Sunday, 27 May 2018

The plan doesn't have to succeed, but it can't fail

People die in car crashes not because the driver hits a wall, a tree or another car. They die (usually) because the cabin of their own car hits them (wheel or dash, and the impact area is about 2cm^2).

The purpose of crumple zones and material choices in the vehicle body are designed to model a shock absorber between the point of impact and the position of the driver. In other words, crumple zones ensure the driver's acceleration curve is different to the car's and that the cabin is able to traverse a slightly longer distance than the front of a car. Even an additional meter of travel makes a huge difference. More distance = lower acceleration = lower force. An inverse relationship between the car surviving and the driver surviving.

Surviving is a function of force, not acceleration. If you fall into a hard chair from a standing position, you experience about 10G's on impact. But the force is spread over a half square meter of the tissue of your ass, which absorbs much of the force before it passes on to bones. But 10g's spread over 1 square cm will pass right through you like a bullet.

In this sense, 92 G is roughly normal for a 100mph car crash, but G tells you nothing. It's only attempting to calculate deceleration. G (32 ft/s/s) is a measure of acceleration, not force (F=ma).

Car impact analysis is massively complicated. Watch this car crash video and notice how the front left wheel collapses and bits of metal fly off the car. Those breakage events represent a force applied to that part of the car exceeding its mechanical limits. At breakage, the force isn't transferred through the part to the rest of the car, it's absorbed entirely by the part which snaps. Commensurate with that breakage is a reduction in acceleration.

Cars in the fifties weighed about as much as they do now, believe it or not. The reason they look like tanks is that they were built to survive impacts. So the steel was thick and heavy, and everything was bolted together as strongly as possible. The result was cars survived crashes, but the drivers didn't, seriously cutting down on repeat business.

Car manufacturers began to design breakage points. Lift the hood of your car and look at the underside. You'll see the steel rolled into a box around the perimeter of the hood supplying rigidity. But look closely and you'll see little notches taken out of it. That notch shows you precisely where the hood will bend on impact. Manufacturers know exactly how much force that notch can take before the hood bends around it.

As the body crumples, acceleration is lost, and force is absorbed by the car body and not the driver. So, the proper way to model a collision is at a minimum as a three-body problem: the wall, the cabin, the driver. As you add collapsible steering columns and breakaway dashes, axles, engine parts, etc, the number of bodies in the collision magnifies.

Some objects aren't as solid as others. A softer wall might absorb the force of impact both through friction (car slides between pieces of the wall and pieces slide onto the road) and as less-than-ideal springs (the wall squishes). This combines to help reduce the 'a' in F=ma. This is also why abutments on motorway exit ramps are often filled with sand or water. It dissipates the energy even further, boosting the effectiveness of crumple zones.

Also, the deceleration is non-linear and non-uniform, especially with the car falling apart as it heads towards the wall. If the front of the car crumples by one meter on impact, it means the driver moves an additional meter after the front of the car has stopped.

So assuming the front of the car crumples by 1m, that actually gives you a distance of 3.44 meters the driver travels, not 2.44m. This drops the G's to about 66.6 from 92. That's 30% less force felt by the driver. Factor in the skidding, the smashed tire, the dirt and all the rest and even with speed far below 150kmph, the force a driver feels is often well within the range of minimal bruising. Most people can just walk away from a crash.

You can now appreciate why the single most important safety feature in a car is the seatbelt. Without seatbelts, the deceleration of the car and the human are independent. The car decelerates first on impact, which means the driver starts moving in the cabin at a speed equal to the difference between the speed of the car at the moment of impact and a moment later. Even if the car was going 100kmph and a moment later was going 40, the driver is moving 60kmph.

The seatbelt links the human's acceleration curve to the midpoint of the car body, allowing the entire front half of the car to be destroyed in the process of absorbing the impact force and slowing the midpoint down before any part of the car touches the driver.

And yes, I am talking about #MeToo.

Bet you didn't see that coming.

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