A math question for the traffic engineers.

Factual Questions
1

Are there formulas that you all use to determine how wide a highway has to be? For example, do you say, well, we have X number of cars that travel this section of the road during morning rush hour, and when the density of cars reaches Y per lane, then everyone slows down to Q, so if we had one more lane, then everyone could drive at 1.4Q.

Maybe that just makes sense in my head, but what prompted it was driving home the other night, leaving a narrow 3 lane highway to get on an 8 lane highway. I understand why the 3 lane highway is 3 lanes (lack of foresight in the early 1900s), but why is that particular stretch of the other highway 8 lanes?

Any light you can shed on this would be swell.

2

Just the opposite - an abundance of foresight. There are also models for population growth, and perhaps speed limit growth (as cars get safer, they can let us drive faster) so perhaps now, with more foresight and mathematical ability, we can figure out not only how many lanes we need, but how many we will need 50 years from now.

[/WAG]

3

I think you are operating with some misconceptions. Extra lanes don’t equal higher speed, they tend to increase capacity, but that increased capacity in congested areas sometimes leads to lower speeds.

What increasing capacity of a road does is draws traffic away from other routes, and if appilcable from mass transit. Basically if you build it they will come.

Note major roads with HOV lanes during rush hours. Typically the main road is jammed while the HOV lane goes along pretty nicely. If there is some reason the HOV rule breaks down and everyone can enter it, you will quickly find all lanes including the former HOV lane now jammed. The rate that the former HOV lane jams is mainly a factor of lane switching to it.

If you are able to build enough lanes to overcome the tendancy of more lanes draw people to that road, you do have the issue of growth along this underused route, but that will take some time.

4

I’d have thought that all sorts of other variables would make a simple formula pretty much useless. Anything from the number of slower-moving vehicles on the road to driving styles in the locality (speeds, lane usage, average distances between cars) will all have a large effect on the real-world capacity of a road.

And as for why any one particular stretch of road is built with X lanes, add in the funding available, land used, and all related politics. (One hearsay example: I’ve heard a claim that Britain’s motorway network suffered from too many too-narrow roads being built in the boom of the 1960s/70s, because politicians liked to take the credit for building so-many hundreds of miles of new road, and more distance could be built of 2-lane highways than 3-lane ones with the same cash.)

5

Well, I’m a mechanical engineer rather than civil, but yes, there is certainly math in deciding how many lanes. Hard to see it when you’re driving though, especially out here in the Seattle area.

2000 passenger cars/hr is what one lane of freeway is worth, at max capacity. Try to push more cars through than that, and the road basically locks up. At that capacity level, everyone is going about 30-40 mph.

If you want everyone to drive 60+, 1400 cars/hr is the max for one lane, each extra lane is 1000 more cars per hour.

This is summary from my dusty civil engineering handbook (Perry et al, 1976), I’m sure if we have any currently employed highway designers they’ll have better info.

The book I have has expressions that attempt to account for the percentage of trucks to cars and intersection operating loads as well - there’s something here call a “load factor” which is how many green signals are “fully utilized”, and some consideration of how sight distances influence the flow of traffic as well. Adding to the fun are right and left turn percentages, number of buses, and a “location factor” which addresses people pulling off the road between intersections (residential vs business district).

Apparently there are five levels of intersection usage, once you start using more than 85% of each green for cars, it’s considered to be above capacity and “jammed” is the final level with flow of traffic ultimately controlled by downstream conditions. Seems accurate, I’ve seen this effect on my morning commute quite often. Once there appears an unbroken line of cars are packed with two stoplights, the difference in timing between the lights and the distance between them determines how many cars can flow; and quite often the signal will be green, but no one can go since the “wave” from the intersection ahead hasn’t caught up yet.

Anyway, the city street lane is worth about 700 cars per “hour of green” for peak capacity. Since any practical street can’t be 100% green, real capacity is probably about half that. Seems like a good estimate, although I’ll admit that I may not be reading the charts correctly.

Hopefully a civil guy can chime in with more…

6

The obligatory IANATE. That said you have undoubtably seen the black tubes across roads here and there, sometimes two, one across the second to the center line. These connect into a box near the curb and a light pole to get power. They count the cars each way and the time. T.E.s have been in business long enought to develop criteria for the number of lanes needed to accomodate the traffic density by time of day, day of the week, time of year etc. Speed limits may also have some bearing on the final decisions.

7

There’s a “Highway Capacity Manual” and other esoteric software programs described at

http://www.akcelik.com.au/HCM.htm

Highway traffic flow is classed in 6 ranges or levels of service (LOS), A thru F with A being free flow and F being lockup.

Studies are done to determine the volume to capacity ratio (v/c) and origins and destinations based on tripmaking reported in o/d surveys of several types and travel demand forecasting. The results of the studies are plugged into the transport planning/budgeting/political process which decides when to widen a road or to provide transit alternatives.

I was interviewed once in the Boston area and had to report every trip and its mode of travel that I had made the day before. This was done for x percent of the households and is combined, or used to be, with roadside interviews. These can include questions for each vehicle driver/transit rider, "Where did you start theis trip? Where will you end it? For what purpose? (work, shopping, to home, recreation, etc.) The responses are plugged into a math model and it spits out the answers. That’s how it was explained to me quite a while ago.

I knew someone who actually inventoried every 6th residence in the Portland, Maine, area and then supervised interviewers who went door-to-every-6th-door asking “where did you go yesterday?”, etc. The extension of I-295(?) was then put in the location to serve best the most folks. Improvements to local roads and intersections were also made based on the results of the survey.

It’s apparently a growth industry.