Thursday, 19 September 2013

More on Speeding

     A video is making the rounds, supposedly pulling the rug out from under the "Speed Kills" campaigns of the insurance industry, police, and the media. Essentially the argument is that speed limits are too low in many places, and that it's perfectly safe to drive at higher speeds and the only reason police enforce these limits the way they do is to generate revenue, not to promote safety. The insurance companies, it is alleged, are also making money from this because they get to raise premiums when someone gets a speeding ticket, while media is just lazily repeating the "speed kills" rhetoric because it makes a better story.

     Where to begin? Well, let's start with the basic claim, that speed doesn't kill. No, of course it doesn't. It's an abrupt change in speed that kills, such as the sort that arises when two objects of greatly differing vectors collide. And as we know from our basic high school physics, kinetic energy is proportion to the square of the velocity, which means if you double the speed, you quadruple the energy. It takes energy to crumple fenders and bones, so the greater the speed, the greater the capacity to do damage. This much is obvious, but that kinetic energy formula is important in another way, which I'll get to in a moment. The point here is that actually, yeah, higher speeds are more dangerous, and in a non-linear way: going 10% faster is more than 10% more dangerous.
     To be fair, that's not really the point of the video, which argues that higher speeds (on highways or other roads that can handle higher speeds) do not necessarily increase the likelihood of a collision. Well,  maybe not, but even if the chance of a collision remains constant (and it would be bizarre to claim that higher speed limits reduce the chance), the fact remains that higher speeds do more damage.

     This, by the way, answers part of another one of the claims of the video, namely that insurance companies love for people to get speeding tickets because it gives them an excuse to raise premiums. Actually, and actuarially, insurance premiums are supposed to be calculated to reflect the expected cost of insurance. Insurance companies have limited information upon which to make accurate estimates of the likelihood that a given customer will be responsible for a claim, and how much of a claim. Knowing that a driver has earned a speeding ticket reveals a little bit of data about their driving habits which allows for somewhat more precise estimates. Now, I'm the last person to trust in the selfless integrity of the insurance industry, and I haven't actually researched the actuarial data here, but it seems likely to me that at least part of the reason your insurance rates go up when you get a speeding ticket is because statistically speaking, you are a bigger risk.

     The video makes a similar argument about police departments making money from speeding tickets, and while I agree that it's problematic to introduce a profit motive to law enforcement, it's worth noting that the police are still not actually a for-profit organization; the money governments raise from traffic enforcement doesn't exactly go to line the pockets of shareholders.
     And yes, police use stealth traps to catch speeders, when the visibility of a police car is much more effective at getting people not to speed. So what? Is this supposed to show that speed traps are aimed at making money rather than promoting safe driving? Nonsense. It's easy to get people to obey the law when there's a cop around. The point of speed traps is to encourage drivers to obey speed limits when they don't see a cop. Sorry, I shouldn't need to explain that, but apparently I do.

     But my main beef with this video is that it misses the main point of speed limits, which as I've written before, aren't just (or even mostly) about the state deciding how fast you can be trusted to stay in control of your vehicle. Cruising along in your private vehicle, it's easy to feel free and independent and lose sight of the fact that our public roads and highways are part of a complete system of transportation, and that they are a shared public resource. We hire traffic engineers to design and manage this system for us, and we want them to make it serve our needs as efficiently as possible. So they do things like place stop signs and traffic lights and turning lanes and set speed limits and so on with the goal of minimizing the time it takes to make a typical trip. In other words, speed limits are meant to speed up traffic. Let me say that again in a separate line all by itself for emphasis.

     Speed limits are meant to speed up traffic.

     That sounds counterintuitive, I know, but it's true. If you thought the purpose of speed limits was to reduce accidents, well, sure, that's nice, but considering that even very minor accidents create huge delays and reduce average speeds by a ridiculous amount (and accidents where there are injuries or deaths even more so), it's enough to say minimizing accidents is just a good way for system engineers to minimize delay.

     Time for a simple chart.

     Obviously, if the enforced speed limit is zero, traffic's not going to be moving very efficiently. As we increase the enforced limit, the effective speed of traffic increases, but only up to a point. At that point, higher speed limits can actually decrease the effective speed of traffic. Why?
     In an ideal world, where everyone is zipping along at a uniform speed, it doesn't really matter what the maximum is so long as everyone is going close to the same speed. Yes, we need to worry about stationary obstacles, but presumably an ideally-built highway will be free of obstacles.
     But this ideal world is sort of like the ideal universe of basic high school physics, where friction and air resistance are ignored. In the real world of driving, cars do not simply travel along at uniform speeds in happy obedience to Newton's First Law; they are generally moving because the people in them are travelling from point A (where they presumably were at rest for a while) to point B (where they presumably intend to stop for a bit). So unavoidably, there's going to be some acceleration involved somewhere along the way. Moreover, since not everyone has the same points A and B, there's going to be some merging of traffic along the way also, which means that not everyone is going to be travelling at the same speed. And sometimes people are going to need to stop in places they didn't intend to stop, such as by the side of the highway.
    So in the real world, there will be a range of different speeds we have to accommodate, and unfortunately one of those speeds will be zero. Now, traffic can cope with a range of speeds, especially if there are multiple lanes. But changing from a slower lane to a faster one involves acceleration, and remember that whole kinetic energy equation? Among other things, it means that accelerating from 90 km/h to 100 km/h takes almost twice as much energy as accelerating from 50 km/h to 60 km/h. So lane changes and passing are going to be more demanding, and you'll need a bigger break in traffic to be able to execute them safely. That means that if you happen to be stuck in the slower lane, you don't actually benefit from the fact that the faster lane is really really really fast.

     To put it another way, road space is a scarce public resource, and you use more of it when you go faster, leaving less available for others to use. Speed limits are an attempt to distribute that resource equitably, so everyone can enjoy the benefits of a public roadway. People who drive faster may not recognize it, because the delays they cause to other people are barely visible in their rear-view mirror, but they are slowing everyone else down, even if they never actually cause an accident. Oddly enough, a lot of the time they complain about being stuck behind some inexplicable delay in traffic, it's actually due to the ripple effects of some other selfishly impatient driver.

     Are some speed limits too low? Possibly. But not for the reasons given in the video. Want to get where you're going faster? Drive at a reasonable speed, leave a reasonable gap ahead of yourself for other vehicles to change into and out of your lane, and be a patient, strategic driver. Let the speed limits do their job.


  1. A related topic (especially in Edmonton) is potholes and road reconstruction. Why so bad? Road damage goes up with the 4th power of axle weight. Fourth! Trade in our old Beetles, Datsun 510s, and once upon a time much smaller 1975 F-150 pickups. Buy now much heavier pickups and SUVs. Do the math.
    But no-one will address the elephant in the room and say "We have seen the enemy and he is us."
    Especially not to voters.

  2. Tom: Good work. I remember most of this from traffic class, and you hit most of the high points.

    Alan: The axle weights in question for passenger vehicles do negligible damage to roadways. You need to get into things like dump trucks and other axle weight restricted vehicles before the damage becomes significant (think bus weight or higher). It should also be noted that the damage is more significantly related to the amount of time that the weight is on the road, so a semi stopping at or creeping along at a slow speed at a stop light does the most damage. This damage generally shows up as rutting in the pavement surface, not immediately as potholes.

    The main cause of potholes is small failures in roads which allow water infiltration, and then the freeze thaw cycle. The way to deal with that is more regular maintenance of the roads than anything else.

    So, I guess the story here is to ensure that governing agencies spend time worrying about the axle weights of heavy trucks (which they do enforce) and ensure that your government spends money in infrastructure maintenance, not just new construction and glamour projects.

  3. Edmonton is currently trying 40 kph limits in suburbs to see if it has an impact on pedestrian mortality.

    And it will.

  4. I have to agree except for your second last paragraph, though I may have missed the point you were trying to make with it.

    "To put it another way, road space is a scarce public resource, and you use more of it when you go faster, leaving less available for others to use. " If you look at it as total time on the asphalt, the faster you go the sooner you are off the road leaving free for others. If everyone travelled faster there would be more free road. Of course if you were trying to say that should the speeder cause an accident, or force others' to slow down to avoid him, then yeah I'll agree with that..

    Dave Busch

  5. Actually, that is precisely the point I'm making, but also if you do the math, it's also a scarce resource in a hard physical sense. Remember the two second rule: you should always leave at least two seconds between yourself and the vehicle ahead of you. At a speed of zero, you need exactly as much pavement as your car covers. At a speed of 30 m/s, you need that much space plus 60 meters. There is a finite amount of pavement to go around, and most of it isn't where anyone wants to be driving.

    Sure, if you travel at the speed of light, you'll be out of everyone's way almost instantaneously, and the road is free for the next user two seconds later. But the whole road can only handle one driver every two seconds at that speed, which means you spend WAY more time waiting for a chance to use the road than the time you save actually travelling. Obviously no one will be driving at such an extreme speed, but that's just to show the limit of the equation: one driver every two seconds. If you reduce the speed to the point where you can cover the entire route in 4 seconds, then your travel time is increased by four seconds, but the road can handle two times as many vehicles at once, so wait times are cut in half. As speed declines, the road can handle more vehicles at once, reducing wait times but increasing travel times. The optimum speed is the one at which the sum of wait times plus travel times is a minimum.

    So you see, people who exceed this speed really ARE using up more than their fair share of a scarce resource.