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Firefighter Math: 9.8 Production Rates

When planning an attack on a fire, the length and width of the line must be estimated, along with the capabilities of the hand crew(s), to determine how many crews will be needed. Generally, a 15-person crew should be able to construct a 3-foot fireline around a 1-acre grass fire in 1 hour. Below are some average ideal rates for hand crew production rates in various vegetation.

Firefighter Math: 9.7 Planning

Hand crews primarily construct fireline but can also assist on hose lays, firing operations, protecting structures, mopping up, cleaning up, and other logistical support functions. It is important to match the task to crew capabilities. Use the best, most experienced crews for the toughest jobs and the hottest firelines. Crew effectiveness is controlled by these factors:

Firefighter Math: 9.5 Deviation/Variability

The deviation of a set of numbers is the difference between the average and the individual terms.

Example 1 - Jane paces off the following fire run lengths. Find the deviation of the fire run lengths, given as 6.5, 6.0, 8.0, and 7.5 chains.

Step 1. Calculate the average (see Section 9.3). Sum the numbers and divide by the number of individual elements: 28/4 = 7.0 

Step 2. Now, subtract each term from the average.
6.5 - 7.0 = -0.5
6.0 - 7.0 = -1
8.0 - 7.0 = 1.0 

Firefighter Math: 9.4 Range/Variance

Range refers to the difference between the smallest number and the largest number possible for a given quantity.

Example 1 - Philip paces off some fire run distances and gets the following values in chains: 7.5, 6.0, 8.5, 5.5, 9.0. Find the range for the measurements.

Step 1. Arrange the numbers in ascending order (from the smallest to the largest).
5.5, 6.0, 7.5, 8.5, 9.0 

Step 2. Subtract the largest number from the smallest number.
9.0 - 5.5 = 3.5

Firefighter Math: 9.3 Average

The average, or the mean, is the sum of all the numbers divided by the number of terms.

Example 1 - The line production rates for the members of a hand crew were as follows: 8.0 chains per hour, 7.0 chains per hour, 6.0 chains per hour, 7.5 chains per hour, and 7.0 chains per hour. What is the average number of fireline chains constructed per hour?

Step 1. Add all the numbers.
8.0 + 7.0 + 6.0 + 7.5 + 7.0 = 35.5 chains

Step 2. Count the number of terms.
5 terms

Firefighter Math: 8.8 Probability and Number of Ignitions

Probability is the chance that an event will happen and is expressed in terms of percent, or per 100. For example, if there is a 40 percent chance of a spot fire starting, that means that out of 100 glowing embers that fly off, 40 embers will likely start spot fires, and 60 will not. Percent is calculated by changing the percent into a fraction by dividing by 100, then multiplying by the total number of possible situations.

Example 1 - The probability of ignition is 80 percent. How many ignitions are likely to occur if 90 glowing firebrands land on receptive fuel?

Firefighter Math: 8.6 Head, Flank, and Rear Fire Terms

Each side of the fire is described in terms of head, flank, and rear. The head is the fastest spreading part of a fire's perimeter. The head is usually the side toward which the wind is blowing, and will also often be the upslope side of a fire. The head of the fire is of primary interest. 

The right and left flanks describe the sides of the fire. Flanks are perpendicular to the head of the fire. 

The rear of the fire is the side of the fire opposite the head.
 

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