17.4 Version 1: Fixed Starter
For this section, I pick how much starter I’m going to use, and then derive how much more flour and water I need.
Inputs
- Total flour (\(F_{l}\)): How much flour do you want to use?
- Loaf hydration (\(H_{l}\)): The hydration of the resulting loaves
- Starter (\(S\)): Weight of starter to use
- Starter hydration (\(H_{s}\)): The hydration of the starter
Both hydration values here are in a proportion (some decimal between 0 and 1). For example, if you keep the starter at 75% hydration, then \(H_{s} = 0.75\).
Final Formulas
- Flour from starter: \(F_{s} = S / (H_{s} + 1)\)
- Water from starter: \(F_{s} = S \left( \dfrac{H_{s}}{H_{s} + 1} \right)\)
- Flour to add: \(F_{a} = F_{l} - S / (H_{s} + 1)\)
- Water to add: \(W_{a} = W_{l} - S \left( \dfrac{H_{s}}{H_{s} + 1} \right)\)
- 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’ve not made any loaves without salt, but from what I’ve read your bread will taste like cardboard without it.
Derivations
Recall the hydration is \(H = W/F\), from which we can obtain \(W = HF\) and \(F = W/H\).
For the loaf, we use \(F_{l}\) flour, and with a target hydration of \(H_{l}\), this means we need \(W_{l} = H_{l}F_{l}\) water.
Then from the starter, note that the weight is \(S = W_{s} + F_{s}\). Using the hydration formula we can rewrite this in terms of a single unknown.
\[ \begin{aligned} S &= W_{s} + F_{s}\\ &= H_{s}F_{s} + F_{s}\\ &= F_{s}(H_{s} + 1) \\ F_{s} &= S / (H_{s} + 1) \end{aligned} \]
Follow a similar process for the water.
\[ \begin{aligned} S &= W_{s} + F_{s}\\ &= W_{s} + \dfrac{W_{s}}{H_{s}} \\ &= W_{s} \left(1 + \dfrac{1}{H_{s}}\right) \\ &= W_{s} \left(\dfrac{H_{s} + 1}{H_{s}}\right) \\ W_{s} &= S \left( \dfrac{H_{s}}{H_{s} + 1} \right) \end{aligned} \]
So now we have the total amount of flour in the loaf (an input), the amount of water (from the flour and loaf hydration), and the amount of flour and water from the starter. 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 \(W_{a} = W_{l} - W_{s}\)
The salt and sugar are computed using a baker’s percentage.
The inoculation is the percent of flour in the loaf which comes from the starter. So it would be \(F_{s} / F_{l}\). I generally keep my loaves in the realm of \(20\% - 25\%\).
Examples
I generally use about 850 - 880 grams of flour. The table below provides some pre-computed values assuming the following:
- \(850\) grams of flour in total (making two loaves),
- \(300\) grams of starter
This is for two loaves, though I guess you can bake it however you want. I’ve tried to keep the inoculation around \(20\%\)
Loaf Hydration | Ingredient | Hs = 0.75 | Hs = 0.85 | Hs = 1 |
Hl = 0.63 | Flour to add | 678.6 | 660.8 | 662.5 |
Water to add | 406.9 | 374.7 | 348.0 | |
Salt | 17.0 | 17.0 | 17.0 | |
Sugar | 12.8 | 12.8 | 12.8 | |
Inoculation | 0.202 | 0.223 | 0.221 | |
Hl = 0.65 | Flour to add | 678.6 | 660.8 | 662.5 |
Water to add | 423.9 | 391.7 | 365.0 | |
Salt | 17.0 | 17.0 | 17.0 | |
Sugar | 12.8 | 12.8 | 12.8 | |
Inoculation | 0.202 | 0.223 | 0.221 | |
Hl = 0.7 | Flour to add | 678.6 | 660.8 | 662.5 |
Water to add | 466.4 | 434.2 | 407.5 | |
Salt | 17.0 | 17.0 | 17.0 | |
Sugar | 12.8 | 12.8 | 12.8 | |
Inoculation | 0.202 | 0.223 | 0.221 | |
Hl = 0.75 | Flour to add | 678.6 | 660.8 | 662.5 |
Water to add | 508.9 | 476.7 | 450.0 | |
Salt | 17.0 | 17.0 | 17.0 | |
Sugar | 12.8 | 12.8 | 12.8 | |
Inoculation | 0.202 | 0.223 | 0.221 |