Map Scale

What Is Scale?

In cartography, scale is the ratio between a distance on a map and the corresponding distance on the ground. It represents how much the Earth's surface has been reduced to fit onto the map.

Essentially, it tells us how many units of measurement on the map represent the same units on the Earth's surface.

Importance of Scale:

• Representation: It allows us to represent vast geographical areas on a manageable flat surface (the map).
• Accuracy: It ensures that the relative distances and sizes of features on the map are proportionally correct to their real-world counterparts.
• Measurement: It enables users to measure distances, calculate areas, and determine the relative locations of features on the map.

The scale of a map is crucial for its interpretation and usability. Without an understanding of the scale, a map is just a collection of symbols and lines with no real-world reference.

Methods Of Scale

There are three primary methods used to express the scale of a map:

Statement Of Scale

Description: The scale is expressed in words, clearly stating the relationship between map distance and ground distance using standard units of length.

Format: "1 cm represents 10 km" or "1 inch represents 1 mile."

Advantages: Easy to understand for most users, as it directly relates map units to familiar ground units.

Disadvantages: Can be problematic if the map is enlarged or reduced, as the statement will no longer be accurate. Also, units of measurement might differ between countries (e.g., miles vs. kilometers).

Graphical Or Bar Scale

Description: This method uses a line or bar marked with distances on the map, which corresponds to distances on the ground. It is a visual representation of the scale.

Format: A line is drawn and divided into segments. The length of each segment on the map is shown alongside the corresponding distance on the ground (e.g., a bar marked with 0, 5, 10, 15 km).

Advantages:

• Accuracy with Reductions/Enlargements: If the map is resized, the graphical scale on the map will also be resized proportionally, so measurements remain accurate.
• Unit Independence: It doesn't rely on specific units of measurement (like cm or inches) and can be interpreted using any unit (e.g., you can measure with a ruler on the map and then use that same ruler to measure the scale bar).

Disadvantages: Less intuitive for users not accustomed to reading graphical scales directly.

Representative Fraction ( R. F. )

Description: The scale is expressed as a ratio or fraction, where the numerator represents the distance on the map and the denominator represents the distance on the ground. Both distances must be in the same units.

Format: 1:10,000 or 1/10,000.

This means that 1 unit (e.g., cm, inch, mm) on the map represents 10,000 of the same units on the ground.

Advantages:

• Unit Independence: Since units are the same for both numerator and denominator, it's universally applicable regardless of the measurement system.
• Precision: Clearly defines the exact ratio of reduction.

Disadvantages: Can be less intuitive for casual users compared to a statement scale. Requires calculation if measurements need to be converted to specific units like kilometers or miles.

Conversion Of Scale

Understanding how to convert between different methods of scale expression is essential for accurate map use and creation.

Statement Of Scale Into R. F.

Process:

1. Identify the Statement: For example, "1 cm represents 5 km."
2. Ensure Same Units: Convert the ground distance unit to the map distance unit. Since the map distance is in centimeters, convert the ground distance (kilometers) into centimeters.
3. Conversion Factor: Remember that 1 km = 100,000 cm (1 km = 1000 m, and 1 m = 100 cm).
4. Calculate:
• Ground distance = 5 km
• Convert to cm: 5 km * 100,000 cm/km = 500,000 cm
• So, 1 cm on the map represents 500,000 cm on the ground.
5. Express as R.F.: The Representative Fraction is 1:500,000.

Example: If scale is "1 inch represents 1 mile."

• 1 mile = 63,360 inches.
• R.F. = 1:63,360.

R. F. Into Statement Of Scale

Process:

1. Identify the R.F.: For example, 1:250,000.
2. Interpret the Ratio: This means 1 unit on the map represents 250,000 of the same units on the ground.
3. Choose a Map Unit: Select a common map unit, like centimeters.
4. Calculate Ground Distance:
• Map distance = 1 cm
• Ground distance = 250,000 cm
• Convert ground distance to kilometers: 250,000 cm / 100,000 cm/km = 2.5 km
5. Express as Statement: "1 cm represents 2.5 km."

Example: If R.F. is 1:50,000.

• 1 cm on map = 50,000 cm on ground.
• 50,000 cm = 500 meters = 0.5 km.
• Statement: "1 cm represents 0.5 km" or "2 cm represents 1 km".

Construction Of The Graphical/bar Scale

Purpose: To create a visual scale that remains accurate even if the map is resized.

Steps:

1. Determine the Scale: Start with either a statement scale or an R.F. For example, let's use R.F. 1:250,000.
2. Choose a Convenient Ground Distance: Select a ground distance that will result in a manageable map length. Let's aim for a main division of 1 km.
3. Calculate Map Length:
• 1 km on the ground corresponds to 1 km (100,000 cm) on the map.
• So, 100,000 cm on the map represents 1 km on the ground.
4. Determine the Length of the Bar: Let's decide to make the main division (representing 1 km) a convenient length on the map, say 4 cm.
5. Mark the Main Divisions: Draw a rectangle. Divide its length into equal segments of 4 cm. If you want the scale to show up to 5 km, you'll need 5 such segments.
6. Label the Divisions: Label the divisions from 0 on the left to 5 km on the right, marking every 4 cm interval (0, 1 km, 2 km, 3 km, 4 km, 5 km).
7. Subdivide the First Segment (Optional but Recommended): For more accuracy, divide the first 4 cm segment (representing 0-1 km) into smaller units, like 5 segments of 0.8 cm each, to represent 200 metres (0.2 km) each. Label these subdivisions (0, 0.2, 0.4, 0.6, 0.8, 1.0 km).
8. Coloring (Optional): Often, alternate segments of the bar are colored differently (e.g., black and white, or grey) for better readability.

Finished Graphical Scale: You would have a bar representing, for example, 5 kilometers, divided into main 1 km sections, and the first section further divided into 0.2 km segments, all marked clearly with their ground distance equivalents.