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 

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

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

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?

When fire moves upslope, the fuel ahead of the flame front is closer to the flame than if the slope were flatter.  This set-up "preheats" the fuels. The effects of slope on fire spread become greater as the slope increases. 

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.
 

Map spread, in inches, is the size of a fire as scaled to a map. See Section 5.3 for more detailed information.

Example 1. For a rate of spread of 4 chains/hour and a projection time of 3 hours, find the map distance for the fire spread. Plot the distance using a tenths ruler for accuracy. The map scale is 1:24,000.

Step 1. Convert the map scale to feet per inch. 24,000 in × 1 foot/12 in = 2000 feet.

Step 2. Convert the spread distance to feet. 12 chains × 66 feet/chain = 792 feet.

The flame length is the distance between the flame tip and the midpoint of the flame depth at the base of the flame. Flame length is an observable, measurable indicator of fireline intensity. 


Spread distance, in chains, is the distance of forward fire spread for a specified amount of time. 

spread distance (SD) = 
rate of spread (ROS) × projection time (PT) 

The rate of spread is in chains per hour (ch/h) and is defined as the speed with which the fire is moving away from the site of origin. Wind, moisture, and slope drive the fire. The flaming zone, or fire head, moves away from the origin quickly with great intensity.

Midflame windspeed (MFWS) is defined as the velocity of the winds, in miles per hour (mi/hr), taken at the mid-height of the flames. MFWS will directly affect the direction of movement of the flaming front and is important in fire spread calculations. The midflame windspeed is determined by use of the wind adjustment table, which provides values in terms of fuel overstory exposure and fuel model.