A strength test for wood-ash lye without instruments

Wood-ash lye needs to fall within a narrow concentration band for soap-making, yet the household maker usually has no hydrometer or titration kit. The traditional substitute is the floating-egg test: lye is judged ready when a fresh egg floats with a small cap exposed. This paper calibrates that test in a physical model, derives a sizing rule for ash, water and leaching passes, and sets a failure bound. The central egg, at 1.060 g/mL, reaches neutral buoyancy at 65.2 g/L of alkali as potassium carbonate, but eggs spanning 1.030 to 1.090 g/mL indicate anywhere from 32.6 to 97.8 g/L at the same visual point, a range 65.2 g/L wide against a target band only 40.0 g/L wide. An egg floating with 5% exposed corresponds to 125.9 g/L, near the top of the target band of 90.0 to 130.0 g/L. The sizing rule for mixed household ash is 15 kg of ash per 10 L of water leached in 2 passes, giving 115.5 g/L. The same recipe across ash sources gives 64.2 to 154.0 g/L, a 2.4-fold spread. The claim that stronger lye is always better does not survive: dosing a fixed volume sized for mid-band lye with lye at 180 g/L leaves 89.7 g of excess potassium hydroxide equivalent per kilogram of tallow, an upper-bound free alkali content of 6.85% in the finished bar, 68.5 times a 0.1% reference limit.