The formula for walking in heels

Those who have seen me on a night out will know that I cannot for the life of me walk in heels. My attempt to walk in high heels has been likened to ‘bambi on ice’, and the associated throbbing pain in the balls of my feet usually turns me into ‘that skank who is bare footed carrying her heels’. It is not a good look, so I usually resign myself to flats, (also not a good look for me, I’m only 5ft 2”ish).

This made me think, is there a way that physics can make heels comfier, so I don’t look like an idiot?

How high?

Ever wondered why some people can wear the sky high heels with no problem, and why some people like me can’t stand a couple of inches? A Professor at the University of Surrey has developed a formula for the best height of a heel for each person. The fancy formula looks like this: h=Q x (12 + 3s/8) and includes factors such as:

-Shoe size

-Cost of the shoe; more expensive means more height allowed, we apparently put up with more pain for pricey shoes

-How fashionable the shoe is and how many heads it will turn; beauty is painful, and we know it.

– Experience in wearing heels; practice makes perfect, so you can go slightly higher without wobbling.

-Amount of alcohol consumed; apparently this makes higher heels more difficult to walk in. (Personally I always find heels easier the more drunk I get, but maybe I just become less aware of how much I am falling over).

So considering all these factors it suggests that a woman with some experience in walking in heels should go no higher than a 5 inch heel to remain stable. This does however refer to stiletto heels, and physics suggests that a wider heel would be more stable at a greater height than a stiletto.

Smaller surface area of the shoe = more pressure = more pain:

In basic terms, the smaller the surface area of the heel (i.e. stilettos), the greater the pressure is on the area of your foot which is in contact with the floor. A wider, chunkier heel would create a larger surface area, which would reduce the pressure felt on your feet.

Here is the maths: pressure = force/area.*

My stilettos (shown below) have a heel surface area of 70mm² and lets say for simplicity the force applied on walking is x. That would make the pressure x divided by 70.

My stilettos, thin heel means more pressure.
My stilettos, thin heel means more pressure.

My chunky wedges have a heel surface area of 950mm², reducing the pressure to x divided by 950. As x/950 is much less pressure than x/70, in theory that should make these lovely shoes much more comfy….

My chunky platform shoes: wider heels mean less pressure.
My chunky platform shoes: wider heels mean less pressure.

Heels that Pythagoras would be proud of:

Research also suggests that the placement of the heel at the correct distance along the shoe is also important, to reduce the angle of the foot (it’s based on Pythagoras theorem, it actually has a use!). If the foot is at a steeper angle, more pressure is on the ball of the foot and your foot and ankle will feel strained.

So when you’re looking for comfy shoes, think of the heel as part of a right angled triangle (see below). The steeper the angle of the longest edge of the triangle, the more uncomfortable the shoe is likely to be.

The red and blue lines show the angle of the foot in the shoe, a steeper angle means more pain and less balance.
The red and blue lines show the angle of the foot in the shoe, a steeper angle means more pain and less balance.
The blue line is steeper than the red, which could explain why the pink heels are much more painful and wobbly than the white ones.
The blue line is steeper than the red, which could explain why the pink heels are much more painful and wobbly than the white ones.

 Heels designed with physics in mind:

I stumbled across some shoes that use springs, rubber balls and hydraulics to absorb impact, so less pressure is felt on your feet. These shoes designed by Silvia Fado are not only beautifully intriguing, but very functional. Although they aren’t what I would consider as ‘everyday wear’ the principles explored on impact absorption could one day lead to comfortable, gorgeous shoes.

Shoes with a spring and hinge hydraulic system: http://www.silviafado.com/kinetictraces/
Shoes with a spring and hinge hydraulic system:
http://www.silviafado.com/kinetictraces/

So there we have it, heels 5 inches or less, with a larger surface area are the way forward. Somebody didn’t give these girls the memo though:

Till next time,

Lucy

xxx

*If you’re being technical you would use metres squared, and work out the force=mass*acceleration, and state pressure in pascals, but I have simplified this for the purpose of this explanation in layman terms. 
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One thought on “The formula for walking in heels

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