# Applications of Scale questions Hey , Please read the assignment carefully and accept the deal if you are confident to do it right. See the attached file

Applications of Scale questions Hey , Please read the assignment carefully and accept the deal if you are confident to do it right.

See the attached file as support to you . Also, look to the chapter 2 in the text book( Map Use )

It is often useful to know the relationship between map scale, map size, and ground coverage. The problems below are meant to demonstrate the far-reaching usefulness of the map scale in its different expressions. They show only a few of the many ways you can manipulate scale information to solve problems involving distance relations. As you work through the problems, show your work, as well as the answers. You will only get points for the correct answer if you also include a meaningful description of how you derived it. If necessary, you may attach an additional sheet. Be sure to include the appropriate units of measure in your answers. You may also wish to refer to Chapter 2 in the textbook.

1. If the RF of a map is shown as 1:75,000, what is the verbal scale in “centimeters to the kilometer”? Round the answer to the nearest tenth. Draw a scale bar that correctly represents the verbal scale.

2. If the scale bar of a map shows, by measurement, that 1 cm represents 50 km, what is the RF?

3. If the scale bar of a map shows, by measurement, that 1 inch represents 75 mi., what is the RF?

4. The scale of Map A is 1:1,000,000 and the distance between two cities shown in that map measures 9 inches. The distance between the same two cities on Map B is 6 inches. What is the scale of Map B?

5. Using a photocopy machine, you enlarge a 1:24,000 map to 135% of its original size. What will be the scale of the enlarged map? Round the answer to the nearest ten (in the scale denominator). Map Scale and Abstraction

Map Scale

• maps generally smaller than environment

reduction factor

SCALE

= “relationship between map units and actual

ground units”

1

Map Scale

•

Linear Scale Expressions

1. verbal

2. fraction

3. graphic

Map Scale

•

Linear Scale Expressions

1. verbal

2. fraction

3. graphic

word statement of map distance in

relation to earth distance

e.g.,

“1 cm represents 10 km”

“1 inch to 16 miles”

2

Map Scale

•

Linear Scale Expressions

1. verbal

2. fraction

3. graphic

Representative Fraction (RF)

Ratio Scale

e.g.,

1:1,000,000

1/1,000,000

Map Scale

•

Linear Scale Expressions

1. verbal

2. fraction

3. graphic

scale bar

bar scale

a ruler printed on the map in which

distances on the map may be

measured as actual ground

distances

3

Map Scale

•

Linear Scale Expressions

1. verbal

2. fraction

3. graphic

Variable scale bar

–

for some small-scale maps

example: Mercator Map

Map Scale

•

Linear Scale Expressions

1. verbal

2. fraction

3. graphic

•

Areal Scale Expressions

1. verbal

2. graphic

e.g., “1 sq inch to 4 sq miles”

e.g.,

= 100 sq miles

4

Map Scale

Converting Map Scales

Examples

1. “3 inches represents 10 miles”

What is the representative fraction?

2. “1:79,200”

How many miles are in one inch?

3. “1:47,520”

Construct a graphic scale!

5

Converting Map Scales

Examples

1. “3 inches represents 10 miles”

What is the representative fraction?

known: 1 mile = 63,360 inches

therefore:

10 miles = 633,600 inches

3 inches represents 633,600 inches

3

1

633 ,600

x

x=211,200

1:211,200

Converting Map Scales

Examples

2. “1:79,200”

How many miles are in one inch?

known: 1 inch represents 79,200 inches

1 mile = 63,360 inches

therefore:

79,200/63,360 = 1.25

“1.25 miles to the inch”

6

Converting Map Scales

Examples

3. “1:47,520”

C

Construct

t t a graphic

hi scale!

l !

known: 1 mile = 63,360 inches

therefore:

47,520/63,360 = 0.75

1 inch = 0.75 miles

but: full miles are more useful than full inches

1in/0.75mi = x in/1mi

x = 1.33in

Draw graphic scale with 1.33 in for every full mile

Determining Scale

of map or aerial photograph

1. measure distance b/w two points on map (MD)

2. determine horizontal distance b/w corresponding points

on the ground (GD)

HOW?

3. utilize RF formula:

RF = 1/x = MD/GD

4. attention: MD and GD must be in same unit of measure

7

Determining Scale

of map or aerial photograph

1. measure distance b/w two points on map (MD)

2. determine horizontal distance b/w corresponding points

on the ground (GD)

HOW?

3. utilize RF formula:

RFknown

= 1/x =

MD/GD features

(a) use

terrestrial

football

field,and

… GD must

4. attention: MD

be in same unit of measure

(b) use reference material

– atlases, other maps of similar scales, distance logs, …

– small-scale maps: length of equator

(c) use spacing of parallels and meridians

– one degree of latitude = ~ 69.2 miles

– one degree of longitude = cos(lat) * 69.2 miles

Determining Scale

of map or aerial photograph

1. Select two points on the map with unknown RF1.

1. measure distance b/w Measure

two points

on map

(MD)

the distance

between

them (MD1).

2. Locate those same two points on the map with known

2. determine horizontal distance

b/w

corresponding

pointsU RF

RF . Measure

M

th

the di

distance

t

b

between

t

th

them (MD ). Use

on the ground (GD) of thisHOW?

map to determine GD, which is the same for both

3. utilize RF formula: 3. maps.

Use GD and MD to determine RF .

2

2

1

1

RFknown

= 1/x =

MD/GD features

(a) use

terrestrial

RF1 = 1/x = MD1/GD

4. attention: MD and GD must be in same unit of measure

football

field,

…

4. attention: MD and GD must be in same unit of measure

(b) use reference material

– atlases, other maps of similar scales, distance logs, …

– small-scale maps: length of equator

(c) use spacing of parallels and meridians

– one degree of latitude = ~ 69.2 miles

– one degree of longitude = cos(lat) * 69.2 miles

8

Abstraction in Mapping

•

Why?

1. graphical constraints

1

2. physiological constraints

3. maps should show the typical aspects of a

geographic phenomenon (in accordance

with purpose) and preserve that through

different scales

Abstraction in Mapping

•

Why?

9

Abstraction in Mapping

• When?

1. environment map

2. map 1 map 2

Abstraction in Mapping

• When?

1. environment map

–

2. map 1 map 2 –

usually done by subject experts

– surveyor; geologist; soil scientist

measurement issues

– e.g., inclusion of a certain building

based on minimum size

classification issues

– e.g., soil type determination based

on 5-class vs. 50-class scheme

10

Abstraction in Mapping

• When?

1. environment map

cartographic generalization

2. map 1 map 2

important implications for mapping and

GIS:

– know your sources ( metadata)

– careful with enlargement

g

of smallerscale maps

(scale of map 1 should be

larger than scale of map 2)

Scale

geometric accuracy

typical of a landscape

Cartographic Generalization

Example: Representation of a City

From: Zondervan (1901)

Allgemeine Karten kunde,

Leipzig: B. G. Teubner.

(Original source: SydowWagners Methodischer

Schulatlas)

11

Cartographic Generalization

Elementary Processes

1. Graphic Generalization

focus on location & geometry

2. Conceptual Generalization

focus on attributes & symbology

Cartographic Generalization

Elementary Processes

1. Graphic Generalization

focus on location & geometry

processes:

2. Conceptualelementary

Generalization

– simplification

focus on attributes & symbology

– exaggeration/enlargement

– only possible at expense of other symbols

– distorts relative spatial relationships b/w features

– often leads to displacement

– displacement

– merging/aggregation

– selection

12

Cartographic

Generalization

Graphic

Generalization

From: Kraak and Ormeling (2011)

Cartography: Visualization of Spatial Data.

Guilford Press.

[graphic generalization

examples on transparencies]

13

Cartographic Generalization

Elementary Processes

1. Graphic Generalization

focus on location & geometry

2. Conceptual Generalization

focus on attributes & symbology

elementary processes:

– merging

g g

– selection

– symbolization

rules: visual complexity decreases with simpler symbols

conceptual complexity increases with simpler symbols

– enhancement/exaggeration

Cartographic

Generalization

Conceptual

Generalization

From: Kraak and Ormeling (2011)

Cartography: Visualization of Spatial Data.

Guilford Press.

14

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