Lecture

Exercise

Introduction to Map Scale

Paired Scale Conversion Exercise

41.242: Map Use and AnalysisDr. Jennifer Y. Pomeroy

Map ScaleToday’s Fun Map

Source: Harris, J. 2003. International Network Archives of Princeton University. [accessed Feb 8, 2013] URL: http://dianhasan.wordpress.com/2011/05/16/global-brands-how-big-is-big-anyway/

In This Lecture:

1. What is scale?2. What are the three methods describing map scale? 3. What is the distinction between large-scale map and small-scale map?4. Scale conversion exercise

How are these maps different and why?

Warm-up Question:

Maps differ in terms of scale.

So What is Scale?

1. Map Scale Map Scale: Degree to which the real world space has

been reduced to be represented on the map. “Scale” = mathematical relationship between:

– Distance shown on map– Actual distance represented on Earth surface

2. Three Methods Describing Map Scale

2.1 Verbal Scale: 1 inch equals 16 miles 1 cm represents 25 km

2.1 Verbal Scale

2.2 Graphic or Bar Scale

2. Three Methods Describing Map Scale

Note: 0 is not at the far left, allowing for the measurement of more precise distances such as ¼, ½…of a mile, or tenths of a kilometer

Only type of scale you can reduce/enlarge Easiest for map users to use

2.1 Verbal Scale 2.2 Graphic or Bar Scale2.3 Representative Fraction (RF)

2. Three Methods Describing Map Scale

2.3.1 Expressed as a fraction or ratio Example: 1/50,000 or 1:50,000

The part of the earth is 50,000 times larger than the map2.3.2 Dimensionless/Unitless

For the above RF, one unit of measurement on the map is equal to 50,000 units of the same measurement on the surface.Example: 1 foot = 50,000 feet or 1cm =

50,000 cm

3. Large and Small Scale Maps Often a source of confusion

Large Scale refers to maps with a large representative fraction

i.e. the RF denominator is small 1:1,000, 1:10,000, 1:65,000

The map represents a smaller area with greater detail Small Scale refers to maps with a small representative

fraction i.e. the RF denominator is large

1:500,000, 1:1,000,000 The map represents a larger area with less detail

So, what exactly are you saying? Large scale map → Displays a small area in more

detail

Small scale map → Displays a large area in less detail

Now, your turn ! Which of the following is a smaller scale map?

1: 10,000 1: 100,000

Which of the following is a larger scale map? 1:250,000 1:63,360

1:50,000 scale map of Harrisburg

1:500,000 scale map of Harrisburg

Some Common ScalesScale 1 inch on map

represent1 cm on map represent

1:24,000 2,000 feet 240 meters1:50,000 4,166 feet 500 meters1:63,360 1 mile 633.6 meters1:100,000 1.6 miles 1 kilometer1:250,000 4 miles 2.5 kilometers1:500,000 8 miles 5 kilometers1:1,000,000 16 miles 10 kilometers

Large

Small

Three Big Ideas1.Map scale is a ratio between the distance of

any two points on the map compared to the actual ground distance represented.

2.Three methods describing map scale are Verbal, Graphic (Bar), and Representative Fraction (RF).

3. Large scale maps cover smaller geographic extent with more detail where small scale maps show large geographic coverage with less detail.

Now, ready to get your hands dirty ???

RF = MD : GD* Only issue is different units. i.e. feet, yards, miles; cm, m, km

Example: Convert verbal scale of “ 1” to 18 miles” to RF

1 h𝑖𝑛𝑐18𝑚𝑖𝑙𝑒𝑠 ∗

1𝑚𝑖𝑙𝑒5,280 𝑓𝑒𝑒𝑡 ∗

1 𝑓𝑜𝑜𝑡12 h𝑖𝑛𝑐 𝑒𝑠=

1 h𝑖𝑛𝑐(18 𝑋 5,280 𝑋 12 )

=1 h𝑖𝑛𝑐

1,140,480 h𝑖𝑛𝑐 𝑒𝑠OR

18 miles X 63,360 inches = 1,140,480 inchesSo, 1: 1,140,480

A

B

Paired in-class Exercise

1. Convert verbal scale of “ 1” to 3.9 miles” to RF

2. Convert verbal scale of “2cm to 14km” to RF/Ratio.

3. Convert from RF of 1:25000 to a verbal scale, in metric cm.

4. Roughly, how many miles to the inch is 1: 1,000,000 ?

English and Metric Measure of Length to Use

1 inch (in) = 2.54 centimeters1 centimeter (cm) = 0.39 inch1 foot (ft) = 12 inches = 30.5 centimeters = 0.3 meter1 yard (yd) = 36 inches = 3 feet = 91.44 centimeters = 0.9 meter1 meter (m) = 100 centimeters = 39.37 inches = 3.28 feet = 1.09 yards1 mile (mi) = 63,360 inches = 5,280 feet = 1,760 yards = 1.609 kilometers1 nautical mile = 1,852 meters = 1.852 kilometers1 kilometer (km) = 1,000 m = 100,000 cm=1,094 yards = 0.6 mile

Note: When you carry out an calculation with fractions, make sure that all units in equation are cancelled correctly. If necessary, invert the RF for that purpose.

Paired in-class Exercise:1. Convert verbal scale of “ 1” to 3.9 miles” to RFANSWER: 247,1042. Convert verbal scale of “2cm to 14km” to RF/Ratio.ANSWER: 1: 70,0003. Convert from RF of 1:25000 to a verbal scale, in metric cm.ANSWER: 1 cm on map equals 0.25 km on the ground4. Roughly, how many miles to the inch is 1: 1,000,000 ?ANSWER: 16 miles

Convert verbal scale of “2cm to 14km” to RF/Ratio.

Convert from RF of 1:25000 to a verbal scale, in metric cm.

1𝑚𝑎𝑝25,000𝑔𝑟𝑢𝑛𝑑=

1𝑐𝑚𝑚𝑎𝑝25,000𝑐𝑚𝑔𝑟𝑜𝑢𝑛𝑑 ∗

100 ,000𝑐𝑚1𝑘𝑚 ∗

1100,0001

100,000

=1𝑐𝑚

0.25𝑘𝑚𝑔𝑟𝑜𝑢𝑛𝑑

Scale Conversion Map scales can be converted from one to

another Verbal to RF RF to Verbal

RF to graphic Graphic to RF

Scale Determination When maps do NOT have scale on a map, then:

Use of known features Reference features as football field or

baseball diamond Use of map comparison

Another map from the same area, having similar features can be helpful

Use of line of latitude and longitude Distance of 1° of latitude is 69 miles (111.

133 km)

What are three big ideas again?

Thank You!