It has been widely reported that 300,000 people watched Auckland’s 2010 Santa Parade but this number is so awry that it is both absurd and amusing.

Crowd counting can be contentious, especially when issues of sponsorship and measures of political support are at stake. Therefore it’s no surprise that crowd counts can vary wildly depending on who is doing the counting.

Washington, D.C. is a city famous for political rallies attracting massive crowds. An example is the Restoring Honor rally which was held there on August 28 this year. The crowd sizes reported in the media were mostly around the 300,000 to 500,000 figures but some estimates were as high as a million. Also two scientifically conducted counts came up with figures of 87,000 and 80,000. You would think that Washington would have mastered the science of crowd counting by now.

Could similar conflicting estimates apply to the Santa Parade? With so much commercial sponsorship in this event some bias could perhaps be expected.

Let’s wade into some numbers. We shall estimate the crowd number as an armchair exercise and for validation we shall also calculate the numbers using a scientific method.

The first observation is that there simply isn’t enough room on the parade route to squeeze in 300,000 people.

The parade route is 2270 metres long and Queen and Albert Streets have a width of 26m including the footpaths. Customs Street is a bit wider at 33m.

Multiplying those numbers together and adjusting for Customs Street gives us 60,000 square metres maximum road and footpath area to fit people. But you still have to fit in the parade itself.

The distance between the blue limit lines varies but it averages about 60 percent of the total road width. That leaves us with a maximum people area of 24,000 square metres.

To fit 300,000 people into this space they would have to be squished in at a rate of 12.5 people per square metre. That’s virtually impossible.

If you draw a square on the floor one metre by one metre and get 12 and a half volunteers you will see that even four people in the area is pretty uncomfortable.

To refine our numbers we shall use crowd figures from the “Jacobs method” invented by Professor Herbert Jacobs of the University of California at Berkeley. His office overlooked the grid-marked plaza where students frequently gathered to protest and he could make accurate counts of people.

His rule of thumb holds that a “tightly packed” crowd fills 2.4 persons per square metre. The number drops to 1.6 per when people are standing with elbow room at the sides and at the front and at the back.

Let’s take a middle value of 2.0. This is the same as our estimate of 2.0 persons per square metre for Eden Park’s West Stand which looks tightly packed when full.

So if the whole parade route were packed then there would have been at most 48,000 people. But the route wasn’t packed. There were stretches on Albert Street where there were no people. Even the densest areas on Customs Street still had room for walking and even more people.

If we take a stab and guess that a third of the total area wasn’t occupied we come up with the number 32,000 people tops. This is a guess from an armchair exercise. Now let’s go into the field for some accurate counts.

We took photos of the crowd along the route – not to count every person individually but to obtain estimates of the people density at various points. The idea was to estimate the crowd density by counting the number in a five metre length of road. Dividing this number by five gives us the number of people per metre. We counted both sides separately since people were more numerous on the shady side of the streets.

This work can be automated by computer using scientific concepts such as “fractal dimension” to turn images of people into “Minkowski sausages.” We had just 28 photos so we did it using our own brains.

Four sample photos are shown. For each photo the caption gives the estimated number of people per metre on just the far side of the road.

Queen Street 10.0 people per metre | |

Customs Street 13.2 people per metre | |

Albert Street 10.1 people per metre | |

Albert Street 2.2 people per metre |

Our estimates of people per metre of road range from 17 on Queen Street and 24 on Customs Street, down to zero on parts of Albert Street and Mayoral Drive. The average was 13.4. Multiply this by the parade length of 2270 metres and we get around 30,000 people.

The margin of error is about 5000 so there’s no way we could support the figure of 300,000 as being realistic.

Next time you are at the Santa Parade look at the crowd. For each person you see ten people will be reported as having occupied that spot. Quite amusing really.

Read Brian Rudman's Herald reference to this article

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