Experimental Study on Individual and Group Evacuation of Passengers from an Aircraft Cabin in the Pitch/Roll State

Abstract

After an aircraft is forced to land, it is easy for it to become stuck in a tilt state of pitch or roll. The pitch/roll state of the aircraft cabin is a critical factor affecting the safe evacuation of the cabin. However, evacuation therein deserves more attention. In this research, an aircraft cabin simulator was developed to study the impact of pitch and roll on the individual and group evacuation speed. The values of the pitch angle θ and roll angle γ considered in the experiments were both 0, ±5, and ±10°. It was found that the average individual passenger speed could be attenuated in an aircraft cabin in pitch or roll conditions, but a pitch angle less than 0 had an acceleration effect on the walking mode. The results of the group evacuation experiments showed that, in addition to affecting the speed of individual passengers, the pitch/roll state also affected the evacuation interval time between a passenger and the preceding one. In addition, the linear fitting models introduced in this paper, which linked the motion of individual and group passengers, could predict the movement speeds accurately. This study provides a valuable benchmark for simulating the evacuation of an aircraft cabin and a reference for the safety design of actual aircraft cabins.

1. Introduction

Aircraft, especially airliners, are among the safest transportation means today. In recent years, they have also increasingly been the focus of researchers. Although the probability of safety accidents in civil aircraft generally is showing a downward trend, the consequences may be dire once an accident occurs. According to a survey by the National Traffic Safety Commission (NTSB), 78% of deaths occurred after an impact, and 95.4% of deaths were caused by slow and inefficient evacuation [1]. For example, on 2 June 1983, the Air Canada Flight 797 accident in America claimed 23 lives due to fire after a forced landing. NTSB claims that if survivors can be evacuated quickly after being told to do so, the survival rate will increase by 98.3% [2]. Therefore, after a non-disintegration accident occurs, prompt passenger evacuation of the aircraft is key to improving the survival rate of the personnel.

In 2016, flight UAE521 made an emergency landing due to wind shear. Due to the damage to the structure, the aircraft had a nearly 10° pitch angle after the aircraft stopped. Although the crew started an emergency evacuation immediately, evacuating took about six and a half minutes. However, according to the requirements of civil aircraft for airlines, passenger planes should be evacuated in a conventional state within 90 s [3]. This shows that the existing emergency evacuation rules and supporting experiments have certain limitations because the impact of the pitch and rolling state have not been considered in the model design.

Experiments and numerical simulation research on aircraft cabin safety evacuation have been widely reported. However, in most contributions, the cabin’s overall evacuation time and evacuation efficiency under a conventional situation were considered. Mclean and others studied the impact of aircraft emergency exits’ features on the evacuation time and factors such as seat configuration, channel width, group motivation, and individual characteristics on the exit evacuation efficiency [4,5,6,7]. Muir et al. researched the impact of smoke and motivation on the evacuation time [8,9]. Wilson and others studied different cabin layouts and evacuation times of wing exit layouts [10,11]. There are only a few simulation studies that emphasized the impact of the cabin structure on the speed of the personnel. The speed of the personnel movement is an important parameter that determines the evacuation performance of an aircraft, which is affected by the complexity of the environmental structure. In recent years, research on aircraft cabin evacuation has mainly used numerical simulations. Galea and others developed evacuation simulation software for large and wing-tier passenger aircraft [12]. Kirchner and others considered the competitive behavior of individual passengers in the emergency evacuation of a plane [13]. Xue and Yu and others considered the impact of passengers’ physical characteristics on the evacuation time of aircraft [14]. Most research has focused on evacuation movements in aircraft in a horizontal state and used numerical simulations or data statistics [15,16,17].

However, the speed of the passengers on a plane will be affected by the pitch/roll state. In an actual accident, the aircraft may be in an unfavorable position after a forced landing [18]. The unfavorable position will affect the speed of the personnel’s movement and the evacuation efficiency [19]. When there is a rolling or a pitch angle, the gait of the passengers on board changes, leading to changes in their movement speed [18]. In addition, changes in friction between passengers’ soles and the ground will also have a considerable impact [20], causing a loss of personal speed.

There needs to be more research on the evacuation of airplane cabins in the tilt state. Similar research has been mainly concentrated in the shipping field. The Research Institute of Marine Engineering of Japan (RIME) built a sidewalk model with a size of 6.0 m (L) × 1.2/0.9/0.6 m (W) for static tilt tests to study the impact of vertical and cross leaning on individual movement behavior [21,22]. Fleet Technology Limited (FTL) and the Fire Safety Engineering Group (FSEG) of the University of Greenwich devoted joint efforts to establish the Ship Evacuation Behavior Assessment Facility (SHEBA) [23,24,25]. In addition, the Dutch Applied Science Research Organization (TNO), the University of Science and Technology of China, and the Korea Research Institute of Ships and Ocean Engineering (Kriso) reported similar research [26,27,28]. Based on experience results, Germanischer Lloyd proposed a model in Aeneas (ship evacuation software) widely used in ship design to depict changes in human speed under different pitch/roll angles [29]. Evacuation from an inclined aircraft cabin is different from that in a floating ship or a static inclined corridor. On the one hand, evacuation from an aircraft cabin must be completed quickly (less than 90 s). Hence, the passengers in the aircraft need to move as quickly as possible during the evacuation process, such as by running, rather than walking briskly as usual. On the other hand, the structure of an aircraft cabin is complex, and the space is narrow. Evacuation from an inclined aircraft cabin is easily affected by the seats, walls, and other structures. For example, when an aircraft cabin was rolling inclined, the passengers caught their feet between the seat legs along the aisle or fell into the space between the seat rows [30]. Therefore, it is necessary to study the movement characteristics of passengers in inclined aircraft cabins.

Hitherto, there is a need for more research on the movement of passengers in an aircraft cabin under the pitch/roll state, and statistical data that can be used for quantitative analysis are limited. Therefore, research in this study is focused on the movement of passengers when an aircraft cabin is under pitch/roll conditions. To this end, this article presents an aircraft cabin simulator developed based on the cabin layout of a real airliner. The experiments are divided into two parts: individual movement and group evacuation. Individual movement speed with different pitch/roll angles was a concern for individual evacuation experiments. For group evacuation experiments, the effects of the pitch/roll angles on the density, individual space interval, and interval time were analyzed. Finally, based on the motion parameters and rules derived from the experiments, a mathematical model of individuals’ movement speed in an inclined cabin was integrated. This study also examined the movement of a passenger in the pitch/roll cabin and provides reference data for the design of safety measures and aircraft evacuation simulation works.

2. Methodology

2.1. Experimental Setup

To investigate the factors affecting passengers’ walking speed in an aircraft cabin, this article developed a set of aircraft cabin simulators with the size of a standard single-channel narrow-body aircraft, as shown in Figure 1 and Figure 2. Their internal size was 20 m × 3.8 m × 2.6 m, and the seats were 3 per 3 lines in 18 rows. The aircraft had standard economy class seat specifications, the aisle width was 0.51 m, and the seat spacing was 0.81 m. As shown below, the simulation cabin was equipped with four hydraulic systems responsible for controlling the rolling and pitch of the aircraft cabin simulation, and the maximum inclination angle was ±15°. In order to simulate the real aircraft cabin environment, the simulator was equipped with facilities such as lighting facilities, carpets, and luggage racks. Aircraft portholes were installed, such as multiple electronic displays, and the display screen was set to different dynamic screens to simulate a variety of scenes, such as normal landings, forced landings, and fire scenes. In addition, six high-definition cameras and multi-channel control devices were installed in the cabin simulator to control the inclined state of the cabin and the emergency evacuation experiment.

2.2. Experimental Design

According to the design guidelines of civil aviation aircraft, the pitch angle and rolling angle that may appear after a crash is within the range of ±15°. Therefore, we carried out experiments with pitch and rolling angles of ±5°, ±10°, and ±15°. The results showed that a passenger will fall when the rolling and pitch angle reach ±15°. In order to avoid safety accidents in the experiment, the values of rolling angle γ and pitch angle θ in this experiment were 0, ±5, ±10, as shown in Figure 3.

The aircraft cabin evacuation simulation experiments were divided into individual and group evacuation experiments, as illustrated in Figure 4. In individual movement experiments, the passengers were asked to sit in the 15A position. After the aircraft cabin simulator was set to a different pitch/roll angle, they moved to the front cabin exit. The instructions included normal walking and rapid evacuation. In the normal walking mode, they were instructed to walk normally away from the aircraft, with normal walking meaning walking comfortably and naturally. In the rapid evacuation mode, they needed to evacuate at the fastest speed. A total of 24 passengers participated in the experiment (10 men and 14 women, aged 25~41, 158.5~183.1 cm tall, and weighing 50.5~99.6 kg).

In the group evacuation experiments, 18 passengers in each experiment (9 males and 9 females) were allocated to seats in the 14~16 rows. Similarly, the experimental commander issued an evacuation instruction after the aircraft cabin simulator was set to a different pitch/roll angle. When hearing the evacuation instructions, the passengers evacuated to the front cabin door at a speed as fast as possible. In this case, 5 groups of 90 people participated in the experiment (aged 25~50, 155.3~183.1 cm, and 45.2~84.7 kg).

In order to simulate the situation of a real forced landing, the experimental commander first controlled the aircraft for continuous dynamic shaking and released the evacuation instruction after a particular experimental condition was achieved. In addition to the evacuation instructions, the passengers were informed only on the safety precautions of the experiment. All experiment cases were repeated twice.

2.3. Measurement Method

In this experiment, the speed v_i of the individual i was determined by the length S of the observation area and the time t_i required to pass through the observation area. In addition, t_i,in is the moment when the body of an experimental object enters the boundaries of the experimental area, and t_i,out is the moment when the body of the experimental object ultimately leaves the experimental area.

$$t_i=t_{i,out}-t_{i,in}$$

(1)

$$v_i=S/t_i$$

(2)

In order to present the change in speed, speed reduction (defined as the ratio of an individual walking speed under inclined conditions to that under normal conditions) was calculated as

$$r_b^a=\frac{v_b^a}{v_b^0}$$

(3)

where α is the category angle. When the corner is rolling, α = γ, and α = θ during pitch angle; b is the category of motion mode. When walking normally, b = w; for a rapid evacuation, b = e.

In the group experiments, the starting interval time, arrival interval time, distance from the preceding passenger, and momentary linear density can be calculated using the following formula:

$$\Delta t_{i,in}=t_{i,in}-t_{i-1,in}$$

(4)

$$\Delta t_{i,out}=t_{i,out}-t_{i-1,out}$$

(5)

$$d_i=v_{i-1}\times \Delta t_{i,in}$$

(6)

$${\rho }_i=\frac{1}{d_i}$$

(7)

Furthermore, in order to quantify the mutual dependence between the speeds of two individual passengers, the correlation coefficient of the average speed between the ith experimental subject and the jth experiment subject was calculated by

$$c(i,j)=\frac{\Sigma (v_i-\overline{v_i})(v_j-\overline{v_j})}{\sqrt{\Sigma {\left(v_i-\overline{v_i}\right)}^2\Sigma {\left(v_j-\overline{v_j}\right)}^2}}$$

(8)

3. Results

3.1. Individual Movement Experiment

3.1.1. Speed

The average individual speed measured in a standard cabin is shown in Figure 5. Due to the influence of individual characteristics, the distribution of the individual evacuation speed showed a certain discrete distribution. In a relatively wide aisle area, the individual evacuation speed (2.19~3.55 m/s) was significantly greater than the walking speed (1.21~2.04 m/s). However, in the seating area, because the leg space between the seats is relatively narrow (d = 0.31 m), an individual can only move horizontally, as shown in Figure 6. As a result, the movement speed is lower (0.39~0.89 m/s).

Gender also affects the speed of individual movement. In the walking state, the speed of males and females was relatively close. In the rapid evacuation state, the movement speed of males was about 13% quicker than that of females, which is caused by differences in physical characteristics between different genders.

Table 1. Male and female average individual speed in different areas (as benchmark values).

Mode	Gender	Speed (m/s)
		Seat Area	Aisle Area	Whole Area
Evacuation	Male	0.81	3.08	2.01
	Female	0.67	2.70	1.80
Walking	All	0.53	1.49	1.14

reports the average movement speed of passengers in a standard aircraft cabin as benchmark values for subsequent research.

3.1.2. Pitch or Roll Angle

The statistical results of the individual speed at different pitch and roll angles are shown in Figure 7. It can be seen that the speed of individual passengers decreased rapidly with the increase in the tilt angle, and the lowest speed was measured at θ = 10°. The average individual walking speed and evacuation speed in the seat area were reduced to 0.356 m/s and 0.487 m/s. In the aisle area, the average individual walking speed and evacuation speed were reduced by 1.21 m/s and 2.19 m/s. An exception was observed when the pitch angle was negative (θ < 0°): the individual walking speed of the seat area was unchanged, because when walking horizontally, the support of the seat in the back offset the impact of gravity. In the aisle area, the walking speed increased slightly with an increase in the angle.

Based on the observations from the experiment and the investigation of the passengers, this was mainly due to the impact of gravity components. In the presence of a rolling angle, the gravity component of the passenger is perpendicular to the direction of movement. For any motion status, it is necessary to decelerate to maintain balance and the correct direction of the movement. Therefore, the deceleration effect of positive and negative roll angles was similar. Furthermore, the results of the one-way repeated-measures analysis of variance (ANOVA) for passengers’ movement speed at different pitch/roll angles are shown in

Table 2. The results of one-way repeated-measures ANOVA for movement speed in different individual experimental conditions.

Source			F	p
Aera	Angle	Movement Mode
seat	roll	walking	22.970	<0.001
	roll	evacuation	13.867	<0.001
	pitch	walking	53.126	<0.001
	pitch	evacuation	81.350	<0.001
aisle	roll	walking	11.917	0.002
	roll	evacuation	22.370	<0.001
	pitch	walking	52.556	<0.001
	pitch	evacuation	73.263	<0.001

. At the 95% confidence level, the results indicated that the influence of the pitch/roll angle of the aircraft cabin on the passengers’ movement speed was statistically significant.

When the pitch angle was positive, the gravity component of the elevation angle was opposite to the direction of the movement, and any movement mode was decelerated. When the pitch angle was negative, the gravity component was the same as the movement direction, and the walking speed increased due to the impact of gravity. As the angle increased, the experimental subjects reduced their speeds to maintain balance and avoid falling.

3.1.3. Speed Reduction

In order to clearly present the changes in individual movement speed, the average speed reduction at different pitch/roll angles (defined as the ratio of individual movement speed under inclined conditions to that under normal conditions) was calculated, as shown in Figure 8. In order to facilitate the discussion considering the results of other experimental research, the individual speed in the aisle area was selected as the calculation object, similar to the experimental conditions in others’ studies.

In the normal walking mode, there was a linear relationship between the speed reduction ratio and the angle. The walking speed reduction decreased to 91.9% as the roll angle γ increased from 0 to 10. Under pitch conditions, it was reduced from 108.1% to 81.0% as the pitch angle θ increased from −10° to 10°. This conclusion is consistent with those reported by FTL and FSEG, Aeneas, FTL, and Sun. Our experimental result values are slightly different from those of the other studies. This might be due to differences in experimental conditions and subjects.

Nevertheless, in the rapid evacuation mode, the results of this work are significantly inconsistent with those of other research institutes. FTL and FSEG and Aeneas reported that an increase in pitch-down (θ < 0) slope would result in a reduction in the movement speed. TNO and Sun reported that the movement speed would increase first and then decrease with an increasing pitch-down slope from 0° to 20°. The maximum value for the average individual speed could be achieved at a pitch angle θ of −10°. By contrast, in this work, the maximum value for the average individual speed reduction was 101.1% when the pitch angle θ was −5°. In addition, the average individual speed reduction was significantly reduced at the same angle. The average speed reduction was 80.6% at a roll angle γ of 10° and 76.7% at a pitch angle θ of 10°. This could be due to the difference in movement mode. Previous research required the personnel to keep walking (1~2 m/s). This work considered the evacuation process with passengers running (2~3.5 m/s) during the evacuation. In other words, the influence of the pitch/roll angle is different for different speed ranges of movement.

Based on the data obtained from the experimental research of this work, the average individual speed reduction ratio was established through the data fitting method. The adjusted R-square values were close to 1.

For walking:

$$\begin{gathered} r_{w,aisle}^{\gamma }=1-7.98\times {10}^{-3}\times \left|\gamma \right|,\left|\gamma \right|\le 10 \\ {r}_{w,aisle}^{\theta }=\left\{\begin{array}{c}1-8.25\times {10}^{-3}\times \theta ,\\ 1-1.858\times {10}^{-2}\times \theta ,\end{array}\right.\begin{array}{c}-10\le \theta <0\\ 0<\theta \le 10\end{array} \end{gathered}$$

(9)

For evacuation:

$$\begin{gathered} r_{e,aisle}^{\gamma }=1-9.0\times {10}^{-3}\times \left|\gamma \right|-1.04\times {10}^{-3}\times {\gamma }^2,\left|\gamma \right|\le 10 \\ {r}_{e,aisle}^{\theta }=1-9.0\times {10}^{-3}\times \theta -1.52\times {10}^{-3}\times {\theta }^2,-10<\theta \le 10 \end{gathered}$$

(10)

3.2. Group Evacuation Experiment

3.2.1. Evacuation Time

The evacuation time is the most important parameter for evaluating the evacuation efficiency. Figure 9 shows the evacuation time of repeated experiments at different pitch/roll angles. It can be seen that, except for the pitch angle θ = −5°, all other angles increased the evacuation time, and the larger the angle, the longer the evacuation time. Compared to the roll angle, the same pitch angle had a more significant impact and led to higher dispersion in the evacuation time results. A one-way ANOVA was undertaken; the results showed that the group evacuation time significantly changed with the roll angle (F = 3.793, p = 0.0187) and pitch angle (F = 11.683, p < 0.001) at a 95% confidence level.

3.2.2. Speed

The average evacuation speed observed in the experiments in the normal walking mode is shown in Figure 10. With an increase in the evacuation sequence, the average evacuation speed of single individuals in the entire process and observation area gradually decreased, and the speed difference between the front and the rear order personnel gradually reduced and finally stabilized at 1.22 ± 0.23 m/s. This result is related to the density changes in the aisle area. During evacuation, the person who entered the aisle first had enough space to accelerate. Due to the restrictions on traffic at the exit door, the speed of a passenger entering the aisle was greater than that of one leaving the aisle, the crowdedness in the aisle area continued to increase, and the movement speed decreased.

In order to further analyze the impact of the pitch/roll angles on the individual speed in the group evacuation, the average individual speed reduction ratio of the average individual speed at different pitch/roll angle conditions was calculated. As shown in Figure 11, the variation in the average individual velocity reduction ratio with the pitch/roll angles in the group evacuation experiment was similar to that observed in the individual evacuation experiment. However, most values were not between the walking speed reduction ratio and the evacuation speed reduction ratio. This showed that in group evacuation, in addition to directly affecting the individual speed, the pitch/roll angles also changed the characteristics of other group movements, such as density, distance headway, and time headway, and affected the individual’s speed.

In addition, the correlation curve of the average speed of the individual and the front passenger’s speed is shown in Figure 12. It can be seen that the speed of individuals in group evacuation showed a clear correlation with the front passenger’s speed (c_i,_j ≈ 1). The movement speed of the passenger in front is an essential factor that determines the evacuation speed of an individual.

3.2.3. Fundamental Diagram

The fundamental diagram of passengers shows a relation between the passenger speed and the passenger density [21,22]. The speed of individuals during group evacuation was mainly influenced by the passenger density. The fundamental diagram of passenger density and speed under different pitch/roll angles in the aisle area is shown in Figure 13a. With a change in the roll/pitch angles, the density distribution showed an insignificant change, which indicated that the pitch/roll had no direct effect on the passenger density. It could also be concluded through ANOVA that the roll angle (F = 1.927, p = 0.1050) and pitch angle (F = 2.199, p = 0.0683) had a statistically insignificant influence on the passenger density in group evacuation. As shown in Figure 13b, compared with other studies, this experiment had fewer data points in extremely high-density areas (ρ > 2 p/m), and most data refer to normal-density areas (0 > ρ > 2 p/m). On the one hand, this is because the linear density of passengers in the aisle area increased as the passengers entered the aisle. When the density reached a high value, most passengers were at the end of the aisle or had passed the aisle, and only a few passengers needed to be evacuated. On the other hand, most passengers kept a particular distance from the passenger in front during the evacuation, so that the passenger’s linear density did not reach a high value. This result can suggest the passenger density range of real group evacuation in the aircraft cabin.

In addition, the fundamental diagram in this work shows a relatively wide data distribution, which might be produced by differences in the experimental conditions, such as the physiological characteristics of the passengers and the pitch/roll angles of the aircraft.

3.2.4. Distance from the Passenger in Front

The distance from the passenger in front distribution is an important parameter for quantifying the spatial distribution of group motion and also affects the speed at which individuals move within a group [31]. The distance of a passenger from the preceding passenger was measured in the aisle area, and the relationship between the distance from the passenger in front and the pitch/roll angle as well as the individual speed was analyzed. The statistics of the distance from the passenger in front under different pitch/roll angles is shown in Figure 14a. As the angles increased, there was no significant change in the distribution of the distance headway. It can also be concluded through ANOV that, the roll angle (F = 1.058, p = 0.3771) and pitch angle (F = 1.228, p = 0.2983) were statistically insignificant to the distance from the passenger in front in group evacuation. The relationship between the distance from the passenger in front and the individual speed in the aisle area is shown in Figure 14b. In this experiment, the individual did not move until the distance from the preceding passenger was greater than 0.32 m, indicating that the minimum safe distance (d0) maintained between individuals was 0.32 m. When the distance from the passenger in front exceeded 1.5 m, there was no significant relationship between the individual speed and the distance from the passenger in front. Overall, the individual movement speed showed an upward trend with increased headway distance. In addition, as all the experimental passengers were required to evacuate as fast as they could, the individual speed in this work showed a larger value than in other studies in which the experimental subjects were required to walk. Different from other research, which presented a narrow difference, the experimental results in this work showed a much broader range in the distance from the passenger in front for the same individual walking speed, which might be due to the different experimental conditions.

3.2.5. Time Headway

It was concluded from the individual movement experiments that the pitch/roll angles can affect the passenger speed. So, the speed should be disregarded to analyze the effect of the pitch/roll angles on the group evacuation characteristics. According to Formula (6), the distance from the passenger in front can be split into the product of the forward passenger’s speed and the time headway, from which the time headway of the passenger in the aisle area under different experimental conditions can be calculated. The time headway distribution is an important value that characterizes the spatial distribution of individuals in evacuation movements [32]. The time headway under different pitch/roll angles is shown in Figure 15. It can be seen that the average time headway interval increased significantly as the angle increased. It could also be concluded through ANOVA that the roll angle (F = 4.784, p < 0.001) and pitch angle (F = 5.150, p < 0.001) were statistically significant to the time headway in group evacuation. It can be deduced that in group evacuation, the pitch/roll angles will affect not only the individual speed but also the time headway between individuals. The two influence laws are similar, as both appeared to have a linear relationship, and the pitch angle had the larger impact. Therefore, the relationship between the average time headway and the angle could be obtained using the same fitting method as follows:

$$\begin{gathered} \begin{array}{l}{t}_{i-1}(\gamma )=0.58+1.31\times {10}^{-3}\times \gamma +8.67\times {10}^{-4}\times {\gamma }^2\\ t_{i-1}(\theta )=0.58+7.7\times {10}^{-3}\times \theta +1.64\times {10}^{-3}\times {\theta }^2\end{array} \\ \left(-{10}^{\circ }\le \gamma ,\theta \le {10}^{\circ }\right) \end{gathered}$$

(11)

3.2.6. Prediction Model of Passenger Speed

The efficiency of group evacuation is determined by the speed of individual passengers in the group. Research has shown that the distance from the passenger in front and the current velocity affect a passenger’s acceleration, thereby determining the movement of the entire population [33]. According to the experimental results of this article, it can be concluded that the individual movement speed during the group evacuation process of the cabin is mainly influenced by the movement speed of the individual in front, the size of the pitch/roll angles, the distance headway, and the time headway. Therefore, these data could be used to establish a motion model for individual passenger speed in group evacuation under unfavorable attitudes, with the specific relationship as follows:

$$v_i=f\left(v_{i,0},v_{i-1},d_{i-1},t_{i-1},\gamma ,\theta \right)$$

(12)

where v_i represents the ith individual’s speed, d_i−1 represents the distance headway, and t_i−1 represents the time headway.

According to the previous conclusions, the speed and distance from the passenger in front are positively related to the speed of individual passengers, and the distance from the passenger in front can be expressed by the product of the front passenger’s speed and the time headway. Therefore, the speed of individual passengers in group evacuation can be described by the formula listed in

Table 3. Linear fitting functions and results of individual passenger speed prediction.

Function	a	b	c	Adj-R2
Vi = a × Vi−1 + b	0.943	0.026	-	0.95
Vi = a × (di−1 − d0)	2.835	-	-	0.88
Vi = a × (Vi−1 × ti−1 − d0)	2.904		-	0.977
Vi = (a + b × ti−1) × Vi−1 + c × d0	0.954	−0.026	0.088	0.95
Vi = a × Vi−1 + b × (di−1 − d0) + c	0.99	−0.06	−0.014	0.94

, and linear functions were used to fit the experimental data. The high value of the adjusted R-square value showed that these linear functions could fit the experimental data well. From the results, it could be inferred that predicting the individual velocity in group evacuation through the preceding passenger’s speed and the time headway was the most reliable method. The correlation between the distance from the passenger in front and the individual speed was very low, especially when the front passenger’s speed exerted a significant effect. The correlation coefficient of the distance from the passenger in front approached 0, while the correlation coefficient of the preceding passenger’s speed approached 1. This indicated that the distance from the passenger in front was not the main factor determining the individual movement speed in group evacuation.

In summary, the individual passenger speed during the group evacuation of the cabin can be predicted. The formula is:

$$v_i(v_{i-1},t_{i-1},\gamma ,\theta )=\left\{\begin{array}{cc}{v}_{i,0}\left(\gamma ,\theta \right)& d_{i-1}>1.5m\\ \min \left[2.9*v_{i-1}*t_{i-1}\left(\gamma ,\theta \right)-2.9*0.32 , v_{i,0}\left(\gamma ,\theta \right)\right]& d_0\le d_{i-1}\le 1.5m\\ 0& d_{i-1}<d_0\end{array}\right.$$

(13)

4. Conclusions

The pitch/roll state of the aircraft cabin is an important factor affecting the speed of passengers’ movement, and the speed of the passengers in the aircraft is an important parameter that affects the evacuation efficiency. Based on previous studies, this study independently developed a full-size cabin emergency evacuation simulator and studied the impact of the roll or pitch angles on the aircraft cabin’s individual and group evacuation speed. The specific conclusions we reached are as follows:

(1)

The speed in the seat area was 25% to 35% that in the aisle area. Males and females had the same walking speed, but males’ evacuation speed was 13% higher than females’.

(2)

With an increase in the pitch/roll angles, the speed of individual passengers gradually decreased. Only when the pitch angle was negative, the acceleration effect could occur.

(3)

At different speeds, the deceleration rules of the pitch/roll angles changed, which was mainly reflected in the value of the speed reduction ratio.

(4)

The pitch/roll angles affected the interval time between a passenger and the preceding passenger. The larger the angle, the larger the safety interval time between individuals. The passenger density and the distance from the passenger in front at different pitch/roll angles were similar.

(5)

The individual passenger speed in group evacuation was mainly related to the personal speed, inclined angle, front passenger’s speed, and front-oriented safety interval time. According to the function model based on the experimental data, the predictive model of motion speed appeared valid.

The above conclusions may only apply to this study or other studies considering a similar individuals. When the experimental passengers change, the experimental results may differ, depending, e.g., on the passengers’ cultural background and physical characteristics. Future work will focus on other experimental conditions, analyzing, for example, the influence of smoke, fire, and passenger obesity on aircraft cabin evacuation. However, the results of this study provide valuable information about passengers’ movement behaviors in aircraft cabins at different pitch/roll angles and indicate that passengers’ movement ability in an inclined cabin will be significantly affected. This study offers a basic understanding of passengers’ behaviors during evacuation considering the effect of aircraft pitch and roll and may provide a reference for the safety design of aircraft cabins. The prediction model of the passenger movement speed in an aircraft cabin presented in this study will help establish an aircraft emergency evacuation simulation model and benefit the design of rapid evacuation strategies of aircraft.