Carbon Monoxide: convert gpm to ppm

In the US, car pollution is regulated by specifying gpm (grams per mile) limits. But the usual CO measurement is in ppm (parts per million). How to convert between these units?

Air weighs about 1.2 g per Liter. Warmer air would be less dense, and weigh less.

An old 1989 Volvo in Massachusetts is allowed up to about 30 gpm by state regulation, tested every two years. It is currently testing at about 10 gpm (8.4 gpm), although in previous years it has ranged from 3 to 25 gpm. (Just missed the general implementation by 1990 of a vehicle emissions limit of 3.4 gpm (grams per mile), a large reduction from the previous limit of 87 gpm.)

At idle, it takes about 3 seconds to fill an ordinary plastic shopping bag from the tailpipe. The bag measures about 11.5 L (Liter), so this is about 4 L per sec. If we guess that this idle engine load is equal to travelling at about 4 mph, this works out conveniently to about 1 L per sec per mph, which is also equal to about 1 g of air.

At 1 mph, it would take 3600 seconds to go one mile, putting out 3600 L with a mass of 3600 g. 10 g of CO for one mile, divided by 3600, works out to about 2800 ppm of CO.

2800 ppm would be at a similar level to smoking a cigarette, in terms of CO concentration. Breathing in the vicinity of such exhaust, if you were exposed to air diluted by 28 times, that would be 100 ppm. Not healthy, but not too terrible for a brief exposure for an ordinary healthy person.

Now let’s check against deriving ppm straight from the gpm. A mile is 1609 meters. Consider a car driving one mile, at any speed. Leaving behind an exhaust column of air, 1609 m by 10 cm by 10 cm. 16 m^3. One m^3 equals 1000 Liters, weighing 1000 g. 10 g of CO divided by 16,000 g of air would be 625 ppm, not too out of wack with the previous calculation.

If you are standing next to a stream of moving traffic, if the exhaust of each vehicle were mixed with a cross-section of at least 1 m by 1 m of air, which kept getting replaced with fresh air by convection/diffusion/wind, that would be a dilution of at least a factor of 100, reducing exposure to no more than 6 ppm of CO. Not much of a health concern, though not a good thing for repeated or continuous chronic exposure, particularly for the most vulnerable.

How do these theoretical calculations compare to reality? The higher levels should be easy to measure with current cheap digital home CO detectors, although they may not be very accurate. The lower levels will be harder to check. Current US home monitors are required to not show levels below 30 ppm, to reduce nuisance alarms. They can be forced to show lower levels, as a stored peak reading, but even that function is typically limited to readings over 10 ppm.

Presumably, badly adjusted cars may pollute substantially more. And all vehicles probably pollute more when first started, as they warm up. Most catalytic converters have to warm up before they work well at converting the CO. It is said that internal combustion vehicles can put out up to 25% CO (250,000 ppm).


Do you see a calculation mistake?
Is there a better way to think this through?


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