The Mechanics of Sports Injuries

“Oh crap!!!” is the first thought that runs through your head as you lay on the field/ice/court in excruciating pain immediately following a sports injury.  Whether it is an ankle sprain in soccer, a dislocated shoulder in football, or a broken wrist in basketball, sports-related injuries are painful and frustrating, but unfortunately, inevitable.

The second thought that runs through the injured athlete’s head is, “I wish I could take the last moment back.”  It is an appropriate thought to have, as whenever a collision occurs, the severity of the injury is dependent on just how short the duration of the collision was.  Although impacts in sport between two athletes appear instantaneous, there is actually a small amount of time over which they take place, which we will refer to as dt

The extent of the deformation of the athlete’s bone or joint depends on the force imparted during the collision.  If the magnitude of this force is constant throughout the collision, then the total force, F, may be calculated as F = I/dt, where I is the impulse of the collision.  Impulse is the total change in momentum by the bodies involved in the collision.  If a hockey player skates directly into the boards, his change in momentum is his mass multiplied by his speed just before impact.  However, dt depends on the stiffness of the boards.

If the boards were made of concrete, the roster of a hockey team would deplete very quickly, because the dt during impact would be near zero, and the force imparted when crashing into them would be very high.  High-intensity sports lead to high-impulse collisions because the athletes move at high speeds.  Since high-impulse collisions are unavoidable, it is essential that the duration of these collisions be maximized.  The actual hockey boards have ‘give’, and the collision lasts for say one hundredth of a second instead of one thousandth of a second.  The force at the point of collision is then ten times less, and the deformation of the player is as well.

Another example of minimizing the force of impact is when a skier lands a jump.  If the skier does not bend her knees, the impulse will be transferred all at once, and the imparted force through the knee joint will be a maximum value.  By bending her knees, dt is larger, the impulse is ‘absorbed’ gradually, and the lower magnitude force does no harm.  Injury averted.

Once the force applied to an athlete is minimized, it is hopefully distributed over a large area on the athlete.  This is the function of padding.  The extent of the injury is dependent on the pressure transmitted, and p = F/A, where p is pressure and A is area.  The reason a knife is so dangerous is because it cuts even when the force is small, as the area is so tiny.

Most sports injuries occur at joints.  There are two kinds of loads that pass through a joint: forces, which are linear in nature, and torques, which are angular in nature.  It is in fact the torque that is usually responsible for causing damage to a joint.  The torque in the joint is the result of some force being applied some distance away from it.  When an ankle twists the wrong way under an athlete’s own weight, the bending torque is the product of the upwards (reaction) force of the surface and the small distance from the sole of the foot to the joint itself.  A large torque occurs when a large angular impulse is transmitted swiftly.  Again, whether the cause of injury is linear (force) or angular (torque), the level of devastation of the injury is dependent on how quickly it occurs.

I suppose the key to averting sports injuries is to not compete.  I sprained my ankle last week playing soccer, and, I won’t lie: the thought of hanging up my cleats for good did cross my mind as I repeatedly rested, iced, compressed and elevated my injured joint.  Some years ago, a doctor suggested to me that I take up swimming instead of soccer because it is safer.  That may be true, but swimming is also as boring as sin.

I am not willing to give up high-intensity sports, as the benefits outweigh the potential consequences.  If you use the right padding, you minimize the likelihood of injuries occurring.  Still, there are additional measures that can and should be taken for an injury-prone athlete such as myself.  Sports braces for ankles and knees reduce the likelihood of sustaining an injury, and as an engineer, I can appreciate why that is.

When designing a structure, some analysis for an anticipated worst-case environment allows the designer to predict what the maximum force and torque across a given section of the design will be.  If the anticipated load is greater than what a given joint is able to sustain, then the joint must be reinforced to avoid a failure.  A smart way to reinforce a given joint is to give the load a stiffer path to follow.  Stiff braces do this very thing when the joints they are protecting begin to deform.

When I do return to soccer, some weeks from now, I will be sporting an ankle brace.  As a result, the allowable loads for my ankle joint will be higher, and, hopefully, it will not sustain a failure in the near future.  While injuries leave me with much time to write, I much prefer playing sports to writing about them.

Here is a prayer for all athletes out there: “May all of your loads be distributed over a large area, and may your high-impulse collisions be gradual.”


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