How Fast Should Autonomous Vehicles Be Allowed to Drive?
The speed limit, right? Well, it’s not that simple. In fact, it’s a bit of a trick question. Understanding why requires a bit of background on the history and calculations of speed limits for human-driven vehicles, starting with the counterintuitive reality that the speed limit is determined by how fast people drive.
That sounds backwards. Aren’t people supposed to set their speeds according to the speed limit? In theory, yes. But in reality, as both traffic engineers and urbanists know, the causality runs in the other direction. With the exception of high speed, limited-access roads — highways, motorways, etc. — people drive according to the speed at which they feel comfortable handling their vehicle safely, and for the most part do so without consideration of the signs telling them how fast they should be driving (you might feel like you follow the speed limit because when you look at the speed limit signs they generally confirm that you are driving at the right speed, but the causality is the reverse of what your intuition and popular wisdom would have you think; more on this below).
The main factor in determining the speed limit of a street is actually the speed of free-moving traffic on that street. More precisely, the speed of motorists driving in free-moving traffic — each driving at the speed at which they feel comfortable handling their vehicle — will form a distribution; the speed limit is generally the 85th percentile of this distribution, with slight tweaks for individual circumstances or due to political reasons. This is called the 85th percentile rule. The 85th percentile is chosen because it ensures that most people will not be lawbreakers, and because the police only have enough resources to ticket the most egregious violators. Because the distribution is rather tight, a small shift in either direction of the speed limit can actually make a huge difference in what percentage of drivers are considered speeding.
Consider the distribution of driver speeds on a rural road, below. 60% of drivers are between 70 and 80 km/h, or 44 and 50 mph. 90% of drivers are between 60 and 90 km/h, or 38 and 56 mph. The fact that these distributions are so narrow is why, unless you are a particularly egregious slow poke or speed demon, you will generally find that your natural driving instincts will place you not far from the speed limit.
If motorists drive according to the speed at which they feel comfortable handling their vehicle, lowering the speed limit won’t have the desired impact. How do you slow them down then? By employing one of many of what are called traffic calming strategies. These include everything from speed bumps to narrowing the road to painting crosswalks and medians. These all work to differing degrees and in different situations, and can be mixed and matched according to the traffic engineer’s fancy. If motorists drive at the intuitive speed at which they feel comfortable and safe handling their vehicle, then traffic calming measures are literally designed to make driving too fast feel unsafe, forcing drivers to slow down until they have returned to their comfort level. And we humans do this quite naturally and automatically, without necessarily even realizing it, depending on the specific traffic calming strategy used.
The theoretical model for this behavior is called risk homeostasis. Risk homeostasis says that everyone has a level of riskiness in any given activity that they are willing to tolerate — or said another way, a level of safety that they require — and that if you change the perceived riskiness of that activity, they will adjust their behavior to compensate. More concretely, as applied to our case, a driver has a target level of safety that will dictate how fast he will drive on a given road (he knows that there is always some risk in driving, but he wants to keep it below his risk tolerance and so will not drive too fast). If you make him feel less safe, by narrowing the road, adding warning signs, etc; then he will slow down and drive more carefully to keep his perceived risk below the acceptable level [1].
The question raised by the 85th percentile rule is, shouldn’t speed go up as automobile technology improves, presumably making cars easier and safer to handle at higher speeds? This is what happened over the first 60–70 years of the 20th century, as speed limits climbed from around 10mph in 1901 to the highway speeds of 65–75mph that we know today. I’m not sure why the automobile industry has been unable to introduce any new technologies since 1965 that would enable people to drive faster without compromising safety; perhaps it has something to do with the limitations of human reaction times. In any case, we stand at a juncture today where a new technology is about to be introduced that will allow us to “drive” at much higher speeds while maintaining a level of comfort and safety equal or greater to that which we have today, a technology that is not dependent on human reaction times: autonomous vehicles.
Autonomous vehicles will have reaction times that make even the best Indy 500 race car drivers seem like amateurs, but even AVs have limits. Their reaction times — really the amount of time it takes them to perceive the reacted-to object and the time it takes to actuate the actuators that execute the reaction, as the compute time between the two is effectively zero —are non-zero, and the laws of physics will still apply for how fast they can handle curves or swerve without losing traction with the road. No matter how quickly they react, physical laws will still constrain on how quickly they can come to a stop.
So back to the original question: how fast should we let AVs go? There is no obviously correct way to answer this, so I have tried to go through the thought experiment below and outline a few possibilities.
One option would be to apply the 85th percentile rule to AVs. Unlike human beings, however, who share enough common characteristics around risk tolerance, intuitive physics, and reaction time to naturally form a tight distribution, machines can be engineered to different specifications and will not follow such a distribution. This strategy therefore is unlikely to work. We can calculate a speed limit for any given car, based on its specifications, but not a uniform one [2].
Initially, or as long as human drivers are still the norm, AVs are likely to be required to follow existing, human-risk-tolerance determined speed limits. An AV might be able to drive twice as fast as a human without losing control, but it will terrify and confuse human drivers and human law enforcement, most probably causing accidents and other damage that way.
Even so, the question of how fast AVs should drive is not quite answered. Should they always drive the speed limit, exactly? On city and local streets, this might work as an upper bound. During this initial period in which the public is adjusting to the presence of AVs, and AVs are still the exception on the street — whose length is impossible to predict — you would want them to mimic the driving patterns of human drivers. I.e., slowing down when lanes narrow, at necked intersections, etc, even if they could use their 360 degree sensors to know that no one else is coming, and their precision controls to maneuver with the same degree of control without slowing down. Again, this is for the comfort of other users of the street: human drivers, pedestrians, cyclists, etc.
What about on highways and rural roads where the majority of vehicles do not follow the speed limit? The Solomon curve shows what we all intuitively know to be true, and what the majority of DMVs around the country already recommend: that driving with the flow of traffic is the safest strategy when the flow exceeds the posted speed limit. It’s one thing, however, for individuals to do this on an ad-hoc basis; it’s another for GM or Google to formally program an entire fleet of cars to disobey the law. The former is like an office pool for who is going to win the World Cup, or a friendly game of poker with a $10 buy-in. The latter is like running an casino without a license; it will make a mockery of existing regulation if it is not shut down. We are going to need to either increase existing highway speed limits to reflect what people actually drive — problematic, because raising speed limits on highways does make people drive faster — or find a new legal framework within which to view speed controls. One solution is to have all autonomous vehicles safety-rated to a specific highway speed level, and to consider any vehicle driving the lesser of a) the flow of traffic, or b) its highway safety speed level, to be driving within its legal limit. This both preserves the existing speed limits for human drivers and creates a speed safety framework for AVs that seamlessly blends into existing traffic patters, avoiding distraction to human drivers.
Might AVs and human-driven vehicles eventually have different speed limits? Maybe, but until AVs dominate the road, or at least own a majority of it, it will be politically difficult to pass such a law. It would require significant adjustment on the part of human drivers, and a standard of data sharing with law enforcement to know which cars are autonomous and which are manual (one solution to these issues would be to have autonomous only roads or lanes that have higher speed limits). I will discuss what speed limits might look like in an AV-dominated world in a future post.
[1] Ironically, this means that if you do things to make it “safer” for the driver, such as increase lane width and trim trees from corners to increase visibility, motorists will drive faster and less carefully until their bring their level of perceived risk back to equilibrium. Traffic engineers often make this mistake, and the result is streets that are more dangerous and have more accidents.
[2] It’s actually worse than you think. A single autonomous vehicle make and model may be able to optimize its software — and even hardware — for different variables, such as exterior aesthetics, occupant comfort, or environmental friendliness, and different configurations might have different safe speeds. Further, two identical cars might even have different safe speeds depending on the version of the software they are running, and they could easily be running different versions of their software.
Credit to Scott Le Vine, Professor of Transportation Planning at SUNY New Paltz, for providing the metaphor of the office pool vs the unlicensed casino.
