The Fugue Counterpoint by Hans Fugal


Calipers and Science

Just for kicks I dug up the original Jackson/Pollock paper for skinfold measurements for determining body fat percentage. Turns out there's also a 7-point equation that also takes circumference of waist and forearm into account.

Here's a snapshot of the equations for men from the paper ("Generalized equations for predicting body density of men" by A.S. Jackson and M.L. Pollock, 1978. I couldn't find the PDF for the women paper online).
Generalized body density equations

Important notes: skinfolds are in millimeters, circumferences are in meters, and log is the natural log (ln in most computer languages). I plugged my values from two weeks back into a spreadsheet and got the following results:

JP Equation Density %BF
Sum of seven skinfolds
S, S^2, age 1.0518 20.62%
S, S^2, age,C 1.0476 22.51%
log S, age 1.0506 21.15%
log S, age, C 1.0482 22.25%
Sum of three skinfolds
S, S^2, age (5) 1.0607 16.69%
S, S^2, age,C (6) 1.0549 19.24%
log S, age (7) 1.0578 17.95%
log S, age, C (8) 1.0574 18.14%

The most interesting thing here is that there's a large difference between 7 and 3 site measurements, and the 3 site range is significantly larger. Also very interesting to note is that the one-site (suprailiac) AccuMeasure chart is, for me, in line with the 7-site measurement (22.1%). Given other measurements I've taken and just general guesswork based on what I see in the mirror, I think that is a decent estimate.

It's also curious that there are two sets of equations given, one using logs and one using squares.

Moral of the story: more data is better, sometimes not-enough more data is worse than a simpler estimate, and interesting things can be learned when you go to the original source. (This is just a quick note, but the paper is very interesting and reading it will be an interesting exercise that sets proper expectations for, and understanding of, the JP7 skinfold method).


Measurement Error in Soapmaking

Have you ever wondered what significance the measurement error of your scale has in making soap? What, you didn't realize your digital scale has measurement error?

If your scale has 1-gram precision (the norm these days), then if it says 42 grams it actually means that it most probably is between 41.5 grams and 42.5 grams. The possible measurement error is ±0.5g.

What does this mean in measuring ingredients for soap? Well, there are two extremes: lye surplus and lye deficit (or inversely, fat deficit and fat surplus).

On the one extreme, you may have 0.5g more lye than the scale says, and 0.5g less fat than the scale says. In that case, the extra 0.5g lye is actually close to 4 grams worth of fat. The exact value depends on the saponification value of the fat in question. For example, olive oil has a saponification value of 0.134, so 0.5g/0.134 = 3.7g worth of oil. That means that if you do indeed have an extra half gram of lye, you need 3.7g more oil than the recipe called for (for simplicity, assume the recipe has no lye discount/superfatting). Now factor in the possibility that you have half a gram less oil than the scale says, and you need 4.2g more oil to be 100% sure you are not lye-heavy. Of course your scale only does 1g increments, so you have to bump it up to 5g. So, regardless of the recipe size, if you add 5g oil to the recipe, you're sure to have at least the nominal superfatting, but perhaps more. Actually, probably more.

What about the other extreme—a lye deficit? If you have 0.5g less lye than the scale says, and 0.5g more olive oil than the scale says, then you have 0.5g/0.134 + 0.5g = 4.2g extra oil. Add that to your 5g that you added to be sure you're not lye-heavy, and now you've got about 9–10g more oil than the recipe calls for in the most lye deficit case.

Now, we want to add the first 5g to a non-superfatted recipe, for sure, so we know we're not lye-heavy. Then, the scale threatens to add another 5g, so it's entirely possible we get more fat than we are willing to tolerate.

What kind of impact do those 10 grams actually have? Well that depends on the size of the recipe. For most recipes you'll find on the internet, that 5 grams will be less than 1% of the total weight. No big deal. But if you, like me, are experimenting and making quite small batches it becomes significant. I like to aim for 1–5% superfat, but I'd be ok with 0–8%. So if I want no more than 8% superfat, and I add 5 grams of oil to be absolutely sure I don't go below 0% superfat, and the scale adds another 4.2 in the worst case, then I want a minimum batch size of 9.2g/8% = 115g (before water). That's a nice one-bar batch size.

Well and good, as long as you're not trying to observe the effects of superfatting, since you have such a wide range of possible actual superfat. For that you'd have to break down and make larger batches.

But what is the expected value of your superfatting? The extremes are actually less likely to occur than something much closer to the actual reading. As a simplification, just take the actual reading to be your expected value. So if you add 5g oil to a 120g batch, then you probably have about 4% superfat. 4±4% superfatted soap. It's alright by me.

So, a pure castile soap one-bar ingredient list:

102 g olive oil
13 g lye
25–30 ml water or milk (preferably goat's milk)

So in summary, if you have a 1g scale and you make small batches, the above is important to understand and take into account. If you have a 1g scale and make medium to large batches, then you are going to get within ½–1% of your target superfatting.

Oh, and of course none of this actually takes into account the accuracy or variation of those saponification figures.