Blending arithmetic

Blending a sour is the one place in brewing where the spreadsheet came first. We implement the working one, Michael Tonsmeire’s priming sheet as extended by Crane, rather than invent a model, because the people doing this have been bottling off that sheet for years.

What averages and what does not

Most of a blend averages by volume. Color, alcohol, titratable acidity and final gravity are volume-weighted means. pH is not, and treating it as one is the standard mistake. pH is a logarithm, so the blend’s pH comes from averaging hydrogen-ion concentrations and taking the logarithm at the end. That is exact for a strong acid and an approximation for a buffered beer, and much closer than averaging the pH numbers themselves.

Where the carbonation comes from

A blend arrives at packaging already holding CO₂ from two sources: what the temperature left in each beer, halved where one sat in a barrel long enough to off-gas, and what the bugs will make from the extract still in every component sweeter than the driest one. Add those up and you often find the blend is already at or past your target, which is the answer that saves the gushers. The driest component sets the floor, and we find it rather than making you put it first, a data-entry hazard the spreadsheet has and this does not.

The acid-shock starter

The last step is a small dry pitch acclimatised in half water and half blend for a day or two before packaging, because the yeast that has to carbonate a pH 3.4 beer needs warning. The dose per gallon is the more conservative of the two published rules of thumb.

The beer these numbers come from

Reference pale ale — 20 L into the fermenter, a 60 minute boil.

Grist	Amount	Color
Crisp Maris Otter Pale Ale Malt	4.5 kg	2.8 °L
Thomas Fawcett Caramalt	0.35 kg	9.9 °L

Hops	Amount	Alpha	Addition
Magnum	15 g	13.5 %	60 min boil
Cascade	30 g	6.8 %	10 min boil
Citra	40 g	13 %	20 min stand at 80 °C

It comes out at
Original gravity	1.0507
Final gravity	1.0094
Alcohol	5.52 %
Bitterness	35.66 IBU
Color	5.14 SRM (10.12 EBC)
Into the fermenter	20 L

The numbers

Carbonation the blend already holds

1.69 volumes CO₂, from blend-residual-plus-extract.

predicted = Σ(V × residual(T_peak) × barrelFactor)/ΣV + 0.51 × Σ(V × Δpoints)/ΣV
⇒ Carbonation the blend already holds = 1.69 volumes CO₂

Input	Value	Unit
Components	2	—
Total volume	30	L
Residual volumes	0.565	volumes CO₂
Extract volumes	1.122	volumes CO₂
Driest component FG	1.004	SG
Target volumes	2.6	volumes CO₂
Barrel aged residual factor	0.5	—
Extract CO₂ per gravity point	0.51	—

What it assumes:

• Residual CO₂ is read at each component’s peak temperature after attenuation, and halved where the beer sat in a barrel long enough to off-gas.
• Every component sweeter than the driest still has extract in it, and the bugs will keep eating toward that floor in the bottle.

Sources:

• Priming Barrel-Aged and Blended Sour Beer — Michael Tonsmeire (The Mad Fermentationist), 2014
• Blending and priming spreadsheet for mixed-fermentation beer — Curtis Crane, Council Brewing (NHC)
• Accurately Calculating Sugar Additions for Carbonation — Kai Troester (Braukaiser)

Blend pH

3.46 pH, from hydrogen-ion-volume-weighted.

pH = −log₁₀( Σ(Vᵢ × 10^(−pHᵢ)) / Σ Vᵢ )
⇒ Blend pH = 3.46 pH

Input	Value	Unit
Components	2	—
Total volume	30	L
Titratable acidity	3.87	g/L

What it assumes:

• Exact for strong acids and an approximation for a buffered beer; averaging the pH numbers themselves would be worse.
• Components with no pH are skipped rather than treated as water.

Sources:

• How does blending impact pH? — Techniques in Home Winemaking
• Blending and priming spreadsheet for mixed-fermentation beer — Curtis Crane, Council Brewing (NHC)

Acid-shock starter, dry yeast

2.38 g, from acid-shock-starter.

yeast_g = blend_gal × 0.3;  water_L = acid beer_L = yeast_g / 17
⇒ Acid-shock starter, dry yeast = 2.38 g

Input	Value	Unit
Total volume	30	L
Yeast grams per gallon	0.3	g/US gal
Water	0.14	L
Acid beer	0.14	L

What it assumes:

• Pitched 24–48 h before packaging, split half water and half blend, so the yeast acclimates to the acidity before it has to carbonate anything.
• The more conservative of the two published rules of thumb.

Sources:

• Blending and priming spreadsheet for mixed-fermentation beer — Curtis Crane, Council Brewing (NHC)
• Packaging — Milk the Funk wiki