# Comparing 2 shock scenarios with different magnitudes and times

For example, How does one compare 100 g's for 6 milliseconds to 45 g's for 11 milliseconds. These are two different shock scenarios with different magnitudes and times, so how can I compare them? If I have something that is shock rated at 100 g's for 6 ms does this imply that it will withstand 45 g's for 11 ms?

I have tried finding a "shock equivalence" chart or a metric for comparing two shock scenarios but I haven't found anything.

I was thinking it may depend on the mass of the equipment that is being shock rated:

$$v=at$$ $$F=ma$$ $$Power=Fv$$

An energy metric like power may give me a reasonable estimate to compare, but I am just guessing here. Is there a standard way to compare two scenarios? A chart or equation would be nice..

Thank you for the help!

• The HIC below I think is an empirically derived equation only relevant to human heads. I can't see the applicability of an energy metric to failure stresses of solid objects. Are the two comparable shocks on the same item or are you trying to find equivalence between shocks on different types of objects? – Paul Uszak Apr 15 '17 at 21:06

## 1 Answer

For car exidents there is a meassure, which is called Head Injury Criterion. It is a measure to estimate the possibility of an head injury during a car accident.

The HIC for the time interval $t_1,t_2$ is given by

$$HIC_{t_1,t_2} = (t_2-t_1)^{-1.5}\int_{t_1}^{t_2}a(t)dt.$$

The final HIC is given by the maximum value of the previuos expression, which can be obtained by sliding the interval over the total crash time.

But depending on your application other similar measures can be used.

• I suspect that integrated acceleration is somehow related to the quantity and viscosity of cerebrospinal fluid, and might not be appropriate to a rigid mechanical system. – Paul Uszak Apr 15 '17 at 21:09
• This is helpful. I think the integral of the acceleration curve is definitely a good metric to go by. As this is for shock rated electronics, im sure there is some different normalization other than the $(t_2 - t_1)^{-1.5}$. But still some good insight into how to compare two scenarios. – Mike James Johnson Apr 16 '17 at 17:11