Center-Pivot Outer-Span Application Rate vs Soil Intake
The runoff check center-pivot-runtime's own note warns about: the outer end sweeps the biggest circle fastest, so it dumps the whole pass depth in a few minutes. app_rate = pass_depth x 2 x pi x pivot_length / (revolution_hr x wetted_band). A 1-in pass on a quarter-mile pivot turning once a day through a 100-ft band applies 3.5 in/hr at the end tower - about 7x a silt loam's 0.5 in/hr intake, so it runs off on any slope even when the daily inch is right. Slow the pivot, narrow the band, or pick a lower-rate package. A design screen, not a runoff model.
Formula and source
speed_ft_min = 2 x pi x pivot_length_ft / (revolution_hr x 60); wetting_min = wetted_band_ft / speed_ft_min; app_rate_in_hr = pass_depth_in x 2 x pi x pivot_length_ft / (revolution_hr x wetted_band_ft); ratio = app_rate_in_hr / soil_intake_in_hr.
Center-pivot outer-span application rate (USDA-NRCS center-pivot design; university extension), by name.
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