SC120 Map Interpretation, Air Photos, and GPS

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Module 2 - Map Scale

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Reading Assignment: Chapters 1, 2, and 3 of Sebert text.

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What Does "Scale" Mean?

Scale refers to the relationship between distance on a map (or aerial photograph) and corresponding distance on the ground.

Distance on map          1 inch	          1 
------------------ =  -------------  = --------
Distance on ground    50,000 inches     50,000

Question: 1 cm on the map represents how many centimeters on the ground, if the map scale is 1:50,000?

Answer: 50,000 cm.

Question: If 2 cm on the map represents 100,000 cm on the ground, what is the map scale?

Answer: 1:50,000.

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Large vs. Small Scale

.	Large Scale (e.g., 1:50,000)	Small Scale (e.g., 1:1,000,000)
Area Covered on Map	Small	Large
Spatial Detail	High (Objects appear larger)	Low (Objects appear smaller)
Denominator	Small (1/50,000)	Large (1/1,000,000)
Representative Fraction (RF)	Large (1/50,000)	Small (1/1,000,000)
Example	Topographic map of Vermilion (1:50,000)	Ecoregion map of Alberta (1:1,000,000)
Use	Detailed work	Reconnaissance

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Question: What does "Map not made to scale" mean?

Answer: Distance on a map cannot be used to calculate the actual distance on the ground.

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Question: How many ways the scale of a map may be given?

Answer: Three ways:

• A scale statement (A verbal scale): 1 cm equals 2.5 km. Loses meaning if the map is enlarged or reduced.

• A scale ratio (A representative fraction, or A natural scale): 1:250,000

• A scale bar or bars (A graphic scale): Looks like a ruler. Has primary scale and extension scale.

  

Question: What is the benefit of a "scale ratio"?

Answer: It is unitless. Any unit can be used.

Question: What happens when your map has only a "scale statement" and if the map is enlarged or reduced when xeroxing?

Answer: It loses meaning, because we won't know the actual scale.

Question: What is the benefit of a "scale bar"?

Answer: If the map is enlarged or reduced when xeroxing, "scale bar" will be proportionately enlarged or reduced.

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Map Classification

Maps maybe classified by scale, intented use, and style.

Scale:

• Small Scale: 1:500,000 and smaller
• Medium Scale: Between 1:500,000 and 1:75,000
• Large Scale: 1:75,000 and larger

Intended Use:

• Topographic map: Base maps.
• General maps at scale: Maps of the world, a country, a province.
• Navigational map: Intended for travel on land and sea and in the air. Air and sea navigation maps referred to as "charts".
• Thematic map: Special-purpose maps showing a particular theme such as forestry, geology, climate, land use, etc.

Style:

• Monochrome or multicolored
• Line map (topographic map) or a photomap (a variant of topographic map)

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Question: What kinds of maps are referred to as "plans"?

Answer: Maps at scales larger than 1:1,000 are generally referred to as "plans".

Question: What is the "One-inch Map"?

Answer: The "One-inch Map" was a popular Canadian map in the past. The scale was one inch to one mile. The scale of that map was 1:63,360 -- a rather awkward ratio.

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Distance Measurement Using Representative Fraction (RF)

• Precise map measurement always involves the map scale (1:50,000) or the representative fraction (1/50,000).
• Measurement done across the map, but resulting figures apply to the real earth.

       MD
RF = ------   
       GD

RF = Representative Fraction
MD = Map Distance
GD = Ground Distance

Remember: MD is always reduced to 1.

Question: On a 1:50,000 map, a distance is measured with a centimeter scale and found to be 7.65 cm. What is the ground distance?

Answer:

       MD       7.65 cm              50,000
GD = ------  = --------- = 7.65 cm x ------ = 382,500 cm = 3.82 km
       RF       1/50,000                1

Useful Tip for Calculating Ground Distance: To get GD you multiply MD by the denominator of the RF.

Question: How can you find out the scale of a plan (a map at scale larger than 1:1,000)?

Answer:

First step: Measure the MD on the plan. For example, measure the distance between two road intersections on the plan. Let's say it is 54.05 cm.

Second step: Find a map of a known scale (say, 1:10,000) of the same area. Measure the distance between the same intersection (say, it is 10.05 cm).

Third step: Calculate the GD of the intersection from the map of known scale.

10.81 cm x 10,000 = 108,100 cm.

Fourth step: Use the newly calculated GD (108,100 cm) as the denominator to calculate the RF for the plan (you already know the MD of the intersection on the plan, which is 54.05 cm).

RF = 1/y = MD/GD = 54.05 cm / 108,100 cm

54.05 y = 108.100

Therefore, y = 2,000 and the RF of the plan is 1:2,000

Question: How can you find out the scale of a map if you are out driving and you don't have any other map?

Answer: First step: On your map, measure the MD between two objects, say two bridges. Suppose, MD = 10.52 cm.

Second step: Drive from one bridge to the other and find out the GD from the odometer of your vehicle. Suppose, GD = 26.3 km.

Third step: RF = 1/y = MD/GD = 10.52 cm / 2,630,000 cm

10.52 y - 2,630,000

y = 250,000, therefore, the map scale is 1:250,000

Question: You have been driving on a remote highway with few landmarks. You are using a 1:250,000 map. At the last crossroads teh odometer read 781 km. It now reads 842 km. How many centimeters on the map are you past the crossroads?

Answer: 842 km - 781 km = 61 km = 6,100,000 cm

MD = GD/Denominator of RF

MD = 6,100,000 / 250,000

24.4 cm

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Distance Measurement Using Bar Scale

Straight-Line Measurement:

Question: How can you find GD using bar scale?

Answer:

• Take a piece of paper and lay it on the map with the edge touching two points on the map.
• With a pencil, tick at both points.
• Move the paper to the bar scale, with right hand tick opposite an even division on the primary scale so that the left hand tick falls on teh extension scale.
• First read the even divisions on the primary scale, and then add the distance shown on the extension scale.

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Map Projection

• Map projection is a ystematic representation of surface features from a spherical earth on a flat map.
• Map projection is the geometric transformation of the earth's surface on the map's surface.
• Every flat map misrepresents the surface of the earth in some way.
• No map can rival a globe in truly representing the surface of the entire earth.
• A map or parts of a map can who one or more (but never all) of the following:
  • True directions
  • True distances
  • True areas
  • True shapes
• Many types of map projections exist, typically categorized into three major types based on their projection surface:
  • Planar or Azimuthal (e.g., Orthographic, Stereographic, Gnomonic, Azimuthal Equidistant)
  • Conic (e.g., Simple or Equidistant Conic, Polyconic, Albers Equal Area Conic)
  • Cylindrical (e.g., Mercator, Transverse Mercator, Oblique Mercator)

    

• Each map projection has specific properties that make it useful for specific purposes.
• Therefore, choice of projection depends on the need.

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