Center-Pivot Outer-Span Application Rate vs Soil Intake
Whether a center pivot's outer span applies water faster than the soil can take it.
Example
You enter
- Gross pass depth (in) 1
- Pivot length to outer tower (ft) 1320
- Revolution time (hr) 24
- Wetted band at outer span (ft) 100
- Soil intake rate (in/hr: sand ~1.0, loam ~0.5, clay ~0.15) 0.5
You get
- Outer-span application rate 3.46 in/hr
- Wetting time at a point 17.3624
- Ratio 6.9115
Checked against published worked examples from: USDA-NRCS center-pivot design / university extension.
Details, formula, and sources
ScopeThe outer end sweeps the biggest circle, 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 or tablespeed_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.
Source and editionCenter-pivot outer-span application rate (USDA-NRCS center-pivot design; university extension), by name.
Free accessThe center-pivot application-rate kinematics are public irrigation-engineering results; the pivot design and measured soil intake govern the actual runoff.
What governsEstimate. AHJ and licensed professional govern.
API field namespass_depth_in, pivot_length_ft, revolution_hr, wetted_band_ft, soil_intake_in_hr, app_rate_in_hr, wetting_min, ratio
- Outer span governs the end tower moves fastest (2 x pi x L per revolution), so its instantaneous rate is the highest on the machineUSDA-NRCS / extension
- Average over the band reported as the average over the wetted band; the true elliptical-pattern peak is 4/pi, about 27%, higherirrigation engineering