Mind the gaps
Question: When I stand on a railway platform behind a knot of people trying
to get through the door of a crowded commuter train, do I maximise my chances of
getting a seat by approaching from behind the centre of the group, or along the
sides of the carriage?
Are there any specific mathematical rules governing such crowd behaviour?
Answer: If you arrive before most of the boarders, you stand a greater chance
of getting a seat. So, which part of the crowd moves faster and why?
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My organisation has a range of mathematical and software simulations for
predicting crowd movement at public sites.
The illustrations show a model of the way crowds flow through a doorway. This
model was first shown on the BBC鈥檚 Tomorrow鈥檚 World programme in 1993
and before that had been runner-up in the 鈥淚nnovation of the Year鈥� award. The
dynamics of movement are a function of the number of interactions with other
individuals during your progress towards the door gap.
Crowds flow more slowly down the centre and faster around the edges because
there is more space to manoeuvre at the edges and so there are fewer
interactions.
This may appear counterintuitive because most people think crowds act in the
same way as grains of sand in an egg timer, where the fastest flow is down the
central axis. Crowds are not affected by friction or gravity in the same way as
grains of sand.
At the edges of the queue you are aligned with the flow profile and have
fewer interactions. Your movement towards the open doorway is less impeded and
consequently faster.
The local geometry also has a direct relationship on crowd dynamics. The
introduction of a central barrier (a handrail at right angles to the open door)
changes the nature of the crowd movements. There is no sideways contact across
the barrier and this helps the overall flow rate.
By reducing interactions within the crowd you change its dynamics鈥攐ne
simple measure of this is shown in the interaction curves, drawn over the plan
view of the two diagram models.
To answer the original question, these curves predict that you maximise your
chances of a seat by approaching the train from along the carriage sides.
Keith Still
Legion Crowd Dynamics Limited
Kendal, Cumbria
Taxed roads
Question: What causes the corrugations in dirt or sand roads after they have
been used by vehicles for several weeks? Why do the corrugations occur with the
same frequency despite the differences in vehicle tyres and wheel diameters?
(continued)
Answer: Grains of sand do not have natural frequencies, but the suspension
systems of vehicles do. It is the vehicles鈥� resonant frequencies which are
responsible for the corrugations. Such frequencies are independent of tyre
dimensions.
John Chapman
Perth, Western Australia
Answer: Corrugations can develop on any rolling or sliding surfaces that are
in contact. They can be seen not only on dirt roads (their most jarring and
annoying manifestation), but also on tarmac and even concrete roads, on rail and
tram lines (most commonly following a rail junction and with a pitch of a few
centimetres), on the overhead copper conductors of electrified lines, on
weavers鈥� shuttles, on the vertical guides of lifts, and on ski and toboggan
slopes.
Corrugations may form whenever the force at right angles to the surface is
sufficient to cause permanent deformation. In the case of a wheel on a road,
when the wheel encounters any bump or irregularity, it is projected upward,
moves through an arc, and impacts further along the road, where it tends to dig
in and produce a small crater. Subsequent wheels that ride up from this crater
are likewise projected and again form a little crater beyond. The corrugations
already formed are reinforced by the repeated passage of vehicles, and new
corrugations continue to propagate down the road from the initial bump. You can
watch the pattern develop on a test track. The periodicity, averaging about 70
centimetres (27 inches) on dirt roads, depends on the average vehicle speed
(which determines the impact force), the material of the road, and the tyre and
springing constants of the vehicle. I studied the subject while at Melbourne
University using extensive observations of Australian roads and a circular test
circuit.
For more complete information, a popular account appeared in Scientific
American (January 1963), and a more technical version in Civil
Engineering & Public Works Review (May 1962, p 617 and June 1962, p
781).
Keith Mather
Eugene, Oregon
This week鈥檚 questions
Group therapy: Why have humans developed different blood types and is there
an evolutionary advantage? Surely, if blood types are due to random mutations,
one will be a better performer in general terms than the others? And why can鈥檛
different types be used for all patients requiring transfusions?
Iain Cunningham
Fareham, Hampshire
A similar question was asked by Ross Richardson of South Perth, Western
Australia.
Natural gunk: When walking in the Pennines I often notice that streams have
lumps of foam floating on their surface, particularly near waterfalls. There are
no sources of human pollution upstream, so what causes the foam?
Penny Johnson
Bishop鈥檚 Stortford, Hertfordshire