# In mechanics, is shock really better expressed as jerk instead of acceleration?

Some expensive electronics or mechanical devices are designed to be shock-resistant. However, the manufacturers often market the level of shock-resistance in units of g-force (I know g-force is really a measure of acceleration). I'm not really convinced that that's the proper unit.

In fact, the Wikipedia article for mechanical shock describes shock as a sudden acceleration or deceleration. Here, the term "sudden" seems to imply that the acceleration or deceleration is not constant during a shock, which would mean that there should be a jerk component to the equation that describes the movement or position of the object as a function of time.

So here are my three related questions:

1. Is shock better expressed as g-force per second? If not, why (i.e. why is g-force a better unit)?
2. When you bang a smaller object that is reasonably rigid (e.g. a wristwatch with stainless steel case and bracelet) against another object that is reasonably massive, immovable, and rigid (e.g. a brick wall), how does the plot of position as a function of time actually look like, supposing we can record time and distances with extreme precision?
3. Do common mechanical devices suffer mostly from high acceleration or from high jerk?

Update The ISO 1413 shock resistance standard seems to give some clues. The testing procedure consists of letting a 3 kg hard plastic hammer traveling at 4.43 m/s hit a watch. Which suggests that we really care about the instantaneous transfer of energy or of momentum. But how fast does the transfer happen? Is it in the millisecond or nanosecond granularity?

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why jerk, why not snap, crackle or pop? – alancalvitti Feb 18 '13 at 5:14
The time scale of the transfer is set by the mechanical properties of the watch. If the watch is made out of hard, stiff materials, it will decelerate the hammer more quickly. – Ben Crowell Apr 10 '13 at 5:09

There are definitely situations in materials science and mechanical engineering when jerk is more important than acceleration as a factor in causing damage. A term I've seen used is "load rate." This can refer to either $dF/dt$ or $da/dt$, which differ by a factor of $m$. You'll see the acronyms ALR and ILR for average and instantaneous load rate.

A steady force can't cause wave excitations, but a varying force can. For example, when you're machining something on a mill or lathe, jerk produces "chitter," which can spoil your work. Engineers designing cams work very hard to minimize the jerk of the cam follower: "Remember also that jerk translates to an impulse and excessive impact ultimately leads to scuffed and pitted cam follower." (Blair 2005)

I know of a couple of good examples involving the human body. In crewed spaceflight, astronauts are exposed during a launch not just to high accelerations but also sometimes to what's known as a "pogo," which means an oscillating acceleration in the longitudinal direction. A pogo with an amplitude as small as $0.5g$ can apparently cause extremely unpleasant sensations in the eyeballs and testicles, as well as heating of the brain and viscera (Seedhouse 2013). Heating is a phenomenon you can't get from a static force.

Another human-body example involves running injuries. Measurements using accelerometers attached to runners' feet, legs, or hips show that during a stride cycle, there are typically two different peaks, an impact peak and another "active" peak that occurs during propulsion. The impact peak has a smaller acceleration but a larger jerk, and seems to be the factor that causes injuries: "increased impact loading was associated with an elevated risk of sustaining a running injury while peak vertical force was not." (Davis 2010)

G. P. Blair, C. D. McCartan, H. Hermann, "The Right Lift", Race Engine Technology, Vol. 3 lssue 1, August 2005

Irene Davis, quoted in http://lowerextremityreview.com/news/in-the-moment-sports-medicine/impacts-spell-injury , 2010

Erik Seedhouse, 2013, Pulling G: Human Responses to High and Low Gravity

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Shocks by definitions are discontinuous therefore non-differentiable jumps in the relevant quantities (e.g., pressure jump across a shock mechanical shock in gas). So strictly speaking I think one cannot assign an appropriate derivative description - acceleration, a jerk, and so on. However, from a practical point of it would really depend on what quantity one might want to emphasize on, if the change in force what matters one might call it a jerk.

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How can shocks be discontinuous? Doesn't an object in fact accelerate or decelerate really really fast at the instant of impact only because of the eletroweak force getting into effective range at the particle or atomic level? Doesn't it only appear to be discontinuous because the human eyes and brains cannot capture the motion fast enough? – Kal Feb 15 '13 at 23:49
OK that's fair. What I meant to say was that shock represent changes at the molecular/atomic time and spatial scales. So, in a continuum mechanics approach it is better treated as a jump process. If you are willing to model the molecular dynamics to calculate the changes in force you will have to allow a rather fluctuating description to capture the actual dynamics. Besides, even in the any case not only do you have a force, the force-field is changing at a rate, that also changes, so you will need a much higher derivative than acceleration. – Sankaran Feb 16 '13 at 0:51
So, it really comes down to what derivative you really care about for what the purposes of whatever you are trying to do. I would prefer a jerk over an acceleration and maybe a higher derivative to describe the process. – Sankaran Feb 16 '13 at 0:52
Well I do think shock is a terminology usually reserved for more steady pressure wave propagation kind of situation. For instance in supersonic flow, a blast wave from an explosion. Essentially a process in which a flow propagates faster than the speed of sound such that molecules ahead of it will not see that slap coming. The hammer on a watch situation is much less steep I think (even before the hammer hits the air ahead of it will hit the watch). Anyways regardless, I think it is about what quantity one is interested. Here I think... – Sankaran Feb 16 '13 at 6:46
"impulse" is a much better word. Terminology aside though an impulse is like a delta function or a very sharp gaussian. It is sort of pointless to ask what the maximum force is just like it is meaningless to ask what a delta function is at x=0. I think only a integrated quantity across a small time window has meaning (again like a delta function convoluted with some function). So you are right! It probably is calibrated to some energy delivered in a small unit of time. The unit of time must be chosen or agreed by the regulating agency on some practically-motivated reason. – Sankaran Feb 16 '13 at 6:51

Shock is better expressed as g (or other unit of acceleration) because f = ma. Acceleration is proportional to the mechanical force applied to the object, which in turn quantifies its internal mechanical stresses.

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This is a very superficial answer that doesn't really address the question. Ben Crowell's answer is much better. Jerk can set things vibrating whereas constant acceleration cannot, so both jerk and acceleration can cause damage. – Nathaniel Jul 5 '13 at 3:30