SIMULATED MODEL OF CENTER PIVOTSPRINKLER IRRIGATION SYSTEMS

E. Rapp1, D.S. Chanasyk2, and B.C. Horvath31Departmentof Agricultural Engineering, and 2Department of Soil Science,

University of Alberta, Edmonton, Alberta, T6G 2G6;>Lethbridge Northern Irrigation District, Lethbridge, Aha. T1H3V8

Received 4 June 1979

RappE., D.S. Chanasyk, and B.C. Horvath 1979. Simulated model ofcenter pivot sprinkler irrigation systems. Can. Agric. Eng.

Asimulated model oftwo center pivot (C.P.) sprinkler irrigation systems (Circle Master and Valley 1160), operating underlocal climatic conditions, was developed to examine theeffect ofwind ontheuniformity ofwater distribution andtoevaluate thesystems' performance under actual windy conditions. The uniformity coefficients were affected by both thewind velocity andwind direction. However, the effect ofwind direction was more pronounced. Performance oftheC.P. systems was determinedfrom field measured application depths aswell as those simulated bythemodel. Ingeneral thefield coefficients were lower thanthe simulated coefficients but both the field and thesimulated coefficients were within the acceptable level of 80-90%.

INTRODUCTION

Center pivot (C.P.) irrigation is presentlyan increasingly popular method of irrigatinglarge agricultural areas. By definition, a C.P.system consists of a lateral line of sprinklerscontinuously rotating around a center-pivotpoint. Water under pressure is supplied tothe lateral at the pivot. The lateral issupported by a number of self-propelledtowers, each having a driving mechanismutilizing wheels or tracks. The adjustablespeed of travel allows the application of 10 -100 mm of water per revolution.

The important features of a well designedC.P. system, as recognized by the AmericanSociety of Agricultural Engineers (1978) are:the capacity to meet the peak moisturedemand of the crops irrigated, to replacemoisture in the soil profile frequentlyenough to maintain conditions for optimumplant growth, and to refill the soil moisturereservoir uniformly.

The first two features are directly relatedto the soil type, the crop grown and the areato be irrigated. The usual approach toachieving relatively uniform waterdistribution is to increase the discharge fromthe first to the last sprinkler; that is, byincreasing the application rates inproportion to an increasing area irrigated byindividual sprinklers. Previous research(Bittinger and Longenbaugh 1962) hasindicated that the theoretical uniformityvaries from the actual field uniformity.Large uniformity deviations are the result ofinadequate sprinkler systems design andexternal factors, mainly the wind. The effectof wind on the distribution from stationarysprinkler systems has been documented(Korven 1952). However, the distributionfrom C.P. systems as affected by wind hasnot been examined to any great extent.

This study is an attempt to analyzeexperimentally and theoretically theinterrelationships between wind, sprinklerpatterns and uniformity of waterdistribution and to provide a model forpredicting the application depths from C.P.systems under windy conditions.

MODEL DEVELOPMENT

The model simulating the C.P. irrigationsystem (Horvath 1979) consisted of twoseparate parts. In the first part the dynamicsof water droplets in flight were formulatedas second-order differential equations todetermine the basic wetted patterns. Therequired input information such as the rangeof droplet particle size and initial particlevelocities were obtained from experimentalanalyses and the manufacturer's sprinklerspecification, respectively. Basic information on wind direction and magnitude indiscrete time intervals of 15 min were con

sidered in the analysis to study the distortionof the wetted patterns and the overlappingeffect of the adjacent sprinklers. The wettedpattern of sprinkler for the no-wind condition was described by the equation of a circle.Under windy conditions, however, thewetted pattern was approximated by curvefitting using two overlapping ellipses with acommon minor axis.

Triangular and elliptical cross-sectionalJ distribution profiles were assumed to

represent the extremes for individualsprinkler patterns. Interpolation techniqueswere used to determine the desired wetted

patterns from those derived from closelyrelated initial conditions. This was necessarybecause of the extremely long computersimulation time required to compute theactual wetted patterns from the droplettrajectories.

The second part of the model involvedthe simulation of the operating C.P.system in relation to the rows of measuringreceptacles used in the field measurements.Actual simulation of the moving wettedpatterns for the rotating sprinklers weredeveloped for each one-half degreeincremental angular change of the lateral.Actual wind information monitored duringthe testing period was modelled in theprogram to assess the performance of thesimulation model in terms of applicationdepths and the coefficients of uniformity.

CANADIAN AGRICULTURAL ENGINEERING, VOL. 21, NO. 2, DECEMBER 1979

MATERIALS AND METHODS

Two different C.P. sprinkler irrigationsystems were selected for evaluation of theirrelative performance. Both C.P. systemswere located on sites that were free of windbarriers so that the microclimaterepresented the typical climatic conditionsof southern Alberta. Perennial forage cropswith rapid growth rates such as alfalfa andgrass were grown on the sites. The frequentharvest of these crops permitted repeatmeasurement of application depths withoutcrop interference.

Application depths for the C.P. systemswere measured using the traditionalmeasuring cans set out along a radial pathbeginning at the pivot with a convenientspacing (Ring 1976). As the prevailing winddirections in southern Alberta are west and

southwest, the rows of measuring cans onboth sites were placed in the directionsshown (Fig. la, b) in order that the variedeffect of the wind direction relative to the

lateral could be readily investigated.During the experimental periods,

meteorological data were recordedcontinuously at a station installed at the sitesufficiently distanced away from the effect ofthe sprinklers. The amount of precipitationand evaporation were measured using a setof control receptacles.

Measurements of application depths forboth C.P. systems were made for tworotational speeds of travel during periods ofvaried weather conditions. After the lateral

made a complete pass over a row ofmeasuring cans, the volume of watercollected in each can was measured using agraduated cylinder and converted to anapplication rate. When depth measurementswere delayed, the necessary corrections weremade for either evaporation losses or gainsdue to precipitation. The loss or gain wasestimated from the change in volume of thecontrol cans.

The variations in wind velocities and

wind direction were recorded continuouslythroughout the test periods. Since it was notpossible to determine the application rates

141

measured at each individual can in the rowduring a complete pass of the lateral, theeffects of wind on each sprinkler could not befully evaluated. Therefore, a mean windvelocity and direction was used to relate thewind effects to the uniformity distribution ofthe sprinklers. This mean velocity anddirection was derived as an average of thevalues recorded for every 15-min timeinterval throughout the duration of a singlelateral pass.

Wind velocities and directions were

required as input variables in the C.P.performance model (Horvath 1979).Because of the lengthy time taken for alateral to make a complete pass across therows of measuring cans (approximately 14hfor one-quarter revolution), simulation ofeach change of the continuously fluctuatingwind conditions was not feasible. For thisreason, an approximate time interval of 15min was specified during which arepresentative average wind velocity anddirection was computed for each intervalthroughout the experimental period. Thetime interval was adjusted to ensure aninteger number of one-half degreeincrements of lateral rotation. This wasnecessary to facilitate the iterativecomputation in the main program.

A range of particle sizes and initialvelocities of the droplets emitted by thesprinklers was required as input variables inthe simulation of predicted wetted patterns.A sufficient number of stain samples (Hall1970) were obtained from field tests for allsprinklers to permit the determination of arange of particle sizes. The average sizesmeasured in the field were, therefore,assumed to fall within this range. The rangeof initial velocities, for a given discharge andnozzle size, was determined from themanufacturer's specifications of theindividual sprinklers.

CENTER PIVOT PERFORMANCE

ANALYSIS

In evaluating the performance of thesimulation model, 11 comparisons ofsimulated and field data were available for

the two C.P. systems. The effect of wind wasincorporated in the model as a vector for a15-min sequential interval. Triangular andelliptical distribution profiles were used torepresent the actual case. Evaluation of themodel involved the comparison of theapplication depths and the coefficients ofuniformity.

Comparison of Field and SimulatedApplication Depths

Field application depths were measuredin catch containers spaced 6 m apart andextending radially outward from the centerpivot (Fig. la, b). The individual sprinklerwetted patterns, the angular velocity of thelateral, and the wind characteristics weremeasured and input in the model to allow adirect comparison of field and theoreticalsimulated depths. Attempts to use a

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Figure 1. (Above) Schematic of experimental field layout at site 1. (Cranford, Alberta). (Below)Schematic of experimental field layout at site 2. (Granum, Alberta).

statistical test for comparison to a standardor control set of field measured applicationdepths were not possible because of thechaotic nature of the influencingenvironmental factors. The disparitybetween the measured and simulated depthscan be expressed in terms of the absolutedeviation (AADI) and the percentageabsolute deviation (A A D2) computed by thefollowing relations:

AADI =

AAD2-

where

Of =

S|o(0-r(0|N

(1)

oulN

individual

depths

x 100 (2)

measured application

Tj = individual simulated applicationdepths

N = number of sets of measurements used

in the comparisonThe theoretical application depths were

determined for both triangular and ellipticaldistribution patterns and plotted against thefield measurements. Only small differenceswere observed. The close spacings of theadjacent sprinklers along the lateralprobably concealed the effect of the twoassumed distribution patterns. A similarobservation was made by Heermann andHein (1968). In general, the absolutedeviations of the theoretical applicationdepths for the triangular distributionprofiles were less more frequently than thoseof the elliptical profiles (see Table I and II).

As the triangular distribution profilesgave a slightly better estimate of the actualfield application depths, these were selectedfor further evaluation of the model. A

CANADIAN AGRICULTURAL ENGINEERING, VOL. 21, NO. 2, DECEMBER 1979

ACTUAL DATA

SIMULATED DATA (WIND INCLUDED)25 •— SIMULATED DATA(WIND EXCLUDED)

52 A

- 20 K A l\I l\ * A Ma ^ J\ a / \£ rA tJJ\d m^xv^g 15 " J to Ls

1 t-> t\h ffir^Z II 'v \/o ,« // ' v

H ,0 -// '< / / /

O S f i(l

8! 5J iIt

a.<

0 1 • 1 __....! III!

100 200 300

DISTANCE FROM CENTER PIVOT, M

400

Figure 2. Comparison of field and simulated application depths. Circle Master C.P. System. Test7,row 2.

35 rACTUAL DATA

SIMULATED DATA (WIND INCLUDED)SIMULATED DATA (WIND EXCLUDED)

100 200 300

DISTANCE FROM CENTER PIVOT, M

400

Figure 3. Comparison of field and simulated application depths. Valley 1160C.P. System. Test 2, row2.

comparison was made of the measureddepths and those theoretically derived, usingthe triangular distribution profile, for windand no-wind conditions. Plots were made of

the field and simulated depths for all testscarried out on the two C.P. systems. Only 2of the 11 plots are presented (Figs. 2 and 3).

Some observations were made from these

plottings. There was generally goodagreement between field and theoreticalapplication depths as shown by theapproximately similar trends in the plots. Acloser agreement was obtained when themagnitude and direction of the wind wereconsidered in the simulation model.

However, in some cases where the effect ofthe wind was minimal, either the effect wasinsignificant or an overall "averaging out"occurred. In most tests, a large application

depth was noted near the center of rotation.The application rate near the pivot point waslow but the time of application was long. Asa design attempt to achieve a uniform depth,the time of application at a point decreaseswith a corresponding increase in applicationrate outward from the center pivot.Fluctuations of measured depths along mostof the lateral length was evident. Thesefluctuations can be attributed to thelocalized chaotic effect of the wind on thesuperimposed adjacent patterns. Theoverlapping sprinkler effect may bemagnified or greatly reduced because of arapid change in wind direction. A lagbetween the field and theoretical depths wasnoticeable near the center pivot point.Inaccurate time synchronization in the inputof the simulation model was most likely the

CANADIAN AGRICULTURAL ENGINEERING, VOL. 21, NO. 2, DECEMBER 1979

cause of these shifts.

The simulation model can be bestevaluated in terms of the percentageabsolute deviation (AAD2). On the whole,the theoretical depths deviatedapproximately 14% from the actual fieldmeasurements. The spread of the averagedeviations for the Circle Master C.P. systemvaried from 11 to 18% as compared to theValley 1160 system which varied from 14 to30%. A mean deviation of 15% and astandard deviation of 2% was observed forthe Circle Master system. For the Valley1160 system, the mean deviation was 19%and the standard deviation was 5%. Thisdisparity may be attributed to the individualsystem performance characteristics andprobably statistical differences as eightfewer tests were carried out on the Valley1160 C.P. system.

When the effect of wind was not included

in the model the mean absolute deviations

were increased to 18% for the Circle Mastersystem compared to 19% for the Valley 1160system. The influence of wind was notprevalent in the latter C.P. system because ofthe wide fluctuations of the measured depthsalong the lateral. In terms of the meanabsolute deviation, no valid assessment ofthe theoretical values was possible in thiscase.

Coefficient of UniformityChristiansen's (1942) coefficient of

uniformity was used to evaluate theperformance of the C.P. systems. A similarweighted coefficient of uniformity suggestedby Heermann and Hein (1968) was alsoincluded in the analysis to give more weightto the application depths further from thepivot where the area of influence wasincreasingly larger.

A comparison of the field and modelsimulated coefficients for both weighted andnon-weighted values are presented (Tables Iand II). The uniformity coefficients werecalculated by excluding the area at the outerradius where the larger nozzle (end gun)sprinklers are located. The deviation of themean would be affected by the large area atthe end guns and would reduce thecoefficient accordingly.

The coefficients of uniformitydetermined for both triangular and ellipticaldistribution profiles did not differ greatly(Table III). As mentioned earlier, theoverlapping effect of the closely spacedadjacent sprinklers for the two assumeddistributions gave only small differences. Ingeneral, however, the theoretical simulatedcoefficients were higher than thosemeasured. This was evident from the widefluctuations in the field measured depthsand the initial larger response close to thepivot.

Closer agreements were obtained for themeasured weighted coefficients and thosesimulated in the model as a standarddeviation of 1.26 compared to 1.56 wasnoted. However, the accuracy of thesimulation cannot be definitely assessed

143

TABLE I. EVALUATION OF THE MODEL SIMULATING THE PERFORMANCE OF THE CIRCLE MASTER C.P, SYSTEM

Simulated data (with wind)

Test no. 7

Row avg.

Test no. 8

Row avg.

Test no. 9

Row avg.

Test no. 10

Row avg.

Test no. 11

Row avg.

Test no. 12

Row avg.

Test no. 13

Row avg.

Test no. 14

Row avg.

Field data

Avgdepth CUt(wtd.) CUT (wtd.)(mm) (%) (%)

16.5 85.3 93.2

17.3 88.0 92.1

16.7 87.4 93.0

18.3 90.5 92.7

21.8 88.1 92.2

19.8 88.6 90.5

20.6 88.6 94.4

23.9 89.8 93.9

]Cu Christiansen's coefficient of uniformity.%Cu (wtd.) Heermann and Hein weighted coefficient.

Triangular distribution

Avg.depth CU(wtd.) AADI AAD2 CU (wtd.)(mm) (mm) (%) (%) (%)

16.0 1.52 14.0 90.9 96.1

15.5 1.78 11.4 93.1 96.4

15.2 2.29 15.1 94.4 96.1

18.3 1.78 11.2 94.9 95.1

21.3 2.29 9.1 92.4 93.9

18.8 3.05 13.3 95.4 95.7

20.1 2.29 9.2 95.1 95.7

22.9 2.29 8.9 93.1 94.4

Elliptical distribution

Avg.depth CU(wtd.) AADI AAD2 CU (wtd.)(mm) (mm) (%) (%) (%)

16.0 1.52 12.9 90.5 95.7

15.5 1.78 11.9 93.1 96.1

15.2 2.29 15.6 94.0 94.6

18.3 1.78 11.8 94.3 94.5

18.5 2.54 9.8 92.3 93.5

18.8 3.05 13.1 94.9 95.2

19.8 2.29 9.5 94.0 95.2

22.3 2.54 10.0 92.2 93.7

TABLE IL EVALUATION OF THE MODEL SIMULATING THE PERFORMANCE OF THE "VALLEY 1160" C.P. SYSTEM

Test no. 2

Row avg.

Test no. 3

Row avg.

Test no. 6

Row avg.

Simulated data (with wind)

Field data Triangular distribution Elliptical distribution

Avg. Avg. Avg.depth CUJ depth CU depth CU(wtd.) CUt (wtd) (wtd.) AADI AAD2 CU (wtd.) (wtd.) AADI AAD2 CU (wtd)(mm) (%) (%) (mm) (mm) (%) (%) (%) (mm) (mm) (%) (%) (%)

24.6 88.6 92.1

28.2 86.9 92.6

22.6 87.9 91.2

26.2 2.79 13.0 94.0 95.1

27.4 2.79 12.7 91.8 96.2

26.9 4.06 22.1 94.9 96.2

25.4 2.79 14.1 93.6 94.4

27.4 2.79 13.4 91.8 96.1

26.4 3.81 22.6 94.4 95.8

fCU, Christiansen's coefficient of uniformity.JCU (wtd.), Heermann and Hein weighted coefficient.

irrespective of the reasonable agreements ofthe measured and theoretical computedcoefficients. The coefficient of uniformity isonly a performance parameter of theapplication depths along the lateral and anyvariation of application depths at any givenpoint beneath the lateral cannot beaccounted for without imposing anaveraging effect.

The effect of wind conditions on the

coefficients of uniformity was theoreticallypredicted (Tables IV and V). In this analysis,

144

the wind direction was held constant in adirection relative to the center pivot. At 0°direction, where the line of measurement isdirectly opposite to the wind, a noticeablereduction in the coefficient of uniformityoccurred. The extreme distortion of theoverlapping distribution patterns in thisdirection accounts for the lower coefficients.

Although the coefficients of uniformitywere affected by both the wind velocity andwind direction, the effect of wind directionwas more pronounced. For example, for a

wind velocity of 32 km/h and 0° direction,the coefficients of uniformity were 87.3 and91.4% for the Circle Master and the Valley1160 systems, respectively. For the samewind velocity and 180° direction, theuniformity improved as the coefficients were96.0 and 96.5% for the former and latterC.P. systems, respectively. Generally, thecoefficients of uniformity obtained underthe ranges of wind magnitude and direction(Tables IV and V)were within the acceptable80 - 90% design requirements.

CANADIAN AGRICULTURAL ENGINEERING, VOL. 21, NO. 2, DECEMBER 1979

TABLE III. MEAN COEFFICIENT OF UNIFORMITY

Field distribution

Theoretical distribution (simulated)

Triangular pattern Elliptical pattern

C.P. systemcut

(%)

CU (wtd.)J(%)

CU

(%)

CU (wtd.)

(%)

CU

(%)

CU (wtd.)

Circle Master

Valley 1160

86.9

86.1

91.3

90.2

92.6

92.9

94.6

95.1

92.2

93.0

94.1

94.6

tCU, Christiansen's coefficient of uniformity.tCU (wtd.), Heerman and Hein weighted coefficient.

TABLE IV. PREDICTED COEFFICIENTS OF UNIFORMITY FOR THE CIRCLE MASTER

SYSTEM

Triangular Ellipticaldistribution distribution

Wind

pattern pattern

Wind CU CU

velocity direction CU (wtd.)t CU (wtd.)

(km/h) (degrees) (%) (%) (%) (%)

0 95.0 95.8 93.3 94.8

0 92.0 87.3 91.7 86.9

90 91.7 95.5 90.9 94.8

32 180 89.9 96.0 89.5 95.7

0 85.9 74.5 85.9 74.1

90 81.2 89.3 81.4 89.8

64 180 82.1 93.4 81.3 93.4

TABLE V. PREDICTED COEFFICIENTS OF UNIFORMITY FOR THE VALLEYSYSTEM

1160

Triangulardistribution

Ellipticaldistribution

Wind

direction

(degrees)

pattern pattern

Wind

velocity(km/h)

CU

(%)

CU

(wtd.)t(%)

CU

(%)

CU

(wtd.)

(%)

0 93.7 95.9 93.6 95.3

32

0

90

180

93.8

92.5

89.2

91.4

95.6

96.5

93.3

91.4

89.0

90.8

94.3

94.5

64

0

90

180

88.6

86.8

83.2

78.9

95.3

95.7

88.6

86.1

83.3

79.5

93.5

94.0

SUMMARY AND CONCLUSIONS

The main objective of this study was toevaluate the performance of two C.P.sprinkler irrigationsystems operating underlocal climatic conditions in southernAlberta. A model was developed to simulatethe dynamicoperation of a C.P. system.The

simulation model then was used as a tool todetermine the system performance underactual windy conditions.

Performance was evaluated by a directcomparison of field and theoreticalsimulated application depths and bycomparison of the measured and simulatedcoefficients of uniformity. On the whole, the

CANADIAN AGRICULTURAL ENGINEERING, VOL. 21, NO. 2, DECEMBER 1979

theoretical depths deviated approximately14% from the field measurements. Thespread of the average deviations varied from11 to 18% and from 14 to 30% for the CircleMaster and the Valley 1160, respectively.Where the effect of wind was not included inthe model, the mean absolute deviationswere increased to 17.5% for the CircleMaster system as compared to 19.4% for theValley 1160 system.

Close agreements were obtained betweenthe measured weighted coefficients ofuniformity and those simulated in the model(a maximum deviation of approximately6%). The spread of the weighted fieldcoefficients varied from 87.6 to 93.6% for theCircle Master system and from 88.4 to 92.6%for the Valley 1160 system. The weightedsimulated coefficients varied from 91.8 to

96.1 % for the Circle Master system and from93.4 to 96.1% for the Valley 1160 system. Ingeneral, the field coefficients were lowerthan the simulated coefficients but both

were within the acceptable level of 80 - 90%.The simulation model provided a method

for studying the effect of wind magnitudeand direction. Wind was a continuousphenomenon throughout the experimentalperiod. With further validation of themodel, improvement in design criteria forC.P. sprinkler irrigation systemsis possible.For example, the optimum spacing ofsprinklers, sprinkler type, and sizeof nozzlesfor a given set of known system characteristics may be theoretically determined.

ACKNOWLEDGMENTS

The research described in this article wasfunded by Alberta Agricultural Research Trust.The cooperation and assistance of AlbertaAgriculture, Irrigation Division at Lethbridge,Alberta is also gratefully acknowledged.

AMERICAN SOCIETY OF AGRICULTURALENGINEERS. 1978. Minimum requirementsfor the design, installation, and performanceof sprinkler irrigation equipment. ASAERecommendation: ASAE R 264.2.

BITTINGER, M.W. and R.A. LONGEN-BAUGH. 1962. Theoretical distribution ofwater from a moving irrigation sprinkler.Trans. Amer. Soc. Agric. Eng. 5(1): 26-30.

CHRISTIANSEN, J.E. 1942. Irrigation bysprinkling. Calif. Agric. Exp. Sta. Bull. 670.

HALL, M.J. 1970. Use of the stain method indetermining the drop-size distributions ofcoarse liquid sprays. Trans.Amer. Soc.Agric.Eng. 13(1): 33-37,41.

HEERMANN, D.F. and PR. HEIN. 1968.Performance characteristics of self-propelledcenter-pivot sprinkler irrigation system.Trans. Amer. Soc. Agric. Eng. 11(1): 11-15.

HORVATH, B.C. 1979. A simulated model oftwo center pivot sprinkler irrigation systemsoperating under normal climatic conditions.Unpublished M.Sc. Thesis, University ofAlberta, Edmonton, Alta.

KORVEN, H.C. 1952. The effect of wind on theuniformity of water distribution by somerotary sprinklers. Sci. Agric. 32(4): 226-239.

RING, LJ. 1976. Determining center-pivotsprinkler uniformities. Unpublished M.Sc.Technical Report, Colorado State University,Fort Collins, Colo.

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