## Methodology equating bone fracture tolerance to DeltaV?

Topics Related to Analysis of Motor Vehicle Collisions
brian
Posts: 500
Joined: Tue Jul 14, 2009 10:52 am

### Methodology equating bone fracture tolerance to DeltaV?

Q: I have been given a report that states it takes 6468 Newtons to fracture a bone in the ankle. The report then states this yields a acceleration of 14.5 g and that over a typical contact time of .1 sec during the collision which yields a collision speed change of at least 16 mph. What's the deal with this methodology?
A: So that's how fast I was running when I broke my ankle?!! No wait, that's how fast i was stomping on the ground when i broke my ankle while running??!!
The 'expert' is taking liberties mixing average fracture limits on bones with accident reconstruction equations.
The 'expert' is generally applying the equation: Impulse = Force * Time = Mass * Impact Speed Change
If you convert the N to lbs force, ~1454 lbs, then multiply times the time: 1454 lbs*0.10 sec, you will arive at the ASSumed 'impulse' the 'expert' has decided is apparently required to break the ankle bone (connected to the calf bone, connected to the knee bone, connected to the thigh bone....oops...where was i?)
The assumed impulse is approx 145 lb sec.
Convert the DeltaV to in/sec = 16 mph = 281.6 in/sec
now stick it in the equation:
Force * Time = Mass * Impact Speed Change
(1454 lbs) *(0.10 sec) = Mass * (281.6 in/sec)
Therefore, Mass = 0.516 lbsec**2/in
So the 'experts' ASSumption for the effective Mass participating in the ankle breakage must be = 0.516 lbsec**2/in or ~ 199 lbs.
Some additional ASSumptions by the 'expert':
1) collision duration 0.10 sec?? For vehicle to vehicle, that's within the range. But not for impacts between and ankle and whatever it had contact with? Ankles don't generally crush like the vehicle periphery, they are more brittle! And there is a wide range of tolerance limits for ankles dependant on bone structure, age, health, fitness, position, load path, etc, etc.).
2) What type of collision was this such that the 'expert' assumed the 'effective mass' of 199 lbs (I would guess that is the injured parties weight?) and ALL the weight went through the ankle?
3) Was this a 'foot on brake' or floorboard crumple type accident? Where are any considerations for Dynamic v static, load path, etc.
4) Did the person try to stop a vehicle with their foot? (Was this Ironman? Did he try to stop a moving vehicle with his foot and broke his ankle? Is he suing someone for not building his ankle protector to proper specs??)
Sorry for the lame attempts at wit, be sure to double check my calcs, This is a quick response.
This is meant to get you the underlying equations used in the questionable manner for the simplistic analysis.
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