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The uniform distribution of pesticides via spraying is of crucial importance in achieving effective and environmentally sustainable crop protection. Conventional assessment techniques such as sensor-based patternators and electronic monitoring systems are often expensive, complex to calibrate, and limited in adaptability to different nozzle geometries or operating conditions. The present study introduces and validates a low-cost, image-based method as an alternative to the traditional volumetric approach for evaluating spray pattern uniformity in mechanical patternators. Spray tests were conducted under controlled laboratory conditions in order to minimize environmental variability and ensure repeatability. The present study compared two complementary methods—volumetric measurement and image analysis—to evaluate their agreement and accuracy in determining spray deposition profiles. The findings, which included correlation and multivariate tests, indicated a robust linear relationship between the two approaches (r = 0.990–0.999), with deviations falling below ±3% and no statistically significant multivariate differences (p = 0.067). The image-based approach effectively captured both central and edge regions of the spray pattern, demonstrating precision comparable to volumetric readings. The findings confirm that image analysis provides an accurate, reliable, and repeatable means of assessing spray uniformity without reliance on costly sensor technologies. The proposed method offers a practical and scalable alternative for laboratory calibration, nozzle classification, and research applications focused on optimizing agricultural spraying performance.
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1. Introduction
In order to achieve optimal efficacy following application, it is imperative that agricultural pesticides [1], fertilizers and growth regulators are distributed evenly across the intended surface area [2]. In the absence of uniform delivery of the active ingredient to the target surface, there is a risk of dosage variations, compromised management of harmful diseases and weeds, environmental pollution, increased pesticide resistance [3], reduced soil fertility, and decreased product quality and yield. The most common and effective method of delivering agricultural chemicals, whether diluted or in liquid form, to their target is spraying [4,5,6]. In this method of fluid delivery, characterized by the utilization of droplets, hydraulic nozzles are frequently employed. The operational parameters, encompassing parameters such as operating pressure, spray height, and application speed, are subject to variation in response to changing conditions. It is imperative to note that the aforementioned conditions may encompass a multitude of factors, including but not limited to technical specifications [7], climatic elements [8], and the physical properties of the fluid [9] under consideration. This phenomenon results in alterations to the volumetric distribution pattern in hydraulic nozzles. Furthermore, manufacturing defects in spray nozzles [10], clogging and wear behavior in nozzles during use [11,12], droplet diameter characteristics [7] and target (soil, plant, pest, disease) are factors that alter flow characteristics.
The uniformity of the distribution of the spray is a key factor in determining the efficiency of the application of the pesticide. This uniformity influences such factors as the coverage of the droplets, the effectiveness of the pesticide in controlling the pests, and the extent of drift that occurs beyond the intended target. The achievement of a consistent volumetric distribution across the spray width is imperative to ensure homogeneous deposition of the active ingredient, thus minimizing both excessive and insufficient application, which could lead to yield loss or environmental contamination. It is imperative that spray patterns and nozzle performance are measured with precision to ensure the maintenance of three key elements in agricultural spraying systems: application precision, operational efficiency, and environmental safety.
Conventional assessment techniques, including mechanical patternators, volumetric collection, and water-sensitive paper analysis, have been extensively employed to evaluate nozzle uniformity. Despite the fact that these methodologies offer quantitative or visual forms of feedback, they are encumbered by substantial limitations. These limitations encompass manual handling errors, time-consuming data collection processes, and difficulties in calibration. Sensor-based and automated systems have been shown to offer improved precision; however, they tend to be costly, necessitate intricate maintenance, and are susceptible to the influence of ambient conditions, including temperature and humidity. These challenges restrict their suitability for high-throughput analysis or comparative testing under varied operational scenarios.
The evaluation of the spray pattern and the volumetric distribution uniformity of hydraulic nozzles is conducted through the utilization of spray patternators [13]. The fluid is subsequently collected in channels that are arranged in a lateral configuration with equal intervals on the pattern generator table. The liquid that accumulates in each channel is then transferred to collection cylinders (i.e., graduated cylinder, measuring cylinder, graduated tube, graduated measuring tube) via a fluid transfer line. The objective of the present study is to ascertain the spray pattern or the uniformity of the volumetric distribution. To this end, the volume of fluid in each cylinder is recorded [14,15].
A variety of methodologies have been developed for the purpose of quantifying the fluid accumulations within the collection cylinders of the mechanical patternator. The gravimetric measurement method is based on the direct reading of the fluid volume through graduated tubes. An alternative method of measuring mass involves the weighing of the fluid collected in each cylinder. The advent of digital liquid-level sensors has facilitated the precise measurement of fluid accumulation in the collection cylinders of the patternator [16]. The strategic placement of these strip-shaped sensors within the tube is pivotal to the functioning of the apparatus. The sensors are able to detect the level by measuring the hydrostatic pressure of the fluid. The development of a linear scanner equipped with ultrasonic and optical (laser) sensors on the patternator cylinders has enabled the measurement of fluid levels with high accuracy whilst in a travelling position [17]. In systems characterized by elevated flow rates or in patternators where the utilization of small-volume collection cylinders is a matter of design, the fluid quantity is determined on the basis of the cylinder’s filling time. In this method, variations in the distribution of the spray result in alterations to the time taken for the tube to be filled. Consequently, observations can be made with regard to volumetric distribution [18]. The utilization of spherical markers that are in motion with the fluid within the collection cylinder enables the reading of the fluid level through digital imaging. In order to enhance the efficacy of this methodology, the markers in the digital images are designated by the user with image-processing software. It can thus be concluded that the level of fluid can be determined with ease based on the position coordinates of the marker relative to the reference axis [15]. Nevertheless, from a methodological standpoint, manually executing the object identification process is a time-consuming endeavor. Erroneous object detection is a possibility in instances of multiple identifications, due to the presence of distractions [19]. The present research is concerned with the automatic determination of the position coordinates of markers indicating the fluid level in the measuring cylinders of the patternator by means of image processing.
Advancements in digital imaging and computer vision technologies have engendered novel opportunities for the evaluation of spray patterns. Image-based methodologies are non-destructive, cost-effective, and capable of automatically processing voluminous datasets, thereby providing high-resolution spatial information regarding liquid distribution. These techniques permit the quantification of droplet density, symmetry, and uniformity across the spray profile. Nevertheless, the accuracy of such techniques may be influenced by external factors, including illumination, camera positioning, and reflections from transparent collection surfaces. Consequently, the development of well-calibrated, standardized imaging conditions is imperative to ensure consistent and reliable measurements.
A variety of image processing techniques (e.g., filtering, segmentation and edge detection) are utilized to extract information from digital images, employing software algorithms [19]. This approach has been shown to yield significant advantages in the pharmaceutical and food industries, and it is widely employed for the purpose of object detection [20]. In addition to well-established image processing methodologies, the development of machine learning techniques employing deep learning and convolutional neural network-based models has the potential to yield advanced object detection capabilities [21]. The determination of the descriptive features of digital images, including the position, size and coverage area of objects relative to their reference axes, is achieved by the extraction of numerical attributes belonging to the object [22].
The objective of this research is to develop a cost-effective and practical image-processing method for accurately quantifying liquid distribution in mechanical patternators. Contrary to the methodologies employed in preceding studies, which relied on the manual identification of fluid levels or the utilisation of specialized sensors necessitating intricate calibration procedures, the proposed method employs an automated approach. It utilizes a calibrated image-processing workflow to detect and measure liquid height. The elimination of operator-induced variability and the minimization of dependency on high-cost electronic equipment are key benefits of this automation. Furthermore, the integration of image-based and volumetric evaluation techniques enables a dual-mode validation framework that enhances both accuracy and reproducibility. The integration of multivariate statistical tools, such as PCA and MANOVA, facilitates a robust comparative evaluation of different nozzles under controlled laboratory conditions. This research introduces a novel approach for evaluating spray pattern uniformity. It does so by addressing the key limitations of existing measurement systems and contributing a novel methodology for precision spraying research. Moreover, the study’s objective encompassed the evaluation of the validity of the spray pattern derived through image processing techniques. Furthermore, the study aims to reveal the distinctive characteristics of hollow-cone nozzles in terms of spray pattern behavior.
2. Materials and Methods
2.1. Mechanical Spray Patternator and Spray System
As demonstrated in Figure 1a, the spraying tests were conducted using a 60-channel mechanical patternator prototype [13]. The dimensions of the patternator table, whose channels were composed of stainless steel (AISI 304), were as follows: 125 × 100 cm, with a channel width of 20.5 mm, a channel height of 85 mm, and a table inclination angle of 5°. The primary structural element of the apparatus under consideration incorporated four industrial wheels, a design feature that facilitated the manufacturing process of the patternator frame. The latter was produced using steel profile (S235), and the wheels enabled its position to be changed with ease. The patternator frame was equipped with a spray arm that allowed for adjustment of its height within the range of 20–90 cm. The process of connecting a pressure line to the spray arm was undertaken in order to facilitate the act of spraying through the diaphragm nozzle body. The regulation of the spray pressure was achieved through the utilization of a glycerin-filled manometer (0–16 bar, Ø63 mm, Pakkens®, Bursa, Turkey), which was mounted in close proximity to the nozzle body. The achievement of pressure control was facilitated by the implementation of a secondary manometer, which was situated on the sprayer’s pressure line. The configuration in question facilitated the monitoring of discrepancies between the system’s spraying and operating pressures. The regulation of flow was achieved through the utilization of a solenoid valve. The valve was maintained in a closed position at the commencement of the spraying process. Prior to the initiation of the spraying process, a meticulous examination of the manometric pressure condition was conducted, followed by a precise adjustment of the spraying pressure. Subsequently, the flow was permitted to attain a steady state. During this process, the liquid sprayed was collected in an externally used beaker. Subsequent to the satisfaction of the requisite conditions for the process of spraying, the beaker located beneath the nozzle was detached. This enabled the flow to reach the patternator table. The fluid accumulated in the patternator channels was conveyed to the liquid transfer tubes and permitted to accumulate in the collection cylinders. Polystyrene (PS) graduated tubes, complete with a volume indicator (maximum capacity of 25 milliliters), were utilized as fluid collection cylinders. In order to facilitate the visualization of the fluid level in each collection cylinder, freely movable sphere-shaped markers were employed. The markers were distinguished by their black color, the fact that they were manufactured from expanded PS material, and a density range of 2–40 kg m−3 [23].
The spraying system utilized a conventional field sprayer equipped with a 200-L tank (PE) capacity, as illustrated in Figure 1b. Mains water was utilized as the spray liquid, and the system’s hydraulic agitator was deactivated. The fluid pressure was adjusted using a continuously adjustable pressure regulator (configured with a bypass line) and the operating pressure was additionally controlled using a liquid-filled manometer (0–16 bar, Ø63 mm, Pakkens Turkey).
The hydraulic pressure of the spray system was provided by a belt-driven piston-membrane type sprayer pump (30 L min−1 nominal flow rate, 40 kg cm−2 nominal fluid pressure, 67% efficiency, TAR30 Model, Taral®, İstanbul, Turkey) as illustrated in Figure 1c. The shaft of the pump, which was driven by an electric motor (2.2 kW, 1405 min−1, Gamak®, İstanbul, Turkey), was operated at 500 min−1.
The liquid that accumulated in the collection cylinders post-spray application was then drained using a pragmatic method, as illustrated in Figure 1d. This method involved the fabrication of the steel construction to which the collection cylinders were connected with hinges. The steel construction was maintained in position during the filling process by means of a magnet. The steel profile was tilted forward in order to facilitate the drainage of liquid accumulated in the collection cylinders.
2.2. Spray Nozzles
The mounting of the spray nozzles on the pressure line was facilitated by a single diaphragm nozzle body, thereby enabling the individual testing of the spray nozzles. Disc-core type hollow cone nozzles (POM, Ø1.6 mm orifice diameter; 0.67 L min−1 average flow rate at 3 bar pressure; 85.2° average spray angle; locally manufactured, İstanbul, Turkey) were utilized in the spray tests [24]. Fifteen spray nozzles were selected at random from those supplied by the manufacturer, and the spray pattern of each was recorded individually. Spray tests were conducted at a constant operating pressure of 3 bar, with the spray height set to 60 cm. The spray pattern obtained with each nozzle plate was the result of a single spray. The primary objective of the experiment was not to evaluate within-nozzle repeatability, but rather to characterize and compare the spray distribution patterns generated by different nozzle types. Each nozzle functioned as an independent experimental unit, yielding a distinct spray pattern determined by its hydraulic and geometric characteristics.
The methodological validity of the image processing operation developed within the scope of this study was measured by obtaining different spray patterns. In accordance with this objective, an examination of previous study on the subject of spray tests of hollow cone nozzles revealed that different spray patterns were obtained under the same operating conditions [25]. This intriguing discovery presented a significant opportunity to assess the validity of the image processing methodology.
2.3. Determination of Spray Pattern by Volume Reading Method
Subsequent to the application of the spray, readings were initially obtained from the measuring cylinder in order to ascertain the spray pattern that had been formed in the graduated collection cylinders. Thereafter, the volume of liquid that had accumulated in each tube was meticulously recorded in milliliters. The numerical values obtained were utilized to verify the spray pattern determined by image processing.
2.4. Obtaining of Spray Pattern Images
The visualization of the spray distribution obtained from the same volume reading was achieved by employing the rear camera of a Samsung Galaxy S21 FE smartphone (Android OS) equipped with a 12 MP dual-pixel sensor (1/1.76″ CMOS, 26 mm equivalent focal length, f/1.8 aperture, 1.8 µm pixel size). The device was mounted on a fixed vertical stand, with a distance of 60 cm maintained between the device and the patternator surface. This ensured perpendicular alignment with the collection plane, thus minimizing geometric distortion. All images were captured in manual (Pro) mode, a setting which disabled automatic adjustments of ISO, exposure, focus, and white balance parameters. This ensured full control over imaging conditions.
A white plexiglass sheet was utilized on the rear surface of the fluid collection cylinders mounted on the roof of the pattern generator, and markers were employed to create contrast and reveal the spray pattern. As demonstrated in Figure 2, the camera was affixed to a tripod at a distance of 2.0 m from the patternator [13] table.
2.5. Illumination Conditions and Calibration Procedure
The illumination was provided by two diffuse LED panels (5500 K color temperature, CRI > 90) positioned symmetrically at 45° angles on both sides of the imaging setup to minimize shadowing and reflections. The background surface was coated with a matte white finish to optimize contrast, and the imaging area was enclosed to eliminate ambient light. In order to ensure reproducible image acquisition conditions, it was imperative that lighting intensity and direction remained constant throughout the course of the experiments. Prior to data collection, the camera was calibrated using a reference grid (10 × 10 mm squares) in order to correct lens distortion and to establish a pixel-to-distance conversion factor for subsequent measurements. White balance, ISO, and exposure settings were manually adjusted during the entire image acquisition process to ensure consistent illumination and prevent automatic adjustments that could affect pixel intensity and image contrast. The implementation of these procedures ensured stable imaging conditions, minimized reflection-related variability, and enhanced the repeatability of subsequent image processing and analysis steps.
The relationship between pixel intensity and liquid volume was determined through a calibration procedure in which patternator cylinders were filled sequentially with known water volumes (5–25 mL, at 5 mL intervals). For each calibration level, images were captured under identical camera and lighting conditions, and the liquid height was measured in pixels using the same image analysis workflow applied in the main experiment. A linear regression model was established between pixel height and measured volume obtained from a precision graduated cylinder (±0.1 mL). The resulting calibration curve exhibited a strong linear relationship (R2 > 0.99), while independent validation tests using unused samples yielded a mean absolute percentage error below 3%. Three replicate measurements were taken at each level in order to assess repeatability. It was found that the coefficient of variation (CV) remained under 2%. These results confirm that the pixel-to-volume conversion was accurate, stable, and suitable for quantitative image-based volume estimation.
2.6. Image Processing
Image analysis was conducted utilizing the MATLAB R2022b software environment (MathWorks, Natick, MA, USA). In the initial phase, each spray pattern image underwent processing and conversion to greyscale. Subsequently, the contrast levels were enhanced through the implementation of the imadjust and adapthisteq functions. In the subsequent stage, a Gaussian filter (imgaussfilt) was implemented to attenuate background noise and reflection effects in the image. In the third step, a threshold-based segmentation (imbinarise) method was employed to isolate the spray area and determine the region of interest. Subsequent to this initial step, morphological operations (erosion and dilation; imerode and imdilate commands) were performed on the binary image in order to highlight the black-colored markers. Following the implementation of the thresholding process, a binary image mask representing the spray area was obtained. The center coordinates and radii of the markers were determined by employing the imfindcircles algorithm on the obtained mask. The coordinates that had been detected were subsequently exported in Excel format (writematrix/xlswrite) and organized in separate folders for each spray pattern. Finally, the detected markers were visualized with the viscircles function, and the results were saved in .jpg format and archived with the analysis data. Consequently, the distribution data for each spray pattern were quantitatively calculated, and the results were utilized in the evaluation phase.
The distribution pattern obtained at the conclusion of each spraying process was captured by means of digital imaging, with the resultant image files being stored in the .jpg file format (Figure 3a). The execution of image processing operations was facilitated by the utilization of the software. The image files were opened in the .mfile that had been created for this purpose, cropped, and the top left corner of the image was defined as the origin in order to perform the analyses. (Figure 3b). The image files were converted into a matrix value array by means of Matlab algorithms. The implementation of shadow removal algorithms was instrumental in the reduction of noise in the image, while the application of filtering enhanced the contrast of the markers. The markers were distinguished from the background color, and the coordinates of the markers relative to the origin were digitized in a matrix format (Figure 3c). The generation of a spray pattern was achieved through the utilization of markers, with the position coordinates (x, y) of these markers being determined in pixels (Figure 3d). The calibration of the measurement instrument was undertaken in accordance with the resolution of the images. The pixel measurement unit of the markers was converted into a volume measurement unit (mL) (Figure 3e).
2.7. Statistical Analysis
In order to draw parallels between the spray patterns ascertained by the volume reading and image processing methods, a statistical analysis was conducted. The skewness (S), kurtosis (K), coefficient of variation (), first quartile (Q1), interquartile range (IQR), third quartile (Q3), standard deviation (SD), median (median, M), volumetric symmetry (VS), and bimodality coefficient (BC) statistics were determined [15,26,27,28,29]. The calculation of all statistics describing the spray patterns was conducted using a macro created in MS Excel. The equation was used for the quarter-open value. Volumetric symmetry (VS) was defined as the ratio of the liquid volumes accumulated on both sides relative to the symmetry axis of the spray pattern (i.e., the directional axis of the spray nozzle). The ratio of 1 indicates that equal volumes of liquid accumulate on both sides of the distribution. The bimodality coefficient (BC) is defined as a statistical measure that identifies whether the spray distribution is unimodal or bimodal. The BC value was calculated using the equation of (m3: skewness value, m4: kurtosis value, n: number of observations). It has been asserted that, in instances where the value in question exceeds 0.55, there is an elevated probability of the distribution exhibiting a bimodal nature [28].
To ensure cross-platform consistency, volumetric and image-based datasets were matched on a one-to-one basis according to nozzle ID and channel position. Each corresponding data pair was compared through correlation and deviation analysis, confirming the consistency between both measurement platforms.
In order to ascertain the discrepancy between the two methodologies, the data were subjected to multivariate analysis of variance in the IBM SPSS Statistics (Version 20.0, IBM Corp., Armork, NY, USA) software package [30]. The difference between the methods was explained through the utilization of Wilks’ Lambda and Pillai’s Trace statistics. Principal component analysis (PCA) was performed to reveal the relationship between the variables that define the spray pattern. The utilization of the varimax rotation method was deemed optimal in order to enhance the interpretability of the components. Variables exhibiting a high degree of correlation were excluded from the analysis, thereby mitigating the impact of multiple linear correlation. In the evaluation of component loadings, the rotated component matrix was given due consideration. The regression method was employed to obtain factor scores, and the relationship between the first two components (PC1 and PC2) was elucidated through the utilization of a scatter plot.
In order to categorize the spray patterns according to their similarities, the data were subjected to hierarchical cluster analysis using the Minitab Statistical Software, version 15.0 (Minitab LLC, State College, PA, USA) package [31]. In this analysis, the Euclidean distance measure was selected for the purpose of measuring the inter-cluster distances. The utilization of the Euclidean distance in this particular context is pivotal, as it facilitates the numerical expression of similarities by quantifying the geometric distance between observations. In the context of the clustering method, the linkage method was favored, as it was known to minimize the total variance between clusters and ensure the formation of homogeneous clusters. The objective of this method was to minimize the increase in the sum of squares at each merging stage. The rationale behind this was to ensure that more balanced and meaningful clusters were obtained [32].
Multivariate analysis of variance (MANOVA) was applied in order to evaluate the overall effect of nozzle type on multiple interrelated variables describing spray distribution. MANOVA was selected because it accounts for correlations among dependent variables and provides a comprehensive multivariate comparison while minimizing Type I error. Principal component analysis (PCA) was subsequently used to identify the principal sources of variance and to visualize the relationships among nozzle types. PCA reduced data dimensionality and revealed grouping patterns based on the dominant spray characteristics. Together, MANOVA and PCA provided complementary insights—testing the statistical significance of nozzle effects and interpreting their multivariate similarities within a unified analytical framework.
3. Results
3.1. Comparison Between Volumetric and Image-Based Measurements
The results obtained from the volume reading method in the liquid collection cylinders of the patternator were largely consistent with those from the image processing method (Figure 4). Whilst the liquid volumes ascertained by the two methods were in close proximity to the center of the patternator, minor discrepancies were observed towards the periphery. The liquid volume as determined by image processing at both tails of the spray pattern was found to be marginally higher than that determined by the volume reading method. The deviation observed at the spray edges (2.4–3.1%) was attributed mainly to minor perspective distortion and differential illumination on the outer cylinders. Repeated imaging under different lighting conditions confirmed that the deviation remained below ±3%, indicating that the error did not significantly affect distribution symmetry or CV statistics.
As demonstrated in the findings of the study, the application of sprays was an unstable process. Furthermore, the results indicated that this process was inconsistent with regard to the width and pattern uniformity of the spray. In the spray pattern tests, the range of the spray width was found to vary between 63.6 and 84.2 cm. There was no consensus among the spray patterns regarding the skewness, kurtosis, symmetry, and single or multi-modality that characterize the distribution of spray patterns.
3.2. Statistical Analysis of Spray Pattern Uniformity
As illustrated in Table 1, the statistical analysis of the distribution of sprays was determined by two distinct methods: volume reading (VR) and image processing (IP). The mean statistics of the variables as determined by both methods were found to be almost identical, and the correlation between them (0.9902–0.9997) was deemed to be extremely high. The majority of spray patterns demonstrated negative skewness and kurtosis values. The lowest and highest CV values ascertained by both methodologies are 46.6% and 68.6%, respectively. The standard deviation statistics between the methods were also quite similar. The mean kurtosis was equivalent for both methodologies. The quartile variables determined by the volume reading method demonstrated a high degree of similarity to the variables determined by the image processing method. The discrepancy between the median values of the two methods was minimal. The liquid volumes accumulated in the left and right tails relative to the center axis of the spray distribution was found to be approximately equal to 1.
3.3. Multivariate Analysis
As demonstrated in Table 2, the Wilks’ Lambda and Pillai’s Trace statistics reveal that there was no statistically significant discrepancy between the volume reading and image processing methods (p = 0.067). The variables demonstrating high correlation with each other were eliminated for principal component (PC) analysis. The relationship between spray patterns was defined by the CV and BC variables, and the correlation between them was found to be insignificant (p = 0.242). Following the analysis of the PC, the relationship between the various spray patterns was explained by the components PC1 and PC2. The variance explanation ratios of the PC1 and PC2 components were 59.8% and 40.2%, respectively. Consequently, the observed variance in the spray patterns was attributable to the two components. The largest loadings (0.995) carried by the PC1 and PC2 components were the CV and BC variables, respectively, and the correlation between them was positive.
The distribution of spray applications according to the first two components explaining the relationship between spray patterns is shown in Figure 5a. The CV values of the spray patterns remaining to the right of the PC1 horizontal component were higher than those on the left. In a similar manner, the BC statistics of the distributions remaining above the PC2 vertical component were higher than those below. The PC scores, classified by application number, demonstrate a shift in direction from the origin, indicating an augmentation in CV and BC values. The applications 8 and 11 exhibited the lowest CV values, while the application 9 demonstrated a higher CV compared to the other applications. The applications 1, 5, and 15 demonstrated the lowest BC values for their respective spray patterns. It was demonstrated that applications exhibiting equivalent PC scores are compatible with regard to the distribution of spray.
As illustrated in Figure 5b, the dendrogram (i.e., the hierarchical clustering diagram) demonstrated the distributions that exhibited the closest resemblance in terms of spray pattern. The distributions that were proximate in the clustering diagram were analogous and consistent with the PC scores. The incompatibility of spray applications with BC was a matter of principal significance, and it was therefore essential to divide them into two main groups. The applications numbered 1, 11, 5, 15, 6, 14, and 9 on the left side of the dendrogram form Group I; applications numbered 2, 12, 4, 13, 3, 7, 10, and 8 on the right-side form Group II. The distributions analogous in terms of CV correspond to the smallest subgroups (applications numbered 2–12; 6–14; 3–7; 4–13; 5–15).
4. Discussion
4.1. Methodological Consistency
The observed divergence in the spray distributions obtained from both methods can be attributed to the discrepancies between the volume readings and the image processing methodologies employed. These discrepancies are hypothesized to arise from variations in the referenced origin as indicated by the image file, as well as from parameters associated with image processing (e.g., parallel, selection of viewing distance, camera lens concavity, camera settings, etc.).
Despite the strong correlation between the two measurement techniques, several potential sources of error may slightly influence image-based readings. It is important to note that minor discrepancies may be observed in the data due to variations in ambient lighting, camera angle, and the reflective characteristics of the transparent collection cylinders, particularly in the vicinity of the spray edges [33]. The effects in question are regarded as being systematic in nature, yet they remained within the bounds of acceptability (±3%) throughout the course of the trials. In order to mitigate the impact of these factors, it was necessary to maintain controlled illumination, fixed camera geometry, and consistent background contrast. However, subsequent studies will concentrate on optimizing illumination uniformity and camera calibration to further enhance measurement precision and reliability.
4.2. Statistical Characterization of Spray Patterns
The presence of negative skewness, indicative of a distribution that was skewed to the right, indicated a greater volume of liquid accumulating in the left tail of the distribution relative to the right tail. Conversely, negative kurtosis indicated a distribution that was less peaked than was typical, with a greater accumulation of liquid in the left and right tails in comparison to the central region [34]. The CV value of the spray distribution was a significant metric for quantifying the uniformity of the liquid distribution across the width of the spray [35,36]. Consequently, the distribution of the spray was found to be heterogeneous, as evidenced by the elevated CV value. It has been demonstrated that a spray pattern geometry that is close to triangular or trapezoidal in shape indicates that less liquid is carried to both tails of the distribution [37]. It has been demonstrated that this phenomenon results in an increase in the CV value. The uniformity in the liquid volume collected in each measuring cylinder across the spray width is indicative of a distribution with a standard deviation value of 0. Given that the smallest CV and standard deviation values obtained in this study were 46.7% and 6.055 mm (by image processing), respectively, it could be concluded that the spray pattern shape was best defined as triangular or trapezoidal.
Of the spray applications, those designated 2, 3, 4, 7, 8, 9, 10, 12, and 13 exhibited a bimodality coefficient (BC) greater than 0.55. The presence of a bimodal distribution was indicated by a BC value that exceeds 0.55 [28]. A significant disparity has been identified in the spray patterns produced by 15 distinct spray nozzles, with the variation contingent on the BC value. This outcome provided a rationale for the observed incompatibility among spray nozzles with regard to their capacity for uniform distribution.
In order to demonstrate the consistency between the datasets, the quartiles (Q1, IQR, and Q3) and the median variables were utilized [38]. The quartile and median variables of the spray patterns indicated the potential for similarity between the two methods. In order to demonstrate the similar relationship between the methods, the spray distribution was examined in terms of symmetry. The ratio of liquid volumes accumulated on the left and right sides of the distribution relative to the central axis dividing the spray was revealed to demonstrate the volumetric symmetry of the distribution. An evaluation of symmetry was conducted, with both methods demonstrating comparable characteristics in this regard.
4.3. Multivariate Findings and Spray Pattern Variability
The findings of the multivariate statistical analysis demonstrated that no statistically significant differences were observed between the volume reading and image processing methods. This finding suggests that the image processing-supported measurement method developed for mechanical patternators can be utilized as an alternative to sensor-based electronic systems. This measurement method was demonstrated to offer a number of advantages. Firstly, it provided reliable data, and secondly, it was shown to reduce the production cost of the patternator. Moreover, the image processing-supported measurement method was regarded as advantageous due to its ease of use and practicality, obviating the necessity for maintenance and repair.
The principal component analysis and hierarchical clustering diagram provided a clear illustration of the similarities and differences between the spray nozzles with regard to spray distribution. In the course of the study, 15 spray nozzles were examined, of which 8 exhibited a bowl-shaped (double-peaked) spray pattern. With regard to the distribution of the spray, a total of three applications were found to have a CV that was significantly lower than the CVs of the other applications. Despite the utilization of spray nozzles that possessed identical nominal dimensions in this study, the pattern tests yielded spray distributions that exhibited divergent patterns. The attainment of a uniform pattern in the distribution of the spray was of paramount importance in ensuring the uniformity of the volumetric distribution. Therefore, in this study, it was possible to successfully reveal the differences between the spray nozzles using multivariate statistical analysis methods. Furthermore, the structure of the spray patterns was compared using descriptive statistics.
5. Conclusions
The present study demonstrated that an image-based analysis approach provides a reliable, accurate, and repeatable alternative to the traditional volumetric method for evaluating spray distribution patterns. The strong linear correlation (r > 0.99) and minimal deviation (within ±3%) between both techniques confirmed the robustness of the proposed method. Statistical indicators such as the Coefficient of Variation (CV) were utilized to effectively characterize the spatial variability of the spray patterns. The image-based technique was found to be capable of accurately capturing both the central and edge regions of the spray, thereby ensuring quantitative comparability with volumetric data.
Furthermore, the integration of multivariate analyses (MANOVA and PCA) revealed that differences between measurement approaches were not statistically significant, thereby reinforcing the equivalence of the image-derived results. The method also demonstrated strong sensitivity to variations in nozzle geometry and spray height yet maintained stability across controlled lighting and camera configurations. These findings collectively confirm the practical potential of the method for use in laboratory calibration, nozzle classification, and field spray optimization studies.
It is recommended that future endeavors concentrate on broadening the spectrum of nozzle types and operational parameters, incorporating real-time image acquisition, and utilizing machine learning algorithms for automated droplet detection and classification. These advancements will further augment the universality, speed, and scalability of image-based spray evaluation techniques, thereby enhancing the precision and sustainability of agricultural spraying systems.
Conceptualization, B.S. and M.Ç.; methodology, B.S.; validation, B.S. and M.Ç.; formal analysis, B.S. and M.Ç.; investigation, B.S. and M.Ç.; resources, B.S. and M.Ç.; data curation, B.S. and M.Ç.; writing—review and editing, B.S. and M.Ç.; visualization, B.S. and M.Ç.; supervision, B.S. and M.Ç. All authors have read and agreed to the published version of the manuscript.
The data used in this study were obtained experimentally in my doctoral research titled “Design and Manufacturing of Stroke Motion Spray Test Scanner Prototype” and were further processed using image processing algorithms in MATLAB. The datasets are available from the corresponding author upon request.
The authors would like to acknowledge that this research forms part of the doctoral dissertation of Mustafa Çomaklı, conducted at the Department of Agricultural Machinery, Institute of Science, Atatürk University, Erzurum, Türkiye.
The authors declare no conflicts of interest.
The following abbreviations are used in this manuscript:
| kW | Kilowatt |
| PS | Polystyrene |
| mL | Milliliter |
| kg | Kilogram |
| m | Meter |
| L | Liter |
| min | Minute |
| cm | Centimeter |
| POM | Polyoxymethylene |
| VR | Volume reading method |
| IP | Image processing method |
| m3 | Skewness |
| m4 | Kurtosis |
| CV | Coefficient of variation |
| SD | Standard deviation |
| Mean | |
| BC | Bimodality coefficient |
| r | Correlation |
| Q1 | First quartile (IQ25, 25th percentile) |
| Q3 | Third quartile (IQ75, 75th percentile) |
| IQR | Interquartile range |
| Min | Minimum |
| Max | Maximum |
| M | Median |
| VS | Volumetric symmetry |
| df | Degree of freedom |
| PC | Principal component |
| p | Probability |
| ns | Nonsignificant |
Footnotes
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Figure 1 Mechanical spray patternator with spray system and power supply and fluid discharge [
Figure 2 Image acquisition system.
Figure 3 Image processing operations applied to spray pattern images taken from the graduated tubes of the mechanical patternator (a) An example of a spray pattern, (b) The selection of the area for the spray pattern and the application of image cropping, (c) The automatic selection of markers and determination of position coordinates (x-y) relative to the origin, (d) The generation of the spray pattern through the utilization of raw data, (e) The generation of the spray pattern after the measurement calibration.
Figure 4 The determination of spray patterns obtained from the utilization of the volume readings (VRs) and the image processing (IP) methodologies within the graduated tubes of the mechanical patternator (n: number of data points utilized to derive the spray pattern).
Figure 5 Comparison the distributions according to the variables that define the patterns of the sprays (a) Similarities between spray patterns according to principal component scores (b) Dendrogram determined by means of the cluster analysis.
Descriptive statistics of spray patterns determined by volume reading (VR) and image processing (IP) methods in a mechanical patternator.
| Application | Skewness | Kurtosis | Coefficient of | Standard | Bimodality | Correlation | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| VR * | IP | VR | IP | VR | IP | VR | IP | VR | IP | r * | ||||||||||
| 1 | −0.044 | 0.019 | −1.134 | −1.181 | 57,367 | 53,848 | 6731 | 6454 | 0.479 | 0.489 | 0.9971 | |||||||||
| 2 | 0.001 | −0.020 | −1.584 | −1.580 | 64,948 | 62,737 | 7786 | 7641 | 0.604 | 0.603 | 0.9988 | |||||||||
| 3 | −0.247 | −0.209 | −1.476 | −1.492 | 60,865 | 57,008 | 7368 | 7004 | 0.595 | 0.591 | 0.9984 | |||||||||
| 4 | −0.169 | −0.141 | −1.470 | −1.479 | 62,056 | 61,306 | 7379 | 7295 | 0.581 | 0.580 | 0.9976 | |||||||||
| 5 | 0.223 | 0.237 | −1.140 | −1.064 | 67,184 | 61,569 | 7118 | 6829 | 0.493 | 0.479 | 0.9994 | |||||||||
| 6 | −0.177 | −0.181 | −1.323 | −1.345 | 58,107 | 59,528 | 7558 | 7429 | 0.536 | 0.544 | 0.9902 | |||||||||
| 7 | −0.270 | −0.290 | −1.301 | −1.347 | 57,346 | 56,707 | 6914 | 6711 | 0.559 | 0.578 | 0.9972 | |||||||||
| 8 | −0.570 | −0.589 | −1.058 | −1.030 | 48,865 | 46,688 | 6192 | 6055 | 0.609 | 0.611 | 0.9979 | |||||||||
| 9 | 0.017 | 0.037 | −1.416 | −1.412 | 66.416 | 68,624 | 7785 | 7876 | 0.549 | 0.548 | 0.9996 | |||||||||
| 10 | −0.305 | −0.339 | −1.410 | −1.365 | 57.718 | 53,735 | 6866 | 6686 | 0.605 | 0.602 | 0.9987 | |||||||||
| 11 | −0.337 | −0.381 | −1.195 | −1.129 | 54.649 | 50.201 | 6622 | 6275 | 0.545 | 0.543 | 0.9986 | |||||||||
| 12 | −0.043 | −0.067 | −1.595 | −1.566 | 67,659 | 63,174 | 8040 | 7837 | 0.607 | 0.598 | 0.9990 | |||||||||
| 13 | −0.119 | −0.176 | −1.479 | −1.435 | 64,601 | 59,590 | 7131 | 6676 | 0.586 | 0.580 | 0.9984 | |||||||||
| 14 | −0.149 | −0.123 | −1.314 | −1.326 | 62,321 | 58,790 | 7431 | 7226 | 0.539 | 0.539 | 0.9987 | |||||||||
| 15 | 0.187 | 0.191 | −1.245 | −1.222 | 67,306 | 63,145 | 7610 | 7296 | 0.497 | 0.493 | 0.9997 | |||||||||
| Mean | −0.134 | −0.136 | −1.343 | −1.331 | 61,161 | 58,443 | 7235 | 7019 | 0.559 | 0.559 | - | |||||||||
| SD | 0.204 | 0.217 | 0.166 | 0.173 | 5.451 | 5.616 | 0.504 | 0.555 | 0.044 | 0.044 | - | |||||||||
| Min. | −0.570 | −0.589 | −1.595 | −1.580 | 48.865 | 46,688 | 6192 | 6055 | 0.479 | 0.479 | 0.9902 | |||||||||
| Max. | 0.223 | 0.237 | −1.058 | −1.030 | 67.659 | 68,624 | 8040 | 7876 | 0.609 | 0.611 | 0.9997 | |||||||||
| Application | Q1 | Q3 | IQR ** | Median | Volumetric | |||||||||||||||
| VR | IP | VR | IP | VR | IP | VR | IP | VR | IP | |||||||||||
| 1 | 6000 | 5476 | 16,250 | 15,937 | 10,500 | 10,460 | 13,500 | 13,534 | 0.859 | 0.919 | ||||||||||
| 2 | 4000 | 4639 | 20,000 | 20,023 | 16,000 | 15,384 | 12,000 | 12,255 | 1285 | 1264 | ||||||||||
| 3 | 5250 | 5142 | 18,875 | 18,711 | 14,250 | 13,569 | 13,500 | 13,295 | 1098 | 1100 | ||||||||||
| 4 | 4000 | 4632 | 18,000 | 18,348 | 14,000 | 13,716 | 13,000 | 12,870 | 1147 | 1217 | ||||||||||
| 5 | 4000 | 4431 | 16,000 | 16,451 | 13,000 | 12,020 | 10,500 | 11,031 | 1081 | 1082 | ||||||||||
| 6 | 6000 | 5414 | 19,000 | 18,953 | 13,000 | 13,539 | 14,500 | 13,804 | 1159 | 1052 | ||||||||||
| 7 | 5000 | 4979 | 18,000 | 17,914 | 13,000 | 12,935 | 13,500 | 13,290 | 0.831 | 0.878 | ||||||||||
| 8 | 7500 | 7655 | 17,500 | 17,502 | 10,250 | 9846 | 14,750 | 14,852 | 0.673 | 0.669 | ||||||||||
| 9 | 4000 | 3439 | 18,500 | 18,770 | 15,250 | 15,330 | 12,000 | 11,571 | 1293 | 1326 | ||||||||||
| 10 | 5000 | 5919 | 18,000 | 18,183 | 13,000 | 12,264 | 14,000 | 14,772 | 0.814 | 0.831 | ||||||||||
| 11 | 6000 | 6496 | 17,000 | 17,473 | 11,750 | 10,976 | 14,000 | 14,556 | 1126 | 1125 | ||||||||||
| 12 | 3375 | 4328 | 19,250 | 19,922 | 16,625 | 15,594 | 13,000 | 13,477 | 0.625 | 0.644 | ||||||||||
| 13 | 4125 | 4.340 | 16.875 | 16,858 | 13,250 | 12,518 | 12,250 | 12,338 | 0.888 | 0.902 | ||||||||||
| 14 | 4250 | 4805 | 17,875 | 18,246 | 14,000 | 13,441 | 13,500 | 13,739 | 0.647 | 0.673 | ||||||||||
| 15 | 4500 | 4780 | 16,500 | 16,534 | 12,500 | 11,754 | 11,000 | 11,342 | 1144 | 1131 | ||||||||||
| Mean | 4867 | 5098 | 17,842 | 17,988 | 13,358 | 12,890 | 13,000 | 13,115 | 0.978 | 0.988 | ||||||||||
| SD | 1110 | 1.014 | 1.166 | 1214 | 1783 | 1748 | 1228 | 1206 | 0.228 | 0.220 | ||||||||||
| Min. | 3375 | 3439 | 16,000 | 15,937 | 10,250 | 9846 | 10,500 | 11,031 | 0.625 | 0.644 | ||||||||||
| Max. | 7500 | 7655 | 20,000 | 20,023 | 16,625 | 15,594 | 14,750 | 14,852 | 1293 | 1326 | ||||||||||
*: r: correlation between the volume reading method (VR) and the image processing methods (IP). **: IQ25: first quartile of the data set (25th percentile); IQ75: third quartile of the data set (75th percentile); IQR: interquartile range (difference between Q3 and Q1).
Variables defining spray patterns through principal component analysis (PCA).
| A. Multivariate variance analysis results (SPSS 20.0) | ||||||||||
| Source of variation | Statistics | Value | F | Hypothesis df | Error df | p (sig.) | ||||
| Methods 1 | Wilks’ Lambda | 0.464 | 2.198 | 10.0 | 19 | 0.067 ns | ||||
| Pillai’s Trace | 1.157 | 2.198 | 10.0 | 19 | 0.067 ns | |||||
| B. Correlation matrix | ||||||||||
| Variables | Correlation coefficient | p (sig.) | ||||||||
| CV-BC | −0.196 | 0.242 ns | ||||||||
| C. Principal component analysis eigenvalue statistics | ||||||||||
| Components | Eigenvalue statistics | Explained variance (%) | Cumulative (%) | |||||||
| PC1 | 1.196 | 59,815 | 59,815 | |||||||
| PC2 | 0.804 | 40,185 | 100.00 | |||||||
| D. Rotated component matrix | ||||||||||
| Statistics 2 | PC1 | PC2 | ||||||||
| CV | 0.995 | −0.099 | ||||||||
| BC | −0.099 | 0.995 | ||||||||
1: Image processing (IP) and volume reading (VR) methods; 2: CV: coefficient of variation, BC: bimodality coefficient; ns: nonsignificant.
1. Srivastava, A.K.; Goering, C.E.; Rohrbach, R.P.; Buckmaster, D.R. Chapter 10 Chemical Application. Engineering Principles of Agricultural Machines; 2nd ed. ASABE: St. Joseph, MI, USA, 2006; ISBN 1-892769-50-6
2. Choudhary, M.; Carpenter, G.; Kumar, M.; Jatav, M.; Rani, A.; Thomos, E. Design Modifications of a Horizontal Spray Patternator. Biol. Forum—Int. J.; 2023; 15, pp. 191-194.
3. Sarkar, P.; Raheman, H.A. Comprehensive Review of Mechanized Cabbage Harvesting Systems and Its Present Status in India. J. Inst. Eng. India Ser. A; 2021; 102, pp. 861-869. [DOI: https://dx.doi.org/10.1007/s40030-021-00557-6]
4. Cunha, M.; Carvalho, C.; Marcal, A.R.S. Assessing the Ability of Image Processing Software to Analyse Spray Quality on Water-Sensitive Papers Used as Artificial Targets. Biosyst. Eng.; 2012; 111, pp. 11-23. [DOI: https://dx.doi.org/10.1016/j.biosystemseng.2011.10.002]
5. Kou, H.; Sun, Y.; Dong, Z.; Zhang, Z. Comparison Between Sustained Effects of Spray and Injection Thiamethoxam on Apple Aphids and Non-Target Insects in Apple Orchard. Ecotoxicol. Environ. Saf.; 2021; 207, 111307. [DOI: https://dx.doi.org/10.1016/j.ecoenv.2020.111307]
6. Straw, E.A.; Stanley, D.A. An Introduction to Bee and Pesticide Research. J. Appl. Ecol.; 2025; 62, pp. 19-27. [DOI: https://dx.doi.org/10.1111/1365-2664.14834]
7. Nuyttens, D.; Baetens, K.; Schampheleire, M.D.; Sonck, B. Effect of Nozzle Type, Size and Pressure on Spray Droplet Characteristics. Biosyst. Eng.; 2007; 97, pp. 333-345. [DOI: https://dx.doi.org/10.1016/j.biosystemseng.2007.03.001]
8. Desmarteau, D.A.; Ritter, A.M.; Hendley, P.; Guevara, M.W. Impact of Wind Speed and Direction and Key Meteorological Parameters on Potential Pesticide Drift Mass Loadings from Sequential Aerial Applications. Integr. Environ. Assess. Manag.; 2020; 16, pp. 197-210. [DOI: https://dx.doi.org/10.1002/ieam.4221] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/31589364]
9. Hilz, E.; Vermeer, A.W.P. Spray Drift Review: The Extent to Which a Formulation Can Contribute to Spray Drift Reduction. Crop Prot.; 2013; 44, pp. 75-83. [DOI: https://dx.doi.org/10.1016/j.cropro.2012.10.020]
10. Sayıncı, B. Detection of Shape Manufacturing Defects of Flat Fan-Pattern Nozzle Orifices Using Elliptic Fourier Descriptors. J. Agric. Sci.; 2016; 22, pp. 317-330. [DOI: https://dx.doi.org/10.1501/Tarimbil_0000001390]
11. Milanowski, M.; Subr, A.; Parafiniuk, S. Evaluation of Different Internal Designs of Hydraulic Nozzles under an Accelerated Wear Test. Appl. Sci.; 2022; 12, 889. [DOI: https://dx.doi.org/10.3390/app12020889]
12. Sivri, M.; Çanakcı, M. Determination of Spraying Properties of Nozzle Plates in Greenhouse Sprayers in Use. Tekirdağ Ziraat Fakültesi Derg.; 2024; 21, pp. 648-665. [DOI: https://dx.doi.org/10.33462/jotaf.1325283]
13. Çömlek, R.; Sayıncı, B. Mekanik Püskürtme Paternatörü Tasarımı, Prototip İmalatı ve Pülverizatör Memelerinde Akış Testleri [Design of A Mechanical Spray Paternator, Prototype Manufacturing and Flow Tests on Spray Nozzles]. Anadolu Tarım Bilim. Derg.; 2023; 38, pp. 597-618. (In Turkish) [DOI: https://dx.doi.org/10.7161/omuanajas.1351081]
14. Hassen, N.S.; Sidik, N.A.C.; Sheriff, J.M. Effect of Nozzle Type, Angle and Pressure on Spray Volumetric Distribution of Broadcasting and Banding Application. J. Mech. Eng. Res.; 2013; 5, pp. 76-81. [DOI: https://dx.doi.org/10.5897/JMER2013.0272]
15. Sayıncı, B.; Çömlek, R.; Boydaş, M.G.; Kara, M.; Demir, B. Konik Hüzmeli Memelerde Kullanılan Girdap Plaketlerinin Hüzme Açısı ve Püskürtme Paternine Etkisi [Effect of the Core Discs Used in Hollow Cone Nozzles on Spray Angle and Spray Pattern]. J. Agric. Fac. Gaziosmanpaşa Univ.; 2017; 34, pp. 1-9. (In Turkish) [DOI: https://dx.doi.org/10.13002/jafag4398]
16. Luck, J.D.; Schaardt, W.A.; Sharda, A.; Forney, S.H. Development and Evaluation of an Automated Spray Patternator Using Digital Liquid Level Sensors. Appl. Eng. Agric.; 2016; 32, pp. 47-52. [DOI: https://dx.doi.org/10.13031/aea.32.11381]
17. Sehsah, E.M.E. Vertical Patternator for Evaluation of the Hydraulic Sprayers. Misr J. Agric. Eng.; 2016; 33, pp. 1239-1254. [DOI: https://dx.doi.org/10.21608/mjae.2016.97595]
18. Višacki, V.; Sedlar, A.; Bugarin, R.; Turan, J.; Burg, P. Effect of Pressure on the Uniformity of Nozzles Transverse Distribution and Mathematical Model Development. Acta Univ. Agric. Silvic. Mendel. Brun.; 2017; 65, pp. 563-568. [DOI: https://dx.doi.org/10.11118/actaun201765020563]
19. Öziç, M.Ü.; Çankaya, N.; Özcan, M.; Gökçe, B. An Approach to Counting Legumes Using Coordinate Features in Image Processing. Konya J. Eng. Sci.; 2020; 8, pp. 28-37. [DOI: https://dx.doi.org/10.36306/konjes.822353]
20. Yıldırım, B.; Cagıl, G. Detection of an Assembly Part with Deep Learning and Image Processing. J. Intell. Syst. Theory Appl.; 2020; 3, pp. 31-37. [DOI: https://dx.doi.org/10.38016/jista.710144]
21. Çakmakçı, M.F.; Çakmakçı, R. Uzaktan Algılama, Yapay Zekâ ve Geleceğin Akıllı Tarım Teknolojisi Trendleri [Remote Sensing, Artificial Intelligence and Smart Agriculture Technology Trends of the Future]. Eur. J. Sci. Technol.; 2023; 52, pp. 234-246. (In Turkish) [DOI: https://dx.doi.org/10.5281/zenodo.10439935]
22. Solak, S.; Altınışık, U. Detection and Classification of Hazelnut Fruit by Using Image Processing Techniques and Clustering Methods. Sak. Univ. J. Sci.; 2018; 22, pp. 56-65. [DOI: https://dx.doi.org/10.16984/saufenbilder.303850]
23. Seid, A.M.; Adimass, S.A.; Salilew, W.M.; Vignesh, K.; Paramasivam, V.; Fentaw, B.A. Recent Progress on the Physical, Thermal, and Mechanical Properties of Expanded Polystyrene Waste–Based Composites. Int. J. Polym. Sci.; 2025; 2025, 9285040. [DOI: https://dx.doi.org/10.1155/ijps/9285040]
24. Sayinci, B.; Comakli, M.; Comlek, R. Factors Affecting Spray Angle of Hollow Cone Nozzles Used in Pesticide Applications. Fresenius Environ. Bull.; 2021; 30, pp. 1636-1645.
25. Şahin, M. Pülverizatör Memelerinde Püskürtme Paterni Değişkenlerinin Doğrusal Hareketli Simülatörde Belirlenmesi [Determination of the Spray Pattern Variables of the Sprayer Nozzles Using a Linear Moving Simulator]. Master’s Thesis; Atatürk University, Graduate School of Natural and Applied Sciences, Department of Agricultural Machinery: Erzurum, Türkiye, 2017; (In Turkish)
26. SAS Institute Inc. The CLUSTER Procedure (Chapter). SAS/STAT® 9.3 User’s Guide; SAS Institute Inc.: Cary, NC, USA, 2011.
27. Freeman, J.B.; Dale, R. Assessing Bimodality to Detect the Presence of a Dual Cognitive Process. Behav. Res. Methods; 2013; 45, pp. 83-97. [DOI: https://dx.doi.org/10.3758/s13428-012-0225-x] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/22806703]
28. Pfister, R.; Schwarz, K.A.; Janczyk, M.; Dale, R.; Freeman, J. Good Things Peak in Pairs: A Note on the Bimodality Coefficient. Front. Psychol.; 2013; 4, 700. [DOI: https://dx.doi.org/10.3389/fpsyg.2013.00700] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/24109465]
29. SAS Institute Inc. Chapter 13, Distribution Analysis: Descriptive Statistics. SAS/IML® Studio 14.2: User’s Guide; SAS Institute Inc.: Cary, NC, USA, 2016.
30. IBM SPSS Statistics for Windows; Version 20.0 IBM Corp: Armork, NY, USA, 2011.
31. Minitab Statistical Software 2006; Version 15.0 Minitab Inc.: State College, PA, USA, 2006.
32. Kalaycı, Ş. SPSS Uygulamalı Çok Değişkenli İstatistik Teknikleri [SPSS Applied Multivariate Statistical Techniques]; Asil Yayın Dağıtım Ltd. Şti.: Ankara, Türkiye, 2006; 426.(In Turkish)
33. Schulz, J.; Schunk, C.; Schleicher, E.; Bart, H.-J. Qualification of Image-Based Measurement Systems for Characterization of Sprays. Chem. Ing. Tech.; 2021; 93, pp. 1111-1118. [DOI: https://dx.doi.org/10.1002/cite.202000104]
34. Uysal, İ.; Kılıç, A. Normal Dağılım İkilemi [Normal Distribution Dilemma]. Anadolu J. Educ. Sci. Int.; 2022; 12, pp. 220-248. (In Turkish) [DOI: https://dx.doi.org/10.18039/ajesi.962653]
35. Subr, A.; Milanowski, M.; Parafiniuk, S.; Sawa, J. Testing the Uniformity of Spray Distribution Under Different Application Parameters. Farm Machinery and Processes Management in Sustainable Agriculture; Department of Machinery Exploitation and Management of Production Processes, University of Life Sciences: Lublin, Poland, 2017; pp. 359-364.
36. Butts, T.R.; Luck, J.D.; Fritz, B.K.; Hoffmann, W.C.; Kruger, G.R. Evaluation of Spray Pattern Uniformity Using Three Unique Analyses as Impacted by Nozzle, Pressure, and Pulse-Width Modulation Duty Cycle. Pest Manag. Sci.; 2019; 75, pp. 1875-1886. [DOI: https://dx.doi.org/10.1002/ps.5352]
37. Whitford, F.; Sinha, R.; Latorre, D.O.; Young, B.; Ozkan, E.; Pearson, S.; Obermeyer, J.; Smith, K.L. Agricultural Spray Nozzles: A Comprehensive Review; Purdue University Extention: West Lafayette, IN, USA, 2024; 153.Available online: https://ag.purdue.edu/department/extension/ppp/resources/ppp-publications/_docs/ppp-153.pdf (accessed on 28 October 2025).
38. Cangur, S.; Pasin, Ö.; Ankarali, H. Comparison of Sampling Distributions and Performances of Minitab and Freund & Perles Quartiles. Pak. J. Statist.; 2015; 31, pp. 1-20.
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