I worked as a volunteer at the special Olympics some years ago. The job mainly involved making sure spectators could get into and out of the events easily, that emergency services can easily gain access and that spectators and athletes were kept separate. The venues were not huge and the spectators were happy and sober. Still I got some impression of the kinds of things needed to ensure crowd safety at events.
I want to put a figure on how many people could safely fit through the tunnel that was the sole access point to the love parade venue. A 16 meter width is given by most media outlets.
But some say it is 30 meters wide. Most seem to put the number of people there at 1.4 million but others at only 500,000 'an event set up for 250,000 ended up with an estimated 500,000 to 1 million'.
How long does it take to get everyone into a venue? How many people an hour will try enter a venue? I do not think all 1.4m people try enter in an hour. But I would guess most people try to enter a venue in a three hour period. Each hour you could expect over 300,000 people to try and enter through the tunnel. People are unpredictable meaning that you would need to be able to have more than this safely in case loads turn up at the same time.
Who else deals with crowd volumes like this? Every few years during the Muslim Hajj there is a crowd related accident. They are building a new bridge to improve safety. There is a description of this bridge here (pdf).
the new, multi-level bridge structure which will accommodate and ease the flow of 3 million worshippers during a single daylight period. The proposed new Jamarat bridge is a superior structure formed of 4 platform levels... each of the bridge’s 4 floors is roughly 600 m-long, with variable widths (ranging from 60 m to 97 m
The engineers describe these 4 floors as at least 60 meters wide. Each 60 meters in width is supposed to handle .75 million people if scaled linearly to 16 meters that would be 200 thousand people during the day. The new Saudi bridge is designed with a much larger channel to move people than they had in Germany. Pilgrims may act differently to other crowds as they stop to perform religious ceremonies.
Another terrible crowd incident was the Hillsborough disaster where 96 people died. A quick search about football crowd safety found this document. It is a very interesting article and well worth a read
The document states
"the safety limit for crowd density is defined as 40 people in 10 square metres for a moving crowd" the tunnel at 16m wide and 100 meters long should only hold 6400 people. Walking at 38 meters per minute. 100 meters would mean it would take 156 seconds to get through the tunnel. 6400 people every 156 seconds is 147,000 in an hour. This means it would take ten hours for 1.4 million people to safely travel through.
Reuters here states
"Authorities have not yet been able to explain how exactly the tragedy happened -- near a tunnel that led to a ramp into the festival grounds. Most of the victims were found dead on the ramp and none in the tunnel, authorities said"
The football document also in Section '2.8 Wembley Complex Station' gives this equation
No. of Units of Exit Width = Number of Persons (1)
required (each width = 0.55m) Flow Rate (2) x Evacuation Time (3)
"Where number of persons (1) means the maximum number of people that could be expected to be on a platform at any time. Flow rate (2) means 40 persons per minute for escape routes incorporating stairs, and 60 persons per minute for level escape routes (without stairs). Passenger walking speeds should be assumed to be 38 metres per minute for horizontal circulation."
Using the Wembley equation above 16 meters *.55 meters means 29 people can safely span across the tunnel. 40 flow past a minute if the escape route has a stairs and 60 if it is flat. The ramp sounds like it would hinder flow in a similar way to a stairs.
Once again this is all back of the envelope and as more facts come out a much better estimate of how many people could safely negotiate the site will emerge. A reasonable estimate of the number of people who could travel through the tunnel in an hour is (tunnel width/person width)*number or people per minute * 60 minutes
which in a 16 meter wide tunnel with a stairs at the end is (16/.55)*40*60=70,000
Best case scenario with a wider tunnel and no stairs 30 meters/.55 meters *60 people *60=200,000 which is less than the expected number of people.
This calculation indicates that a cursory look at at the venue entrance would give someone grave concerns about safety for a smaller crowd than turned up on the day.