How to calculate vertical exaggeration?

Vertical exaggeration is calculated by dividing the denominator of the horizontal scale by the denominator of the vertical scale. It quantifies how much the vertical dimension has been stretched or emphasized compared to the horizontal dimension on a map, cross-section, or diagram.

Understanding Vertical Exaggeration (VE)

When creating geological cross-sections or topographic profiles from a map, the vertical scale is often chosen to be larger than the horizontal scale. This is done to make subtle changes in elevation more apparent and easier to interpret. Vertical exaggeration tells you exactly how many times the vertical scale is larger than the horizontal scale. A VE of 1 means no exaggeration (vertical and horizontal scales are the same), while a VE of 25 (as in the provided example) means the vertical distances are shown 25 times larger than they would be if the scales were equal.

The Core Formula

The fundamental formula for calculating vertical exaggeration is:

Vertical Exaggeration (VE) = (Horizontal Scale Denominator) / (Vertical Scale Denominator)

Alternatively, it can be expressed as:

VE = Vertical Scale (as a Representative Fraction, RF) / Horizontal Scale (as a Representative Fraction, RF)

However, using the denominators is often more straightforward, as seen in practical applications.

Applying the Formula: An Example

Let's use the exact calculation from the provided reference to illustrate this:

The reference states: "You get the final. Answer. I would say um fifty thousand divided by two thousand then that will give me 25. So my answer is 25. Times so this means that the vertical distance."

This snippet clearly demonstrates the calculation process. Here's how to interpret it:

• Horizontal Scale Denominator: 50,000 (e.g., from a map's Representative Fraction of 1:50,000). This means 1 unit on the map horizontally represents 50,000 units in reality.
• Vertical Scale Denominator: 2,000 (e.g., derived from a vertical scale where 1 cm represents 20 meters, which converts to 1:2,000). This means 1 unit on the cross-section vertically represents 2,000 units in reality.

Calculation:

VE = Horizontal Scale Denominator / Vertical Scale Denominator
VE = 50,000 / 2,000
VE = 25

This result means that the vertical distances on the cross-section or profile are exaggerated 25 times compared to the horizontal distances.

Step-by-Step Guide to Calculating Vertical Exaggeration

To accurately calculate vertical exaggeration, follow these steps:

1. Identify the Horizontal Scale:

   • This is typically given as a Representative Fraction (RF) on your map, such as 1:25,000, 1:50,000, or 1:100,000.
   • The second number in the RF is your Horizontal Scale Denominator. (e.g., for 1:50,000, the denominator is 50,000).

2. Identify the Vertical Scale:

   • The vertical scale is often given differently, sometimes as a verbal statement (e.g., "1 cm represents 20 meters") or as a graphic scale on the cross-section itself.
   • Convert the vertical scale to a Representative Fraction (RF) if it's not already in that format.
     • Example: If 1 cm represents 20 meters:
       • Convert meters to centimeters: 20 meters = 20 * 100 cm = 2,000 cm.
       • So, the vertical scale is 1 cm : 2,000 cm, or 1:2,000.
     • The second number in this converted RF is your Vertical Scale Denominator. (e.g., for 1:2,000, the denominator is 2,000).

3. Apply the Formula:

   • Divide the Horizontal Scale Denominator by the Vertical Scale Denominator.

   • Example:

     • Horizontal Scale (RF): 1:50,000
     • Vertical Scale (RF): 1:2,000
     • VE = 50,000 / 2,000 = 25

Summary Table: Key Scale Components

Understanding the different ways scales are presented is crucial for accurate VE calculations.

Vertical Exaggeration is a dimensionless value, meaning it doesn't have units. It's simply a ratio that indicates the degree of stretching in the vertical dimension, making it easier to visualize topographic features or geological structures that might otherwise appear flat or undramatic at true scale.