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Predict your gravity curve, terminal gravity, ABV, diacetyl rest window, and cold crash timing from your yeast strain, original gravity, and fermentation temperature. Powered by Monod-kinetics ODEs solved with fourth-order Runge-Kutta integration.
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Create free account →Most fermentation calculators use a fixed apparent attenuation percentage to predict terminal gravity. FermPilot solves a system of four ODEs simultaneously at each time step: substrate concentration (wort sugars, °P), ethanol (%ABV), yeast biomass (g/L), and VDK precursor (mg/L). Each variable affects the others, so the model captures how a slow-starting fermentation differs from one that peaks early and crashes fast.
Yeast growth rate follows the Monod model: μ = μ_max × S/(K_s + S) × (1 - P/P_m)^n. As ethanol accumulates, the growth rate declines toward zero. When ethanol reaches P_m (the maximum tolerated concentration), growth stops. This is why high-gravity fermentations stall before full attenuation and why pitching rate matters more at higher OGs.
VDK (vicinal diketones, primarily diacetyl) formation is coupled to growth rate using a Leudeking-Piret expression: dV/dt = α(dX/dt) + βX − γXV. Formation is highest during exponential growth (high dX/dt); reabsorption is driven by yeast contact surface (X) and current VDK concentration (V). The model predicts the hour at which VDK drops below the 0.10 mg/L packaging threshold after a rest phase, using a separate phase simulation at rest temperature.
Each strain has its own set of Monod constants (μ_max, K_s, P_m, n) and VDK kinetic parameters (α, β, γ). These are sourced from Boulton & Quain, Brewing Yeast and Fermentation (2001) and Casey & Ingledew, CRC Critical Reviews in Microbiology 13:219 (1986). Custom strain calibration from your own batch data is available in FermPilot Pro using Nelder-Mead optimization.
| Parameter | Ale | Lager | Notes |
|---|---|---|---|
| Fermentation temp | 18–22 °C | 8–14 °C | Arrhenius rate correction applies (colder = slower) |
| Pitch rate | 0.75–1.0 M/mL/°P | 1.0–1.5 M/mL/°P | Higher OG requires proportionally more cells |
| OG range | 10–18 °P (1.040–1.073 SG) | 10–16 °P (1.040–1.065 SG) | High-gravity stall risk above 18 °P |
| VDK threshold | 0.10 mg/L | 0.05–0.10 mg/L | Lagers are more sensitive to diacetyl off-flavor |
| Rest temp | 18–22 °C | 18–20 °C | Raise to rest temp after terminal gravity confirmed |
| Typical duration | 5–10 days | 10–21 days | Lager conditioning adds time after fermentation |
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