For most people, ‘speed’ is a pretty straightforward term. As a noun, we’re either talking about amphetamines, or, more commonly, how fast someone is driving. As a verb, it’s something that will land you a pretty nasty ticket. For a traffic engineer, though, ‘speed’ requires clarification. We have three speeds, and no, they’re not ‘slow,’ ‘glacial,’ and ‘planet formation.’
The first speed is the design speed. Pretend you’re driving a tractor-trailer on a warm, dry day. The road’s in good shape. Your rig has seen better days. You’ve had a couple drinks; your head’s halfway between fuzzy and swimming. Oh, and you’re 80 years old. This is our design driver.
If you’re driving at the design speed, your tires will squeal around every corner. You’ll be able to read signs and react to them just in time to avoid gristly accidents. You’ll have to slam on the brakes pretty often.
Granted, most of us don’t drive like this. People who do should probably not be driving at all, in fact. All the same, we’ll design for them. This is a recurring theme among traffic and highway engineers: 99,999 people a day might use your road and have no problem with it. But if just one guy a day messes up and careens off the road, you’ve done a bad job. That’s why our design driver is so atypical.
When calculating a horizontal curve’s radius, the design speed is the main factor. You all remember a=v2/r, the equation for centripetal acceleration. If a car goes twice as fast around a curve, the radius needs to be four times as large to accommodate it, or increase the acceleration somehow. The easiest way to do this is superelevation, which is tilting the road to force you around the curve.
For a crest curve, which is going over the top of a hill, the length must be sufficient to ensure the design driver will be able to spot an object in the road (about the size of an enraged leprechaun) and stop before he hits it. Comfort is also a factor; make the crest too small, and you’ll fly over it in a graceful arc, digging a nice gouge out of the pavement downstream.
In a sag curve, driving into a valley, you can see much better, and you don’t need to steer. At night, though, that enraged leprechaun can totally sneak up on you and ruin your grille. Sight distance, then, is limited by how far your headlights can shine (about 1 degree above horizontal in the design vehicle). And, of course, the curve has to be long enough so you can actually screech to a halt once you finally see the obstacle.
Take the most dangerous curve on a road, and that’s the constraint for the design speed. A wide, flat, straight road has a tremendously high design speed. Most freeways are designed for around 70 mph, which is a pretty good clip for a buzzed octogenarian in a semi.
Next up, we have the 85th Percentile Speed (V15 in France). It’s super important for traffic engineers, because it shows us how fast people are actually driving. To get the 85th percentile speed, take the speed of 100 cars, and pick the 85th slowest (15th fastest, in other words). This speed is the key ingredient when finding red and yellow intervals at signals, the size and spacing of signs, and deciding whether or not an intersection needs a left turn lane.
Looking at variations in 85th percentile speed can tell you a lot about a road. If the shoulder narrows or there’s a leprechaun crossing, people will drive slower. Narrowing the travel lane, putting poles and trees near the edge of the road, and putting subtle curves in the road will drop the 85th percentile speed even more. Putting up a speed limit sign? Well, about that…
The third kind of speed, and the least useful to us, is the Posted Speed. I hope for your own sake you’re familiar with these black-and-white signs. By the way, the yellow ones you see posted at ramps and sharp curves aren’t speed limits; they’re advisory speeds. They’re not regulatory signs (the color is a big hint) and carry no statutory backing. That doesn’t mean you can’t get nailed for going 90 down an offramp, though; you’re still expected to go a safe and reasonable speed. Speed limits are used to set signal progression in a coordinated system. Drivers traveling at the limit should get a string of green lights.
So, how do these three speeds interact? In theory, all three should be equal. The speed people drive on a road should reflect its design speed, with a few people driving faster (hopefully not in the design vehicle) and most driving a bit slower. The speed limit should be in the same neighborhood, since the design speed is safe for almost all drivers, and very few will significantly exceed it.
As a designer, I put up that 45 mph speed limit, keeping the road safe for all. The next week, the mayor gets an angry call from an elderly citizen complaining about “those damn speed demons endangering my street!” The next day, the speed limit gets bumped down to 20 mph.
“That’s nice!” you may say. “Lower speeds mean safer roads! I learned that in driver’s ed!” Well, buddy, you’ll never be a traffic engineer with that attitude. High-speed roads (85th percentile speed over 45 mph) carry the vast majority of our traffic, but they have fewer accidents overall than low-speed roads. Yes, high-speed accidents are more dangerous than low-speed ones, but the accidents themselves are fewer. What’s really dangerous is the speed differential. When one car is driving the speed limit, 20 mph, and the guy behind him doesn’t notice the sign and drives the design speed, 45 mph, there’s a 25 mph speed differential and a big potential for accidents. If everyone drives between 40 and 50 mph, the potential is much lower.
We try to keep speed limits close to the design speed for a reason. If motorists are allowed to drive at what they feel is a safe speed, they’re more at ease and tend to group around the 85th percentile speed. With our artificially low speed limits, however, the 85th percentile speed is generally 10 mph greater than the speed limit; that difference sometimes reaches 20 mph on low-volume roads. The result is that a majority of drivers are breaking the law. Those that choose to obey the limit increase the risk of accidents.
Note that I’m not encouraging you to break the law. You’d have a tough time finding a judge who understands that you were doing 95 on the Parkway because it’s a safe speed for your car. The next time you see a speed limit, though, you’ll understand what it means and who decides it (the same drunk old lady driving the design vehicle.)