Vertical Exaggeration (Grade 12 NSC Matric Geography): Revision Notes

Vertical Exaggeration

Understanding cross sections and the need for vertical exaggeration

In mapwork, we create cross sections to better understand what a landform looks like from the side. A cross section is essentially like 'cutting through' a landscape to see its profile, similar to how you might cut through a cake to see the layers inside.

To create a cross section, we use contour lines from topographic maps. These brown lines show us the height of different parts of the landscape, and by following them, we can trace the ups and downs of the terrain.

When we draw a cross section on a graph, we use the vertical axis to show height and the horizontal axis to show distance. However, there's often a problem when both the vertical and horizontal scales are the same.

Why do we need vertical exaggeration?

To overcome this problem, we make the profile more obvious by using a different vertical scale from the horizontal scale. This technique is called vertical exaggeration.

By using a larger vertical scale (where 1 cm might represent 20 m instead of 100 m), the changes in slope and elevation become much clearer and easier to analyse.

When we create this type of cross section, we say it has been exaggerated, and we need to calculate exactly how many times steeper it has been made. This calculation is called the vertical exaggeration.

The formula for vertical exaggeration

Step-by-step method for calculating vertical exaggeration

Here's a systematic approach to calculating vertical exaggeration:

Step 1: Convert the vertical scale from words to numbers

• If given "1 cm = 40 m", you need matching units on both sides
• Convert 40 m to cm: $40 \times 100 = 4000$ cm
• So the scale becomes 1 cm = 4000 cm, or 1:4000

Step 2: Identify the horizontal scale

• This is usually already given as a number scale (e.g., 1:50 000 for topographic maps, 1:10 000 for orthophotos)

Step 3: Write both scales as fractions and divide

• $\text{VE} = \frac{1}{4000} \div \frac{1}{50000}$

Step 4: 'Flip and multiply' the fractions

• Swap the numerator and denominator of the horizontal scale fraction
• $\text{VE} = \frac{1}{4000} \times \frac{50000}{1}$

Step 5: Calculate the final answer

• $\text{VE} = \frac{50000}{4000}$
• Use your calculator: $50000 \div 4000 = 12.5$

Step 6: Write your final answer

• VE = 12.5 times
• This means the cross section has been exaggerated 12.5 times to make landscape changes more visible

Worked examples

Summary