In January, the reversals to speed limit reductions on the state highway network began. Councils have been asked to reverse all reduced speed limits since 2020 by July. A retired rural healthcare worker found something missing from the conversation – a maths equation she learned in high school.
As told to Gabi Lardies
Ask anyone about the effect of a crash when a car is travelling at 100kph as opposed to 80kph, and I bet they would estimate that the former would cause 25% more damage, because 100 is 25% more than 80, right?
Wrong.
In media reporting, there’s been plenty of discussion that reversing the speed limit reductions will cause more damage, but not exactly how much more. In high school 60 years ago, I learned an equation, the one which calculates the kinetic energy of a moving body. In a car crash it’s the dissipation of this kinetic energy, when the car abruptly stops, that causes damage to the car, the people in the car and whatever the car hits. It is calculated by multiplying half the mass of the moving body by the square of the velocity, like so:
Kinetic energy = mass/2 x velocity²
Or, in a simpler form, KE = m/2 x v²
Now I’m 74 so the faculties are not all that they used to be, but that little superscript ² is the key to understanding the impact of speed on a crash. It’s not linear, like people assume, but exponential. Here’s a simple example. Consider a 100g ball striking, for example, a gentleman’s nether region. At 20kph, the kinetic energy dissipated into his tender parts is 50 x 20 x 20 = 20,000 units of hurt. The same ball travelling at 40kph delivers a kinetic energy of 50 x 40 x 40 = 80,000. If you double the speed, you quadruple the damage.
So looking at a vehicle, the kinetic energy at 80kph is m/2 x 6,400, whereas at 100kph it is m/2 x 10,000. The increase in kinetic energy for that 20kph increase in speed is just over 56%, not the 25% that people may assume. Then consider that a lot of crashes – particularly on nice, level, straight roads – involve two vehicles, and if they meet head-on, as happens all too often, the velocities are additive. If both vehicles are going at 80kph it will be 160kph. At 100kph it will be 200kph. That could easily be the difference between St Johns putting you on a stretcher or in a body bag.
I worked at rural North Island hospitals for over 30 years. If you’re working in a very small hospital when an accident comes in, it’s very much all hands on deck. You aren’t discriminating between the surgeon and the physician and the anesthetist, everybody does what they are able to do, especially if there is more than one casualty. I’ve seen the fractured skulls, the lacerated livers, the crushed chests, the dead children. There are many times when I remember thinking, “I’m so glad that their relatives will not see them like this”. By the time their family arrives at the hospital, we’ve managed to clean up some of the mess, but there are some messes you cannot clean up.
You see all sorts of injuries, it depends very much on the impact. Was it a head on collision? Did the car get struck from the side by another vehicle? Were the occupants restrained or unrestrained? You could say there’s almost no injury that you can’t see as a result of a car crash. There’s just so much potential for damage. If you look around the inside of a car – even modern, well-designed cars – there are just so many parts that a human being can strike. People think “I’m driving a nice modern car, it has front and lateral air bags. I have seat belts. I always put my seat belt on”. Those are going to mitigate the damage a bit, they just might make the damage survivable.
The government’s rationale for putting the speed limits back up is to help drive economic growth and improve productivity. It’s been calculated that an average 20-minute urban car trip will be 12-14 seconds faster when the lowered speed limit is removed. When I get overtaken on central North Island roads, I find myself just behind that same car at the next intersection. You’re not gaining that much. If you crash a car at 100kph, the damage will be more than 56% worse than if you crash at 80kph, but you’re not cutting your travelling time down by much at all. The gain in time is very trifling compared to the loss in terms of safety.
If people crash when driving faster, there will be worse injuries, and there will be deaths, where, at the lower speed, there would have been survivable injuries. There is a lot that we can do for a lot of injuries, but we can’t do anything if you’re already dead by the time they’ve cut you out of the car. It’s as simple and as brutal as that. I know what that 20kph increase means, and it isn’t increased productivity.
