The CS Viamonde school board provided a response about the status of ventilation and air filtering at the La Mosaïque elementary school in the east end of Toronto on August 24, 2021. The letter is included at the bottom of this blog post

Executive Summary

Air filtering is vital to keep our kids safe in the face of COVID, especially in schools with little to no mechanical ventilation, filled with children who are unable to be vaccinated.

The CS Viamonde La Mosaïque elementary school plans to deploy two air purifiers per classroom and four in large room like gymnasiums.  The math doesn’t work.  This is an insufficient number of air purifiers.  More need to be deployed: at least three in classrooms and more in larger rooms.

The school board says that two air purifiers per classroom is acceptable to achieve the air change (ACH) target they have set.  It is not.  At least three are required if we run them at the noisiest fan setting, up to six are needed otherwise.

Discussion

In a letter from the CS Viamonde school board administration, dated August 25, the state of air purification plans for La Mosaïque were presented as 

1. There are to be two portable air purifiers in each classroom.  
   1. Assume these to be Austin Air HM400
2. A claimed performance of 7 ACH (air changes per hour) is achievable in the classrooms with these purifiers
   1. That’s 3.5 ACH per purifier, set by the board as the target performance
3. No details about class size are given (no surface area, no volume)
4. No details given about assumed fan speed setting
5. No details given about the rate at which air is cleansed by the filter.

With these issues in mind, we will look at four main scenarios: two based on the board’s assumption about air flow and class size (Scenarios 1 and 2), and two based on larger class surface area and a larger number of air purifiers (Scenarios 3 and 4).

Scenario 1: Optimistic flow rate (400 CFM) at highest (noisiest) fan setting

If the school administration assumed 400 cubic feet per minute (CFM), then the maximum class size for a total of 3.5 air changes per hour (ACH) per purifier can be calculated as follows:

Here is the equation in plain language: 

Here is the equation, stated in terms of measurement units:

Where “air change” is made to be unitless, so this simply gives us the square footage.  Next, let’s look the same equation, with numeric values used (400 CFM air flow rate, 3.5 air changes per hour, and 10 foot ceilings).  The equation, with units and numeric values, yields:

This means that the administration is assuming a classroom surface area of 686 square feet (e.g. about 25 feet by 28 feet), assuming a ceiling height of 10 ft.  This is very small. According one Ministry of Education document, regular classrooms can be assumed to be 750 square feet.^[1]

Scenario 2: Less Optimistic CADR value used on School Board’s Assumed Class Size

While 400 CFM is posted on the Austin Air website for the HM400, that value is determined without the filter in place on the purifier.  A more realistic, and accepted, value is 250 CFM, as this better represents air flow rate with the purifier’s filter engaged. 

Using the 250 CFM value, we can calculate the room size given the school board’s target of 3.5 air changes per hour (ACH).

This results in a class size of 429 square feet.  Clearly, this is an impossibly small size.  It seems reasonable to conclude that the CADR value was not used by the school board in its allocation of air purifiers.

Scenario 3:  CADR Values on 750 Square Foot Classroom At High and Medium Fan Speeds 

Let’s examine manufacturer values for air flow on a more representative class size: 750 square feet, with 10 foot ceilings, using CADR values for air flow.  We will also reduce the air change rate  from 7 to 6 ACH, as that is what is typically aimed for as  the top end target for schools.

3a: Fastest fan speed & 750 square feet (noisy)

We need to furnish a sufficient number of purifiers to cleanse the air.  We will use a class size of 750 square feet and 10 foot ceilings (7500 cubic feet), as per the Ministry’s document, and the air purifier set to maximum fan speed and the CADR value at that fan speed to determine the number of air purifiers needed.

It is apparent that for a 750 square foot classroom, with the purifiers set to the noisiest and highest fan setting we need three purifiers, not two, per classroom.

3b. Medium fan speed & 750 square feet (less noisy)

Noisy fans are likely to be turned down to a quieter setting unless teachers, staff, parents and students accept the noise as necessary.  In the event that the noise is not tolerated, we need to see the effect of a medium fan speed setting on the number of purifiers needed.  Here is the required number of air purifiers for this scenario:

Six air purifiers are needed for a 750 square foot classroom if we only run the air purifier on the medium speed setting.  That’s three times the number of air purifiers currently being allocated per classroom!

Scenario 4:  CADR Values on 900 Square Foot Classroom At High and Low Fan Speed 

A conservative approach is appropriate in scenarios like this, so let’s assume a slightly larger class size -- larger than 750 square feet.  Most certainly, the gymnasium, which has a target of only four air purifiers, is.  Let’s run the numbers for fast and medium speeds for 900 square foot rooms.  Again, we’ll use 6 ACH instead of 7 ACH as that is more typical of what is envisioned as top end target for schools.

4a. Fastest fan speed & 900 square feet (noisy) using CADR value for air flow

Four HM400 air purifiers are needed in this scenario, not two as suggested by CS Viamonde.

4b. Medium fan speed & 900 square feet (less noisy) @ using CADR value for air flow

Seven HM400 purifiers are needed in this scenario, not the two suggested by CS Viamonde.  In the gymnasium, which is much larger than a regular classroom, it may be best to aim for this number, rather than only four.

Recommendations

It is apparent that more air purifiers are needed in the classrooms before the start of the school year.  This could be done by employing one or more of the following strategies: (1) buying more HM400 units from Air Austin, (2) redistributing the existing stock so that rooms with no or little mechanical ventilation are prioritized for reception of air purifiers, or (3) alternative approaches to construction of air purifiers using off-the-shelf components be examined.

The CADR values were provided by an Austin Air representative when requested.  As with all large scale purchases of this nature, the customer (CS Viamonde) should do its due diligence and have the flow rate of the air purifiers verified by a third party to make sure that it’s not even lower than the CADR value provided.

Conclusion

Air filtering is vital to keep our kids safe in the face of COVID, especially in schools with little to no mechanical ventilation, filled with children who are unable to be vaccinated.  

The CS Viamonde’s La Mosaïque elementary school plans to deploy two air purifiers per classroom and four in large room like gymnasiums.  The math doesn’t work.  This is an insufficient number of air purifiers.  More need to be deployed: at least three in classrooms and more in larger rooms like gymnasiums and special care should be taken whenever children are required to remove their masks (e.g. when eating).

The school board says that two air purifiers per classroom is acceptable to achieve the air change (ACH) target they have set.  It is not.  At least three are required if we run them at the noisiest fan setting, up to six are needed otherwise.

James Andrew Smith, PhD

Associate Professor, Lassonde School of Engineering

York University

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^[1] 750 square feet per classroom value from pg 11 in https://efis.fma.csc.gov.on.ca/faab/Capital%20Programs%20Branch/Report%20of%20Expert%20Panel%20-%20Building%20Our%20Schools_Building%20Our%20Future%20-%20ENG.pdf.

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It's important to point out that I have an interest in this, generally, but do not have a technical background in ventilation or PPE, in spite of my mechanical engineering degree or any work I've done in biomedical engineering -- so any opinion I express on this topic is not officially within my area of technical competence and should not be taken as a "professional engineering recommendation". If you're looking for proper professional advice on PPE, HVAC, etc., hire a registered Professional Engineer who is trained and who practices in those domains.