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Geography: Class 11 (Part 3) — Chapter 2: Map Scale

Introduction to Map Scale

A map scale provides the relationship between the map and the whole or a part of the earth's surface shown on it. It is an essential element of all types of maps; without it, a network of lines and polygons is merely a "sketch".

What is Scale?

Map scale is the ratio of distances between two points on the map and the corresponding distance between the same two points on the ground.

$$\text{Map Scale} = \frac{\text{Distance on the Map}}{\text{Distance on the Ground}}$$

Glossary of Terms

  • Numerator: The number above the line in a fraction. It represents the map distance and is always expressed as unity (1).
  • Denominator: The number below the line in a fraction. It represents the actual ground distance. For example, in a fraction of $1 : 50,000$, $50,000$ is the denominator.
  • Representative Fraction (R. F.): A method of scale of a map or plan expressed as a fraction showing the ratio between a unit distance on the map and the distance measured in the same units on the ground.
Systems of Measurement

Map scales are expressed in specific systems of measurement. The two primary systems used globally are the Metric System and the English System.

SystemUnitEquivalent Value
Metric System of Measurement1 km1,000 Metres
1 Metre100 Centimetres
1 Centimetre10 Millimetres
English System of Measurement1 Mile8 Furlongs (or 63,360 Inches)
1 Furlong220 Yards
1 Yard3 Feet
1 Foot12 Inches
Methods of Scale

The scale of a map can be expressed in three main ways:

1. Statement of Scale

The scale is indicated in the form of a written statement (e.g., "1 cm represents 10 km" or "1 inch represents 10 miles").

  • Advantages: Simplest and easiest method to understand for laypersons.
  • Limitations: Highly specific to a particular system of measurement. If the map is reduced or enlarged, the statement becomes redundant.

2. Graphical or Bar Scale

This method shows map distances and corresponding ground distances using a line bar with primary and secondary divisions marked on it.

  • Advantages: Remains valid even when the map is reduced or enlarged because the scale bar changes size proportionally with the map.
  • Limitations: Can only be used easily by those familiar with the specific units shown.

3. Representative Fraction (R. F.)

Shows the relationship between map distance and ground distance in units of length as a ratio or fraction (e.g., $1 : 50,000$).

  • Advantages: Universally applicable and independent of any specific system of measurement (units are dimensionless).
  • Limitations: Requires conversion calculations to be practically useful for measuring real-world distances.
Conversion of Scale

Statement of Scale into R. F.

To convert a statement of scale into an R. F., both map distance and ground distance must be converted into the same unit of measurement.

Problem: Convert "1 inch represents 4 miles" into R. F.

Solution:

  1. 1 inch represents 4 miles
  2. Since $1 \text{ mile} = 63,360 \text{ inches}$
  3. $4 \text{ miles} = 4 \times 63,360 = 253,440 \text{ inches}$
  4. Therefore, 1 unit represents 253,440 units.

Answer: R. F. $1 : 253,440$

R. F. into Statement of Scale

Problem: Convert R. F. $1 : 253,440$ into a Statement of Scale in the Metric System.

Solution:

  1. $1 : 253,440$ means $1 \text{ cm}$ represents $253,440 \text{ cm}$ on the ground.
  2. Convert cm to km: $1 \text{ km} = 100,000 \text{ cm}$.
  3. $\text{Distance in km} = \frac{253,440}{100,000} = 2.5344 \text{ km}$.
  4. Rounding to two decimal places gives $2.53 \text{ km}$.

Answer: $1 \text{ cm}$ represents $2.53 \text{ km}$

Construction of Graphical Scales

Metric System Example

Problem: Construct a graphical scale for a map drawn at a scale of $1 : 50,000$ to read distances in kilometres and metres.

Calculations:

  • By convention, a length of nearly $15 \text{ cm}$ is taken to draw a graphical scale.
  • $1 : 50,000$ means $1 \text{ cm}$ represents $50,000 \text{ cm}$ ($0.5 \text{ km}$).
  • $15 \text{ cm}$ represents $15 \times 0.5 = 7.5 \text{ km}$.
  • Since $7.5 \text{ km}$ is not a round number, we choose $5 \text{ km}$ as the round number.
  • To find the length of the line for $5 \text{ km}$: $$\text{Length} = \frac{15 \times 5}{7.5} = 10 \text{ cm}$$

Construction Steps: Draw a straight line of $10 \text{ cm}$ and divide it into 5 equal parts (each representing $1 \text{ km}$). Divide the extreme left division into 10 equal parts to represent intervals of $100 \text{ metres}$ each.

English System Example

Problem: Construct a graphical scale when the given Statement of Scale is "1 inch representing 1 mile" to read distances in miles and furlongs.

Calculations:

  • By convention, a length of nearly $6 \text{ inches}$ is taken for English system scales.
  • $1 \text{ inch}$ represents $1 \text{ mile}$, so $6 \text{ inches}$ represent $6 \text{ miles}$.

Construction Steps: Draw a line of $6 \text{ inches}$ and divide it into 6 equal parts. The right 5 divisions represent $1 \text{ mile}$ each. Divide the extreme left division into 4 equal parts to represent $2 \text{ furlongs}$ each (since $1 \text{ mile} = 8 \text{ furlongs}$).