## PCU factors – are they just pseudoscience ?

Road traffic is made up of a great variety of different types of vehicles – from large articulated lorries and busses, to minicars and bicycles. The different vehicle types have different characteristics – length, or typical speed, or rate of acceleration, and so they also have a different impact on road capacity etc. Here, capacity is not just “vehicles per hour” but “the number per hour each of “articulated lorries, busses, minicars, bicycles etc.

Rather than trying to deal with so many vehicle types engineers came up with the idea of passenger car units (PCUs – sometimes also known as passenger car equivalents) – where the effect of a vehicle type on the road is expressed as so many times that which a typical passenger car would have. These pcu factors are widely used across the world, in a large number of different types of traffic analysis.

However, there are some problems with the concept of PCUs.

1.  Methods of estimating pcu’s

There are several different ways which people can use to estimate values for pcu’s. A read through references (2006, 2019, 2023, 2024) gives the following list (of 16 values):

• multiple regression analysis
• homogenization coefficient
• semi-empirical method
• Walker’s method
• multiple linear regression method
• simulation method
• density method
• micro-simulation
• platoon formation methods
• speed based methods
• methods based on delay
• density methods
• travel time methods
• vehicle hours methods

Since these methods are measuring different things (delay, or headway, or density) then it seems fair to suppose that the pcu values that they produce are different things (delay-based pcu’s, density-based pcu’s and so on).

1. PCU’s are not stable values

Another search through some literature on pcu’s shows that pcu values vary with many features, such as those in the list (of 17 items) below:

• vehicle mix, driver characteristics and intersection geometry (see e.g. ref. 2019)
• difference between homogeneous traffic (strict lane discipline) and heterogeneous traffic (very loose lane discipline) (ref. 2023)
• volume to capacity ratio (e.g. ref. 2021)
• the width of the road (ref. 2021)
• traffic composition (ref. 2023)
• traffic volume (ref.2024)
• magnitude and length of gradient (ref. 2024 and ref. 2025)
• position of large vehicles in the traffic queue (ref. 2026)
• lane width (ref. 2027)
• length of passenger cars (ref. 2015)
• type of weaving section (ref. 2007)

And (from ref. 2008)

• vehicle characteristics (such as length, width, power)
• stream characteristics (e.g. mean speed, flow conditions, longitudinal gap distribution)
• roadway characteristics (horizontal alignment, location, sight distance, pavement surface etc)
• environmental characteristics (e.g. terrain type)
• climate conditions (fog, mist, wet, dry etc)
• control conditions (e.g. posted speed limit)

Comment

If engineers cannot agree on a consistent method of measuring them then we already have a problem. When engineers then go on to say that pcu values can change with at least 17 different variables then the whole exercise begins to look like nonsense. In fact this variation (or rather, uncertainty about the correct value of a pcu) is covered in definitions such as:

“Passenger-car equivalent – The number of passenger cars displaced by a single heavy vehicle of a particular type under specified roadway, traffic, and control conditions” (Ref. 961)

This definition, and the other listed variables, suggests that when a standard does quote values for pcu’s, the values should be accompanied by a warning note on the lines of:

“These pcu values are only headway based pcu values, and can only be applied where the study uses headway based pcu values and the same background conditions – that is, the same traffic flow and composition, the same position of large vehicles in the traffic queue, the same type of driver characteristics, road section and terrain, and the same conditions of dry, sunny weather and good visibility”.

Some people have tried to work around the difficulties by suggesting alternative approaches, such as treating pcu’s as a dynamic quantity rather than a constant (ref. 2021, 2024, 2025, 2008), or using “passenger car space equivalents” PCSE which “accounts only for the relative space occupied by a vehicle on the road” (ref 856), or even using vehicles and truck percentages (see e.g. ref. 2007).

As long ago as 1974 people were expressing concern about the use of pcu’s. For example Hobbs (ref. 167) was saying that

“(The use of pcu’s) must however be treated with considerable reserve. The effect of a heavy vehicle in a stream in equivalent car units may vary between 1.0 to 7.0, or more on heavy gradients, so that the arbitrary selection of a figure like 3 will not apply in all cases. Further, in using such an equivalent volume for design purposes it must be expanded to anticipate future requirements. If it is expanded by, say, 150%, over-design may well result when it is seen that the rate of growth of heavy vehicles is very much lower than that for cars and motor cycles. The use of equivalent passenger car units can prove helpful for a broad comparison of the importance of different routes, but it must be used warily and preferably not for design purposes.” (own emphasis)

Wikipedia (here) says that pseudoscience is “a claim, belief or practice which is falsely presented as scientific, but does not adhere to a valid scientific method, cannot be reliably tested, or otherwise lacks scientific status”. It seems to me that the present concept of pcu’s comes a little too close to meeting this definition.

After-thought

Table 1 above gives pcu values of 1.0 for a car and 2.0 for busses. If we accept these values as applying to traffic through a junction, then we might be saying that moving one piece of iron through a junction has a value of 1.0 on capacity, and moving a bigger piece of iron through the junction has a value of 2.0 – approximately implying that busses have twice the damaging effects on capacity as a passenger car.

But what roads and traffic are really about is the movement of people (and goods) and not the movement of pieces of iron. So the basic concept of pcu’s may be wrong. If we look at the movement of people, then maybe we should be more interested in the productivity of different vehicle types rather than the impedance (pcu values) of vehicle types. In this case, a bus might take twice as long as a car to move through a junction (conventional pcu’s). But since busses carry more people, the productivity of a bus through the junction could be several times better than that of a car.

The table show productivity for passenger carrying vehicles, where productivity = number of passengers / pcu factor

References

167 – UK, Hobbs, Hobbs- Traffic planning and engineering; Pergammon Press, 1974

294 – Tanzania, Road Geometric Design Manual (2011 ed); Ministry of Works

856 – Robinson and Thagesen, Road engineering for development, 2nd ed. SPON 2004

961 – USA, Highway capacity manual 2000, TRB

2006 – India, Metkari et al “Review of Passenger Car Equivalence Studies in Indian context”, IJCA 2006

2007 – Netherlands, Vermijs “New Dutch capacity standards for freeway weaving sections based on micro simulation” ; 1998

2008 – Malaysia, Anand et al “Development of pcu values for Malaysia”, Joumal of the Eastern Asia Society for Transportation Studies, 1999

2019 – Ghana, Adams et al “Passenger Car Unit Values for Urban Mixed Traffic Flow at Signalised Intersections on Two Lane Dual Carriageways in the Tamale Metropolis, Ghana; International Refereed Journal of Engineering and Science (IRJES) 2014

2021 – USA, Brooks, “Influence of roadway width and volume to capacity ratio on pcu values”, Transport Problems vol. 5 issue 2; 2010

2023 – India, Tiwari et al “Passenger Car Units for Heterogeneous Traffic Using a Modified Density Method” Transportation Research Circular E-C018: 4th International Symposium on Highway Capacity

2024 – India, Arkatkar and Arasan “Micro-simulation Study of Vehicular Interactions on Upgrades of Intercity Roads under Heterogeneous Traffic Conditions in India, European Transport \ Trasporti Europe; 2012

2025 – India, Joshi et al “Heterogeneous Traffic Characterisation and Flow Behaviour Modeling for Metropolitan Arterial in India”, Journal of the Eastern Asia Society for Transportation Studies 2011