Black Cat Worker Collective operate Krakatoa, a 200 capacity grassroots music venue in Aberdeen, Scotland. We followed the coronavirus saga with interest, and were so alarmed by reports of what was unfolding in Italy, that we voted to enter into lockdown on 12th March 2020. This was eleven days before the UK government first imposed a nationwide lockdown. Since then we’ve been monitoring the advice issued by SAGE (the UK’s Scientific Advisory Group for Emergencies). This release in April was particularly interesting, because it mentioned ventilation as one possible means of mitigation.
We’ve spent the past three months investigating using MVHR (Mechanical Ventilation Heat Recovery) systems as a solution to ventilating our building in order to mitigate the transmission of COVID-19. Key to this is fluid dynamics and how air moves around. This would be in addition to the usual hygiene and distancing measures. As part of this we’ve developed a spreadsheet calculator (downloadable from this page) that can run various scenarios.
Based on this research we’re attempting to crowdfund a ventilation system for Krakatoa, if you find the information and tool on this page useful then please consider making a donation to our appeal via GoFundMe or PayPal, thank you!
Many scientists are now of the opinion sufficient evidence exists that breathed out coronavirus can travel through the air, and remain infectious well beyond 2m social distancing.
This isn’t such an issue outdoors where the aerosol is quickly dispersed into the atmosphere and the virus irradiated (hence so few infections linked to BLM protest marches), but does present a significant hazard indoors, where it can build up and linger. This week 239 scientists signed a letter calling for international bodies such as the World Health Organization (WHO) to acknowledge the possibility of this type of airborne spread.
“… it is especially important to address the issue now that people in many countries are returning to workplaces, restaurants and pubs, says signatory Julian Tang at the University of Leicester in the UK. Improving ventilation will reduce the risk, he says. “You can’t rely on people wearing masks.”
The accuracy of this depends on various factors relating to the virus. Here’s some of what’s needed in order to build an accurate model:
- How much virus does a typical infected person exhale? From a recently published research paper this is estimated to be anywhere between 1000 and 100,000 cells per minute. Assuming the worst case scenario, then at a typical respiration rate of 15 breaths per second comes out at 6,667 cells being exhaled in every breath. Note that spreaders might be breathing more rapidly than non-spreaders.
- Is breathing in 10 cells 100x in the space of a few minutes is just as likely to deliver an infectious dose as breathing in 1,000 cells in a single breath. If not then just how much of a factor is this? We haven’t been able to locate any info on this, but anecdotal evidence from the ‘pub outbreak’ here in Aberdeen and data from other outbreaks around the world appear to suggest that a concentrated dose is more likely to result in infection.
- How many cells are present in an infectious airborne dose (ID50)? Nobody knows and estimates such as here and here are somewhat vague. For MERS it’s reckoned to be several thousand cells, but some scientists suspect that it might be as few as several hundred cells for COVID-19. From running data from outbreaks through our calculator, a figure of around 1,000 cells per minute appears to best match those outcomes. This is all largely dependent on the previous points though, so much more data is needed to improve the accuracy of the model.
Please get in touch if you have any information that would be useful to refining our model (such as links to scientific research), if you can see any flaws in it, or if you simply have any suggestions on how we could improve upon it.
Concerns have been raised that ventilation might actually assist the spread of the virus, but this paper appear to indicate that wouldn’t be the case. Firstly exhaled breath mostly dissipates in less than normal social distance. Secondly the chances of inhaling someone else’s breath are greatly reduced by breathing through the nose. Thirdly, such a mode of transmission only really presents a risk where people are face to face. Lastly correctly designed ventilation ducting will help dissipate the virus more quickly.
Schools reopening might provide some real world insights into 2) & 3). Whether they should be reopening at all is another matter, but in theory the various authorities should soon be in a position to compile the following data:
- Physical volume of each classroom in m3.
- Ventilation rate for each classroom.
- Number of children in any given classroom at any given time.
- Duration they were confined together.
- Number of spreaders, who were present in hindsight.
- Resultant number of infections.
Which could then be checked against air samples, now that the a method may exists for obtaining those.
Download the Calculator
This is a complex workbook and uses features of MS Excel that might not display properly on some handheld device. Suggest opening it on a computer.
Changes for This Version
- “Safe Time” concept scrapped.
- Air density estimates introduced.
The default data shows a scenario with 2 spreaders in a 300m3 space for 3 hours, against 1 MVHR unit delivering 4,200m3 of fresh air per hour combined, with the target entering the space an hour after the spreaders, then staying a further hour beyond their departure.
It’s as yet unclear whether an infectious dose via aerosol occurs as the result of a single breath, and/or cumulative exposure over a prolonger period of time. For this reason the calculator focuses on the density of the aerosol in cells per litre, and the number of cells likely to be inhaled in the space of 1 minute. It could be that lower doses over a longer period are also lead to infection, but what’s being observed in various outbreaks makes this seem less likely.
Instructions for Use
The workbook needs to be opened on a computer rather than a phone or tablet, else the formatting won’t work; it’s quite a complex worksheet, and a bit messy inside. The easy way to perform the calculation is based around the air changes, else it becomes recursive (and a spreadsheet lacks that sort of capability). This means that the time column down the lefthand side will change depending on the capabilities of the equipment. This makes it necessary to edit the spreaders and target columns in order to make a comparison between different MVHR specs. It’s easy to get caught out by this, but provided the data is input correctly the worksheet will produce consistent output. The could all be addressed by programming a proper app, rather than using a spreadsheet, but that’s beyond our capabilities. This worksheet is still capable of the job, it’s just a little fiddly to operate.
The seven green boxes along the top are where the parameters can be entered.
The first box is where the volume of the space can be input in cubic meters. This is presently set to 300m3 (the size of our venue), but can be changed.
The second and third green boxes both relate to Covid-19. The second box is the infectious dose in terms of cells inhaled per minute. This is presently set to 1,000, which is our best estimate based on the available evidence, and running reported scenarios through the calculator. Unfortunately there is much data around to help refine the ID50. The third box is the number of cells exhaled in each respiration. For reasons stated above this is presently set to 6,667.
The fourth green box is where respiration rate in breaths per minute can be entered. Please note that the worksheet assume only healthy adults in the room and a mean a tidal volume of 500ml. We suggest increasing the respiration rate to 18 for a bar, cafe, or music venue type environment like ours.
The final three green boxes relate to the spec of the MVHR unit. This is just a huge box with a pair of powerful duct fans and a heat exchanger. It blows fresh air in from outside, and sucks stale air from the room. The heat exchanger (up to 90% efficiency) is to mitigate heat loss. The air streams don’t mix. It’s a fresh air alternative to aircon, and the heat exchanger can be bypassed should the temp in the room gets too high. Here’s an example of a MVHR unit, with a spec sheet.
The first of these boxes is the number of MVHR units installed. This is default set to 2 (the number of units we’re aiming to install). Other than cost, the main limitation here is the size and weight of the units, and the space consumed by the ducting (the default Carma 9035 unit uses ducting with a 500mm cross section). The ducts reduce in size as they branch off from the unit though. Our venue can accommodate a maximum of 2 units due to structural limitations, but we’ll probably start with one unit then aim to install another later in the year. Three units would have been better, but impossible due to structural limitations.
The next box is each unit’s maximum throughput measured in cubic meters per hour.
The air change period is time divided by the volume of the space divided by the throughput of the unit. So if a room is 1,000m3 and a unit is rated at 10,000m3/h the air will be changed once every 6 mins. However… an air change is never 100% efficient, and how much air actually gets changed depends on how well the vents are laid out. A typical ventilation system will have an ACH efficiency of 63.2%, meaning only 63.2% of the air will actually be replaced in any one air change, which is encapsulated by that last green box along the top.
The time on the left coincides with the air change periods, and the frequency of those vary depending on the capabilities of whatever MVHR unit is specified. The table defaults to 100 air changes, but it’s easy to copy and paste more to expand it. Bear in mind that these time intervals will vary depending on the capabilities of the equipment…
The spreaders column denotes how many spreaders are present during any given air change period. This is presently set to show 2 spreaders spending 3 hours in the space before leaving. This column can be used to model spreaders entering or leaving the space over the course of time.
The target column describes whether an uninfected person is present or not. This can be used to model how likely someone is to be infected depending on when they arrive/depart in relation to the spreaders; it takes a while for the aerosol to build up or be depleted, depending on the comings and goings. Only a “y” can be used to denote that a target is present (not case sensitive). Entering anything else in that column will mean that an uninfected person isn’t present during that air change period. This is presently set to show a someone entering the space after the spreaders have already been there for a while, then staying after the spreaders have left. Using this it’s possible to simulate people coming into the space at different times, before, after, or during the times that X number of spreaders have been breathing in there.
This only deals with aerosol risk, not contact risk or larger expelled droplets being coughed in someone’s face etc. It’s also assuming that people are properly distanced, as it can only predict the aerosol risk at distances where the aerosol has mostly dispersed into the rest of the air.
A spreadsheet is not the best way to calculate anything involving air changes; this is better done recursively. The spreadsheet does therefore result in some minor discrepancies. It might be possible to improve on this with an engineering formula that can calculate the percentage of air changed over a set time period, but we’ve been unable to locate one.
The calculator illustrates that a decent MVPR system may afford a cost efficient solution for mitigating the risk from aerosol infection, and that retrofitting such systems would be a useful measure in safely combatting the spread of this disease.