Thursday, June 25, 2009

Deceleration And Force Of A Helmeted Head Impact

For a final post this week, I'd like to make you wonder what it is like to slam your head bolt on in an accident while cycling. The agenda is objectively put some numbers out there and give a feel for things, using myself as an example. I'll show you how you can do the rough math yourself without much paper and ink.

So I went over to the shelf and grabbed my utilitarian Giro bike helmet to see what the foam thickness on it would be. It came out to about 1.8 inches, so let's take it as 2 inches for sake of simplicity.

Now say one morning, I'm out riding my bike at 25mph on my street. Suddenly, out comes this mad old lady from hell, backing out of her driveway in her car without spotting me over her shoulder. Unable to react quickly, (yeah I had a hangover from last night) I can't swerve away in time and CRASH I do right onto the vehicle, with my helmeted head slamming onto glistening sheet metal.

My head just decelerated from 25mph to 0mph in seconds. What was my head's deceleration? Let's assume it is constant deceleration for an ideal condition. The best helmets should offer this condition.

Avoiding lengthy kinematics derivations, remember this equation for constant deceleration :


a = deceleration of the head with a negative sign

vo = initial speed = 25mph ~ 36.7 ft/s

d = distance the head moves after impact before coming to rest, which is the distance the foam crushed = 2 inches = 0.167 ft

Plug in the values and you get a = -4032.6 ft/sec^2 ------------> A

The acceleration due to gravity on the earth's surface is 32.2 ft/sec^2 -----------> B

Dividing A by B, my head just experienced a constant deceleration of 125 times that of gravity (125 g). That is after wearing a helmet!

If you look at the equation for deceleration above closely, the 2d term is in the denominator. Hence, the bigger thickness of foam you have, the lesser the deceleration becomes. If I had 2 times the foam as I originally had, my head's deceleration would be close to halved and I would have more distance to 'take' this deceleration over. But too much foam thickness doesn't yield a good helmet design as it can cause a host of other problems. So there's a trade off. You will also appreciate the fact that since the velocity term is in the numerator, the faster I go, the more g's of deceleration I experience.

So what about the force my head experiences during this impact? Well, here's another simple equation for you to remember, derived from the work and change in kinetic energy relationship :


m = mass of my head and F is negative in sign indicating a retarding force

Say my head weighs about 10 pounds or 4.5 kgs. Now (vo^2/2d) is simply acceleration we found above, which is 125g. Multiply that with 'm' = 10lbs and you get something in the order of 1250 lbs of retarding force smack against my head. To put that into perspective, that's half a metric ton hitting me right where I don't want it. What makes this so uncomfortable for me, even just to realize, is that its doing this to me in a fraction of a second. That fraction of a second yank on my head is a yank on my brain and its internal blood vessels.

The thing to realize is that 125g of force maybe enough to cause brain injury, leave alone anything higher than this. Rarely is constant force ever experienced in a real collision. A more realistic model would perhaps be force following a curve, reaching a peak when the foam is close to being fully crushed. Hence, the ideal helmet assumed here is sort of...well, ideal. As comments have told me, I acknowledge that this is a simplistic model that does not take rotational characteristics of the acceleration into account. Rarely does an impact between the helmet and the road go through the center of gravity, hence causing rotation of the head.

Another thing you will appreciate is that if I were without a helmet, there would be no soft landings at all. If epidemiological evidence suggests that, on averge, chances of serious brain injury are reduced by a factor of 5 by wearing a helmet, I get a big zero by not wearing one. Lost out there, didn't I?

Having said all this, I sincerely believe that in the coming years as we push the frontier into new materials, we will come up with better solutions for this energy management problem in helmets. We will realize the goal for softer landings, constant decelerations and peak forces of lesser magnitude. Until then, we are struck with what's out there in the market. Some of these helmets are improperly designed. On one hand, too stiff foam liners are used that break catastrophically on impact instead of crushing. On the other, to satisfy the goals of lightweight designs, there is also a tendency to select low density foams that absorb much lesser energy than what is required. Hopefully, these issues wil be addressed soon to give sportspeople the protection they need to keep their heads right.


How A Bicycle Helmet Works

How Bicycle Helmets Are Made (Video)

How Materials Are Selected For Helmet Foam Liners [An extract from Gibson, L.J. and Ashby, M.F. 'Cellular Solids, Structure and Properties', 2nd edition, Cambridge University Press (1996)]

Anatomy of the human skull

Engineering Aspects Of Human Skull Fracture (University of Tokyo, Japan)

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John K. said...

Ron, your comment about using ballistics gel to simulate the head may not be practical as high vibrations in it might make the mean accelerations difficult to compute in a test simulation. Thanks.

Major Taylor said...

Vary unique blog.Bicycles math!

Gabbie said...

I really really like your blog,Ron. Its very different&interesting.Keep up the good work.

Ron said...

There's a reason those mythbusters use ballistics gel to simulate human heads when blowing them up.

Stan Slevinski said...

Interesting discussion. May I also add the mythbuster's use pig cadavers. The ethical implications of using animal body parts are many. I still think if you want to save a human's life, its best to test on a human cadaver.

gsport george said...

The honeycomb/folding design looks really neat, you can see comfort and ventilation being very good. However I think there is an inherant problem with using a member that will buckle, as I would think these ribs will. The stiffness will start at a maximum, tail off slightly as it begins to buckle, then drop almost to zero once buckling really starts. I suppose with this shape, as the first ribs to hit buckle, others will come into play as they make contact, so that may counteract it somewhat, however you are giving up any protection in the initial zone..

Chances of selling a helmet that looks like that and ties on with a ribbon like a bonnet to serious cyclists in any discipline? Pretty much zero I would think...

Bike_Boy said...

Ron, the design brief said the objective was to create something for minor bumps and falls. The issue of buckling seems real, so my question is ...after a minor fall, is it elastic enough to come back into its original shape? Who knows. Its still not a bad idea, and it looks like it will really excel in the cooling of the head.

gsport george said...

1. My understanding is that even in collisions that did result in injury to the brain there was little compression of the foam. If that is correct then SURELY the foam is too stiff? I would personally rather have a helmet that "runs out" of cushion (just) before I get brain damage, than one which will still have travel left long after the acceleration on my head becomes critical.

2. I understand that angular acceleration is often thought to be far more serious than direct impact, but arent we still looking at (broadly) a situation in which the initial angular acceleration is still the critical factor?

4. My point is that the deformation of the skull will effect how the helmet is loaded rather than the brain. In turn, a lower pressure on the helmet would necessitate a less stiff foam.