Re: What is the physics of running shoes?

As with all products that involve human interaction (such as cars,
clothing, computer interfaces, chairs, you name it), the design and
engineering involved must take several "needs" into account.  These include
functionality, performance, reliability, cost, recyclability, safety,
compatibility, aesthetics, ergonomics, user-friendliness, and life span (as
all so eloquently put by one of my Mechanical Engineering professors). 
However, many of these needs compete with each other, so every piece of
engineering and design comes with compromise.  What is more durable is
generally more costly, or perhaps does not perform as well.  It also may
not be as comfortable.  You can look at cars and see this very
clearly...high performance race cars are less comfortable because they must
be very rigid and light, and the priority is given to performance parts
such as large engines.  There are a few luxury cars which are high
performance, but the level of power required to overcome the excessive
weight caused by all of the luxury accessories pushes the cost up very,
very high.  

With shoes, it is no different.  Running shoes place high importance on
performance and functionality.  Ergonomics are also pretty high on the
list, but aesthetics are not quite as important, maybe.  The overall
struggle that you'll probably encounter in running shoes is the balance
between performance, ergonomics, life span, reliability, and compatibility
(due to different foot types).  

A big struggle with shoes is overcoming the different foot types.  A
neutral foot is easy to deal with, but what about someone with an
over-pronated footstrike (foot rolls in) or a supinated foostrike (foot
rolls outward)?  A neutral runner can get the best performance because his
shoe does not require a lot of additional support.  Therefore, the shoe can
be lighter, more flexible, etc.  A pronated foot will require a lot of
additional support, and therefore the shoes will be less flexible.

Concerning the more PHYSICS aspect of this, we're going to look at a
neutral foot for ease.  Running shoes are differently constructed based on
their purpose.  A training shoe for long distance runners will be
considerably more durable and "cushy" than a racing shoe.  A long distance
shoe or training shoe needs to protect the runner from impact, since impact
can damage the joints and is painful.  The midsole will probably be pretty
soft, with a heel that is more resistant to compression and the forefoot
area being even MORE resistant to compression than the heel area.  Also,
the heel and forefoot areas would be made to absorb shock more than the
center of the foot.  This makes sense, because the center of the foot
(arch) does not take very much impact.  The heel and forefoot areas take
higher impacts, and therefore must be made to take those impacts. 
Furthermore, they also need to be resistant to compression (particularly
the forefoot) because if the midsole compresses a lot, the runner will be
wasting a lot of energy in compressing the midsole rather than putting that
energy into motion.  It would be like running in sand!

However, it would be a bad idea for the manufacturers to put this thicker
and more resilient material down the length of the whole shoe, since it
will most likely weigh more and be more costly.  These things have to be
taken into account.

A racing shoe will have far, far less padding and will be constructed to be
as light as possible.  Less energy is wasted in lifting the shoe, less
energy is wasted in the compression of padding, and the shoe will be
faster.  However, the shoe will not be as durable and will leave the joints
prone to pain and suffering over long term use.  

Concerning grip and friction, the bottom of a running shoe may be flat for
a track surface or spiked for a grassy surface.  The point here is to keep
the shoe from slipping on the ground.  Energy = force x distance, so if
your foot slips, you've lost energy through that distance of slipping. 
Congratulations!  You've warmed the ground by turning your kinetic energy
into thermal energy, but that wasn't what you were after...you wanted to
move.  A flat shoe is good for the track because it provides a full surface
area contact and will not have additional weight/material on the outsole. 
A spiked shoe is good for the grass because once the spike drives into the
ground, there are not only frictional forces involved but also normal
forces between the spike's surface and the dirt pushing against the spikes.
 Normal forces tend to be a lot more effective than frictional forces in
stopping movement.

Also concerning grip, the INSIDE of the shoe would provide better
performance, perhaps, if the lining were a high-grip rubber.  However, this
would tear and blister the skin, so the shoes are designed with a slicker
interior (and with the intention that you will wear socks).  The foot is
held in place by the normal forces on the heel and a combination of
frictional and normal forces on the top of the foot.  The heel counter is
the stiff piece behind the heel that provides stability, but it also
surrounds the heel to help keep it in place.  Tightly lacing the shoes
helps hold them in place by increasing the normal force on the top and
sides of the foot.  Since the friction coefficient of the material inside
is not changing, the higher normal force will cause an increase in the
maximum static friction force and will help keep the foot from slipping. 
Again, any slipping will result in a loss of energy to heat, and that is
not the goal of a running shoe.

In the purest sense, the most efficient shoe will be as light as possible,
not compress at all, and will not slip at all on the ground.  However,
compromises must be made to accommodate the requirements of the human body
concerning comfort.  Of course, marketing requires that it look good, too,
but I, as an engineer, do not deal with aesthetics so much, so you will
have to look elsewhere for advice on that.

Hope this helps you some....

Joel Chapman

shoe information:  http://www.runningwarehouse.com/LearningCenter/
(the best shoe-specific information I could find)

concerning friction:  Hibbeler, RC.  "Engineering Mechanics:  Statics"
Tenth Edition 2004, Chapter 8.