The Cloche Bound: Night Temperature Protection Delivered by a Cut Plastic-Bottle Cloche and a Low Tunnel over a Young Tomato Transplant

Gardeners are told that a cut plastic bottle placed over a young plant protects it against frost, and that a low tunnel of hoops and plastic film protects a whole row. This paper computes how much protection each cover actually delivers, from stated assumptions, for a young tomato transplant whose canopy is damaged at 0.0 degrees C. The night model is a steady energy balance at the canopy: heat supplied from a soil store at 10.0 degrees C through a conductance of 3.0 W/m2/K, heat exchanged with the outside air through each cover, and net longwave radiation lost to a clear-night sky 18 degrees C below air temperature, with an effective infrared factor of 0.95 for an uncovered canopy, 0.18 for a condensation-covered polyethylene terephthalate bottle, and 0.42 for a condensation-covered polyethylene tunnel film. On a clear, calm night with an outside minimum of -2 degrees C, the uncovered canopy falls to -4.57 degrees C, the canopy under the bottle holds at 0.5 degrees C, and the canopy under the tunnel holds at -1.44 degrees C. Measured against the exposed plant rather than against the air, the lifts are 5.07 degrees C for the bottle and 3.13 degrees C for the tunnel. The bottle protects the transplant through an outside minimum of -2.77 degrees C and absorbs 7.07 frost degrees relative to the exposed plant, which is already damaged when a clear, calm night falls to 4.3 degrees C; the tunnel protects only through 0.29 degrees C, absorbing 4.01 frost degrees, and with a dry film it protects through only 3.5 degrees C, which is to say it provides almost no frost protection on the clear nights when frost actually forms. A closed cover in sunshine is a separate hazard: under 600 W/m2 of solar radiation a closed bottle rises 34.9 degrees C above the outside air in the dry-soil, no-transpiration bound, so venting is not an optional refinement but a daily requirement. Over 14 days the bottle keeps 25.9 litres of water per square metre of sheltered ground in the soil, and the tunnel keeps 19.7 litres per square metre. The study is simulated, not measured.