A Junction Efficiency Metric: Vehicles Per Square Meter Per Minute
Article Table of Contents
- Introduction
- How To Calculate Vehicles per Square Meter per Minute
- First, determine the size of the junction
- animation of what 3x efficiency could look
- Different ways the efficiency could be expressed
- An audacious goal
- Additional Reading
- Footnotes
still sorta drafty, but also its entirely possible the point is easily apprehended, and I’m way over-explaining
Introduction #
Elsewhere, I’ve been referring to a ‘vehicles per square meter per minute’ calculation, when talking about junctions on mobility networks. The first place was this substack piece, A Pattern of Repair: The Traffic Bean, then more recently this traffic bean concept applied specifically to 17th & Monaco piece.
I’ve noticed wishing for better ways to calculate some of the stunning differences in efficiency of certain road junctions.
I’ve put this together partially by cutting the relevant pieces of other posts, and aggregating it here.
In some circles, it’s necessary or helpful to be able to put on a very engineering-coded hat. Remove all other components of a conversation, and make some possibly judgy comparisons between things.
If one was doing that, one could imagine a metric for evaluating junction efficiency, for comparing different junctions, or junction designs against each other and themselves.
It allows someone to say something like:
configuration A gave 1 vehicle per 20 square meters per minute throughput. Configuration B gave 3 vehicles per 20 square meters per minute, and was preferable in many other ways, so we’re going with configuration B.
or:
the current junction moves .5 vehicles per 10 square meters per minute
It allows two different junctions, of different sizes, to be compared. If one junction moves 30 cars per minute, and a different design moves 45 cars per minute, which one is better? If the 2nd junction is twice the square meters of the first one, it’s less efficient per square meter, even though it moves more vehicles.
How To Calculate Vehicles per Square Meter per Minute #
every junction moves vehicles, and can move a certain number of vehicles through it, in a certain time, and that junction has a certain shape/area.
First, determine the size of the junction #
I think this is the easy part. Crack open Google Earth, and draw boxes around junctions. I’ve got a bunch of examples of other junctions here:
https://zoningverydifferentthanours.substack.com/p/traffic-congestion-as-solvable-part-510
There’s a few different ways a junction could be shaped. Everything is full of tradeoffs!
Consider reading that piece (or the entire series) as context for this junction efficiency metric.
It lets one say:
such-and-such junction is 290 square feet/26 sq meters, and such-and-such number of cars moved through it in five minutes. (3-5 minutes is probably the minimum time you’d want to do counts on a junction to get a per-minute time. One probably doesn’t need to count for a full hour to get an accurate time)
If a junction was 600 square meters, and in a 5 minute time at rough hour counted it as moving 150 cars, we could calculate it’s ‘vehicles per square meter per minute’ value. in this case, it would be:
v/m²/min =
150 vehicles / 600 sq meters × 5 minutes =
150 / 3000 = 0.05
thus, it could be expressed as:
.05 vehicles per sq meter per minute
or could be expressed in square meters per minute per vehicle:
1 vehicle per 20 m² per minute
Who knows yet what the actual values are we might see for a junction.
The expression seems reasonable enough, aids in reasoning about different junctions or plans. I think it might make more intuitive sense once we start looking at certain junctions.
Calculating vehicles per square meter per minute of the 17th & Monaco junction #
What do you think the value might be for the junction in question, in terms of vehicles per square meter per minute?
How many square meters do you think the junction is?
These are the two questions I posed in the above drone video. Without actually doing the counts or looking yet at google earth, my predictions are:
the junction size is probably about 40 meters in both directions/on two sides, which is 1600 square meters
as far as throughput:
The vehicles in 5 minutes is probably ~150.
Thus, 150 vehicles / 1600 square meters / 5 minutes would be how many vehicles per square meter per minute?
≈ 0.01875 vehicles per square meter per minute
gonna round that to .02, which is two percent of a vehicle per square meter per minute!
Or flipped:
1 vehicle per ~53.3 m² per minute
rounding it to 1 vehicle per 54 square meters per minute. Or 1 vehicle per 580 square feet per minute
I contend that 1 vehicle per square meter per minute (1 vehicle per 10 square feet per minute) is a better reasonable expectation for an efficient, performant junction. I’ll accept getting half-way there as a mid-point. :)
this 1 of a vehicle per square meter per minute goal would be like two orders of magnitude higher than it currently is. that’s a ludicrous improvement, i say impossible in the USA, but i’ll settle for half of that improvement. 1 half of a vehicle per square meter per minute, or 1 vehicle per two square meters per minute. This is, I think, realistic. A typical sedan is 90 square feet. 1 square meter is 11 feet. so, a normal vehicle is about 10 square meters. or 10% per square meter per minute.
This isn’t the first intersection I’ve done this evaluation for, I’m developing an ability to estimate, the last time I did the math on Colfax & Franklin, the final figure was atrocious. Like 2% of a vehicle per meter per minute. :(
I’m going to watch the video again and count the total vehicles for a five minute period.
The video is running at a 3x timelapse, in a continuous fashion, so every vehicle can be counted. It was taken at the peak of a morning rush hour. On my scooter I’m unimpeded by traffic, so it’s effortless for me to pop out to somewhere, even when traffic is maxed out.
five minutes is 300 seconds, and since the video is a 3x time lapse, that means I’m going to count the total number of vehicles that pass through the marked polygon in 100 ‘video seconds’:
Before we start counting, lets determine exactly how large the junction is:
Lets see the square foot value for both of those polygons. We’ll do the math all the way through for both, of course.
Above is the view of this junction in google earth. Next I’ll use the measuring tool to open a polygon drawing menu. The image below is what this looks like:
So the ‘larger’ polygon is 1691 square meters.
Lets look at the smaller option:
Simple enough, the smaller polygon is 1230 square meters.
I’ll pause here for now, but the next step will be to measure the vehicles entering that shape.
I’ll use the video I mentioned before, starting from when the intersection comes into view at the 15 second mark and continuing to the 115 second/1:55 mark, which is an equivalent of 5 minutes of real-time car counting.
How I do the counts #
Feel free to check my math or methodology.
I’m sorta counting by light cycle. Pausing and replaying sections as needed, counting all the vehicles in that particular part of the light cycle.
- 13 cars in initial light cycle, as the junction pans into view
- 38 cars on the southbound leg
- 9 cars on the northbound leg, ‘second blob’ after the start of the counting.
- 11 more on the next cycle going east
- 9 vehicles on the westbound cycle
- 13 more vehicles on the east-bound cycle, some turning south on monaco, some going west on 17th, some ending up north-bound monaco.
I’m at the 59 second mark on the video, that’s about half-way through the five clock minute sample. We’ve got 93 cars that I’ve counted going through the intersection at this point. I’m absolutely going to count twice.
I’ve also paused to serve myself some food. Dinner’s ready. […]
- 32 more cars on the next southbound monaco light cycle
- 14 cars on the same northbound monaco light cycle (approx 59 seconds to 1:23 in the video)
- 9 more cars on the westbound cycle
- 8 cars on the matching eastbound cycle
ooh, the video pans away for a few seconds, so need to pause the vehicle counting
pans back into sight at 1:39, there was 5 seconds of missed light cycle time (15 real-time seconds. I’ll extend the ‘end point’ that we time to by 5 seconds. We’re now going to the two minute mark)
- 27 cars in the south bound monaco cycle, that’s visible
- 11 cars north bound
almost at time
- 2 more eastbound 17th
- 7 more westbound.
We’re at time, lets count it up:
110 more vehicles, in this second half of counting.
There was 93 in the first half, so 203 vehicles passed through this junction in that five minute time span. “about 203” is true, might be 195, could I have over-counted? Or 208, maybe I under-counted. And maybe under some certain situations, like a bit more traffic from one direction, more cars would have gone through the junction because there WAS some time it was green and no one was using it.
oh, what a sidebar, the amount of time a junction direction is usable but empty, or the time there are people waiting to use the junction, AND the junction is completely empty, as a percentage of the time it’s in operation.
The junction was completely empty while there were vehicles waiting to enter 28% of the time
or something like that.
So, like we’re discussing, how many vehicles in 5 minutes? 203 vehicles in five minutes
Let’s plug these values into the formula:
203 vehicles | 5 minutes | 1690 square meters
0.0240 vehicles per square meter per minute
Or flipped:
1 vehicle per 41 m² per minute
41 square meters is about the size of:
- A small studio apartment (6.4 m x 6.4 m)
- Half of a tennis court
- A single parking space (with buffer) plus some sidewalk
Half of a tennis court to move a single vehicle in a minute? Seems ‘obviously inefficient’ to me.
The way to make it more efficient, at first pass, would be to simply find a smaller area for the junctino. A square piece of asphalt controlled by lights does the job, sort of, but so too would a much smaller, circular junction with access/departure points for all directions of travel as needed.
earlier I said, I contend that 1 vehicle per square meter per minute is a reasonable accomplishment. How might we get closer? The first pass would be to improve the number of vehicles that can use the junction, in a few ways, and reduce by a significant percentage the amount of space directly allocated to the junction.
If we could get 30% more vehicles through it, and it was half the size, we’d have accomplished technically a stunning increase in efficiency.
A first pass would be to reduce the junction size. Ironically, to reduce the size (and allow the continuous flow type design) would probably also increase the number of vehicles that can fit through the junction, but the number doesn’t have to budge for this to still be a gain in efficiency. If the junction was smaller, and the volume of vehicles stayed the same, the efficiency would obviously go up, relative to the reduction in junction size.
For instance, compare the following:
203 vehicles | 5 minutes | 1690 square meters
203 vehicles | 5 minutes | 550 square meters
203 / 5 * 1690? 203 / 5 * 550
203 / 8450 = 0.024 203 / 2750 = 0.054
40.6 vehicles/minute 1690 sq meters = 0.02 vehicles per square meter per minute 40.6 vehicles/minute 550 sq meters = 0.072 vehicles per square meter per minute
That second value would be 3x the efficiency: 0.23704142
animation of what 3x efficiency could look #
3x the efficiency could be achieved purely by making the junction much smaller - 500 square meters vs 1600 square meters.
Here’s a way this could be visualized. Do you see a the way that this exhibits better efficiency? This is only one possible way the difference can be viewed, obviously. This isn’t how junctions work exactly, but it perfectly shows one of the dimensions of efficiency improvements.
Intersection Efficiency Comparison #
If you had limited space and needed junctions in three different places, and nothing else about the space could be used for anything BUT moving these vehicles, which would you want more of?
Both intersections process 203 vehicles in 5 minutes
My desire with the traffic bean isn’t even necessarily to move more cars through - it’s to reduce certain forms of pollution, difficulty, distress, waste, excesses.
I think of the potential harm to everyone of a crashing car as a form of pollution.
Conversation with the people who live in that house indicate that everyone has become extremely aware of all sounds/implications of passing vehicles.
One notes intrusive thoughts when one hears the sound of a whining, high-speed engine, wondering if it’ll take the turn or crash into a building. click here to read about how this plan handles the wide range of potential inbound speeds
Different ways the efficiency could be expressed #
≈ 0.081 vehicles per square meter per minute
Or flipped:
1 vehicle per ~12 m² per minute
Part of the reason the traffic bean would be so much more effective than a light-controlled junction is there is no need for the junction to ever be completely empty, while there is anyone queued up to use it.
So, a traffic bean allows anyone to go if there is room for them to proceed, no waiting around for a light to change.
The space needed would be JUST a single lane in a large enough circle/bean shape to wrap around the center island, which would be be ‘hollow’, the inner space being returned to non-car uses.
It being hollow like this would allow the junction size to be considered even smaller. Instead of a fully enclosed volume of space being allocated to the junction, JUST a unified connecting travel path the width of a medium-sized car lane running in a circle.
The inside and outside would be unavailable to cars, so the junction square footage could be so much smaller.
There’s some image mock-ups below.
I’m thinking lots of space could be carved out, on the inside and outside of the ‘bean’ thing, which is how I’m getting to such a low square meter value:
260 vehicles
5 minutes
400 square meters
An audacious goal #
Lets see if a workable junction of that size could be achieved. Can we replace this 1600 sq meter junction with a 400 sq meter junction that moves even more cars per minute?
If so, it would give us:
0.13 vehicles per square meter per minute
Or flipped:
1 vehicle per ~7.7 m² per minute
Which might be good enough for now. That gets us the 10x improvement I want.
It’s such a ludicrous improvement, that even if it came with zero other benefits, it would be worth trying, but in reality this traffic bean thing comes with TONS of other benefits.
An order-of-magnitude-improvement on efficiency, larger potential throughput, and reductions in all forms of emissions (noise, tailpipe, tire rubber microplastic, brake dust). (this is the result of the slow, non-rushed procession of vehicles through the junction, please refer to the poynton videos I have elsewhere on the page)
Achieving a 400 square meter junction #
to get this junction, we’d want something bean shaped, with the inner shape hollowed out, like a doughnut. This frees up lots of square meters.
The following shape is 147 sq meters:
So, this inside space can be subtracted from the outer space. Lets jot down a shape that could work for the outside.
It needs to be only a single lane wide, with entry/exit points wherever needed.
How would you feel about this shape? its 360 sq meters, which of course includes the 147 sq meters we’re gonna count as ‘for the people’ and not as space for cars:
its 360 sq meters.
so, less the inner area that doesn’t need to be counted,
360 sq meters (outside shape) - 147 square meters (inside shape) = 213 square meters
I had proposed that this junction could be 400 square meters, and we’ve used only a little more than half. I don’t think it will take 200 square meters to provide the access points for vehicles. the main shape could be clear now, I think, thus ‘the vibe of what I speak’.
Lots of the remaining space would need to be ‘shaped down’ with traffic cones, until the right shape was found. Here’s a very crude example:
The red inner lines are 11 feet long, which is certainly not a wide lane, but isn’t super narrow, either. The dimensions here are pretty comfortable, even for commercial vehicles, I think. A normal sedan is almost 6 feet wide (and 14 feet long) A cement truck is 9.5 feet wide, including the mirrors, or 8.5 feet not including mirrors.
The above was my super wonky first mockup. Can you see what I’m aiming for, even as it’s obviously not the exact right shape?
The junction has sorta widely-separated inputs and outputs, so this is a sorta extreme example of the paths that would be ‘carved out’ of the existing junction space.
Additional Reading #
- the traffic bean
- my first pass at this calculation, looking at a junction near my house
- “Traffic Congestion” as Solvable, Part 4: Junction Repair: Decrease Dangerous Complexity by Increasing Safe Complexity
- Traffic Congestion as Solvable, Part 3: Intro to Path Shaping