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Yay! It’s been a couple of months since we’ve done a dive into a measurement! If you happen to work w/ an interesting unit or measurement method, let me know!
It’s summer, and there was always a weird unit that never made any sense to me — SPF, Sun Protection Factor. It’s spattered all over sunscreen products, but no one really explained the the scale was. Thirty years ago, you’d find often things with SPF 15, then later SPF 30 products. Nowadays, it’s easy to find as SPF 50+ products. But I could never understand what that number meant.
So this week, I went on a bit of a research journey to understand this weird … unit? Is it even a unit? Somehow it turned into a wild goose chase that ended with learning about solar spectra.
Understanding SPF is a bit of a mess because there’s a ton of material published that is targeted at laypeople. There’s a lot of articles, posts, literature, and marketing that exists purely to explain to laypeople what SPF means in practical consumer terms. For consumers, it boils down to “higher is more protective of the sun”
Sun protection factor (SPF) value. The UV energy required to produce an MED [minimal erythema dose] on protected skin divided by the UV energy required to produce an MED on unprotected skin, which may also be defined by the following ratio:
SPF value = MED (protected skin (PS))/MED (unprotected skin (US)),
where MED (PS) is the minimal erythema dose for protected skin after application of 2 milligrams per square centimeter of the final formulation of the sunscreen product, and MED (US) is the minimal erythema dose for unprotected skin, i.e. , skin to which no sunscreen product has been applied.
In effect, the SPF value is the reciprocal of the effective transmission of the product viewed as a UV radiation filter.
— From the current FDA regulations FDA on sunscreen products
To understand the above definition, you’d first have to know that “erythema” is a medical term for when your skin turns red, whether from injury, disease, or most important in today’s context, extended exposure to sunlight. Sunburn is also known as “solar erythema”.
The “minimal erythema dose” has a ridiculously messy definition: The quantity of erythema-effective energy (expressed as Joules per square meter) required to produce the first perceptible, redness reaction with clearly defined borders.
So, as defined, the SPF is easier understood as the RATIO of the minimum amount of solar energy needed to cause skin reddening for skin protected by the product, divided by the amount of solar energy needed to cause reddening for unprotected skin of the same person. For example, for convenience let’s say the MED is 10 J/m2 for unprotected skin (a completely made up number here). If we coat the skin in a sunscreen product, and now it takes 150 J/m2 to get to the same MED reaction, we divide 150 by 10 and have an SPF 15 product.
If we assumed that we get constant solar radiation while outside and ignored things like moving, angle of sun, breakdown/erosion of the skin product, we could translate the solar energy units into time. So in theory, if it takes 5 minutes of sunlight to turn unprotected skin minimally red, SPF 15 product should give you 15x that, 75 minutes, because it’s filtering the sunlight that is reaching the skin.
But, even from that hypothetical example alone, you can see there’s a ton of assumptions needed to make SPF “work” from a practical perspective. We move around, go in and out of shade, the clouds do weird things to the spectra of the sunlight but still will let some amount of UV through. We sweat and rub the sunscreen off when we move. It also clearly states that that the protected skin has been coated with 2mg of product per square centimeter, which is a LOT of product. Significantly more than most consumers use.
So, despite the rough notion that “higher is better”, SPF still doesn’t really tell us all that much.
On top of the general low utility of SPF, there’s a lot of measurement issues involved in SPF. For example, the notion of MED, the minimal dose of sunlight that causes reddening of the skin obviously depends on an individual’s skin properties. People with darker skin are going to have massively different reactions to the same amount of sunlight. Plus, is there an objective measure of erythema? Someone with trained eyes might spot reddening before I could. Plus, measuring erythema must interact with skin tones. How does all this even work?
How SPF testing is done
The FDA regulations specifies a testing procedure for products to determine the SPF. It first breaks down human skin into 6 types, based on how their skin reacts based on 30-45 minutes of sun exposure after a winter season of no sun exposure.
I - Always burns easily; never tans (sensitive).
II - Always burns easily; tans minimally (sensitive).
III - Burns moderately; tans gradually (light brown) (normal).
IV - Burns minimally; always tans well (moderate brown) (normal).
V - Rarely burns; tans profusely (dark brown) (insensitive).
VI - Never burns; deeply pigmented (insensitive).
SPF testing is only done on subjects that are classified as Type I, II, and III. Subjects also have their medical history examined to make sure they don’t have abnormal responses to sunlight, like photoallergic responses. A minimum of 25 subjects are chosen, the number determined ahead of time, and a minimum of 20 subjects must produce valid data for the study.
These subjects have their skin on the back inspected to find a test site sufficiently even skin tone and without significant defects. That skin area of at least 50 square cm is divided into multiple areas used for testing.
The subject is then exposed to a “solar simulator” that provides doses of UV energy to the area. The time of exposure follows a geometric series where each exposure time is 25% more than the previous one, and they have to do a minimum of five exposure areas (and thus five different amounts of radiation).
Once exposed to UV, the immediate skin reactions of the subjects is recorded, apparently skin can redden or turn greyish/purplish as an immediate response to UV light but it fades within an hour. After responses are noted, the area is shielded from additional UV exposure and then the MED results are recorded 22-24 hours later. When done correctly, the subject would get a series of skin patches where some will have turned red from the UV (aka, become sunburnt) while other patches will not show any signs of sunburn. The MED is the first perceptible patch of skin that has turned red.
The MED is the quantity of erythema-effective energy required to produce the first perceptible, unambiguous redness reaction with clearly defined borders at 22 to 24 hours postexposure
Only after this time-consuming protocol is followed is the individual’s MED determined. Then, effectively a day after, the product test can begin, with a similar section of skin marked off and product applied. Product is applied to make a uniform film of 2mg/cm2 on the skin. After a 15 minute waiting period, the subject test area is then exposed to a a prescribed amount of radiation based on the expected SPF of the product. For products with an expected SPF greater that 15, the exposures shall be the unprotected MED times 0.76X, 0.87X, 0.93X, 1.00X, 1.07X, 1.15X, and 1.32X, where X equals the expected SPF of the test product. At the same time, one control site is given 1 MED’s worth of radiation to confirm that it’s the MED for that subject.
Then, another day later, the tester will check the protected skin to see which amount of radiation is the one that turns red. The data is collected from all 20+ subjects, and a mean SPF value with 95% confidence intervals using a t-distribution is calculated. There’s then some rules about how to round the numbers and various labeling requirements but those aren’t particularly interesting to us.
A problem with units
Throughout all this, I’m sure you’ve noticed that everything hinges on that magical MED number that is unique to every individual based on that particular subject’s skin reaction to simulated sunlight. There’s also the some procedural difficulties around exactly what “the first perceptible, unambiguous redness reaction with clearly defined borders” means in practice. So while the SPF rating is a standardized protocol designed to yield somewhat consistent results, it’s far from objective.
In fact, the International Commission on Illumination, the CIE, who you might remember as the group that defines color spaces and many things involved in color and light from a previous post about color measurement/distribution actually put out a publication in 1997 calling for adoption of a “Standard Erythema Dose” (SED). That is an objective measure of radiation set to 100 joules per square meter from the UV spectrum that’s tuned to the sunlight spectrum. They were concerned that practitioners were using MED like an objective unit and didn’t want things to get even more confusing.
This SED unit is useful because it’s an objective universal measure of a specified amount of radiation exposure, unlike MED which is individualized. For every individual, a certain amount of SED exposure will reach that individual’s MED level and their skin will redden from the exposure after 24 hours. For fair-skinned individuals, their MED is typically around 2.0-2.5 SED (source).
But despite these definitions, the SPF rating is still tied to the specified test procedure outlined in the FDA regulation (very similar procedures have also been adopted by various countries that also use SPF). In theory, it would be possible to calculate an SPF value based on measuring how many SED units a coating of sunscreen allows through over time, but the rating specifically demands this in vivo testing to be valid.
Either way, the utility of the SPF value is still a mystery. Perhaps the only thing I learned on this trip is that if I manage to put 2mg per centimeter of skin, I’d actually get the full protection of the sunscreen until the stuff wears off. In unrealistic perfect conditions, an SPF 50 sunscreen is supposed to give me 50x more time in the sun than unprotected skin, which is nuts.
Incidentally, there’s a separate rabbit hole of figuring out what the surface area of your body is and estimating how much percent of the body each body part takes to figure out how many grams of sunscreen you’re actually supposed to use. I’ll leave that for you to ponder over.
A deeper dive into the radiation from the sun
After reading all the stuff about SPF, I started wondering what was going on under the hood with the SED definition. Why did they specify a certain amount of radiation, why is it weighted to some mysterious “erythema action spectrum”, and how does it tie in with general UV exposure and the Sun itself?
After a lot of digging, slamming into a bunch of ISO standards hiding behind annoying paywalls, I came across the Tropospheric Emission Monitoring Internet Service of the ESA. Finally, someone posted a chart of the erythema action spectrum which describes how much our biology reacts to various wavelengths (the gist is UV-C is super bad compared to UV-A). They then take that action spectrum and multiply it with the distribution of UV reaching the surface of the Earth, which luckily absorbs a lot of the UV-C and UV-B. Doing so yields the chart above, and if you sum the area under the black dots, you get the value the UV Index in watts per square meter. Apparently, because on a typical summer day at the time the UV Index scale was developed was around 250 mW/m2 then they divided the amount by 25 mW/m2 to get the unitless UV Index numbers that range from 0-11+.
What’s interesting is that there’s a relationship between the UV Index and SED. Both use the same fundamental models for understanding the effects of UV radiation on the skin. SED is a dose measured in J/m2, and let’s assume a fair-skinned person takes 2 SED to reach MED and have their skin redden a day after exposure. A UV Index value is an integer of 0 to 11 that you multiply by 25 mW/m2. A watt is 1 joule per second. With a lot of annoying unit conversion, you can use these facts to figure out how many minutes it would take of unprotected exposure before you get a sunburn.
Sadly, there doesn’t seem to be an easy way to figure out what your personal MED level is, since the tests require specialized equipment. In theory if you had a lot of time on your hands, you could try to expose patches of skin on your arm to sunlight with a known UV Index. That would give you an extremely rough estimate of the amount of sunlight it’d take to make you sunburn.
It’s funny how just about the only thing there is to learn about SPF is that… SPF 50 is BEYOND enough for us… IF ONLY people used it properly. Apparently there have been calls from various people that the SPF definition needs to be redefined to be more in line with typical consumer usage. It’d probably take government action because no single company will ever want to adopt a new SPF standard that makes their rating lower while their competitors would show bigger numbers.
But who knows, maybe one day it’ll change.
While researching this, I stumbled on a short summary of the history of sunscreen and SPF that was pretty interesting.
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About this newsletter
I’m Randy Au, Quantitative UX researcher, former data analyst, and general-purpose data and tech nerd. Counting Stuff is a weekly newsletter about the less-than-sexy aspects of data science, UX research and tech. With some excursions into other fun topics.
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