The Basic Physics of Collisions and Thoughts on a Concussion-Preventing Helmet

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Will is exactly right. How do you prevent concussions with a helmet? From my layman’s understanding of concussions, the traumatic brain injury happens when the head decelerates faster than the brain can handle; when it “rebounds” off of the skull, injury occurs. With this in mind, the goal of modern helmets should be to reduce the deceleration rate of the skull. The focus right now is rightly on football helmets, but I think that it’s just as important in hockey, a sport where information about injuries might as well be top-secret.

Barth, et al. discussed a basic Newtonian model for deceleration back in 2001. A player running nine yards per second [a 4.44 40-yard dash time] who is tackled and comes to a complete stop in just six inches decelerates at over 22.6g (g being the acceleration due to gravity). If you need reference points on just how hight that is, Wikipedia presents examples of typical G-loads. You can argue that no player runs that fast in game speed, but I’d turn around and argue that few players running full speed who are really lit up by a tackler are decelerating in less than six inches.

Let’s consider a few more things, starting around the premise that not all hits are the same. I’m not talking about the power of hits so much as I am the stopping distance for the head. As a player runs downfield, the various parts of his body are all moving at roughly the same speed—close enough that you can consider it the same as the ground coverage speed. When the player gets hit, there are three scenarios:

  1. The hit is such that the stopping distance for the brain is even shorter than it is for the rest of the body: the head stops moving while the body rotates forward underneath, usually resulting in the legs “flying out from underneath him”. You would see this mainly when a player is mid-air and the collision hits his upper body, specifically above the armpits. This is almost assuredly going to be a helmet-to-helmet collision. For a mental picture, consider a wide receiver sprinting downfield, jumping in stride to catch a pass, and being absolutely lit up by a DB. The only saving grace for the wideout here is that he will have reduced his ground coverage speed to jump, as the human body can’t maintain full forward speed while accelerating vertically. The football historians among you will be thinking of Darryl Stingley at this point.
  2. The hit is such that the stopping distance for the brain is the same as it is for the rest of the body. This is the default assumption people have, and it works in many cases. That said, “body lean” has to be involved, because the hitting force is going to have to be applied to the head, shoulders, or high in the upper body for the neck not to increase the stopping distance by whiplash. For the worst hits in this scenario, you will see people leading with their heads and the players being generally of equal mass and footspeed (momentum) who are both making a stride at the same time they hit. Collisions are about momentum, and if both players carry the same momentum into the hit and have a foot planted when it happens, their bodies don’t get to translate much linear deceleration into rotation.
  3. The hit is such that the stopping distance for the brain is larger than it is for the rest of the body. In this scenario, the tackler has hit the player at or below the bottom of the chest pads, planting their shoulder into the solar plexus. Yes, you’re going to knock the breath out of the guy, but as the player’s midsection stops, his upper body will fly forward, greatly increasing the stopping distance for the head, lowering the deceleration.

Considering the above, part of the issue is clearly in tackling technique: “cleaning a guy’s clock” with a mid-air collision or leading with the head results in bad, bad hits. Past technique, helmet makers need to look at the very important “increasing the stopping distance” problem. I think the issue is fairly simple: a bigger helmet with some sort of gel sack that allows the head to move around inside the helmet while maintaining integrity. The brain floats in a volume of cerebrospinal fluid that’s encased by the neurocranium. As the cranium decelereates, the brain pushes CSF out of the way and to the back of the skull; TBI happens when the brain actually impacts the cranium. That said, the natural choice of having the brain encapsulated in fluid, allowing the brain to increase its stopping distance, is a good analogue for what should be done. I propose that an encapsulated gel be used because the force of impact can drive the gel to the opposite side of the helmet, allowing the head to move more than the helmet does in a way that compressive padding alone cannot. The encapsulated gel, of course, would be enclosed by some compressive padding, probably on all sides, for comfort for the wearer and because you want padding there when the gel has fully transferred.

Let’s go back to that deceleration discussed in the open.

  • Let’s put a half-inch of the gel inside the helmet and repeat the collison: (-9)*(-9)/(2*0.181*10.73) = 20.9g That’s an 8% reduction, all other things being equal.
  • What about a full inch? (-9)*(-9)/(2*0.194*10.73) = 19.5g That’s 14%.
  • Heck, why not two inches? (-9)*(-9)/(2*0.222*10.73) = 17.0g That’s 25%.

Let’s now address the objections:

  1. Making the helmets bigger just means you’re going to see more helmet-to-helmet collisions. This is true, but reduction of helmet-to-helmet hits is on the NFL and its enforcement, not on the helmet manufacturer. Also, making a bigger helmet could provide for decreasing the forward curvature, making the helmet “pointier” and making it harder for straight-on, face-to-face hits.
  2. You’re not going to see full re-distribution of the gel on all hits. Yes, but you likely will on the worst ones, and those are the ones that need it the worst.
  3. You’re just making the helmet heavier. This slows players down and makes them tired. I fail to see the problem here.

Let me finish with a couple thoughts on future study:

  • Going back to the larger helmet idea, I do think that you could make the helmet more appropriately represent the human skull if you make it overall larger: elongated in the front, with little direct frontal area. A glancing blow to the facemask is going to let the brain take longer to stop; if you can deflect blows from the face to the side, this will improve concussive hits, albeit at the risk of neck torsion and injury as the head rotates.
  • Along the lines of designing a helmet fully, you’d want impact data from all sides of the helmet. Can you have a thicker front section of gel and voids along the sides for it to move into? Probably. The issue then becomes returning the gel back to its normal state. I think the easiest way would be a compressed air system, with players seeing an impact above a certain level required to sit out a play while their helmet is restored.
  • The above idea indicates that you’d want some form of real-time data on player helmet accelerations. What’s truly concussive? I don’t know. Is a 17g hit okay where a 22g hit isn’t? I don’t know. Much as there’s the baseline test for neurocognitive functions that smart football organizations now require, I think the NFL should be leading the way in real-time data gathering on collisions in order to assist sports medicine and helmet manufacturers better understand the problems that they face. The best testing for helmets is field testing, and that requires real-time gathering.

Let’s be honest: as a multi-billion-dollar industry, the NFL can afford to make these changes and investigate this further, and it should. Why? If football ends up being deemed too violent, parents won’t let their kids play it at the youth level, and the quality of the sport will then decrease as coaching fundamentals will be required at increasingly higher levels. If the quality of play goes down, the NFL probably loses viewers, and that’s bottom line. Viewed otherwise, if the NFL can use its financial success to increase the sophistication and efficacy of helmets, it should do so, as improved equipment eventually is mass-produced down the chain. If youth football becomes safer, more parents will let their kids play, instruction is moved down the chain, and the NFL has a better product as a result. Football is a sport that American kids love and want to play, and the NFL, in seeking the best product possible, should be getting them to learn the game as early as possible. The only way to do that is to make it as safe as possible, allaying parental concerns about their children’s well-being.

[Nota bene: I am an aerospace engineer by education, a systems engineer and project manager by training, and a football and hockey fanatic. Despite being a wide-body, I refused to play HS football because I wanted to walk without pain when I hit 30. I think I made the right choice for me. I mention this only in case Will Carroll links to this and people wonder who the hell I am to be talking about helmet design. I am decidedly a layman, but a reasonably educated one.]