Geog 258: Maps and GIS


Map scale

 

January 13 (Fri)

Reading: Chapter 2

 

Determining map scale from the spacing of parallels and meridians in p. 39 – 40 will be discussed later (right before midterm exam)


What is scale?

= map distance / earth distance

Tells us how much is reduced when the earth area is transformed into the map plane

 


Expressing scale

1) Representative Fraction (RF) 1:25,000

2) Word Statement “one centimeter represents 10 kilometers”

3) Scale Bar                  

 

Would RF or Word Statement be still valid if maps are enlarged or reduced?


Large and small-scale maps

 

Maps that cover large area are called small-scale maps

Maps that cover small area are called large-scale maps

 

This term comes from the numerical value of the RF

For example, 1/100,000,000 < 1/1,200

 

Examples of small scale maps are world map

Examples of large scale maps are cadastral map

 

See Table 2.1

 

The distinction between small-scale and large-scale maps is functional

 


Converting Scale

 

1) Word Statement (WS) Representative Fraction (RF)

 

e.g.

Three inches to 10 miles → ?

 

Remember that map scale is map distance:ground distance in the same unit.

 

3 inch : 10 miles

because 1 mile = 63360 inches

3 inch : 10 * 63360 inch

3 inch : 633600 inch

1 inch : 211200 inch

 

Therefore RF is 1: 212,200

 

2) RF → WS

 

 

e.g.

1:500,000 → one inch represent x miles?

 

1 inch :500,000 inch

          because 1 inch is 1/63360 mile

1 inch :  500,000 * (1/63360)

1 inch : 7.89 mile

 

Therefore WS would be 1 inch on the map represents 7.89 miles on the ground (or 7.89 miles is reduced to 1 inch)

 


Determining Map Scale

 

What if a map doesn’t show map scale? Can we determine map scale without map scale?

 

1) Using known distance of terrestrial feature

 

For example, U.S. football field is 100 yards long

If the map distance of football field is 0.5 inch, what would be the map scale?

 

Map distance: ground distance

0.5 inch : 100 yard

          because 100 yard = 3600 inch

0.5 inch : 3600 inch

1 inch : 7200 inch

 

Therefore RF is 1:7200

 

2) Using reference material

 

If you already know the ground distance of features (let’s say length of lake), simply the ratio of map distance of the feature to ground distance of the feature you already know will become map scale

 

Example 1

Let’s suppose you find out that the length of equator extends across 8 inches in the map below (the length of red line), what would be the scale of this map?

 

Map distance: ground distance

8 inch : ?

What is the real distance of equator (circumference of earth)?

8 inch : 25,000 miles

8 inch : 25,000 * 63,360 inch

8 inch : 1,584,000,000

1: 198,000,000

 

Example 2

Let’s suppose you have two maps showing the same area. The scale of one map is 1:100,000 but the scale of the other map is unknown.

You measure the real distance of road segment (say the road segment from the intersection between 25th ave and 45th street to the intersection between 35th ave and 45th street)

The length turns out 0.7 cm in the map whose scale is known as 1:100,000. The length is 0.5 cm in your map. What would be the scale of your map?

 

First of all, what is the real distance of the road segment?

From the map whose scale is known, we can obtain this

0.7 cm : x cm = 1:00,000

x = 70,000

 

Now what’s the scale of your map?

Scale is map distance: real distance

In your map

0.5cm:70,000 cm = 1:x

x = 70,000 / 0.5 = 140,000