Stress Analysis of Athletic Equipment: Shoes

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Stress Analysis: Athletic Shoe Properties

Foot with Tennis Shoe RunnerAthletic gear can benefit from engineering efforts, mainly mechanical engineering and materials science engineering.  Athletic gear must be strong yet flexible, and light weight.  In sports such as football, hockey and baseball, athletes put gear to the test repeatedly.  For safety reasons,  the players wear different types of protective padding and gear which must be able to withstand multiple shocks and stresses.  In this blog, we will be looking at the stress analysis of shoes and how they are designed to benefit the runner.

Shoes are probably the most common piece of equipment used in sports of all kinds.  The main stress that they experience is known as compressive stress, coming obviously from the compressive force of standing.  Compressive stress in shoes is analyzed using two different methods, the individual cell gas pressure and the deformation of the polymer structure.  To analyze the air pressure’s contribution to the overall stress each of the cells in the shoe’s base is assumed to act as a piston, in that it recoils when a force is applied to it and returns to its original state after the force is removed.  If each individual cell is assumed to be a piston then the entire sole of the shoe can be assumed to act as a piston for the purposes of stress analysis.  Elastic recovery degrades with usage; simply, the athletic shoes lose their ability to bounce back or recover over time.  A new shoe using Ethylene-vinyl acetate (EVA) foam requires nearly 20 N (4.5 lbf) to deform, whereas a shoe that experiences an hour of running will deform almost 1mm from the same force.  This may not seem like much, but it is a considerable amount when the foam of a shoe is only about 14mm thick; a small deformation can make a large difference.  A new shoe will stop deforming at about 160 N of compressive force, or about 36 lbf, with a deformation of about 6.5 mm, whereas the same shoe after an hour of use will deform up to 7.5 mm under the same force.  Another similar study used finite element analysis (FEA) to analyze the stress under the heel of the shoe which experiences more compressive force than the rest of the shoe.  They analyze the Nike Shox shoes that claim to use 4 polyurethane springs to increase the cushioning on the heel.  In the lab tests with simulated running these claims were in fact verified, showing that the heels’ construction was able to handle a much larger stress than a regular EVA shoe.  However, in the practical tests it was seen that while the shoes were more cushioned they changed the running style of many wearers so that they began to land on their heel first instead of their toes.  At first the increased padding makes this tolerable for the runners body, but as the cushion wears down in time the heel first method will increase stress on the runners legs and lead to wearing down of tendons and cartilage.

One of the factors often overlooked while analyzing shoes is the impact the rise in temperature has on the dependence of stiffness on temperatures, or the abilities of the materials used in the shoe.  It takes about 20 minutes for the shoe to reach its plateau temperature, while receiving heat from both the runners’ foot and the ground.  As the temperature nears the foams melting temperature, around 70o C, it becomes less able to bounce back to its original form and thus delivers less support and cushioning to the runner. Therefore,, manufacturers make shoes of varying hardness for winter and summer.  Thus, athletes should use the proper athletic shoe, or risk injury.

Engineering Options In Future Design

The demand for more efficient and beneficial shoes is always increasing, and as of now there are a couple of tool and design options available that help with the engineering of new product.  One design option is to begin integrating a rubber shock absorber that can provide more cushion and better stability than the current foam design; however it is a trade off in terms of weight, seeing as rubber weighs much more than foam and could slow runner’s feet down and fatigue them faster.  Some of the tools available that the engineers could make use of would be Computer Assisted Design (CAD) software to produce better imaging to examine the deformation of the foot while running.  This coupled with Computational Fluid Dynamics (CFD) techniques will also attempt to reshape shoes to become more aerodynamic and allow for increased air flow into the shoe to better control the temperature while in use.

As we move forward in our series, we will examine the other types of sports equipment and how their materials and design make an impact on the athletes within their sport.



Aerts P, Ker R F et al.  (1995) The Mechanical Properties of the Human Heel Pad.  J. of Biomech., 28, 1299-1304.

Aguinaldo, A Mahar A et al.(2002) Ground Reaction Forces in Running Shoes, Proc 20th International Sym Biomech in Sports University of Extramedura, Spain.

Bobbert M F, Yeadon M R and Nigg B M (1992), Mechanical Analysis of the Landing Phase in Heel-Toe Running, J.  Of Biomech., 25, 223-234.


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