The burn-time law for candles

Two rules of thumb about candle burn time are widely repeated: that a candle gives so many hours per inch of height, implying burn time is proportional to height at fixed diameter, and that doubling the diameter doubles the burn time. This paper derives burn duration from a melt-and-consumption model and shows that neither rule survives in its simple form. In the model, burn rate grows as diameter to the power 1.5, so burn time at fixed height grows only as the square root of diameter: doubling diameter multiplies burn time by 1.414, not by 2. For beeswax at 100 mm height, burn times are 18.8 hours at 25 mm diameter, 26.5 hours at 50 mm, and 37.5 hours at 100 mm. Height scaling is not proportional either, because a 10 mm stub is left unburned: at 50 mm diameter, doubling height from 50 mm to 100 mm multiplies beeswax burn time by 2.25, from 11.8 hours to 26.5 hours, while hours per inch rise from 5.99 to 6.74. Draught and warmth shorten life through dripping loss; in a strong draught at 32 °C the waste fraction reaches 0.326 and beeswax burn time falls by 30.5%. The paper also gives production arithmetic for dipped tapers: 25 dips at 0.35 mm per dip build a 200 mm taper to 20.5 mm diameter, using 62.0 g of beeswax, at 86.4 candles per hour of hands-on dipping labour. All results are model calculations. SIMULATED, NOT MEASURED.