Dependent and independent variables: A real-life example (from fire protection)

In the real world, dependent and independent variables are utilized to predict various processes, such as forecasting the paths of tornadoes or wildfires. This article provides a practical example to illustrate how these concepts work.

Measuring Fire Spread Speed: The Role of Dependent and Independent Variables


To effectively investigate and analyze wildfires, one must possess a solid understanding of fire behavior, particularly how fire spreads. This understanding enables experts to predict and respond to fires more efficiently. Delving into the variables influencing fire spread speed is crucial for enhancing this knowledge.

Dependent and Independent Variables of Fire Spread Speed

Fire spread speed is influenced by several factors, such as the nature of the burning material (e.g., dry hay or deciduous forest) and the strength of the wind. These factors, aptly termed variables, can vary independently, as the condition of the deciduous forest does not depend on wind strength. Consequently, these variables are labeled as independent. However, the fire spread speed is dependent on what is burning and the wind strength, hence it’s termed a dependent variable.

Now, let’s delve into a detailed examination.


Moving on to a practical example, fire protection specialists use the following formula for theoretical calculations of fire spread speed:

\[ \small V_{\text{fire}} = V_{\text{initial}} \times k_{\text{fuel}} \times k_{\text{wind}} \times k_{\text{slope}} \]

To calculate the fire spread speed, we multiply four independent variables:

  • Initial fire spread speed (\(V_{\text{initial}}\))
  • Factor of fuel type (\(k_{\text{fuel}}\))
  • Factor of wind force (\(k_{\text{wind}}\))
  • Factor of terrain slope (\(k_{\text{slope}}\))

Below, you can find tables detailing these factors.

Three tables listing factors for three independent variables: fuel type, wind speed, and terrain slope. For the fuel type 'meadow,' a factor of 1 corresponds; for a wind speed of 5 m/s, a factor of 2.91 corresponds; and for a terrain slope of 5 degrees, a factor of 1.2 corresponds.

For instance, if a wildfire occurs in a meadow with an initial spread speed of 0.3 m/s, a wind speed of 5 m/s, and a hill slope of 5 degrees, the formula predicts a fire spread speed of approximately 1.05 m/s:

\(\tiny V_{\text{fire}} = 0.3 \times 1 \times 2.91 \times 1.2 \approx 1.05 \, \text{m/s}\)

Why This Calculation is Important?

In the event of a wildfire, knowing where it started is crucial, but equally important is the ability to predict its path by the time fire engines arrive. Accurate predictions enhance firefighting efficiency by ensuring resources are deployed to the right locations.


In summary, the example illustrates how fire spread speed relies on various independent variables like fuel type and wind force. It serves as a compelling instance of applying knowledge about dependent and independent variables to simulate real-world scenarios, such as a wildfire. This application extends to all mathematical topics learned in school, where mathematical concepts and operations play a vital role in modeling and predicting real-life situations.


Video Version

Discover more in our video adaptation of this article. The video explores additional examples of independent variables influencing fire spread speed, provides extra calculations presented in an animated, easy-to-follow format, and discusses the essential school knowledge needed for effective fire protection specialists. Enjoy a preview below or subscribe to access our complete video collection.

Further Reading

Curious to learn more about the types of dependent and independent variables in real-life situations? If you’re already acquainted with linear functions, explore how these variables come into play when controlling stage lighting for a performance:

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