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Firefighter Math: 5.4 Perimeter and Area Estimation Charts

The perimeter and area of a fire can be determined by using estimation charts as shown below. These charts require knowledge of the spread distance in chains and the effective windspeed in miles per hour. A fire area/size worksheet is provided to be filled out with the data collected.

EFFECTIVE WINDSPEED

Effective windspeed is the midflame windspeed, corrected for the effects of slope on fire spread. Changes in slope affect how wind influences a fire and the overall fire spread. For slopes above 20%, each additional 20% increase in slope translates to an additional 1 mph increase in the effective equivalent “upslope” component of the wind. For slopes between 20% and 40%, for example, a 1-mph slope-equivalent upslope component would be added to the flame-level wind. Between 40% and 60%, a 2-mph slope-equivalent upslope component would be added, and above 60%, flame-level winds would increase by 3 mph.
 

screengrab of animation of flame heights increasing as slope increases
Click to view animation of slope effects on fire

Example 1 - A fire starts at point A. Given the following values, determine the fire perimeter. 
rate of spread = 5 ch/h, projection time = 3 h, effective windspeed = 10 mi/h

Step 1. Use the equation for determining the spread distance (see Section 5.3).
ROS × PT = 5 ch/h × 3 h = 15 chains spread distance.

Step 2.> Look at the perimeter estimation chart. Find a spread distance of 15 chains on the vertical axis. Move your gaze across horizontally.

Step 3. Find an effective windspeed of 10 miles/hour on the horizontal axis, which is between 9 miles/hour and 11 miles/hour. Follow the column down vertically.

Step 4. Where the two lines intersect, read the number. In this case there are two numbers.
34 chains and 33 chains

Step 5. Take an average of the two values.
34.0 chains + 33.0 chains / 2 = 33.5 chains

The perimeter of the fire is 33.5 chains.

Example 2 - Determine the area of the fire in Example 1 and complete the fire area/size worksheet. The spread distance is the same, 15 chains.

Step 1. Reference the area estimation chart for a spread distance of 15 chains. Follow the row across horizontally.

Step 2. Look for an effective windspeed of 10 miles/hour, which is between 9 miles/hour and 11 miles/hour. Follow the column down vertically and read the numbers from the two windspeeds.
4.9 acres and 5.7 acres

Step 3. Take an average of the two values.
4.9 acres + 5.7 acres / 2 = 5.3 acres

The area of the fire is 5.3 acres.

Perimeter estimation for point source fires.
Table showing Perimeter Estimation

Area estimation for point source fires.
point source fires

Fire Area/Size Worksheet

Line Input    
0 PP Projection point A
1 ROS Rate of spread, ch/h 5
2 EWS Effective windspeed, mi/h 10
3 PT Projection time, h 3
4 SDF Spread distance, ch 15
  Output    
  PER Perimeter, ch 33.5
  AC Area, ac 5.3

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