Establishing safety distances for wildland fires

ARTICLE IN PRESS Fire Safety Journal 43 (2008) 565–575 www.elsevier.com/locate/firesaf Establishing safety distances for wildland fires Luis Zárate, Josep Arnaldos, Joaquim Casal Centre for Technological Risk Studies (CERTEC), Universitat Politècnica de Catalunya—Institut d’Estudis Catalans, ETSEIB, Diagonal 647, 08028 Barcelona, Catalonia, Spain Received 13 February 2007; received in revised form 18 December 2007; accepted 7 January 2008 Available online 5 March 2008 Abstract In wildland fires, safety zones should be considered concerning people who are intervening in the emergency or attempting evacuation. To establish such zones, the solid flame model, together with the view factor calculated from a previously selected equation, was used to estimate the thermal radiation emitted by the flame front of a wildland fire. After determining the flame heights yielded by the 13 fuel types in the Rothermel classification for surface fires, and for crown fires in various Mediterranean forests, the thermal radiation was calculated for each scenario as a function of the distance. These data, together with threshold values for the vulnerability of people (protected or unprotected) and houses to thermal radiation, allowed for a set of safety distances for different situations to be obtained. These safety distances can be applied both in territory planning and in emergency situations. r 2008 Elsevier Ltd. All rights reserved. Keywords: Wildland fire; Safety distance; Thermal radiation; Flames 1. Introduction The mathematical modelling of wildland fires has traditionally had two main objectives: firstly, the prediction of the velocity at which a fire will spread and secondly, the estimation of the heat released from the flame front of the fire. One of the most interesting possibilities of the prediction of the thermal radiation emitted by wildland fires is the establishment of safety distances, which allow for the definition of safety zones both for people (firefighters and the general population) as well as for houses and equipment. Within these safety zones, people extinguishing fires can work without endangering themselves and, furthermore, these zones provide safe evacuation routes. Such zones must be established on the basis of the thermal radiation that, in the event of fire, is foreseen to reach a given position, as well as on vulnerability data (maximum tolerable thermal radiation) for the people or equipment that will be subjected to the radiation. Corresponding author. Tel.: +34 934016704; fax: +34 934011932. E-mail address: joaquim.casal@upc.edu (J. Casal). 0379-7112/$ - see front matter r 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.firesaf.2008.01.001 Safety distances are widely used in a variety of fields for both preventive planning and emergency interventions. For example, they are commonly applied throughout the chemical process industry, not only in preventive terms in plant design (the minimum separation required between certain pieces of equipment in the event of a fire) and plant operation, but also in terms of emergency planning. Though the concept of safety distances is also used in dealing with wildland fires, quantitative approaches to determining such distances have been addressed by very few authors. This is probably due to the fact that predicting the thermal radiation from wildland fires is more complicated and less accurate than in the case of hydrocarbon combustion (whose properties are usually much better defined). Furthermore, the features of wildland fires can change due to the ground features (slope) and meteorological conditions: for example, through mechanisms such as spotting, wind can propagate the fire to locations remote from the flaming front. Nevertheless, despite these difficulties, the establishment of safety distances can be highly useful in such fields as regional planning (in terms of the construction of houses or roads in or near forests) or emergency planning. ARTICLE IN PRESS 566 L. Zárate et al. / Fire Safety Journal 43 (2008) 565–575 Notation Ep Eb F FB H L NMSE Qr Ta Tf average emissive power of the flame, kW/m2 emissive power of the black body, kW/m2 view factor, dimensionless fractional bias, dimensionless flame height, m flame length, m normalized mean square error, dimensionless radiative heat flux transmitted per unit area, kW/m2 atmospheric temperature, K flame temperature, K A considerable research effort has been done in this field, and diverse authors have published quantitative proposals. Tran et al. [1] developed the ‘‘Structure Ignition Assessment Model’’ (SIAM), later discussed by Cohen [2]. Cohen and Saveland [3] applied this model to reduce the damage in the wildland–urban interface. Ahern and Chladil [4] analysed the damage from diverse bushfires as a function of distance. Gettle and Rice [5] proposed criteria for determining the safe separation between structures and wildlands. Butler and Cohen [6] proposed safety zones for firefighters (assuming them to be completely protected, including their necks and heads). These authors presented a theoretical model describing the net radiant energy transfer from a fire of a specific height to a standing firefighter; the predictions from the model were then compared to four cases of wildland fire entrapment, with good agreement. As a rule of thumb, they suggested a minimum distance between the firefighter and the fire of four times the average height of the flames; in a later paper [7], the same authors stated that their model underestimated thermal radiation within 10 m of the flame. Cohen [8] arrived at the conclusion that home ignitions were not likely unless flames and firebrand ignitions occurred within 40 m of the structure, although more recently the same author reduced this distance, as a general criterion, to 30 m [9]. There are also several other references, such as certain government regulations; the Generalitat (Autonomous Government) of Catalonia (1995) established a 25-m-wide perimeter protective zone in the wildland–urban interface for houses located less than 500 m from forests. However, if one analyses all the information available in this field, it is evident that there is a significant gap concerning the specific design of safety distances or zones. This paper presents a methodology for establishing such distances on the basis of the conditions that could potentially influence fires: firstly, the type and condition of vegetation, and secondly, the worst meteorological conditions (in terms of atmospheric humidity and wind) that could reasonably be expected. u x y z wind speed, m/s coordinate on the x-axis; distance, m coordinate on the y-axis; distance, m coordinate on the z-axis; distance, m Greek letters a b e g s t angle, deg (Fig. 2b) angle, deg (Fig. 2b) flame emissivity, dimensionless angle, deg (Fig. 2b) Stephan–Boltzmann constant (kW m2 K4) atmospheric transmissivity, dimensionless 2. Prediction of thermal radiation To determine safety distances, the heat flux from the fire must be known. In the case of wildland fires, an essential component of this is thermal radiation. Convection is not usually taken into account concerning the effects on people and structures. As stated by Gettle and Rice [5], no references in technical literature suggest that convective transfer to structures would be as significant heat as radiative heat transfer from flames at a distance from a solid surface. Convective transfer is important to transfer heat to the canopy, but not from the point of view of heat transfer to structures located at a certain distance from fire. A number of methodologies have been proposed for calculating the thermal radiation emitted by fires [5,10–14]. A method that has been used by some authors [6,15] in the field of wildland fires is the solid flame model. This model is widely used in the chemical process industry to predict the behaviour of hydrocarbon pool fires [16]. The authors’ experience [17] with relatively large-scale fires of this type (of up to 28 m2 in surface area) has confirmed the good results obtained when applying it. Therefore, the solid flame model was chosen for the estimation of the thermal radiation. The solid flame model considers the visible flame to be a geometrical body that emits radiative energy uniformly throughout its entire surface area; the nonvisible zones of the flame are usually not taken into account (in fact, these zones emit significantly less than the average radiation emitted by the visible flame). The thermal radiation reaching a target located a distance x from the flames is estimated using the following expression: Qr ¼ E p tF . (1) The emissive power of the flame (Ep) is the amount of heat emitted by the unit surface of the flame; it depends on the luminosity of the flame and can be estimated using theoretical or semi-empirical expressions [16]. It is ARTICLE IN PRESS L. Zárate et al. / Fire Safety Journal 43 (2008) 565–575 567 calculated as E p ¼ E b , (2) where e is the flame emissivity and Eb is the emissive power of the black body, which is determined using the following expression: E b ¼ sT 4f . (3) The atmospheric transmissivity (t) is the fraction of the thermal radiation that is transmitted through the atmosphere; it is a function of the atmospheric humidity, the concentration of carbon dioxide and the distance, and can be calculated using semi-empirical equations. Once these two parameters have been determined, only the view factor is required in order to apply the solid flame model. The emissive power has been calculated assuming that e ¼ 1. This implies the worst situation, as in practice the existence of black smoke in the flame would decrease the average value of Ep. However, due to the lack of accuracy in establishing the fraction of flame surface covered by black smoke, this conservative approach seems more convenient. 3. View factor The view factor is a geometrical parameter which determines the fraction of radiative thermal energy emitted by a surface that reaches a receptive surface. Its value depends on the relative position of both surfaces and can be determined using analytical equations for simple geometries. Determining the view factor requires that a shape be assumed for the flame front. In an approximate way, the different flame shapes can be generalized into two simplified types: either a flame front with a plane surface (corresponding to a parallelepiped) (Fig. 1a), or a cylindrical flame (Fig. 1b). The former corresponds to a fire front and the latter to the combustion of, for example, one tree. Though the second scenario may be useful in analysing the thermal radiation emitted by an ignited tree to the rest of the forest, the establishment of safety distances requires the first one to be used. Although the use of these two types imply a simplification of the scenario, a series of variables (flame angle, ground slope) are in fact taken into account in the view factor [5]. Similar simplifications have been applied by Sullivan et al. [12] with adequate results. Taking into account that the two targets to be considered in this study were the vertical surfaces of a person or a house, two geometrical configurations were selected: (a) an emitting source with a finite rectangular area, vertical and parallel to a differential receptor element located in front of one of the emitting surface corners (Fig. 2a) and (b) an emitting source with a finite rectangular area, parallel to a differential receptor element located in front of its centre (Fig. 2b). Fig. 1. (a) Flame front with a plane surface. (b) Cylindrical flame. A set of equations for calculating the view factor was selected from equations proposed by different authors. Table 1 shows these equations, together with a geometric scheme. It should be noted that, due to the complexity of these expressions, typographic errors are relatively frequent, as commented [18] in the literature. Fig. 3 shows the view factors calculated using these four equations for a scenario in which a rectangular flame front irradiated a receiving surface located at a distance of 15 m. It can be seen that the trend is practically the same in every scenario, although there is a significant divergence between the results obtained using the McGuire2 equation [19] and the others. McGuire2 gives significantly higher values, due to the different position of the target with respect to the flame front, while the other three give very similar results; those from McGuire1 [19] and Hollands [20] were practically the same. The view factor decreases in every scenario as the distance between the two surfaces increases, the highest values being obtained at x/Ho2. In other words, at a distance between the flame front and the target approximately twice as great as the flame is high, the values of the view factor can be assumed to be low. Out of these equations, the McGuire2 equation [19] was finally selected, as—due to the geometrical arrangement assumed—it gave the most conservative results. Furthermore, the fact that it considers a target located exactly in ARTICLE IN PRESS 568 L. Zárate et al. / Fire Safety Journal 43 (2008) 565–575 þ b  g in itt ce m E urfa s H Fh Fv F θ z y target x x z (-y1 , z2) Emitting surface γ (y2 , z2) α β x normal (-y1, -z1) x target y (y2, -z1) Fig. 2. (a) Emitting source with a rectangular area, vertical and parallel to a differential receptor element located in front of one of the emitting surface corners (position assumed in the equations of McGuire1, Hollands and TNO). (b) Emitting source with a rectangular area parallel to a differential receptor element located in front of its centre (position assumed in the equation of McGuire2). 0 1 x cos g B y2 y1 C qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi @tan1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi þ tan1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi A 2 2 2 2 2 2 z1 þ x z1 þ x 2p z1 þ x 0 1 x cos g B y2 y1 C qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi @tan1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi þ tan1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi A. 2 2 2 2 2 2 z2 þ x z2 þ x 2p z2 þ x (4) Fig. 4 shows the variation in the view factor for different distances (calculated using Eq. (4)) as a function of the height of the flame; a flame front width of 20 m and a maximum flame height of 40 m were assumed. The target is located at a height equivalent to 50% the height of the flame, i.e. a height ranging from 0.5 to 20 m. The thickness of the flame was assumed to be 2 m, which justifies, in the solid flame model, the assumption that emissivity is equal to unity [21,22]. This value was also assumed by Butler and Cohen [6]. In Fig. 4 the target is located at the worst position, i.e. at a height ¼ H/2. As it can be observed, for a target located at a given distance, the view factor increases with the flame height. The variation is more significant at lower values and decreases as the flame height increases. Furthermore, the view factor also decreases as the distance between both surfaces increases: the greater this distance, the smoother the variation in F as a function of the flame height. Of course, Fig. 4 could also be obtained for other arrangements as, for example, a person facing the flame front on ground level (i.e. for a point located at a height of approximately 1.7 m); the corresponding value of the thermal radiation would be lower than that corresponding to the aforementioned worst case. 4. Variation of incident radiant heat flux as a function of distance front of the flame front means that it implies the worst possible situation (Fig. 2b). The analytical equation proposed by McGuire is as follows: F 12 ¼ 1 0 x cos a z2 z1 C qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi B @tan1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ tan1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiA 2 2 2 2 2 2 y1 þ x y1 þ x 2p y1 þ x 1 0 x cos a B z2 z1 C qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi @tan1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ tan1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiA 2 2 2 2 2 2 y2 þ x y2 þ x 2p y2 þ x   9 8 y2 > > z2 ffi z1 ffi 1 pffiffiffiffiffiffiffiffiffi > > pffiffiffiffiffiffiffiffiffi ffi tan1 pffiffiffiffiffiffiffiffiffi þ tan > > 2 2 2 2 2 2 > > y2 þx y2 þx y2 þx > > > > > > > >   > > > > > y1 z2 ffi z1 ffi > 1 pffiffiffiffiffiffiffiffiffi 1 pffiffiffiffiffiffiffiffiffi > þ pffiffiffiffiffiffiffiffiffi > ffi > > tan þ tan > > 2 2 2 2 2 2 < = y1 þx y1 þx y1 þx cos b    > > 2p > y2 y1 > z2 > > þ pffiffiffiffiffiffiffiffiffi þ tan1 pffiffiffiffiffiffiffiffiffi tan1 pffiffiffiffiffiffiffiffiffi > > > z22 þx2 z22 þx2 > z22 þx2 > > > > > > > >   > > > > > > y y z 1 pffiffiffiffiffiffiffiffiffi 1 pffiffiffiffiffiffiffiffiffi > > 2 1 1 p ffiffiffiffiffiffiffiffiffi > > þ tan tan þ : ; 2 2 2 2 2 2 z þx z þx z þx  1 1 1 The following conservative assumptions were made in the application of the solid flame model: atmospheric transmissivity ¼ 1, average flame temperature ¼ 1200 K (as assumed by other authors; see, for example [6]), atmospheric temperature ¼ 295 K. Fig. 5 shows the results obtained for the geometric arrangement in which the differential target surface was located in front of the centre of the emitting surface and parallel to it (Fig. 2b). A front flame width of 20 m was assumed [7] and the flame heights ranged from 1 to 40 m; the zone of interest has been zoomed in the insert. The figure clearly shows how the radiant heat flux (RHF) that reaches the target decreases as the distance increases, and that its influence is greatest at small distances. Of course, the thermal radiation increases with the height of the flames. The overall behaviour of the RHF is summarized in Fig. 6. The zone nearest the flame front (Zone A) shows a negative slope that is higher than the slope in Zone B, and Zone C has the lowest slope. The most significant change occurs in Zone B, which is in fact a zone of transition ARTICLE IN PRESS 569 L. Zárate et al. / Fire Safety Journal 43 (2008) 565–575 Table 1 Equations for the calculation of the view factor Geometrical arrangement z Author Description TNO [10] Emitting source with a finite and vertical surface parallel to the receiving element Hollands [20] Rectangular emitting source parallel to a differential element that can be sloped with respect to the normal Rectangular emitting source parallel to the receiving element (0, z 2) g in itt ce Em rfa su (y2, z 2) ( 0, 0 ) Receiving element x y1 = z1 = 0 x (y2, 0) y McGuire [19] (McGuire1) z g in itt ce Em urfa s (y , z ) A 2 McGuire [19] (McGuire2) (-y1, z2) B Rectangular emitting source parallel to a differential element that can be sloped with respect to the normal and moved in front of the source Receiving element x 2 D (-y1, -z1) x C y (y2, -z1) Angles a, b and g must be considered positive in the direction of coordinates x, y, z 1 0.5 McGuire1 [19] and Hollands [20] McGuire2 [19] TNO [10] 0.8 0.3 View factor View factor 0.4 x=5m x = 20 m x = 10 m x = 25 m x = 15 m x = 40 m 0.2 0.6 0.4 0.1 0.2 0.0 0 1 2 3 4 5 x/H Fig. 3. View factor for a rectangular flame front and a receptor element located at 15 m (flame width ¼ 20 m). between the other two. This means that small changes in distance are very significant while the target is near the flames (Zone A), while they are less important in Zone B and practically negligible in Zone C. That is to say, though 0 0 10 20 H (m) 30 40 Fig. 4. View factor calculated with Eq. (4) (flame width ¼ 20 m). The target is located at the worst position (height ¼ H/2). a variation of a few metres in Zone A can determine whether a victim will suffer serious injury, in Zone C this variation is most likely irrelevant. ARTICLE IN PRESS 570 L. Zárate et al. / Fire Safety Journal 43 (2008) 565–575 15 120 RHF (kW/m2) . 100 RHF (kW/m2) 80 10 5 60 0 0 10 20 30 40 40 50 60 70 80 H=1m H = 30 m H=5m H = 40 m H = 10 m H = 20 m x (m) 20 0 0 20 40 60 80 100 x (m) 120 140 160 180 200 Fig. 5. Thermal radiation as a function of the distance for diverse flame heights (differential target surface located in front of the centre of the emitting surface and parallel to it). The inset shows the zone of major interest (flame width ¼ 20 m). 120 108.5 100 Zone B Zone C RHF (kW/m2) RHF Zone A Zone of danger for people without protection 80 60 42.0 40 20 12.8 5.4 4.7 Distance between flame and receiving target 0 Fig. 6. Variation of the thermal radiation flux as a function of distance. The RHF for different scenarios can be seen in Figs. 7 and 8. These figures assume a flame front of 20 m and flame heights of 5 and 15 m, respectively (the geometric arrangement is the same as that in Fig. 2b). The variation in the thermal radiation reaching the target follows the same trend as the view factor, there being a significant variation in the radiation at short distances. To determine the flame heights that are representative of different wildland fire scenarios, first a sensibility analysis of fireline intensity was performed using the Nexus code [23]. Nexus uses the Microsoft Excel code to simulate the behaviour of fires and considers the fuel models proposed by Rothermel [24] and modified by Albini [25] and Anderson [26]. Then, flame heights were calculated by Nelson and Adkins’ equation [27], considering both fireline intensity and wind speed. 2.2 1.4 8 10 0 2 4 6 x/H 1.0 12 Fig. 7. Thermal radiation flux for a rectangular flame front 20 m wide and 5 m high (equation of McGuire2). To perform this analysis, severe conditions were assumed in terms of flame generation and propagation (conditions corresponding to a severe summer: high temperature, wind and low humidity contents in air and fuel; see Table 2). Two different situations were studied, which corresponded to surface fires and crown fires, respectively. Taking into account that the wind velocity is variable, as are the fluctuating and turbulent features of the flame front, establishing the height of the flames at any given instant is extremely complex; in fact, this height ranges from the values estimated for the length to the height of the flame itself. Another parameter which is influenced by the tilt of the flame is the view factor. ARTICLE IN PRESS 571 L. Zárate et al. / Fire Safety Journal 43 (2008) 565–575 The results obtained for surface fires (flame length and flame height) for each scenario are summarized in Table 2. As is well known, the length of a flame increases with the wind speed. Although rather severe conditions were assumed, if compared to crown fires the flame lengths are relatively small; the greatest length was 13 m, while the shortest one occurs in the scenario in which fuel type number 8 was used (0.7 m at wind speeds of 14 m/s). As for crown fires, we were not able to find any specific data on the height of the flames in the literature; what information was available was limited. A survey of experienced firefighters yielded flame heights values ranging from 2.5 to 3.5 times the height of the trees. Therefore, in the absence of a better criterion, flame heights in crown fires were arbitrarily assumed to be three times the average height of the trees. 5. Validation of the model To test the proposed model, it has been compared with the data published by different authors. Fig. 9 shows the agreement, for different flames heights, between the model and the data obtained by Butler and Cohen [7] when burning square surfaces which side ranged between 75 and 150 m (Jack pine, 12 m height; sensors located at 1.2 m above the ground). The RHF has been calculated for a height of 1.2 m above ground. As it can be seen, except for the value corresponding to the RHF at a distance of 10 m with a flame height of 20 m, the agreement between the model and the experimental data is fairly good. In Fig. 10 the model has been compared with the data from Knight and Sullivan [13], obtained in an experimental 70 120 115.7 100 50 83.4 Zone of danger for people without protection 80 RHF (kW/m2) RHF (kW/m2) Proposed model Butler and Cohen [7] H = 17 m H = 17 m H = 20 m H = 20 m H = 30 m H = 30 m 60 60 40 30 20 34.2 20 40 10 15.3 6.6 4.3 4.7 3.0 0 0 0 1 2 x/H 3 0 4 10 20 30 40 50 60 70 x (m) Fig. 8. Thermal radiation flux for a rectangular flame front 20 m wide and 15 m high (equation of McGuire2). Fig. 9. Agreement of the proposed model with Butler and Cohen [7] data (radiant heat flux (RHF) calculated for a height of 1.2 m). Table 2 Values of flame length and height for the 13 fuel types used by Nexus Type of fuel u (m/s) 0 1. Short grass (1 ft) 2. Timber (grass and understory) 3. Tall grass (2.5 ft) 4. Chaparral 5. Brush 6. Dormant brush, hardwood slash 7. Southern rough 8. Closed timber litter 9. Hardwood (long-needle pine) litter 10. Timber (litter and understory) 11. Light slash 12. Medium slash 13. Heavy slash 3 6 8 11 14 Lf (m) H (m) Lf (m) H (m) Lf (m) H (m) Lf (m) H (m) Lf (m) H (m) Lf (m) H (m) 0.4 0.6 1.1 1.8 0.5 0.6 0.5 0.2 0.4 0.6 0.4 1.1 1.5 0.4 0.6 1.1 1.8 0.5 0.6 0.5 0.2 0.4 0.6 0.4 1.1 1.5 0.8 1.6 3.5 4.5 1.8 2.0 1.8 0.3 0.7 1.8 0.9 3.4 4.1 0.1 0.5 2.8 5.0 0.6 0.8 0.6 0.01 0.1 0.7 0.2 2.4 3.8 3.4 4.0 5.1 6.9 4.3 4.2 4.1 0.4 2.9 5.0 4.2 6.3 7.2 1.1 1.6 2.9 6.2 1.9 1.7 1.7 0.02 0.8 2.8 1.8 4.9 7.0 4.6 5.6 6.2 8.7 5.9 5.6 5.6 0.5 5.4 7.0 6.1 8.4 9.6 1.5 2.4 3.1 7.3 2.8 2.4 2.5 0.02 2.2 4.2 3.1 6.7 9.2 5.4 6.5 7.2 10.3 6.9 6.5 6.6 0.6 6.3 8.2 7.2 9.9 11.3 1.6 2.5 3.3 7.8 2.9 2.6 2.6 0.02 2.3 4.5 3.3 7.1 9.9 6.1 7.3 8.2 11.7 7.8 7.4 7.4 0.7 7.1 9.3 8.1 11.2 12.9 1.7 2.7 3.6 8.5 3.2 2.8 2.8 0.02 2.5 4.9 3.5 7.7 10.7 One-hour moisture content 3%; 10-h moisture content 4%; 100-h moisture content 5%; moisture content of live fuel: 100%; moisture content of foliage: 70%. ARTICLE IN PRESS 572 L. Zárate et al. / Fire Safety Journal 43 (2008) 565–575 80 Table 3 Agreement of analyzed models with Butler and Cohen data [7] Knight and Sullivan [13] Model Butler and Cohen [6] Proposed model (McGuire2) NMSE FB 0.376 0.467 0.134 0.205 RHFcal (kW/m2) 60 40 Table 4 Agreement of analyzed models with Knight and Sullivan data [13] Model OB [12] STF [13] Proposed model (McGuire2) NMSE FB 0.121 0.263 0.016 0.004 0.004 0.013 20 0 0 20 40 RHFexp 60 80 (kW/m2) Fig. 10. Agreement of the proposed model with Knight and Sullivan [13] data. setup in which a set of propane burners simulated a fire front [28]. In this case, due to the wide range in the experimental variables, a direct comparison between the experimental data and the values predicted by the model has been chosen. The agreement is even better than in the previous case. This must be attributed to the fact that the data from Butler and Cohen [7] were obtained in real fires and, therefore, their geometry is not so well defined as in the simulated fires used by Knight and Sullivan [13]. Furthermore, a statistical analysis has been performed comparing the agreement between the experimental data from the aforementioned authors and the values predicted by the models proposed by Butler and Cohen [6], Sullivan et al. [12] and Knight and Sullivan [13]. To perform this analysis the normalized mean square error (NMSE) (a measure of the correlation degree) and fractional bias (FB) (which indicated the degree of deviation) have been used. These two parameters are defined by the following expressions: NMSE ¼ FB ¼ n 1X ððRHF exp Þi  ðRHF cal Þi Þ2 , n i¼1 ðRHF exp Þi  ðRHF cal Þi n 1X ðRHF exp Þi  ðRHF cal Þi 2 . n i¼1 ðRHF exp Þi þ ðRHF cal Þi (5) (6) The values of NMSE and FB for the different models can be seen in Tables 3 and 4. It can be observed that the proposed model has a better correlation and a smaller deviation with respect to the experimental values from Butler and Cohen [7] than the model proposed by these authors [6] (Table 3). The comparison with the data published by Knight and Sullivan [13] shows that the model proposed in this work has a better agreement than Table 5 Consequences of diverse thermal fluxes [16] and thermal radiation threshold values Thermal radiation (kW/m2) 1.4 1.7 2.1 4.0 4.7 7.0 10.0 11.7 12.6 25.0 37.5 Effects Harmless for persons without any special protection Minimum required to cause pain Minimum required to cause pain after 60 s Causes pain after an exposure of 20 s (first degree burns) Causes pain in 15–20 s and burns after 30 s Maximum tolerable value for firefighters completely covered protected by special Nomex protective clothesa Certain polymers can igniteb Thin steel (partly insulated) can lose mechanical integrity Wood can ignite after a long exposure; 100% lethalityc Thin steel (insulated) can lose mechanical integrity Damage to process equipment and collapse of mechanical structures a Butler and Cohen [6]. Lilley [30]. c Crocker and Napier [29]. b the opaque box model (OB) proposed by Sullivan et al. [12] and has practically the same accuracy than the semitransparent flame model (STF) proposed by Knight and Sullivan [13] (Table 4). 6. Vulnerability to thermal radiation Once the effects of thermal radiation (as a function of the distance) are calculated, the consequences for people or houses can be estimated using vulnerability models or threshold values. A set of values proposed by different authors [6,16,29,30] were selected to represent thermal radiation. Table 5 shows the varying values of heat flux and the corresponding effects. ARTICLE IN PRESS 573 L. Zárate et al. / Fire Safety Journal 43 (2008) 565–575 The ‘‘maximum tolerable value’’ of heat flux for people is considered to be approximately 4.7 kW/m2. At this heat flux the minimum time before pain is felt (assuming unprotected skin) is approximately 13 s, and 40 s can lead to second-degree burns. Generally speaking, it is maintained that no pain is caused—regardless of the exposure time—by thermal fluxes lower than 1.7 kW/m2. If a victim is wearing clothes that are resistant to thermal radiation, these act to reduce the surface of the body that is exposed: it is generally accepted [16] that in such a case only 20% of the body is irradiated. This 20% comprises the head (7% of the body surface), the hands (5%) and the arms (8%). Of course, the situation is quite different if the person is specially protected (such as in the case of a firefighter), in which case it is assumed that the whole body is protected from thermal radiation. On the contrary, if the clothes do catch flame, their combustion will cause severe burns. wearing protective garments and houses. Table 7 shows the safety distances for crown fires for the same scenarios. These distances have been calculated for a flame width of 20 m (the same as considered by Butler and Cohen [7]). In practice, wider values do not increase significantly the thermal radiation at the distances of interest (Fig. 11). Of course, these values have been established by taking into account just the thermal radiation from the flames. The effect of eventual spotting has not been considered. As was to be expected, in every scenario the maximum safety distance from fires of each type of fuel is that required by people without any protection, which is practically twice that required by wooden houses. The Table 7 Safety distances for persons and houses (crown fires) Type of three Safety distances (m) 7. Determination of safety distances Persons The maximum tolerable values of thermal radiation for people—without protection—(4.7 kW/m2) and houses (10 kW/m2) were taken from Table 5. For houses, the possibility of their having been built using commonly used plastic materials (expanded polyurethane, polystyrene, PVC, etc.) was considered. By taking into account the values in Table 5 as well as the estimated values for thermal radiation for the different types of fuel as a function of distance, it was possible to determine the minimum safety distances required for the various scenarios considered. Table 6 shows the safety distances for surface fires for unprotected people, people Pine tree (Pinus sylvestris) Pine tree (Pinus nigra) Pine tree (Pinus halepensis) Evergreen oak (Quercus ilex) Spruce (Abies alba) Houses Without protection With protection Plastic Wood 77 62 51 45 74 71 60 57 49 47 43 41 60 49 40 35 98 79 65 56 120 Width = 20 m Width = 30 m Table 6 Safety distances for persons and houses (surface fires) Persons 1. Short grass (1 ft) 2. Timber (grass and understory) 3. Tall grass (2.5 ft) 4. Chaparral 5. Brush 6. Dormant brush, hardwood slash 7. Southern rough 8. Closed timber litter 9. Hardwood (long-needle pine) litter 10. Timber (litter and understory) 11. Light slash 12. Medium slash 13. Heavy slash a Rothermel fuel types [24]. 100 Safety distances (m) Houses 80 Without protection With protection Wood Plastic 15 32 11 26 7 18 9 21 35 43 35 32 28 34 28 26 20 25 20 18 23 28 23 21 32 10 32 26 7 26 18 4 18 21 6 21 37 30 21 24 35 41 44 28 33 36 20 24 26 23 27 30 RHF (kW/m2) Type of fuela 60 40 20 0 0 10 20 30 40 50 x (m) Fig. 11. Thermal radiation as a function of the distance for two flame widths (differential target surface located in front of the centre of the emitting surface and parallel to it. Flame height ¼ 20 m). ARTICLE IN PRESS 574 L. Zárate et al. / Fire Safety Journal 43 (2008) 565–575 safety distances for people without any protection are interesting for their use in planning evacuation routes. The value to be taken into consideration regarding houses should be that which corresponds strictly to houses themselves, as presumably their inhabitants will have been evacuated or will be protected from the thermal radiation by the house. Taking into account the fact that the convection flux has not been considered, a 20% increase in the values of the safety distances in Tables 6 and 7 is recommended. 8. Conclusions Although a number of authors have studied the thermal radiation emitted by wildland fires, very few have used this information as a basis for establishing zones in which people—both people who are in the process of fighting against the fire and those who are attempting evacuation— or houses are safe in the event of fire. In this study, thermal radiation was estimated using the solid flame model, together with a view factor obtained from a previously selected equation. The resulting values were applied in the determination of safety distances. For surface fires, flame heights were estimated, at different severe meteorological conditions, for each of the 13 types of fuel proposed by Rothermel. The thermal radiation was then calculated as a function of the distance. These values, together with values for the vulnerability to thermal radiation of people (protected or unprotected) and houses, allowed for the establishment of safety distances (Table 6). A similar method was followed for crown fires. Due to the lack of adequate literature data, the average height of the flames was obtained from a survey of experienced firefighters. The safety distances obtained (Table 7) are, of course, higher than the distances required by surface fires. In houses, plastics (polyurethane, PVC, etc.) and wood were determined to be the most vulnerable building materials. Plastics were more susceptible to fire than wood, and required safety distances were between 12% and 17% higher than those required by wood. Safety distances for people without any protection are, generally, 22–25% higher than those needed by people with adequate protection. 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