Documentation:FIB book/problems/HIC1

Head Injury Criterion (HIC) is calculated as follows: $HIC=\left[{\frac {1}{t_{2}-t_{1}}}\int _{t_{1}}^{t_{2}}a_{r}dt\right]^{2.5}(t_{2}-t_{1})$
Where a_r is resultant head acceleration in g’s, and t₁ and t₂ are in seconds.

Question 1

Where does the HIC equation and limit come from?

SOLUTION (expand to show)
The equation comes from human volunteer, cadaver and animal tests, which found an empirical relationship between head acceleration, time over which the acceleration is applied, and head injury. From this information, probability curves were created (what HIC relates to a certain % risk of head injury). The limits (IARVs) come from these curves, and represent about a 5% risk of head injury. They depend on body size and age.

Question 2

How is HIC used by regulatory bodies?


SOLUTION (expand to show)
Regulatory bodies use limits based on IARVs (i.e. close, but not exact) to set safety standards for vehicles (e.g. FMVSS). In this case, by crash testing a car/ATD, calculating a HIC from measured accelerations, and comparing that value to the limit in the standard, they determine whether a car meets the standard. (Note that the IARVs are updated more frequently than the standards, so the standards may be out of date compared to the latest research).

Question 3

Calculate a HIC15 for the acceleration plot below:


SOLUTION (expand to show)
The HIC15 is the maximum area under the curve for any 15 ms time window (or less). In this case, it’s easy to see which 15 ms time window will produce the largest HIC. Using the equation: $HIC15=\left[{\frac {1}{0.015s}}(30g0.005s+30g0.005s+25g0.005s)\right]^{2.5}(0.015s)=64$ We also need to check smaller time windows (recall that HIC15 is the maximum value of HIC for any time window 15 ms or less). Given our data, the two time windows we can check are 10 ms and 5 ms. By observation, we can determine which specific range of our data will produce the maximum HIC value for each of these two smaller time windows (that is, 10-20 ms and 10-15 ms). $HIC15=\left[{\frac {1}{0.010s}}(30g0.005s+30g0.005s)\right]^{2.5}(0.010s)=49$ $HIC15=\left[{\frac {1}{0.005s}}(30g*0.005s)\right]^{2.5}(0.005s)=25$ The HIC15 is 64, occurring from 10-25 ms, which is under the FMVSS limit of 700.

Question 4

Calculate a HIC36 for the acceleration plot below:


SOLUTION (expand to show)
In this case, it’s not clear which 36 ms window will have the largest area immediately, so we may have to calculate over several windows (alternately, since the time intervals are the same, you could sum up accelerations for 6 intervals and pick the largest to do the full HIC calculation. For illustration purposes, I’m presenting the calculation for each one). $HIC36=\left[{\frac {1}{0.036s}}(0.006s)(20g+50g+60g+70g+40g+60g)\right]^{2.5}(0.036s)=637$ $HIC36=\left[{\frac {1}{0.036s}}(0.006s)(50g+60g+70g+40g+60g+20g)\right]^{2.5}(0.036s)=637$ $HIC36=\left[{\frac {1}{0.036s}}(0.006s)(60g+70g+40g+60g+20g+40g)\right]^{2.5}(0.036s)=585$ $HIC36=\left[{\frac {1}{0.036s}}(0.006s)(70g+40g+60g+20g+40g+10g)\right]^{2.5}(0.036s)=364$ $HIC36=\left[{\frac {1}{0.036s}}(0.006s)(40g+60g+20g+40g+10g+20g)\right]^{2.5}(0.036s)=364$ Considering only the 36 ms window, the maximum value of HIC36 is 637, which occurs from 6 to 42 ms, and from 12 to 48 ms. This is under the FMVSS limit of 1000.