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The Physics of Hamstring Injuries

Illustration: Elia Pirtle

Illustration: Elia Pirtle

By Bronwyn Dolman

A spring-mass “hamspring” system explains why one particular muscle in the hamstring group is so prone to injury in sprinting sports.

Hamstring strains are a common sporting injury at all levels of football, from weekend warriors through to the professional ranks. Each Australian rules football club will have six or seven players sidelined with hamstring strains each year, and the 2013 AFL Injury Report states that “hamstring strains are still the number one injury in the game in terms of both incidence and prevalence (missed games)”.

Your hamstrings are three muscles in the back of your leg – the semimembranosus, semitendinosus and biceps femoris. All three muscles attach at the same point in your hip at one end, and to both sides of your knee at the other.

As you move, your quadriceps on the front of your thigh accelerate your leg forwards, and your hamstrings then kick in as the brakes to slow your leg down, plant your foot on the ground, and repeat.

There are two common types of hamstring strains. The first occurs in overstretch activities, where the hamstrings are forcibly pulled, such as in a water skiing accident when the skis are pulled out from under you. The second and more common injury occurs in sports that involve sprinting or sudden changes in direction.

When hamstring strains occur in sprinting activities, doctors will anticipate that the biceps femoris has been injured. They are right approximately 80% of the time. Why is this muscle so predictably injured in sprinting endeavours?

No one really knows. Most theories revolve around the different structure and architecture of the biceps femoris compared with the other two hamstring muscles. We have examined the physics of hamstring function to see if this could shed any clues.

Muscle contraction – the act of a muscle lengthening and shortening to move a body part – is conceptually very similar to the oscillation of a spring. Therefore it is logical to model the hamstrings as a spring–mass system, or “hamsprings”!

We built the hamspring system using a simulated modelling program called Interactive Physics. In our simulation, each of the three hamsprings had two non-contractile tendons at each end joined by a spring representing the muscle. We allowed the model to run under gravity, and attached a weight of 7 kg to the bottom of each hamspring, representing an average human lower leg.

Illustration: Elia Pirtle

To determine the lengths of each of these components we followed the work of Drs Stephanie Woodley and Susan Mercer of The University of Otago, who measured the lengths of individual hamstring muscles in cadavers ( They found that while all three hamstrings were the same total length, which makes sense since they all start at the hip and end at the knee, the lengths of the components varied.

Illustration: Elia Pirtle
Prof Darryl Thelan of The University of Wisconsin-Madison had also studied hamstring kinematics using anatomical markers and a motion capture system, and concluded that all three hamstring muscles reach their maximum change in length at the same time (

Remember that Woodley and Mercer found the lengths of the “springs” varied between muscles? Physics then tells us that the shortest spring must expand and contract faster than the longer springs so they all reach their maximum change in length at the same time.

It makes sense when you think about attaching two springs of different lengths to the back of your leg from your butt to your knee – it sounds rather painful for one of those springs to lengthen while the other shortens!

So our hamsprings are oscillating at different rates to make the hamspring system act as a unit and reach its maximum change in length at the same time. Guess what? It turns out at the little engine that could is the biceps femoris, chugging away at a quicker rate than the other two hamstring muscles.

So the biceps femoris is always working harder, and is therefore more susceptible to fatigue, which is a well-known risk factor in many muscle strain injuries. Field studies confirm that hamstring strains typically occur late in the race in athletics, and in the second half of AFL, rugby and soccer matches.

This very simple physics model gives some insight into hamstring function, and offers a plausible explanation as to why one muscle of the hamstring group is so prone to injury under certain conditions.

The next logical question is to determine what can we do with this information to help prevent hamstring strains in the future. The first step to finding a solution is always to clearly define the problem, and that is what we believe we are doing with this simple model.

The next step is to create a more detailed model, and correlate model behaviour with athlete motion to be sure we have the problem understood.

The problem then moves out of the realm of physics and into the hands of doctors and physiotherapists, who can try to create stretching regimes that help the hamstrings perform better as a unit, and decrease their susceptibility to fatigue.

Bronwyn Dolman is a Senior Scientist at ATRAD Pty Ltd, and a Visiting Research Fellow at The University of Adelaide.