Know Your Math & Science Skills!

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Although we don't always associate math with firefighting, in fact firefighters-and company officers as their instructors-will often need to draw on alegbra to determine needed fire flow or estimate flashover potential. Photo Brian Bastinelli

The fire captain was upset with me. As his division chief, I had made a request of him that he could not fulfill-a request he was not prepared for-and he was not used to this. He was a newly promoted captain, a long-time career firefighter who had previously served as a paramedic instructor, teaching recruits in basic firefighting skills in their initial training. He had worked part-time as a flight medic and was known as one of the best paramedics in the area. He had been the firefighter that any company officer would want on their truck-highly skilled at the task level of firefighting. But now I had asked him to do something that was well within his new job description as fire captain, but that he was not accustomed to thus far in his career-math.

A New Set of Tools

In the fire service we operate at three different levels: task, tactical and strategic.

Firefighters perform at the task level, carrying out assignments, such as laddering a building, advancing a hoseline or administering first aid. They are trained at this level from the very beginning in recruit school, and receive task-level training daily throughout their career. Rarely do they receive anything beyond that level.

Chief officers (executive staff) operate at the strategic level, providing overall direction for the event, establishing goals and objectives to mitigate concerns on the fireground and in everyday operations. The fire chief (department head) also works at the strategic level to create policy, develop budgets and provide vision and leadership for the organization.


Between the task- and strategic-level work is the critical tactical-level work. Company officers operate at the tactical level. They are mid-level managers and supervisors who have oversight of a small number of firefighters, and this requires a different skill set than task-level firefighters.

Getting back to the upset fire captain from the introduction, my request of him demanded more than the task-level training he had received over his years as a firefighter; it required him to obtain new skills and utilize new tools. He would no longer think of an axe, hook and nozzle as his only tools. As part of his daily duties, he would now be working in software programs and performing data-collection activities that call for knowledge of math and statistics. With these new tools would come training, but he must also have the knowledge to perform at that level.

Higher Education Helps

At some point in your career, you must take responsibility for your professional development. This is an investment that will pay off in the long run; however, you need to first make the decision to move in the right direction-and a formal education is often the right direction.

Universities offer structured programs that provide the academic foundation for leadership and administrative positions in fire service organizations. A model curriculum containing general education courses-such as English, behavioral studies and math-creates the foundation to build upon, but it doesn't stop there. You need to have a solid understanding of fire dynamics, human behavior in fire, and personnel management, too. Science, math and social skills play an important role in this area, and should be part of a company officer's educational program.

Math & Science for Company Officers

While assigned to the training division, I asked a senior fire captain to teach a driver operator course because I knew of his extensive knowledge of fire pumps and hydraulic calculations. On the first morning of the course, I slipped into the back of the classroom and sat beside one of the students. The captain had the class well under his control, providing useful information and keeping their attention.

As I sat there, I realized that the instructor really understood the need for math skills, which many firefighters may not possess or that many have lost over a period of time. These skills often appear to be the most difficult in all the "water supply for fire protection" courses. Knowing that, the captain had incorporated a condensed pre-algebra lesson into the hydraulic section of the course. Delighted, I jokingly asked the firefighter sitting beside me if the instructor had covered "Please Excuse My Dear Aunt Sally," the acronym for the order of operations. The firefighter flipped back a few pages in his notes, and sure enough, the captain had already covered it.

Company officers act as instructors in their day-to-day operations, so it is vital that they have a good grasp of basic math skills. After all, math comes into play in many areas. For example, it is imperative to learn simple algebraic expressions, such as V = LWH, with V for volume, L for length, W for width and H for height.

Here's an example: During the extinguishment of a warehouse fire, ladder pipe master streams are used to flow water onto the roof. Once the fire is contained, firefighters begin performing overhaul inside the warehouse. But then a tactical-level supervisor radios command to report that there's about a foot and half of standing water on the roof. The roof area covered in water is 50 feet in length and 35 feet wide, with about 1.5 feet of standing water (height). In other words, 50 x 35 = 1,750 square feet x 1.5 = 2,625 cubic feet of water. A cubic foot of water contains 7.48 gallons of water, so 2,625 x 7.48 = 19,635 gallons of water. With water at 8.33 lbs. per gallon, that is 163,559 lbs. or 81 tons of water on the roof with firefighters working under that weight. Is that safe?

Further, a first-arriving officer on a working structure fire may utilize the fire flow formula [(length x width) ÷ 3] x percent of involvement to determine the water and gpm required to extinguish the fire.

Here's an example: An engine company officer arrives on the scene of a one-story residential structure that's 100 feet x 50 feet with 50% involvement. The structure is 100 x 50 = 5,000 square feet, which is then divided by 3, which = 1,666 x 0.50% = 833 gpm. Fire attack lines and water supply selection can be made based off the information obtained.

In another example of a math-related skill that company officers should possess: A British Thermal Unit (BTU) is the amount of heat required to raise the temperature of 1 lb. (0.454 kg) of liquid water by 1 degree F. Being able to estimate this can be very helpful when a company officer is providing training or describing the reasons for certain tactical decisions. Flashover potential increases exponentially for rooms loaded with materials, such as plastic, which has a heat release rate twice that of traditional ordinary combustibles. The initial IC can use this knowledge to make more informed tactical and strategic decisions.

Consider this: A new company officer arrives on the scene of a well-involved warehouse in an industrial district. He is informed that the warehouse is divided into two areas of storage-one contains rolls of 100% polyester carpet and the other area has wood pallets that are used in the transportation of the carpet. Which area will produce the greater amount of BTUs and what will be the required gpm? The water distribution system becomes a factor at this point, and the IC must now understand a typical grid system. Can the system produce the required volume of water to extinguish a fire giving off that amount of BTUs?

Courses in fire behavior and fire dynamics deliver that knowledge and reinforce the ability to calculate the required mathematical equations.

Data Collection & Analysis

Another critical part of knowing basic math skills is for data collection and statistical analysis. The first National Fire Incident Reporting System (NFIRS) report I completed was a one-page document, and it came with a large, three-ring binder with all the associated codes that could be entered. After completing a few, you began to learn the many different numbers and could enter them without having to look them up.

Things have changed a little since then, but the importance of capturing that information has not. That information collected over the years has allowed the U.S. Fire Administration to track the number of structure fires and the estimated dollar loss. Fire deaths are also monitored to identify trends and reduce the fire death rate. A course in community risk reduction permits students to examine threats in their district, and provides them the opportunity to make adjustments and recommendations to address that risk.

Company officers perform most of the data collection duties in fire service organizations. The information obtained at a fire-such as whether a smoke detector was present, what type of material was involved, or how many people lived in the home-is used to produce fire safety education programs that save lives. Knowing basic statistics is important to understanding how to analyze the data and provide valid conclusions.

Lastly, consider this: A firefighter enters a burning structure and is caught in a flashover and loses his life. We read the NIOSH report and wonder how this can happen time and time again. A company officer must learn the make-up of the building, the chemical reaction of the materials and understand fire conditions. Chemistry will illustrate physical properties of different materials and how they burn. It will demonstrate how buildings are extinguished and what type of extinguishing agent should be utilized. A course in fire dynamics or fire protection systems explores this process and the concept.

In Sum

The training you receive as a task-level firefighter is insufficient to prepare you to succeed as a company officer. You must make the commitment to develop the math and science skills that will separate you from the pack to show that you are the right person for the job. The fire captain from the introduction eventually completed his degree. What's your next step?



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October 2017
Volume 12, Issue 10
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