“Someone who builds a mathematical model can get carried away with all the clever things that can be done with it. The model becomes a safe little world, free from anxiety, free from office politics, rewarding in its own right. This often results in a very clever model that has little to do with reality.” Sam L Savage, Consulting Professor at Stanford University

A recent debate on a computational science forum about a “new model of crowds” revolved around a key question: Would you feel safe driving a car welded together from parts of other cars?

Or a vehicle that had never passed an MOT, had no quality assurance during its manufacture? So why do major clients accept similar standards for crowd models, especially when they are safety critical?

Over the last quarter of a century there have been significant developments in both computational power and simulation graphics. The dividing line between computer generated image (CGI) and reality is difficult to determine in the movies.

This has raised expectations on crowd modelling and, specifically, client expectations for major event crowd modelling. A Hollywood blockbuster has a budget of millions and years for perfecting the final output.

Neither the budget, nor the time, for simulating crowd safety in the built and complex environment is available. As a result, crowd models typically bear little resemblance to reality, but look realistic enough to convince a client.

Pinch point

On the right is an example from a report on a recent major event, warning about a crowd density that reaches dangerous proportions at a pinch point for crowds departing the site. It is a simulation – but a quick look at Google Earth and Google Maps reveals a very different situation on the ground.

The model shows a density approaching crush limits (greater than six people per square metre).

Let us review the fundamental model of this section of road. It is 10m wide (with a level field on the left (photograph below).

An egressing crowd would have a flow rate of approximately 82 people per metre per minute, which is 820 people per minute on a 10m wide road and 160m long.

There are some published safety limits (no more than four people per square metre) from the Green Guide (UK Guide to Safety at Sports Grounds) which gives us the following parameters:

Area = 160m x 10m = 1600 square metres
Capacity (at four people per square metre) = 6,400 people

So from a simple model (calculation) the safe limit is 6,400 people.

 

We can the estimate the number of people entering the system (leaving the stadium) and leaving the system (crossing the road). By way of example, if the exit gates leaving the stadium are greater than 10m then the queue will begin to form at the road entry but only if crowd numbers exceed a flow rate of 820 people per minute.

At the so-called pinch point the crowd must be approaching faster than the crowd can cross the road.

Basically, this is a queuing model and a simple spreadsheet provides a minute-by-minute answer to the crowd build-up’s nature and the basis for a crowd-management plan.

Using models rather than simulations, this plan gives operators the means to both assess risk and understand situations on a minute-by-minute basis. We teach this in a two-hour session using similar examples.

Simulation is not the same as reality. Crowd simulations consist of welded-together parts – a graphics engine, a simulation model, assumptions on crowd behaviour – and are typically driven by people who have clearly not visited the site or had the foresight to use free tools such as Google Maps and Street View.