Stress Analysis in Sports: Orthopedics

Prosthetic Leg If you watched the Summer Olympics this past summer, specifically the men’s 400m race, you may have noticed something different. Oscar Pistorius, the South African athlete more commonly known as “The Blade Runner” has two prosthetic limbs in place of his legs, below the knees, that have spawned quite a bit of debate into their legality within the realm of the Olympics. As a double below knee amputee, Oscar has been fitted with carbon fiber transtibial prostheses upon which to run. As we continue our current series on stress analysis pertaining to the world of sports, this week’s blog will discuss at the differences between a human leg and Pistorius’ blades.

Engineering Accomplishments in Prosthetics

Human legs’ tendons are a viscoelastic material, meaning that they demonstrate both viscous and elastic properties. A prosthetic limb, conversely, is only almost purely elastic. The difference is that a human tendon will extend and return to its original state at about the same rate while a carbon fiber prosthetic will return much quicker than it is extended. While running, a human’s ankles, hips and knees absorb the energy from the impact between the ground and the foot. This similar action in the prosthetic is achieved as the J-curve absorbs the energy. The difference being that because it returns to its normal state much easier than a normal leg it has improved energy efficiency. In a 2007 study, this was confirmed when Pistorius was found to use 25% less energy than runners with 2 human legs. While this may seem to give him an unfair advantage, the lower viscosity of the blade demands that he move his legs about 16% faster than a normal bodied runner. Also, when examining the torque in a human foot the lever arm is not technically very long, especially when compared to a prosthetic blade. This means that if Pistorius were to push of the ground with the same force as an able-bodied runner he would create a much larger amount of torque and thus move his legs with more strength than competitors. However because he lacks ankles and the viscous resistance of a regular leg, he cannot produce nearly the same amount of force


The material that the prosthetic is made of has a very large impact on not only the price of the part but the ultimate strengths and stresses of the prosthetic. The more affordable materials for prosthetics such as Polypropylene and Polyethylene have Ultimate Tensile Strengths around 5,000 psi whereas the top of the line Carbon Fiber prosthetics, such as the blades worn by Pistorius have an Ultimate Tensile Strength around 500 ksi, a factor of 100,000 stronger[2].  A finite element analysis of a Polypropylene revealed that under max stress the prosthetic would have a 5% elongation, while the percent elongation that the carbon fiber of Pistorius’ blades can top out at 24%[3].

Pistorius’ activity in the Olympics has caused quite an interesting debate to come about. If it takes him technically less energy to move his feet, but is able to produce less torque and unable to manage corners well due to his lack of ankles, should he still be able to compete?  Researchers are currently working on completely replicating a human leg instead of the current J-curve prosthetic design, but have yet to make any real advancement due to weight and strength capabilities. Regardless of whether or not his blades have given him an advantage or a disadvantage, it is still incredible to see someone overcome such adversity with the advances in mechanical engineering and biomedical technology.



[1] Hasish, Rami “Oscar Pistorius’ Prosthetic Legs…” Huffington Post 8/10/2012 University of Southern California

[2] Richardson, Victoria “Analysis of a Lower Limb Prosthesis” Worecester Polytechnic Press 4/24/2008

[3] Gerschutz, Maria “Tensile Strength and Impact Resistance…” Journal of Rehabilitation Research and Development The Ohio Willow Wood Company, Mt. Sterling Ohio ,Volume 48 Number 8, pgs. 987-1004. 2011