| Going with the Flow |
| Tuesday, 10 June 2008 | |
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Sue Kirk walks us through the role of fluid dynamics in controlling crowds Walking through Cambridge on a Saturday afternoon, most of us have experienced dynamic crowd behaviour, navigating a maze of bikes, pedestrians and lamp posts without a second thought. However, sometimes this flow behaviour breaks down, as anyone who has arrived at Sainsbury's around 5pm can testify. But, annoying as it is snaking slowly around the aisles, this is nothing compared to the serious consequences that can occur when crowds become more densely packed. Many people are killed every year as a result of panic stampedes and trampling at mass gatherings such as religious pilgrimages, festivals, or simply in busy train stations or the rush for seats at a concert. One of the worst such events in recent times took place during the Hajj pilgrimage in 2006, where over 300 people were killed as a result of crushing and trampling in an extremely dense crowd. Dirk Helbing and physicists at the University of Köln were invited by the Saudi government to study video footage of the period leading up to these events. Analyzing crowd flow in this footage has allowed them to help establish the reasons for the observed behaviour by analogy to other flow systems studied in physics. By identifying key warning signs in the way the crowd moves, their suggestions have helped to ensure a safe Hajj in 2007 and may have implications for other crowd situations. The study of pedestrian flow dynamics has been an active area of research since 1995, when the first computational models were applied to human crowds. It had been thought that the decision-making capacity of humans would make it difficult to model the behaviour of crowds, but in large groups, individual thought is often superseded by a herd mentality, meaning that a relatively simple analysis can explain many commonly observed phenomena. For example, consider walking down a busy corridor. Flow seems to segregate naturally into two lanes moving in opposite directions without any prior planning. Similarly, where two corridors cross, flow in the perpendicular directions can be maintained without any need for direct communication. This self-organization behaviour can be simulated using many-particle models, similar to those which would be used in a range of physical problems from granular flow (the interaction of small particles such as sand, which bears strong analogy with pedestrian dynamics) to the emergence of superconductivity in crystal lattices. Each person is modelled as a unit which responds in a defined way to the situation in which it finds itself, which is in turn defined by the motion and position of the surrounding people. But defining this behaviour is not always simple, and requires some understanding of the people within the crowd. For example, cultural factors are important, as the personal space which someone from Cambridge would consider comfortable is likely to be much larger than that for a person used to the crowds of Delhi or Bangkok. Similarly, the age composition of the crowd will be important in determining how fast the average pedestrian would wish to move. A group of people at a train station, which will typically have a mix of ages including families and elderly people, will tend to move slower than a crowd leaving a football match. This approach has allowed researchers to reproduce well-known behaviour, but the availability of experimental data from extreme crowd situations against which the models can be tested has always been limited for ethical reasons. Some experimental data exist from studies of the behaviour of animals. Altshuler and co-workers from the University of Havana studied the behaviour of ants in a confined space with two equivalently located exits. Both exits were roughly equally favoured in normal circumstances, but when panic was generated by the insertion of repellent, one exit became favoured over another. Researchers at the University of the Philippines also studied the behaviour of mice escaping from a water pool through a single exit, the size of which was varied. They found that queuing behaviour was seen as the mice self-organized to efficiently escape the water and confirmed other findings from the models, such as the rate of increase of escape with increased door size, which follows a power law. The observation of human behaviour in crowds has only recently been possible through the developments of high throughput video analysis software. This was used by Helbing's group to look at the crowd behaviour at the 2006 Hajj disaster. They recorded the position and velocity of people in an area 20 metres by 12 metres over a period of 45 minutes prior to the events described. By analysing small-scale variations in crowd density they were able to identify two key transition points which led to panic behaviour in the crowd. In normal crowd situations, people tend to move in a laminar flow pattern, walking at a steady rate in one direction. However, if crowd density increases, the number of people becomes too high to maintain this steady motion and the first transition to stop-and-go flow takes place. In this regime, people move in waves, continually stopping and starting. This is similar to what is observed in long queues at traffic lights, where cars have periods of movement and then periods where they are stationary. This kind of transition had been predicted from conventional models which liken pedestrian dynamics to fluid-dynamic flow-behaviour. In this fluid dynamics model, the flow rate is given by the product of the density of people and their velocity. However, velocity is dependent on the density and will fall to zero when people can no longer move as they are too tightly packed. Modelling crowd behaviour in this way reproduces stop and go flow at high densities. However, Helbing found that even at high crowd densities, local movement within crowds did not tend towards zero, contradicting a key assumption of these models. In fact, at much higher densities of around 9 people per square metre (equivalent to packing seven and a half people into a phone box!), there was a second transition to a new type of motion which they termed 'turbulent' by analogy to similar behaviour in, for example, granular materials. As a result of the close packing, people start to try and push neighbours to gain more space. Under these conditions, people are moved randomly in all directions as a result of waves of pushing within the crowd. These shock waves and irregular flows in all directions cause people to trip and fall. As the people behind them are also subject to the wave of motion, they cannot stop moving to allow people to get back up, so people become trampled by those behind them. Under these conditions, people also overheat or become unable to breathe, and with no means by which to remove them from the congested environment, they are more likely to fall when moved randomly by the crowd. Fallen people act as an obstacle to the remaining crowd, making further tripping and trampling events more likely such that the situation rapidly escalates. These events of sudden, uncontrollable stress release can be analogised to earthquakes, where the build up of pressure over an extended period results in one violent quake. Helbing extended this analogy to look at the pressure within the crowd, which he defined as the local density multiplied by the local velocity variation, and found that this was the critical factor in determining the transition to dangerous turbulent behaviour. So how can these findings be applied to prevent dangerous crowd behaviour? Once crowd panic and trampling starts, it is uncontrollable and little can be done to prevent death and injury. But Helbing's team found that there were warning signs. The event at Hajj 2006 occurred around 10 minutes after turbulent motion set in and more than 30 minutes after the onset of stop and go flow. In Hajj 2007, one of the methods employed was automated video surveillance, programmed to recognise stop and go flow, giving an advance warning in time for the organisers to take preventative measures such as flow control, pressure relief and separation of the crowd to prevent shock-wave propagation. These measures helped to ensure that the event passed with no serious incidents. However, this method requires some prior knowledge of likely crowd hotspots to set up the appropriate surveillance systems. At present, no model exists which can simulate both transitions from laminar, through stop and go flow, to turbulent flow. To fully understand crowd behaviour and prevent future crowd disasters, further work needs to be done to create complete models of the behaviour of crowds at extreme densities. Sue Kirk is a third year PhD student in the Department of Physics |
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