Center Pivots and Lateral Moves

Dean E. Eisenhauer, Derrel L. Martin, Derek M. Heeren, Glenn J. Hoffman

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Pages 277-296 (doi: 10.13031/ISM.2021.13) in Irrigation Systems Management. ,

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Abstract.  See https://www.asabe.org/ISM for a PDF file of this entire textbook at no cost.

Keywords. Center Pivot Characteristics, Application Rate, Sprinkler and Nozzle Selection, Depth of Water Applied, Remote Monitoring of System Operation and Control, Variable Rate Irrigation, Community Shared Center Pivot Systems, Textbook

13.1 Introduction

In 1948 Frank Zybach invented a device he called the “self-propelled irrigator.” This led to the development of center pivot and linear or lateral move irrigation systems (Bittinger and Longenbaugh 1962; Heermann and Hein, 1968). A chapter is devoted to these systems because of the unique management needed to capitalize on the capability of these systems. Additionally, the growth of center pivot irrigation during the last three decades far exceeds the growth of any other method of irrigation. In some areas the amount of land irrigated with surface systems has receded. Many of the fields, previously surface irrigated, have been converted to center pivot irrigation. The growth in center pivot irrigation in one year almost equals the total amount of land irrigated with microirrigation in the U.S. The growth has been very substantial and will likely continue. Three principal reasons drive this growth. First, the systems have the ability to be very efficient. They can apply small depths of water at the time that the crop needs irrigation. Second, the systems require less labor than surface or moved lateral systems. In many areas the scarcity of available labor is a limitation to the amount of land that a farmer can irrigate. Third, the systems have the capability to irrigate crops, soils, and terrains that are infeasible with surface, or periodically-moved sprinkler systems.

The basic components of a center pivot (Martin et al., 2007) are illustrated in Figure 13.1. The pivot lateral is a pipeline with sprinkler outlets. The pivot lateral is supported by a tower assembly. The towers include a structure to support the pipeline plus a motor to propel each tower. Today most pivots are powered by electricity. However, some manufacturers use oil hydraulic motors. The pivot base or pivot point is located at the center of the field. The base can be permanently installed or, for smaller systems that are towed from field to field, the base is mobile. Water is supplied to the inlet pipe on the pivot base. The water is pressurized by a pump upstream of the pivot. Water is carried up the pivot base through a rotating elbow to the inlet of the pivot lateral. Power is supplied continuously to motors installed at each tower using a slip-ring assembly. This device contains contacts that allow the pivot to pick up power from the pivot base while the lateral rotates. A control panel is usually located on the pivot base where the operator can adjust the speed of rotation of the pivot and check on other factors. A road is usually necessary so the operator can conveniently reach the pivot base.

The combination of the pivot lateral, the truss support structure, sprinkler devices, and the tower are called a span. The length of a span can vary from 100 to 200 feet. Installation costs are less with longer spans; however, the maximum length of a span is determined by the diameter of the pipe and the slope and undulation of the terrain. The length of a span can vary along the pivot to adjust to the dimensions of the field. Spans of the pivot can be connected together in either a rigid or flexible fashion. For rolling terrain it is necessary to provide a flexible coupler between spans.

Figure 13.1. Illustration of the components of a center pivot irrigation system.

(a) (b)

Figure 13.2. (a) Example of a center pivot irrigation system (Valmont Industries) with seven spans, an overhang, and an end gun. (b) Example of a center pivot with a corner system (photo b courtesy of Lindsay Corporation).

A pipe called the overhang is often attached beyond the last tower of the pivot (Figure 13.2a). The overhang could be up to 80 feet long. A special sprinkler can be attached to the end of the overhang to increase the amount of area irrigated. This sprinkler is usually called an end gun and is used to water part of the corners not reached by the last sprinkler on the lateral. It only operates when the water from the end gun stays within the field. Since about 1975, there has been a major effort in the center pivot industry to reduce the amount of pressure required to operate center pivots. Systems originally required 75 psi of pressure at the inlet to the pivot. Now, many are designed to operate at 30 psi or less. These pressures are often too low for proper operation of end guns, so a booster pump is installed at the last tower to pressurize the end gun. A valve is used to control when the end gun operates.

Center pivots can also be equipped with corner watering systems (Figure 13.2b). These systems have a corner lateral that hinges or rotates from the last tower of the main system. The corner system can be guided by GPS or a buried cable that emits a radio signal for the corner tower to follow. Sprinklers on the corner system have special valves that open and close depending on how far the corner lateral has rotated away from the main pivot lateral. Recent developments in center pivot irrigation include remote monitoring and control, high-speed variable frequency drive motors for the towers, low-energy precision application (LEPA) sprinkler packages, variable rate irrigation, and variable frequency drive for the pumping plant (Lamm et al., 2019).

To irrigate rectangular fields, or to irrigate a larger portion of square fields, mechanically moved systems were developed where the lateral moves along a straight line (Martin et al., 2007). These systems are called linear or lateral move systems (Figure 13.3). The spans of these systems are nearly identical to those of center pivots. The unique feature of these systems is how the water is supplied to the lateral. Two types of water delivery systems are common:

• systems that drag a supply hose and
• systems that pump water from a canal that runs parallel to the direction of travel.

(a) (b)

Figure 13.3. Hose-fed linear or lateral move irrigation systems. (a) A four-span system driven by electric motors (photo courtesy of Lindsay Corporation). (b) A drive unit for a linear move irrigation system driven by oil hydraulic motors (photo courtesy of T-L Irrigation Company).

Systems supplied by either a hose or buried valves are usually pressurized with the main supply pump. Systems that obtain water from a canal carry a pump along with the system to obtain and pressurized the water. The main supply pump, or surface water supply system, must be hydraulically interfaced with the system so that the water supply is continual but does not exceed the canal capacity or the discharge of the system. The water supply features of these systems affect management.

13.2 Center Pivot Characteristics

13.2.1 Sprinkler Discharge

(13.1)

Figure 13.4. Diagram of the area associated with a sprinkler along a center pivot lateral.

Since center pivot laterals rotate around the field, the delivery of water along the lateral is much different than for other lateral-based systems. The area that is irrigated by an individual sprinkler increases with distance from the pivot base (Figure 13.4). The goal in irrigation is to apply the same depth of water to all parts of the field; therefore, the discharge from a sprinkler must be larger near the distal end of the lateral than close to the pivot point. The required discharge is given by:

where: q_s= the discharge from an individual sprinkler (gpm),

R = the distance of the sprinkler head or spray nozzle from the pivot base (ft),

S = the local spacing between successive sprinklers along the lateral (ft),

C_g = the gross system capacity required for the irrigation system (gpm/ac) = Q/A

The discharge from the sprinkler increases linearly with the distance from the pivot, i.e., a sprinkler 1,000 feet from the pivot will require twice as much discharge as a sprinkler at 500 feet. The discharge also depends on the spacing between sprinklers and the gross system capacity. The system capacity is determined by the crop, climate, and soils as described in Chapters 4 and 5, and does not vary by location along the pivot. The system capacity (C_g) must be determined from the field requirements and should not be determined arbitrarily.

Table 13.1. Sprinkler discharge requirement per unit length along the lateral (qs/S), gpm/ft.
Distance from Pivot (ft)	Gross System Capacity (gpm/ac)
	4	5	6	7	8	9	10
100	0.06	0.07	0.09	0.10	0.12	0.13	0.14
200	0.12	0.14	0.17	0.20	0.23	0.26	0.29
300	0.17	0.22	0.26	0.30	0.35	0.39	0.43
400	0.23	0.29	0.35	0.40	0.46	0.52	0.58
500	0.29	0.36	0.43	0.50	0.58	0.65	0.72
600	0.35	0.43	0.52	0.61	0.69	0.78	0.87
700	0.40	0.50	0.61	0.71	0.81	0.91	1.01
800	0.46	0.58	0.69	0.81	0.92	1.04	1.15
900	0.52	0.65	0.78	0.91	1.04	1.17	1.30
1000	0.58	0.72	0.87	1.01	1.15	1.30	1.44
1100	0.63	0.79	0.95	1.11	1.27	1.43	1.59
1200	0.69	0.87	1.04	1.21	1.38	1.56	1.73
1300	0.75	0.94	1.13	1.31	1.50	1.69	1.88
1400	0.81	1.01	1.21	1.41	1.62	1.82	2.02
1500	0.87	1.08	1.30	1.51	1.73	1.95	2.16
1600	0.92	1.15	1.38	1.62	1.85	2.08	2.31
1700	0.98	1.23	1.47	1.72	1.96	2.21	2.45
1800	1.04	1.30	1.56	1.82	2.08	2.34	2.60
1900	1.10	1.37	1.64	1.92	2.19	2.47	2.74
2000	1.15	1.44	1.73	2.02	2.31	2.60	2.88
2100	1.21	1.51	1.82	2.12	2.42	2.73	3.03
2200	1.27	1.59	1.90	2.22	2.54	2.86	3.17
2300	1.33	1.66	1.99	2.32	2.65	2.99	3.32
2400	1.38	1.73	2.08	2.42	2.77	3.12	3.46
2500	1.44	1.80	2.16	2.52	2.88	3.25	3.61
2600	1.50	1.88	2.25	2.63	3.00	3.38	3.75

Originally, pivots were manufactured with a constant spacing of about 32 feet between sprinklers. Spacing sprinklers closer together at the distal end allows lower operating pressures to be used while maintaining excellent uniformity. Today pivot laterals are manufactured with sprinkler outlets spaced at 7.5 to 10 feet. Near the pivot base sprinklers are not placed in every available outlet. Somewhere along the lateral the discharge required from a sprinkler becomes too large if outlets are skipped. Then the spacing must be reduced. This generally allows for using the same size of sprinkler device along a major portion of the lateral. Equation 13.1 has been solved in terms of discharge per unit length along the lateral (i.e., q_s /S) for a range of conditions for pivots (Table 13.1).

13.2.2 Area Irrigated

The area irrigated with a center pivot depends on the radius irrigated with the main lateral and the radius gain when the end gun is turned on. Typically, a center pivot is positioned into a square land area similar to that shown in Figure 13.5. The end gun can only be operated when the spray pattern stays within the field boundary. In the example in Figure 13.5 the end gun operates over an angle (ß) of 42° in each corner.

Usually the end gun discharges water only about half of the time that the main system operates. The time that the end gun operates depends on the radius of the main system and the gain from the end gun.

The amount of area irrigated with a pivot placed in the center of a square tract of land with the end gun operating in all four corners is computed with the following equation (von Bernuth, 1983):

(13.2)

Figure 13.5. Diagram of the effect of end-gun operation on the area irrigated (adapted from Martin et al., 2017).

where: A_t = the total irrigated area (ac),

R_l = the radius irrigated with the main system lateral (ft),

R_eg = the radius gain from using the end gun (ft), and inverse cosine is evaluated in radians.

Table 13.2. Total irrigated area for different lengths of the main system and the end gun coverage.
Radius Irrigatedwith MainLateral (ft)	Gain of Wetted Radius from End Gun Operation (ft)
	0	50	75	100	125	150	200	MaximumArea[a]
800	46	49	50	51	51	51	-	51
900	58	62	63	64	65	65	-	65
1000	72	77	78	79	80	80	80	80
1100	87	92	94	95	96	97	97	97
1200	104	109	111	113	114	115	116	115
1300	122	128	130	132	133	134	135	135
1400	141	148	151	152	154	155	157	157
1500	162	170	172	175	176	178	180	180
1600	185	193	196	198	200	202	204	205
1700	208	217	220	223	225	227	230	231
1800	234	243	246	249	252	254	257	259
1900	260	270	274	277	280	282	286	289
2000	288	299	303	306	309	312	316	320
2100	318	329	333	337	340	343	348	353
2200	349	361	365	369	373	376	381	387
2300	382	394	399	403	407	410	415	423
2400	415	428	434	438	442	445	451	461
2500	451	464	470	475	479	482	489	500
2600	488	502	507	512	517	521	528	541
[a] Maximum area occurs when the radius gain is 21% of the main lateral length.

Increasing the radius gain from the end gun does not ensure more irrigated area since the angle of the section that can be irrigated with the end gun decreases. The maximum irrigated area will, in fact, occur when the radius gain from the end gun is about 21% of the length of the main pivot lateral. Usually, however, the availability of end gun nozzle sizes, discharge requirement of the end gun, and available system pressure dictate the radius gain from the end gun. Solutions to Equation 13.2 have been developed in Table 13.2. The values in this table apply when all four corners are irrigated. Sometimes a road along the property reduces the angle of operation of the end gun in the corner of the field. Table 13.2 also assumes that the entire area wetted by the end gun is planted to the irrigated crop. This may not be done in some cases if the depth of application tapers off near the end of the radius of coverage of the end gun. This will reduce the values from Table 13.2 slightly, but usually not by a significant amount. The values in Table 13.2 should be adequate for planning and management.

13.2.3 Pressure Distribution

Nozzle selection and center pivot evaluation require knowledge of the pressure distribution along the pivot lateral. The distribution is unique for pivots since the discharge required of sprinklers increases along the pivot lateral. The pressure at a point along the pivot lateral is given by:

(13.3)

where: P_R = the pressure at point R along the lateral (psi),

P₀ = the pressure at the inlet to pivot lateral (psi),

P_lp = the pressure loss due to friction in the pivot lateral (psi/1000 ft),

E_g = the elevation gain from the lateral inlet to point R on the lateral (ft),

R_l = the distance from the pivot base to the last sprinkler on the main lateral (ft), and

f_p = the pressure distribution factor at fraction distance R/R_l (dimensionless) (Figure 13.6).

Table 13.3. Pressure loss in center pivot laterals without end guns, psi/1,000 feet of pipe. Multiply losses by 1.037 for laterals with end guns.
Hazen Williams Equation C Value = 140Multiple Outlet Factor for Center Pivots = 0.54
Flow Rate into Pivot Lateral(gpm)	Outside Diameter of Pipe (in)
	6	6 5/8	8	10
	Inside Diameter of Pipe (in)
	5.782	6.407	7.782	9.782
200	0.93	0.57	-	-
300	1.98	1.20	-	-
400	3.38	2.05	-	-
500	5.10	3.10	-	-
600	7.15	4.34	-	-
700	9.51	5.77	3.57	-
800	12.18	7.39	4.43	-
900	15.15	9.20	-	-
1000	18.42	11.18	-	-
1100	21.98	13.34	5.18	-
1200	-	15.67	6.08	2.00
1300	-	18.17	7.06	2.32
1400	-	20.85	8.09	2.66
1500	-	-	9.20	3.02
1600	-	-	10.36	3.41
1700	-	-	11.60	3.81
1800	-	-	12.89	4.24
1900	-	-	14.25	4.68
2000	-	-	15.67	5.15
2100	-	-	17.15	5.63
2200	-	-	18.69	6.14
2300	-	-	20.30	6.67
2400	-	-	-	7.22
2600	-	-	-	8.37
2800	-	-	-	9.60
3000	-	-	-	10.91
3200	-	-	-	12.29
3400	-	-	-	13.75

The desired pressure at the inlet to the lateral is selected when the pivot is designed. The actual pressure is determined by the performance of the pump, wear of sprinklers and pressure regulators, and water or pressure loss along the mainline that supplies the pivot. Adding a pressure gauge to the lateral at the inlet is an excellent way to monitor center pivot performance. If the inlet pressure drops much below the design specification, the cause of the problem should be determined and corrected if feasible.

Figure 13.6. Pressure loss distribution factor for center pivot laterals.

The pressure loss due to friction along center pivot laterals is computed similarly to that for moved lateral systems. The multiple outlet factor for center pivots does not change with the number of sprinklers along the lateral. The multiple outlet factor for center pivots without an end gun is about 0.54 and 0.56 for systems with an end gun.

Center pivot laterals are specially made to conduct the water and to provide the strength needed to suspend the lateral above the ground. The lateral diameter is also unique for center pivots and moving lateral systems. The typical lateral is made of galvanized steel pipe with a wall thickness of 0.109 inches. A C value in the Hazen-Williams equation (Equation. 8.11) of 140 is typically used to compute friction loss along the pivot. Values for the pressure loss per unit length of center pivot laterals are given in Table 13.3 for typical lateral diameters. Table 13.3 is for laterals that are all one size. As will be illustrated below, 80% of the pressure loss of a pivot lateral occurs in the first half of the lateral. Pressure loss can be reduced by using larger diameter pipe for the initial portion of the lateral rather than one diameter for the whole lateral. The pressure loss for systems with multiple pipe diameters are given in Table 13.4. The pressure distribution factor for center pivots is given in Figure 13.6. The elevation gain in Equation 13.3 is elevation of the point of concern minus the elevation at the pivot base. If the pivot base is higher than the point of concern, then E_g < 0.

Variation of pressure as the pivot rotates around the field affects the uniformity of water application. It is useful to monitor the pressure of the outer end of the pivot as it rotates around the field. The critical points will be the highest and lowest elevations of the outer half of the pivot lateral. If the pressure varies more than 20% of the design pressure for the end of the lateral, consideration should be given to the use of pressure compensating nozzles or pressure regulators. Lower pressures than expected at the highest elevations may be a sign that the pump is not operating as originally designed or that there are leaks in the system.

Table 13.4. Pressure loss in center pivot laterals with two diameters of pipe, psi/1,000 feet. Values are for laterals without end guns. Multiply by 1.037 for systems with an end gun.
Pressure Loss in Laterals Composed of 8- and 6-inch Diameter Pipe
FlowRate(gpm)	Fraction of Lateral That Is 8-inch O.D. Galvanized Steel Pipe
	1.0	0.9	0.8	0.7	0.6	0.5	0.4	0.3	0.2	0.1	0.0
900	3.6	3.6	3.7	3.9	4.2	4.7	5.4	6.2	7.1	8.1	9.2
1000	4.3	4.4	4.5	4.7	5.1	5.8	6.6	7.6	8.7	9.9	11.2
1100	5.2	5.2	5.3	5.6	6.1	6.9	7.8	9.0	10.4	11.8	13.3
1200	6.1	6.1	6.2	6.6	7.2	8.1	9.2	10.6	12.2	13.9	15.7
1300	7.1	7.1	7.2	7.6	8.3	9.4	10.7	12.3	14.1	16.1	18.2
1400	8.1	8.1	8.3	8.8	9.6	10.7	12.3	14.1	16.2	18.5	20.8
1500	9.2	9.2	9.4	10.0	10.9	12.2	13.9	16.0	18.4	21.0	23.7
1600	10.4	10.4	10.6	11.2	12.3	13.7	15.7	18.0	20.7	23.7	26.7
1700	11.6	11.6	11.9	12.6	13.7	15.4	17.6	20.2	23.2	26.5	29.9
1800	12.9	12.9	13.2	14.0	15.2	17.1	19.5	22.4	25.8	29.4	33.2
Pressure Loss in Pivot Laterals Composed of 10- and 8-inch Diameter Pipe
FlowRate(gpm)	Fraction of Lateral That Is 10-inch O.D. Galvanized Steel Pipe
	1.0	0.9	0.8	0.7	0.6	0.5	0.4	0.3	0.2	0.1	0.0
1900	4.7	4.7	4.8	5.2	5.8	6.7	7.8	9.2	10.8	12.5	14.2
2000	5.1	5.2	5.3	5.7	6.4	7.3	8.6	10.1	11.8	13.7	15.7
2100	5.6	5.7	5.8	6.2	7.0	8.0	9.4	11.1	12.9	15.0	17.1
2200	6.1	6.2	6.4	6.8	7.6	8.7	10.2	12.0	14.1	16.4	18.7
2300	6.7	6.7	6.9	7.4	8.2	9.5	11.1	13.1	15.3	17.8	20.3
2400	7.2	7.3	7.5	8.0	8.9	10.3	12.0	14.2	16.6	19.2	22.0
2500	7.8	7.8	8.1	8.6	9.6	11.1	13.0	15.3	17.9	20.7	23.7
2600	8.4	8.4	8.7	9.3	10.3	11.9	13.9	16.4	19.2	22.3	25.5
2700	9.0	9.0	9.3	10.0	11.1	12.8	15.0	17.6	20.6	23.9	27.3
2800	9.6	9.6	9.9	10.6	11.9	13.7	16.0	18.8	22.1	25.6	29.2
2900	10.2	10.3	10.6	11.4	12.7	14.6	17.1	20.1	23.5	27.3	31.2
3000	10.9	11.0	11.3	12.1	13.5	15.5	18.2	21.4	25.1	29.0	33.2

13.3 Application Rate

13.3.1 Center Pivots

The rate of water application under a center pivot has unique characteristics that are important in design and management. A tower at the end of a conventional center pivot might move at 2 feet per minute. The first tower on the pivot might move at 1/10 that speed. Since each location should receive the same depth of water each irrigation, water must be applied 10 times as rapidly at the outer tower compared to the inner tower. The very high rate of water application can exceed the soils infiltration rate. If adequate storage is not provided on the soil surface to retain the water while infiltration occurs the water may run downhill. This runoff process can be acute with center pivot irrigation on steep slopes and soils that have low infiltration rates. Yet pivots can work in these conditions if they are properly designed. Therefore, it is important to determine the factors that control the rate of application.

Figure 13.7. Comparison of the application rate of the pivot and the infiltration rate of the soil (adapted from Martin et al., 2017).

The typical application rate is shown in Figure 13.7. The example shows that water will only be applied for about 25 minutes at the distal end of the lateral for this pivot. The rate of water application reaches a peak when the pivot lateral is directly overhead of the point of concern. Then the rate decreases as the pivot continues to move forward. The application pattern is generally described as an elliptical rate.

Two characteristics are important to evaluate the elliptical rate:

• the highest or peak rate of application when the pivot lateral is directly overhead and
• the total length of time that water is applied to the location, called the time of wetting.

The peak application rate is given by:

(13.4)

and the time of wetting is given by:

(13.5)

where: A_p = the peak application rate (in/hr),

T_w = the time of wetting (hr),

R = the radial distance from the pivot point (ft),

D_c = the diameter of coverage of the sprinkler at position R (ft),

C_g = the gross system capacity (gpm/ac), and

d_g = gross application depth (in).

These relationships show that the peak application rate is totally determined by the design of the center pivot. The length of the pivot lateral, the type of sprinkler used, and the system capacity determine the peak application rate. The peak rate does not change with the speed of rotation of the pivot. The time of wetting at a point is a factor of these variables and the depth of water applied per irrigation. Thus, the time of application can be controlled by management, i.e., by changing d_g.

The rate of infiltration of a hypothetical soil is also shown in Figure 13.7. The diagram shows that the application rate of the pivot exceeds the infiltration rate for most of the time of wetting. During this time water could runoff if it is not stored on the soil surface.

What can be done to reduce runoff? The three design variables, C_g, D_c, and R that affect the peak application rate and the time of wetting could all be changed when the pivot is designed and installed. The system capacity used in selecting an irrigation system is based on the crop needs for the soil and climate at the location. Thus, the system capacity should not be reduced much below the requirement just to prevent runoff. The length of the pivot lateral is determined by the geometry of the field. In some cases, there is a choice between installing one very long system or several shorter systems. The investment cost per acre will be less for the longer system but the potential for runoff is higher.

The primary alternative to reduce runoff problems is to select sprinkler devices that provide the necessary diameter of coverage. This is generally done at the time the system is purchased but can be changed later. Once the pivot is installed the only system management alternative to reducing runoff is to reduce the depth of application. The maximum depth of application and the appropriate types of sprinkler devices are discussed in the next section on sprinkler and nozzle selection.

13.3.2 Linear or Lateral Move

One inherent advantage of linear or lateral move systems over center pivots is that peak application rates are much lower for these systems. This is because with linear move systems, the discharge is distributed uniformly throughout the lateral’s length while with center pivots, discharge increases with distance from the pivot point. The peak application intensity of a linear move can be calculated with the following equation:

(13.6)

where: Q = the system’s flow rate (gpm),

L = the lateral length, and

D_c = the diameter of coverage of the sprinkler heads on the system.

13.4 Sprinkler and Nozzle Selection

The center pivot operator should be concerned with the following questions regarding the sprinkler and nozzle package installed on a center pivot.

• What type of sprinklers and nozzles to install on the pivot?
• Are the proper sprinklers and nozzles installed at the correct location along the pivot lateral?
• Are the sprinklers working properly?

Determining the proper nozzle size for each sprinkler along the center pivot lateral is complex. The number of nozzles needed, the size of the nozzles, spacing of sprinklers at the point of concern, the diameter of coverage, pressure loss along the lateral, the use of pressure regulators, and the elevation gain around the field are all issues. In addition, every sprinkler along the pivot lateral is considered individually. The details of this design process will not be considered here. Generally, the nozzle sizes along the lateral will be determined by the center pivot or sprinkler manufacturer. The center pivot owner and operator should obtain a copy of the sprinkler package chart. This chart specifies the type of sprinkler and nozzle sizes to be used at a particular location along the lateral. The operator can use the chart to check the final installation to determine if errors were made in shipping or construction.

An important decision for the center pivot manager is the type of sprinkler device to use. Many choices of sprinklers are available. Early center pivots used only impact sprinklers. These have the same performance characteristics as presented in Chapter 11. Impact sprinklers are appealing because they provide a large diameter of coverage which produces lower application rates and less runoff potential. Recently these sprinklers have been made of plastic leading to sprinkler packages that are price competitive because fewer sprinklers are required with the larger diameter of coverage. The primary disadvantages of impact sprinklers are the higher operating pressures required and the higher potential for evaporation and drift losses. To reduce the evaporation potential low angle impact sprinklers have been developed. The range nozzle on conventional impact sprinklers emits water at an angle 23° above the horizon. The low angle sprinklers discharge water at an angle of about 7°. Low-angle sprinklers can be used with special nozzles for operation at lower pressures than conventional sprinklers.

Special spray head devices that discharge water onto pads have been developed for use on center pivots. The pad could either be stationary or moving. The devices can generally be installed in an upright position or inverted. When the pad devices are inverted they are attached to drop tubes that allow the devices to be positioned below the truss assembly, or even lower to apply water just above the crop canopy. Dropping the devices closer to the crop canopy reduces the potential for evaporation or drift but increases the runoff potential. The advantage of the rotating and wobbling pad devices is the increased diameter of coverage requiring fewer devices while providing lower application rates and better uniformity.

Various types of pads can be used with both the stationary and moving spray heads. The face of the pad can be smooth or grooved. The smooth pad produces smaller droplets. Grooved pads produce small streams of water off of the pad leading to larger drops than the smooth pad. The depth of the groove and the number of grooves on the pad determine the size of the droplets. Pads are also designed for use when the device is upright or inverted. If the device is placed on top of the pivot lateral, a concave pad is used to direct the spray toward the soil. When the device is inverted and dropped below the pivot lateral, a flat or convex pad is used to direct the water horizontally to maximize the diameter of coverage. Two issues are important when selecting the type of pad: drift and energy of impact of the droplet. Small droplets contain less kinetic energy when they reach the soil surface than large droplets. If the soil at the site has low aggregate stability, the large droplets (from pads with large grooves) can cause a seal to form at the soil surface leading to lower infiltration rates. If you irrigate when there is little cover on the soil, then smooth or shallow grooved pads would be desirable. Small drops are affected by wind much more than larger drops. If you irrigate in a windy area and infiltration rates are good, you may choose a deeper grooved pad. In windy areas mounting the spray pad devices below the pivot lateral closer to the crop may be a good idea. In areas with low infiltration rates and/or steep slopes, impact sprinklers may still be preferable because of the smaller runoff potential.

13.5 Depth of Water Applied

The depth of water applied each irrigation greatly affects the amount of potential runoff. As indicated earlier, the maximum application rate does not change with the depth of water applied. However, the time required to apply the water is directly proportional to the depth applied. Since the infiltration rate of the soil decreases with time, the longer it takes to apply water the greater the chance of runoff. The example in Figure 13.8 shows that there would be little runoff for an application of 0.8 inches each irrigation. Contrast that to the potential runoff for an application of 2.4 inches. There would certainly be substantially more runoff for the larger irrigation. It is desirable to apply smaller depths of water each irrigation with center pivots than to apply one large irrigation. It is common to apply from 0.70 to 1.25 inches per irrigation with pivots. This will usually require irrigation every 3 or 4 days.

Two other factors affect the depth of water to apply each irrigation: the condition of the soil surface where the pivot must travel and the evaporation rate of the applied water. If large irrigations are applied the soil surface becomes much wetter, and in some conditions, the traction of the pivot suffers. Any water that runs off often accumulates in the tracks left by the pivot wheels. The water then either flows downhill in the track or ponds in the track and surrounding area. If the pivot still has to pass through the low spot for that irrigation, or if the water remains at the time of the next irrigation, the wheel tracks from the pivot can become very deep and the pivot may have difficulty moving through these areas. Applying smaller depths of water each irrigation can mitigate some of these factors leading to more dependable operation.

Figure 13.8. Effect of application depth on the potential for runoff (adapted from Martin et al., 2007).

The loss of water due to evaporation can be important for high-frequency irrigation. The amount of water that evaporates while the water droplets are in the air is much lower than many producers estimate. The maximum loss of evaporation while the drops are in the air is less than 5% for even the most severe wind and drying conditions. The major loss of water to evaporation comes after the water has reached the crop and soil. Research has shown that water on the canopy and bare soil will evaporate very quickly. In windy, arid conditions, such as the Great Plains of the U.S., corn canopies dry in about 1 hour after irrigation in the middle of the day. The water that evaporates from the canopy uses some energy that would have caused transpiration had the crop not been irrigated. Thus, not all of the canopy evaporation is truly a loss. However, high-frequency irrigations that wet the crop or soil will lead to increase evaporation and somewhat lower efficiency. Estimates are that under very windy and arid conditions in the southern High Plains of the U.S. the efficiency of pivots equipped with impact sprinklers is about 85%. The efficiency increases to about 90% for devices that apply water just above the crop canopy and to as high as 95% for LEPA systems that apply water near the soil surface without wetting the canopy. For application efficiencies to be this high, water must not runoff the field.

In any case, very high-frequency irrigation with small depths can lead to reduced efficiency if canopy evaporation becomes excessive. There have been reports that high- frequency irrigation maintains a wet soil surface that leads to reduced infiltration rates and increased runoff.

There are several conflicting conditions regarding the proper depth of application for pivots. It is critical that managers develop a routine of observing the performance of the pivot on the steepest areas of the field near the outer half of the pivot. Managers should experiment to determine the maximum depth that can be applied without runoff problems occurring. This depth may decrease during the season so monitoring during the season is important. Managers could then adjust the depth of application down from the maximum depth if desired. Irrigation intervals shorter than 2 days are probably impractical. If the system has to operate at that or shorter frequencies, the sprinkler package may be inappropriate or special tillage may be needed to prevent runoff.

The depth of application on pivots is adjusted by controlling the average speed of the end tower. On electric-drive pivots a timer can be set between 0 and 100%. At 100% the distal end tower is supplied power continuously and the tower moves at a constant speed. This setting produces the smallest depth of application possible. To apply larger irrigations the timer setting is reduced. The timer setting represents the percent of a 1-minute interval that the end tower receives power. For example, a 50% timer setting provides power to the end tower for 30 seconds and it moves at a constant speed. The end tower remains stationary for 30 seconds. Operation of hydraulically powered systems is slightly different. The end tower on these machines moves constantly. The control setting regulates the delivery of oil to the end tower and controls the speed. The control setting represents the relative speed of the end tower.

For electric drive systems the relationship of the control setting and the depth of water applied is given below:

(13.7)

where: C_s= control setting (%),

R_l = distance from pivot base to end tower (ft),

C_g = gross system capacity (gpm/ac),

v_m = maximum continuous speed for the end tower (ft/min), and

d_g = gross depth of irrigation water to apply (in).

For example, to apply 1.3 inches of water with a pivot that has a maximum speed of 8 feet per minute, a capacity of 7 gpm/ac and the last tower is 1,280 feet from the pivot base; a control setting of 20% would be required. Manufacturers supply a tabular solution of Equation 13.7 for specific pivot designs.

The maximum depth of application that can be applied with a center pivot depends upon the soil infiltration, surface storage available, and peak application intensity of the system. The Natural Resources Conservation Service (NRCS, formerly the Soil Conservation Service) has categorized soils into intake families. Examples are shown in Table 13.5. In general, a low intake family, such as 0.1, is characterized by its high clay content and low infiltration rate. A high intake family, such as 3.0, is characterized by its high sand content and high infiltration rate.

Table 13.5. NRCS soil intake families (adapted from https://efotg.sc.egov.usda.gov//references/public/NE/NE_irrig_Guide_index.pdf).
Intake Family	Surface Soil Texture and Subsoil Permeability	Representative Soil Series
0.1	Clays, silty clays, clay loam, silty clay loams (with slowly & very slowly permeable soils)	Albaton c Luton sic Wabash sic Filmore sicl	Crete sicl Pawnee cl Wymore sicl
0.3	Silt loam, loam silty clay loam, loams (with slow or moderately slow permeability)	Butler sil Colo sicl Wood River sil Belfore sicl	Burchard cl Hastings sicl Moody sicl Sharpsburg sicl
0.5	Silt loam, loam (with moderately slow or moderate permeability)	Hall sil Holder sil Holdrege sil	Judson sil Keith l Richfield l
1.0	Fine sandy loam, sandy loam, silt loam, loam, very fine sandy loam (with moderately slow to moderately rapid permeability) Loam, silt loam, very fine sandy loam, clay loam, sandy clay loam (with moderate or moderately rapid permeability)	Hord fsl Keith fsl Mitchell fsl	Crofton sil Monona sil
1.5	Fine sandy loam, loam, very fine sandy loam, sandy loam, silt loam (with moderate or moderately rapid permeability)	Anselmo vfsl Bayard vfsl Cass vfsl Alda fsl Brocksburg fsl	O’Neill fsl Rosebud fsl
2.0	Loamy fine sand, loamy very fine sand, loamy sand (with moderately rapid permeability)	Alice lfs Anselmo lfs Libory lfs Ovina lfs	Hersh lfs Jayem lfs Sarben lfs Otero lvfs
3.0	Loamy fine sand, loamy sand, fine sand, fine sandy loam, loamy very fine sand (with rapid permeability)	Bankard ls Dunday lfs Inavale lfs	Thurman lfs Valent lfs Valentine lfs

As stated earlier, the storage of water on the soil surface in depressions can help avoid runoff in cases where application intensity exceeds soil infiltration rate. Figure 13.9 illustrates the concept of the storage in depressions. The amount of storage that is available depends upon field slope. For “conventional” tillage practices, this storage can be estimated from Table 13.6.

Figure 13.10. Effect of sprinkler packages on application rate.

Table 13.6. Allowable soil surface storage (without artificial storage) values for various slopes (from Dillon et al., 1972).
Slope(%)	Allowable Soil Surface Storage (in)
0–1 1–3 3–5 5	0.5 0.3 0.1 0.0

Figure 13.11. Illustration of wetted diameter (adapted from Martin et al., 2017).

Peak application intensity is an important factor when considering the potential for runoff of water (maybe we’ve lost sight by now—we want to avoid runoff). Peak application intensity can be calculated from Equation 13.4. The results of Equation 13.4 are shown in Figure 13.10. Obviously, wetted diameter, illustrated in Figure 13.11, has a major influence on peak intensities as does system capacity and the distance from the pivot point (Figure 13.12).

Figure 13.9. Influence of field slope on depressional storage. Photograph courtesy of USDA-NRCS (adapted from Martin et al., 2017).

Figure 13.13 provides a “management guide” for avoiding runoff during water application (Gilley, 1984; Martin et al., 2007). The figure uses the important factors that we’ve just discussed to indicate how much water can be applied and yet avoid runoff. The use of Figure 13.13 is illustrated in the following Examples 13.1 and 13.2.

What if runoff is a problem? There are several design, management, and cultural practices that can be used if runoff is a problem. These practices are summarized in Table 13.7.

Figure 13.12. Effect of distance from pivot point on application intensity.

Figure 13.13. Maximum irrigation application depth (dg) for different soils and peak application rates for zero potential runoff. Applies to center pivot and lateral move systems of any length.

Table 13.7. Methods for reducing runoff under center pivot and lateral move sprinkler systems and their potential disavantages (bullet items).

1. Reduce system capacity need to irrigate more hours per year increases chances of soil water stress 2. Reduce application depth requires more revolutions per year increases frequency of leaf wetting 3. Change sprinkler package to increase wetted diameter may require higher pressure changes to pump and power unit may be needed 4. Increase surface storage special interrow tillage practices may be needed increased field operations 5. Increase soil surface cover with crop residues may require significant change to farming operations

In Table 13.8 we present a method for estimating the required sprinkler wetted diameter to avoid runoff for various soil textures, surface storages, and desired application depths for the case of a 1300-ft center pivot lateral. The table is based on methods discussed in Martin et al. (2012), including the Green-Ampt approach for infiltration. The increase in soil surface storage using crop residues is also presented in Martin et al. (2017). One method for increasing wetted diameter is to use boom backs, illustrated in Figure 13.14. Boombacks have also been used to address problems with rutting in center pivot wheel tracks by keeping the wetting pattern from the sprinkler behend the wheels.

13.6 Remote Monitoring of System Operation and Control

Figure 13.14. Boom backs used to increase wetted diameter for center pivot or lateral move irrigation systems (from Martin et al., 2017).

GPS and communication technology used by the center pivot and lateral (linear) move irrigation industry makes it relatively easy to remotely monitor system operation and control the water application using a computer, tablet, or mobile device. With little effort, irrigation managers can implement important water management decisions and detect system malfunctions or operational problems. For example, did it rain at the site and should the system be shut off? Does the soil moisture sensor suggest that the field is too wet or too dry? Are the system pressure and flow rate in agreement with what they should be? If the flow rate is high given the system pressure perhaps there is a broken sprinkler head. If both the flow rate and pressure are too low there could be a problem with either the well or pump. High pressure and low flow may indicate plugged nozzles in the system. The latter three cases will warrant a field inspection which could include the use of binoculars or unmanned aircraft (drone) to check for leaks or plugged nozzles.

13.7 Variable Rate Irrigation

Variable rate irrigation (VRI) technology allows for spatial management of soil water (Camp et al., 1998; Evans et al., 2013). Different depths of irrigation can be applied based on the irrigation requirement for each part of the field depending on variability in soils, topography, and ET. VRI technology is available for both center pivots and lateral moves, although it is more common for center pivots.

Sector control (speed control) is a lower cost option for VRI that simply varies the speed of the last tower on a center pivot. Increasing the speed results in a lower application depth. This method results in irrigation management zones shaped in sectors (“pie slices”) (Figure 13.15).

In addition to varying the speed of the irrigation system, zone control VRI also controls the nozzle flow rate for individual sprinklers or groups of sprinklers along the pivot lateral (Figure 13.15). The nozzle flow rate is typically reduced from the design flow rate by using a valve to pulse the nozzle on and off. This provides a finer resolution of control compared to speed control, and irrigation management zones can be defined to follow the shape of irregular soil patterns. One drawback of zone-control VRI is the higher investment cost compared to speed control VRI. Zone control is most likely to be profitable in situations where VRI can be used to increase yield quantity and/or quality.

If the growing season starts at field capacity, soils with lower available water capacity with need to be irrigated before soils with a larger available water capacity. VRI can also be used to manage problems associated with topography, e.g. applying less water in a low spot that tends to be wet from accumulated runoff. Prescription maps for VRI are often based on soils maps and yield maps (Kranz et al., 2014). Irrigation scheduling for VRI is discussed in Chapter 6. VRI capability is being incorporated into cloud-based monitoring and control systems for center pivots. A thorough review of VRI, including advantages and disadvantages, is presented in O’Shaughnessy et al. (2019).

Figure 13.15. Example variable rate irrigation control scenarios: sector/speed control (left), and zone control (right).

13.8 Community Shared Center Pivot Systems

Figure 13.16. Shared center pivot irrigation systems for smallholder farms in Rwanda. (Photo courtesy of Ankit Chandra, DWFI.)

Since the cost of a center pivot increases proportionally with the length of the pivot, but the area irrigated increases proportionally with the square of the pivot length, the cost of the pivot per unit of land area ($/ha or $/ac) is lowest for large (longer) pivots. Therefore, pivots have been widely adopted on large fields (e.g., 60-70 ha). However, a large pivot can also be used to irrigate several small fields. This approach is being implemented on some smallholder farms in Sub-Saharan Africa (Figure 13.16; Chandra, 2020). Application depths can easily be changed for different sectors, either by changing the pivot speed for different angles in the pivot panel or using speed control VRI. Changing application depths enables the shared pivot to accommodate various crop types and planting dates in different sectors. It is ideal if fields within a sector all have the same crop and planting date, resulting in similar irrigation needs. It is conceivable that zone control VRI could be used to provide unique irrigation management for many small fields of any shape and size, although zone control increases the complexity of the system and the level of management required. A shared center pivot required water users within the pivot to cooperate in a way similar to an irrigation district with canals for water deliver.

13.9 Summary

Center pivots are now used on more cropland than all of the other irrigation systems combined in the United States. Worldwide, center pivots and lateral move systems are gaining in popularity. Center pivots have grown in popularity because they can be very efficient (85 to 95% is possible), they can apply whatever depth of water is needed, and these systems have the capability to irrigate where surface and periodically-moved sprinkler systems are not feasible. Manufacturers have continued to improve pivots to operate at lower pressures and have improved sprinkler performance.

Equations to determine sprinkler discharge, area irrigated, and pressure distribution are presented. Minimization of surface runoff from pivot sprinklers is a major management concern discussed in detail. Application depths of 0.70 to 1.25 inches per irrigation resulting in irrigation every 3 to 4 days during peak periods of evapotranspiration are typical management decisions for center pivots.

Monitoring the operation and remote control of center pivot and lateral move systems is relatively easy using GPS and communication technology. Variable rate irrigation (VRI) technology permits different depths of water depending on variability in soils, topography, and evapotranspiration. VRI technology can be accomplished by speed control or varying the flow rate from the sprinklers. This technology is suitable for pivots shared to irrigate several small fields.

Questions

1. Describe the benefits and limitations of mechanized sprinkler irrigation systems.

2. A center pivot will be installed with 6 5/8-inch outside diameter pipe. The system will include 7 towers (178-ft spans), with a system length of 1,280 ft (including overhang). The flow rate of the entire system is 700 gpm. Determine the pressure loss due to friction (psi) in the pivot lateral without the end gun operating (Table 13.3).

3. For the center pivot in the previous question, determine the pressure required at the bottom of the pivot riser considering the nozzle pressure (10 psi), minor losses in regulator (assume 5 psi), pressure loss due to friction in pivot lateral, height of nozzle above ground (8 ft), and elevation change along the pivot lateral. The height of the pivot riser is 12 ft. The highest elevation in the field is at the north edge of the field, 14 feet higher than the elevation at the pivot point.

4. Calculate the nozzle flow rates and specify the nozzle sizes at the mid-point and at the outside end of the pivot lateral described in the previous questions. The sprinkler spacing (S) is 10 ft. Assume straight-bore nozzles.

5. For the irrigation system in the previous questions, determine the well pump total dynamic head, pump motor horsepower, and the number of pump stages required. The pump will be a Flowserve 12SKL (32.60) semi-open impeller (Figure 8.11). Choose the impeller diameter with the best efficiency. Assume that the well is located at the pivot point.

6. The predominate soil texture in the field is a Holdrege silt loam. What is the NRCS Intake Family?

7. The diameter of coverage for the sprinklers is 25 ft. The typical slopes in the field are 1-2%. Using the nozzle flow rates calculated in Question 4, determine the peak application rate and the maximum application depth that can be applied (in) without causing runoff. Is this acceptable?

8. Find the pivot speed (timer setting) for the application depth determined in the previous question. The maximum tower speed is 6 ft/min. Use the system characteristics provided in Question 2.

References

Bittinger, M. W., & Longenbaugh, R. A. (1962). Theoretical distribution of water from a moving irrigation sprinkler. Trans. ASAE, 5(1), 26-30.

Camp, C. R., Sadler, E. J., Evans, D. E., Usrey, L. J., & Omary, M. (1998). Modified center pivot system for precision management of water and nutrients. Appl. Eng. Agric., 14(1), 23-31.

Chandra, A. (2020). Water-energy-food linkages in shared smallholder irrigation schemes. MS thesis. Department of Biological Systems Engineering, University of Nebraska-Lincoln.

Dillon Jr, R. C., Hiler, E. A., & Vittetoe, G. (1972). Center-pivot sprinkler design based on intake characteristics. Trans. ASAE, 15(5), 996-1001.

Evans, R. G., LaRue, J., Stone, K. C., & King, B. A. (2013). Adoption of site-specific variable rate sprinkler irrigation systems. Irrig. Sci., 31(4), 871-887.

Gilley, J. R. (1984). Suitability of reduced pressure center pivots. J. Irrig. Drain. Eng., 110(1), 22-34.

Heermann, D. F., & Hein, P. R. (1968). Performance characteristics of self-propelled center-pivot sprinkler irrigation system. Trans. ASAE, 11(1), 11-15.

Kranz, W. L., Irmak, Martin, D. L., Shaver, T. M., & van Donk, S. J. (2014). Variable rate application of irrigation water with center pivots. University of Nebraska-Lincoln Extension Circular EC2000.

Lamm, F. R., Porter, D. O., Bordovsky, J. P., Evett, S. R., O’Shaughnessy, S. A., Stone, K. C., Kranz, W. L., Rogers, D. H., & Colaizzi, P. D. (2019). Targeted, precision irrigation for moving platforms: Selected papers from a center pivot technology transfer effort. Trans. ASABE, 62(5), 1409-1415.

Martin, D. L., Kincaid, D. C., & Lyle, W. M. (2007). Design and operation of sprinkler systems. In G. J. Hoffman, R. G. Evans, M. E. Jensen, D. L. Martin, & R. L. Elliot (Eds.), Design and operation of farm irrigation systems. St. Joseph, MI: ASABE.

Martin, D., Kranz, W., Smith, T., Irmak, S., Burr, C., &Yoder, R. (2017). Center pivot irrigation handbook. University of Nebraska-Lincoln Extension Circular EC3017.

Martin, D. L., Kranz, W. L., Thompson, A. L., & Liang, H. (2012). Selecting sprinkler packages for center pivots. Trans. ASABE 55(2): 513-523.

O’Shaughnessy, S. A., Evett, S. R., Colaizzi, P. D., Andrade, M. A., Marek, T. H., Heeren, D. M., Lamm, F. R., & LaRue, J. L. (2019). Identifying advantages and disadvantages of variable rate irrigation: An updated review. Appl. Eng. Agric., 35(6), 837-852.

von Bernuth, R. D. (1983). Nozzling considerations for center pivots with end guns. Trans. ASAE, 26(2), 419-422.