## Friday, October 28, 2011

### Reckoning on Ratios

Ratio: A quantitative relation between two amounts; the number of times one value contains or is contained within the other value.

In English, the origin of ratio dates back to about 1636, coming from Latin and meaning "reason, rationale, reckoning, calculation, procedure, or think." It's been used in a mathematical sense since 1660.

For example, my garage contains 2 red cars and my driveway contains 4 blue cars, so the ratio of red cars to blue cars is 2 to 4, also written 2:4. A ratio can also be expressed as a decimal or percentage.

I provided examples of ratios in the past two blogs: Power to Weight, and Height to Width.

Today I want to show how in bread, the key ratio is water to flour, by weight. I'm not going to use volume for the measurements, and you will soon see why.

Here's some water. One pound; or 16 ounces; or 450 grams by weight.

Yeast goes in next. It doesn't really weigh anything, as I use only a quarter-teaspoon.

Now I add a bunch of flour.

One and one quarter pounds; or 20 ounces; or 560 grams by weight.

Our ratio is 16 water to 20 flour, which we can simplify to 4 water to 5 flour or 4:5.

I'm a little overweight here on the flour. I will take 3/8 ounce out before I add a bit less than one tablespoon of kosher salt.

Mix up the ingredients with a spoon and it looks like this.

When the yeasts start to eat up the complex carbohydrates in the flour they give off gas. It makes the batter start to expand and rise. Here we have one quart by volume, but the ratio by weight is still the same.

They keep eating and the dough keeps rising. Here we have three quarts by volume, but the ratio by weight is still the same! The dough is less dense, but we have the same weight.

Now it comes out onto the table and is dusted with a tiny bit of flour so it won't be sticky. I shape it into a ball. The ratio is still the same - 4 water and 5 flour.

The dough goes into a hot cast iron pan in my oven. It keeps rising. The volume has increased a great deal since we put the water and flour together with yeast and salt.

Here's the final loaf after it comes out of the oven. We have added water, flour, yeast, salt, time and temperature. The volume has increased. Is the ratio of water to flour still the same? Yes or No?

Sorry. The answer is no. When you bake the bread lots of the water evaporates. By my measuring, about 20% of the weight of the water is gone, so the bread weighs 2 pounds, instead of 2 pounds 4 ounces. The ratio is now 4 to 4 or simplified - it's 1:1.

And it's time for my lunch!