Calculating vertical scale involves determining the ratio that represents how a vertical distance on a profile or diagram relates to the actual vertical distance on the ground. You can calculate the standard ratio form if you are given the vertical scale as a statement, like the one mentioned in the reference.
Unlike a standard map scale which represents horizontal distances, vertical scale is used on profiles, cross-sections, and geological diagrams to show the relationship between a vertical measurement on the diagram and the corresponding vertical height or depth in the real world.
Think of it as the "height scale" for a side view of terrain or geological layers, distinct from the "distance scale" used on the top-down map view.
Representing Vertical Scale
Vertical scale can be expressed in a couple of ways:
- Statement Scale: A phrase relating a unit on the diagram to a unit on the ground (e.g., "1 cm represents 20 meters").
- Ratio Scale (Representative Fraction - RF): A fraction or ratio where both sides have the same units, showing the proportion (e.g., 1:2000 or 1/2000). This means one unit on the diagram represents 2000 of the same units on the ground.
Calculating the Vertical Scale Ratio (RF) from a Statement
If you are given the vertical scale as a statement, you can easily calculate its Representative Fraction (RF).
According to the reference, you might have vertical scale information given as:
"...one centimeter equals 20 meters."
To convert this statement into a ratio scale (RF), you need to ensure both sides of the comparison are in the same units.
Here’s how to calculate the RF using this example:
- Identify the given relationship: 1 centimeter on the profile equals 20 meters in reality.
- Convert units to be the same: Convert meters to centimeters.
- There are 100 centimeters in 1 meter.
- So, 20 meters = 20 * 100 centimeters = 2000 centimeters.
- Form the ratio: The relationship is 1 centimeter on the diagram represents 2000 centimeters on the ground.
- This ratio is written as 1:2000 or as a fraction 1/2000.
Therefore, if "one centimeter equals 20 meters" is your vertical scale statement, the vertical scale ratio (RF) is 1:2000.
You can use a simple conversion table to help with units:
| Unit | Equivalent |
|---|---|
| 1 Meter | 100 Centimeters |
| 1 Kilometer | 1000 Meters or 100,000 Centimeters |
| 1 Inch | Approximately 2.54 Centimeters or 0.0254 Meters |
| 1 Foot | 12 Inches or Approximately 0.3048 Meters |
The key is always to convert both the diagram distance and the ground distance into the same unit to find the Representative Fraction (RF).
Vertical Scale and Vertical Exaggeration
As hinted by the reference, the vertical scale is often used in conjunction with the horizontal map scale to calculate vertical exaggeration. Vertical exaggeration occurs when the vertical scale is larger (shows more detail) than the horizontal scale. This makes slopes and elevation changes more apparent on profiles or cross-sections.
Calculating vertical scale typically involves converting its stated form (like "1 cm = 20 m") into a standardized ratio (RF) for analysis or comparison with the horizontal scale.
