The Upwind Shadow: Where Wind Refraction Ends a Horn Signal, and Where to Place the Post

Sound does not travel equally in all directions on a windy day. Wind that strengthens with height bends sound travelling upwind upward, leaving a shadow near the ground, and bends sound travelling downwind back toward the ground. This paper computes the shadow boundary and the resulting signalling range for a horn or whistle of 112 dB at 1 m at 700 Hz. Without refraction the range is 1.13 km. In a moderate daytime wind of 5 m/s the upwind range falls to 115 m, the crosswind range is 703 m, and the downwind range rises to 1450 m. A dawn temperature inversion restores the crosswind range to 1130 m but, while the wind still blows, lifts the upwind range only to 124 m; calm dawn conditions restore 1130 m in every direction. A placement rule follows: put the signal post downwind of the settlement it must reach, or accept that upwind signalling is a calm-hours method. SIMULATED, NOT MEASURED.