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19 TABLE 2 The transmittance T of smoke is defined as: EXPOSURE TIME AND INCAPACITATION Maximum Exposure T = I x Io (7) Exposure Temperature Time Without °C °F Incapacitation (min) where: 80 176 3.8 75 167 4.7 70 158 6.0 Io is the intensity of light at the beginning of the path; and 65 149 7.7 Ix is the intensity of light remaining after it has passed 60 140 10.1 through the path length. 55 131 13.6 50 122 18.8 45 113 26.9 The OD per unit distance is related to the transmittance 40 104 40.2 by the following equation: Source: NFPA 502 Standard for Road Tunnels, Bridges, and Other Limited Access Highways. =- ( log10 T ) (8) x TOXICITY The toxicity of fire smoke is determined primarily by a small where: number of gases, which may act additively, synergically, or antagonistically (21). For example, the addition of the influence x is the distance travelled by light (the path length). of CO and hydrogen cyanide (HCN) may be represented by: The attenuation (or extinction) coefficient per unit dis- CO HCN tance K is defined in the same way as the OD, but using A= + (6) ( 50 30 ) ( 50 30 ) Neperian logarithms: LC CO LC HCN where: K=- ( loge T ) (9) X [ ] indicates the actual concentration; LC50CO30 = 4,600 ppm (concentration level at which K = 2.303 (10) 50% of all individuals will die solely from CO after 30 min); and Sometimes the percentage obscuration is used and is LC50HCN30 = 160 ppm (concentration level at which defined as: = 100 (1 - T ) 50% of all individuals will die solely by (11) HCN after 30 min). If A = 1, approximately 50% of the victims will Eq. 8 can then be replaced by die. log10 (1 - 100 ) This relation has been shown to hold for concentrations of = (12) CO and HCN equal to 25%, 50%, and 75% of their respec- x tive 30-min LC50 values. The visibility distance V(m) can be estimated using the Eq. 6 has been termed the fractional summation approach. extinction (or attenuation) coefficient K(m-1) of the air­ An easier approach considers only the maximum allowable smoke mix: concentration for a certain fire. Klote and Milke (22, 23) have presented comprehensive lethal levels for 5 min and 30 min V=A K (13) exposure, although it is evident that different authors propose different values. where: A is a constant between 2 and 6 depending on the signs to SMOKE OBSCURATION LEVELS, VISIBILITY be seen (reflecting or illuminated). Smoke obscuration levels need to be continuously maintained below the point at which a sign internally illuminated at 80 lx AIR VELOCITIES (7.5 fc) is discernible at 30 m (100 ft), and doors and walls are discernible at 10 m (33 ft). Air velocities in the enclosed tunnel need to be greater than or equal to 0.76 m/s (150 fpm) and less than or equal to 11.0 m/s The properties of smoke are commonly expressed in terms (2,200 fpm). The maximum limit is set based on the ability of of transmittance, as well as either optical density (OD) or atten- people to walk in a high air speed environment (NFPA 502 uation coefficient (also called the extinction coefficient) (21). Standard).