A Power-Free Livestock Water Trough That Resists Freezing: Design, Thermal Bounds, and the Exact Conditions Under Which It Fails

Livestock in cold climates need open drinking water every day, and the standard remedies — electric immersion heaters and heated troughs — fail exactly when they are needed most: during storms and power cuts, on pasture far from a supply, and on farms where running a cable to a trough is impractical. This paper designs and bounds a power-free alternative: a 630 L trough wrapped in 100 mm of expanded polystyrene, fitted with a floating insulated cover that leaves only a small sheltered drinking opening, and using the water itself as the thermal store, topped up by solar gain absorbed on a dark cover surface. A lumped thermal model, with every number computed from stated assumptions, gives the design a heat-loss coefficient of 5.07 W/K against 77.6 W/K for a conventional uninsulated steel trough. Starting from water at 8 °C, the trough survives 2.76 consecutive sunless days at a constant −15 °C (wind 5 m/s) before the bulk water reaches 0 °C, with roughly a further 9.5 hours before a 25 mm ice skin closes the drinking opening. With clear December sun every day it survives 4.61 days at −15 °C, and it holds indefinitely only down to −8.1 °C. Below that line it is a countdown device, not a permanent solution, and this paper prints that failure line rather than rounding it away: at −25 °C, sunless, it lasts 1.75 days, and if the drinking opening loses its wind shelter the −15 °C sunless survival falls from 2.76 to 1.82 days. AI DISCLOSURE: This paper was drafted and computed with the assistance of Dave, an AI system built and operated by Aldred Industries. The design brief, authorship, and responsibility for the claims rest with the named author. The AI assistance is disclosed here in accordance with the author's standing practice for all publications from this programme of work. No part of this paper describes a device that has been built or tested; all performance statements are simulation results and are labelled as such. Status: design study. All performance figures are SIMULATED, NOT MEASURED. Nothing described has been built or tested.