Saturday 4 December 2021

Permission To Cross

Prompted by a question from Leo Murray, I have somewhat fallen down a little bit of a rabbit hole on the relationship between people asking for help to cross the street and how local authorities ration access to crossings.

Leo's (excellent) question was;

"How many pedestrians need to be crossing a main road at a location before a crossing is advised? I’ve been reading the Local Transport Note on pedestrian crossings but it does not give a number."

The question in itself suggests a run-in with a local authority policy which is so old, anyone working there probably doesn't know its origin and thus it has reached groupthink. It is so old, that it has never been recommended as a method throughout my entire postgraduate career (1995 onwards) and I had to go back to relearn it because I was so rusty!

The question alludes to a long defunct way of assessing whether a pedestrian crossing is warranted (bear with me), based on the relationship between traffic flow and pedestrian flow. This is known as the PV² rule and it was developed as a measure of the degree of conflict between people walking and driving to aid decisions on whether controlled crossings should be provided.

The technique requires continuous surveys to be undertaken with pedestrian and traffic flows. Pedestrian crossing flows are taken within 50 metres of either side of the proposed crossing site (which should try and pick an "average" crossing position if it is not clear) and both traffic and pedestrian flows in both directions added. The counts of pedestrians within 50 metres assumes that a crossing will see people within 50 metres migrating to it. 

Taking the pedestrian flow, P and multiplying it by the square of the vehicle flow, V, gives PV², which will be a large number and is expressed as 10(dividing the PV² value by 100,000,000 - 8 zeroes).

The PV² thresholds shown graphically

Where PV² is less that 1x108, then a crossing isn't warranted, where PV² is between 1x108 and 2x108, then a controlled crossing should be considered. Where PV² is more than 2x108, then we're looking at split controlled crossings. If we are considering a dual carriageway, then we would have to look at each carriageway separately, although that's going to make things even more complicated. 

The graph I have reproduced above comes from "Re-Examination of PV² Criteria for Developing Pedestrian Crossing Warrants", by Jain and Rastogi, 2016. It shows the type of crossings to be considered with the two thresholds, but with some nuances to pinpoint where zebra crossings might be appropriate which is essentially high levels of pedestrians and medium volumes of vehicles.

Interestingly, this graph is referenced in a few documents (mainly local authorities and reviews being done for them), giving a 1987 reference which I believe to be TA52/87 "Design Considerations for Pelican and Zebra Crossings". However, the graph actually combines two graphs in an older document, TA10/80, also titled "Design Considerations for Pelican and Zebra Crossings", below (apologies for the quality).

It's a bit tricky to understand all of this, so let's have some worked examples.

In the table above, I have shows hourly traffic and pedestrian flows for a 12-hour period. I have then found the four highest PV² values and taken their average in the penultimate line at the bottom of the table. Just below that, I have divided by 1x108, (100,000,000) to give the assessment score. In this example, we have 0.05x108 which means the site doesn't qualify for a crossing. You'll have to trust me, but the traffic flows (based on an urban area) are fairly modest and the pedestrian flows quite low. Let's run another example.

I have done the same again with different flows and this gives an assessment score of 1.41x108 which means we should be considering a controlled crossing as we are between the two thresholds and from the graph, probably a pelican (pedex now). In this example, we've a busier road with distinct peaks which could be a fairly busy distributor road and maybe even an urban A-road. We've also quite a lot more people crossing. Let's look at another.

This time, we have an assessment score of over score of 2x108 which means we should be looking at a split crossing, probably a pelican (pedex now). This is definitely an urban A-road, but it's far busier for more of the day than the previous example and we've more people crossing. One issue with the graph is that notwithstanding the score, you need at least 50 to 60 people crossing to hit the lines.

I want to show you two more tables. In the table below, I have taken the lowest traffic flows of the the three examples above and the highest pedestrian flow. The assessment score suggests no crossing is needed on the basis there is little crossing conflict with traffic.

The final table below does the opposite. Here we have the busiest road and lowest number of people crossing. Again, the assessment score suggests that no crossing is needed.

I wonder if you have worked out the pattern here yet? Let's work backwards. Given that very roughly speaking 2,000 vehicles per hour at peak is the upper threshold of an urban A-road (maybe a touch higher or lower, depending on the site), then we can reverse the PV² calculation to see how many pedestrians we need crossing to hit that 1x108 lower threshold. So, 100,000,000 divided by 2,000, divided by 2,000 again gives us 25 pedestrians crossing to hit the threshold, although 25 pedestrians doesn't really hit the curve on the graph either.

People crossing a dual carriageway on the desire line.
The lower PV² threshold won't be reached here.

If we are surveying a site with very high traffic flows, but few people crossing, does this take into account that the very reason so few people are crossing is because there is so much traffic? It has taken me a while to work through to this point, but this is one of the fundamental flaws with PV² because it immediately ignores suppressed demand and it requires a sweet spot of traffic flow and pedestrians. 

If you go back to the tables, lower flows of pedestrians or traffic skew the result. In other words, a quieter road means people don't need help crossing or a busy road can mean stopping drivers to let a few people an hour cross isn't warranted. It's a system of rationing the opportunity to cross based on current conditions and the numbers of people currently willing to cross. TA10/80 suggests that PV² is fine for most situations, but sometimes there are special cases;
  • Where a road divides a substantial community.
  • Adjacent to community centres and homes for the elderly, infirm or blind [this is the language as used in the document].
  • Adjacent to hospitals or clinics.
  • Busy shopping areas.
  • Outside school entrances.
  • Where the number of heavy vehicles exceeds 300 per hour during the 4 busy hours.
TA52/87 also adds bus lanes, intermittent pedestrian flows (e.g. railway stations) and "other local considerations".

Let's go back to the history lesson. At the start, I mentioned 1995. As well as it being the year I graduated, it was the year that two Local Transport Notes were published - LTN1/95 The Assessment of Pedestrian Crossings and LTN2/95 The Design of Pedestrian Crossings. The former superseded TA52/87 and the whole concept of PV² was withdrawn from official advice. LTN1/95 uses a much more detailed framework approach based on the local conditions (the special cases in the earlier documents) and the users who are crossing and who might wish to cross and so is therefore a subjective, but structured approach. Plus of course, traffic volumes (and driver speed) and pedestrian flows are useful pieces of data which can help inform a design strategy.

LTN1/95 continued to be the official guidance until 2019 when it was incorporated (along with LTN 2/95) into Chapter 6 of the Traffic Signs Manual. LTN 1/95 and 2/95 were then withdrawn. Unfortunately, Chapter 6 doesn't include the full detail of LTN1/95, including a proposed crossing assessment record sheet, although nothing stops practitioners using it or something similar.

So, since at least 1980 we have moved from a pseudoscientific method of assessment through to a structured assessment process to a perhaps simplified assessment process. Why does PV² matter then? Well, go and search the term "PV2 crossing" with your favourite search engine and wonder at just how many local authorities are still using it to assess requests for new crossings - it's startling.

Some local authorities use a modified version where they might add a weighting because of local conditions or lower the threshold. In many cases, the local authority talk about LTN1/95 (even in very recent policy documents) and then continue to use PV² as if a couple of decades of it being withdrawn don't matter. Some won't look at anything unless it meets the PV² criteria, despite the early guidance actually setting out special cases.

PV² isn't just old fashioned, it is discriminatory. If the site being assessed doesn't have dropped kerbs, then it's going to be hard to count people using mobility scooters or wheelchairs who cannot cross there now. It ignores older people who need more time to cross and who cannot judge vehicle speed very well, it also ignores visually-impaired people who tend to prefer controlled crossings, people travelling with children who will move more slowly, older children (who still cannot judge vehicle speed) and all those who aren't crossing because it's intimidating. Like much in traffic engineering, we end up counting those who turn up and they are either the fit and the brave or those who really don't have much of a choice and brave it anyway.

Using PV² in today is very much a system of rationing and even where used with weighting and structured assessments, it is a way for local authority staff to weed out requests and indeed to put people off from requesting crossings in the first place. I am not really blaming the staff because resources are tight and things have to be prioritised. Of course, there might be an officer who doesn't want to hold up drivers for which PV² is a handy tool and there are still dinosaurs out there. In the main it's a system of triage designed to protect councillors who make resource decisions, rather than actually admitting that people need help to cross the road at a particular site.

Pushchair crossing a dropped kerb with tactile paving.

If you help one group to cross the road, you
make it easier for everyone to cross.

One thing we should also consider. Pedestrian crossings are (like many features of the street) driver infrastructure and so if we remove (or significantly reduce) the source of danger for people on foot (i.e. traffic), then we don't need formal crossings and limited resources can be targeted at main roads where people very much do need help crossing. This is another piece of traffic engineering lore which has its roots in the 1980s and yet persists into the 2020s.

One thing I haven't found yet and that is where PV² actually came from in the first place. Jain and Rastogi's paper suggest the thresholds "were formulated using empirical data based on peak flows of 1980s", but that assertion is not referenced and in any case, neither TA10/80 or TA52/87 give any hints. TA10/80 replaces in part Departmental Circular Roads 19/74 which might have shed some light (but I have not tracked this down as yet), although it does pop up in Hansard.

My bet would be that this goes back to a time where UK traffic engineering started to import ideas from the USA. In the web based Manual on Uniform Traffic Control Devices (MUTCD), the "pedestrian four-hour volume" is used to justify a signalised crossing. Here, less than 107 pedestrians per hour doesn't warrant a crossing. It's not PV² of course, but it does rather seem to ignore the fact that people might not be willing or able to cross now.

This post has been fascinating to to research, although in truth, I may have been able to dig deeper if I had time to do more than internet research (but hey, I have a day job). If you think I have got something wrong (yes, maybe my maths) or if you have any other insight, I'd love to hear from you. I should thank Simon Hartshorne of National Highways for providing me with copies of TA10/10, TA52/87 and some other background documents which have helped me piece together 40 years of history.


  1. Hi Mark. Thank you for this. I have only scratched the surface but learnt a lot already. Cheers, Also a Mark.

  2. Fascinating reading and i'm constantly shocked how we remove the human element and rely on dated data ideas regarding safety. If you look at it from a different perspective is it really solely about cost saving and traffic flows, therefore stick with the dated method which protects these two elements. We need drastic changes in planning policy.