Thornton’s Rule: Anticipating the Heat-Release Rate


For many years now, fire service publications have published numerous articles on how today’s fires require higher flow rates. Some have even advocated minimum flows as high as 180 gallons per minute (gpm), the need for which is always attributed to the higher heat of combustion from plastics and synthetics in today’s fire environment. Although plastics and synthetics do have a higher heat of combustion, this does not necessarily translate to hotter fires.

W. M. Thornton first mentioned this in his 1917 article, “The Relation of Oxygen to the Heat of Combustion of Organic Compounds.”1 He explains how the heat (energy) liberated from the combustion of hydrocarbons depends on the amount of oxygen available for combustion and that each unit of oxygen would release an almost identical amount of energy, regardless of the hydrocarbon burning.

The fact that the temperature of a fire is largely oxygen dependent should not come as a complete surprise. Recall that a blacksmith stokes his fire (i.e., introduces more oxygen) to make the coals hotter. Acetylene will burn in air with no more than ambient oxygen and produce a flame of approximately 4,000°F. When additional oxygen is added to acetylene for an oxyacetylene torch, the resulting flame burns at approximately 6,000°F. Although other factors, such as the form in which the material is used, can affect the temperature at which the materials burn, the availability of oxygen will ultimately define the final temperature.

This principle is one of the driving factors in the development of the Iowa State University Rate-of-Flow formula. As Keith Royer and Floyd Nelson were conducting their experiments that ultimately led to the Iowa Rate-of-Flow formula, they were keenly aware of the limits of heat output based on oxygen availability. In fact, on page 3 of “Water for Fire Fighting: Rate-of-Flow Formula” it states, “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.”2

Although the above examples are evidence that oxygen has a deciding role in the heat output of hydrocarbons, it is not as readily evident that all hydrocarbons would produce the same heat of combustion per unit of oxygen. But in the late 1970s, fire researcher C. Huggett at the National Institute of Standards and Technology (NIST) verified Thornton’s Rule using the oxygen consumption calorimetry technique, developed at NIST in the early 1970s.

In “Estimation of Rate of Heat Release by Means of Oxygen Consumption Measurements,” Huggett shows how much energy was released per gram of oxygen for common combustibles.3 Where Thornton was only able to estimate the energy release based on the oxidation of carbon-carbon and carbon-hydrogen bonds, Huggett, with modern technology, was able to make actual measurements. Huggett simply verified Thornton’s earlier observation, which is the reason it is known today as Thornton’s Rule.


In his measurements, Huggett was able to measure the precise heat of combustion of various hydrocarbons based on their oxygen consumption. For example, methane (a major component of natural gas) has a heat of combustion of –12.54 kJ/gO2 (kilo Joules per gram of oxygen). An average of –12.72 kJ/gO2 is used for all hydrocarbon gases. Compare this with natural fuels, such as wood (maple) with an energy release of –12.51 kJ/gO2 and cotton with an energy release of –13.61 kJ/gO2. The average heat release for all natural fuels is –13.21 kJ/gO2.

Now, compare these numbers with the heat release from common synthetic polymers. For example, polyethylene has an energy release of –12.65 kJ/gO2 and nylon-6,6 liberates –13.23 kJ/gO2. The average for the common synthetic polymers is –13.02 kJ/gO2. Notice that the average heat output for these synthetic polymers is actually less per unit of oxygen than natural fuels. The difference is not significant enough to be meaningful, but the point is they do not contribute more heat per unit of oxygen than other fuels. Yet, they are the very materials we blame for fires being hotter. The truth is, they will produce more heat if allowed to be completely consumed. This is a critical technicality, since ideally we are trying to extinguish fires before they completely consume the fuel.

As a result of his research, outlined above, Huggett put an average value of –13.1 kJ/gO2 ± 5 percent as the heat release from fires involving conventional organic fuels. Conventional organic fuels are essentially all hydrocarbon fuels whether liquids, gases, synthetic polymers, or natural fuels.

To put this in context, consider a 20- × 20-foot room with an eight-foot-high ceiling. If the room were loaded with 1950s-era furnishings and set on fire, once the fire in the room was fully developed, it would burn with a maximum heat output we will call X. If we took the same room and furnished it with furniture typical of 2010 and set it on fire, after it reached the fully developed stage, it would burn with a maximum heat output of X ± 5 percent. Since most compartment and building fires are ventilation limited4 after they reach the fully developed stage, ventilation becomes critical to any discussion of heat production.


Above I have tried to emphasize the critical role oxygen plays in total heat release because the heat released per unit of oxygen is the same. However, it would be incorrect to leave the impression that some hydrocarbon fuels don’t produce more heat if totally consumed than others.

Let me illustrate with a couple of examples. Methane has the chemical formula CH4. When it oxidizes, we have the chemical reaction:

CH4 + 2O2 → 2H2O + CO2

What this says is that one molecule of methane requires two molecules (or four elements) of oxygen to completely oxidize (burn).

Now let’s look at the oxidation of styrene (C8H8), a common plastic, and see how much oxygen it requires. When it oxidizes, we have the chemical reaction:

C8H8 + 10O2 → 4H2O + 8CO2

In these examples, we see it is possible for each molecule of styrene to produce significantly more heat than a molecule of methane. In fact, the heat output per molecule of styrene is approximately five times that of methane since it consumes five times as much oxygen.

Together, these two examples prove that it is possible for the more complex hydrocarbons to produce more heat than simple ones, but it is also very evident that this increased heat release is oxygen dependent. To get five times as much heat out of the oxidation of the styrene, the reaction consumes five times as much oxygen. If we only had six molecules of oxygen in each example above, we would have complete oxidation of three molecules of methane, yet we would not have enough oxygen for the complete combustion of even one molecule of styrene. But in either case, with six molecules of oxygen, we will have the same amount of heat produced.

This proves that our average compartment fire (room and contents) is driven by the oxygen that gets to the fire. In the early stage of the fire, it is a fuel-limited fire—i.e., the fire will burn at a fuel-surface-controlled rate. As long as there isn’t much fuel burning in relation to the amount of oxygen available, regardless of type, the fire will grow fast and rapidly increase in temperature. Up to full development, the fire is growing essentially without restriction and has more than enough oxygen for the maximum heat output of the limited amount of combustibles burning—that is, until the room’s temperature reaches about 500°F, at which point the transition to full development begins, with the fire reaching 1,000°F in less than a minute. (4) At the point of full development, all the combustibles in the room are burning. Ultimately, after the room reaches the fully developed stage, maximum temperatures will be between approximately 1,500°F and 1,800°F.

Post full development, most compartment and building fires are ventilation (oxygen) limited. Since the fire cannot get all the oxygen it wants for complete combustion of all the contents of the room/structure, the heat output is limited. This will be independent of what or how much is burning. In short, post full development, it does not matter how much plastics and synthetics are in the room; the room will burn with the same heat output as if all the fuel were paper or wood, and vice versa.

Many fires are already vented by the time we get there. It would seem that logic would dictate that a fire that has vented itself is burning at a fuel-limited rate! Once again, our popular belief is incorrect. Even a fire that has vented itself is not likely to be fuel limited. For a fully developed compartment fire to go from ventilation limited to fuel limited, ventilation will need to be equivalent to removal of at least 25 percent of the wall area. In his example, Hossein Davoodi5 states that for a fire in a 20- × 20- × 8-foot room to burn at a fuel-surface-controlled rate (fuel limited), it would have to create a ventilation opening of more than 25 percent of the wall area. For the room in his example, we would have to remove more than 160 square feet of wall area. There is simply no way that the vast majority of rooms will have sufficient window/door area to meet this requirement. Subsequently, the temperature of a typical compartment fire, even if ventilated through the windows in the room, will be limited by the amount of oxygen it can get.

To illustrate this point, photo 1 shows an office on the third floor of the Harrisonburg (VA) Public Safety Building (yellow arrow). From this view, it is evident that this office has an abundance of wall area taken up with windows. It would appear that this office is a candidate for being the exception to the ventilation-limited fire.

(1) Photos by author.

Photo 2 shows that same office from the inside. The office is 12- × 17-feet, 4 inches with an eight-foot-high ceiling. This gives the room a total wall area of 469 square feet. The windows are 5 ft., 6 in. × 15 ft., 4 in. for a total area of 84 square feet. Add another 20 square feet for the door, and you have a total ventilation area of 104 square feet. That is just 22 percent of the total wall area.


Something else that will interfere with getting sufficient ventilation area, even with this much glass, is that this type of window is designed not to fail. Since the office in photo 2 actually has four panes of glass, all four would have to fail to even approach sufficient ventilation area to allow the fire to burn at a fuel-limited rate. Even if the fire department takes the windows out (assuming it can be done quickly), the fire will burn at a ventilation-limited rate until the windows are removed. By then, an interior attack line should be in place and water applied long before the room has had time to increase in temperature.

We need to remember that the vast majority of our fires will never approach the point of becoming fuel limited. Residences comprise 78 percent of all structure fires and usually don’t have entire walls of windows, except for some passive solar homes.

Many articles over the past few years have focused on the need to increase fire flow to meet the increasing heat of combustion.6,7 But if the heat output is restricted by limited oxygen, why increase the fire flow? What was adequate yesterday is still adequate today.

Now, make no mistake: There are many factors that affect today’s fireground and required fire flow, but the heat release rate is considered to be the single most critical variable in assessing fire hazard.(3)8 With increased fire flows, we are requiring that firefighters work harder in the already hostile environment of an interior fire attack.

Does it make sense that we should go with larger flows on even the more common fires just so we have them when they are needed? That is like dispatching a multiple alarm assignment on the report of an odor of smoke, just in case we need it! Or perhaps we should just empower our company officers to decide what line and what flow are needed on a case-by-case basis. Anticipating the heat release rate is really not hard if you understand Thornton’s Rule.

Thanks to Scott Lewis, Ph.D., and Ron Raab, Ph.D., technical advisors to the Harrisonburg (VA) Hazardous Materials Response team, for their technical review of the article, and to Captain Mike Brady of the Harrisonburg (VA) Fire Department, for his peer review of the article.


1. Thornton, W.M. “The Relation of Oxygen to the Heat of Combustion of Organic Compounds.” Philosophical Magazine and Journal of Science, Series 6, (1917) 33:194, 196-203.

2. Royer, Keith and Floyd W. Nelson. “Water for Fire Fighting: Rate-of-Flow Formula.” Iowa State University Engineering Extension Service Bulletin No. 18, (1959).

3. Huggett, C. “Estimation of Rate of Heat Release by Means of Oxygen Consumption Measurements,” Fire and Materials, (1980) 4:2, 61-65.

4. Quintere, James G. Principles of Fire Behavior. Albany, New York: Delmar (1998).

5. Davoodi, H. “Confinement of Fire in Buildings.” Chap. 18-1 in National Fire Protection Association Handbook, 20th Ed., A.E. Cote (ed.), (Quincy, MA: National Fire Protection Association, 2008).

6. Shovald, Bob. “Improving Preconnect Function and Operation.” Fire Engineering, October 2008, 161:10, 83-89.

7. Sheridan, Daniel P. “Getting the First Hoseline in Operation.” Fire Engineering, November 2009, 162:11, 89-95.

8. Babrauskas, V. and R.D. Peacock. “Heat Release Rate: The Single Most Important Variable in Fire Hazard.” Fire Safety Journal. (1992) 18: 255-272.

WILLIAM F. CRAPO served as deputy chief with the Harrisonburg (VA) Fire Department until his retirement in January 2011. He joined the department in 2001 as an assistant chief. Crapo began his fire service career in 1965 with the Brentwood (MD) Volunteer Fire Department and joined the District of Columbia Fire Department in 1973, serving for 20 years before retiring with the rank of captain. Crapo taught fire science for several semesters at the Lord Fairfax Community College in Frederick County, Virginia, and has written several articles for Fire Engineering.

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