Centre-Pivot Irrigation: A Pipe That Walks Round the Well

Fig. 6 shows one tower from the side. Water from the pipe comes down a small tube 23 through a regulating valve 51 into cylinder 50. The piston 52 rises slowly and its rod lifts crank 54; a ratchet 55 on the crank turns the toothed wheel 57 fixed to drive wheel 24, and pawl 59 stops it turning back. At the top of the stroke the crank lifts stop 71 on rod 70, flips a spring toggle 64 over centre and opens valve 62 on the large outlet 61: the cylinder drains faster than the small tube can fill it, and the piston falls. At the bottom, stop 72 flips the toggle back and closes the outlet. The outlet spouts 63 point to each side of the wheel track, so the drive water lands on the crop, not in the rut. Fig. 5, above it, shows the alignment wire 75 fixed to the pipe on each side of the tower, running to the regulating valve. The patent makes it of Invar, whose tiny thermal expansion stops the sun from upsetting the alignment.

Cap one end of a 1.2 m length of 20 mm PVC pipe and connect the other end to a garden hose through a ball valve and pressure gauge. Lay it level on two stands over a line of cups, one under each hole. Call the hose end the pivot. **Equal holes.** Drill 1.5 mm holes every 100 mm. Open the valve to a steady low pressure and collect for one minute. Measure each cup in a graduated cylinder: the flows are nearly equal. Divide each by the ring area its hole must water, $2\pi r \times 0.1$ m, and the depth falls steeply with radius. **Zybach's rule.** On a second pipe, drill 14 of the same holes spaced closer together towards the far end, so that each waters an equal share of the circle: hole $k$ at $r = 1.2\,\text{m} \times \sqrt{(k - \tfrac12)/14}$, which is 227, 393, 507, 600, 680, 752, 818, 878, 935, 989, 1039, 1088, 1134 and 1178 mm. Repeat the test. Now the flow per metre of pipe grows with radius. Work out the depth each hole delivers to its own ring: it should be nearly flat.

**Frank L. Zybach** of Strasburg, Colorado, filed **US 2,604,359**, *Self-Propelled Sprinkling Irrigating Apparatus*, on 27 June 1949; it was granted 22 July 1952. The design was taken into production in Nebraska in the 1950s, and later machines replaced the water drive with an electric motor at each tower while keeping the master-tower-and-alignment idea. Pivot circles are the green discs seen from the air over dry farmland across the world. **Honest limits.** A circle leaves the corners of a square field dry unless a corner arm or separate watering is added, as the patent itself says. The outer spans must put water down fast, which can run off on heavy soils. And pivots draw heavily on groundwater: in parts of the High Plains the aquifer has fallen far faster than it refills.