Limiting Performance Studies of Sports Helmets

Principal Investigator: W. D. Pilkey, Ph.D.
Institution: University of Virginia

Title: Limiting Performance Studies of Sports Helmets

In this work, we use a limiting performance analysis to find the absolute optimal performance of the helmet for the prevention of head injuries. A two-mass translational head injury model developed by R.L. Stalnaker, et al. is used, and the related translational energy criteria are employed as the head injury criteria. The criteria include: (a) the amount of energy imparted to the brain which was found to be directly proportional to the severity of brain injury; (b) the power developed in the skull which is related to the probability of skull fracture; and (c) the peak acceleration of the head. The limiting performance is conducted by replacing the characteristics of the padding liner by the control force and for a prescribed thickness of the liner, finding the optimal control force such that one of the head injury criteria is minimized while the others are bounded.

The main findings are the following.

  1. As expected, the larger the liner thickness, the better the limiting performance of a helmet. Also, as the initial impact energy increases, the limiting performance of a helmet becomes worse.

  2. For the different directions of the impact of a helmeted head–front to back, back to front, top to bottom, and left to right, the difference among the peak accelerations of the head is small, but the difference among the amounts of the energy imparted to the brain is large. The sequence of the directions in which brain is more susceptible to injuries is: front to back, top to bottom, back to front, and left to right.

  3. Generally speaking, among the three head injury criteria, the energy imparted to the brain is the first factor of concern. In the case of high initial impact energy (say, over 100 J) and small liner thickness (say, below 17.5 mm), the limiting performance of the helmet would fail to protect the head from significant injuries to the brain. The power developed in the skull is very low for the cases of low initial impact energy and large liner thickness. However, it could be high when the initial impact energy is high, the liner thickness is small, and there is a jerk in the head acceleration. High power developed in the skull leads to high probability of skull fracture.

  4. The minimization of the amount of the energy imparted to the brain results in the head acceleration close to a half-sine pulse. The minimization of the peak acceleration of the head leads to a constant acceleration of the head, which means there is a jerk of the head at the onset of the impact.

These findings, together with obtained trade-off curves in which the relationship between the helmet performance and the liner thickness is given, provide guidelines for the evaluation and improvement of helmet performance in head injury prevention.


Limiting Performance of Sports Helmets for the Prevention of Head Injury, Zhiqing Cheng, Walter D. Pilkey, and Jeff R. Crandall, submitted to Journal of Applied Biomechanics.

Abstract: A limiting performance analysis provides a means of measuring the effectiveness of a sports helmet in preventing head injuries. Based on a translational head injury model, the limiting performance of helmets has been investigated at two different impact energy levels, with the maximum acceleration of the head and the energy imparted to the brain as the performance indices. Trade-off curves for the evaluation of helmet performance have been determined, and the characteristics of the control force and the head response have been shown. For anterior to posterior and superior to inferior impacts, the trade-off curves obtained from the tranlational head injury model have been compared with that based on a single degree of freedom model and with experimental results using a rigid headform.