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Thornton’s Rule
Fire is usually defined as a hydrocarbon air diffusion flame process, that is, a chemical reaction in which hydrocarbon fuels unites with the oxygen in air in diffusion flames which produce heat and light. The fire triangle states that there are three elements needed to ignite or start a fire—oxygen, fuel, and heat. All three elements are needed for ignition to occur. There is a relevant question to ask about this fire behavior.
Could the amount of fuels or oxygen present affect the rate of heat release in a confined structure fire and nullify the Royer Nelson formula?
First of all, fire engineers are unanimous in agreement that the heat content of fuels has no relation to the rate of heat release in a given fire. What does determine the rate of heat release is the surface area of the fuels involved. It is well known that within the past 50 years plastics have come into widespread use. It is also well known that the heat content of plastics is on the average twice that of ordinary cellulosic (wood based) fuels. Does this mean that fires are hotter today than fires that do not involve plastics? The answer is “no”. One expert has said that “If fires are hotter today, plastics have nothing to do with it.” Fires may be different today because of better insulation, but it is not necessarily true that all fires are hotter today.
However, there is one type of glazing that behaves differently in a fireOne thing that has not changed is the behavior of plate glass windows in a fire. Plate glass windows break from thermal stress early in the development of a structure fire. This begins at temperatures from 550° F (288° C) to 600° F (316° C). It is a common occurrence for fire to break out a window before flashover occurs. What about double pane windows? In one published test of side-by-side single pane and double pane windows, the double pane window broke out first because the vinyl frame melted. An expert writing in the NFPA Handbook has said, that “Window glazing quickly cracks because of the temperature difference between the surfaces. Double-glazing does not provide much improvement. No glazing should be relied upon to remain intact in a fire.” However, there is one type of glazing that behaves differently in a fire. Wired glass contains a net of steel that distributes heat and lowers stress. Wired glass remains intact until 1,470° F (799° C) when it begins to weaken. It will drop out at about 1,600° F (871° C).
Only a small part of the surface area is involved in fire and the rate of heat release is limited by the fuel surface area available to the fireFuels come in a wide variety of compounds with many different properties. However, the second element of the fire triangle involves only one element—the molecular oxygen in air. One of the most important facts about fire behavior of confined fires is that the rate of heat release is limited by the amount of oxygen in the fire area. There is one exception to this at the very beginning of a fire immediately after ignition, in the early flame spread stage. Only a small part of the surface area is involved in fire and the rate of heat release is limited by the fuel surface area available to the fire. Of course, once a structure fire breaks out into the open through the ceiling and roof the fire becomes an open fire with a practically unlimited supply of oxygen.
An important feature of confined fires is that the rate of heat release is limited by the amount of oxygen available. Remember that a fire can be burning out one or two windows, or a door, and it is still a confined fire. More than ¼ the wall area would have to be gone before a confined fire is not longer confined. Thornton’s Rule is the key to fire behavior of confined structure fires.. W. H. Thornton discovered his rule in 1917 but it was not used in fire engineering research until fairly recently. Thornton’s Rule was published in the 17th Edition of the NFPA handbook in 1991 in Appendix A. Thornton’s Rule is stated as follows.
The heat of combustion per kilogram of oxygen consumed is nearly constant for most organic fuels. It can be shown that the value of
| Δh1 / ro = 13.1 MJ/ kg of O2 |
is a near constant. (5622 btus/lb of oxygen)
What this rule means for fire behavior is that while the heat of combustion is quite different for different hydrocarbon fuels, the heat produced per unit of oxygen consumed is the same within about 10% Let’s illustrate Thornton’s Rule by using cellulose, the common substance of all wood based products, and ethylene a common plastic.
| Cellulose C6 H10 O5 | |
| Heat of Combustion | 16.12 mJ/kg |
| Ratio O2 mass/fuel mass | 1.184 |
| 16.12/1.184 = 13.6 mJ/kg of O2 | |
| Ethylene C2 H4 | |
| Heat of Combustion | 47.17 mJ/kg |
| Ratio O2 mass/fuel mass | 3.422 |
| 47.17/3.422 = 13.78 mJ/kg of O2 | |
Note that13.6 mJ/kg is very close to 13.78 mJ/kg and that both are close to the average of 13.1 mJ/kg (5622 Btu/lb) This happens because ethylene requires about three times more oxygen for complete combustion compared to cellulose.
Also Thornton’s Rule provides a solid, scientific foundation for fighting firesThornton’s Rule is a key scientific fact used in fire engineering today. Also Thornton’s Rule provides a solid, scientific foundation for fighting fires. Not only is the rate of heat release controlled by the amount of oxygen available but also this is a near constant for each unit of oxygen consumed. Now let’s consider how Thornton’s Rule affects how much water is needed to fight confined structure fires.
So Thornton’s Rule and the Royer Nelson formula work hand in hand, since both are based upon the volume of a confined spaceThornton’s Rule states that confined spaces of the same volume have the same volume of oxygen available so that the rate of heat release is the same. Larger spaces have more oxygen available and consequently have a greater rate of heat release. The Royer Nelson formula works in exactly the same way. Confined spaces of the same volume require the same amount of water to fill that space full of steam. Larger spaces require larger amount of water to fill larger spaces. So Thornton’s Rule and the Royer Nelson formula work hand in hand, since both are based upon the volume of a confined space. Further, the amount of water applied by the Royer Nelson formula is sufficient to absorb all the heat produced by the amount of oxygen in the confined space. This is one of the two scientific facts upon which the Royer Nelson formula is based.
