Scale

Scale

The scale is defined as the ratio between the distance of two points on the map and their corresponding distance on the ground. The scale is an essential element in all types of maps. The scale of the map permits the user to convert distance on the map to distance on the ground.

A map scale provides the relationship between the map and the whole or a part of the earth’s surface shown on it. We can also express this relationship as a ratio of distances between two points on the map and their corresponding distance on the ground. The scale can be represented as a fraction where the numerator refers to map distance and the denominator refers to ground distance.

There are at least three ways of which representing scale. They are:

1.        Statement Scale

2.        Representative Fraction (R. F.)

3.        Graphical or Bar Scale

1. Statement Scale

The scale of a map may be indicated in the form of a written statement. For example, if on a map a written statement appears as stating 1 cm represents 10 km, it means that on that map a distance of 1 cm is representing 10 km of the corresponding distance on the ground.1 inch equals 16 miles. This example tells us that 1 inch on the map represents 16 miles on the ground. This is the easiest scale to understand because it generally uses familiar units.

Example : 1 centimetre 5 10 kilometres

Simple statement has the following characteristics :

•            If the numerator is in centimeters, then the denominator is in metres and kilometres.

•            If the numerator is in inch, then the denominator is in miles.

2. Representative fraction (RF)

It shows the relationship between the map distance and the corresponding ground distance in the same units of length. R. F. is generally shown as a fraction. For example, a fraction of 1 : 40,000 shows that one unit of length on the map represents 40,000 of the same units on the ground i.e; 1 cm or 1 inch on the map represents 40,000 cm and 40,000 inches, respectively on the ground.

RF is represented as 1/40,000 or 1:40,000

3. Graphic or bar scale

In this type of scale the map distances and the corresponding ground distances are marked using a line bar with primary and secondary divisions on it. However, unlike the statement of the scale method, the graphical scale stands valid even when the map is reduced or enlarged. This is the unique advantage of the graphical method of representing scale.

Example:

Example

Statement of Scale into R. F.

1. Convert the given Statement of Scale of 1 inch represents 5 miles into R. F. Solution

The given Statement of Scale may be converted into R. F. using the following steps.

1 inch represents 5 miles or 1 inch represents 5 3 63,360 inches (1 mile 5 63,360 inches) or 1 inch represents 316,800 inches

Answer R. F. 1 : 316,800 or 1/316800

R. F. into Statement of Scale

2. Convert R. F of 1 : 200,000 into Statement of Scale (In Metric System) Solution

The given R. F. of 1 : 200,000 may be converted into Statement of Scale using the following steps :

1 : 200,000 means that 1 unit on the map represents 200,000 units on the ground.

or 1 cm represents 200,000 /100,000 (1 km 5 100,000 cm)

or 1 cm represents 2.0 km

Answer 1 cm represents 2 km

3. Convert the given Statement of Scale into Representative Fraction (R. F.).

5 cm represents 10 km

2 inches represents 4 miles

1 cm represents 100 metres

 5 cm represents 10 km

Step 1: convert into same units of measurement

(1 Km 5 100000 cm)

Step 2: 10 km 5 1000000 cm Therefore

5 cm: 1000000 cm

Step 3: simplify the ratio

1: 1000000/5

Answer : R.F. 5 1: 200000 or 1/200000

b. 2 inches represents 4 miles

Step 1: convert into same units of measurement

(1 mile 2 63,360 inches)

Step 2: 4 miles 5 63,360 3 4 5 253440

Therefore 2 inches: 253440 inches

Step 3: simplify the ratio

1: 253440/2 5 126720

Answer : R.F. 5 1: 126720 or 1/126720

c) 1 cm represents 100 metres

Step 1: convert into same units of measurement

(1m 5 100 cm)

Step 2: 100 m 5 10000 cm Therefore

1 cm: 10000 cm

Answer : R.F. 5 1: 10000 or 1/10000

Construction of the Graphical/Bar Scale

1. Construct a graphical scale for an R.F. 1 : 50,000 and read the distances in kilometre and metre.

(NOTE: By convention, a length of nearly 15 cm is taken to draw a graphical scale.)

Calculations

To get the length of line for the graphical scale, these steps may be followed:

R.F. 51 : 50,000 means that 1 unit of the map represents 50,000 units on the ground or 1 cm represents 50,000 cm or 0.5 Km (1 Km 5 100000 cm). Therefore, 10 cm represents 5.0 km

Construction

The graphical scale may be constructed by following these steps:

Draw a straight line of 10 cm and divide it into 5 equal parts these are the primary division. Mark the first division as 0. Assign the value of 1 km for the four divisions starting from 0. Therefore the primary scale has 4 divisions and is 4 km long.

Divide the extreme left side division into 10 equal parts and mark each division by a value of 100 metres, beginning from 0. This is the secondary scale representing 1000 mts.

Exercise

1. Convert the statement into RF.

a.        1 cm 5 10 km

b.        1 cm 5 5 km

c.         1 cm 51 km

d.        1 cm 5 50km

e.         1 cm 5100 km

2. Convert the RF into statement:

a.        1: 100000

b.        1: 50000

c.         1: 250000

d.        1: 5000000

e.         1: 30000

3. Construct a graphical scale for the following:

a.        1 cm 5 10 km

b.        1 cm 5 5 km

c.         1 cm 51 km

d.        1 cm 5 50km

e.         1 cm 5100 km