Some fascinating calculations, and one conclusion

Lots of people have asked me about the kind of forces involved in producing injuries similar to those Michael has suffered. It’s an interesting question, and after doing some calculations, it’s emphasised to me something that I think must be done relatively urgently. More of this later.

Let’s make a few assumptions as to baseline conditions. This means any results are at best approximations of the real world, but they allow us to “ballpark” the forces in question, and to perhaps compare with other mechanisms. And while I’m on the qualifiers, I’m SO not a physicist!

I’m assuming that the mechanism of injury is a near vertical fall onto the head, after Michael was “launched” by contact with a rock. I’ll assume his head was at 2.5 meters, not unreasonable for this kind of mechanism (and only slightly higher than one’s own height), that there was only a vertical component to his movement, and that he weighs 70 kg. This results in an energy of 1715 joules. Never mind the units for the moment – we’ll just generate some more energy data and then compare.

How about Felipe Massa’s accident? We know the spring weighed 800 gm (0.8 kg), and that Felipe was moving at 260 km/h (the spring is considered to have no horizontal velocity). This gives an energy of 2085 joules.

The same kind of calculation shows us that the bullet from a Kalashnikov (7.9 gm, muzzle velocity of 715 m/s, thanks Wikipedia!) has . . . 2019 joules!

To compare some other energies, let’s look at a soccer player heading the ball. Just to simplify, I’ll assume the player has no vertical speed when he heads the ball, and that the ball is falling from, say, 20 meters. This gives a “measly” 86 joules. Nothing, eh? (The actual value will be higher because of the player’s vertical momentum, and also if the ball falls from higher). Well how about this: there is a direct correlation between a the number of heads a soccer player has in his career and his cognitive function. So even this relatively tiny force, repeated many times, will likely damage a brain!

What about American football, where we read every day about cases of chronic traumatic encephalopathy (the damage done by years of hits)? Again, a few assumptions. Defensive lineman, 100 kg. Offensive lineman, 150 kg. Speed of each at impact? 1.2 meters/sec. What does this give? This gives us 180 joules combined. Again, doesn’t sound like much, but repeated over a career from high school, through college, to the pros, it seems often to result in very significant damage to the brain.

But back to the object of our concern. What explains the dramatic difference in outcomes between Michael and Felipe?

The obvious first (and perhaps only significant) answer is their helmets. Felipe was wearing the latest spec full face carbon kevlar racing helmet. Michael was wearing a . . . ski helmet.

Remember that force is not the only factor – we have to consider the area over which the force is spread. When a 70 kg man steps on your foot with his loafers, it hurts, but nowhere NEAR as much as when a 70 kg woman does the same with a stiletto heel. In one case, the force is spread over a much larger AREA, giving a lower pressure. And it’s pressure that actually does the damage. One of a helmet’s main roles is to distribute a force over a (much) larger area, dramatically reducing the pressures generated.

Now, the FIA Institute has done remarkable applied research in helmet design, and the helmet Felipe was wearing reflects that research. This helmet was designed specifically with very demanding requirements for impacts with objects having rounded edges as well as those having sharp edges, and equally for penetration resistance. These requirements were based on known mechanisms of injury in the sport concerned, and the levels of energy seen.

Ski helmets, on the other hand, are designed and homologated (WHEN they’re homologated) almost solely to prevent skull fractures. While this provides an easy method of evaluation in testing labs, we know that this has VERY little (if anything) to do with the actual mechanisms of brain injury. And unfortunately, Michael is a living demonstration of this.

Therefore, I’d like to throw a few ideas out there:

  • the Federations responsible for skiing, from recreational to competitive, should convene a working group of experts to look at the epidemiology of head injury in the sport
  • conclusions should be drawn about the kind of head protection likely to mitigate the injuries ACTUALLY SEEN
  • Jean Todt should offer the full resources of the FIA Institute (data, expertise, etc) to help design this helmet, to make it affordable, and to make sure it is used as widely as possible.

Michael’s injury is no more tragic than those of every patient who suffers severe head trauma. If, however, his public persona spurs action that goes on to significantly improve the safety of skiing, it will be another of his many remarkable accomplishments!

28 thoughts on “Some fascinating calculations, and one conclusion

  1. I am fairly certain the Snell Memorial Foundation tried to provide a rated helmet to the skiing industry but found that industry had no interest. If you are not aware of Snell see

  2. I do believe all of the concepts you have presented to your post.
    They’re very convincing and can certainly work. Still, the posts are too short for novices.

    May you please lengthen them a little from subsequent time?
    Thanks for the post.

  3. I do believe all the ideas you have offered in your post. They are very convincing and can certainly work. Still, the posts are very short for novices. May just you please prolong them a bit from next time? Thank you for the post:

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  5. Thanks for the fascinating look at the energy in the collision.

    My only comment is that doesn’t the calculation for Michael presume a mass, 70kg, that is solid? Surely, that isn’t the case as the body is quite flexible, so should one use the whole 70kilos in the calculation or some partial amount?

    And, I suppose I have another comment now that I think about it. Are carbon fiber helmets for recreational skiers even a cost-effective solution? Can it be solved with less expensive materials?

  6. Very interesting reading Gary. I gathered various other articles from around the web and came up with a similar view. Whilst I can appreciate that in the past ski helmet companies maybe had to err on the side of what was acceptable for a skier to wear I believe we are past that now and that skiers would pay for premium protection.

    Personally I don’t think existing ski/snowboard helmets are fit for purpose and they only appear to be tested up to the forces experienced whilst traveling at no more than 20mph.

    I only recently switched from snowboarding to skiing and regularly exceed 25mph and I’m not even pushing. If a beginner can quickly get to a standard whereby they are regularly skiing at above the limits required for helmet certification then surely the suggestion has to be that the certification is not fit for purpose.

    Anything that can be done to improve existing protection can only be a good thing.

    My post as “Agent Orange” on another forum

    Keep fighting Schumi!

  7. Three thoughts:
    1) Consider doing a Venn diagram of the forces. Or have someone do it. (I think it will increase the force considerably in Schumi’s case when you take in the horizontal component. Of your examples only Massa’s is a simple impact, while all the others involve more than one direction of movement and need compound resolution.

    2) Consider “Impact” ie Force x time. (or maybe pressure x time) (this also as related to deceleration or G force) This may well have a direct relationship to the amount of injury. (Though one might also think of blast damage which can be almost instantaneous as a comparison, the armed services should have this info)

    3) Look at the paper cycle helmet report link I sent previously. Extremely light cellular structure but a progressive collapse lessens impact by a large percentage. Ideally a gel as in an F1 helmet but anti thicksotropic ie gets progressively thicker under pressure instead of initially hardening.

    I am a little surprised that this is not part of the FIA road safety programme as it applies to pedestrians, cyclists, farm workers etc. as well as motorists.

  8. Hi Gary,

    There is no doubt, that when it comes to world class competition level, be it F1 or Ski to take your examples, the creme de la creme, all those guys get what is best for their safety, no questions asked (But even there, as the Massa incident proves it, you can never be 100% sure..). And I am not sure the FIS needs the FIA or the NFL or vice-versa to work on the problem of safety although I do agree that sharing their feedback is beneficial (and I have no doubts it is already done).

    One of the broader issue that your post brings forward, and one that will be extremely hard to address in my opinion, is when it comes to recreational activity and the “average Joe” out there: it will be very very difficult to dramatically reduce the amounts of traumas and accidents, and for 2 main reasons:

    #1/ Modern Technology: The technological development of our “toys” (Skis, bikes….) is way way faster than the human body’s ability to evolve. By creating Skis that are so easy to handle that even my grand-ma would feel like Alberto Tomba, or by coming up with mountain bikes with so much built-in technology that you could almost go down the face of Mt Everest without putting your foot down, we pretty much allow anybody out there to go way beyond the limits. And when things go wrong, they go wrong badly. Nowadays, the material makes the sport so accessible that you can very quickly feel like you have total control of what you’re doing, and it encourages you to take a lot more risks than you should. You feel safe no matter what. That problem didn’t exist 20 years ago: it took you every ounce of energy to make your skis turn in powder snow, your bike was so stiff with no suspensions that going down a trail at 15mph was like making a statement of how much pain your whole upper-body could tolerate.
    Faster, higher, bigger comes at a price: a price the human body cannot afford when things go bad. I know a lot of companies are heavily investing in developing better products (Helmets for example, visit, it is a gold mine of information) but will this be enough? Will they ever catch up? How can you EVER protect someone doing front and back flips, taking-off of a 30ft ramp at 50mph ON A SNOWMOBILE! Seriously!!! (thank you X-Games) I don’t know what can be done to reverse this trend as it seems this is yet another impact of our modern way of living…

    #2/ Money: Safety equipment comes at a price. Top notch safety equipment at an even higher price. And most dads out there simply cant afford it. When you know how much is costs to take a family of 4 up the mountains for a week long ski trip, what money is there left? Once you take out the must have (travel expenses, ski rental, ski pass…), how much is left for safety equipment? Will you replace your kid’s $100 helmet because he simply dropped it on the parking lot and possibly damaged its integrity, making his next fall potentially lethal?
    I am a firm believer that no matter the price, safety should always come first, especially if it’s the difference between life and death (or life as a vegetable). But is it realistic for all of us riding our bikes out there every day?

    PS: Thanks so much for sharing your thoughts on all the various subjects you post about.
    Always an interesting read! Keep it up doc!

  9. Thanks for another insightful and thought-provoking post!

    One quick question. You say that skiing helmets could sdo with more research and improvement to better protect the brain. How to you feel about bicycle helmets?

    I lost a very good friend to a head injury while cycling. He wasn’t riding very fast (perhaps at a jogging pace,) and fell, head-first while wearing a bicycle helmet of current design.) I also have a young daughter who will be learning to ride a bicycle this coming summer and she’ll need a helmet (among other things.)

    So the current state of the art in bicycle helmets is very much on my mind these days.

  10. Gary
    DoD has instrumented soldiers helmets to correlate acceleration data from actual IEDs explosions with actual injuries. If there is correlatio then e this would allow better diagnosis. It seems to me that F1 could use this too.

  11. I am in a line with many thanking you Gary for your honesty and willingness to teach us about TBI. Kevin Pearce, an expert snowboarder, suffered same and he has started a “Love Your Brain” Foundation. I agree that those that can MUST participate in reducing TBI by helmet design and redesign so others can be protected.

    It is sincerely my hope that Michael would not have to give his life in order for such change to occur. I remain one who believes in miracles…

  12. Dear F1 Doc !

    Thank you very much about this remarkable insight. We all hope that the long induced coma will help Michael to heal his injuries.

    We all pray it works.

    In your article I missed comparison to a professional Boxer, no helmet.

    All the Best.

    Thomas M Kann


  13. Excelent article and excelent item for discussion. How safe are helmets used in sky (and many other sports) and waht can be done to improve it. Thanks for sharing it with us

  14. There is a strong horizontal component to the accident vector as well, but I’m not too sure that discussion goes off in the direction Gary intended.
    I think the underlying question Gary is asking here is what would it take to design a helmet to withstand the impact sustained by Schumacher. Ultimately it would have to be a helmet that retailed at an acceptable price for individual skiers – so we are looking at perhaps $200. F1 helmets are handmade and cost about $6000.
    Full enclosure helmets offer much better protection than open face but the former wouldn’t work for skiing as full vision is required. Otherwise the rate of collisions skyrockets. So the helmet would have to offer the full vision available in open face helmets. That impacts the design.
    Schumacher’s helmet shattered on impact shedding off much of the energy but then exposing his skull to the secondary impact. Without question a F1 helmet would have protected the skull from this contact.
    So I think Gary is right in asking can’t we use this accident to spur further research into recreational helmet design that goes beyond preventing skull fractures, ultimately leading to a design to be mass marketed at a price point people will actually pay. Calling the design Schumacher would be fitting.

    • F1 driver helmets are “handcrafted” for weight and aerodynamics reasons. The retail price of the same strength/standard helmets is more than 3 times lower, they’re just not 100% to your head and slightly heavier. This price has been steadily going down, even though the market is mostly limited to the elite racing series. You’re required to wear carbon helmet from F3 onwards!
      The calculations might be a bit off, so you don’t really need the same quality of helmets like in F1. But there are a lot of lessons to be learnt! When I read about Michael’s accident, I checked to see what is the best cycling/skiing helmet and it turned out there were only a handful with little pieces of carbon in them, with the most expensive one at $350. These were helmets approved by FIS, the ski federation. Most shockingly, they have very, very little padding and Gary will tell you that this padding is very important in de-accelerating the head during impact. This padding quite often prevents concussions in smaller impacts and as we now know from NFL, small concussions are not healthy:)
      For a moment, let’s forget about regular skiers. These same helmets, open face, they’re approved for skiers to go racing Super G at 155km/h!!! Now this is crazy. Top karts reach these speeds and the kids are required to wear much, much safer full face helmets with a lot more padding. Now there are carbon ones for around 900$.
      OK, 900$ is a lot and they’re full face. But FIM, the motorcycle federation also has higher standards for MotoX even though the speeds are lower and yes, I found full carbon helmets from $550. When you consider how much people pay for ski passes or just one night at some of the resorts, $550 is nothing for your health. And of course the price will go down… The helmet is the cheapest ski equipment! Cheaper even than gloves.

  15. Again, Gary, brilliantly informative and so helpful to those of us that are avidly following what is happening on a daily basis, and fulfilling our need to fully understand what’s going on from a highly regarded, medical perspective. Thank you.

  16. I agree with the conclusion, but the energy involved in a fall of a 75kg mass from 2.5m under normal earth gravity is not 1715 Joules.

    If you fall from 2.5m it will be 0.505 seconds before you hit the ground, during this time you are continuously accelerated towards the ground at 9.8m/(s*s). At the point of collision your velocity is 4.95m/s in the direction of the ground – let’s round it up to 5m/s to make the rest of the maths easier. This is quite fast: around the same speed as a non-runner can sprint.

    The energy involved in the collision is given by 1/2 * mass * velocity * velocity and is therefore 1/2 * 75 * 5 * 5 which comes out as about 938 joules. If I redo the calculation without making the 5m/s approximation the result is 918 Joules.

    This is a lot of energy: more than being shot with a .357 magnum at point-blank range.

    • First, i’m not a physicist. Second, 1000 and 1700 are ballpark similar. Third, calculate potential energy at 2.5 meters, 0 vertical speed at top of trajectory, all of which is converted to KE and brought to 0 on landing. PE is 1715 j with my assumptions. Not gonna discuss ANY calcs further with anyone – for illustration and comparison only, not for engineering accuracy.

      • I want to thank you for your analytical and informative postings considering Michael Schumacher. Unfortunately though, I must agree that the calculations considering the impact are a bit off. Michael might weight something like 70 kilograms but his head weights only 5 kilograms. This gives us 123 joules. The rest of the body and limbs can bend, twist and stretch. It is highly probable that most of the kinetic energy of the body will be absorbed by the body itself.

    • …and doesn’t that assume normal gravitational acceleration from zero starting velocity with no allowance for the whiplash of tripping over a rock whilst travelling at skiing speed?

    • I would like to add my thoughts. First, there might be much higher forces involved than just falling down from 2, 5 meters (where the velocity at impact would be around 7m/s = 25km/h).
      Hitting a rock usually catches your ski, and it act like fixed point turning his translational
      speed into impact speed. So if he was traveling with 50km/h the impact energy might have been four times as high as Gary estimated. Moreover, my personal judgment is that extreme declaration is the most harmful to the brain, and unfortunately the skiing helmets are total crap when it comes to cushioning. I roughly would say the a skiing helmet will deform by 0,5 cm while my Arai Motorbike helmet is likely to give me 4cm of deformation. So even if the hulls of the helmets would spread the loads similarly, and even if we compute with the originally assumed 25km/h,the acceleration to zero in 4cm gives an acceleration of 610m/s^2=61g, while the acceleration with skiing helmet would be eight times as high, i.e., 4880m/s^2=488g. Both numbers sound very unpleasant but the second is clearly what causes such severe damage.

      As far as Massa is concerned, there was certainly a backwards motion of his head absorbing
      some of the energy and limiting the deceleration. Unfortunately a rock is very hard and
      contribute nothing to the deceleration path.

      A final comment: motorbike helmets are up to high standards, and there is no need to
      use F1 technology for everyone going skiing. Just give us helmets that are as good as
      motorbike helmets, and that will reduce brain injuries very, very significantly.

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