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.
Engineering, history and ecclesiology 
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