Geog 258: Maps and GIS
Map scale
January 13 (Fri)
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,
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
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