(This blog has been updated: the CO2 generation rates for teenagers and children have been corrected to match the figures in the Harvard materials.)
Welcome to the second part of our four-part series on Indoor Air Quality (IAQ) Advocacy Basics.
In the last blog, Dispelling Dimension Disorientation, we went over the basic units in which we've seen ventilation and portable HEPA filtration quantified. The lack of an obvious relationship between some of these disparate units can make them difficult for IAQ advocates to compare, evaluate, and advocate around. This is especially true where CO2 concentration (ppm of CO2) is concerned.
This blog is meant to Clear Up Conversion Confusion by providing a reference for converting between these units, based on equations disseminated by public health and HVAC experts.
The first contestant will be the unit we've found most prevalent in scientific literature, air change rate, indicated in air changes per hour.
Air Change Rate (ACH)
To compute an air change rate in imperial units, you need to know the airflow in cfm, the room area in square feet, and the ceiling height in feet.
You can compute air change rate as shown in Equation (1):
(1)
In our experience, many people underestimate room area. For reliable results, it is best to get measurements. A laser measuring tool can be had for $15 - $30, and can make the job a lot quicker than using a tape measure.
If you need to compute the combined clean air delivery rate (CADR) you'll need from portable HEPA filters to achieve a particular air change rate, you can algebraically solve Equation (1) for cfm, yielding Equation (2):
(2)
When advocating, it is important that both you and the facilities staff you speak with understand that the relevant kinds of airflow for decreasing the spread of airborne illness are from Outdoor Air or from portable HEPA filtration. If recirculated air is filtered, it can produce some proportion of equivalent clean air, but this may have considerably less impact than Outdoor Air or portable HEPA filtration unless a MERV 13 or at least MERV 11 filter is used with significant, continuous airflow. If you suspect that you are receiving answers in terms of air changes from supply air that includes recirculated air, elicit clarification and reiterate that the recommendations are applicable to Outdoor Air or portable HEPA filtration, and are not directly applicable to recirculated air (at least, not without proper calculation).
Air Change Rate Scratch Pad
We've created a spreadsheet for computing values involving Clean Air Delivery Rate (CADR, in cfm), air change rate, and room area (in square feet), here:
You can copy or download this spreadsheet to begin calculating numbers on your own.
Airflow per Person (cfm/person)
To compute airflow per person, you need to know the overall airflow and the count of occupants, as shown in imperial units in Equation (3):
(3)
If you know the airflow per person and wish to compute the overall airflow (such as to use along with room dimensions to compute an air change rate), you can solve for cfm and compute overall airflow as shown in Equation (4):
(4)
US advocates will most often encounter airflow per person expressed in imperial units (such as in state mechanical code); meanwhile, foreign and international organizations commonly use the SI liters per second per person (L/s/person). It is helpful to remember that 10 L/s equals about 21 cfm.
CO2 Concentration (ppm of CO2)
This one's detailed, so we're going to show you a spreadsheet that you can copy and use to perform this calculation.
First, we'll caveat:
These equations are only accurate if the CO2 concentration has stabilized to a single value (i.e. is not significantly increasing or decreasing over time).
Second, we'll show you where the equations come from.
The Harvard T. H. Chan School of Public Health indicates that you can compute an estimated/expected CO2 concentration if you know the cfm of incoming Outdoor Air, and the number (and age) of the roomâ€™s occupants, shown in Equation (5).
(5)
You can measure the concentration of CO2 outside and plug it into this equation, usually between 400-450 ppm; in the T. H. Chan School's slides, the outdoor CO2 concentration is assumed to be 400 ppm. Meanwhile, you can estimate the CO2 generation rate by counting the occupants of each type and adding their CO2 generation rates together. Following are the CO2 generation rates disseminated by the T. H. Chan School of Public Health in their slides, which have yielded very close agreement between computed estimates and reference figures in the test calculations we've performed using school CO2 data that parents have submitted to us here.
Type of Occupant | Estimated CO2 Generation Rate |
Teacher - standing, speaking, age 30-40 | 0.013 cfm |
Teenagers (age 12+) | 0.0087 cfm |
Children under age 12 (ages 6-11) | 0.0066 cfm |
As parent advocates, we most often find ourselves in the reverse situation compared to the equation presented in the T.H. Chan School's slides: we wish to determine the airflow, but we only know the CO2 concentration we see on our CO2 monitor. We can algebraically solve Equation (5) for airflow, yielding Equation (6).
(6)
One source claims that ASHRAE has used this equation since 1981 to relate outdoor airflow rates to individual CO2 generation rates; dividing both sides by room occupancy yields Equation D-1 in ASHRAE Standard 62.1 Addendum D for relating per-person outdoor airflow to per-person CO2 generation rate.
Ventilation Rate Scratch Pad Spreadsheet
If you need to square up school ventilation claims with observations made using CO2 monitors and with recommendations and risk reductions from scientific literature and authoritative sources, we've created a spreadsheet you can use:
Like the air change rate spreadsheet, you can copy or download the spreadsheet to begin calculating numbers on your own.
To get started, enter the room dimensions and occupancy for the classroom environment for which you would like to convert ventilation rates. The spreadsheet starts with an example size and occupancy that you can change to fit your scenario:
Once you are satisfied with the classroom, you can use the scratch pad to convert from one ventilation rate to another. For instance, if you are given a ventilation rate in cubic feet per minute per person (cfm/person), you can type that in place of the cfm/person value to learn how many air changes per hour, liters per second per person, and how many ppm of CO2 that would coincide with in your hypothetical classroom scenario.
The constants for outdoor CO2 concentration, and for per-person CO2 generation rates, are listed in the Constants section of the spreadsheet. For information about the equations used to convert between units, you can refer to the Equations sheet of the spreadsheet (or just scroll up in this very blog).
Conclusion
We hope this second part of our four-part blog series provides clarity for parent advocates trying to make sense of the disparate units that appear both in the expert recommendations, and in the answers that they are getting from schools.
Now that you know the units and how they relate, stay tuned for our third blog in this series: Eliminating Recommendation Consternation!
Comments