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Kitchen Notes: Analyzing a Baking Recipe
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Cooking For Engineers

Joined: 10 May 2005
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PostPosted: Tue Jul 13, 2010 2:00 am    Post subject: Kitchen Notes: Analyzing a Baking Recipe Reply with quote

One of the most embarrassing moments of my life involves baking muffins for a visitor in my apartment back in April of 2007. At a little before 8 in the morning I had flour, oil, and eggs but no milk. I knocked on the door of my neighbor - who I'd seen only twice before and luckily she was home and let me borrow some milk. Like the good ol' days, huh?

One problem was averted yet another arose.
These "muffins" I was making actually had to be good, not the barely eatable non-sense I usually made. Having no other game plan I threw something together, prayed, and dished out my questionable muffins to my guest. What a bad host I am!
That day, I thought really hard... so what exactly are baked goods? We say "pie crust, muffin, cupcake, coffee cake, puff pastry, and croissant", but do we know what they actually mean?

I used to dismiss baking as making goo or sugar covered pillow-like bread, but this is not entirely true. Yes, the essence of baking can be hidden behind all the goo, but this is obscenity encroaching on the fine art of baked goods and unfortunately unless one is a connoisseur the fundamental distinctions are not noted very well. So I spent some time - a really long time - baking, serving, and eating cakes, cookies, coffee cakes, etc. trying to figure out what fundamentally defines baked goods. I finally came up with an answer which was naturally due to my initial false assumptions and failures.
I tried using a numerical range, but after following this method and getting unsatisfactory results I knew there was still room for culinary error, something that was unacceptable. I envisioned having a few criteria one could follow and from there spontaneously throw in random ingredients like a flux capacitor to get a satisfactory batter or dough for a baked good.

After pouring through countless recipes I finally created a procedure to accurately characterize baked goods, in it, we must employ three calculated values. These values are the moistness value, butter(oil) content, and the egg content; all obtained from a recipe.
Of course, a recipe provides a list of ingredients and measurements, which includes instructions for combining the ingredients. Each ingredient can be considered either a wet or a dry ingredient. In the following procedure, most wet ingredients are given constant values (see Table1.), while flavorings, leavenings (baking powder, baking soda, yeast, etc.), seasonings (e.g. salt), and food pieces (shredded coconut, walnut pieces, blueberries, etc.) are omitted. The constant values are multiplied by their respective quantities (in cups) yielding a product. The products are summed and finally divided by the dry ingredient product (obtained from Table 2.) to yield a solution called the moistness value.

I know... "How can you possibly use volume (cups)?" Either volume or mass can be used assuming standard mass/volume conversions, but I found using volume greatly simplifies the calculations.

But what is this beast of a procedure? Does it design baked goods? Does it analyze baked goods? After years of reinventing itself, the procedure has settled in the role of a design tool which aides in creating new recipes, an analysis tool for reviewing recipes with no need for baking, and a characterization tool which attempts to define all possible baked goods. Immense, yet its most useful role is likely in allowing one to substitute ingredients.

Wet IngredientValue/cup
banana (mashed)0.375
butter, oil, shortening0.5
cream cheese0.35
cooked (sweet) potatoes0.5
cranberries mashed/pulsed with sugar0.2
grated carrots1/3
jumbo eggs1/4
extra-large eggs1/5
large eggs1/6
large egg yolk1/8
large egg white1/24
honey, milk, molasses, orange juice, water1
sour cream, yogurt, whipping, heavy cream0.7

Table 1. Values for some common wet ingredients

Dry IngredientValue/cup
almond paste1
finely ground pecans, walnuts, almonds1/3
flour (cocoa powder, whole wheat, all-purpose, etc.)1
old fashioned rolled oats0.5
melted chocolate (non-dark)0.5
peanut butter2/3

Table 2. Values for some common dry ingredients

All values in Table 1 and Table 2 are "per cup" except for eggs which is "per egg". Let's look at an excerpt from an example recipe.

3 1/2 cupsall-purpose flour-3.5
1 teaspoonbaking powder--
1 teaspoonbaking soda--
3/4 teaspoonsalt--
16 tablespoonsbutter0.5-
2 cupssugar--
3large eggs0.5-
2 teaspoonsvanilla extract--
2 cupsold-fashion rolled oats-1

Table 3. Sample mystery recipe

 wet/dry = (ax1+bx2)/(cx3+dx4) = y(1)

wet/dry = (16*(1/16)*(1/2)+3*(1/6))/(3.5*1+2*0.5) = 0.22(2)

In equation (1), a, b, c, and d represent quantities for wet ingredients x1 (butter) and x2 (eggs) and dry ingredients x3 (flour) and x4 (oats) respectively. Equation (2) provides an accompanying practical calculation for equation (1).

Note the following relations:
3 teaspoons = 1 tablespoon
16 tablespoons = 1 cup

The resulting moistness value, butter content, and egg content are: 0.22, 11.1%, 0.67E; (0.5/4.5) and (3/4.5) gave us the butter and egg content respectively (see next section for an explanation of moistness, butter content, and egg content). These are our characterization numbers. From using Table 4 and our characterization numbers, we see this is some sort of a cookie.

[Note from the editor, Michael Chu: Michael Ohene's Table 4 was too detailed to present in HTML here, so click on this image to load a PDF showing the complete table.]
Periodicity of Baked Goods in the USA
Table 4. Periodicity of Baked Goods in the USA

Explanation of the chart (Table 4)
Moistness - wet ingredient to dry ingredient percentage1 2.A higher moistness value corresponds to a more fluid/less stiff batter.
Butter content - butter/oil/shortening to dry ingredient ratio. On the chart the butter content values are divided into "low", "medium", "high", and "very high" to make the chart more intuitive.
Egg content - number of eggs to dry ingredient ratio.

Table 4 was formed by plotting hundreds of recipes. Anything falling within a grid is what that grid is labeled (e.g. scone). Some grids are empty because it would not make sense for them to exist. For example, a very moist bread (0.60) with a low butter content would be airy and tasteless.

Results and interesting facts
Unlike most other baked goods cakes have an extra criterion, when buttermilk is replaced by a constant value of 1.75, a cake must equal a value between 1 - 1.25. This requirement is due to the acid content in buttermilk.

Also notice that having one or more eggs per a cup of dry ingredients results in a cakey baked good. Therefore if you are experimenting with chocolate chip recipes and use a cup of flour, you must discard some of the egg you plan to use.

A moistness value of 0.35 - 0.47 usually results in a yeast dough. A moistness value above 0.50 cannot be kneaded.

The baked goods (brownies, cookies, cakes, etc.) that kids like are on the outer edges of Table 4.

Can you find a recipe that defies the logic (is outside the groupings) of this chart? Sometimes, but it most likely received bad reviews.

Final notes: Mixing instructions, directions on how to combine ingredients, are usually shared for similar types of baked goods. For example, you always use cold water for pie crust recipes.

Leavening (baking soda and baking powder): used to make a dough or batter rise when baked. Table 5 below shows common leavening ratios. What is a leavening ratio? Comparing teaspoons of leavening to cups of dry ingredients is a good rule of thumb. For example, in Table 3 the leavening ratio was 0.44 for our cookie. Also, if you use an acid (e.g. buttermilk, vinegar), baking soda must be included.

Baked GoodLeavening Ratio
shortbread cookie0 - 0.15
cookie0.15 - 0.5
pound cake0 - 0.8
muffin0.8 - 1.66
cake0.8 - 1.66
biscuit1 - 2.5

Table 5. Leavening ratios

Have fun!

1When a glaze is used - usually for pound cakes - the moistness value increases by 0.05. For example a moistness value of 0.66 will become 0.71 if a glaze is used.^
2This assumes standard/normal baking temperature and pressure/altitude.^

Michael Ohene is an electrical engineer by profession with a mathematical interest in simplification through pattern discovery. Baking analysis is only one aspect of his fascination with modeling and classification.
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Steve C

PostPosted: Tue Jul 13, 2010 6:04 pm    Post subject: Sweet Potato Reply with quote

This is good information for the next time I attempt a sweet potato gnocchi.
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PostPosted: Wed Jul 14, 2010 1:01 am    Post subject: Ratios Reply with quote

Something tells me you would very much enjoy the book Ratio: The Simple Codes Behind the Craft of Everyday Cooking

Eric Means
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PostPosted: Thu Jul 15, 2010 3:19 pm    Post subject: Reply with quote

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PostPosted: Fri Jul 16, 2010 9:35 pm    Post subject: Brilliant! Reply with quote

For the past year I've often considered deleting Cooking for Engineers from my RSS feed, as updates are few and far between these days, but always ended up deciding to keep it around for whatever reason. Now I understand why. Nowhere else (afaik) can you find brilliant analyses like this one. A formula that breaks down an entire field within food preparation into three simple variables is nothing short of beautiful. I'm not even sure I'll ever use it, but the thought process alone has provided me more pleasure than a day at the museum. You sir are a legend!
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Michael Chu

Joined: 10 May 2005
Posts: 1654
Location: Austin, TX (USA)

PostPosted: Sat Jul 17, 2010 5:48 am    Post subject: Re: Brilliant! Reply with quote

Anonymous wrote:
You sir are a legend!

Don't forget all the credit goes to Michael Ohene who came up with, developed, and wrote this! I'm planning some new articles, but life's been really busy the last couple years... so, if you do delete CFE from your RSS feed, be sure to check in once in a while in case I find myself with enough free time to write a new article.
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Michael Ohene

PostPosted: Thu Jul 22, 2010 4:20 am    Post subject: comments Reply with quote

Thanks for the comments everyone. Eric, I have read Michael Ruhlman's book and I have scanned his website. His work is definitely interesting. His attempt is to show the coincidence between a simple number sequence (1-2-3, 3-2-1, etc) and recipes; basically numerology. I want to define baked goods and show people the underlying process and my ideas on how logic can become logical visualization; and even more.

I am in the process of automating the calculations in this project, so people can readily realize its usefulness, but I am also bundling it with other features to make the project complete. I want to take this from the lab to the kitchen.

Again, thank you.
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PostPosted: Sat Jul 24, 2010 9:08 am    Post subject: Reply with quote

Sir or Dear Michael, as a scientist who gave up twenty years ago to follow the money, I am excited by your work on baked goods. Finally a pattern appears. Woderful stuff. Thank you
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Michael Chu

Joined: 10 May 2005
Posts: 1654
Location: Austin, TX (USA)

PostPosted: Sat Jul 31, 2010 7:06 am    Post subject: Reply with quote

I added a link to Michael Ohene's web-based recipe characterization numbers calculator in the article.
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Paula Bauer

PostPosted: Mon Nov 22, 2010 8:28 pm    Post subject: Reply with quote

also your captcha verivication is kinda cool Laughing Out Loud
keep up the good work...
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PostPosted: Mon Apr 04, 2011 12:34 am    Post subject: this is great Reply with quote

I consider myself more of a cook then a baker, but love the chart on moister level in baking. I will use it next time I bake something.
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PostPosted: Mon Apr 25, 2011 7:01 pm    Post subject: Reply with quote

This, Sir, is gastronomy science at its best! Thank you!!
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PostPosted: Sun Jul 15, 2012 12:03 am    Post subject: Analytical Cooking Continued? Reply with quote

I really like your information on the calculation of moisture, butter and egg content. However, I think further investigation can be made with other aspects of baked goods. Acidity, Sugar content, Salinity,...etc, should be considered to more precisely calculate the flavor as well as the texture of the final product.
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PostPosted: Tue Dec 02, 2014 2:25 am    Post subject: Thanks Reply with quote

Just tried my first gluten-free recipe for crackers -iti was way too dry.

So, i searched for dry to wet ratios in baking and VOILA, what a wonderful surprise to find your site. I figured that somewhere out there some number lover like me would have already done the work for me - only I figured it would be an accountant.
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PostPosted: Sat Dec 06, 2014 3:46 am    Post subject: baking program Reply with quote

I have a question
How have you taken into consideration the fact that flour is hygroscopic in nature in the formulation of your program.
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