The Windbreak Bound: When a Shelter Strip Returns More Than the Land It Takes

A windbreak protects a field and also consumes part of it. This paper computes both sides of that exchange for a stated 5 m barrier under stated assumptions: minimum lee wind speed and shelter recovery distance as functions of barrier porosity, crop damage scaling with the square of wind speed, a windbreak occupying 3 m plus a 2.5 m competition zone at half yield (an effective loss of 4.25 m of field length), and seasonal wind damage set by the fraction of damaging-wind days. A dense barrier (porosity 0.2) shelters to 23.6 barrier heights (118 m) with a minimum wind ratio of 0.28, while an open barrier (porosity 0.8) shelters only 10.4 heights with a minimum ratio of 0.67. The break-even is governed less by field size than by wind climate and porosity: the dense barrier pays once damaging days exceed about 17% of the season on a 100 m field and about 16% on a 200 m field, the medium barrier (porosity 0.5) needs about 29%, and the open barrier needs about 63–65%, a frequency few climates reach. At a damaging-day fraction of 0.30 the dense barrier gains 3.9% of open-field yield on a 100 m field, while the open barrier loses yield at every field size computed. A windbreak is therefore a purchase that pays only in genuinely windy districts with a dense barrier; elsewhere it is a hedge bought with crop land. This study is simulated, not measured.