Tech. Note: High Extraction Flour

The recipe for Miche calls for high-extraction flour. From looking around the Internet and in some of my bread books, there appears to be some confusion about just what high-extraction flour is and how you can come by it (or fake it). So it seems worthwhile to describe what I've been able to piece together.

First, recall that a kernel is composed of three parts: indigestible outer coating or bran; the embryo or germ, the part that will develop into a plant; and the food for the developing plant or endosperm. With bread flour the germ and bran are removed leaving just the endosperm. With whole wheat flour, the germ and bran are also included in the flour.

Extraction is a measure of how much flour is extracted or milled from a given amount of wheat, i.e., how much flour is left after remove bran and germ. If you start with 100 pounds of wheat and end up with 70 pounds of flour, then you have an extraction rate of 70%. With whole-wheat flour, the entire wheat kernel is used so 100 pounds of wheat yield 100 pounds of flour and you have an extraction rate of 100%. With typical bread flour, the extraction rate is much lower, in the neighborhood of 70% to 75%. High-extraction flour lies somewhere between bread flour and whole-wheat flour. That is, more (but not all) of the bran and germ included in the flour. You can think of whole-wheat flour as the highest-extraction flour. Since high-extraction flour lies between whole-wheat and bread flour, its baking properties lie between the baking properties of whole-wheat and bread flour.

Since high extraction flour can be difficult to locate, home bakers typically simulate it. There are two approaches. First, you can take coarse or medium ground whole-wheat flour and put it through a sieve to remove some to the larger pieces of bran in the flour. If you start with 100 grams of flour and you "extract " or sieve out 10 grams of bran, then you are left with flour with a 90% extraction. It may seem odd that you are removing or "extracting" bran to get high-extraction flour, but you can think of it as going from "highest-extraction" flour to "high-extraction" flour. (I suspect this double use of "extraction" is a major part of the confusion.) You'll need to weight the flour before and after to determine the extraction rate. The extraction fraction is just the weight of the flour left divided by the weight of the flour you stared with.

Unfortunately, unless you have a whole range of different sieves, you won't have a lot of control over the extraction rate. Also, you'll need to use coarse or medium ground whole wheat flour, or everything will likely pass straight through your sieve. Working with King Arthur Organic Whole Wheat flour and using two different sieves, I was only able to remove about 4% of the bran.

A second, simpler approach is to simply combine bread flour and whole-wheat flour. This is much easier to do, but, unfortunately, calculating the quantities needed can be more complicated. Using the definition of extraction, I worked out the following formulas to calculate flour quantities. If

Q = quantity of flour desired
R1 = desired extraction rate (average high extraction rate)
R2 = given extraction rate (for bread flour)
W = amount of whole-wheat flour to use (100% extraction)
B = amount of bread flour to use (R2 extraction)

then

B = Q (R2 -R1R2)/(R1 - R1R2), and,
W = Q (R1-R2)/(R1-R1R2)

For example, if you want 100 grams at 85% extraction and you have 70% extraction bread flour, then

B = 100 * (0.7 -0.85*0.7) / (0.85 -0.85*0 .7) = 41 grams, and,
W = 100 * (0.85-0.7) / (0.85*0.7-0.85) = 59 grams.

This is the approach I used with my second go at the miche and it worked great!
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(There remainder of this post can be safely skipped by most readers. At this point I explain how I arrived at these equations. But, if you are so inclined, please read on and let me know if you see any problems.)

So, if you are interested, here is my reasoning:

First, a little background. Lets assume you want high-extraction flour with a 90% extraction weight and you are starting whole wheat flour and bread flour with a 70% extraction rate. If you have 100 grams of bread flour, that was what was left when 100/0.7 = 142.86 grams of flour was extracted. To get a 90% extraction rate, you will want to add enough whole-wheat flour so that the ratio of the total flour you have is 90% of the whole wheat flour plus the weight of the original flour that was extracted. If x represent the added whole-wheat flour, you'll need to satisfy the equation:

(100 + x) / (142.86 + x) = 0.90

That is, you'll need to add 285.71 grams of flour given a total of 385.71. In general, you can take the amount of flour you'll want and multiply it by 100/385.71 = 0.259 to get the amount of bread flour you'll need and multiply it by 285.71/385.71 = 0.741 to get the amount of whole-wheat flour you'll need.

Generalizing, let Q be the quantity of flour you desire, R1 is the extraction rate you desire, R2 is the extraction rate you have, W the amount of whole-wheat flour you will use, and B the amount of bread flour you will use. First, clearly the total amount of flour is just the sum of the whole-wheat and bread flour: Q = W + B

Next, the total amount of flour I would have started with before removing the bran/germ would be Q/R1, or, W + (B/R2). In the first case, we are averaging the removal over both flours, i.e., finding the effective extraction. In the second case, we are calculating the removal based on the actual bread flour used. Think of it this way---starting with a fixed amount of whole-wheat flour, we could sieve all the flour, case 1, or we could separate out part of the wheat flour, sieve the remaining wheat flour, and then add the removed flour back, case 2. Since these are equivalent, we can write: Q/R1 = W + (B/R2).

Its all downhill from here. Substituting (Q-B) for W and solving for B gives the first formula. Substituting (Q-W) for B and solving for W gives the second formula.