improved accuracy Designed for local regions
North American Datums NAD27
Clarke 1866 spheroid Meades Ranch, KS 1880’s
NAD83 GRS80 spheroid Earth- centered datum GPS- compatible
GPS 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
NADCON HARN/ HPGN CNT (NTv1) Seven parameter Three parameter
15 cm
5 cm
10 cm
1- 2 m
4- 5 m
International datums Defined for countries, regions, or the
world World: WGS84, WGS72 Regional:
ED50 (European Datum 1950) Arc 1950 (Africa)
Countries: GDA 1994 (Australia) Tokyo