Sport Science

 Football helmets

The collisions experienced by participants in contact sports and other potentially injurious endeavors are often strong enough to give rise to mild traumatic brain injuries (MTBI) such as concussions. This has created a health hazard of epidemic proportions, with several million incidents of MTBI occurring yearly at all levels of play in all sports. In response to the MTBI epidemic, more protective helmets have been introduced and used by participants in sports and other endeavors, but the frequency of MTBI has remained alarmingly high.  It was recently reported that a study of the brains of 111 (deceased) former NFL players revealed that 110 of them had Chronic Traumatic Encephalopathy, the degenerative MTBI caused by repeated blows to the head. 

The first line of defense against MTBI for contact game participants is their protective helmet.  It is therefore extremely important that these helmets provide as much protection for the user as possible.  This has been recognized since the early days of American football, but it was not until 1973 that a serious effort to measure the protective capability of helmets was made by the National Operating Committee on Standards for Athletic Equipment (NOCSAE).  NOCSAE introduced a helmet testing method and related standard, and a number of other helmet testing devices and protocols have subsequently been proposed.  Unfortunately, all of these protocols are inadequate because the impacts they analyze, generated using testing laboratory (lab) equipment, differ in significant ways from the impacts experienced by game participants.  Also, the existing standards only relate to head accelerations resulting from impacts, but ignore the equally important distribution of impact-created forces transmitted through helmets onto a user’s head. 

In the NOCSAE standard drop test method, the helmet to be tested is affixed to a head-form attached to a rigid aluminum frame.  The frame is constrained to slide down a pair of vertical wires, so that the head-helmet falls onto a fixed metal anvil.  Accelerometers attached to the head-form record the acceleration of the head-helmet during the impact with the target.  The NOCSAE standard states that the severity index (SI) evaluated from the recorded acceleration profile is less than a specified upper bound when the head-helmet impacts at a specified speed.  In the newer proposed NOCSAE standard linear impact (LI) test method, the helmet to be tested is affixed to a head-form attached to a neck and torso mounted on a translating joint.  The impactor is a hemispherical solid attached to a horizontal cylindrical piston, guided within a straight cylindrical tube by linear bearings, and propelled by a compressed air cannon.

The above test methods, and all others known to us, create impacts that are very different from those (essentially unconstrained free body) impacts that arise in the field.  In the current NOCSAE method, the impacting head-helmet is constrained to descend down and rebound back up in a purely vertical direction.  Field impact rebounds on the contrary are almost always occur at angles that differ significantly from the incident angle.  Also, in the current NOCSAE method, the target is fixed and therefore effectively infinitely heavy and completely constrained.  Also, measuring only the applied accelerations ignores the fact that the transmitted forces applied to the head can be larger than those applied to the helmet at times during the impact, and ignores the degree to which these forces can be spread out by a helmet.  The proposed NOCSAE LI method is an improvement in that both the impactor and the target have finite weight, and large impact speeds are readily obtainable.  However, the impactor is even more highly constrained because the impacting element and attached piston are required to move in a purely horizontal direction.

The artificial constraints placed on impacts by the NOCSAE methods can drastically change the nature of the impacts.  In an unconstrained impact of one object onto another at an oblique angle, the velocity of the impacting object will decrease in the tangential direction because of the sliding friction between the objects, and the velocity will decrease in the perpendicular direction because of the elastic damping between the objects.  The rebound angle will therefore be very different from the incident angle, and the rebounding object will acquire both rotational and linear motion. 

An illustration of this is given in Fig. 3.20(a).  An incoming curved object (such as a helmet) strikes a second object (such as another helmet or shoulder pad) at an oblique angle.  During the brief period that the objects are in contact, the first object slides over the second object as they compress together.  This tangential sliding motion is opposed by the sliding friction force, which exerts a torque on the first object, causing it to rotate forward.  When the objects separate after they compress and decompress, the first object rebounds at a generally different oblique angle, with a velocity and spin determined by the incident velocity, the masses and curvatures of the objects, the coefficient of restitution between the objects, and the coefficient of sliding friction between the objects.  In terms of this illustration, the current testing devices artificially constrain the incoming object to rebound in exactly the same direction as the initial direction, with no acquired rotation, as shown in Fig. 3.20(b).  A consequence of this is that the force and acceleration profiles associated with the impacts created by constraining testing equipment do not accurately replicate the profiles created in game impacts.

The forces and torques exerted on a helmet arising from such constrained impacts are different from those arising from unconstrained impacts at the same location and velocity.  The perpendicular components of these forces are often similar, but the (torque causing) tangential components are usually very different.  The tangential component of a constrained force depends on the impact speed and the masses and elasticities of the colliding bodies, whereas the tangential component of an unconstrained force depends in addition on the more detailed properties of the bodies such as their curvatures, moments of inertia, and sliding friction coefficients.  Depending on the values of these quantities, the applied tangential constrained force can be considerbly more than or less than the tangential unconstrained force.  The use of constrained impacts therefore introduces large and uncontrolled elements of uncertianty into the force and torque measurements.  Such impacts can therefore not be expected to provide an accurate descriptrion of realistic game impacts. 

Since neither sliding nor rotating are possible with the impacts created by constrained testing methods, and none of these methods involve measuring transmitted forces, there is a definite need for a testing method that improves upon these deficiencies.  In collaboration with Division, LLC, we have invented an improved class of helmet testing devices that provide impacts that replicate field impacts much more realistically. Our devices create impacts that approximate the substantially unconstrained free body field impacts as closely as possible, our target reacts in the way that a free body reacts, our system of sensors records all the important characteristics of these impacts, and our data analysis protocols effectively summarize these characteristics.  We believe that such devices and protocols are required in order to accurately evaluate and compare the protective capabilities of helmets.

Our impactor and target are completely free and unconstrained before, during, and after an impact.  Each impact is implemented by a helmet-shaped impacting element (impactor) propelled from a spring-loaded cannon (Fig. 3.22) at a target consisting of a helmet attached to an instrumented head-neck-torso model.  In the cannon, the impactor is in contact with a spring that is compressed and then released in order to propel said impactor towards the target.  The target is initially supported from above by attached thin wires.  The target is released just prior to the impact so that both the impactor and target are completely free during the impact.  These targets have three aspects: (1) the target body that consists of a head/neck/torso model with an attached helmet, (2) a mechanism for rendering this assembly as a free or substantially free body before an impact, and (3) incorporated sensors that record the forces applied to and through the attached helmet.  By adjusting the wire lengths and/or the orientation of the model, the impact can be directed at any location on the helmet.  The system is shown in Fig. 3.22(a).

The force exerted on the target by the impactor is measured by accelerometers placed at appropriate locations within the impactor and the target.  It is especially important to record accelerations at the center of mass of the target in order to measure the total applied force, and at the head model section of the target, in order to measure the acceleration of the head.  (The total applied force can also be measured by an accelerometer placed at the COM of the impactor.)  As explained above, in addition to measurements of such applied forces, it is important to measure the forces transmitted through a helmet onto the head model.  An invented device that measures these transmitted forces is shown in Fig. 3.23.

We have used our cannon and target to demonstrate the free body impact illustrated in Fig. 3.20(a).  In this drawing, the impacting body (left side) compresses onto the target body as it slides forward so that the impactor is subject to an upward elastic force in the direction perpendicular to the local target surface and a backward sliding friction force in the direction parallel to the local target surface.  The elastic force is in effect until the impactor rebounds off of the target, and the sliding friction force is in effect until either the impactor begins to execute pure rolling on the target or it departs from the target. (Pure rolling occurs when the linear speed equals the product of the rotational speed and the effective radius.)  In either case, the impactor rebounds from the target after decompressing and after moving forward a certain distance on the target, while acquiring a certain amount of forward rotation.  (For clarity, the sliding/rolling distance shown in the drawing is greatly exaggerated.)  If, on the other hand, the impactor is not a free body but is constrained to rebound in the same direction as the incident direction, as illustrated in Fig. 3.20(b), the impactor can neither slide on the target nor acquire a rotation.  In this case, the forces acting on the impactor are the physical perpendicular elastic force and the artificial constraining force that prevents the sliding motion and, together with the elastic force, directs the impactor to rebound in the incident direction.  In other words, the constraint replaces the backward-directed physical friction force, a force that decreases the impactor’s forward sliding speed and increases it’s rotational speed, with a very different backward-directed artificial constraining force that completely prevents these motions from occurring. 

The above physical consequences of such free body impacts are demonstrated in the photographs shown in Fig. 3.21.  These impacts were created by the cannon described above.  The first photo (a) shows the cannon on the left, the propelled impactor in flight in the center, and the instrumented target on the right.  The second photo (b) shows the position of the impactor immediately after it rebounds from the target (before gravity has an observable effect).  The rebound direction is clearly seen to differ from the (horizontal) incident direction, and the impactor is clearly seen to have acquired a (counterclockwise) rotation after the impact.  Neither of these physical effects can occur in the constrained impacts.  The rebound motion that occurs in such impacts would look exactly like the incident motion shown in photo (a).  (Slow motion videos of the impact provide more detailed information.)

It is clear from the above theoretical and experimental demonstrations that important differences exist between the unconstrained impacts taught herein and the constrained impacts used previously.  Depending on the values of the sliding friction coefficient and COR between an impactor and a helmet, the maximum acceleration recorded in a constrained impact can be significantly less then that which obtains in a real impact between the same impactor and helmet at the same location and velocity. This means in particular that the helmet testing and certifications provided by the use of constrained impacts are not effective in furnishing accurate information about the degree of protection provided by football helmets. 

The data obtained from our invented helmet testing equipment are analyzed using performance metrics that effectively characterize the measured data.  These metrics are used to compare lab and field impacts, to determine the protective capabilities of helmets, and to compare and regulate available helmets.  Some relevant metrics include the peak and average recorded accelerations, the SI, and the impact duration. However, these metrics alone do not adequately characterize the impact because they fail to describe important details about the acceleration data.  These details include descriptions of the shape, slopes, and local curvatures of the data plots. To supply these missing details, we evaluate the harmonic frequency (Fourier) spectrum of the acceleration data.  An excellent fit to acceleration data is provided by the sum a5 of the first five harmonics.  A plot of a typical acceleration profile is shown in Fig. 3.24 (in blue) and the superimposed plot of the corresponding a5 profile (in red) is seen to be almost identical.  Plots of the five included harmonics are shown in Fig. 3.25. 

The acceleration data described above are, however, only a part of the determination of the protective capabilities of a helmet.  For a given applied force profile, the helmet that spreads the consequent forces transmitted through the helmet onto the skull of a user over the largest area and largest time interval will offer the best protection.  Our method to determine this force distribution is to place suitably designed force sensors at various locations on the target skull model under the helmet. 

If a total of N such force sensors are used, our metrics that summarize the transmitted force values are the following.  (1) The maximum force recorded on each of the N sensors.  (2) The largest of these N maximum forces.  (3) The sum of these N maximum forces.  (4) The maximum of the sum of the N forces as a function of the impact time.  The significance of this information is as follows.  (1) The maximum force measured on a sensor under the helmet a measure of the effectiveness of a helmet in spreading the applied force over the body of the player.  The smaller the collective values of these transmitted forces compared to the maximum applied force, the more effective is the tested helmet in spreading out the force over the surface of the user’s head.  (2) In particular, it is obviously desirable to have the maximum individual transmitted force, and the sum of such forces that act together in the same area, significantly less than a force capable of causing a MTBI, even if the maximum applied force is above that level.  (3) The sum of the maxim force values is a simple measure of the distribution of the applied force.  (4) The maximum of the sum of the transmitted forces (MSTF) is the best force distribution metric because it takes into account the fact that the individual force maxima can occur at different times during the impact.  It is highly desirable for the maximum values of at least some of the transmitted forces to occur at different times during the impact so that the combined effect of these forces is diminished and the MSTF is reduced. 

To exhibit a transmitted force profile, we consider the impact whose applied force profile is shown as the blue plot in Fig. 3.26. The maximum recorded force of 217.2 lbs occurs after 0.0239 sec.  The measured transmitted force profiles from five sensors are given in Fig. 5.27.  The profile for the sum of these forces is given in Fig. 3.26 (in red) superimposed with the applied force profile (in blue).  The total transmitted force is seen to exceed the applied force at various times during the impact.  The maximum total transmitted force is 224.2 lbs,  which is larger than the maximum applied force of 217.2 lbs.  This example illustrates the importance of measuring the transmitted forces in addition to the applied force.  Examination of the applied force alone would undervalue the size of the maximum force applied on the helmet user’s head during the given impact.      

Fig. 3.20.  (a) Illustration of a free unconstrained impact between two free bodies.  The impacting body compresses onto and slides on the target body, acquiring forward spin from the sliding friction force, and rebounding with a reduced speed.  (b) Illustration of a constrained impact between two bodies.  The impacting body is constrained to rebound from the target body in the incident direction with no rotation.