For effective firefighting, firefighters must have a thorough and accurate knowledge of fire behavior. Fire behavior is defined as what happens in a structure when fire occurs where the only controls are those factors built into the structure itself. Most often, the process of combustion involves the burning of organic solids. These materials may be simple or highly complex compounds with carbon as the principal element. Almost all contain hydrogen. Many contain oxygen, nitrogen, and other elements in smaller amounts.

The products of combustion are heat, water (H2O is an oxide of hydrogen), and carbon dioxide (CO2). Incomplete combustion results in the formation of carbon monoxide (CO) and soot–a carbonaceous particle.

The heat of combustion is the amount of heat released by a substance and is measured by megajoules per kilogram (MJ/kg). A joule is an International Unit (IU) of heat energy. A joule is related to the more familiar calorie, which is not an international unit. A calorie is the amount of heat required to raise the temperature of one gram of water one degree Celsius at 15°C. One calorie equals 4.183 joules.

A megajoule is 1,000,000 joules; a kilogram is 1,000 grams. A kilogram is equal to the mass of one liter of water in air at 4°C.

The heat of combustion supposes complete combustion. Since this is rarely the case in actual fires, the heat of combustion represents the upper limit of the heat produced by substances under normal conditions. It is symbolized by


D h


which is read, “the upper heat of combustion.”A lower level heat of combustion is also defined, and its symbol is


D h


The lower heat of combustion is the heat produced under normal conditions.

The tables in the NFPA (National Fire Protection Association) Handbook (Appendix A of the 17th Edition) contain information about the heat of combustion and other data about three classes of substances. Here are some examples from each of the three classes.

In general, the heat of combustion for plastics in many cases is nearly twice that for “ordinary” combustibles.

Both classes of substances are solid organic compounds, of which there are two kinds: (1) hydrocarbon-based materials and (2) cellulose-based materials. Plastics belong to the first kind, while most common substances belong to the second kind. Both kinds contain carbon and hydrogen atoms. However, cellulose materials are based on a partially oxidized carbon unit; hence, they consume less oxygen and produce less heat.

So, one important conclusion from the tables is that hydrocarbon-based materials (plastics) consume 50 percent more oxygen and thus produce 50 percent more heat than cellulose-based materials. In a pound-for-pound comparison, hydrocarbons produce twice as much heat as cellulosics. This generalization in recent years has been used to justify the use of 134- and two-inch attack lines in firefighting. The rationale is that fires now produce more heat than several decades ago; hence, the need for greater fire flows.

However, other data in the table should be considered before making any conclusions. Two of the tables contain the value of the stoichiometric oxygen-fuel mass ratio. This number is the ratio of the molecular mass of oxygen and fuel as they combine in the combustion process. The symbol is “ro.” Stoichiometric refers to the combustion process. Then, one additional step is taken. The heat of combustion for each substance is divided by ro, which gives the ratio of the heat of combustion per kilogram of oxygen consumed. The symbol for this ratio is


D h

c ro for O2

where O2 is molecular oxygen present in air.

The following table lists this ratio for the pure and simple substances and the plastics previously listed. There are no data for the common substances.

These data are quite remarkable. There is no doubt about the conclusion drawn by Dr. Vytenis Babrauskas, the author of these tables, when he states:

“Recently, however, increasing engineering use is made of the observation that the heat of combustion per kilogram of oxygen consumed is nearly constant for most organic fuels. It can be shown that the value of

D h 1c

ro = 13.1 MJ/kg for O2

is near constant.”1

Dr. Frederick B. Clarke reinforces this conclusion in his article, “Fire Hazards of Materials: An Overview,” when he states:

“Examination of the heat of combustion tables in Appendix A will show that, while the heat of combustion is quite different for different organic materials, the heat produced per equivalent of oxygen consumed is the same within about 10%. This fact, sometimes called `Thornton`s Rule,` allows one to use oxygen consumption as a reasonable measure of the heat produced by a burning organic material.”2

Thus, we have arrived at Thornton`s Rule.

I will examine the consequences of Thornton`s Rule for oxygen-limited fires (typical ventilation-controlled compartment fires). John A. Campbell, in his article “Confinement of Fires in Buildings,” states:

“Considerable ventilating area is required for a fully developed fire to burn at a fuel-surface controlled rate. For example, over one-fourth of the wall area would have to be open in a 20- ¥ 20-ft room (6.1 m ¥ 6.1 m) with an 8-ft ceiling (2.4 m) and an exposed combustible surface of 800 ft2 (74.3 m2) of ordinary combustibles. Many, if not most, building fires will be ventilation controlled at least during the period of time in which containment is a consideration.”3

Thus, firefighters confront oxygen-limited fires all the time. Since 73 percent of all structure fires and 75.5 percent of all house fires are confined to the room of origin, the consequences of Thornton`s Rule are enormous.

In oxygen-limited fires, the type of organic material burning is irrelevant, since the amount of heat released is constant for a given amount of oxygen consumed. Therefore, the widespread use of plastics does not indicate a need for greater fire flows than in years past. In oxygen-limited fires, cellulose-based materials release just as much heat as hydrocarbon-based materials.


This is the first consequence of Thornton`s Rule, and it contradicts a widespread belief held by many in the fire service.

The second consequence of Thornton`s Rule is that it validates the Iowa Rate-of-Flow formula. The Iowa formula was discovered in the 1950s by Keith Royer and Floyd W. Nelson at Iowa State University. The formula is

NFF (30 sec) = L ¥ W ¥ H


where NFF = the rate of flow in gpm, L = length, W = width, and H = height, and their product equals the volume of a confined space in cubic feet.

The denominator is derived from the expansion ratio of water to steam at 212°F, which is 227 cubic feet per gallon. In the experiments conducted at Iowa State, it was determined that water need be applied for only 30 seconds. So instead of one gallon flowing for one minute, thereby creating 200 cubic feet of steam, only 12 gallon flows for 30 seconds, creating 100 cubic feet of steam. The time of 30 seconds, should always be included in the Iowa Rate-of-Flow formula.

The validity of the Iowa formula rests on two facts. Keith Royer has explained how this formula emerged in this way.

“1. Study of expansion ratios of water to steam indicates that one gallon of water will produce, with a margin of safety, 200 cubic feet of steam.

2. Study of heat production in relation to oxygen also indicates that in the conversion of water to steam, one gallon of water will absorb, with a margin of safety, all the heat that can be produced with the oxygen available in 200 cubic feet of normal air.

These two factors lead to the formula: Cubic area in feet divided by 200 equals the required gallonage of water for control of a specific area involved in fire.”4

Note the relevance of Thornton`s Rule to #2.

The preceding gallonage formula stated in symbols is:

Gal = Vol


where Gal = the number of gallons of water and Vol = the volume of a confined space. It is worth noting that, with a 90 percent rate of conversion of water to steam, only five gallons of water are needed to produce 1,000 cubic feet of steam, which will control a room-size fire. Also, only 100 gallons of water are needed for a fully involved average-size house (20,000 cubic feet). However, this is not so easy to do because of the constraints that restrict the use of a fog attack.

(1) The fire must be confined (i.e., ceiling or roof intact) so that the steam blanket will hold for at least two minutes. This limit constitutes an absolute maximum constraint.

(2) The water must be distributed properly–that is, evenly throughout the fire area. This requires about 10 seconds, which constitutes an absolute minimum constraint.

(3) Within the lower and upper constraints, if the right amount of water is exceeded, then an effective fire attack is disrupted. This constitutes a variable constraint caused by too great a rate of flow or by application for too long a time.

If constraint (3) is exceeded, the result is thermal imbalance. Thermal balance exists before a fire attack is made and returns quickly if the right amount of water is used. Thermal imbalance results in extreme turbulence, a disruption of the even layering and distribution of temperatures and blocking of the smooth energy flow into and out of the fire. Thermal imbalance will delay overhaul, prevent the extinguishment of all of the fire, and may even blow or spread products of combustion into other areas of the structure. None of this happens if the right amount of water is used. The Iowa Rate-of-Flow formula gives you the right amount of water.

Now, we have arrived at the third consequence of Thornton`s Rule. Using too much water disrupts an effective fire attack on confined fires. Let`s find out how much is too much.

Starting with the gallonage formula

(1) Gal = Vol


the right amount of water can be applied at different rates depending on time–that is, how long the needed fire flow is applied. This relationship is expressed by the following equation:

(2) NFF ¥ t = Gal

where NFF = needed fire flow in gpm, t = time in minutes or fraction of a minute (please note this), and Gal = a constant for a given size fire, the number of gallons needed for fire control.

Since the volume of water needed is constant for a given size fire, increasing the flow decreases the time needed for fire control. Likewise, decreasing the flow increases the time needed for control. For example, a 2,000-cubic-foot fire requires 10 gallons of water. If the flow is 60 gpm, then

60 ¥ 16 = 10

where 16 is a fraction of a minute, or 10 seconds. If the flow is 30 gpm, then

30 ¥ 13 = 10

where 13 is 20 seconds.

Combining the two preceding equations by eliminating Gal from both gives the following equation:

(3) NFF ¥ t = Vol


Now, suppose there is a small room, 10 ¥ 12 ¥ 8 feet, which is approximately 1,000 cubic feet, and that this room is fully involved in fire. Suppose further that an attack is made on the fire with a 112-inch line flowing 100 gpm. Substituting 100 into equation (3) gives

100 ¥ t = 1,000


Dividing both sides of the equation by 100 gives

t = 1,000



t = 120

which is equal to three seconds. Therefore, it is not possible to properly execute a combination attack that would distribute water evenly throughout the fire area. The 112-inch line flows too much water since this attack falls outside the absolute minimum constraint of 10 seconds.

The results are even worse with 134- or two-inch attack lines. Remember that at least 75 percent of all structure fires are confined to the room of origin. The conclusion then is that firefighters would have to be extremely careful in using present-day attack lines to avoid using too much water, thereby creating thermal imbalance.

I have one suggestion. I hesitate to recommend going back to booster lines even though the 30 gpm controls the 1,000-cubic-foot fire in 10 seconds. Instead, I suggest opening the fog nozzles only halfway for smaller fires. Halfway on a 112-inch line means flowing 50 gpm and 75 gpm for 134-inch lines. These lines should be closed down more than this for the small 1,000-cubic-foot room fire.

For larger fires involving an entire house, proper distribution requires multiple attack lines. The most effective attack occurs when water is applied simultaneously to all rooms of the structure. This calls for small attack lines instead of larger ones. The reader should do some calculation with (3) to see what is required to properly distribute water for such fires.

I would like to conclude with an experience I had in attacking a house fire in February 1991. The fire occurred in a small, square-shaped, four-room house. There were two bedrooms on the left side (B side), one behind the other. On the right side (D side), there was a living room with a kitchen behind. A small bathroom was to the right of the kitchen.

When the first fire truck arrived, the fire was burning out the front door, the right front window (A side), and the first window of the D side. A mass of flames was enveloping the small porch at the front door. Later, we found out that a two-gallon can of kerosene sitting just inside the front door had exploded. The fire had spread into the kitchen at the ceiling level and almost burned through the wood panel bathroom door at the top. The front bathroom was scorched at the ceiling level. The rear bedroom had some smoke damage.

A combination attack was made through the living room window on the D side with a 134-inch line. I opened the nozzle halfway and rotated the nozzle clockwise two complete turns inside the window. Almost immediately, the flames changed to white condensing steam. Instinctively, I backed away from the window as condensed steam spread out the window and enveloped the house. There was no evidence of any more fire. Much to my surprise, the flames outside the house were extinguished, too. I had to use a straight stream to hit some burning embers above the front living room window, and that was it.

The 134-inch nozzle was open halfway for about 10 seconds. The estimated flow was 75 gpm. The actual water used was less than 15 gallons. Fifteen gallons create at least 3,000 cubic feet of steam at 212°F. The volume of the three rooms (excluding the rear bedroom) was 2,750 cubic feet, so it is possible to use larger attack lines on smaller fires.

If you understand the consequences of Thornton`s Rule, I believe that you will be able to do a more effective job of firefighting. In reality, this rule says that a confined fire is highly vulnerable to an effective fog attack that hits the fire where it is limited–in the amount of oxygen available. Also remember that the Iowa Rate-of-Flow formula is the only valid formula that can guide you in making such a fire attack. n


1. Babrauskas, Dr. Vytenis, Appendix A. NFPA Handbook, 17th Edition. National Fire Protection Association (NFPA), One Batterymarch Park, Quincy, MA 02269-2101, 1991), p. A-7.

2. Clarke, Dr. Frederick B., “Fire Hazards of Materials, An Overview,” NFPA Handbook, pp. 3-15.

3. Campbell, John A., “Confinement of Fires in Buildings,” NFPA Handbook, pp. 6-80.

4. Royer, Keith, “Water for Fire Fighting,” Bulletin No. 18, Engineering Extension Service, Iowa State University, Ames, Iowa 1959, p. 1.

n JOHN D. WISEMAN, JR., is a volunteer firefighter with the Kittrell (TN) Fire Department and has been a firefighter with volunteer departments in New Jersey and Tennessee. A 33-year veteran of the fire service, he has completed the third-level fire officer course at the Tennessee State Fire School. He is author of The Iowa State Story, which discusses the development of the Iowa Rate of Flow formula, soon to be published by Iowa State University Press.

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