Calculating the square root of a baguette
How often do we home bakers find the words “Let the loaves rise until doubled in size” in bread recipes? I have no idea, but I am guessing in every second formula. But how do we know a baguette or a boule has doubled in size? And what does it even mean?
In the case of a baguette, the length of the loaf is more or less a constant throughout the entire final stage of fermentation. Consequently, we can use the width and the height of the baguette as a measure for “size”. If width and height have simultaneously doubled, we can be sure it has doubled in size, i.e. volume? Of course not.
If we’d like to know if the volume has doubled, we must know what happens to volume if width and height change. Let’s say a slice of baguette is an ellipse (if it’s underproved it’s more like a circle, but that’s a special case of an ellipse). The area A of an ellipse is proportional to the product of the small diameter d and the large diameter D of the ellipse:
A = pi/4 * d * D
Thus, if d and D double to d’ = 2d and D’ = 2D, we obtain
A’ = pi/4 * d’ * D’ = pi * d * D = 4 * A.
The area of the slice (and volume of the baguette) has grown by a factor of four!
Alternatively, supposing d and D grow with the same speed, A’ = 2 * A holds true if and only if d’ = sqrt(2) * d and D’ = sqrt(2) * D, where sqrt(2) is the square root of 2, which equals approximately 1.41.
So look for a growth by a factor of 1.41 whenever your baguette is supposed to double in size.
P.S. For boules the factor is 2^(1/3) which roughly equals 1.26, pan loaves can only increase their height, and a doubled height results in a doubled voluime, so the factor approx. equals 2.
P.P.S. Use for breads only.