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I recently saw a post (that was pretty old) asking why we don't consider the jerk function more often in sciences that deal with impacts or sudden accelerations. The general belief was that impacts, as functions of time, do not play nice and are not smooth functions on a scale where the sudden acceleration is apparent. Another observation was that sudden accelerations producing "jerk" tend to also produce oscillations whereas simple accelerations do not.

Over the course of my career I have reviewed the data from hundreds of airbag modules from vehicles involved in real-world traffic collisions. Among these data are some that are typically organized into graphs showing acceleration (typically in units of g) as a function of time over 250 ms or so in intervals of 1 ms. What you begin to notice is that impacts of a sufficient force produce clear oscillations in the acceleration data, which occur due to the materials used to construct vehicles and the type of impact (e.g., sideswipes produce less oscillations than head-ons).

This got me to thinking what would be required to actually be able to analyze the jerk of a real-world event like a collision. Another thing that is apparent about the data is that the accelerations tend to be very sharp at their maxima and minima, which makes them difficult to define as "nice" functions.

Typically, I am interested in the delta-v of a crash (among other things) so I either find a integratable function that will closely approximate the crash impulse graph and integrate, or if that is not possible, I will use numerical methods (like the trapazoid rule) to directly calculate the delta-v from the data. Usually the time increments are small enough that either way will provide useful approximations. But delta-v is far from the whole story. I think that the oscillations that a vehicle experiences are directly related to the injuries sustained by the occupants.

The question I have is, can a jerk function somehow provide insight into the oscillations that occur during a vehicle crash? If so, can a spring constant or other parameters for this oscillation be estimated using such methods? If a 3rd order non-constant function for the motion of a body can be determined, does that necessarily mean that the body was exposed to a sudden acceleration? That seems counter-intuitive.

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  • $\begingroup$ I am not an expert on airbags but I can comment on one part of your post. That the acceleration vs. time looks "very sharp at their maxima and minima" implies you may not be fully resolving the data. If you use a higher sampling rate (e.g., one sample per 0.1 ms), it should resolve the "spiky" nature of the data (assuming the sample rate is high enough). Another thing to be careful of is aliasing and leakage in any sampled data. While the oscillations may very well be real, there could be artifacts of higher frequency changes leaking into your time domain causing issues... $\endgroup$ – honeste_vivere Apr 12 '16 at 19:35
  • $\begingroup$ That approach is worth some consideration. Conventional thinking is to filter the data in order to achieve an integratable function, but that makes analysis less accurate. I like the idea of resolving the spikes to achieve a well-behaved function by using a higher sample rate rather than tossing out or averaging data. The modules are capable of recording at smaller intervals, but their primary purpose is to run algorithms to fire the bags, not record forensic data, so the recording capabilities are somewhat limited by design. $\endgroup$ – David Eisenbeisz May 18 '16 at 23:13
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As it happens, auto manufacturers (and the NHTSA I believe) have rules about maximum allowable jerk during cruise control, automatic braking, and similar machine-based events. (Trust me -- I work for an automotive active safety product company)

Certainly airbags are required to have a maximum 'acceleration' as they open up, to reduce (and sadly, not eliminate, as history has shown) the injury risk from the airbag itself. However, I suspect translating known jerk (and jerk vs. time!) into induced oscillations in what are most likely non-linear systems will be a daunting task.

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  • $\begingroup$ I can't argue with that. Much of reconstructing real-world events is daunting, and there is rarely enough data to achieve great precision in the kinematics involved. I am always adding new techniques to my toolbox because one never knows when that type of thing will come up again. By the way, I like your alto clef icon. $\endgroup$ – David Eisenbeisz May 18 '16 at 23:20
  • $\begingroup$ @DavidEisenbeisz Thanks, but it's a tenor clef. On account of how I like to think I know how to play the 'cello :-) $\endgroup$ – Carl Witthoft May 19 '16 at 11:31

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