Irrigation Improvement Through Geometry

I ran across this aerial photograph of irrigated fields and noticed that the circular patterns produced by the central pivot irrigation systems are all aligned on a grid. This means that only 78.5% of the land is watered. If the farmers placed the irrigation spigots to form a hexagonal packing, like a honeycomb, it'd increase land use to 90.7%, yielding a 15% improvement. In theory a specially designed rotary valve could be used to vary the pressure at the appropriate angles to reach the spaces between.