Module 2, lesson 1 · 50 minutes
Force, not panic: how a crowd crushes
People in a dense crowd die because the pushes of many rows add up on a few chests, not because anyone loses their head.
You’ll be able to
- explain compressive asphyxia, and what the evidence says and does not say about how fast it kills;
- describe how pushing forces accumulate through the rows of a crowd, and why density decides whether they do;
- quote the main force figures with their provenance, and state Fruin’s FIST.
Introduction
After fatal crowd incidents, investigators keep finding the same thing: steel that has been bent out of shape. John Fruin, whose Levels of Service you met in Module 1, put it this way: “Evidence of bent steel railings after several fatal crowd incidents show that forces of more than 4500 N (1,000 lbs.) occurred”
That is a horizontal force roughly equal to the weight of 450 kg. Nobody can push that hard. In one test Fruin reports, five people pushing as hard as they could managed 3,430 N between them
The answer is addition. In a crowd packed tightly enough that nobody can step back, every lean and every shove from behind travels forward through the bodies in between and arrives at the front. This lesson is about that addition: what it does to a human chest, how quickly the total grows, and how sure we are of the numbers.
What kills: compressive asphyxia
The interim report of the Taylor inquiry into the Hillsborough disaster gave the cause of death in a single sentence:
“In virtually every case the cause of death was crush asphyxia due to compression of the chest wall against other bodies or fixed structures so as to prevent inhalation.”
Fruin, writing about crowd disasters in general, reached the same conclusion: “Virtually all crowd deaths are due to compressive asphyxia and not the ‘trampling’ reported by the news media”
Hillsborough also shows that victims can be upright or fallen. Taylor describes some held upright “by pressure all round”; when a barrier broke, “Many fell and the involuntary rush of those behind pressed them down”
Taylor’s report, paragraph 77: “If no relief came in four minutes there would be irreversible brain damage; if longer, death”
The Hillsborough Independent Panel in 2012 cast “significant doubt on the single unvarying pattern” contested. It found that 28 victims “did not have traumatic asphyxia with obstruction of the blood circulation”, and that in 31 “the heart and lungs had continued to function after the crush”
Both sources are serious, and they are not about the same question. Taylor gives a general physiological rule of thumb; the Panel looked at the evidence for each victim. For Hillsborough, “death within minutes” is contested. Treat compressive asphyxia as something whose speed varies from person to person, which means rescue time matters.
Two short lines from the field’s best-known researchers say the same thing from opposite directions. Keith Still: “People don’t die because they panic. They panic because they are dying”
How pushes add up
Start with a sparse crowd. Someone behind you leans on you. You take half a step forward, the lean is spent moving you into empty space, and the person in front of you feels nothing. Each person absorbs the push they receive.
Now pack the crowd until every body touches the next. There is no empty space to step into. A push from behind cannot be spent moving you, so it passes through you to the person in front, and through them to the next. It behaves like a row of books on a shelf pushed from one end: every book carries the push to the end of the shelf.
Oberhagemann’s 2012 technical report for the German vfdb, “Static and dynamic crowd densities at major public events”, describes this transition with numbers. At 2 p/m² people are “completely decoupled” and a fall does not affect others. At 5 p/m² there is still limited room to absorb forces. At 6 p/m² force can no longer be absorbed; the critical density is “around 6.0 p/m²”
A model you can hold in your head
Here is a deliberately simple model of that idea. Each of N rows pushes forward with the same force p. Of any push that reaches a person, a fraction t is passed on to the person in front, and the rest is absorbed. The front row feels its own push in full, the next row’s push times t, the row after that times t², and so on.
F = p · (1 + t + t² + … + tᴺ⁻¹) = p · (1 − tᴺ) / (1 − t) when t < 1; F = p · N when t = 1
- F
- force on the front person, N
- p
- push from each person, N
- N
- number of rows pushing
- t
- share of a push passed on, 0 to 1
The two cases behave completely differently. If t is less than 1, the series converges: however many rows push, F never exceeds p / (1 − t). If t equals 1, nothing is lost and F grows in proportion to the number of rows, without limit. Density decides which case you are in. In the interactive below, t is 0 at 2 p/m² and rises in a straight line to 1 at 6 p/m², anchored on Oberhagemann’s descriptions
Worked example
Ten rows, each person pushing with 150 N (about the weight of 15 kg).
- At 3 p/m², t = (3 − 2) / 4 = 0.25. F = 150 × (1 − 0.25¹⁰) / 0.75 ≈ 200 N. Adding rows changes almost nothing: the ceiling is 150 / 0.75 = 200 N, about one and a third people’s push.
- At 5 p/m², t = 0.75. F = 150 × (1 − 0.75¹⁰) / 0.25 ≈ 566 N, with a ceiling of 600 N.
- At 6 p/m², t = 1. F = 150 × 10 = 1,500 N. Seven rows are enough to pass 1,000 N (7 × 150 = 1,050 N), which is about the safe static chest force estimated by Kroll and colleagues
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Nobody in that crowd is doing anything unusual. Each person is leaning with the weight of a toddler. The danger comes from adding, not from any individual’s behaviour.
- Leave density at 3 p/m² and drag the rows from 1 to 20. The force on the front person barely moves past 200 N.
- Set density to 6 p/m² and drag the rows up again. Watch the row count at which you cross 1,000 N.
- At 5 p/m² with 20 rows, raise the push per person until the front person passes 1,000 N. What does “Most force any number of rows can give” tell you?
- Pick a state just under a threshold and press “A surge”. A brief doubling of everyone’s push doubles the front force too.
Below about 6 p/m² the force on the front person saturates: at 3 p/m², twenty rows give barely more than one or two people’s push. At 6 p/m² and above nothing is absorbed, so force grows with every row, and seven rows at 150 N each pass 1,000 N. Danger depends on how many people are behind you, not just on how many are around you.
Illustrative, not a validated biomechanical model. The transmission rule (0 at 2 p/m², 1 at 6 p/m², linear between) is our teaching assumption, anchored on Oberhagemann’s descriptions
Why can a crowd bend steel that no individual could?
Because at high density nobody has space to absorb a push, so the pushes of many rows pass through the people in between and add up at the front. Twenty modest leans of 150 N sum to 3,000 N if nothing is absorbed. The same twenty rows at a lower density, where each person can step and absorb, put only a few hundred newtons on the front.
How big the forces are, and how we know
Force figures are quoted widely in crowd safety, often without their origins. They come from very different kinds of evidence: a measured test, damage inspected afterwards, a biomechanical model, a conference paper known only through a quotation. Each kind deserves a different amount of trust.
| Force | What it describes | How it was obtained | Source |
|---|---|---|---|
| 623 N | Tolerable force against a bar for men, rising to 800 N with push-back (a subjective discomfort threshold) | Hopkins et al. 1993, as quoted by Still. Secondary | |
| ≈ 1,000 N | Safe static force on the chest | Biomechanical model (Kroll, Still and colleagues, 2017), not crowd data | |
| 1,112 N | Death after 4–6 minutes of this load | Hopkins et al., as quoted by Still. Secondary | |
| 2,550 ± 250 N | Flail chest, a severe rib injury, under a static load; 4,050 ± 320 N under a dynamic one | Same biomechanical model | |
| 3,430 N | Five people under a simulated “panic” | Measured in an Australian handrail study, reported by Fruin | |
| > 4,500 N | Bent steel railings after fatal incidents | Inferred from damage; no measurement cited. An order of magnitude | |
| 6,227 N | Death 15 seconds after this load | Hopkins et al., as quoted by Still. Secondary | |
| 6.0 kN per metre | Test load for a crush barrier: “an evenly distributed force of 6.0kN/metre width to be applied for 3 five minute periods” | A structural test standard, quoted by Taylor (paragraph 238) |
Three points of care follow from the table.
- Do not merge the barrier test with the body figures. 6.0 kN per metre is how hard a barrier must be able to resist, spread along its length, for a structural test. 6,227 N is a load on a single person. They happen to be close numbers; they measure different things
. - Fruin wrote more than 4,500 N. You will sometimes see “4,450 N”. That is just 1,000 lbf converted at 4.448 N per lbf, and it appears in no source
. - The fatal figures are the least certain. The Hopkins numbers come to us only through Still’s quotation of a 1993 conference paper. Kroll and colleagues’ figures come from a biomechanical model and comparison with historical cases, not from measurements in a crowd
.
The Hopkins figures pair a force with a duration: 1,112 N over 4–6 minutes, 6,227 N within 15 seconds
Fruin’s FIST: four things to control
Fruin summarised what shapes a crowd incident in four words
- Force: “FORCE (F) of the crowd, or crowd pressure”
- Information: “INFORMATION (I) upon which the crowd acts or reacts, real or perceived, true or false”
- Space: “SPACE (S) involved in the crowd incident, standing area, physical facilities…”
- Time: “TIME (T) duration of incident, event scheduling, facility processing rates”
Read FIST against what you have just seen. Force is what accumulates. Space is what lets people absorb it, and what a crush takes away. Time is both how long the force lasts on a chest and how long the arrival of a crowd is spread over. Information is what people know about what is happening ahead of them: a crowd at the back that cannot see the crush at the front keeps pushing. Module 3 shows how much that last word matters.
A concert crowd is at about 6 p/m² in front of the stage, twelve rows deep. Use the model to say what happens to the front row if people at the back lean forward a little harder when the headline act appears. Which letters of FIST would you act on to prevent it?
At 6 p/m² and above the model passes on every push, so the front force is the sum of all twelve rows. Each extra newton of lean at the back reaches the barrier, multiplied by twelve. The obvious levers are Space (keep the front section below the density where force accumulates, for example with pens or a lower capacity), Information (let the back of the crowd know what is happening at the front) and Time (spread the build-up so density never reaches that point, and be ready to stop the show quickly). Force is the outcome you are controlling, not a lever in itself.
- “People in crowd disasters are trampled to death.” Virtually all crowd deaths are from compressive asphyxia, not trampling
. People die standing up as well as on the ground. - “The victims are at the front because they ran or pushed.” They are at the front because that is where force accumulates. The people doing the pushing are usually rows back, often unaware of what is happening ahead.
- “Fruin measured 4,450 N.” Fruin wrote more than 4,500 N, and inferred it from bent railings. 4,450 N is a unit-conversion artefact
. - “The Green Guide’s 6 kN is the force that kills.” 6.0 kN per metre is a barrier test load, a property of a structure, not a load on a person
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