Fractional effective concentration - Revision history

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	Other effects do not build up in this way. Irritant smoke products cause pain in the eyes and upper airways as soon as the exposure starts, and the severity depends on the concentration.<ref name="P-87" /> As the exposure continues, the effects usually become weaker rather than stronger, because the person adapts to the painful stimulus although the dose keeps rising.<ref name="P-88" /> Low oxygen and high carbon dioxide behave in a similar way once the lungs and blood have adjusted, which usually takes a few minutes. After that, their effect depends on the concentration and hardly changes with time.<ref name="P-88" /> For this reason, sensory irritation is assessed with a fraction of the current concentration rather than with a dose.<ref name="P-89">Purser (2002), p. 2-89.</ref>		Other effects do not build up in this way. Irritant smoke products cause pain in the eyes and upper airways as soon as the exposure starts, and the severity depends on the concentration.<ref name="P-87" /> As the exposure continues, the effects usually become weaker rather than stronger, because the person adapts to the painful stimulus although the dose keeps rising.<ref name="P-88" /> Low oxygen and high carbon dioxide behave in a similar way once the lungs and blood have adjusted, which usually takes a few minutes. After that, their effect depends on the concentration and hardly changes with time.<ref name="P-88" /> For this reason, sensory irritation is assessed with a fraction of the current concentration rather than with a dose.<ref name="P-89">Purser (2002), p. 2-89.</ref>
			[[File:fse-fractional-effective-concentration-v2.svg\|thumb\|upright=1.5\|alt=Two graphs of one rising and falling gas concentration: left, the fraction follows the curve; right, the shaded area keeps growing.\|A concentration fraction (left) follows the concentration of the moment, while a dose fraction (right) keeps growing with the area under the curve. Based on Purser (2002), pp. 2-88–2-89.]]

	The toxicity chapter of the SFPE Handbook distinguishes three main toxic effects in fires.<ref name="P-91">Purser (2002), p. 2-91.</ref> Irritant gases can impair escape or incapacitate people through their concentration. Asphyxiant gases cause confusion and loss of consciousness through the dose inhaled. Lung irritants can also cause death after the fire through inflammation of the lungs, once a sufficient dose has been inhaled.<ref name="P-91" /> Time to impaired escape, incapacitation and death is estimated by combining FIC and FED calculations for smoke, irritants and asphyxiant gases with curves of concentration against time.<ref name="P-95">Purser (2002), p. 2-95.</ref> The chapter describes this combination as a physiological model for predicting the time to incapacitation of occupants in full-scale fires, and it is central to its treatment of [[fire toxicity]].<ref name="P-132">Purser (2002), p. 2-132.</ref>		The toxicity chapter of the SFPE Handbook distinguishes three main toxic effects in fires.<ref name="P-91">Purser (2002), p. 2-91.</ref> Irritant gases can impair escape or incapacitate people through their concentration. Asphyxiant gases cause confusion and loss of consciousness through the dose inhaled. Lung irritants can also cause death after the fire through inflammation of the lungs, once a sufficient dose has been inhaled.<ref name="P-91" /> Time to impaired escape, incapacitation and death is estimated by combining FIC and FED calculations for smoke, irritants and asphyxiant gases with curves of concentration against time.<ref name="P-95">Purser (2002), p. 2-95.</ref> The chapter describes this combination as a physiological model for predicting the time to incapacitation of occupants in full-scale fires, and it is central to its treatment of [[fire toxicity]].<ref name="P-132">Purser (2002), p. 2-132.</ref>
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	Experiments by Jin in Japan, in which people walked along a smoke-filled corridor, showed how strongly smoke slows movement. In non-irritant smoke, the walking speed fell from about 1.2 m/s without smoke to 0.3 m/s at an optical density of 0.5 per metre. Under these conditions people felt their way along the walls as if they were in darkness.<ref name="Jin1976">Jin (1976), as cited in Purser (2002), p. 2-118.</ref> In irritant smoke, made by heating wood chippings, the speed dropped to the same value at an optical density of only 0.2 per metre, and the experience was more distressing.<ref name="Jin1976" /> Studies of fires in buildings found that about 30 per cent of people turned back rather than pass through smoke, on average at a visibility of about 3 m.<ref name="P-118" />		Experiments by Jin in Japan, in which people walked along a smoke-filled corridor, showed how strongly smoke slows movement. In non-irritant smoke, the walking speed fell from about 1.2 m/s without smoke to 0.3 m/s at an optical density of 0.5 per metre. Under these conditions people felt their way along the walls as if they were in darkness.<ref name="Jin1976">Jin (1976), as cited in Purser (2002), p. 2-118.</ref> In irritant smoke, made by heating wood chippings, the speed dropped to the same value at an optical density of only 0.2 per metre, and the experience was more distressing.<ref name="Jin1976" /> Studies of fires in buildings found that about 30 per cent of people turned back rather than pass through smoke, on average at a visibility of about 3 m.<ref name="P-118" />
			[[File:fse-fractional-effective-concentration-v3.svg\|thumb\|upright=1.5\|alt=Chart of walking speed against smoke density: speed in irritant smoke drops to 0.3 m/s at a much lower density than in non-irritant smoke.\|Walking speed in non-irritant and irritant smoke against the extinction coefficient of the smoke. Based on Purser (2002), p. 2-118, and Australian Building Codes Board (2020), p. 282.]]

	To turn these findings into a single design check, the handbook divides the optical density of the smoke by a limiting value.<ref name="P-119" /> The limit is 0.2 per metre for small enclosures with short travel distances, which corresponds to a visibility of about 5 m. For large enclosures with long travel distances it is 0.08 per metre, which corresponds to about 10 m.<ref name="P-118" /> The fraction for visual obscuration is then:		To turn these findings into a single design check, the handbook divides the optical density of the smoke by a limiting value.<ref name="P-119" /> The limit is 0.2 per metre for small enclosures with short travel distances, which corresponds to a visibility of about 5 m. For large enclosures with long travel distances it is 0.08 per metre, which corresponds to about 10 m.<ref name="P-118" /> The fraction for visual obscuration is then:
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	Both values are above 1, so in this minute the smoke would be expected to impair and possibly prevent escape.<ref name="P-133" /> The handbook's table gives a total FIC of 1.83 for the same minute, because its hydrogen chloride term is 0.83 instead of 0.75. The conclusion is the same.<ref name="P-132" />		Both values are above 1, so in this minute the smoke would be expected to impair and possibly prevent escape.<ref name="P-133" /> The handbook's table gives a total FIC of 1.83 for the same minute, because its hydrogen chloride term is 0.83 instead of 0.75. The conclusion is the same.<ref name="P-132" />
			[[File:fse-fractional-effective-concentration-v4.svg\|thumb\|upright=1.5\|alt=Stacked bar of 0.75, 0.50 and 0.50 giving a total irritant fraction of 1.75, above the limits 0.3 and 1, below the band of 3 to 5.\|Contributions of three irritants to the total FIC in the third minute of the armchair fire, compared with the limits for vulnerable people, impaired escape and incapacitation. Based on Purser (2002), pp. 2-91, 2-121 and 2-132.]]

	One minute earlier, the smoke had 0.2 per metre with 50 ppm hydrogen chloride, 0.8 ppm acrolein and 1.2 ppm formaldehyde. The same method then gives an FEC for smoke of exactly 1 and a total FIC of 0.65. The limit of 0.3 for vulnerable people had therefore already been passed in the second minute, as the handbook also concludes.<ref name="P-133" /> According to the rule of thumb for visibility, 0.2 per metre corresponds to about 5 m for a reflecting sign.<ref name="VR-6.5" />		One minute earlier, the smoke had 0.2 per metre with 50 ppm hydrogen chloride, 0.8 ppm acrolein and 1.2 ppm formaldehyde. The same method then gives an FEC for smoke of exactly 1 and a total FIC of 0.65. The limit of 0.3 for vulnerable people had therefore already been passed in the second minute, as the handbook also concludes.<ref name="P-133" /> According to the rule of thumb for visibility, 0.2 per metre corresponds to about 5 m for a reflecting sign.<ref name="VR-6.5" />

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	One minute earlier, the smoke had 0.2 per metre with 50 ppm hydrogen chloride, 0.8 ppm acrolein and 1.2 ppm formaldehyde. The same method then gives an FEC for smoke of exactly 1 and a total FIC of 0.65. The limit of 0.3 for vulnerable people had therefore already been passed in the second minute, as the handbook also concludes.<ref name="P-133" /> According to the rule of thumb for visibility, 0.2 per metre corresponds to about 5 m for a reflecting sign.<ref name="VR-6.5" />		One minute earlier, the smoke had 0.2 per metre with 50 ppm hydrogen chloride, 0.8 ppm acrolein and 1.2 ppm formaldehyde. The same method then gives an FEC for smoke of exactly 1 and a total FIC of 0.65. The limit of 0.3 for vulnerable people had therefore already been passed in the second minute, as the handbook also concludes.<ref name="P-133" /> According to the rule of thumb for visibility, 0.2 per metre corresponds to about 5 m for a reflecting sign.<ref name="VR-6.5" />
			[[File:fse-fractional-effective-concentration-v1.svg\|thumb\|upright=1.5\|alt=Line chart: smoke and irritant fractions rise over four minutes and cross the limit of 1 in the second and third minutes.\|Smoke fraction (FEC) and total irritant fraction (FIC) during the first four minutes of an armchair fire, compared with the limits of 0.3 and 1. Based on Purser (2002), pp. 2-132–2-133.]]

	== Use in hazard analysis and design ==		== Use in hazard analysis and design ==

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	The time at which the first tenability criterion is exceeded defines the [[available safe egress time]] in the Australian and New Zealand verification methods.<ref name="AU-10">Australian Building Codes Board (2022), p. 10.</ref><ref name="NZ-17">Ministry of Business, Innovation and Employment (2025b), p. 17.</ref> Their criteria use other quantities than concentration fractions. In New Zealand, C/VM2 (second edition, 2025) measures tenability at 2.0 m above the floor with the FED for carbon monoxide, the FED for thermal effects and visibility.<ref name="NZ-17" /> In Australia, the Fire Safety Verification Method Standard (2022) uses a thermal FED of 0.3 and a visibility of 10 m. The visibility limit drops to 5 m in rooms smaller than 100 m² or where the exit is no more than 5 m away.<ref name="AU-10" /> Both documents note that visibility is usually the first criterion to be exceeded.<ref name="AU-10" /><ref name="NZ-17" />		The time at which the first tenability criterion is exceeded defines the [[available safe egress time]] in the Australian and New Zealand verification methods.<ref name="AU-10">Australian Building Codes Board (2022), p. 10.</ref><ref name="NZ-17">Ministry of Business, Innovation and Employment (2025b), p. 17.</ref> Their criteria use other quantities than concentration fractions. In New Zealand, C/VM2 (second edition, 2025) measures tenability at 2.0 m above the floor with the FED for carbon monoxide, the FED for thermal effects and visibility.<ref name="NZ-17" /> In Australia, the Fire Safety Verification Method Standard (2022) uses a thermal FED of 0.3 and a visibility of 10 m. The visibility limit drops to 5 m in rooms smaller than 100 m² or where the exit is no more than 5 m away.<ref name="AU-10" /> Both documents note that visibility is usually the first criterion to be exceeded.<ref name="AU-10" /><ref name="NZ-17" />

	Irritant smoke enters these methods in other ways. The Australian data sheets (2020) handle it through the walking speed of occupants, which is multiplied by a factor of 0.3 at a visibility of 10 m with illuminated signs.<ref name="AU-DS">Australian Building Codes Board (2020a), pp. 282–283.</ref> The tenability limit itself is not changed. In the Netherlands, no limits are formally laid down. For escape through mixed smoke in non-enclosed spaces, the explanatory notes to the Dutch Building Decree (Bbl) use a visibility of at least 30 m for illuminated objects. In corridors, a visibility of only 5 m is often accepted.<ref name="VR-7.7" />		Irritant smoke enters these methods in other ways. The Australian data sheets (2020) handle it through the walking speed of occupants, which is multiplied by a factor of 0.3 at a visibility of 10 m with illuminated signs.<ref name="AU-DS">Australian Building Codes Board (2020a), Data Sheet D1, pp. 282–283.</ref> The tenability limit itself is not changed. In the Netherlands, no limits are formally laid down. For escape through mixed smoke in non-enclosed spaces, the explanatory notes to the Dutch Building Decree (Bbl) use a visibility of at least 30 m for illuminated objects. In corridors, a visibility of only 5 m is often accepted.<ref name="VR-7.7" />

	== Limits and uncertainty ==		== Limits and uncertainty ==

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	In the worked example, the curves rise very steeply once they pass 1. As a result, even if the true incapacitating concentrations were higher than the chosen limits, the predicted time of incapacitation would change only a little.<ref name="P-133" /> The limits apply in the breathing zone of an occupant, so some time passes between ignition and the moment they are reached.<ref name="P-121" /> In the worked example, the head of the occupant was assumed to be in the smoke at all times. A more refined analysis can allow for a lower position in the room when the height of the smoke layer is known.<ref name="P-133" />		In the worked example, the curves rise very steeply once they pass 1. As a result, even if the true incapacitating concentrations were higher than the chosen limits, the predicted time of incapacitation would change only a little.<ref name="P-133" /> The limits apply in the breathing zone of an occupant, so some time passes between ignition and the moment they are reached.<ref name="P-121" /> In the worked example, the head of the occupant was assumed to be in the smoke at all times. A more refined analysis can allow for a lower position in the room when the height of the smoke layer is known.<ref name="P-133" />

	The time at which the first tenability criterion is exceeded defines the [[available safe egress time]] in the Australian and New Zealand verification methods.<ref name="AU-10">Australian Building Codes Board (2022), p. 10.</ref><ref name="NZ-17">Ministry of Business, Innovation and Employment (~~2025~~), p. 17.</ref> Their criteria use other quantities than concentration fractions. In New Zealand, C/VM2 (second edition, 2025) measures tenability at 2.0 m above the floor with the FED for carbon monoxide, the FED for thermal effects and visibility.<ref name="NZ-17" /> In Australia, the Fire Safety Verification Method Standard (2022) uses a thermal FED of 0.3 and a visibility of 10 m. The visibility limit drops to 5 m in rooms smaller than 100 m² or where the exit is no more than 5 m away.<ref name="AU-10" /> Both documents note that visibility is usually the first criterion to be exceeded.<ref name="AU-10" /><ref name="NZ-17" />		The time at which the first tenability criterion is exceeded defines the [[available safe egress time]] in the Australian and New Zealand verification methods.<ref name="AU-10">Australian Building Codes Board (2022), p. 10.</ref><ref name="NZ-17">Ministry of Business, Innovation and Employment (2025b), p. 17.</ref> Their criteria use other quantities than concentration fractions. In New Zealand, C/VM2 (second edition, 2025) measures tenability at 2.0 m above the floor with the FED for carbon monoxide, the FED for thermal effects and visibility.<ref name="NZ-17" /> In Australia, the Fire Safety Verification Method Standard (2022) uses a thermal FED of 0.3 and a visibility of 10 m. The visibility limit drops to 5 m in rooms smaller than 100 m² or where the exit is no more than 5 m away.<ref name="AU-10" /> Both documents note that visibility is usually the first criterion to be exceeded.<ref name="AU-10" /><ref name="NZ-17" />

	Irritant smoke enters these methods in other ways. The Australian data sheets (2020) handle it through the walking speed of occupants, which is multiplied by a factor of 0.3 at a visibility of 10 m with illuminated signs.<ref name="AU-DS">Australian Building Codes Board (~~2020~~), pp. 282–283.</ref> The tenability limit itself is not changed. In the Netherlands, no limits are formally laid down. For escape through mixed smoke in non-enclosed spaces, the explanatory notes to the Dutch Building Decree (Bbl) use a visibility of at least 30 m for illuminated objects. In corridors, a visibility of only 5 m is often accepted.<ref name="VR-7.7" />		Irritant smoke enters these methods in other ways. The Australian data sheets (2020) handle it through the walking speed of occupants, which is multiplied by a factor of 0.3 at a visibility of 10 m with illuminated signs.<ref name="AU-DS">Australian Building Codes Board (2020a), pp. 282–283.</ref> The tenability limit itself is not changed. In the Netherlands, no limits are formally laid down. For escape through mixed smoke in non-enclosed spaces, the explanatory notes to the Dutch Building Decree (Bbl) use a visibility of at least 30 m for illuminated objects. In corridors, a visibility of only 5 m is often accepted.<ref name="VR-7.7" />

	== Limits and uncertainty ==		== Limits and uncertainty ==
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	== References ==		== References ==
	* Australian Building Codes Board. (~~2020~~). ''~~Fire safety verification method data~~ sheets: Handbook annex''.		* Australian Building Codes Board. (2020a). ''Data sheets: Fire Safety Verification Method'' (Handbook annex, Print version 1.1).
	* Australian Building Codes Board. (2022). ''Fire ~~safety verification method standard~~ 2022''.		* Australian Building Codes Board. (2022). ''Fire Safety Verification Method Standard 2022''.
	* Ministry of Business, Innovation and Employment. (~~2025~~). ''Verification ~~method~~ C/VM2: Framework for fire safety design'' (2nd ed.).		* Ministry of Business, Innovation and Employment. (2025b). ''Verification Method C/VM2: Framework for fire safety design'' (2nd ed.).
	* Purser, D. A. (2002). Toxicity assessment of combustion products. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall, Jr., & J. M. Watts, Jr. (Eds.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 2-83–2-171). National Fire Protection Association.		* Purser, D. A. (2002). Toxicity assessment of combustion products. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 2-83–2-171). National Fire Protection Association; Society of Fire Protection Engineers.
	* Van Rossum, E. (2027). ''Introduction to Fire Safety Engineering''. Fire Safety Academy.		* Van Rossum, E. (2027). ''Introduction to Fire Safety Engineering''. Fire Safety Academy.

	[[Category:Smoke, Toxicity & Tenability]]		[[Category:Smoke, Toxicity & Tenability]]

Mark: New FSE wiki article: Fractional effective concentration (written by Claude Opus 5.5)

2026-11-01T22:01:15Z

New FSE wiki article: Fractional effective concentration (written by Claude Opus 5.5)

New page

'''Fractional effective concentration''' ('''FEC''') is the ratio between the concentration of a fire product at a given moment and the concentration that is expected to make escape significantly less efficient. The concept comes from the toxicity chapter of the Handbook of Fire Protection Engineering of the Society of Fire Protection Engineers (SFPE). There, the smoke concentration is expressed as a fraction of the concentration considered to affect escape efficiency significantly.<ref name="P-119">Purser (2002), p. 2-119.</ref> When the fraction reaches 1, the effect is predicted to occur. The same method applied to irritant gases is called the fractional irritant concentration (FIC).<ref name="P-121">Purser (2002), p. 2-121.</ref>

Both fractions are tools for checking [[tenability criteria]], the limits used to judge whether conditions in a building still allow people to escape.<ref name="VR-7.7">Van Rossum (2027), §7.7.</ref> They differ from the [[fractional effective dose]] (FED), which adds up an inhaled dose over time.<ref name="P-88">Purser (2002), p. 2-88.</ref> A concentration fraction looks only at the conditions of the moment. The pain caused by irritant smoke and the loss of sight in dense smoke depend on how strong the exposure is, not on how long it has lasted.<ref name="P-87">Purser (2002), pp. 2-87–2-88.</ref> In a worked example in the handbook, smoke obscuration and irritancy were the first hazards to reach their limits, while collapse from asphyxiant gases was predicted only during the fifth minute.<ref name="P-133">Purser (2002), p. 2-133.</ref>

== Concentration and dose ==
Toxicologists describe the effect of an inhaled substance with two basic quantities: its concentration in the air and the duration of the exposure.<ref name="P-87" /> For many substances the effect depends on the dose, which is roughly the product of concentration and time. The FED method uses this idea. The dose received in each short period of the fire is divided by the dose that causes the effect, and these fractions are added until they reach 1.<ref name="P-88" /> The approach works well for carbon monoxide: monkeys exposed to concentrations between 1000 and 8000 parts per million (ppm) became unconscious after inhaling about the same dose of roughly 27,000 ppm·min.<ref name="P-87" />

Other effects do not build up in this way. Irritant smoke products cause pain in the eyes and upper airways as soon as the exposure starts, and the severity depends on the concentration.<ref name="P-87" /> As the exposure continues, the effects usually become weaker rather than stronger, because the person adapts to the painful stimulus although the dose keeps rising.<ref name="P-88" /> Low oxygen and high carbon dioxide behave in a similar way once the lungs and blood have adjusted, which usually takes a few minutes. After that, their effect depends on the concentration and hardly changes with time.<ref name="P-88" /> For this reason, sensory irritation is assessed with a fraction of the current concentration rather than with a dose.<ref name="P-89">Purser (2002), p. 2-89.</ref>

The toxicity chapter of the SFPE Handbook distinguishes three main toxic effects in fires.<ref name="P-91">Purser (2002), p. 2-91.</ref> Irritant gases can impair escape or incapacitate people through their concentration. Asphyxiant gases cause confusion and loss of consciousness through the dose inhaled. Lung irritants can also cause death after the fire through inflammation of the lungs, once a sufficient dose has been inhaled.<ref name="P-91" /> Time to impaired escape, incapacitation and death is estimated by combining FIC and FED calculations for smoke, irritants and asphyxiant gases with curves of concentration against time.<ref name="P-95">Purser (2002), p. 2-95.</ref> The chapter describes this combination as a physiological model for predicting the time to incapacitation of occupants in full-scale fires, and it is central to its treatment of [[fire toxicity]].<ref name="P-132">Purser (2002), p. 2-132.</ref>

The motivation is practical. Surveys in the United Kingdom showed that about half of the people killed in dwelling fires were recorded as overcome by smoke and toxic gases rather than by heat and burns. The same applied to about a third of those injured.<ref name="P-83">Purser (2002), p. 2-83.</ref> Statistics of this kind were a major reason for developing methods to assess the hazards of [[smoke inhalation]].<ref name="P-83" />

== Smoke obscuration ==
Dense smoke affects the choice of exit, the decision to escape, the ability to find the way and the walking speed of occupants.<ref name="P-118">Purser (2002), p. 2-118.</ref> The density of smoke is usually expressed as an optical density, the weakening of light per metre of path, with the unit m−1. In practice this quantity is used more than any other to judge whether people can still find their way in smoke.<ref name="VR-6.4">Van Rossum (2027), §6.4.</ref>

Experiments by Jin in Japan, in which people walked along a smoke-filled corridor, showed how strongly smoke slows movement. In non-irritant smoke, the walking speed fell from about 1.2 m/s without smoke to 0.3 m/s at an optical density of 0.5 per metre. Under these conditions people felt their way along the walls as if they were in darkness.<ref name="Jin1976">Jin (1976), as cited in Purser (2002), p. 2-118.</ref> In irritant smoke, made by heating wood chippings, the speed dropped to the same value at an optical density of only 0.2 per metre, and the experience was more distressing.<ref name="Jin1976" /> Studies of fires in buildings found that about 30 per cent of people turned back rather than pass through smoke, on average at a visibility of about 3 m.<ref name="P-118" />

To turn these findings into a single design check, the handbook divides the optical density of the smoke by a limiting value.<ref name="P-119" /> The limit is 0.2 per metre for small enclosures with short travel distances, which corresponds to a visibility of about 5 m. For large enclosures with long travel distances it is 0.08 per metre, which corresponds to about 10 m.<ref name="P-118" /> The fraction for visual obscuration is then:

<math display="block">\mathrm{FEC}_\mathrm{smoke} = \frac{OD}{0.2} \quad \text{(small enclosures)}, \qquad \mathrm{FEC}_\mathrm{smoke} = \frac{OD}{0.08} \quad \text{(large enclosures)}</math>

{| class="wikitable"
! Symbol !! Description !! Unit
|-
| <math>\mathrm{FEC}_\mathrm{smoke}</math> || fractional effective concentration for visual obscuration || dimensionless
|-
| <math>OD</math> || optical density of the smoke per metre of path || m−1
|}

When the fraction reaches 1, the obscuration is predicted to be severe enough to affect escape attempts seriously.<ref name="P-119" /> The two limits reflect the size of the space. In large spaces, occupants who do not know the building need to see much further to orient themselves and find an exit.<ref name="P-118" />

A simple rule of thumb links optical density to visibility. For objects that reflect light, the visibility in metres is about 1 divided by the optical density, and for objects that emit light, such as illuminated exit signs, about 2.5 divided by it.<ref name="VR-6.5">Van Rossum (2027), §6.5.</ref> With this rule, the small-enclosure limit of 0.2 per metre gives a visibility of 5 m for a reflecting sign and 12.5 m for an illuminated one.

Some sources state smoke density as an extinction coefficient instead. In the pairs of values given in the handbook, the extinction coefficient is about 2.3 to 2.5 times the optical density per metre. An example is 1.15 m−1 against 0.5 per metre.<ref name="P-118" /> A limit quoted on one scale is therefore not directly comparable with a limit quoted on the other.

== Irritant gases ==
Smoke irritants consist of inorganic acid gases, such as hydrogen chloride, and organic compounds, mainly small aldehydes such as formaldehyde and acrolein.<ref name="P-119" /> More than twenty irritants have been found in smoke. The yield of acid gases depends mainly on the chemical elements in the burning material, while the yield of organic irritants depends mainly on the burning conditions. Smouldering fires and flaming fires with too little air tend to produce irritant smoke, while efficient, well-ventilated flaming fires tend to produce non-irritant smoke.<ref name="P-119" />

Sensory irritation is a painful stimulation of the eyes, nose, throat and lungs. It ranges from mild eye irritation to severe pain in the eyes and airways, with tears, involuntary closing of the eyes, coughing and difficulty in breathing.<ref name="P-119" /> Irritant gases are often acid gases, in particular compounds of the halogens chlorine, fluorine and bromine, and they hamper both sight and breathing during escape.<ref name="VR-7.7" />

For hydrogen chloride, concentrations of roughly 100 to 500 ppm are considered painfully irritant and may slow escape without preventing it. At about 1000 ppm and above, the effects may be so severe that escape becomes impossible.<ref name="P-119" /> People differ widely in their response. Most are expected to be affected at about 200 ppm, some already at about 100 ppm, while others tolerate more than 500 ppm without serious effects on escape.<ref name="P-120">Purser (2002), p. 2-120.</ref>

Because all these irritants can damage lung tissue, their effects are assumed to add up.<ref name="P-121" /> The fractional irritant concentration therefore divides the concentration of each irritant at a given moment by the concentration that impairs escape, and adds the fractions of all irritants present.<ref name="P-89" /><ref name="P-121" /> With the limiting concentrations of the handbook, the sum reads:
<math display="block">\mathrm{FIC} = \sum_i \frac{C_i}{C_{i,\mathrm{lim}}} = \frac{C_\mathrm{HCl}}{200} + \frac{C_\mathrm{HBr}}{200} + \frac{C_\mathrm{HF}}{200} + \frac{C_\mathrm{SO_2}}{24} + \frac{C_\mathrm{NO_2}}{70} + \frac{C_\mathrm{acrolein}}{4} + \frac{C_\mathrm{formaldehyde}}{6} + \ldots</math>

{| class="wikitable"
! Symbol !! Description !! Unit
|-
| <math>\mathrm{FIC}</math> || total fractional irritant concentration || dimensionless
|-
| <math>C_i</math> || concentration of irritant <math>i</math> in the breathing zone at the moment considered || ppm
|-
| <math>C_{i,\mathrm{lim}}</math> || concentration of irritant <math>i</math> predicted to impair escape in half the population || ppm
|}

{| class="wikitable"
! Gas !! Impairs escape in half the population (ppm) !! Incapacitates half the population (ppm)
|-
| Hydrogen chloride (HCl) || 200 || 900
|-
| Hydrogen bromide (HBr) || 200 || 900
|-
| Hydrogen fluoride (HF) || 200 || 900
|-
| Sulphur dioxide (SO2) || 24 || 120
|-
| Nitrogen dioxide (NO2) || 70 || 350
|-
| Acrolein || 4 || 20
|-
| Formaldehyde || 6 || 30
|}

The table lists the limiting concentrations together with the concentrations expected to incapacitate half of the exposed population.<ref name="P-121" /> A total FIC of 1 is the tenability limit at which escape is expected to be impaired.<ref name="P-91" /> A total of 0.3 is suggested to allow nearly all exposed people to escape safely, including vulnerable individuals.<ref name="P-121" /><ref name="P-133" />

For incapacitation the chapter gives several values: about 3 to 5 in one passage, a factor of about four or more in another, and about 5 to 10 in the worked example.<ref name="P-91" /><ref name="P-121" /><ref name="P-132" /> In the table above, the incapacitating concentration of each gas is 4.5 to 5 times the concentration that impairs escape. Where acrolein and formaldehyde have not been measured, a term based on a smoke density of 0.5 per metre may be used as an indication of irritancy.<ref name="P-121" /> In small-scale tests, the RD50 of a material's smoke, the concentration that halves the breathing rate of mice, is taken as a total FIC of about 0.5 for humans.<ref name="P-92">Purser (2002), pp. 2-91–2-92.</ref>

== Worked example ==
The handbook illustrates the method with the first six minutes of a fire in an armchair of polystyrene with polyurethane cushions and covers. The chair stood in a room of 39 m³ with an open doorway, and smoke and the main gases were measured in the doorway at a height of 2.1 m.<ref name="P-132" /> The concentrations of hydrogen chloride, acrolein and formaldehyde were estimates, added to illustrate the calculation. In the third minute, the smoke had an optical density of 0.5 per metre, with 150 ppm hydrogen chloride, 2.0 ppm acrolein and 3.0 ppm formaldehyde.<ref name="P-132" /> For a small enclosure, the smoke fraction follows from the limit of 0.2 per metre, and the irritant fraction from the limiting concentrations of the three gases:
<math display="block">\begin{aligned} \mathrm{FEC}_\mathrm{smoke} &= \frac{0.5}{0.2} = 2.5 \\ \mathrm{FIC} &= \frac{150}{200} + \frac{2.0}{4} + \frac{3.0}{6} = 0.75 + 0.50 + 0.50 = 1.75 \end{aligned}</math>

Both values are above 1, so in this minute the smoke would be expected to impair and possibly prevent escape.<ref name="P-133" /> The handbook's table gives a total FIC of 1.83 for the same minute, because its hydrogen chloride term is 0.83 instead of 0.75. The conclusion is the same.<ref name="P-132" />

One minute earlier, the smoke had 0.2 per metre with 50 ppm hydrogen chloride, 0.8 ppm acrolein and 1.2 ppm formaldehyde. The same method then gives an FEC for smoke of exactly 1 and a total FIC of 0.65. The limit of 0.3 for vulnerable people had therefore already been passed in the second minute, as the handbook also concludes.<ref name="P-133" /> According to the rule of thumb for visibility, 0.2 per metre corresponds to about 5 m for a reflecting sign.<ref name="VR-6.5" />

== Use in hazard analysis and design ==
In a hazard analysis, the FEC for smoke, the FIC for irritants and the FED for asphyxiant gases and heat are each plotted against time. A limit is reached when a line crosses 1.<ref name="P-137">Purser (2002), p. 2-137.</ref> In a full-scale test with an armchair fire in the lounge of a house, the ionisation smoke detector responded after 0.5 minutes and the optical detector after 1.5 minutes.<ref name="P-137" /> The line for irritant smoke crossed its limit at about 1.5 minutes. From then on, eye pain, smoke and breathing difficulties would hamper, but probably not prevent, an occupant from leaving the room.<ref name="P-138">Purser (2002), p. 2-138.</ref> The line for obscuration alone, treating the smoke as non-irritant, reached its limit of 2 m visibility one minute later.<ref name="P-139">Purser (2002), p. 2-139.</ref>

In the worked example, the curves rise very steeply once they pass 1. As a result, even if the true incapacitating concentrations were higher than the chosen limits, the predicted time of incapacitation would change only a little.<ref name="P-133" /> The limits apply in the breathing zone of an occupant, so some time passes between ignition and the moment they are reached.<ref name="P-121" /> In the worked example, the head of the occupant was assumed to be in the smoke at all times. A more refined analysis can allow for a lower position in the room when the height of the smoke layer is known.<ref name="P-133" />

The time at which the first tenability criterion is exceeded defines the [[available safe egress time]] in the Australian and New Zealand verification methods.<ref name="AU-10">Australian Building Codes Board (2022), p. 10.</ref><ref name="NZ-17">Ministry of Business, Innovation and Employment (2025), p. 17.</ref> Their criteria use other quantities than concentration fractions. In New Zealand, C/VM2 (second edition, 2025) measures tenability at 2.0 m above the floor with the FED for carbon monoxide, the FED for thermal effects and visibility.<ref name="NZ-17" /> In Australia, the Fire Safety Verification Method Standard (2022) uses a thermal FED of 0.3 and a visibility of 10 m. The visibility limit drops to 5 m in rooms smaller than 100 m² or where the exit is no more than 5 m away.<ref name="AU-10" /> Both documents note that visibility is usually the first criterion to be exceeded.<ref name="AU-10" /><ref name="NZ-17" />

Irritant smoke enters these methods in other ways. The Australian data sheets (2020) handle it through the walking speed of occupants, which is multiplied by a factor of 0.3 at a visibility of 10 m with illuminated signs.<ref name="AU-DS">Australian Building Codes Board (2020), pp. 282–283.</ref> The tenability limit itself is not changed. In the Netherlands, no limits are formally laid down. For escape through mixed smoke in non-enclosed spaces, the explanatory notes to the Dutch Building Decree (Bbl) use a visibility of at least 30 m for illuminated objects. In corridors, a visibility of only 5 m is often accepted.<ref name="VR-7.7" />

== Limits and uncertainty ==
The limits behind the FEC and FIC cannot be verified directly, because the human experiments needed to do so cannot be performed.<ref name="P-121" /> They rest on a small number of human exposures at low concentrations, on accidents, on animal tests and on the judgement of physiologists.<ref name="P-120" /> The proposed values are very similar to those of an expert panel of toxicologists in an international standards committee. Some critics consider them too low for practical design, while other expert groups have proposed similar or even lower limits.<ref name="P-121" /> For hydrogen chloride, the Emergency Response Planning Guideline level 2 (ERPG-2) of the American Industrial Hygiene Association is 20 ppm. This level is meant to protect the ability to take protective action during an exposure of up to one hour, and it is an order of magnitude below the design limit of the handbook.<ref name="P-121" />

Sensitivity varies between people. About 15 per cent of children and 5 per cent of adults have asthma, and people with asthma can react with a severe narrowing of the airways to brief exposures at very low irritant concentrations.<ref name="P-90">Purser (2002), p. 2-90.</ref> A limit that affects half of the population is therefore not a safe value for everyone, which is why the lower total of 0.3 is suggested.<ref name="P-121" /> The assumption that all irritants add up is a simplification, made because data on the effects of irritant mixtures are lacking.<ref name="P-120" />

The smoke limits also involve judgement. Jin suggested an extinction coefficient of 0.15 m−1 for occupants who know the escape route and 0.5 m−1 for those who do not.<ref name="Jin1981">Jin (1981), as cited in Purser (2002), p. 2-118.</ref> Rasbash proposed a visibility limit of 10 m.<ref name="Ras">Rasbash (1975), as cited in Purser (2002), p. 2-118.</ref> Babrauskas suggested an extinction coefficient of 1.2 m−1 for fires in dwellings.<ref name="Bab">Babrauskas (1979), as cited in Purser (2002), pp. 2-118–2-119.</ref> Large spaces, unfamiliar occupants and highly irritant smoke call for stricter limits, and the complexity of the space, the lighting and the visibility of signs also play a part.<ref name="P-118" /> The rule of thumb that converts optical density into a visibility distance is itself only approximate.<ref name="VR-6.5" />

== Common misconceptions ==
An FEC or FIC of 1 does not mean collapse or death. It marks the point at which escape becomes impaired, while incapacitation by irritants is expected only at several times this value.<ref name="P-91" /><ref name="P-132" /> A second misconception is that the fraction behaves like a dose. The FED can only grow during an exposure, but a concentration fraction describes the conditions of the moment and falls again when the concentration drops.<ref name="P-89" /> In the worked example, the hydrogen chloride term fell from 1.39 to 1.11 between the fifth and sixth minutes as its concentration decreased.<ref name="P-132" />

The amount of visible smoke is also a poor guide to irritancy. Some fires produce large amounts of sooty smoke that blocks the view but hardly irritates. In other cases a highly irritant atmosphere has been reported with little or no visible smoke.<ref name="P-119" /> Finally, the fractions for smoke, irritants, asphyxiants and heat are not added into one number. Each hazard has its own line, and a tenability limit is reached when any of these lines crosses 1.<ref name="P-137" />

== See also ==
* [[Visibility in smoke]]
* [[Optical density]]
* [[Haber's rule]]
* [[Oxygen depletion]]
* [[Carbon dioxide]]

== Notes ==
<references />

== References ==
* Australian Building Codes Board. (2020). ''Fire safety verification method data sheets: Handbook annex''.
* Australian Building Codes Board. (2022). ''Fire safety verification method standard 2022''.
* Ministry of Business, Innovation and Employment. (2025). ''Verification method C/VM2: Framework for fire safety design'' (2nd ed.).
* Purser, D. A. (2002). Toxicity assessment of combustion products. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall, Jr., & J. M. Watts, Jr. (Eds.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 2-83–2-171). National Fire Protection Association.
* Van Rossum, E. (2027). ''Introduction to Fire Safety Engineering''. Fire Safety Academy.

[[Category:Smoke, Toxicity & Tenability]]