OUTLINE: scale definition types of scale projection definition projection properties and...

OUTLINE: scale definition types of scale projection definition projection properties and

classification choosing a map projection

MMAP AP PPROJECTIONSROJECTIONS ANDAND SSCALECALE

PPROJECTIONSROJECTIONS

THE GLOBETHE GLOBE

Advantages:

most accurate map

latitude and longitude lines

Disadvantages

expensive to make

cumbersome to handle and store

difficult to measure

not fully visible at one

PROJECTIONSPROJECTIONS

process of transforming earth’s spherical surface to a flat map while maintaining spatial relationships.

Curved Earth

Flat Map

projection process involves stretching and distortion


no matter how the earth is divided up, it can not be unrolled or unfolded to lie flat (undevelopable shape).


PROJECTION PROCESSPROJECTION PROCESS

most projections are combinations of the following characteristics:

characteristic of earth features that are maintained

shape of the projection plane (developable shape)

aspect of the projection plane

points or lines of tangency or secancy

location of the false ‘illumination source’

PROJECTION PROPERTIESPROJECTION PROPERTIES

properties in which distortion is minimized when producing a map

AreaArea

equal area or equivalent

area sizes are correct everywhere on map

shapes greatly distorted

DistanceDistance

equidistant

distance is correct in all directions from a point

i.e. equidistant projection centered on Winnipeg would show the correct distance to any other location on the map, from Winnipeg only

distorting area and/or direction


EquidistantEquidistant


DirectionDirection

azimuthal

compass bearing is maintained in all directions only from a point

shapes, distances and areas are badly distorted


ShapeShape

conformal

shape maintains its shape across the map distorting area

latitude and longitude cross at right angles

used for navigation


Area Distance Direction Shape

Equal-Area No Yes No

Equidistant No Yes No

Azimuthal Yes Yes Yes

Conformal No No Yes


Tissot’s IndicatrixTissot’s Indicatrix

convenient way of showing distortion

size and shape of the indicatrix will vary from one part of the map to another

Mercator projection

Equal-Area projection


made by projecting a globe onto a surface – developable surface

distortion is least where developable surface touches the earth

accomplished by use of geometry and mathematics

2))sin(1sin(124tanln eeesay

sax

Mercator:


PROJECTION CLASSIFICATION


Tangent caseTangent case – shape just touches the earth along a single line or at point.

Secant caseSecant case – shape intersects or cuts through earth as two circles.

ConicalConical

globe sits under a cone, touching along pre-selected line of latitude

projection developed by cutting cone lengthwise and unrolling



normal case:

parallels – concentric circular arcs, meridians – straight equally spaced lines



Lambert conformal conic projection

Albers equal-area conic projection



Conical Distortion



ConicalConical

PolyconicPolyconic – envelopes globe with an infinite number of cones, each with its own standard parallel



CylindricalCylindrical

projected onto a cylinder which is also cut lengthwise and unrolled




evenly spaced network of straight, horizontal parallels and straight vertical meridians (grid like)



Cylindrical DistortionCylindrical Distortion

projection of the entire world, significant distortion occurs at the higher latitudes

parallels become

further apart and poles

can not be seen



Cylindrical DistortionCylindrical Distortion

sizes of Greenland vs. Africa

Mercator Projection True size




straight line between any two points follows a single direction called a rhumb line

useful in construction of navigational charts



Planar/AzimuthalPlanar/Azimuthal portion of earth’s surface is transformed from a

perspective point to a flat surface



Planar/AzimuthalPlanar/Azimuthal perspective point/light source

Light rays



Planar/AzimuthalPlanar/Azimuthal

true direction only between center and other locations

most often used to map polar regions



NORMAL

OBLIQUE

TRANSVERSE



ConicCylindrical

Planar

CANADA PROJECTEDCANADA PROJECTED

Pseudo map projectionsPseudo map projections

pseudoconic and pseudocylindrical projections - have curved meridians instead of straight ones

Pseudocylindrical



Pseudo map projectionsPseudo map projections modified projections - changes have been made to

reduce the pattern of distortion or add more standard parallels

modified to reduce the distortion in the size of areas



Pseudo map projectionsPseudo map projections individual or unique projections – can not be easily

related to one of the three developable geometric forms

Goode’s Projection



CHOOSING PROJECTIONCHOOSING PROJECTION

depends on:

purpose for which the data is to be used

property in which distortion is minimized

extent and location of area

steps:

1. size of area of interest

small area has little distortion, any projection.

2. latitude of area of interest

low-latitudes – cylindrical

mid-latitudes – conical

polar latitudes - planar


3.3. shape of area of interest:shape of area of interest: E-W extent: conic or cylindricalE-W extent: conic or cylindrical N-S extent: cylindricalN-S extent: cylindrical square or circular: planarsquare or circular: planar

4.4. purpose:purpose: navigation – planar or cylindricalnavigation – planar or cylindrical world distributions – cylindricalworld distributions – cylindrical specific locations - planarspecific locations - planar


COMMON PROJECTIONSCOMMON PROJECTIONS

Albers Equal-Area ConicAlbers Equal-Area Conic

equal area, secant conical projection (two standard parallels)

resembles earth graticule

MercatorMercator

cylindrical, conformal projection

angular relationships are preserved parallels and

meridians appear as straight lines

parallels are farther apart with increased distance from equator


MercatorMercator

change in N-S scale exactly offset change in E-W direction (shapes preserved)

scale is true at equator or at two standard parallels equidistant from equator

all rhumb lines appear as straight lines, while great circle arcs are not (except equator and meridians)

used primarily for navigation and large scale maps


Transverse MercatorTransverse Mercator

cylindrical, conformal projection

similar to Mercator except the axis of projection cylinder is rotated 90o from polar axis

scale is true along central meridian or along two straight lines equidistant from and parallel to central meridian

used to portray areas with larger N-S than E-W extent.


Lambert Conformal ConicLambert Conformal Conic

conformal, secant conical projection with two standard parallels

possesses true shape of small areas with area distortion

concentric parallels (increasing intervals) and equally-spaced straight meridians


MollweideMollweide

pseudocylindrical, equal-area projection

N-S scale is decreased in high latitudes, increased in low latitudes; opposite in E-W direction

parallels are straight, spaced closer together from equator


Polar StereographicPolar Stereographic

directions are true from center point

conformal projection: over a small area, angles in the map are the same as the corresponding angles on Earth's surface

meridians are straight and radiating; parallels are concentric circles

shows only one hemisphere


Polar StereographicPolar Stereographic

preserves circles - all great and small circles are shown as concentric arcs or straight lines

scale true only where the central parallel and meridian cross

used in polar aspect for topographic maps of polar regions, regions that are circular in shape


Eckert IV Equal AreaEckert IV Equal Area

pseudocylindrical and equal-area

scale is true along the parallel at 40:30 North and South


RobinsonRobinson

developed to minimize appearance of angular and area distortion

distorts shape, area, scale and distance in an attempt to balance errors of projection properties


RobinsonRobinson

based on tables of coordinates not mathematical formulae

overall effect – more than 75% of earth is shown with less than 20% departure from true scale size

used for thematic and reference maps


OTHER PROJECTIONSOTHER PROJECTIONS

Berghaus Star

Sanson-Flamsteed


Conoalactic


Hammer


Eisenlohr


Gall Stereographic Cylindrical


Cassini


SSCALECALE

SCALE

size of an object on a map compared to the actual object on the ground

distance

distance

ground

mapscalemap

may not be the same in all directions from a point

SCALE TYPESSCALE TYPES

Verbal scale

describes the scale in words

i.e. “one centimeter represents one kilometer”

commonly found on popular atlases and maps

Visual scale (bar scale or graphic scale)

graphically illustrates relationship between map distance and ground distance.

one end can be divided

most common

remains correct if reduced or enlarged


Visual scale (bar scale or graphic scale)


Representative Fraction (RF)

ratio (proportion) between map distance to earth distance

i.e. 1:50,000

most versatile; not tied to any specific units


SCALE FACTORSCALE FACTOR

Representative Fraction

Globe distanceEarth distance

=

Map Scale:

(e.g. 1:24,000)

Map Projection:

Scale Factor

stated scale is correct only at selected points

statement of relation between given scale and actual scale value

scaleprincipalscaleactual

SF

i.e. SF of 2.000 would mean that actual scale is twice the principal scale

SCALE FACTORSCALE FACTOR

large scale: show a small area with a large amount of detail.

small scale: show a large area with a small amount of detail

all relative

LARGE VS SMALL SCALE

LARGE VS SMALL SCALE

DETERMING SCALE DETERMING SCALE use map scale to convert map distance to ground

distance.

for verbal and RF scales - multiply by the scale, then convert the ground distance to units suitable for ground measurements.

i.e. we have a map with a scale of 1:50,000. We measure the distance along a property boundary as 1.7 cm. What is the length in the real world?

for graphic scales – mark off a distance on the map and compare it directly to the bar scale.

Verbal to RF

write verbal scale as a fraction then convert so that both numerator and denominator have the same units and numerator has a 1

i.e. convert verbal scale “1 cm represents 100 km” to RF

RF to Verbal

i.e. convert from RF of 1:25,000 to verbal scale, in metric

TRANSFORMING SCALES

TRANSFORMING SCALES

Graphic Scales and RF/Verbal

take the measurement from the bar scale to determine the map distance and corresponding ground distance.

i.e. 10 km on ground measures 2.4 cm on map.

use method for verbal scale to RF conversion.

TRANSFORMING SCALES

TRANSFORMING SCALES

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