Log-Lognormality of cargo mass x journey distance and appropriate design

Imagine a single parameter that can characterise any required journey, that makes no presumption about the vehicle required.? I can suggest one - the product of the mass of the cargo required (not including the vehicle) and the journey distance one way.?

Note that what is not accounted for in that is time.? An assumption that we don’t mind if things are a little bit slower.? A parameter also including time could also be envisaged but let’s keep it simple for now.?? That can be one for another day.

So we have a parameter that can be used to describe any journey.?? At one end we might have a child biking to school 1 km away so 30kg x 1km = 30 kg.km.? At the other we might have a large lorry transporting something heavy to the other side of the country, let’s imagine 40 tonnes and 1000km, or 40000000 kg.km.

Let’s call this parameter “cargodistance”. People of course are just one type of cargo in this context.?

We are assuming here for a start, that the journey wants a vehicle of some description, i.e. that we can’t, or don’t want to walk it.? We could also go bigger if we like, with rail and shipping, but let’s stick to road transport for the interim. We are also assuming that it is a single uninterrupted journey, so with human limitations built in, that effectively means within one day. ?

It seems kind of intuitive that the distribution would be roughly lognormal in two dimensions.?? That is to say the distribution of the weight of the cargo is probably something like lognormal – journeys of smaller cargoes (e.g. one or two people with bags) being far more common than bigger ones (heavy truck loads).?? Similarly we could probably imagine the same of distance.? ?Short trips being more common than longer ones.

One of the issues with this parameter “cargodistance” then is that it covers a very large numerical range in both components.? To try and capture it in a single lognormal distribution alone is tricky.? Believe me I tried, and it tends to deliver fairly nonsensical results, however you tweak it, for the minimum, or the mode, or both.? To get anything vaguely sensible, seemed to rely on applying a lognormal distribution to the natural log of this parameter instead.? ?That is just an empirical observation. ?But it makes some sense if we have a product of both distance and mass distributions that are each lognormal.

By achieving a description that is “vaguely sensible”, what I mean by that is trying to honour the minimum as something like a 5-year-old on a bike travelling a short distance to school, or 18kg x 1 km = 18.? Similarly the maximum is probably something like the legal road capacity max of 44 tonnes at 12 hours x 80 km/hr = 44000 x 960 = 42240000.? Also in any fit, trying to frame the mode at the same time so this is something not too far off a work commute. ?

Bearing in mind that we are calculating the cargo mass here, and not including the mass of the vehicle.?? The reason for that is we have our thinking cap on, looking at an issue where the mass of the vehicle appropriate to the cargo is a key part of the thing we are thinking about.? Hence, we don’t want to freeze the current status-quos for that into our parameter.? That would defeat the purpose.

The method of defining that distribution as a first go on my part has been unashamedly arbitrary, and the object is not really to find the actual answer, but a curiousness as to whether some single distribution like this can get reasonably close -i.e. close to reasonably defining this parameter we’ve called cargodistance, and its cousin log-e (cargodistance).? I’m not acting under any pretense that the precise distribution which falls out of this effort accurately describes road transport in the UK.? The interesting thing though is that it’s not too bad, I suspect.?Or at least could be tweaked to be so by those with more knowledge of the topic.

In reality it may be a bit more bimodal for people-carrying and cargo-carrying distributions, but given we have to (or at least habitually do) design roads to do both, it seemed a useful exercise to capture it in one distribution.? If we were ever going to think about designing roads separately for carrying "non-human cargo" and people, that might allow further examination of that question in separated distributions.?

The point of all this though, is to envisage what “cargodistance” we are designing vehicles and infrastructure for when we think about transportation, and in this case road transportation. And if emissions reduction is a key part of that design criterion, what is the optimal suite (read mass distribution), of vehicles that can deliver those cargodistance requirements.?

What we have to immediately realise is that a whole lot of optimisation can be achieved by looking around where the peak of the distribution lies, i.e. the mode, and designing for that – both vehicles and infrastructure.? In our case, at 6.33 for log-e cargodistance, it’s really in that “cargodistance” ballpark of a single adult travelling to a place of work – which is probably where the mode, or most common journey, should be roughly. ?It doesn’t seem too illogical cap’ n, with a Spock hat on.?

Immediately though we also have to realise that that does not mean the other journeys can be neglected.?? They do not cease to be important.?? So we also have to design for the tail ends of the distribution as well.? But where the mode is, gives us a heads-up on where the most optimisation potential for transport lies.? It seems to fall largely in either in the a) one to two adults or b) one person with some cargo (equipment, shopping, work-bag, 1 or two children) and short local journey arena.

This is no revelation or surprise, but the question then becomes - is designing roads ubiquitously and primarily for vehicles the mass of SUV’s or similar the way to address this distribution, if we want to reduce emissions?? No.

At the same time, there has to be infrastructure that can cope with the tails of the distribution too, and still be safe.?? The individuals setting off to see relatives the other side of the country for two weeks, in a vehicle (or vehicles) fit for that purpose, still have to be able to do so. Even if it is just to the nearest rail station.? Another obvious example is when we might want to move home.? We would want the capability for a truck, or several, to come to our home and do that.?

This immediately highlights that we have to design for vehicular access infrastructure at both arterial route and residential access level that can accommodate not just the mode, but to some extent the tails of the distribution.? While there might be a case for separating the heavier and lighter vehicles at arterial route level, we still would like access for both at the residential access level too.

However, and it’s a big however, we hit the lion’s share of need at a residential access level by aiming at the mode of the distribution curve +/- a standard deviation.? A standard deviation is calculated around a mean, sure, but it’s really the mode that is of most interest in this context, and the standard deviation just fits the bill of a convenient range.? Together they capture what is happening most commonly.? ?

The vehicles and infrastructures that optimise emissions and effective transportation for that part of the curve are really where the most gains lie.? At the same time, to stress it again, allowing access for the tail ends of the curves where necessary.?? Perhaps not optimally so, but allowing, nonetheless.? That might be possible by slowing the big more occasional stuff down - through design – speed control measures etc.? The dominant journey activities are then safe and easy, with infrastructure focused on them, but the others are neither precluded.? And in some places, there can be dedicated infrastructures along arterial routes for the heavier stuff.?

The point is, that at the minute, our road traffic design everywhere, seems to be – by accident of history – working to provide the P10 of “cargodistance” an ability to go fast almost everywhere, to the detriment of what the mode of that distribution might do.?

That is not compatible with reducing emissions, or other material demands.? What we want to do is optimise travel for the typical cargodistance figure, aiming at an optimal vehicle type required.? That doesn’t have to always be the stereotypical imagining of bikes or e-bikes.? It can be smaller EV’s, new generations of three-wheelers, and all sorts of imaginative stuff to help cater for as broad a demographic and cargodistance as possible, while still allowing the “outliers” of the distribution to function too.? And again, not calling for the extinction or exclusion of larger vehicles for those other occasional times, when they are required, perhaps increasingly as part of wider community car-sharing/car hire options, but just aiming core design at the right quartile.?

To be clear, this is the kind of design project that takes decades and is easiest in newbuild suburbs. Retrofitting old is never simple.? Never impossible either…

What I am trying to stress here though is that we cannot design one vehicle type that would meet all needs.? That would be absurd.?? Yet it is not absurd to centre our transport design infrastructures around what happens most commonly in terms of cargo and distance – “cargodistance” in a given area.? The less common occurrences are still catered for, but it is a matter of the weighting. ?They might be allocated dedicated infrastructure that is optimal for them with a certain spacing, where enough of them can be collected to justify the cost involved, but where the shorter journey for individuals with a bit of cargo is the dominant requirement, the infrastructure for that can dominate design. ?At least more than it does now. ?Not to the exclusion of all else, but with a shift in focus.

To be clear this is not forcing any individual or organisation to have a particular vehicle.? It is just maximising the “ease and safety of journey” for the optimal-emission vehicle size and character that hits the lion’s share of the cargodistance journey distribution.? The other journeys for other vehicles still happen on infrastructure that remains designed to allow it - they are just no longer the focus of the sentence “making it easiest for …”.?

A focus on design criteria that permit hitting - not the whole distribution for the whole time - but rather the most important parts of the distribution most of the time, while still allowing for the other more occasional needs to occur, even if with compromise (e.g. slower).

Controversial maybe, but it’s been an interesting thought experiment.?

In the figures below, for the numbers’ nerds like me, I capture a crystal ball experiment (a piece of kit for playing with probabilistic distributions and their combination).??

The table shows an example calculation of the described parameter “cargodistance” for a suite of scenarios and its natural log.? Emphasis being again, on the cargo mass, not the mass of the vehicle plus cargo.? From this we get a sense of what the range of this parameter “cargodistance” and its natural log equivalent is.?

By allocating certain scenarios a certain percentile value, we can come up with a distribution of the character also shown in the four accompanying boxes.? The reason for the input percentages to the distribution (highlighted in gold) being so arbitrary (P96, P60, P01) was the need to come up with a distribution that was at least value sensible in the predicted percentile for all of the scenarios listed.?? Most especially the minimum, the mode, the P50 and the P10.? ?I don’t pretend it does that perfectly, and I have no way of checking what the real numbers are – but I think the objective point is clear.? Designing transport infrastructure optimally for emissions around this cargodistance distribution is not what is happening now, and ideally it is something we want to move towards, however long it might take.

Overly simplistic? Of course. Highlighting nevertheless a glaring issue? I think so.

Cheers,

Dave

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