17.5 Version 2: Fixed inoculation

When making the table above, I realized it’s probably better to do this in terms of the inoculation, so that the inoculation would stay consistent in the table. So, let’s redo the calculations!

Inputs

• Total flour (\(F_{l}\)): How much flour do you want to use?
• Inoculation (\(I\)): The inoculation as a proportion (0-1).
• Starter hydration (\(H_{s}\)): The hydration of the starter
• Loaf hydration (\(H_{l}\)): The hydration of the resulting loaves

Final Formulas

• Flour from starter: \(F_{s} = F_{l}I\)
• Water from starter: \(W_{s} = H_{s}F_{l}I\)
• Flour to add: \(F_{a} = F_{l} - F_{l}I = F_{l}( 1 - I)\)
• Water to add: \(W_{a} = W_{l} - H_{s}F_{l}I\)
• Salt: Approximately \(2.0\%\) of the weight of the flour.
• Sugar (optional): Approximately \(1.5\%\) of the weight of the flour.
• Olive oil (optional): A tablespoon or two.

The salt, sugar, and oil can be varied. Sometimes I include oil, sometimes I don’t. I’m not entirely certain what effect it has. The sugar can also be varied, sometimes I don’t include any. I have not made any loaves without salt, but from what I’ve read your bread will taste like cardboard without it.

Derivations

Again from the inputs, we can first get the total amount of water as \(W_{l} = H_{l}F_{l}\) (this is rearranging the formula for hydration).

Then we use the inoculation formula \(I = F_{s}/F_{l}\) to get the amount of flour from the starter, \(F_{s} = F_{l}I\). From this, we can once again use the hydration formula to get the amount of water from the starter, \(W_{s} = H_{s}F_{s}\) (or in terms of the original inputs, \(W_{s} = H_{s}F_{l}I\). This means that the total amount of starter to use is \(S = F_{l} + W_{l}\).

The amount of flour we need to add is just taking the difference of these:

• Flour to add: \(F_{a} = F_{l} - F_{s}\)
• Water to add is \(W_{a} = W_{l} - W_{s}\)

Examples

Again, here are some pre-computed values, again assuming:

• \(850\) grams of flour in total (making two loaves),

• \(20\%\) inoculation.

• Since the inoculation is constant, the amount of flour to add is also constant at \(F_{a} = F_{l}(1 - I)\), which comes out to be \(850(1-0.2) = 680\) grams.

• Constants: Since I’m targeting a fixed total weight of flour and a fixed inoculation, several derived quantities are also fixed:

  • Flour to add: \(850 \times (1-0.2) = 680\)
  • Salt: Approximately \(850 \times 0.02 = 17\) g
  • Sugar (optional): Approximately \(850 \times 0.015 = 12.75\) g

Loaf Hydration	Ingredient	Hs = 0.75	Hs = 0.85	Hs = 1
Hl = 0.65	Starter	297.5	314.5	340.0
	Water to add	425.0	408.0	382.5
Hl = 0.7	Starter	297.5	314.5	340.0
	Water to add	467.5	450.5	425.0
Hl = 0.75	Starter	297.5	314.5	340.0
	Water to add	510.0	493.0	467.5

Happy baking!