# 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”
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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
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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!
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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”
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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
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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
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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?
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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
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Abstraction in Mapping
• When?
1. environment  map
cartographic generalization
2. map 1  map 2
important implications for mapping and
GIS:
– 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)
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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
– displacement
– merging/aggregation
– selection
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Cartographic
Generalization
Graphic
Generalization
From: Kraak and Ormeling (2011)
Cartography: Visualization of Spatial Data.
Guilford Press.
[graphic generalization
examples on transparencies]
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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.
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