Walking speed in smoke

Setup. Subjects wore no air masks and waited in a normally lit room before entering (text below Table 1, p. 13). The corridor was lit (about 80 lx at the floor) or blacked out (0.1–0.5 lx from the sign and the meters), and the two gave the same speeds (p. 15). In the blackout runs the sign also switched from a 10 W fluorescent lamp to three 2.5 V tungsten bulbs (Jin 1972, abstract and p. 13), so the comparison changes corridor light and sign luminance together. Speed came from a wire each subject unwound from a reel, averaged over the whole corridor including stops (pp. 12, 15); K came from two 4 m-path and one 1 m-path light meters 1.5 m above the floor (p. 13).

Scatter. The irritant fit explains almost none of the scatter: at an average K = 0.42 1/m the speeds ranged from 0.37 to 1.1 m/s, mean 0.75 m/s (standard deviation (SD) 0.21). In non-irritant smoke, at an average K = 0.73 1/m, the mean was 0.74 m/s (SD 0.17) (Ch. 63, pp. 2339–2340).

Ranges. Report Fig. 2 has no non-irritant point below about 0.5 1/m; Jin (1997, Fig. 3) redraws the same data. Purser and McAllister’s non-irritant point at K ≈ 0.2 1/m (about 1.1 m/s) sits, in our reading, at the start of Jin’s drawn non-irritant trend line, not on a measured point, and their replotted speeds lie a few hundredths of a m/s below Jin’s. Their stated range 0.2–1.13 1/m is therefore that of the trend line; Jin’s points cover about 0.5–1.13 1/m. In report Fig. 2 the irritant trend line starts near 0.30 1/m and stops near 0.47 m/s, so Ronchi et al.’s “1.0 to 0.3 m/s as K rose from 0.1 to 0.5 1/m” (p. 414) does not follow it; in our inference it follows Jin (1997, Fig. 3), where the non-irritant curve starts near 0.1 1/m and the irritant dotted line falls towards zero.

Darkness. The 0.3 m/s is not a measurement in this experiment. Jin writes that as smoke thickens “the condition becomes very much like walking in darkness (0.3–0.7 m/s)”, citing Togawa (1969) for that range (report p. 14), and calls 0.3 m/s “the speed in darkness shown by a horizontal broken line in Fig. 2”, without a citation (p. 17). Jin (1978, p. 148) ties the 0.3 m/s to Togawa: “the speed in darkness (0.3m/s [19])”, ref. 19 being Togawa (1969), not read, so what Togawa measured or assumed is still unknown. Jin (1978, p. 146) repeats that walking speeds in the lit and the blacked-out corridor showed “no differences” in his Fig. 8. Jin takes the density at which the average speed slows to 0.3 m/s as the maximum for people familiar with the building, “approximately 0.5/m–1.2/m” (p. 17). No non-irritant point in Fig. 2 is below about 0.45 m/s, so the 1.2 1/m end rests on the trend line extended (our reading). In our inference, Ch. 63’s “at an extinction coefficient of 1.15 … approximately 0.3 m/s” (p. 2339) and “has been shown” (p. 2413), Ronchi et al. (p. 415) and Purser (2003, p. 98) all go back to this reference line; the 1.15 1/m itself is not in the report (pp. 12–18). Ch. 63 pairs K 1.15 with OD/m 0.55 in its prose but with OD/m 0.5 in Table 63.5 on the same page; only 0.5 is consistent with base 10.

Allowable smoke density. Two routes lead to Jin’s conclusion. From the minimum visibility proposed by others (3–5 m if familiar, 15–20 m if not) and the rule “Visibility (m) × Extinction coefficient ≈ 2” (p. 17, citing Jin 1971, FRI Report 33), Table 3 gives 0.4–0.7 1/m for familiar people and 0.1 1/m for strangers. From the walks, the density that slows the average speed to 0.3 m/s gives 0.5–1.2 1/m for familiar people, and the density below which irritancy does not affect speed gives 0.2–0.3 1/m for strangers (p. 17). The conclusion merges the two: about 0.4–1.2 1/m for familiar people and 0.1–0.3 1/m for strangers (p. 18). Jin (1978, Table 3, p. 147, and p. 148) repeats Table 3, “where \(C_s \cdot V\) = 2”, without citing FRI Report 33, gives 0.5–1.2 1/m for familiar people and “approximately 0.2/m” for strangers from the walks, and has no merged conclusion; his Table 2 adds Rasbash’s 10 m and 0.2 1/m.

Speed against sign visibility. Report Fig. 4 and Jin (1978, Fig. 9, p. 145) plot walking speed against the distance at which the words of the EXIT sign became legible to each subject: about 3.4–12.8 m and 0.45–1.1 m/s (our reading), with a drawn rising line and no equation. Jin (1978, p. 145) writes that walking speed “will be affected more strongly by the visibility range than the degree of irritation”.

Group walking. Report Fig. 5 and Jin (1978, Fig. 10, p. 146) show Horiuchi’s data, cited secondhand (Horiuchi, Murozaki and Jin 1974, not read): 20 groups of five to seven people led by someone familiar with the building walked a corridor in smoke-bomb smoke of about 0.6 1/m, with drawn mean lines near 1.85 m/s (lit) and 1.57 m/s (blackout) (our reading), “about 1.5 times faster” than Jin’s single subjects (p. 146).

Irritant smoke. The report (p. 13) and Jin (1972, p. 12, Japanese text, our translation) describe burning wood cribs with very narrow spacing; the English abstract of Jin (1972, p. 11) calls the same smoke “generated from smoldering wood (nearly white smoke)”. Purser’s “smoke from non-flaming wood” (2003, p. 98) matches that abstract; Ch. 63’s “heating wood chippings” (p. 2339) may, as our inference, mix it up with the wood-chip furnace smoke of Jin and Yamada (1985, 1989).

Source chain. FRI Report No. 42 (September 1976, p. 12) states that the distance at which the sign became visible was recorded “and at the same time the speed at which each subject managed to walk”, citing ref. 1, Jin (1972); Jin (1972) used the same corridor and the same ten observers (its Table 1 is identical) and reports the sign visibility. Jin and Yamada (1985, §3 and Fig. 3, p. 82) reprint the walking data as “an example data of the experiment … conducted before”, without a citation for the figure; their ref. [5], Jin (1978), is attached to the corridor-task sentence on p. 81; Jin 1978 does contain the corridor figures (Figs. 6–9). Jin (1997, §1.3 and Fig. 3) repeats that section almost word for word and cites it as ref. [2], with pages 79–89; the paper’s header and Crossref give 79–90, and the scan ends at p. 89. Purser (2003) dates Report No. 42 1975; the cover says 1976. Fridolf et al. (2019) name the study Jin 1976 (Fig. 1 legend), Jin 1978/1997 (§3.2.1) and Jin 1979 (Table 2).

Participants. Ronchi et al. (p. 414) report 17 women and 14 men aged 20 to 51. That is the population of Jin and Yamada’s 11 m corridor study of emotional instability (Jin and Yamada 1989, “Subjects”, p. 513; Jin 1997, §2.2). The walking study had ten men aged 23–37 (report Table 1), as Fridolf et al. (2019, Table 2) state.

A third data set. Jin and Yamada (1989) also measured walking speed against K (Fig. 7, p. 517), with smoke from smouldering Japanese cedar crib chips in an electric furnace, set to 1.2 1/m and decaying to about 0.1 1/m over 30 minutes (p. 512, “Experimental condition of the corridor”), under radiant heat. The subjects breathed through a 16-layer towel that removed about 90 % of the smoke and lessened its irritation (pp. 513, 517), so these data do not give a law for unprotected walkers.

Units. Purser does not define OD/m; Ch. 63 defines it as log₁₀(I₀/I) over 1 m (p. 2413). Jin and Yamada (1985, p. 80, footnote) define the extinction coefficient with the natural log; applying that definition to the 1976 data is our inference, hence the factor ln 10.

Range. The upper end, OD/m 0.55 (K ≈ 1.27 1/m), is close to the top of Jin’s “approximately 0.5/m–1.2/m” (p. 17) but matches neither Jin’s 1.2 (OD/m 0.52) nor Ch. 63’s 1.15 (OD/m 0.50); in our inference it comes from Ch. 63’s prose pairing of 1.15 with OD/m 0.55 (p. 2339). It lies beyond Jin’s measured points.

Fit. No fit quality or number of points is given, and the squares in Fig. 1 lie exactly on the line (1.010, 0.888, 0.715, 0.541, 0.454, 0.280 at OD/m 0.13–0.55), so Fig. 1 shows the fitted line, not Jin’s points.

Floor. It is written as an absolute 0.3 m/s (0.25 of the 1.2 m/s unexposed speed that Ch. 63 uses; FRI Report No. 42 gives no such value), while the line reaches 0.28 at OD/m 0.55 and Fig. 1 shows about 0.27.

Participants. 30 men and 16 women, mean age about 22, mostly students (Table 1). The 32 lit runs pool four wayfinding scenarios, 1–4 in Table 3.

Measurement. K is the mean of two laser extinction meters (670 nm, 1 m path, 2.0 m above the floor), averaged over each person’s time in the tunnel (§2.5.1, App. D). The walking speed is the distance each person actually walked, measured from the video on the tunnel plan, divided by the time in the tunnel, stops included (§3.3.1). The speed over the straight-line distance to the chosen exit (the “gross speed”, Fig. 12) was on average 0.88 of it (SD 0.09; Fig. 11). Measured speeds ranged from 0.2 to 0.9 m/s (§3.3.1), although the lit points in Fig. 9 reach only about 0.76 m/s.

Smoke and light. The acetic acid concentration was 10–15 ppm (§2.3). Fridolf et al. (2019, Table 2) call the smoke “semi-irritant”, and Ronchi et al. (2013, p. 421) call the irritation much less severe than in Jin’s experiments. It follows, as our inference, that the regression already includes the effect of this mild irritancy. The ceiling lighting gave 2–21 lx without smoke and 0–8 lx with smoke (§2.2).

Range and scatter. The report’s text gives K ≈ 2–7 1/m (§3.2). The 95 % prediction interval at K = 4 1/m is about 0.2–0.7 m/s (§3.3.2); adjusted \(R^2\) is 0.320.

Other models. With the lighting off (12 runs) the slope was not significantly different from zero (Table D1). A second model with the share of the route walked along the wall fitted better (Eq. 4, Table D2 model 2: α = 0.692 m/s, β₁ = −0.073 m²/s, β₂ = 0.139 m/s per unit share; adjusted \(R^2\) 0.416 against 0.320): walking along the wall raised the speed. For dense smoke (K = 8 1/m) the authors state that a randomly chosen person could walk at anything between 0 and 0.6 m/s (§5), and expect a real population to do worse than their young, fit participants (§3.1.1).

Pooling. The fit combines smoke from real fires with artificial smoke made mildly irritating, which is the pooling the Known limits section warns against; Purser and McAllister do it deliberately, as a conservative envelope.

Behaviour outside the data. The logarithm has no upper bound as \(\alpha_k \to 0\): it exceeds 1 m/s below \(\alpha_k\) ≈ 0.07 1/m (our arithmetic).

Other fits on the same page. Fig. 63.16 also gives logarithmic fits to other combinations of the Jin, Frantzich–Nilsson and Fridolf et al. data (Ch. 63 ref. 55, Interflam 2013); the three that leave out the Fridolf data are “quite similar” (p. 2341). Ch. 63 takes the Frantzich–Nilsson data from their 2004 Human Behaviour in Fire paper (ref. 54), not from report 3126, and its straight-line fit to them, v = 0.7099 − 0.0573 K (\(R^2\) = 0.349), differs slightly from the report’s.

Population values. p. 2341 also suggests drawing each person’s speed from a normal distribution “with a mean from Equation 63.12 and standard deviation of 0.125”; Eq. 63.12 in this edition is the irritant FIC sum, so the reference is probably meant to be Eq. 63.10, and 0.125 differs from the 0.157 given on the same page. For clear air it suggests a mean of 1.2 m/s with SD 0.15 m/s. It compares Frantzich and Nilsson’s mean of 0.45 m/s (SD 0.21) with Jin’s 0.3 m/s in dense smoke, noting that the slowest speed measured by Jin was 0.37 m/s (p. 2341); Frantzich and Nilsson measured 0.2–0.9 m/s.

The visibility constant. A is chosen for each data set from its lighting (§3.3.1); the paper does not list which A was applied to which set. Jin (1970, English abstract, p. 1) gives V = (5–10)/Cₛ for light-emitting and (2–4)/Cₛ for reflecting signs, repeated by Jin and Yamada (1985, p. 81) and Jin (1997, Eqs. 3–4). Jin (1971, Fig. 1) and Jin and Yamada (1985, Fig. 1) draw the line Cₛ·V = 8 for light-emitting signs, which matches A = 8; A = 2 is the lower end of the reflecting range, and Jin (1976, p. 17, citing Jin 1971, FRI Report 33) uses “Visibility (m) × Extinction coefficient (1/m) ≈ 2” to turn the visibility needed for escape into an allowable density. FDS uses C = 3 for reflecting signs by default (see Visibility through smoke). A = 2 is also the constant Frantzich and Nilsson (2003, report Eq. 2) used for lit walls and objects. Jin’s constants come from a chamber lit at 22–180 lx (Jin 1970, Figs. 5–11) and from signs at 40–80 lx (Jin 1971, Figs. 1–2); the σV of 5–8 that Cheung et al. (2026, §4.1, Fig. 8) take from Jin for light-emitting signs refers to 180 lx; in dimmer light the constant for light-emitting signs is larger (see Do the sources conflict?).

The data sets. Jin’s non-irritant data only, Frantzich and Nilsson (2003), Akizuki et al. (2007), Fridolf et al. (2013, 2014), Ronchi et al. (2017) with Fridolf et al. (2015), and Seike et al. (2016) (§3.3). They include an older group (Akizuki et al., mean age 70) and walks of up to 700 m (Table 2). Frantzich and Nilsson’s data are an input to Eq. 2, so the two laws agreeing is not an independent check.

The data range. The points in Fig. 3 span x ≈ 0.3–3 m, with none between about 1.17 and 1.78 m. The value at x = 0, 0.31 m/s, is an extrapolation. In terms of K, x = 0.3–3 m corresponds to K = A/3 to A/0.3 (our arithmetic; each data set was converted with its own A).

Speed definitions. All speeds include pauses. Table 2 codes Frantzich and Nilsson’s speed as “shortest way with pauses”, whereas the report’s Eq. 3 uses the speed along the actual path, about 1/0.88 of the shortest-way speed (report Fig. 11).

Irritancy. The authors call the selected data sets “non-irritant” (§3.3). Table 2 marks Frantzich and Nilsson and Fridolf et al. (2013, 2014) as “semi-irritant” and Ronchi et al. (2017) as non-irritant, while §4 names Fridolf et al. (2013) and Ronchi et al. (2017) as the experiments with acetic acid. They caution that the recommendation may not be conservative in irritant smoke, where Jin saw speeds drop at visibilities of about 5 m, against below 3 m in non-irritant smoke (§4).

The floor. The 0.2 m/s floor is attributed to Purser and McAllister (2016) (§3.3.2); Ch. 63 gives about 0.3 m/s for walking in darkness (pp. 2339 and 2413).

The three design methods. \(w_{\text{smoke free}}\) is 1 m/s for everyone (method 1, Eq. 3); 1.35, 1.10 or 0.85 m/s for medium, slow and very slow walkers (method 2, Eqs. 4–6); or drawn for each person from a normal distribution with mean 1.35 m/s and SD 0.25 m/s, truncated at 0.85 and 1.85 m/s (method 3, Eq. 7). The authors describe the reduction as absolute, because every person loses the same speed, and fractional, because it starts from each person’s own clear-condition speed (§3.3.3 and §4). Worked example: at 2 m visibility, 1.2 m/s becomes 0.86 m/s and 1.0 m/s becomes 0.66 m/s (§3.3.3).

Citation chains. Ronchi et al.’s population of 17 women and 14 men belongs to Jin and Yamada’s 1989 heat-and-smoke study; the walking study had ten men aged 23–37 (FRI Report No. 42, Table 1). Ch. 63’s “has been shown” 0.3 m/s in darkness (pp. 2339, 2413) and Purser’s 2003 floor go back, in our inference, to Jin’s horizontal reference line in report Fig. 2 (p. 17; the report cites Togawa 1969 for a darkness range of 0.3–0.7 m/s, p. 14, and Jin 1978, p. 148, for 0.3 m/s); no non-irritant point in that figure is below about 0.45 m/s. Purser’s stated non-irritant range starts at 0.2 1/m, at the start of Jin’s trend line, while Jin’s points start near 0.5 1/m (our reading of report Fig. 2). The irritant smoke is burning wood cribs in the report and in Jin (1972, 1997), “smoldering wood” in Jin’s 1972 English abstract, non-flaming wood in Purser (2003) and heated wood chippings in Ch. 63. The report is dated September 1976 on its cover; Purser (2003) gives 1975. Jin 1978 runs pp. 135–155; 135–157 in some citations does not match the paper. Fridolf et al. date the walking study 1976, 1978/1997 and 1979, and take a 0.2 m/s floor from Purser and McAllister, who give about 0.3 m/s.

Different measurements. Smoke: real-fire smoke, irritant or not, in Jin; cold artificial smoke with 10–15 ppm acetic acid in Frantzich and Nilsson. Light: 0–8 lx in the smoke-filled Frantzich–Nilsson tunnel. Speed: along the corridor for Jin, along the walked path for Frantzich and Nilsson (about 1/0.88 of the shortest-way speed that Fridolf et al. record). K: Jin’s data end near 1.1 1/m and Frantzich and Nilsson’s begin at 1.9 1/m.

Cheung et al. rebuilt Jin’s 5.5 m chamber (2.4 × 2.4 m cross-section), viewed a light-emitting Landolt “C” through industrial white smoke at 5.5, 10.5 and 15.5 m, and varied the ambient light from 1 to 222 lx (§3). Findings relevant here:

• Jin’s σV range of 5–8 for light-emitting signs refers to 180 lx; at that light they measure 5.3–9.5 at 5.5 and 10.5 m and 4.7–8 at 15.5 m (§4.1, Fig. 8). At 1 lx σV is 7.5–11, and at 22 lx 6–11 (§4.4, Fig. 11), over sign luminances of 128–22 500 cd/m²; at 135–492 cd/m² their §4.3 values give about 6.2–8.4 for seeing the gap of the “C” (our arithmetic; see Visibility through smoke). σV rises with the logarithm of the normalised sign brightness πLₜ/E, so it is constant only for a given brightness.
• At 60 and 22 lx, a sign of the same luminance was seen at about 7 % and 11 % higher extinction in Jin’s data than in theirs (§4.1, §6); the abstract states the direction the other way round.
• The critical extinction coefficient falls by about 40 % for every 5 m added to the viewing distance (§4.3).
• Limits they state: one observer with visual acuity 1.0 who knew the sign’s shape and location, industrial smoke rather than fire smoke, a laboratory sign, and no reflecting signs, so the reflecting range C = 2–4 is not retested (§5).

They identify Jin’s source for the sign experiment as Jin (1970), Visibility through fire smoke (I), with parts II (1971) and III (1972) following; all three are read for Visibility through smoke. FRI Report No. 42 (1976) carries the same English title as “Part 5”, under a different Japanese title (煙中の視程について 第5報).