Applications of Scale questions

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timer Asked: Jan 30th, 2019
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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

Tutor Answer

Borys_S
School: New York University

The solutions are ready, please ask if something is unclear.docx and pdf files are identical

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.

There are 100 ∙ 1000 = 100,000 centimeters in one kilometer.
The given map represents 75,000 centimeters in one centimeter,
75,000
i.e. its verbal scale is “1 cm represents 100,000 = 0.75 km”.
Rounded to the nearest tenth this gives “1 cm represents 𝟎. 𝟖 km”.
Further, one kilometer on this map has the length of

100,000
75,000

≈ 1.3 (𝑐𝑚). The picture:

(the length of one part is supposed to be 1.3 cm and it represents one km on the map).

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

5...

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Anonymous
awesome work thanks

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