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## Sex and the City stars stay upright because h=Q.(12+3s/8) say scientists

22.03.2004

As Sex and the City’s Carrie finally wanders off our television screens, physicists at the Institute of Physics have devised a formula that high-heel fans can use to work out just how high they can go. Based on your shoe size, the formula tells you the maximum height of heel you can wear without toppling over or suffering agonies.

h = Q.(12+3s /8)

h is the maximum height of the heel (in cm)

Q is a sociological factor and has a value between 0 and 1 (see below to work this out)

S is the shoe size (UK ladies sizes). This factor makes sure that the base of support is just good enough for an experienced and sober, high-heel wearer not to fall over.

“Although at first glance our formula looks scary” said Dr Paul Stevenson of the University of Surrey who carried out the research for the Institute, “It’s actually pretty simple as it’s based on the science you learnt at school and which you never thought you would use in real life, in this case Pythagoras’ theorem (1) Applying this to shoes can tell us just how high the heel of the foot can be lifted above the ground.”

Dr Stevenson went on to describe how ‘Q’ – the essential sociological factor had been worked out.

“Essentially this part of the formula explains what women have always known – that you don’t buy shoes just because they are comfortable, you can afford them and they look good – many other variables come into play”

‘Q’ is defined as follows:

p.(y+9).L
Q = ----------------------------------
(t+1).(A+1).(y+10).(L+£20)
The variables are:

p – the probability that wearing the shoes will help you ‘pull’ (in a range from 0 to 1, where 1 is pwhooar and 0 is stick to carpet slippers). If the shoes are a turn-off, there’s no point wearing them.

y – the number of years experience you have in wearing high heels. As you become more adept, you can wear a higher heel. Beginners should take it easy.

L – the cost of the shoes, in pounds. Clearly, if the shoe is particularly expensive, you can put up with a higher heel.

t – the time since the shoe was the height of fashion, in months (0 = it’s the ‘in thing’ right now!). One has to suffer for one’s art, and if the shoes are terribly fashionable, you should be prepared to put up with a little pain.

A – units of alcohol consumed. If you’re planning on drinking, be careful to give yourself a little leeway for reduced co-ordination.

So using this formula, if Carrie Bradshaw, who is an experienced high-heel wearer (let’s guess at 5 years experience) wears her latest drop-dead gorgeous designer originals when sober, she can cope with a heel height of a staggering 12.5 centimetres (just over 5 inches).(2) However, if she over-indulges in cocktails, the ‘safe’ heel height (and perhaps also Carrie) plummets. Using the same example as above, if she consumes 6 units of alcohol she would be better advised to stick to shoes with only 2cm heels(3).

Laura Grant, a physicist from Liverpool University welcomes the Institute’s new formula commenting, "many of my physicist colleagues have no trouble understanding quantum mechanics but can’t figure out how women can wear high heels. Now I can explain to them how I minimise the probability of tripping up”.

The Institute of Physics website, physics.org has more fascinating facts on the physics of shoes, including high heels. Just type ‘high heeled shoes’ into the enquiry box.

1 Pythagoras theorem: In a right-angled triangle the square on the hypotenuse (longest side) is equal to the sum of the squares on the other two sides.

2 In this example, shoe size (s) is 6
p = 1, y = 5, L = £300, t = 0, A = 0 giving a Q factor of 0.88
so heel height is 12.54 cm

3 As above but with A (alcohol) = 6, Q factor falls to 0.15, giving a heel height of 2.01cm

Dianne Stilwell | alfa
Further information:
http://www.iop.org

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