Why do I get the feeling that you wouldn't have said a murmur had I said that the threshold of fatal injury was 300g's?
And to answer your question, I know because the Wayne State Tolerance Curve
says so. In fact, for your hypothetical 100g example, impact duration is 6 ms and the threshold of life threatening injury is 90-95g for this duration.. And this assumes that the helmet not merely performs perfectly (does not fail under load by brittle fracture as opposed to crushing) but compresses to a density significantly higher than that of bulk polystyrene. This simply is not possible. And I'm neglecting the (incompressible) polycarbonate shell! Under the most favourable conditions, with the most benign of assumptions, helmet wearing fails to prevent fatal injury. [1]
actually average radius is most important factor and that helmet increases it by about 28% - implying that the probability of a fatal impact load is increased by helmet wearing. Agreed, but the probability increase will be tiny
Incorrect. Collisions take place at
surfaces, not radii. Which is why physicists talk about "collision cross sections", measured in units of
area. It is not the length of the barn door, nor its height - or even its volume, but its
frontal area which determines your chances of hitting it at 6 paces. Your 28% increase in radius (assuming circular geometry, because I CBA to work out a more complex model) means a collision cross section increase of over 60%. And how do you know that the probability increase will "be tiny"? Kindly show your workings.
That is 12 mph head on, like a bash to a car. I calculated it from a fall from a height to pavement, ie like being knocked off the bike and free falling to ground
Absolutely not. You cannot simply discount lateral velocity: momentum does not disappear!
Hint: conservation of momentum. One of the more fundamental postulates in physics. Lateral velocity simply cannot be ignored as you claim.
[1] For any innocent bystander - if there's anyone left after all this time! - this actually is the perfect example of why common sense breaks down in situations like this. The human body is surprisingly resilient to extremely high accelerations - for 2-3 ms duration a acceleration of 200g's or more can be tolerated without fatal injury. But it's time dependent! The longer the duration of the acceleration load, the less can be endured. A 75g load will induce a life threatening injury if it lasts for more than 10 ms.
In other words, it is not sufficient merely to reduce impact loads, as common sense suggests. This does not reduce impulse (that pesky conservation of momentum again) any decrease in the collision forces must necessarily be accompanied with a increase in impact duration. Since acceleration tolerance falls substantially as duration increases, this means any protective headgear must act to reduce the experienced force by a greater magnitude than is commonly realised. In fact, given the shape of the Wayne State Tolerance Curve (negative exponential), it is perfectly possible for an inadequate helmet to simply increase the impact duration such that a very short duration but high force impulse which will not cause potentially fatal injuries is extended such that the duration enters the lethal zone simply because it cannot reduce the impact acceleration sufficiently. This worse outcome due to protective head gear is not one that "common sense" would ever predict...
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