The Head Injury Criterion (HIC) and Crash Tests



The Head Injury Criterion (HIC) and Crash Tests

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In the 1950s, cars were efficient killing machines. There were no such things as airbags, safety belts, anti-lock breaking, crumple zones or plastic knobs. Ralph Nader pressured car manufacturers in the 1960s and 1970s to produce safer cars - and it worked.

This section is about how we analyse crash test data and how it relates to the average value of a function, using integration.

Head Injury Criterion - Normal Breaking

Normal braking in a street car: 10 ms-2 (or about 1 g).

Normal braking in a racing car: 50 ms-2 (or about 5 g). This is due to aerodynamic styling and large tyres with special rubber.

When we stop in a car, the deceleration can be either abrupt (as in a crash):

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or more gentle, as in normal braking:

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Either way, the area under the curve is the same, since the velocity we must lose is the same.

Head Injury Criterion - Crash Tests

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Diana's smashed car... RIP

I wrote this section just after Princess Diana died.

Notice how the front crumple zone of the Mercedes did its job while the cabin retained its shape. Unfortunately, it was not enough to save her.

Photo source:

american- (now defunct)

Imagine a car travelling at 48.3 km/h (30 mph). Under normal braking, it will take 1.5 to 2 seconds for the car to come to rest.

But in a crash, the car stops in about 150 ms and the life threatening deceleration peak lasts about 10 ms.

Crash test experiments include the use of dummies, dead bodies, animals and boxers!

Mercedes Benz Crash Test Data - Deceleration of the Head

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Our head is like a pendulum and so it is the most vulnerable part of our body in a crash. In cars without an airbag, the deceleration is quite violent and lasts a very short time. The Head Injury Criterion (HIC) is very high, indicating that the occupants' heads will be injured. (See the Description of HIC in a later section.)

The A-3 ms Value

The A-3 ms value in these graphs refers to the maximum deceleration that lasts for 3 ms. (Any shorter duration has little effect on the brain.)

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If an airbag is present, it will expand and reduce the deceleration forces. Notice that the peak forces (in g) are much lower for the airbag case.

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The blue rectangles in these deceleration graphs indicate the most critical part of the deceleration, when the maximum force is exerted for a long duration.

With an airbag, you are far more likely to survive the crash. The airbag deploys in 25 ms.

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Severity Index

We aim to describe the risk of head injury in a crash by a number.

The first model used was the Severity Index (SI).

It was calculated using

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where

T is the duration of the deceleration during the crash

and

a(t) is the deceleration at time t.

The index 2.5 was chosen for the head and other indices were used for other parts of the body.

The Head Injury Criterion (HIC)

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It was found that the Severity Index did not accurately describe the likelihood of certain injuries in a crash.

The head Injury Criterion (HIC) was developed and it is based on the average value of the acceleration over the most critical part of the deceleration (shown in the blue rectangles in the Mercedes data before). We met average value of a function earlier in this chapter.

The average value of the acceleration a(t) over the time interval t1 to t2 is given by

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For the HIC, this was modified (based on experimental data) as follows:

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The formula means:

The HIC is the maximum value over the critical time period t1 to t2 for the expression in {}. The index 2.5 is chosen for the head, based on experiments.

Modelling the HIC

Our approach is to model the deceleration curve with a function. We recognise that the shape of the crash data graph is basically like the curve:

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(This similar to the 'bell-shaped curve' in statistics.)

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Let's look at the curve using LiveMath:

LIVEMath

Model for the Acceleration

By modifying the function above, we can get curves very close to the Mercedes experimental data.

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[This model was obtained by observing 2 peaks in the deceleration graph, centred at 68 ms and 93 ms. By adding the 2 bell-like curves, we get a model very close to the required graph.]

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The computer time to calculate the HIC expression is high, so we need to simplify things a bit...

We can simplify that part of the HIC formula in {} for different values of d = t2 − t1. We define a family of curves:

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We then vary the value of d. The value of the highest peak of the family of curves obtained gives us the HIC.

HIC without Airbag

We now use the model for a(t) from above and maximise the value of H for different values of d.

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We see that the highest peak occurs when d = 50 and reading from the graph we see that the HIC is approximately 725. This is reasonably close to the Mercedes Benz data. (Other values for d are shown, but not all, of course. The value d = 50 did in fact give the highest curve.)

HIC with Airbag

The model is simpler for the airbag case, as the deceleration is smoother and is almost bell-shaped. Some modelling achieves the following expression for the acceleration:

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The graph is as follows (drawn with the same vertical scale as the non-airbag case):

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Now to apply the formula for H again. We get a family of curves and once again, d = 50 gives us the maximimum value, hence the HIC.

The HIC for the airbag case is around 310, close to the Mercedes Benz data.

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Our main aim here is to reduce the effects of rapid deceleration. If the curve is low and flat, injury to the head is reduced.

Let's get LiveMath to draw these models for us:

LIVEMath

The Head Injury Criterion (HIC) - What Does it all Mean?

Generally, experts agree that HIC values above 1000 are life threatening.

Recent crash tests have HIC values as low as 142 (an Audi 8, with airbag, in 1995).

Conclusions:

• You cannot hold a child firmly in your arms in a crash

• Safety belts save lives

• Airbags save heads

• Areas under curves and average values have interesting applications.

Reference: Henn, H Crash Tests and the Head Injury Criterion, Teaching Mathematics and its Applications, Vol 17, No 4, 1998.

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