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