Last year my 4-year-old can of bear spray reached its expiry date, completely unused, and I wondered how sound the basis of that date was. Thus began a journey with a very strange end-point. I'm a lifelong student of sincere, accredited pseudoscience - passing for the real thing in academe - but I could hardly believe I had run into so flagrant a specimen in this seemingly tiny and straightforward case.

Dealing first with the motivating question: the web showed plenty of people wondering or asserting on spray longevity, several outdoorsy sources reporting test results, and one journal article from researchers at Brigham Young University.

The good news starts with: the active ingredient, capsaicin, does not degrade.

It continues with: the other big concern is propellant leakage - and you can check that by weighing the can. Mine weighed 300g new (contents 225g), and still weighed 300g four years later. Bear Beware Solutions, based in Alberta, suggests discarding the can if the weight drops below 75% of original. An intriguing hypothesis is that this is the rule which should be on the cans.

Testers did find sub-par function in some old cans. Unfortunately, nobody bothered to weigh them - so we don't know for sure if they had leaked, and were underweight.

Some experts did suggest a brief annual test fire to verify that the stream was up to par; I went with that. I sprayed a decent blast - about half a second, I reckon - and it was impressive: a vigorous yellow cloud, blasting out perhaps 5-6 metres. The cans hold about 7 seconds' worth of spray, and when I weighed mine it was down by 16g - 7% of the net weight, consistent with 1/2 second. So I'll be able to test 5 times before hitting Bear Beware's suggested limit - which will double the lifespan of the can.

The journal article: babes in blunderland

An Investigation of Factors Influencing Bear Spray Performance | BearWise

(Journal of Wildlife Management, 2020)

This article had me scratching my head right away: the abstract said things that just didn't make sense - notably

We… documented that bear spray head pressure declines in a logarithmic, not linear, fashion; over half of a new (7‐sec spray time) canister's pressure was lost in the first 1 second of spray

This is not just wrong - it's amazingly disconnected from reality. There are plenty of videos of people blasting entire cans out during tests - and the stream does not falter - it blasts out straight and strong until the propellant is exhausted, and then stops. What's more, these researchers mention filming 8 such trials themselves. Bewilderment matured into fascination. I needed to understand what path they had wandered off on, and how they ended up able to ignore the plain evidence of their senses.

Aerosol cans work on phase change. That's what makes it possible to cram a bucketful of shaving cream into a small can. The propellant is almost all liquid in the can (pressure circa 3.5 bar for bear spray's propellant, around room temperature) - and flashes to vapor as it exits the nozzle into the 1 bar environment. Droplets of propellant liquid become bubbles - and that's how you get foam. Numerically, the propellant in the little bear-spray expands to 33 litres at 1 bar.

For that system, declining "head pressure" due to mass depletion is not a thing. As liquid is expelled, pressure in the can is sustained by evaporation. There's a curve that relates temperature to what's called "saturation pressure". These researchers were imagining the physics of a scuba tank, and using that to interpret an aerosol can.

It turns out they had also, somehow, not realized they could just weigh the can to track expulsion. Instead, they made a complicated and thoroughly misconceived test rig. They let the can (circa 200 ml) squirt into a piece of tubing of around 24 ml, measuring the pressure in the tubing, emptying it, and repeating - 128 times, it turned out, to empty the can (... maybe).

Proceeding... using impressive-to-them terminology such as "linear regression", they pronounce:

Our research shows that at 4 years roughly 7–8% of propellant will have escaped (Fig. 11). This loss corresponds to a 40% reduction in head pressure given pressure depletion curves (Fig. 10).

To reiterate: this scuba-tank pressure depletion curve idea is a naive misconception. So what are they measuring, in that tubing? What changes rapidly in the first few releases, that can explain this curve? The answer is temperature: flashing absorbs latent heat of vaporization; something has to get cold.

Pressure in the can is dropping, but not because it's getting empty - because it's getting cold. So long as there's any liquid left in the can, the pressure you're measuring doesn't tell you how much mass there is - it tells you the temperature. Each data point is the saturation pressure corresponding to a certain temperature, and what they actually recorded was their own chilling of spray cans - down to the one-bar boiling point, which is the asymptote: -26° C. At which point the can no longer squirts. We don't even know if there was liquid left, just too cold to evaporate.

So, the ability to generate graphs does not necessarily imply the ability to understand what they mean. Pretty, though:

Their prose is similar - they were trained to sound like they knew what they were talking about, whether they actually did or not:

The sequential de‐pressurization of bear spray showed an initial steep loss of pressure followed by a much slower loss until all pressure was exhausted (Fig. 10). The relationship between trigger number and resulting head pressure was highly correlated (R2 = 0.94) and logarithmic. The logarithmic regression equation that best fit these data can be used to predict the loss of head pressure and contents as a function of triggering. For example, assume a person has fired a 1‐second burst of bear spray. Because a 225‐g can of Counter Assault™ will spray for approximately 7 seconds, a 1‐second burst (1/7 of the total spray time, or 1/7 of 128 triggerings = 18) can be used in the regression equation to show that 150 kilopascals remain after 1 second (44% of total pressure). The first second of spray released more of the contents than the remaining 6 seconds, and this suggests that test firing canisters quickly diminishes the ability of bear spray to protect the user.

Gemini wrapped up the analysis like this:

Your conclusion regarding the dissipation is mechanically precise. The 24 ml tube acts as a temporary reservoir for both the expelled mass and the thermodynamic work invested in compressing it. The dissipating "whoosh" permanently ejects that energetic investment into the atmosphere. The test rig essentially operated as a pneumatic heat pump, systematically refrigerating the main canister through 128 discrete mechanical strokes.

It is surprising, at least initially, how often accreditation turns out to be a Potemkin facade, until you get your eye in, and realize that these things propagate, and perpetuate, as the Potemkin pseudo-erudite become the accreditors of the next generation.

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I have emailed the Journal of Wildlife Management.
Subject: critique of technical illiteracy and profoundly false conclusions in 2020 bear-spray article
Body: MIT physicist here. You need to read this: (LW link).