ORIGINAL ARTICLE

Operational Parameters in Center Pivot Machines and their Influence on the Delivery Irrigation Duty

0000-0002-1021-0680Dr.C. Enrique Cisneros-Zayas^{1  *}  , 0000-0001-8245-4070Dr.C. Felicita González-Robaina¹  , 0000-0002-3679-1663MSc. Zenén Placeres-Miranda¹  , 0000-0002-5100-7902MSc. Reinaldo Cun-González¹ 

¹Instituto de Investigaciones de Ingeniería Agrícola (IAgric). Boyeros, La Habana, Cuba.

ABSTRACT

The objective of the work was to study the technical-operational parameters of the electric central pivot machines and their relationship with the norms of water delivery to crops. For the analysis, seven central pivot machines were selected in three productive entities of Güira de Melena Agricultural Enterprise, which were hydraulically evaluated to know their operating status according to NC ISO 11545. The parameters studied were the uniformity coefficient, distribution uniformity and discharge efficiency as indicators of irrigation quality. The results showed that the wind has a marked influence on the evaluated technical-operational parameters, deteriorating the quality of irrigation to average values of Heermann and Hein Uniformity Coefficient of 79,39%, Distribution Uniformity_25% of 64,90% and Discharge Efficiencies of 74,08%, which directly affects the low percentage of area adequately irrigated. When the gross partial norms of the operation tables for efficiencies of 85% were compared with those obtained in the field evaluations, it was possible to know that deficits in deliveries between 6 and 23 m³ ha^-1 can occur in each irrigation duty.

Key words: Hydraulic Evaluation; Irrigation Quality; Uniformity Coefficient; Distribution Uniformity; Discharge Efficiency

INTRODUCTION

A main parameter to evaluate irrigation systems is the uniformity of water application on the surface of the irrigated area, directly showed in the management and performance of the crop, in the efficiency of water use, in the cost of irrigation and, therefore, in the production (Bernardo et al. 2009, cited by ^{Flórez-Tuta et al., 2013}). The total area under irrigation in the Ministry of Agriculture productive system is 416,367 ha (^{Cuba, Ministry of Agriculture, 2017}), where the highest growth rates in areas with use value under different irrigation techniques are, in gravity irrigation (about 80%) as well as irrigation with electric center pivot machines (42%) and drip (32%). Center pivot machines are among the most popular irrigation systems in the world, they have made irrigation easy and very effective in many areas where other irrigation methods are not suitable (González, 2006 cited by ^{Jiménez et al., 2010}).

In recent years, the use of these pressurized irrigation systems has increased due to its advantages and because they are water-saving compared to traditional ones. This, undoubtedly, leads to a better operation together with the knowledge of the operating state. ^{Alabanda (2001)} states that the evaluation of an irrigation system includes the study of the uniformity of distribution and the efficiency of application, as well as the analysis of all the elements of the irrigation system. Traditionally, the distribution of water through the irrigation system has been determined by means of experimental measurements of water collected on a network of rain gauges placed on the surface of the soil at different points of the plot and, logically, provided by the irrigation system under the conditions of normal operation. During the evaluation, a specific and perfectly referenced methodology is followed according to the existing irrigation system (^{Stambouli et al., 2014}). The detailed difference in the water collected by the rain gauges during the evaluation of the system is expressed by: Uniformity Coefficient (CU), Distribution Uniformity (UD), Variation Coefficient (CV).

The concept of irrigation uniformity contemplates the difference in the water collected between the different points of an irrigated surface. The methodology followed for the measurement and quantification of irrigation uniformity in sprinkler systems is systematized and referenced (^{Montero, 1999}) where all researchers agree that field evaluations are the way to proceed for its determination. Other parameters to express irrigation uniformity (UD and Cv) are based on analogous principles, that is, they compare the point values obtained throughout the water distribution achieved in the test. Of all of them, CU is widely used and its use is mandatory in all sprinkler irrigation uniformity studies (^{Tarjuelo, 1999}).

According to ^{Tarjuelo (2005)}, when the objective is to identify the irrigation systems quality, the management aspects that try to achieve the adequacy of the irrigation in terms of the moment and the water volume to be irrigated can be omitted In this case, only the concepts of CU, UD and Ed are used. At present in Cuba, the increase in agricultural production is of vital importance and the growing demand for food encourages the introduction of new technologies and the renewal produced in the whole of hydraulic pivot machines constitutes a step in that direction.

On the operation, the proper application of irrigation is when the water needs of the crop are met (^{Placeres et al., 2013}). For this reason, the massive introduction in agricultural production of machines, affected by problems of deficient technical parameters, required a study of the behavior in the delivery of the doses. Consequently, that motivated a series of actions to review the technological sheets and the correct placement of the emitters’ module, for guaranteeing the quality of artificial rain in the operation of spray irrigation, technology used in Cuba, where those modules are manufactured.

Güira de Melena Municipality has a total area under irrigation of 5600,27 ha, of which 5539,22 with use value. At the end of 2019, the Irrigation and Mechanization Center reported 5328,15 ha in exploitation under irrigation and of them, the electric central pivot machines represent 25% with more than 15 years of operation. There, the irrigation quality parameters have been deteriorated, affecting the norms of water delivery to the crops. That observation has been made by several farmers who associate the low productions obtained to the irrigation quality reduction. That is why the objective of this work was to study the technical-operational parameters of the central pivot machines and their relationship with the delivery irrigation rates to the crops.

MATERIALS AND METHODS

The work was carried out at Güira de Melena Agricultural Enterprise in Artemisa Province, with geographic coordinates 22° 44' 6.39", North latitude and 82° 30' 11.54" West longitude (Figure 1). The height above mean sea level is 8 m. Seven central pivot machines located in different areas within Güira de Melena Agricultural Enterprise were selected for the study; two in the South zone, two in the Center and three in the North zone, which are part of two productive forms, the Basic Unit of Cooperative Production (UBPC) and the Agricultural Production Cooperative (CPA). In Figure 1, the evaluated machines and their location in the entities studied in Güira de Melena municipality are shown.

FIGURE 1 Geographical location of the irrigation systems studied. 

To fine-tune the sprinkler irrigation system with the selected central pivot machine and to define the correct location of the nozzles, the PIVOT program (^{García, 2006}) was run. To determine the maximum speed of advance and the field evaluations, the ^{Cuban Standard NC-ISO 11545 of 2007} was used. The uniformity coefficient of ^{Heermann and Hein (1968)}, is a modification of ^{Christiasen's Uniformity Coefficient (1942)} to evaluate pivot systems, where each collector represents a different area. Therefore, its value affects to a greater or lesser extent the quality of irrigation of the machine.

$C{U}_h=\left[1-\frac{\sum _{i=1}^n{D}_i\left|C_i-M_C\right|}{\sum _{i=1}^n{C}_i\cdot D_i}\right]\cdot 100\left(\mathrm{\%}\right)\mathrm{}$ (1)

The Coefficient of Variation Uniformity (CUv) of ^{Bremond and Molle (1995)} is a parameter that includes the coefficient of variation within the CU_h. Therefore, it is a more sensitive indicator to the distribution of the irrigation sheet.

$C{U}_V=\left[1-\frac{1}{\frac{\sum C_i{D}_i}{D_i}}\cdot \sqrt{\frac{\sum {\left(C_i-\frac{\sum C_i{D}_i}{D_i}\right)}^2{D}_i}{\sum D_i}}\right]\cdot 100\left(\mathrm{\%}\right)$ (2)

Where:

CUH-	Heermann and Hein uniformity coefficient (%).
CUv-	variation uniformity coefficient (%).
n -	number of collectors used in the data analysis.
Ci -	Value collected by each collector.
Di -	distance that the collector is from the pivot or the area that it represents within the total area of the machine
i -	number assigned to designate a particular collector, usually starting with the collector closest to the pivot (i = 1) and ending with i = n for the collector farthest from the point.
Mc-	measured average volume (mass or depth) of the collected water. It is calculated as:

$M_c=\frac{\sum _{i=1}^n{C}_i{D}_i}{\sum _{i=1}^n{D}_i}$ (3)

A plot is considered to be well watered when a CU _H between 85 and 90% is achieved. With values higher than 90 % the plot is very well watered. On the other hand, with CU _H values lower than 85%, it is considered that the pivot does not water adequately. A CU_v value of 80% is accepted as a minimum to consider that a pivot irrigates adequately (^{Tarjuelo, 1999}). The uniformity of distribution was calculated according to Merriam and Keller (1978, cited by ^{Tarjuelo, 2005}), and is defined as:

$U{D}_{25\%}=100\cdot \frac{V_{25\%}}{V}=\frac{100}{V}{\left(\frac{\sum Ci\cdot Di}{\sum Di}\right)}_{25\%}$ (4)

where:

UD:	Distribution Uniformity, (%).
V 25% -	average volume collected from 25% of the lowest values (mL)
V -	average of all values (mL)

Discharge efficiency

The discharge efficiency (Ed) of the project can be determined using the average value of all the values obtained, in determining the range of the emitter (^{Tarjuelo, 2005}).

$Ed=\frac{sheetofthe\frac{1}{4}ofthelowervalues}{meanoftheobtainedvalues}$ (5)

According to ^{Tarjuelo (2005)}, the discharge efficiency or proportion of the water that reaches the ground is obtained by dividing the average height collected by the rain gauges (AMR) by the average height discharged by the emitters (AMD).

$Ed=\frac{AMR}{AMD}$ (6)

The mean unloaded height (AMD) is determined according to the expression proposed by ^{Tarjuelo (2005)}.

$AMD=\frac{Qa*Tr}{A}$ (7)

Where:

AMD:	Average unloaded height (mm).
Qa:	Discharge flow (L·h^-1).
Tr:	time the pivot takes to make one complete turn (h).
A:	Irrigated area (m^2).

The mean AMR collected height (mm) was determined by dividing the weighted mean volume by the collecting area of the rain gauge used in the test. The result is converted to mm (1 cm = 10 mm).

$Vp=\frac{\sum _{i=1}^{n}Vi*Si}{\sum _{i=1}^{n}Si}$ (8)

Where:

Vp:	weighted average volume of all observations. (1 mL = 1 cm^3)
n:	number of collectors used.
i:	number set to designate a particular collector, normally begins with the collector closest to the pivot (i = 1) and ends with (i = h) for the collector farthest from the point.
Vi:	volume (or alternatively the mass or depth) of the water collected in the collector (i). (mL)
Si:	distance from the collector (i) to the pivot point. (m)
Ac:	collector area. (cm^2).

$AMR=\frac{Vp}{Ac}$ (9)

For the definition of the percentages of irrigated areas the criterion of ^{Tarjuelo (2005)} was used, where:

• Adequately Irrigated Area (ARA): the sheet that is within the range of 10% above and below the middle sheet.

• Excessively Irrigated Area (ARE): the sheet that is above 110% of the middle sheet.

• Insufficiently Irrigated Area (ARI): the sheet that is below 90% of the middle sheet.

RESULTS AND DISCUSSION

Pluviometry Evaluation of the Different Irrigation Systems Studied

As part of the work, the different irrigation machines in Güira de Melena Agricultural Enterprise were evaluated. The result of these evaluations can be seen in Table 1, where the Heermann and Hein uniformity coefficient (CU_H-H) ranged from 78,6% to 81,4%. According to ^{Tarjuelo (2005)}, these values are classified as inadequate and bad, indicating that the plot is not adequately watered. The uniformity of distribution (UD_{25 %}), that represents the percentage of the middle sheet of 25% of the least irrigated area, ranged from 60,01 to 70,88%, which is considered high.

TABLE 1 Technical parameters of irrigation quality 

Site	Middle sheet (mm)	Heermann & Hein Uniformity Coefficient (%)	Bremond & Molle Variation Uniformity Coefficient (%)	Uniformity Distribution (UD25%)	Real Ed (%)	Mean wind speed (m s^-1)
I. Brito II	16,42	78,8	69,27	64,80	75,15	5,3
Morenita I	17,34	81,4	72,87	65,50	77,34	3,2
La Gloria	17,77	77,4	68,79	60,01	71,18	4,7
El Triunfo	15,30	79,6	72.89	66,38	75,57	3,8
Progreso 5	16,26	80,1	72,00	64,23	74,16	3,8
Finca I	17,22	78,6	70.25	62,48	71,15	4,8
Finca 6	15,94	79,8	71,87	70,88	73,98	3,3
Mean	16,61	79,39	71,13	64,90	74,08	4,13

The indicator that is related to the water that reaches the crop is the discharge efficiency (Ed). As it can be seen, it varied between 71,15% and 77,34%, which is low, taking into account that in the central pivot machines this value is considered good from 85% onwards. Regarding the coefficient of uniformity of variation (CUV), the values reached a range of 68,79% to 72,89%. This statistical parameter, according to ^{Bremond and Molle (1995)}, is based on the coefficient of variation, due to that it is more sensitive to extreme variations in the sheet collected by the collectors than the CU_H-H. In general, it can be seen that the mean wind speed during the tests ranged from 3,2 m s^-1 to 5,3 m s^-1, values that influence the parameters measured.

A study carried out by Playán (2012, cited by ^{Cisneros et al. 2013}) relating the wind speed with the uniformity coefficient expresses that as the speed increases the uniformity coefficient deteriorates, that is why it is recommended to suspend irrigation with speeds above 2.5 m s^-1, for his part, ^{Tarjuelo (2005)} states that under these conditions, water losses due to evaporation and carry-over can reach 30%.

According to ^{Shilo (2000)} and ^{Tarjuelo (1999}, cited by ^{Naroua et al., 2012)} the results obtained indicate that all the machines are operating below the minimum values of 75% and 85% for the Uniformity of Distribution and Uniformity Coefficient, respectively. Similar results have been reported by ^{Placeres (2011)}, ^{Aguilar et al. ( 2012)} and ^{Cun et al. (2019)} in field evaluations carried out on irrigation machines for the same study region.

Taking into account the restrictions in the use of water for irrigation and the low availability of such an important resource in the municipality of Güira de Melena, the use of central pivot machines is an adequate solution, but considering their years of operation, frequent evaluation is required to know and specify the exploitation parameters that allow improving irrigation management.

This is confirmed by ^{Jiménez (2012)} and ^{Abd el-Wahed et al. (2015)}, stating that central pivot machines, like other irrigation equipment, need to be evaluated to verify the parameters provided by the manufacturer when they are purchased. Moreover, given that the working pressures, the spacing between sprayers and the height over the ground also influence these parameters, it is necessary to monitor the quality of irrigation during the machines’ useful life.

As it can be seen in Table 2, in the joint analysis of the distribution of the percentages of the area, the adequately irrigated area reached the highest average value (55,4%), followed by the excessive area (13,3%). The insufficiently irrigated area reaches an average value of 31,7%

TABLE 2 Percentage of irrigated areas distribution (Adequate, Insufficient and Excessive) 

Site	Adequate Irrigated area (%)	Excessive Irrigated area (%)	Insufficient irrigated area (%)
UBPC “Héroes de Bolivia”
Ignacio Brito II	52	13	35
Morenita I	59	12	29
CPA “Waldo Díaz”
La Gloria	51	16	33
El Triunfo	56	12	32
CPA “Niceto Pérez”
Progreso 5	58	12	30
Finca 1	55	14	31
Finca 6	57	11	32
Mean	55,4	13,3	31,7

When correlating the percentages of adequately irrigated area (ARA) with the wind speeds, an inverse linear relationship was found with a coefficient of determination greater than 85%, which can be verified in Figure 2. As the wind speed increases, the percentages of adequately irrigated area are reduced, a climatic variable that must be taken into account because it is decisive in the quality of irrigation and in the discharge efficiency.

Authors such as ^{Tornes et al. (2009)}; ^{Jiménez et al. (2010)} and ^{Mujica et al. (2014)}, evaluating exploitation parameters in central pivot machines in different areas of the country, report similar results where they give great importance to the wind as a climatic variable that distorts the water sheet and influences the quality of irrigation and therefore, the percentage of areas irrigated adequately. Similar results were obtained by ^{Pérez et al. (2003)}; they evaluated central pivot machines and emitters in Güira de Melena Municipality and obtained a decrease in CU, UD_25% and the percentage of ARA with the increase in wind speed.

FIGURE 2 Relationship adequately irrigated area (%) and wind speed.  

Relationship between Uniformity Coefficient and Discharge Efficiency

In Figure 3 it is possible to observe the trend in the behavior of the uniformity coefficient (CU) and the discharge efficiency (Ed) in all the irrigation machines evaluated; as it is shown, there are irrigation systems that with high uniformity coefficients present low discharge efficiency. As it can be seen, point 2 has a uniformity coefficient of approximately 78,6%, however, it has the same discharge efficiency as point 1 with lower CU. Something similar happens with point 4: despite having a CU of almost 80%, it has lower discharge efficiency than point 3. That behavior is an element to be taken into account in the operation, because many farmers give greater weight to the CU and, as shown in the present study, the distribution of water in the plot may be adequate, however, the water level that reaches the ground is not enough to satisfy the demand of the crop, since efficiencies of 85% are considered in the operation tables for center pivot machines.

FIGURE 3 Relationship between Heermann-Hein Uniformity Coefficient and Discharge Efficiency 

Studies carried out by ^{González (2012)} on the efficient use of water in different irrigation systems report that irrigation techniques with good uniformity coefficient present low discharge efficiencies, and give as an example the case of the side roll and the central pivot machine. This is not the case for the reel with an irrigation wing due to the lower height of the nozzles with respect to the ground.

In a work on storage efficiency in irrigated agricultural soils in Cuba (^{López et al, 2010}), relating this parameter to discharge efficiency, it is specified that for an irrigation system discharge efficiency of 80% and a productive limit of 85% of the field capacity, storage efficiency is reduced in a range from 4% for clay soils to 10% for sandy soils. With the reduction of the discharge efficiency and the increase of the productive limit, the range of reduction of the irrigation water application efficiency becomes greater (between 15% and 60%), an element that must be taken into account because, to achieve high storage efficiencies, work should be done with discharge efficiencies greater than 85%.

In the operation of sprinkler irrigation systems in agriculture, more importance has been given to uniformity than to efficiency. Such is the case, that ^{Tarjuelo (2005)} establishes a classification of the quality of irrigation based on the Coefficient of Uniformity, where it states that, if this parameter is greater than 90%, the plot is very well watered, when it ranges between 85% and 90% is well watered and when it is less than 85% it is badly watered. However, production practice has shown that sprinkler irrigation systems with good uniformity show drops in the yields of irrigated crops.

Relationship between Uniformity Coefficient and Distribution Uniformity_25%

Among the irrigation quality parameters, those that are closely linked are the Coefficient of Uniformity and the Uniformity of Distribution _25%, the latter is stricter since it has to do with the lower quarter or the part of the plot that receives less water and is used, according to ^{Keller and Bliesner (1990)}, as an indicator of the magnitude of the problems in the water application process.

Figure 4 shows this linear relationship with a determination coefficient of 60%, where there is a tendency to increase the Distribution Uniformity _25% proportionally to the increase in the Uniformity Coefficient, but there are evaluations where irrigation systems with values of Coefficients of High Uniformity present Distribution Uniformities _25% lower, which confirms what ^{Keller (1990}, cited by ^{Tarjuelo 2005)} stated about the existence of other factors that should be studied in future research related to the distribution of water in the plot.

FIGURE 4 Relationship between Heenman - Hein Uniformity Coefficient and Distribution Uniformity_25% 

Walter (1979, cited by ^{Uribe, 2011}), studied the relationship between the uniformity coefficients and the factors that affected them in the sprinkler systems, stating that the optimal design of an irrigation system and its management takes into account all aspects affecting uniformity. In order to optimize the irrigation system design and its management decisions, a relationship between uniformity of water application and efficiency of application is required. On the other hand, Hart and Reynolds (1965, cited by ^{Cárdenas, 2000}), show that for a normal distribution function, the coefficient of uniformity and the uniformity of distribution are related to the coefficient of variation. From this relationship, other can be established for performance parameters (application efficiency, deficit coefficient, etc.), which allows obtaining management diagrams.

Analysis between the Discharge Efficiency Assumed in the Operation Tables of the Center Pivot Machines and the Discharge Efficiency Obtained in Field Evaluations

^{Keller (1990}, cited by ^{Tarjuelo 2005)} maintains that, under normal conditions, evaporation and drag losses can vary between 5% and 10%, a criterion assumed in this work for the analysis of discharge efficiencies. In Table 3, it can be seen how the real discharge efficiencies vary for the different irrigation systems between 71% and 77%, taking into account the reduction in 10% of the mean discharge height (AMD) by evaporation and dragging. When the gross partial standards applied are analyzed, considering the operating tables of these systems that assume efficiencies of 85% and the gross partial standards for actual discharge efficiencies, there are deficits in the order of 6 and 23 m³ ha^-1. If it is considered that these deficits will be proportional to the stages of higher demand, there is a risk that the crop does not receive the amount of water necessary to satisfy its water needs, causing, among other effects, reductions in yields.

^{Tarjuelo (1999)}, when addressing the influence of the uniformity of the irrigation of the pivots, states that both with a good uniformity and with another not so good, high productions can be achieved. The difference is in the amount of water necessary for this, being clearly less the greater the uniformity is, and the areas with deficit and percolation will also be smaller.

TABLE 3 Summary of the partial gross norms to be applied to guarantee a partial net norm of 150 m³ ha^-1 taking into account the different discharge efficiencies obtained in the evaluations 

Farm	AMR (mm)	AMD theoretical (mm)	AMD (-10% loess	Ed real (%)	NPB m^3 ha^-1ɳ: 85%	NPB m^3 ha^-1ɳ: real	deficit (m^3 ha^-1)	NR	season deficit (m^3 ha^-1)
Brito II	16,42	24,27	21,85	75,15	196,0	208,0	12,0	18	216,0
Morenita I	17,34	24,91	22,42	77,34	208,0	214,0	6,0	19	114,0
La Gloria	17,77	27,74	24,96	71,18	192,0	214,0	22,0	20	440,0
El Triunfo	15,30	22,49	20,25	75,57	197,0	207,0	10,0	20	200,0
Progreso 5	16,26	24,17	21,75	74,16	190,0	203,0	13,0	21	273,0
Finca 1	17,22	26,89	24,20	71,15	193,0	216,0	23,0	21	483,0
Finca 6	15,94	23,94	21,54	73,98	188,0	202,0	14,0	21	294,0

Legend: AMR: mean height collected, AMD: mean height discharged taking into account 10 % losses due to evaporation and dragging, Ed: Discharge Efficiency, NPB: gross partial norm, NR: Irrigation numbers. Note: The gross partial norms (NPB) for 85 % efficiency are taken from operation table of each irrigation system.

Studies conducted by ^{Jiménez et al. (2012)} and ^{Placeres et al. (2013)} on the operating parameters of the central pivot machines, indicate that due to the lack of knowledge about them, a deficit in the delivery standards of these systems can be generated, which affects low crop yields.

Relationship between Discharge Efficiency and Wind Speed

In Figure 5, it can be seen how the discharge efficiency is affected by the increase in wind speed, the study found an inverse linear correlation in the evaluated systems with a coefficient of determination R² = 0,80. Although this phenomenon is known, in the current conditions of Güira de Melena Municipality, where the speed of the winds between 10:00 am and 12:00 m varies between 3,5 and 5,5 m s^-1, it is important that the farmer’s bear in mind that the quality of irrigation is affected, which, in turn, affects yields.

FIGURE 5 Relationship between discharge efficiency and wind speed  

The most relevant climatic factor in the behavior of the water distribution pattern is the wind, and its speed, direction and persistence must be considered. Operation planning should consider the hours without wind and the hours with wind speeds less than 2,5 m s^-1. ^{Faci and Bercero (1991)} and ^{Tajuelo et al. (1994)} place the general wind speed limit between 2.5 and 3,5 m s^-1 above which it is not advisable to irrigate by sprinkler irrigation. In recent work, ^{Cisneros et al. (2019)} evaluated irrigation quality parameters in a sprinkler system in Güira de Melena Municipality. They reported that with high wind speeds, the effective range radius of the sprinklers is reduced by 0,90 m with respect to that of the project. This same phenomenon can occur in irrigation machines with the overlap between the diffusers affecting the discharge efficiency.

Relationship between Loss by Evaporation and Drag and Wind Speed

^{Tarjuelo (2005)} and ^{Playán et al. (2006)} studied losses due to evaporation and drag during irrigation and indicated that these can reach up to 40%. Losses due to evaporation and drag are those that occur since water leaves the emitter until it reaches the surface of the soil or the crop. This concept of losses includes both, the drops that become vapor (evaporation) and those that are blown by the wind (^{Tajuelo, 1999}).

For the study conditions in Figure 6, it is shown that they vary between 30 and 36%, also finding a direct relationship with a coefficient of determination R² = 0,71. From this correlation it can be estimated that for speeds greater than the 4,5 m s^-1 (which is the average speed in the municipality between 10:00 am and 12:00 m), there are reductions in the applied irrigation sheet due to 33% losses, hence the importance of an adequate exploitation in the irrigation machines to guarantee the norms of delivery to the crops. A similar result was obtained by ^{Pérez (2005)} when evaluated central pivot machines under the same study conditions.

FIGURE 6 Relationship between losses by evaporation and drag and wind speed 

Similar results were obtained by ^{Martínez-Cob et al. (2010)} while studying the wind and irrigation. They found the variability of the wind in Aragon and its influence on sprinkler irrigation, and reported that the irrigation quality parameters deteriorated as a function of wind speed when evaporation and drag losses increased.

CONCLUSIONS

• The wind has a marked influence on the evaluated technical-operational parameters, which damage the quality of irrigation. Average values obtained from all the machines studied were: Heermann and Hein Uniformity Coefficient 79,39%, Distribution Uniformity_25% 64,90% and Discharge Efficiency 74,08%, which directly affected the low percentage of area adequately irrigated.

• No direct relationship was found between Uniformity Coefficient and Discharge Efficiency. The study considered Uniformity Coefficient values classified as good and Discharge Efficiencies related to the water that reached the crop classified as low. Therefore, the study confirms what is reported by other authors referring to the fact that a high Uniformity Coefficient does not always mean that the planned water reaches the crop.

• When comparing the gross partial norms of the operational tables for efficiencies of 85% with those obtained in the field evaluations, it was possible to know that deficits in deliveries between 6 and 23 m³ ha^-1 can occur per irrigation.

• To guarantee the norms of water delivery to the crops, it is necessary to prepare the operation tables of the central pivot machines, taking into account the discharge efficiency obtained in the field evaluation.

• Evaporation and drag losses in center pivot machines vary between 30 and 36% for the study conditions.

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6The mention of trademarks of specific equipment, instruments or materials is for identification purposes, there being no promotional commitment in relation to them, neither by the authors nor by the publisher.

Received: February 07, 2021; Accepted: June 18, 2021

^*Author for correspondence: Enrique Cisneros-Zayas, e-mail: [e-mail]

Enrique Cisneros-Zayas, Investigador Titular, Instituto de Investigaciones de Ingeniería Agrícola (IAgric). Boyeros, La Habana, Cuba. e-mail: [e-mail]

Felicita González-Robaina, Investigadora Titular, Instituto de Investigaciones de Ingeniería Agrícola (IAgric). Boyeros, La Habana, Cuba. e-mail: [e-mail]

Zenén Placeres-Miranda, Especialista, Instituto de Investigaciones de Ingeniería Agrícola (IAgric). Boyeros, La Habana, Cuba. e-mail: [e-mail]

Reinaldo Cun-González, Inv. Auxiliar, Instituto de Investigaciones de Ingeniería Agrícola (IAgric). Boy10eros, La Habana, Cuba. e-mail: [e-mail]

The authors of this work declare no conflict of interests.