Horizontal track movement

The relationship between the velocity of people in the flow V(D) and its density D is determined depends on the profile of people and is presented in [1] and [2].

Test group description

The scenario is a corridor 4 m wide and 50 m long, with an exit at one end. A registering device is located in the middle of the corridor. There are such a number of people in the corridor to provide the necessary density of accommodation. The start time of movement of all people is zero. The time of the last person passing through the registering device, calculated using the Fenix+ 3 program, is compared with the time determined by the formula:

$$ t(D) = \frac{0.5 \cdot L}{V(D)}(1) $$

where L is the corridor length and V(D) is the speed. (An explanation of why it is the time for the last person to pass through the recorder, rather than the entire corridor, that is being compared is provided in the Analyzing Results section) The flow density is determined by the formula:

$$ D = \frac{Nf}{S} (2)$$

where N is the number of people in the corridor, S is the area of the corridor, and f is the area of the horizontal projection of a person. Projects were developed for each contingent of people. Each project consists of several scenarios (each scenario corresponds to a certain flow density).

Expected results

The time of the last person passing through the recorder coincides with the time calculated by formula (2). Modeling results

Test_001 People profile “Females 30-50 years old [IMO]”

Movement of people flow of “Females 30-50 years old [IMO]” profile horizontally.

(a) Flow density 0,01 m²⁄m² (b) Flow density 0,05 m²⁄m² (c) Flow density 0,1 m²⁄m² (d) Flow density 0,15 m²⁄m² (e) Flow density 0,20 m²⁄m² (f) Flow density 0,25 m²⁄m² (g) Flow density 0,3 m²⁄m² (h) Flow density 0,35 m²⁄m² (i) Flow density 0,4 m²⁄m² (j) Flow density 0,45 m²⁄m² (k) Flow density 0,5 m²⁄m² (l) Flow density 0,6 m²⁄m² (m) Flow density 0,7 m²⁄m² (n) Flow density 0,8 m²⁄m² (o) Flow density 0,9 m²⁄m²

Flow density, m²/m²	Number of people	Movement time, s (Fenix+ 3)	Movement time, s (Expected)	Deviation, %
0.01	20	24.6	26.3	-6.5
0.05	100	26	26.3	-1.1
0.1	200	31	31.3	-1
0.15	300	44.8	38.5	16.4
0.2	400	63	49.9	26.3
0.25	500	88.4	69.8	26.6
0.3	600	117	116.2	0.7
0.35	700	147	316.5	-53.6
0.4	800	171.8	316.5	-45.7
0.45	900	199.6	316.5	-36.9
0.5	1000	226.8	316.5	-28.3
0.6	1200	278.4	316.5	-12
0.7	1400	328.6	316.5	3.8
0.8	1600	348.6	316.5	10.1
0.9	1800	353.6	316.5	11.7

Table 1. Movement of people flow of “Females 30-50 years old [IMO]” profile horizontally.

Figure 2. Movement of people flow of “Females 30-50 years old [IMO]” profile horizontally.

Test_002 People profile “Females older than 50 years [IMO]”

Movement of people flow of “Females older than 50 years [IMO]” profile horizontally

№	Flow density, m²/m²	Number of people	Movement time, s (Fenix+ 3)	Movement time, s (Expected)	Deviation, %
1	0.01	20	33.6	33.3	0.9
2	0.05	100	36.4	33.3	9.3
3	0.1	200	43.4	39.6	9.6
4	0.15	300	55.2	48.7	13.3
5	0.2	400	78	63.1	23.6
6	0.25	500	113.4	88.2	28.6
7	0.3	600	146.8	146.9	-0.1
8	0.35	700	185	396.8	-53.4
9	0.4	800	217.2	396.8	-45.3
10	0.45	900	253	396.8	-36.2
11	0.5	1000	284.6	396.8	-28.3
12	0.6	1200	352.4	396.8	-11.2
13	0.7	1400	413.8	396.8	4.3
14	0.8	1600	439.6	396.8	10.8
15	0.9	1800	439.4	396.8	10.7

Table 2. Movement of people flow of “Females older than 50 years [IMO]” profile horizontally.

Figure 2. Movement of people flow of “Females older than 50 years [IMO]” profile horizontally.

Test_003 People profile “Females older than 50, mobility impaired (1) [IMO]”

Movement of people flow of “Females older than 50, mobility impaired (1) [IMO]” profile horizontally

№	Flow density, m²/m²	Number of people	Movement time, s (Fenix+ 3)	Movement time, s (Expected)	Deviation, %
1	0.01	20	38.6	43.9	-12.1
2	0.05	100	44.2	43.9	0.7
3	0.1	200	50.4	52.1	-3.3
4	0.15	300	70.8	64.1	10.5
5	0.2	400	101.2	83.1	21.8
6	0.25	500	145.8	116.2	25.5
7	0.3	600	190.4	193.3	-1.5
8	0.35	700	236.4	520.8	-54.6
9	0.4	800	284.2	520.8	-45.4
10	0.45	900	330.8	520.8	-36.5
11	0.5	1000	378.2	520.8	-27.4
12	0.6	1200	460.4	520.8	-11.6
13	0.7	1400	542.2	520.8	4.1
14	0.8	1600	571.8	520.8	9.8
15	0.9	1800	571.8	520.8	9.8

Table 3. Movement of people flow of “Females older than 50, mobility impaired (1) [IMO]” profile horizontally.

Figure 3. Movement of people flow of “Females older than 50, mobility impaired (1) [IMO]” profile horizontally.

Test_004 People profile “Females older than 50, mobility impaired (2) [IMO]”

Movement of people flow of “Females older than 50, mobility impaired (2) [IMO]” profile horizontally.

№	Flow density, m²/m²	Number of people	Movement time, s (Fenix+ 3)	Movement time, s (Expected)	Deviation, %
1	0.01	20	48.8	51	-4.3
2	0.05	100	50.8	51	-0.4
3	0.1	200	64.4	60.6	6.3
4	0.15	300	82.6	74.5	10.9
5	0.2	400	119.8	96.4	24.3
6	0.25	500	176.2	134.9	30.6
7	0.3	600	231.6	224.1	3.3
8	0.35	700	279.2	609.8	-54.2
9	0.4	800	328	609.8	-46.2
10	0.45	900	381.4	609.8	-37.5
11	0.5	1000	434.4	609.8	-28.8
12	0.6	1200	534.8	609.8	-12.3
13	0.7	1400	634	609.8	4
14	0.8	1600	681	609.8	11.7
15	0.9	1800	670.4	609.8	9.9

Table 4. Movement of people flow of “Females older than 50, mobility impaired (2) [IMO]” profile horizontally.

Figure 4. Movement of people flow of “Females older than 50, mobility impaired (2) [IMO]” profile horizontally.

Test_005 People profile “Females younger than 30 years [IMO]”

Movement of people flow of “Females younger than 30 years [IMO]” profile horizontally

№	Flow density, m²/m²	Number of people	Movement time, s (Fenix+ 3)	Movement time, s (Expected)	Deviation, %
1	0.01	20	19.4	20.2	-4
2	0.05	100	22	20.2	8.9
3	0.1	200	23.6	23.9	-1.3
4	0.15	300	35.8	29.5	21.4
5	0.2	400	47.8	38.2	25.1
6	0.25	500	70	53.4	31.1
7	0.3	600	90.8	88.8	2.3
8	0.35	700	111.4	242.7	-54.1
9	0.4	800	131	242.7	-46
10	0.45	900	153.2	242.7	-36.9
11	0.5	1000	174	242.7	-28.3
12	0.6	1200	216.2	242.7	-10.9
13	0.7	1400	251.6	242.7	3.7
14	0.8	1600	269.8	242.7	11.2
15	0.9	1800	270	242.7	11.2

Table 5. Movement of people flow of “Females younger than 30 years [IMO]” profile horizontally.

Figure 5. Movement of people flow of “Females younger than 30 years [IMO]” profile horizontally.

Test_006 People profile “Males 30-50 years old [IMO]”

Movement of people flow of “Males 30-50 years old [IMO]” profile horizontally.

№	Flow density, m²/m²	Number of people	Movement time, s (Fenix+ 3)	Movement time, s (Expected)	Deviation, %
1	0.01	20	19.2	19.3	-0.5
2	0.05	100	20.8	19.3	7.8
3	0.1	200	22.8	22.9	-0.4
4	0.15	300	32.4	28.2	14.9
5	0.2	400	44.4	36.5	21.6
6	0.25	500	65.4	51.1	28
7	0.3	600	86	85	1.2
8	0.35	700	108.6	231.5	-53.1
9	0.4	800	126.2	231.5	-45.5
10	0.45	900	148.6	231.5	-35.8
11	0.5	1000	167.8	231.5	-27.5
12	0.6	1200	205.8	231.5	-11.1
13	0.7	1400	242	231.5	4.5
14	0.8	1600	257.8	231.5	11.4
15	0.9	1800	259.4	231.5	12.1

Table 6. Movement of people flow of “Males 30-50 years old [IMO]” profile horizontally

Figure 6. Movement of people flow of “Males 30-50 years old [IMO]” profile horizontally

Test_007 People profile “Males older than 50 years [IMO]”

Movement of people flow of “Males older than 50 years [IMO]” profile horizontally

№	Flow density, m²/m²	Number of people	Movement time, s (Fenix+ 3)	Movement time, s (Expected)	Deviation, %
1	0.01	20	22	22.3	-1.3
2	0.05	100	24.2	22.3	8.5
3	0.1	200	26.6	26.5	0.4
4	0.15	300	40.8	32.6	25.2
5	0.2	400	54	42.3	27.7
6	0.25	500	76.8	59.1	29.9
7	0.3	600	101.4	98.3	3.2
8	0.35	700	122	268.8	-54.6
9	0.4	800	146.4	268.8	-45.5
10	0.45	900	170.2	268.8	-36.7
11	0.5	1000	191.6	268.8	-28.7
12	0.6	1200	236.8	268.8	-11.9
13	0.7	1400	279.8	268.8	4.1
14	0.8	1600	299	268.8	11.2
15	0.9	1800	297.2	268.8	10.6

Table 8. Movement of people flow of “Males older than 50 years [IMO]” profile horizontally.

Figure 8. Movement of people flow of “Males older than 50 years [IMO]” profile horizontally.

Test_008 People profile “Males older than 50, mobility impaired (1) [IMO]”

Movement of people flow of “Males older than 50, mobility impaired (1) [IMO]” profile horizontally.

№	Flow density, m²/m²	Number of people	Movement time, s (Fenix+ 3)	Movement time, s (Expected)	Deviation, %
1	0.01	20	29	29.4	-1.4
2	0.05	100	30.2	29.4	2.7
3	0.1	200	36.2	34.9	3.7
4	0.15	300	46.4	42.9	8.2
5	0.2	400	67.8	55.6	21.9
6	0.25	500	98.8	77.8	27
7	0.3	600	130.2	129.4	0.6
8	0.35	700	161.8	352.1	-54
9	0.4	800	190.8	352.1	-45.8
10	0.45	900	222.8	352.1	-36.7
11	0.5	1000	252.2	352.1	-28.4
12	0.6	1200	309.4	352.1	-12.1
13	0.7	1400	367.8	352.1	4.5
14	0.8	1600	391.4	352.1	11.2
15	0.9	1800	386	352.1	9.6

Table 8. Movement of people flow of “Males older than 50, mobility impaired (1) [IMO]” profile.

Figure 8. Movement of people flow of “Males older than 50, mobility impaired (1) [IMO]” profile horizontally

Test_009 People profile “Males older than 50, mobility impaired (2) [IMO]”

Movement of people flow of “Males older than 50, mobility impaired (2) [IMO]” profile horizontally

№	Flow density, m²/m²	Number of people	Movement time, s (Fenix+ 3)	Movement time, s (Expected)	Deviation, %
1	0.01	20	32.8	34.2	-4.1
2	0.05	100	32.6	34.2	-4.7
3	0.1	200	42	40.7	3.2
4	0.15	300	60.4	50	20.8
5	0.2	400	80.8	64.8	24.7
6	0.25	500	117.2	90.6	29.4
7	0.3	600	151	150.6	0.3
8	0.35	700	189.2	409.8	-53.8
9	0.4	800	223.6	409.8	-45.4
10	0.45	900	258	409.8	-37
11	0.5	1000	293	409.8	-28.5
12	0.6	1200	363.8	409.8	-11.2
13	0.7	1400	427.6	409.8	4.3
14	0.8	1600	455.6	409.8	11.2
15	0.9	1800	454.6	409.8	10.9

Table 9. Movement of people flow of “Males older than 50, mobility impaired (2) [IMO]” profile.

Figure 9. Movement of people flow of “Males older than 50, mobility impaired (2) [IMO]” profile horizontally

Test_010 People profile “Males younger than 30 years [IMO]”

Movement of people flow of “Males younger than 30 years [IMO]” profile horizontally

№	Flow density, m²/m²	Number of people	Movement time, s (Fenix+ 3)	Movement time, s (Expected)	Deviation, %
1	0.01	20	15.2	16.9	-10.1
2	0.05	100	17.2	16.9	1.8
3	0.1	200	23.2	20.1	15.4
4	0.15	300	30	24.7	21.5
5	0.2	400	41.4	32	29.4
6	0.25	500	58	44.7	29.8
7	0.3	600	77.6	74.4	4.3
8	0.35	700	95.8	203.3	-52.9
9	0.4	800	111.8	203.3	-45
10	0.45	900	128.8	203.3	-36.6
11	0.5	1000	146	203.3	-28.2
12	0.6	1200	180.6	203.3	-11.2
13	0.7	1400	213.6	203.3	5.1
14	0.8	1600	228.2	203.3	12.2
15	0.9	1800	227.2	203.3	11.8

Table 10. Movement of people flow of “Males younger than 30 years [IMO]” profile horizontally

Figure 10. Movement of people flow of “Males younger than 30 years [IMO]” profile horizontally.

Test_011 People profile “SFPE contingent”

Movement of people flow of “SFPE contingent” profile horizontally

№	Flow density, m²/m²	Number of people	Movement time, s (Fenix+ 3)	Movement time, s (Expected)	Deviation, %
1	0.01	20	18.4	20.8	-11.5
2	0.05	100	21.8	20.8	4.8
3	0.1	200	24.4	24.3	0.4
4	0.15	300	35.8	29.7	20.5
5	0.2	400	47.6	38.1	24.9
6	0.25	500	66.8	53.1	25.8
7	0.3	600	88.6	87.7	1
8	0.35	700	110	252.1	-56.4
9	0.4	800	130	4000	-96.8
10	0.45	900	153.4	4000	-96.2
11	0.5	1000	172.4	4000	-95.7
12	0.6	1200	214	4000	-94.7
13	0.7	1400	257.8	4000	-93.6
14	0.8	1600	296.2	4000	-92.6
15	0.9	1800	338.6	4000	-91.5

Table 11. Movement of people flow of “SFPE contingent” profile horizontally

Figure 11. Movement of people flow of “SFPE contingent” profile horizontally

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