Reinventing the Bread Baker’s DDT Formula, Pt 1

If you’re a bread baker, you might have heard of the desired dough temperature (DDT) formula, which bakers use to start their dough out at the right temperature. It looks something like this:

I’ve always been a bit bothered by this strange formula. The math behind it doesn’t seem to make sense and worse, it’s just never been that accurate for me. For the last couple of months I’ve been working on developing a better one and I’m really happy with the result.

TL;DR

• Even though it’s been in use for over 100 years, the currently accepted DDT formula doesn’t work well for many bakers.
• I developed a newer formula based on the principles of thermodynamics that’s 12x more accurate (YMMV!).
• The new formula is open source and freely available. There’s an online version so anyone can use it and javascript source so you can put it on your own website, blog, etc.
• It’s also built into our iOS app Rise.
• Part 1 covers background and history.
• Part 2 covers the math and science behind the new formula.
• Part 3 looks at the accuracy of the new formula.

For me it was quite a journey, involving 51 dough experiments, 52.3kg of dough, 600 individual temperature readings, and a minor ecological disaster when my trashcan full of spent dough unexpectedly fermented and spilled out onto the street.

Background

First, some background about the concept itself. In bread baking, “desired dough temperature” (DDT for short and sometimes called “final dough temperature”) is an important idea. If you’re following a recipe that says the dough should be 78°F (26°C) after mixing but you instead start with 70°F (21°C) dough, all of the fermentation times in the recipe are going to be off by a wide margin and you might end up underproofing and ruining the bread.

To understand why this is, take a look at this graph which shows how sourdough yeast activity changes based on temperature:

Just a 2°C increase in temperature can result in a 25% increase in fermentation rates! So clearly it’s important to begin the process with your bread mix near the prescribed temperature. But how do you do that?

Most bakers today solve this problem by using what I’ll be calling the common DDT formula. The idea is that you can’t easily control the temperatures of your ingredients or the air around you, but you can control the water temperature. So you give the formula the desired final temperature, the temperature of the air, flour, and (optionally) starter, and it tells you what the temperature of the water should be to arrive at the final temperature of the mixed dough.

It works like this:

• Multiply the target temperature by 3
• From that, subtract the air temperature, flour temperature, and a “friction factor” (more on this in a bit)
• The result is the temperature to measure out the water to

The friction factor is meant to account for heat added by friction during the mixing process.

Here’s another example:

Here the formula tells us that the water must be 89°F (32°C) to arrive at the target temperature of 78°F (26°C).

Strangely, this formula doesn’t take into account how much flour or water there is and seems to give air temperature as much importance as flour temperature even though air is obviously much less dense. And as I mentioned, it’s never been very accurate for me. Even while continually adjusting my “friction factor”, my final temperature was regularly off by 3-5°F or more.

Given my difficulties with the formula I was really curious why for at least 100 years so many baking books, magazines, websites, and apps (including our own…until now) have espoused this method, often without any caveats. (E.g. the Food and Agriculture Organization of the United Nations, which doesn’t even mention “friction factor”.)

Origin Story

Where does this “common DDT formula” come from and how did it become so widely used?

While I still don’t have the full picture of how this practice originated and evolved, I did manage to put some of the pieces together.

One of the oldest references to a DDT formula I could find is from the Journal of Industrial and Engineering Chemistry, Vol 12 (1920)(p. 762–763). Ironically, this old formula is also the most sophisticated of all that I’ve found published. It uses constants such as the specific heat capacity of flour and water, heat of hydration in BTU/lb along with thermodynamics concepts such as the conservation of energy and, as they call it, “the law of mixtures”. Interestingly, they eventually boil their formula down to a very simple:

Where Tw is the temperature of the water and Tf is the temperature of the flour.

But as the book warns,

This formula is an "ideal" one and does not hold under practical working conditions, which are complicated by the heat of stirring and the exchange of heat with the room and with the mixer.

Ultimately the book advises using trial and error to identify the best "K value" and substituting it for the 123 above.

Also interesting from this book is the later discussion and comparison of "common" methods for DDT calculation, just as I'm doing now, but 100 years ago! It goes on to say,

A third formula corrects for the heat of hydration by arbitrarily subtracting 10° from the sum of the temperatures of the flour and the water. Thus if the dough is to be 80°, 150 (2 x 80–10) is the quantity from which the temperature of the flour must be subtracted to obtain the proper temperature for the water.

That sounds exactly the same as the formula commonly in use today. And a footnote tells us that this formula is widely used in the form of copyrighted tables from Washburn-Crosby Co., called the Washburn-Crosby Dough Sheet. After some digging I was able to find the table, first published and copyrighted in 1912:

You might know the Washburn-Crosby Co by its current name, General Mills. (Incidentally, if you've ever listened to WCCO radio in Minneapolis, you're listening to Washburn Crosby Company radio, then known as the Gold Medal Station, after their Gold Medal Flour that's still sold today.)

So it's hard to say for sure but apparently the common DDT formula that's still in use today originated in the early 1900s and was made accessible to the public via Washburn-Crosby's "dough sheet" which was an addendum in many recipe books of the time.

That Pesky Friction Factor

What makes the common DDT formula difficult and potentially unreliable is this seemingly arbitrary "friction factor" (some bakers call it the "fudge factor", which is more apt; friction has little do with it). Unfortunately many popular baking books and websites give specific numbers for the friction factor without barely a hint that these are to be arrived at through experimentation. King Arthur flour, for example, says to use an FF of 22–24°F if mixing with a mixer and 6–8°F if mixing by hand. Cooks Illustrated? 5° or 20°. Unfortunately, this misinformation seems to have propagated through smaller blogs and social media for many years.

So how should this "friction factor" be used?

Both the oft-cited Conversion Factors and Technical Data for the Food Industry by the Pillsbury Company (1959) and Bread Baking, Vol 10 by the United States Army (1969) instruct the baker to first calculate the "friction factor". This can be done by taking the common formula:

And restating it in terms of FF:

With that in hand, you're advised to do a trial run using your own equipment. For example, let's say your flour is 70° (Tf), the air temperature 68° (Ta), and the water is 80° (Tw). You mix them together and the final mix is 75° (Tt). Then:

In part 2 I'll present a newer formula based on principles of thermodynamics and chemistry.

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