Appendix 1 - Method to Calculate the Travel Duration (T)

1 Parameters to be considered

1.1 Clear width (W_c)

Clear width is measured off the handrail(s) for corridors and stairways and the actual passage width of a door in its fully open position.

1.2 Initial density of persons (D)

The initial density of persons in an escape route is the number of persons (p) divided by the available escape route area pertinent to the space where the persons are originally located and expressed in (p/m²).

1.3 Speed of persons (S)

The speed (m/s) of persons along the escape route depends on the specific flow of persons (as defined in paragraph 1.4) and on the type of escape facility. People speed values are given in tables 1.1 (initial speed) and 1.3 below (speed after transition point as a function of specific flow).

1.4 Specific flow of persons (F_s)

Specific flow (p/m/s) is the number of escaping persons past a point in the escape route per unit time per unit of clear width W_c of the route involved. Values of F_S are given in tables 1.1 (initial F_s as a function of initial density) and 1.2 (maximum value) below.

1.5 Calculated flow of persons (F_c)

The calculated flow of persons (p/s) is the predicted number of persons passing a particular point in an escape route per unit time. It is obtained from:

• F_c = F_s W_c (1.5)

1.6 Flow duration (t_F)

Flow duration (s) is the total duration needed for N persons to move past a point in the egress system, and is calculated as:

• t_F = N / F_c (1.6)

1.7 Transitions

Transitions are those points in the egress system where the type (e.g. from a corridor to a stairway) or dimension of a route changes or where routes merge or ramify. In a transition, the sum of all the outlet-calculated flow is equal to the sum of all the inlet-calculated flow:

• Σ F_c(in)_i = Σ F_c(out)_j (1.7)

• where:

• F_c(in)_i = calculated flow of route (i) arriving at transition point

• F_c(out)_j = calculated flow of route (j) departing from transition point

1.8 Travel duration T, correction factor and counterflow correction factor

Travel duration T expressed in seconds as given by:

• T = (ɣ + δ) t_I (1.8)

• where:

• ɣ = is the correction factor to be taken equal to 2 for cases 1 and 2 and 1.3 for cases 3 and 4;

• δ = is the counterflow correction factor to be taken equal to 0.3; and

• t_I = is the highest travel duration expressed in seconds in ideal conditions resulting from application of the calculation procedure outlined in paragraph 2 of this appendix.

2 Procedure for calculating the travel duration in ideal conditions

2.1 Symbols

To illustrate the procedure, the following notation is used:

• t_stair = stairway travel duration (s) of the escape route to the assembly station

• t_deck = travel duration (s) to move from the farthest point of the escape route of a deck to the stairway

• t_assembly = travel duration (s) to move from the end of the stairway to the entrance of the assigned assembly station

2.2 Quantification of flow duration

The basic steps of the calculation are the following:

• .1 Schematization of the escape routes as a hydraulic network, where the pipes are the corridors and stairways, the valves are the doors and restrictions in general, and the tanks are the public spaces.

• .2 Calculation of the density D in the main escape routes of each deck. In the case of cabin rows facing a corridor, it is assumed that the people in the cabins simultaneously move into the corridor; the corridor density is, therefore, the number of cabin occupants per corridor unit area calculated considering the clear width. For public spaces, it is assumed that all persons simultaneously begin the evacuation at the exit door (the specific flow to be used in the calculations is the door's maximum specific flow); the number of evacuees using each door may be assumed proportional to the door clear width.

• .3 Calculation of the initial specific flows Fs, by linear interpolation from table 1.1, as a function of the densities.

• .4 Calculation of the flow Fc for corridors and doors, in the direction of the correspondent assigned escape stairway.

• .5 Once a transition point is reached; formula (1.7) is used to obtain the outlet calculated flow(s) Fc. In cases where two or more routes leave the transition point, it is assumed that the flow Fc of each route is proportional to its clear width. The outlet specific flow(s), Fs, is obtained as the outlet calculated flow(s) divided by the clear width(s); two possibilities exist:

  • .1 Fs does not exceed the maximum value of table 1.2; the corresponding outlet speed (S) is then taken by linear interpolation from table 1.3, as a function of the specific flow; or

  • .2 Fs exceeds the maximum value of table 1.2 above; in this case, a queue will form at the transition point, Fs is the maximum of table 1.2 and the corresponding outlet speed (S) is taken from table 1.3.

• .6 The above procedure is repeated for each deck, resulting in a set of values of calculated flows Fc and speed S, each entering the assigned escape stairway.

• .7 Calculation, from N (number of persons entering a flight or corridor) and from the relevant Fc, of the flow duration t_F of each stairway and corridor. The flow duration t_F of each escape route is the longest among those corresponding to each portion of the escape route.

• .8 Calculation of the travel duration t_deck from the farthest point of each escape route to the stairway, is defined as the ratio of length/speed. For the various portions of the escape route, the travel durations should be summed up if the portions are used in series, otherwise the largest among them should be adopted. This calculation should be performed for each deck; as the people are assumed to move in parallel on each deck to the assigned stairway, the dominant value t_deck should be taken as the largest among them. No t_deck is calculated for public spaces.

• .9 Calculation, for each stair flight, of its travel duration as the ratio of inclined stair flight length and speed. For each deck, the total stair travel duration, t_stair, is the sum of the travel durations of all stairs flights connecting the deck with the assembly station.

• .10 Calculation of the travel duration t_assembly from the end of the stairway (at the assembly station deck) to the entrance of the assembly station.

• .11 The overall duration to travel along an escape route to the assigned assembly station is:

  • t_I = t_F + t_deck + t_stair + t_assembly (2.2.11)

• .12 The procedure should be repeated for both the day and night cases. This will result in two values (one for each case) of t_I for each main escape route leading to the assigned assembly station.

• .13 Congestion points are identified as follows:

  • .1 in those spaces where the initial density is equal, or greater than, 3.5 persons/m²; and

  • .2 in those locations where the difference between inlet and outlet calculated flows (F_C) is in more than 1.5 persons per second.

• .14 Once the calculation is performed for all the escape routes, the highest t_I should be selected for calculating the travel duration T using formula (1.8).