# The calculation of Covid-19 infection rates in churches

## Preamble

In a recent post, I looked at the risk of Covid infection on GB trains, based on the spreadsheet calculation methodology of Professor Jimenez and his team at the University of Colorado – Boulder. This method is based solely on aerosol transmission, which is now regarded as being of much more significance than transmission by surface contamination, and the risk of the latter can be easily reduced by normal hygiene precautions. In this post, I apply the same methodology specifically to the case of churches and include a downloadable EXCEL spreadsheet that might be of use to others. There is a level of self-interest of course, as I am a minister at an Anglican church which will shortly be faced with decisions concerning the nature of worship as the Covid restrictions are removed.  Essentially the spreadsheet gives a numerical value for the risk of Covid infection with specified amelioration methods in place (social distancing, masks, no singing etc.) and allows a rational assessment of safety to be made.

At the outset, it needs to be made clear that there are very many assumptions in the methodology of Jimenez, with some of the parameters not well specified, and the base values of risk that the model gives must be regarded as indicative only and it is best used in a comparative sense. In what follows, I first describe the input and output parameters of the spreadsheet, and then look at how it might be used to compare risk levels for different situations.

The spreadsheet is quite simple and straightforward, and requires no specific expertise to use. A screenshot is given above. The brown cells are input parameters, and the blue cells the output parameters The former are as follows.

• Length, width and height of worship area. The model effectively assumes that the worship area is a three-dimensional box. This is clearly not usually the case, and some degree of judgement will be required in assigning the length, width and height. All dimensions are in metres.
• Duration of worship is specified in hours.
• The ventilation with outside air is specified in air changes per hour. For most old churches that have been well maintained, this will be small and a value of 1.0 can be assumed. For particularly drafty churches, this could be rather higher (at say 3.0). For air-conditioned worship areas a value of 10.0 is appropriate.
• For the decay rate of the virus and the deposition to surfaces standard parameters are assumed. Normally the value for additional control measures will be zero unless there is filtering of recirculated air.
• The number in the choir and congregation are self-explanatory. Ministers should be included in the latter. Because of lack of reliable data on breathing rates and virus emission rates in children, no breakdown by age is required. This is probably a conservative assumption.
• The fractions of time that the choir sings and the fraction of time that the congregation sings are both values between 0 and 1.0. The choir fraction is when they are singing alone – it is assumed they will join with the congregation when the latter sing.
• The fraction of population that is immune is taken to be the proportion of the population that have received a full course of vaccinations, multiplied by 0.9 to allow for virus escape. At the time of writing in the UK, this parameter has a value of around 0.5.
• The parameter that allows for virus transmission enhancement due to variants has a base value of 1.0, a value of 1.5 for the alpha variant, and a value of 2.0 for the delta variant.
• A choice of values for masks efficiency for both breathing in and out are given.
• The fraction of the congregation with masks is a number between 0 and 1.0.
• The probability of being infective is taken from regional ONS data. For example, if the ONS figure of those infected is 1 in 500, then the probability will be 1/500 = 0.002.
• The hospitalization and death rates of those infected can also be taken from ONS data and have small values just above 0.0. At the time of writing the hospitalization rate is around 0.02 (2%) and the death rate is almost negligible and is taken as 0.001 (0.1%).

The next set of parameters in the spreadsheet are those that emerge from the calculation process and are not of direct interest to users. These lead on to the output parameters, which are as follows.

• The probabilities of covid infection, hospitalisation and death of a person attending the service of worship.
• These probabilities expressed as risk – for example a risk of 1 in 1000 of infection.
• The number of covid cases, hospitalisations and deaths arising from attending the service.

## Comparing risk

The absolute values of probability and risk must only be regarded as approximate. Indeed, Jimenez emphasises that there is a great deal of uncertainty around many of the assumed parameter and urges caution in the interpretation of the results. At best, the results will be accurate to within an order of magnitude. The main utility of the model would seem to be to assess changes in risk – for example, any particular congregation may be comfortable with a certain set of Covid amelioration methods (no singing, masks etc.) and the method can be used to see how this risk might change as these measures are relaxed.

As an example of this, let us consider a church (which is not dissimilar to the one where I am a minister), where the congregation is currently capped at 60, there is 100% marks wearing, and only the choir of 6 sings. For the current infection rate of 1 in 150, this gives a risk of infection of 1 in 18100 for a one-hour service. This level of risk would seem to be acceptable to the congregation. Indeed, for one person attending similar services each week for one year, the risk of covid infection is close to the UK risk of injury in a vehicle accident in a year.

Firstly, suppose that a capacity of 100 is allowed (i.e. social distancing regulations are abolished). This increases the risk of infection to 1 in 11800. Now suppose that in addition masks are no longer required. This leads to a risk of infection of 1 in 4100. Allowing congregational singing raises the risk further to 1 in 1600. As all these figures are dependent upon regional infection rate, they also allow for the congregation to decide at what infection level restrictions can be removed. Should the infection level fall to 1 in 1000, then the overall risk with no amelioration measures decreases from 1 in 1600 to 1 in 11300. Whilst these figures are themselves only approximate, they nonetheless give any congregation the information to make a rational choice of how to proceed as restrictions are eased.

## Closing comment

In order to make the spreadsheet as easy to use as possible, I have deliberately kept it simple and have not included too many options. However, if anyone has any suggestions for improvements / useful additions, then please contact me on c.j.baker@bham.ac.uk.

# Covid-19 death rates – an international comparison

## Preamble

One of the things that has become clear during the pandemic is the widespread public misunderstanding of statistics. Nowhere is this clearer than in the attempts to compare the UK performance in the pandemic with that of other countries. Many on social media attempted comparisons with countries of very different social structure (such as those in East Asia), or with very different levels of connectivity (such as New Zealand and Australia) – effectively trying to compare apples with oranges. Comparisons were also made using daily statistics for case numbers and deaths on specific days, completely ignoring day to day statistical variability, the place of the country in the pandemic cycle and indeed the variability in population size. Very often comparisons of this kind were made on Twitter etc. for overtly political reasons and to attack or support the government and were very selective both in their content and timing – government critics were at their most vociferous when infection rates were increasing and strangely quiet when they were decreasing, and the opposite was true for government supporters. All these comments served to do was to illustrate the ignorance and prejudice of the commentator.

In this post, I want to address the same question – how did the UK cope with the pandemic in comparison to similar countries – but to do so in a slightly more rigorous way. It will become clear I am no epidemiologist, but hopefully the argument will be based on a rather more firmly based methodology than in the past.to do so, I will use one statistical measure only – that of deaths due to Covid-19, which seems to me the statistic that is most likely to be recorded accurately. I will not use case numbers as the variations in testing regime between countries means that any such comparisons are unreliable from the beginning. Further, I will only make comparisons with a subset of countries in Western Europe, essentially extending as far east as Poland and Hungary, but not including countries in the Scandinavian or Balkan peninsulas, 18 such countries in all. These are all broadly similar in terms of culture and society. An argument can be made that the comparison should be restricted further to just that small number of countries with populations similar to the UK – France, Germany, Italy, Spain and Poland – and indeed we will use this subset to some degree in what follows.

## Nature of the analysis

The weekly death rates from March 2020 to June 2021 for the UK are shown in figure 1 below from the WHO web site. The curves for all the other countries considered are broadly similar, but the precise shapes and timings of the curves depend crucially upon the lockdown measures that were imposed by different countries, upon the spread of the new variants through the countries (in particular the so-called Kent or alpha variant) and the effectiveness and rapidity of the vaccination programmes.

In the analysis we use WHO data for deaths and data from Wikipedia for country populations. The cumulative death figures at 30th June 2020 and 30th June 2021 are used and are shown in Table 1. The first wave of the pandemic was over by the first date, and the second wave well on the way to being over by the second, at least in terms of deaths. The death rates up to June 30th 2020 and between July 1st 2020 and June 30th 2021 have been calculated from the data and are expressed in what has become the conventional statistic of deaths per 100,000 population.

(At the time of writing – June 30th 2021- the delta variant continues to increase case rates in the UK, in effect a third wave, but deaths remain at a very low level. It is likely that this wave will spread across Europe in the next few months, but hopefully because of the vaccination efforts, serious illnesses and deaths in those countries too will remain at a low level.)

## The first wave

The distinction between the first and second waves of the pandemic is important. For the first wave up to 30th June 2020, it can be seen from Table 1 that some countries were affected significantly whilst others hardly at all. The death rate per 100,000 in the UK of 60.6 was amongst the highest in the countries studied. The reasons for this variation are complex, and can be expected to include the degree of initial seeding of the countries from areas where Covid-19 was already endemic, the age profile of the population etc. The February half term skiing trips by many on the UK seem to have been a significant source of the spread, together with international travel from affected areas. There also seems to have been a pronounced west / east gradient, with the easternmost countries in the sample suffering very few deaths in this phase. Germany seems to have straddled this boundary. To unravel these effects would take a much more sophisticated analysis than I can carry out, and it must be left to those better able to do it, . This is not to say that what happened in this wave is unimportant, and the UK death rates were very high. Indeed, it is likely that the UK government will ultimately have to answer serious questions on their level of preparedness, PPE supplies, and in particular the decisions that were made to send untested elderly hospital patients back into care homes. The government estimate for the excess deaths in care homes up to mid-June 2020 was 19,394. If this figure is excluded from the totals the UK death rate in the first wave falls to 31.5 – close to the average of the death rates in the other countries.  That being said, the level of the analysis I am able to undertake does not enable me to draw any further conclusions concerning the relative performance of the different nations in the first wave of the pandemic.

## The second wave

In the UK the rise in September and October 2020 was brought under control through a fairly severe lockdown from November 5th 2020 to 2nd December 2020 although by the end of the lockdown it had not fallen to pre-lockdown values. There was much criticism if the government at the lateness of the imposition of the lockdown. The rate began to rise again in early December, due to the emergence of the Kent or alpha variant, peaking in mid-January before being brought down by another lockdown which started on January 6th and was relaxed in stages from March 8th. Again, there was a widespread feeling that the government were late these restrictions and should not have allowed social mixing over Christmas. Vaccinations begin in late December 2020, and this also played a significant role in the lockdown. In the other countries under consideration, the peak in early 2021 due to the Kent variant usually began a month or two later, and the vaccination programmes were also a month or two behind those in the UK, so in general the curves were shifted along the time axis by a month or so. But by the end of June 2021 death rates were very low in all countries.

The international comparison shown in Table 1 indicates that in the second wave, the deaths per hundred thousand of all 18 countries varied widely between 33 in Denmark and 299 in Hungary. The population weighted average was 133. The average of the seven most populous countries was 129. The value for the UK was 132 – very close to the average for both the complete data set of all countries and for the restricted number of countries. Many of the death rates are similar with half the countries having rates between 75 and 150. The data offers little encouragement for those who would either praise or denigrate the performance of the UK – it was boringly average. No doubt it’s mistakes in not locking down quickly enough have been compensated by the rapid vaccination roll out, but the same sort of trade offs can be found in all countries. Perhaps the most important questions to ask are how Denmark, Ireland and Holland achieved the lowest death rates of less than half the average. There are almost certainly important lessons to be learnt from these countries.

# The calculation of Covid-19 infection rates on GB trains

## Preamble

In a recent post I looked at the ventilation rate of trains without air conditioning and compared them with the ventilation rate of airconditioned trains. The context was the discussion of the safety of trains in terms of Covid-19 infection. For air conditioned trains, the industry accepted number of air changes per hour is around 8 to 10. For non-air conditioned trains with windows fully open and doors opening regularly at stations, I calculated very approximate values of air changes per hour of around twice this value, but for non-air conditioned trains with windows shut and thus only ventilated by door openings, I calculated approximate values of a of 2.0. On the basis of these calculations, I speculated that the non-air conditioned trains with windows shut probably represented the critical case for Covid-19 transmission. In that post however I was unable to be precise about the level of risk of actually becoming infected and how this related to ventilation rate.

## The work of Jimenez

I have recently come across the spreadsheet tool produced by Prof. Jose Jimenez and his group at the University of Colorado-Boulder that attempts to model airborne infection rates of Covid-19 for a whole range of different physical geometries, using the best available information on pathogen transport modelling, virus production rates, critical doses etc. They base their  analysis on the assumption that aerosol dispersion is the major mode of virus transport, which now seems to be widely accepted (and as anyone who has been following my blogs and tweets will know that I have been going on about for many months). I have thus modified the downloadable spreadsheet to make it applicable to the case of a standard GB railway passenger car compartment.  A screen shot of the input / output to the spreadsheet is shown in figure 1 below.

Figure 1 Screen shot of spreadsheet input / output parameters

The inputs are the geometry of the passenger compartment; the duration and number of occurrences of the journey, the air conditioning ventilation rate; the number of passengers carried; the proportion of the population who may be considered to be immune; the fraction of passengers wearing masks; and the overall population probability of an individual being infected. In addition, there are a number of specified input parameters that describe the transmission of the virus, which the authors admit are best guess values based on the available evidence, but about which there is much uncertainty. The outputs are either the probabilities of infection, hospitalization and death for an individual on a specific journey or for multiple journeys; or the number of passengers who will be infected, hospitalized or die for a specific journey or for multiple journeys.

The spreadsheet is a potentially powerful tool in two ways – firstly to investigate the effect of different input parameters on Covid-19 infection risk, and secondly to develop a rational risk abatement process. We will consider these in turn below.

## Parametric investigation

In this section we define a base case scenario for a set of input variables and then change the input variables one by one to investigate their significance. The base case is that shown in the screen shot of figure 1 – for a journey of 30 minutes repeated 10 times (i.e. commuting for a week);  80 unmasked passengers in the carriage; a ventilation rate of 8 air changes per hour; a population immunity of 50%; and a population infection rate of 0.2% (one in 500). The latter two figures broadly match the UK situation at the time of writing. For this case we have a probability of one passenger being infected on one journey of 0.096% or 1 in 1042. The arbitrariness of this figure should again be emphasized – it depends upon assumed values of a number of uncertain parameters. We base the following parametric investigation on this value. Nonetheless it seems a reasonable value in the light of current experience. The results of the investigation are given in Table 1 below.

Table 1 Parametric Investigation

The table shows the risk of infection for each parametric change around the base case and this risk relative to the base case. There is of course significant arbitrariness in the specification of parameter ranges.  Red shading indicates those changes for which the infection risk is more than twice the value for the base case and green shading for those changes for which the infection risk is less than half the value for the base case. The following points are apparent.

• The risk of infection varies linearly with changes in journey time, population infection rate and population immunity. This seems quite sensible, but is effectively built into the algorithm that is used.
• Changes in ventilation rate cause significant changes in infection risk. In particular the low value of 2ach, which is typical on non-airconditioned vehicles with closed windows, increases the infection risk by a value of 3.5.
• The effect of decreasing passenger number (and thus increasing social distancing) is very significant and seems to be the most effective way of reducing infection risk, with a 50% loading resulting in an infection risk of 28% of the base case, and a 20% loading a risk of 6% of the base case.
• The effect of 100% mask wearing reduces the infection risk to 35% of the base case.
• 100% mask wearing and a 50% loading (not shown in the table) results in a reduction of infection risk to 10% of the base case.

From the above, regardless of the absolute value of risk for the base case, the efficacy of reducing passenger numbers and mask wearing to reduce risk is very clear.

## An operational strategy to reduce risk.

The modelling methodology can also be used to develop a risk mitigation strategy. Let us suppose, again arbitrarily, that the maximum allowable risk of being infected per passenger on the base case journey is 0.1% (i.e. 1 in a thousand). Figure 2 shows the calculated infection risk for a wide range of national infection rate of between 0.01% (1 in 10,000) to 2% (1 in 50). Values are shown for no mask and full capacity; 100% mask wearing and full capacity; and 100% mask wearing and 50 % capacity. It can be seen that the no mask / full capacity curve crosses the 0.1% line at a national infection rate of 0.2% and the 100% mask / full capacity line crosses this boundary at 0.6%.

Figure 2 Effect of national infection rate on infection risk, with and without mask wearing and reduction in loading

Consideration of the results of figure 2 suggest a possible operational strategy of taking no mitigation risks below an infection rate of 0.2%, imposing a mask mandate between 0.2% and 0.6% and adding a significant capacity reduction above that. This is illustrated in figure 3 below.

Figure 3. Mitigation of risk to acceptable level through mask wearing and reduced capacity.

As has been noted above the absolute risk values are uncertain, but such a methodology could be derived for a variety of journey and train types, based to some extent on what is perceived to be safe by the travelling public. Regional infection rates could be used for shorter journeys. Essentially it gives a reasonably easily applied set of restrictions that could be rationally imposed and eased as infection rate varies, maximizing passenger capacity as far as is possible. If explained properly to the public, it could go some way to improving passenger confidence in travel.

# Covid-19 and train ventilation

Recently the Rail Delivery Group has issued a short video animation of which the above is a screenshot. This addresses, for the first time, the need for good ventilation to decrease the risk of Covid infection on trains. Aerosol transmission is now regarded as the primary mode of pathogen transmission and infection is much more likely via this route than from surface transmission, despite the emphasis that has been given to the latter. So this little video is to be welcomed. But in telling us that train ventilation systems change the air every 6 to 9 minutes, giving the number of air changes per hour (ACH) of between 7 and 10, it rather begs the question as to what actually is an adequate ventilation rate to minimize infection risk. In a blog of November 2020, I addressed this issue in a rather simplistic way and came up with the expression shown below. This simple formula says that the time for a critical pathogen dose increases with increases in the value of the critical dose and in the number of air changes per hour, but decreases with increases in the respiration rate of infected individuals and the initial concentration of the pathogen. This all seems very reasonable, but precise values depend crucially on the values of critical dose, respiration rate and initial concentration. I would guess such values are available (or at least arrange of them) but I don’t have easy access to them.

But let us assume for the sake of argument that the current air exchange rates on trains are adequate to keep the risk of infection low (but note that they are significantly less than in aircraft, where 25 to 30 ACH seem to be common). This only applies of course to trains with air conditioning systems, but there are trains that rely on window opening for ventilation – not least the Class 323s on the Cross City line in Birmingham – the trains that I travel on most frequently. How does the ventilation of these trains compare with that for air-conditioned trains.?

For such trains the ventilation mechanism will be what can be referred to as shear layer ventilation – the flow in and out of the train windows and doors due to the relative air movement when the train is moving, or due to wind effects when the train is stationary. In some work from about 20 years ago, a research student and myself derived the simple expression shown below for shear layer ventilation for wind passing across an opening in a large box structure.

The application of this method to train ventilation is a bit of a stretch, and one would not expect any great accuracy. For the Class 323, we the assume the following: 22 windows/carriage, area of window opening window of 0.02m2, giving a total opening area of 0.44m2; 2 open doors per carriage with an opening area of 4m2 giving a total opening area of 8m2; a carriage volume of 80m3.  We also assume that for both doors and windows, the coefficient k=0.05. The train speed when moving is taken as 20m/s, and the wind speed when the train is stationary is taken as 1m/s. In operation we assume that the train is moving for 90% of the time and stationary for 10% of the time. Based on these figures we can calculate the number of air changes per hour for when the train is moving and when it is stationary. For the former we get an ACH of 3600(20*0.44*0.05*0.9) /80= 17.8, and for the latter an ACH of  3600(1*8*0.05*0.1) /80= 1.8.

The simplicity of this method needs to be emphasised and the results should only be regarded as approximations. Nonetheless they are of interest. Firstly the figures suggest that with all windows open, the ventilation of the Class 323 is twice as high as on a typical air  conditioned system. This ties in with my personal experience – when the windows are open to this extent in the summer, there is a strong (and if the weather is hot, pleasant) draft through the carriage. If only half the windows are open, the overall ventilation is equivalent to an air conditioned system. Secondly, the amount of ventilation due to doors opening in stations is small in comparison to the maximum window ventilation. This leads to the third point – if all the windows are shut (as would be the case in the winter) the overall ventilation is well below the air-conditioned case. It is perhaps for such vehicles in such conditions that we should look for the critical case of pathogen transmission on trains.

# A (half hearted) defence of Autonomous Vehicles and other transport innovations

## Preamble

Over recent years it has almost become the norm amongst practicing railway engineers to pour scorn on any new transport proposal that emerges – for example Hyperloop, the autonomous metro system, being developed for Cambridgeshire, autonomous vehicles in general, vehicle platoons, bus rapid transit schemes and so on. Now whilst some new concepts deserve all the opprobrium that they receive and are often ideas looking for an application rather than the more sensible opposite, I want to argue in this post, that there is some merit in some of these concepts that deserves further consideration, particular as components of a rail based public transport network.

Before proceeding however, I need to be a little more explicit about those concepts that I do not believe are viable. These fall within two categories – very high- speed tube transport, and autonomous vehicles in mixed traffic situations. The former, exemplified by the monstrosity that is Hyperloop, faces very major technical difficulties. From my own aerodynamic perspective these include the difficulties of maintaining a controlled vacuum along very long tubes, and the highly complex unsteady forces that exists as flow speeds around some parts of the passenger capsule exceed the speed of sound i.e. locally supersonic flow with the Mach number >1.  With regard to the latter, I have seen no published information that these effects have been properly considered. Formidable as these technical issues are, they are of small concern in terms of the major practical issues of capacity (multiple tubes would be required to give the same capacity as high-speed trains); and safety (how these tubes would be evacuated in terms of an accident or fire). In these terms the concept is flawed.

Much of the hype concerning autonomous vehicles has been around the possibility of them providing door to door service with no human involvement in driving. I used to be of the view that this was a possible, if very long term, aim. I no longer think that that is the case, primarily for reasons of liability and safety. If there is an accident (as there will be) who is to blame – the passenger, the owner of the vehicle; the manufacturer; the software designer etc.? Who would wish to accept responsibility for injuries and fatalities? I believe that this consideration alone will cause the development of high levels of autonomy in private vehicles to stall – again when designers and engineers are faced with practical realities. I fear that autonomous vehicles are in the main “toys for the tech boys”. And they are boys – look at any AV website and count the relative number of males and females.

Having thus been dismissive of these two areas, let us proceed to think about those novel transport concepts that might have an application.

## What are the viable concepts?

The two specific areas where I believe there might be possibilities of large-scale usage are in the field of tracked autonomy and platoons for public transport use.

Whilst I have doubts concerning the use autonomous vehicles on public highways, their use on restricted systems (let us call them tracks) seems to me less problematic. Such systems already exist in busways and bus metro concepts. Whilst many good railway folk would shout loudly that these would be better replaced by light railways or trams, these systems do have the distinct advantage in some areas of going where passengers wish to go rather than to some remote railway station – Cambridge is the classic example of this where the busway from St Ives allows buses to originate at a range of departure points in north Cambridgeshire, use the busway for the majority of the journey, and then end their journey in the city close to their place of work. Similar autonomous systems could equally be conceived, where the vehicle operate in a driverless mode whilst using the tracked system, with reduced staffing costs and redirection of staffing effort towards passenger care and revenue collection. If autonomous vehicles are restricted in this way, then the guidance system could be very much simpler than those currently proposed, with either short range infrastructure mounted wireless systems every few hundred yards or embedded in the tracked pavement.

The other novel area that has potential for significant use is the concept of platooning, particularly when combined with the idea of tracked autonomy. Autonomous tracked systems can in principle easily be configured to operate as platoons with the headway between vehicles along the platoon being controlled by the leading vehicle. Whist close platoon running will reduce aerodynamic drag and lead to reduced fuel use, the major advantage would be scalability, in that the capacity of such systems could be increased easily by adding extra vehicles in platoon, without a corresponding increase in staffing resource required.

## Autonomous Platoon Transport (APT)

These thoughts lead me to propose a new hybrid concept, which I will refer to as Autonomous Platoon Transport  (APT), largely because I rather like the acronym and its associations. APT would have the following components.

• Self-powered vehicles (almost certainly electric, but I would be open to hydrogen power if only to further irritate some of my rail readers) that have the ability to operate as ordinary vehicles on public roads, or as autonomous vehicles on reserved track. I would envisage a typical vehicle capacity to be around 30 to 40.
• A simple paved road, single carriageway track (with passing places) with suitable guidance sensors either at trackside or embedded within the pavement – this would be much cheaper and easier to construct than a light railway or tramway.
• These would operate as driven vehicles away from the reserved track, and as autonomous vehicles, either individually or in platoons, on the reserved track.
• In principle vehicles could be either passenger or freight, although the latter might make significant demands upon pavement design. The operation of freight APTs would be of a different nature to those for passengers, and I won’t consider then further in this post.

I make no claims that such a concept would replace existing public transport systems, but I will argue in what follows that there are some circumstances where it could complement such systems.

## Possible passenger applications

Conventional rail and tram systems have obvious advantages for long distance travel and for travel within major conurbations and meet the journey time and capacity requirements well. The specific areas where APT systems might have a role is where there is large variation of demand either geographically (with many small trip origins) or temporally (with large seasonal variations), or where there are major capital cost constraints that mitigate against the use of conventional rail.

First consider geographical constraints. The type situation here is that of Cambridge and its regions – and indeed the APT system bears a strong resemblance to the proposed Cambridge Autonomous Metro system, although with the use of driver-controlled vehicles at its outer limbs and autonomous platoon running in the central region. Here there is a large, dispersed commuter demand around the city that cannot be met economically by conventional systems but could potentially be met by the cheaper infrastructure required for APT operation. Cambridge is a special case in that the historic nature of the centre requires the hub of the system to be underground, but there are many other towns and cities of a similar size and with similar characteristics, where the central routes, where platoon operation would be in place, would be at surface level.

Typical temporally constrained routes would be rail routes with generally low local usage, but high usage in the summer months – such as coastal branch lines, where overcrowding, often to very unpleasant levels, can occur. The advantage of an APT system would be that it would be easily scalable in terms of capacity without the need for an increase in staffing resource. Whilst the base service might be operated by one APT vehicle, with a driver or passenger manager, this would be supplemented in peak times by other vehicles in platoon – perhaps diverted from those towns and cities with geographical constraints but where demand falls during the summer months and a reduced service is all that is required. This has implications concerning the nature of the infrastructure – either such lines need to be converted to operate in this mode, with paved instead of rail formations, or a new track needs to be constructed along the route, or a hybrid paved / track formation needs to be developed. I suspect the latter would prove to be a challenge, but could allow rail usage when appropriate, although new types of control and safety system would be required. This will bring accusations that I am a closet supporter of converting railways to roads. But no, I am not funded by the TPA (or anyone else come to that) – I am simply interested in providing the most appropriate services for customers that gets them to their destination in reasonable comfort and security. (Interestingly note the reversal in order of acronyms from APT to TPA – a device commonly used in Satanic circles I understand).

The third use of such a system might be in the re-use of old railway lines where rail re-instatement is simply not possible because of major track obstructions / loss of infrastructure. As an example, we might consider the Penrith – Keswick – Workington route in Cumbria. Here an APT system could be used along the existing trackway where this is still in place, with on road / driver sections where major infrastructure no longer exists – primarily in this case at the start and end of the route. Local demand would be small, but the much larger seasonal demand could be met by again scaling the number of vehicles and using platoon running for most of the route.

Finally, the concept could be applied to longer routes where there are both geographical and temporal constraints. A typical case here might be the Cambrian Coat line, where demand is highly seasonal. There are also geographical constraints in the dispersed nature of the communities it serves, and the lack of connectivity to surrounding areas. Thus for example one could envisage the base demand could be met by APT vehicles in short platoons, but joining and leaving the platoons at different places to more directly serve surrounding areas – for example at Harlech to serve the town and connect to Blaenau Ffestiniog, or at Porthmadoc, to again serve the town and to connect to Caernarfon. Such a scheme would rely on a hybrid track form, in order that through trains could operate to Birmingham and that the large summer demand could be met. Again there would be design and operational challenges.

## Final thoughts

I suspect many will disagree with some or all of what I have written in this post – hopefully in a civil fashion. And of course all I have written is provisional and might not survive translation into a practical reality. All I would hope is that it encourages discussion of the use of novel transport systems, and how they might complement a modern transport network, rather than simply dismissing them.

# The NIC report on “Rail needs assessment for the Midlands and the North” – common sense or betrayal?

## Preamble

The National Infrastructure Commission report of December 2020 “Rail needs assessment for the Midlands and the North” has caused something of a stir in the rail industry. The NIC was tasked to look at how the proposals for HS2 and the Northern Powerhouse Rail could best be integrated. It considered two ranges of options  – one that prioritised regional links in the North and Midlands, and one that prioritised long distance links. All options integrated phase 1 and phase 2a of HS2 from London to Birmingham and Manchester, but only the long-distance option included the eastern arm of the original Y shaped network to the East Midlands and Leeds. On the basis of a wide range of indicators, including cost and deliverability, the report concluded that the prioritisation of regional links was to be preferred – cue loud denunciations, accusation of scrapping HS2 abandoning the Midlands and North and so on.

My first reaction was astonishment that the proposals should have come as a surprise to rail industry commentators – it has been evident to me at least for a few months that some post Covid financial realism was necessary to rein in all the potential major railway projects on the table. Also the eminently sensible and rational Greengauge 21 has recently made very similar proposals, urging that the eastern arm of HS2 be built in a number of phases and repurposed to provide links between regional centres. However, my initial reaction was to share the view of those in the industry, that the conclusions were to be regretted, although perhaps with a greater sense of fatalism than most that this was going to happen anyway.

But then I read the report. I found it to be well laid out, with a convincing set of underlying assumptions and methodology. I have to say I have a great deal of sympathy with its conclusions, which should lose me a few followers on Twitter if nothing else. The basic points that came across to me were that the construction of all the rail schemes currently under discussion is unaffordable, and that the number of passengers travelling between regional centres is significantly greater than those travelling between these centres and London . Post-covid this discrepancy is likely to grow. In this brief post, I want to set out what I see as the benefits of the prioritisation of regional links over long-distance links.

## The proposals

The proposals are summarised in figure 1 below from the NIC report. The report firstly sets out a baseline set of improvements that are already underway or committed to – the western leg of HS2, main line speed upgrades (ECML, MML, Manchester-Sheffield); Transpennine upgrade and Midlands Railhub upgrades. Two sets of proposals are provided for each prioritisation – one at the baseline cost plus 25% and one at the baseline cost + 50%. In the main I will consider the baseline + 50% options. The long-distance prioritisation is based on the Y shaped HS2 network, together with a partly new line between Leeds and Manchester, with upgrades to the ECML to serve the north east and Scotland and further upgrades of track in the Midlands and Lancashire. The regional prioritisation assume the western leg of HS2 to Birmingham and Manchester will be completed, but with the eastern leg replaced by high-speed lines from Birmingham to the East Midlands and from Leeds to Liverpool, with major upgrades to the lines from the new East Midlands line to Nottingham, Derby, Sheffield and Leeds; from Sheffield to Manchester; and from Leeds to the North East. Oddly for the regional prioritisation, the baseline + 25% case also sees a major ECML upgrade from Leeds to London, whereas this does not figure in the baseline + 50% option.

The overall benefits from the proposals are set out in table 1 below for the +50% options – taken directly from the NIC report. It can be seen that prioritising regional links delivers the greatest benefit. Journey time and service level details are given in table 2.

## The benefits of regional prioritisation

I will admit that my reasons for liking the regional proposals are very parochial and reflect the fact that I live in the Midlands between Birmingham, Derby and Nottingham. I suspect my views might be different should I live in Leeds. That being said, the major benefits from my perspective are as follows.

• Links between Birmingham and the East Midlands (and Nottingham in particular) are much better than those offered by the current HS2 proposals, which would need to be routed through the proposed East Midlands Hub at Toton (27 minutes as opposed to 53 minutes).
• Nottingham gains a direct link to the high-speed line facilitating faster overall journey times to London. (58 as opposed to 89 minutes).
• The need for the East Midlands Hub at Toton is removed. The proposal for a hub there has always been in my view a mistake of potential historical significance. Such a station would suck the life out of the centres of Nottingham and Derby into a new urban centre at Toton which, because of its proximity to the M1 and A52, would also very likely be a major generator of road traffic in the area.
• Services within and across the East Midlands, Yorkshire and Lancashire would be greatly enhanced – see table 2.

In addition, a link from the line from Derby to Birmingham to HS2 at Tamworth, would allow high-speed running most of the way from London to Derby. It is also of interest to note that the route of the proposed high-speed line to Nottingham appears to be further south than the current HS2 proposal and would allow a new station to be built close to East Midlands Airport. This would thus allow for a high-speed connection with Birmingham Airport, which would allow greater operational flexibility. for both airports.

## The drawbacks of regional prioritisation

The main selling points of the current HS2 scheme are decreased journey times and the release of capacity on the classic network for other services, both passenger and freight. With regard to the former, table 2 shows that for the regional-links option journey times are mostly decreased from the long-distance links option between centres other than London. London to Sheffield, Leeds and Newcastle take 6. 12 and 37 minutes longer for the former than for the latter. The first two I would suggest are hardly significant. If the ECML upgrade is included in the regional-links option, the Newcastle / London time takes just 3 minutes longer than the long-distance option – as noted above this was, oddly, included in the +25% regional links option but not the +50% option.

The issue of capacity has also been addressed by the report. Whilst there can be seen to be significant benefits to the number of inter-regional services that it is possible to schedule, the report admits that the regional-links approach does little to release freight paths on the ECML and in the North and Midlands. This will not please the rail freight sector of course and must be seen as a weakness of the regional-links proposal.

One other point. The report only briefly mentions Scottish links. Those that are proposed in the HS2 plans for the WCML and the western arm of HS2 will not of course be affected. Those that are proposed for the eastern arm and the ECML will be affected to the same level as the Newcastle services – and the effects can be minimised by an ECML upgrade. This being said, I strongly suspect by the time these upgrades are delivered, we will have an independent Scotland and a united Ireland, with a transport focus on an east west corridor with high speed ferries from the continent to Edinburgh connecting with cross Scotland lines to high speed ferries to Ireland. Links to London and England in general will be of less concern, and may well involve customs and passport checks.

## Final thoughts

As noted above, I find the report and its conclusions plausible and convincing. It is not ideal of course, particularly with regard to freight capacity, but it does seem to me to be realistic, and at least from my Midlands perspective, offers significant benefits. I strongly suspect however that that won’t be everyone’s view.

# Engineers, roads and ethical standards

It is now established beyond all doubt that the unrestrained growth in road vehicle traffic is bringing many undesirable effects. Annually  around 1750 pedestrians are killed by cars in the UK, and 25000 seriously injured. The poor air quality that results from gaseous and particulate emissions from roads and vehicles results in significant adverse effects on the health of those who live in urban areas, children in particular. High levels of traffic can be both unattractive and dangerous for other road users such as pedestrians and cyclists and can discourage these active modes of transport. Again, this can lead to adverse health effects, seen particularly in the increase in childhood obesity.  Large areas of land are given over to sterile car parks that could be more profitably used for other activities. The effects on communities and urban environments is also significant and there is clear evidence that restricting car use can increase the vitality and livability of such areas and lead to real social and health benefits for the poorest in society. To these should be added the fact that the road sector is the major cause of greenhouse gas emissions in the developed world, and that road vehicles use precious energy resources in an unsustainable way. All these effects are well known and proven to high levels of reliability, and fully appreciated by most Transportation Engineers and Planners.

And yet…… Major road improvements are still carried out and new roads built, which inevitably results in further induced growth in traffic, magnifying the issues set out above. Induced traffic growth is of course often conveniently ignored in scheme appraisal. New housing developments are built, with major areas given up to parking and no provision for public or active transport. Low Traffic Neighbourhoods are now a political issue within the culture wars narrative and are more often removed than implemented.

My community, that of professional engineers, see these things and in the main recognize the folly of them. We regret them but we shrug our shoulders and carry on. In the end, we say, we have to provide what clients want, and we design and build road scheme after road scheme, housing estate after housing estate, knowing all the time that these will only result in more health problems, more congestion, more accidents and deaths and a degraded environment. The time has come when I would suggest we, as engineers, need to look very seriously at ourselves and our actions.

I am a Fellow of a number of professional institutions. Of these the two most relevant to the issues addressed here are the Institution of Civil Engineers, and the Chartered Institution of Highways and Transportation. The ICE Rules of Professional Conduct include the following clauses

3. All members shall have full regard for the public interest, particularly in relation to matters of health and safety, and in relation to the well-being of future generations.

4. All members shall show due regard for the environment and for the sustainable management of natural resources.

The CIHT Code of conduct contains something similar.

Members of the Institution must give due weight to all relevant law, facts and best practice guidance, and the wider public interest. They must:

• minimise and justify any adverse effect on society or on the natural environment for their own and succeeding generations;
• take due account of the limited availability of natural and human resources;
• hold paramount the health, welfare and safety of others;

It seems to me that there is at least an arguable case that by knowingly being involved in road building developments which will lead to adverse effects for existing and future generations, and will consume limited natural resources in an uncontrolled way, professional engineers are in breach of their own institutional codes of conduct that bind them. Further this action could, in principle, lead to formal complaints made about the involvement of individuals. Indeed  the CIHT code of conduct lays a duty of complaint on its Members and Fellows to “report any violation of this Code by a member to CIHT”.

Without the involvement of engineers very many fewer environmentally, medically and socially damaging schemes would get off the ground and none would be designed and built. I would suggest that we are approaching a point where individuals and firms, and indeed the entire profession will need to make a choice – to comply with our own ethical codes and take them seriously or to ignore them. It is not a question that will be able to be avoided much longer.

# Some thoughts on ventilation and pathogen concentration build up

## Introduction

Up till recently most attention had been focused on the spread of Covid-19 by near field transmission – being in close proximity to an infected person for a certain amount of time, and rather ad hoc social distancing rules have been imposed to attempt to reduce transmission. However, there is another aspect of transmission – the gradual build up of pathogen concentrations in the far field in enclosed spaces due to inadequate ventilation. The importance of this mode of transmission is beginning to be recognised – see for example a recent seminar hosted by the University of Birmingham. The main tool that seems to have been used for both near and far field dispersion is Computational Fluid Dynamics (CFD) – see the graphic above from the University of Minnesota for example. Now whilst such methods are powerful and can produce detailed information, they are very much situation specific and not always easy to generalise. This post therefore develops a simple (one could even say simplistic) method for looking at the far field build up of pathogens in an enclosed space, in a very general way, to try to obtain a basic understanding of the issues involved and arrive at very general conclusions.

## The model

We begin with equation (1) below. This is a simple differential equation that relates the rate of change of concentration of pathogen in an enclosed volume to the pathogen emitted from one or more individuals via respiration and the pathogen removed by a ventilation system. This assumes that the pathogen is well mixed in the volume and is a simple statement of conservation of volume.

From the point of view of an individual, the important parameter is the pathogen dose. This is given by equation (2) and is the volume of pathogen ingested over time through respiration. The respiration rate here is assumed to be the same as that of the infected individual.

Equations (1) and (2) can be expressed in the normalised form of equations (3) and (4) and simply solved to give equations (5) and (6).

Equations (5) and (6) are plotted in figures 1 and 2. Note that an increment of 1.0 in the normalised time in this figure corresponds to one complete air change in the enclosed volume. It can be seen that after around three complete air changes the concentration of pathogen reaches an equilibrium value and the dose increases linearly, whatever the starting concentration. To the level of approximation that we are considering here we can write the relationship between normalised dose and time in the form of equation (7), which results in the non-normalised form of equation (8).

Assuming that there is a critical dose, the critical time after which this occurs is then given by equation (9).

Equation (9), although almost trivial, is of some interest. It indicates that the time required for an individual to receive acritical dose of pathogen is proportional to the volume of the enclosure and the ventilation rate. This is very reasonable – the bigger the enclosure and the higher the ventilation, the longer the time required. The critical time is inversely proportional to the concentration of the emission, which is again reasonable, but inversely proportional to the square of the respiration rate. This is quite significant and a twofold increase in respiration rate (say when taking exercise or dancing) results in the time for a critical dose being reduced by a factor of 4, or alternatively the need for ventilation rate to increase by a factor of 4 to keep the critical time constant. Similarly if there are two rather than one infected individuals in the space, then the respiration rate will double, with a reduction in the critical time by a factor of four.

## Discussion

Now consider the implications of this equation for two specific circumstances that are of concern to me – travelling on public transport (and particularly trains) and attending church services. With regard to the former, perhaps the first thing to observe is that there is little evidence of Covid-19 transmission on trains, and calculated risks are low. In terms of the far field exposure considered here, respiration rates are likely to be low as passengers will in general be relaxed and sitting. This will increase the time to for a critical dose. On modern trains there will be an adequate ventilation system, and the time to reach a critical dose will be proportional to its performance. Nonetheless the likelihood of reaching the critical level increases with journey time – thus there is a prima facie need for better ventilation systems on trains that undergo longer journeys than those that are used for short journeys only. For trains without ventilation systems (such as for example the elderly Class 323 stock I use regularly on the Cross City line) has window ventilation only, and in the winter these are often shut. Thus ventilation rates will be low and the time to achieve a critical dose will be small.

Now consider the case of churches. Many church buildings are large and thus from equation (9) the critical times will be high. However most church buildings do not possess a ventilation system of any kind, and ventilation is via general leakage. Whilst for many churches this leakage this can be considerable (….the church was draughty to day vicar….), some are reasonable well sealed – this will thus, from equation (9) tend to reduce the critical time. In this case too the respiration rate is important. As noted above the critical time is proportional to the respiration rate squared. As the rate increases significantly when singing, this gives a justification for the singing bans that have been imposed.

The above analysis is a broad brush approach indeed, and in some ways merely states the obvious. However it does give something of a handle on how pathogen dose is dependent on a number of factors, that may help in the making of relevant decisions. To become really useful a critical dose and initial pathogen concentration need to be specified together with site specific values of enclosed volume, ventilation rate and expected respiration rates. This would give at least approximate values of the time taken to reach a critical dose in any specific circumstance.

# Pollution, Covid and Trains

There has been a significant amount of research recently to investigate the air quality in railway stations. Perhaps the major study, with which I was very much involved, involved extensive measurements of the air quality at Birmingham New Street by colleagues at the University of Birmingham (Figure 1). Measurements were made of the oxides of nitrogen (NOX) and particulate matter (PM) and concentrations were measured that were considerably in excess of Environmental Health limits. Typical daily average results are shown in Figure 2. This work informed the efforts by Network Rail to improve the air quality at the station through an improved ventilation system. Further work was carried out by Kings College London and Edinburgh University, under an RSSB contract, to measure NOX and PM at Kings Cross in London and Edinburgh Waverley. Typical results are shown in figure 3 and although these results are not as extreme as the Birmingham measurements, do show some exceedances of environmental health limits. Between them, these three investigations have given a great deal of information on station air quality and informed methods for alleviating the worst of the effects.

However, that is not the whole story. There are growing indications that air quality ON trains is also very poor. A study on diesel commuter stock in Canada has shown high levels of ultrafine particles and black carbon within the passenger cabins (Figure 4). In 2016 the BBC reported the measurements made by their reporter Tim Johns  as he commuted into London, which again showed high particulate levels on diesel commuter trains, although not as high as in Black Cabs (Figure 5). Similarly, the BBC in 2019 reported a study by the Committee on the Medical Effects of Air Pollutants which showed very high levels of particulates on the London underground (Figure 6) which resulted in a strong response from the rail unions. These high levels are presumably due to two sources – diesel particulate emissions from trains being ingested into air conditioning systems, and also from ambient particulates in the dirty tunnels of the underground. The levels of particulates measured have significant implications for human health, particularly for those with respiratory conditions.

Similarly, some work has been recently reported from Greece that shows elevated levels of both gaseous pollutants and particulate pollutants on diesel trains, both in excess of EU limits (Figure 7). Again this is presumably due to ingestion of diesel emissions by ventilation systems. Hopefully in the near future we will see the results of more quantitative investigations for the UK of on train NOX and particulate concentrations, and of work to investigate the ingestion of external pollutants, both from diesel emissions and dirty environments, by ventilation systems. However current indications are, that, care should be taken in using ventilations systems that draw external air into the train without the use of extensive filtering of the input.

And then along comes Covid-19. The importance of high levels of ventilation on reducing pathogen concentrations and thus the risk of infection is becoming clear – se for example the recent seminar organized by the University of Birmingham. Ideally, very high (airline) levels of air exchange with the outside are required in internal environments, including trains and buses. An interesting illustration of this is provided by the publicity material in figure 8 produced by SNCF in France. I have seen nothing similar for the UK. There is an obvious dichotomy here between the need to reduce external air intake to minimize NOX and PPM ingestion and to keep internal levels of NOX and particulates at an acceptable level, and the need to increase ventilation rates to decrease pathogen levels. Both could be achieved by aggressive filtration of the air drawn through the train. However, this is likely to require major modification to existing trains in Britain, that won’t be cheap. I suspect train ventilation is going to become a major issue in the near future.

# A brief look at the incidence of Covid-19 in UK Universities

Alarm has been expressed by many commentators at the prevalence of Covid-19 in UK Universities, and on the face of it, the figures do seem to be alarming. For example, the UniCovid UK website that attempts to track the spread of Covid in Universities indicates that, as at October 17th 2020, since the start of term there have been 1650 cases at the University of Manchester and 1522 at the University of Northumbria. This data comes from a variety of sources where it is reported in different ways and needs to be treated with caution, but nonetheless gives a broad indication of the current situation. However these raw figures do not give a real indication of the situation since they do not take into account the size of the institution or the length of time since the start of term, which differs from place to place. To look at this in a little more detail I have carried out the following simple analysis using the UniCovid UK data at October 17th 2020.  I have taken the number of reported cases since the start of term at each institution and divided them by the factor (total student population x days since the start of term / 14). This gives a rough approximation of the proportion of students who might currently be expected to have Covid-19, making the assumption that the illness lasts for 14 days. I am very aware of the other implicit assumptions involved in this calculation (the assumption of constant infection rate,  the neglect of the different demographic profiles of different universities, different rates of testing and so on), but at least it gives a crude normalization of the data. On this basis, the 30 Universities with the highest percentages of students currently with Covid-19 is shown in the table below.

Now the UniCovid UK web site gives the prevalence of the virus amongst the student age population as between 0.24 and 0.52%. Most of the Universities in the above table lie above the upper bound value, but many not by a great amount (and here the assumptions in the analysis need to be kept in mind). Only twelve exceed a value of greater than 1% of the students having the virus. Whilst for some of these top twelve the situation is clearly very serious, with the proportion of those infected many times the expected levels, the numbers suggest that the issues are localized – and indeed mainly in areas where there are high rates of infection in the wider community.