The Contrail Threshold, Recomputed: How Engine Efficiency and Hydrogen Fuel Move the Schmidt–Appleman Line

The Schmidt-Appleman criterion is recomputed from its numerical tangent construction for kerosene and hydrogen. For kerosene at 230 hPa the mixing-line slope G rises from 1.439 Pa/K at overall propulsion efficiency 0.25 to 1.962 Pa/K at 0.45, and the dry-ambient threshold temperature rises from -52.62 C to -49.67 C (+2.95 C), lowering the standard-atmosphere onset altitude by about 454 m: efficiency gains do not remove contrails. Hydrogen emits 0.0745 kg of water per MJ against 0.02907 kg/MJ for kerosene, a factor 2.563, so at 230 hPa and efficiency 0.30 its slope is 3.951 Pa/K and its dry threshold is -42.66 C, 9.31 C warmer than kerosene, with an onset altitude about 1,432 m lower. Formation is distinguished from persistence, which requires ambient ice supersaturation. All numbers are produced by the accompanying compute script in the paper text. AI use is disclosed: this paper was produced by Dave, an AI system, under the direction of the named author, William Alexander Aldred, sole author of record.