Modelling Tawaf (2000 - 2012)

From 2000 - 2012, I modelled crowd movements and behaviours in Saudi Arabia and specifically the complex dynamical behaviour on the Mataf (circling the Ka'abah). In 2008 I was commissioned to define the Design Criteria for Al-Haram (Holy Mosque) in Makkah.

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Several simulations of Tawaf were developed for the client (MoHE) some are shown below.

Tawaf Analysis

We explored the dynamics of this ritual as it is one of the key constraints for any future design. We highlighted that the Mataf (area where Tawaf is performed) has a dynamic equilibrium level that is fundamental to all future design proposals. This is a combination of the unique geometry and the crowd behaviour. The current building was constructed during the Ottoman Empire. 

Tawaf Behaviour

We defined a series of behavioural models that relate to the stability of the Tawaf ritual and highlighted that is has a dynamic equilibrium – a level at which there is a stable throughput. The model was designed to ascertain the maximum stable and safe throughput of Tawaf. We highlighted the previous studies and the crowd models are in accord – giving similar values for output (in the order of 30,000 Tawaf’s per hour) and that there is an upper limit to the efficient (and safe) throughput. The results have profound implications for any future design and for the crowd safety on the Mataf.

Tawaf Dynamics

The capacity for Tawaf is governed by how easily a high density crowd can move round the Ka’abah. Each worshipper wants to get as close as possible to the Ka’abah and, if possible, touch or kiss the black stone. Hence the circling worshipers tend to spiral inwards as they circumnavigate the Ka’abah if space is available. The model reflected this behaviour. However, this increased the density in the areas nearest the Ka’abah and had a significant impact on the efficiency of movement. 

The crowd density in Tawaf during the peak seasons of Hajj and Ramadan reaches 8 persons per square meter, as concluded by Haj Research Centre (HRC) studies, however this is close to the Ka'abah not the overall density.

Measured Tawaf Capacity

Studies. dating back to 1975, had indicated that the capacity of Tawaf was close to 52,000 persons per hour, and that during peak times in Hajj and Ramadan the number of people performing Tawaf ritual was distributed over the three Haram levels (old building design) as follows: 

61% using Ground Floor for Tawaf 

15% using First Floor for Tawaf 

24% using Roof for Tawaf 

We highlighted that the limits are a function of both the available space and a sustainable crowd dynamics, namely that as the crowd density increases the efficiency of movement is significantly reduced, this in turn reduces throughput.

However recent studies (2008 - 2009) indicate a much higher throughput that previously recorded. This may be due to the increased capacity of the Massa'a building (sae'e). 

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These images are from the latest 3D crowd modelling system and photographs from the Mataf. 

Above - Simulation using the Ramadan data (we excluded the peripheral agents and focus on the Tawaf motion). We have models for all levels of the Mataf in both the existing Al-Haram and new designs.

                        Above - Models and simulations                                                        Below - photographs from research studies.


The Mataf has areas of extreme density and a complex dynamic

Over Crowding in Mataf

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