Why is Cecil surprised about exponential SPF?

I guess I’m the first to comment on Cecil’s (half-) column on multiple layers of sunscreen. At the end of the article, he says

Why would it be hard to believe? That’s exactly the effect you’d expect from multiple layers of shielding. SPF 8 means that you can stay out in the sun 8 times longer before you get burned. Approximately, then, that would mean that the sunscreen is only letting through 1/8 of the harmful portion of the light. Well, if you have two layers, then only 1/8 gets through the first layer, and of the portion that gets through the first, only 1/8 gets through the second layer, too. So your total sun exposure is 1/8 of 1/8, or 1/64, for an SPF of 64.

Now, of course, it’s possible that reality is more complicated than that, if, for instance, there’s some correlation between the light that gets through the first layer and the light that gets through the second (gaps in the absorption spectrum of the sunscreen, maybe). So one shouldn’t be surprised if it doesn’t turn out to be completely exponential. But sometimes, the way the world works really is actually simple, so one shouldn’t be surprised if it is exponential, either.

I can’t speak for Cecil directly, but when we were discussing some of the technical research behind it, I think both he, and I, felt like there would be much more to it from a biology and/or luminescence standpoint than a simple mathematical progression. He asked me to dig up a few additional technical papers on the subject for him to confirm it.

Sometimes things in the world are simpler than you’d think, but I’ll wager most of the time they aren’t.

Cecil should have then commented on why do they say beyond a certain SPF rating has no additional benefit? My wife WAGs that, if as Cecil says, people apply less than the recommended dose…then pehaps the higher SPF is to give the right protection at less than the rec’d amount? This theory might just be the real story! What say the sunworshipping Dopers?

I heard that anything over 15 SPF was a waste of money as it offered no added benefit. I’d be interesting in hearing more about that, too.

I’m a stickler for sun safety, so let me fix this. If your skin is totally unprotected, you will burn in 10 minutes of direct sunlight. For each SPF “unit”, you’re protected for another 10 minutes. So if you have on SPF 4, your skin will burn in 40 minutes. If you have on SPF 30, you have 300 minutes (in theory) before you burn. There are many variables that will significantly decrease that time. If you use Cecil’s information, you would expect to be able to be protected from sunburn for 4 hours with SPF 4 on. Anyone who’s ever been on a beach with SPF 4 on knows this is certainly not the case. Here’s a good rule of thumb: Double the time you plan to spend at the beach and use the SPF that will last you that long. Going to the beach for an hour? Plan on 2, so that’s 120 minutes, so slather up with at least SPF 15. And no, no matter how many coats you put on, you’ll still only be protected up to the SPF on the bottle. Cecil, where did you find this info?

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Julie, I merged your separate thread with this existing one.

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For some values of “you”. People will burn at different rates, depending mostly on degree of pigmentation. I (moderately dark but white) can stay out in the sun for an hour, and get a nice tan, while I have friends (pale-skinned redheads) who do indeed burn in ten minutes. Most black folks can, I imagine, safely stay out for significantly longer than I can.

The increase in effectiveness with increase in application would only work to a point, after which I would think consideration of mechanical factors would come into play.

Consider this example: whether you coat a surface in a soft lotion one inch deep or two, after you wipe it a few times with a cloth little will be left, and how much will be left will not be linearly dependent on the depth originally applied. More likely it will be dependent on the inherent properties of the lotion (viscosity and stickiness, how much is absorbed into the surface etc).

I would expect that if you graphed “amount of sunscreen applied” on an x axis against “amount remaining after half an hour of sweating, swimming, brushing against clothing etc” on a y axis the plot would rise initially but then flatten out. Lotion is just not something that can be piled on and expected to remain.

Did Cecil really imply this? He said:

“A sunscreen bearing a rating of SPF 15 means it’ll let you spend 15 hours in the sun and get the same exposure as one hour without protection. SPF 30 means 30 hours, etc. That’s a rough guide; variables include skin type, activity level, and so on.”

This doesn’t seem, to me, to be saying that people wearing SPF 15 can spend 15 hours in the sun and not get burnt. I’d say it means that people in the sun for 15 hours wearing SPF 15 (presumably with reapplication) will only get burnt to the extent they would have had they stayed in the sun for one hour, with no protection. As you noted, you will get burnt in far less than an hour.

So, no, Cecil did not say you can slap on SPF 4 and then spend 4 hours in the sun.

Cecil said

That is true only in a very general sense. One application of sunscreen will simply not last 15 hours. In fact, the SPF rating means how much longer you can stay in the sun without burning only with the following provisos:

[ul]
[li]you apply the specified amount - and people don’t. The correct amount is approximately a golf-ball sized dollop per limb, torso side and head. Assuming no amputations, that is 6-7 golfballs per person (allowing for a bald head, there!).[/li]
[li]you reapply the same amount as you applied as frequently as specified on the container[/li]
[li]you don’t remove any of the sunscreen by sweating it off, rubbing it with a towel or on the sand or washing it off by swimming[/li][/ul]

Given the above amounts, a small tube of sunscreen would do an average family one, maybe two, visits to the beach. Less if it has been sitting in the car glovebox since last summer.
The SPF rating is just a laboratory measure of the relative effectiveness of different sunscreens at preventing initial burning, under ideal specified laboratory conditions. It is best used to compare the effectiveness of one sunscreen to another, not to calculate extended sun exposure times. That is particuarly true of low SPF sunscreens, which are less likely to provide broad spectrum protection.

I too provided technical consultation to the Master on this one. The issue wasn’t theoretical but practical. The research indicates people use much less than the recommended amount. My guess was that’s because they don’t like having a thick layer of greasy stuff on their skin. I found it implausible that anyone would actually use a double thickness - you’d feel like buttered toast. However, I was willing to concede the possibility somebody using the correct amount on the first go-round might add a little more on the second application - maybe enough to boost SPF 8 to 16.

On further thought, though, that’s probably not what happens. The letter-writer is probably your typical mope who uses a quarter of the recommended quantity. If he’s using SPF 16, the actual protection factor is 2. If he adds a second layer, he in fact doubles his protection as he contends - but he’s merely going from 2 to 4. A third app takes him to 8, etc.

I may recommend to the boss that we amend the column to reflect what, in all likelihood, is actually going on.

Nope. High SPFs provide less protection than the label indicates because the SPF test measures skin reddening caused by UV-B radiation from an artificial source. Most sunscreens are not effective against UV-A, so extended sun exposure while using a typical sunscreen lotion will result in nearly unimpeded exposure to UV-A, which will probably not cause a sunburn, but which will result in tanning, skin aging, and an elevated risk of skin cancer. The better products out there incorporate UV-A absorbers to prevent this effect, but there is still no US standard for UV-A absorbance in sunscreen products.

But the Australian Standard does have a UVA test. It is spectrophotmetric rather than erythematous, but it is an attempt to evaluate the UVA absorption of a a sunscreen. Here in Aus, for a sunscreen to be labelled broadspectrum, and to get the higher SPF label, it must pass the UVA requirements as well as the SPF requirements. This is to ensure that the higher SPF claims do provide UVA protection while mitigating the burn aspect.

I think there is some misunderstanding of how sunscreens work (either by me or others in this thread). As I understand it, sunscreens are UV reflecting or absorbing materials (titanium oxides in the ones I use) suspended in a lipid/water base (lotion). You smear it on and the base is absorbed into your skin or evaporates leaving the active portion. Some versions I have used actually advised that you wait a half hour and apply a second coat, which should leave double the amount of active ingredients on your skin.

There are two effects going on:

  1. SPF 15 means that you can stay in the sun 15 times longer and still get the same amount of exposure. This means that 1/15 of the effective energy gets through. Two layers would, naively, mean that 1/15 of 1/15 gets through, or 1/(15^2) – SPF 225.

It is due to this effect, and the unusual way we define SPF, that you can get better than double. But there is another effect going on, which is why you don’t get SPF 225:

  1. The energy that causes tanning and burning is not all the same. Some of it is well-blocked by the sunscreen and some of it is not. For example, suppose you had an SPF 15 sunblock that 100% blocked those frequencies that had 14/15th of the energy but 0% blocked the other 1/15th. In this case, two layers would be no more effective than one. The second layer wouldn’t block any of the frequencies not blocked by the first because the sunblock isn’t effective at those frequencies.

Sunblock that works really well at the frequencies with the most energy but no so well at frequencies that are less important won’t stack well. Sunblock that works more or less equally well across all frequencies, even the ones that are not that important, will stack very well. The net effect depends primarily on the precise absorption profile of the sunblock.

Really? I had no idea there were no federal standards for UVA absorption. That’s very disconcerting :eek:

Seems to me there’s some conceptual problem here. Is sunscreen like paint, that it forms individual layers when it fully dries? Or is it more like an oil layer that gets smeared thin, then another application thickens the layer up a bit?