Cross-Sectional Distribution Profile of Mineral Fertilizers Applied by Remotely Piloted Aircraft Under Different Operating Parameters

Highlights

What are the main findings?

• Although the evaluated factors showed interaction in most variables, flight height was the main factor controlling the application swath width, granule deposition, and relative application error.
• The physical properties of the fertilizers influenced granule dispersion, with urea showing greater lateral dispersion.

What are the implications of the main findings?

• Adjusting altitude and flight speed is essential to improve the distribution of mineral fertilizers using drones.
• Operational limits were defined for urea, potassium chloride, and single superphosphate using the DJI Agras T50.

Abstract

In this study, we determined the distribution profile of different mineral fertilizers applied by a DJI Agras T50 remotely piloted aircraft (RPA) under different flight heights and speeds. The experiment was conducted in a randomized block design in a 3 × 3 × 3 factorial scheme, involving three fertilizers (urea, potassium chloride, and single superphosphate), three flight heights (4, 6, and 8 m), and three flight speeds (16, 18, and 20 km h⁻¹). The methodology included laboratory characterization of the physical properties of the fertilizers and the determination of the transverse distribution profile under field conditions. The data were processed using Adulanço software version 4.0 and subjected to statistical analyses (p-value < 0.05). The results indicated that flight height stood out as the main factor, increasing the total and effective swath widths; however, it reduced deposition per unit area and increased the relative error as height increased. The combination of 20 km h⁻¹ with flight heights of 4 and 6 m maximized deposition within the effective swath and provided theoretical operational capacities greater than 8 ha h⁻¹, regardless of the fertilizers. Correlation analysis indicated an operational trade-off, showing that fertilizers with different physical properties respond differently to flight height and flight speed.

1. Introduction

The Food and Agriculture Organization of the United Nations (FAO) predicts that global food production will need to increase by 70% by 2050 to meet the demand of the world’s population, estimated at 9.7 billion in this period [1,2]. To achieve this goal, it is essential to promote an increase in agricultural productivity and reduce the gap between actual and potential productivity, which can be achieved by adopting efficient practices and technologies. These include proper management of mineral fertilizers and balanced nutrition for agricultural and silviculture crops [3].

The efficiency of this process, however, depends not only on the fertilizer source or dose, but also on the distribution method, which determines the uniformity, precision and, therefore, the effectiveness of the application [4]. Poorly distributed application results in heterogeneous under- or overdosing, reducing nutrient use efficiency, increasing costs and intensifying environmental risks (leaching, volatilization and surface losses) [5,6].

Conventional methods of applying mineral fertilizers include manual practices (broadcast or with backpack applicators), fertigation and mechanized or semi mechanized systems that use helical mechanisms, grooved wheels or gravitational discharge with distribution by centrifugal or pneumatic spreaders [7,8,9]. Although widely used, these systems have operational limitations in areas with uneven terrain, dense crops or obstacles, which can compromise the mobility and uniformity of application, as well as causing impacts such as soil compaction, crop crushing and reduced productivity [10,11].

In extensive cultivation, aerial application with agricultural airplanes and helicopters is a well-established alternative due to its high operational capacity, with solids being dispersed by diffusers (Venturi, Swathmaster or tetrahedral) installed below the hopper [12]. However, this method involves high operating costs, logistical dependence, the need for runways and less precision in small areas or those with complex topography, as well as being directly influenced by aerodynamic flight parameters [13].

In this context, the use of remotely piloted aircraft (RPAs), defined as unmanned aircraft piloted from a remote piloting station and commonly referred to as unmanned aerial vehicles (UAVs) or unmanned aircraft systems (UAS), has been expanding significantly in the agricultural and forestry sectors, being initially consolidated in the application of pesticides and foliar fertilizers in perennial, semi-perennial and annual crops, focusing on the evaluation of the quality of droplet distribution, associated or not with the analysis of biological targets, such as in the control of pests, diseases or weeds [14,15,16,17,18,19,20].

In the context of the dispersal of solid inputs, application with RPAs has evolved from the first applications aimed at sowing rice seeds in China in the early 2000s, to more complex applications of mineral nitrogen fertilization in top dressing, characterized by higher application rates and high operational requirements in wetlands [21,22]. With the advancement of on-board systems, as well as metering mechanisms—gravimetric, grooved wheel/gear and helical—and spreading mechanisms—centrifugal discs and rings, pneumatic systems and distribution devices in lines or strips—[23,24], the use of RPAs has expanded to diverse applications, including direct seeding [25], the application of pesticides in solid formulations [26], assisted pollination [27], the aerial release of biological control agents [28] and the distribution of feed in aquaculture systems [29].

For the application of solid inputs, RPAs offer significant advantages over traditional methods, such as applications on intercropped crops, high operational efficiency, the possibility of localized or variable-rate application regardless of topography, the absence of direct fuel consumption, operation on complex or flooded terrain without the need for airstrips or limitations imposed by the structure of the vegetation [30,31,32,33,34]. In addition, current models have a load capacity of 100–150 kg of solids [35,36,37].

Despite the advances, the application of solid inputs through RPAs still has operational limitations, requiring specialized labor, low battery autonomy and difficulty in ensuring uniform deposition [38,39,40]. These limitations arise from the interaction of multiple factors, particularly the combination of flight operational parameters (flight height and speed, application rate, centrifugal spreader rotation, application swath, and flight path), meteorological conditions, the physical properties of the solid material (relative density, particle size distribution, moisture content, angle of repose, and hygroscopicity), and the characteristics of the dosing and spreading mechanisms employed, all of which affect the deposition pattern and application uniformity [41,42,43,44,45,46,47,48,49,50].

Recent studies have shown that the quality and uniformity of granular fertilizer distribution through RPAs is strongly influenced by the flight operating parameters and the physical properties of the input, affecting the effective application range. The latter, characterized by greater uniformity of granule deposition, is usually assessed by the coefficient of variation (CV), with values of less than 20% considered acceptable for granular fertilizers [51,52].

Song et al. [53] found that the width of the effective range and the CV values are significantly affected by the type of spreading device, with marked differences between centrifugal (disk) and pneumatic systems, as well as by the interaction between height and flight speed in the application of urea. In line with this, Zhou et al. [54] showed that by adjusting the deflector retraction, the rotation of the distributor disk and the flight height, it is possible to achieve a CV of less than 12%, with limited influence from weather conditions and a moderate effect from the airflow generated by the rotors, using the DJI Agras RPA MG-1P model.

In a complementary way, Xia et al. [47] identified that the physical characteristics of fertilizers have a decisive influence on the quality of the application, and their effects are modulated by the height, flight speed and rotation of the centrifugal distributor, in which they observed a 15% increase in productivity in the rice crop using the DJI Agras RPA T40 model. Finally, Wang et al. [55] found that lower flight speeds and smaller particle sizes intensify deposition pattern distortions, while the RPA’s downward airflow reduces the width of the effective application range compared to windless conditions, using the DJI Agras RPA T60 model.

In this sense, the motivation behind this study was to find answers to the theoretical and experimental questions and gaps that still persist in relation to the dispersion of fertilizers by means of RPAs. This study addresses four main gaps: (i) the joint influence of height and flight speed on the distribution of different fertilizers; (ii) the response of physical characteristics to operational variations; (iii) the need for standardized experimental models to assess application uniformity; and (iv) the integration of operational factors and granule properties to predict deposition patterns.

Therefore, the hypotheses raised in this study were: (a) operational flight height and speed are determining factors for the uniformity of mineral fertilizer application through RPAs; (b) lower flight heights tend to generate greater deposition of granules in the effective range, while higher heights expand the total range, reducing application uniformity; (c) higher flight speeds should promote greater lateral dispersion, altering uniformity and increasing the application coefficient of variation; and (d) the physical characteristics of fertilizers significantly influence the distribution pattern when combined with different RPA flight heights and speeds. The aim of this study was to determine the distribution profile of different mineral fertilizers applied by a DJI Agras model T50 remotely piloted aircraft, considering the variability of their physical properties under the influence of different heights and flight operating speeds.

2. Materials and Methods

2.1. Characterization of the Experimental Area

The experiment was conducted at the Experimental Farm of the Centro Universitário Norte do Espírito Santo, of the Federal University of Espírito Santo, located in the municipality of São Mateus-ES, Brazil. The experimental area is located between the coordinates 18°40′25″ S, 40°51′23″ W, on Argissolo type soil with a sandy loam texture. The region’s climate is hot and humid, type Aw, with a dry season in autumn–winter and a rainy season in spring–summer, according to the Köppen classification [56].

For data collection, the experimental area chosen consisted of a large, unobstructed space measuring 5000 m² (50 m × 100 m), ensuring suitable conditions for the evaluations, without the presence of obstacles that could interfere with the execution of the experimental treatments.

2.2. Characterization of Remotely Piloted Aircraft

A DJI Agras remotely piloted aircraft (RPA) T50 model was used (DJI, SZ DJI Technology Co., Ltd., Shenzhen, China), which has a dual-rotor coaxial structure made up of eight rotors distributed above and below the four swing arms, designed to carry out both spraying and solid dispersion applications. For dispersing solids, the tank has a capacity of 75 L, with an internal load of up to 50 kg, is compatible with solid materials with a diameter of between 0.5 and 5 mm and is equipped with a spiral channel rotating disc, complemented by a deflector that blocks the dispersion of the material, preventing damage to the propellers.

This RPA has a quick release device in the hopper, which allows precise adjustments according to the flow of material to be dispersed and the diameter of the granules. In all the experimental treatments, the outlet of the hopper with the largest capacity was used, as indicated by the manufacturer for higher volume applications [57]. The setting was selected on the RPA’s radio control during the calibration process, as recommended by the manufacturer for applications at higher application rates (kg ha⁻¹) (Figure 1).

2.3. Determination of Physical Characteristics of Mineral Fertilizers

Three commercial granular mineral fertilizers were used alone (without mixing): simple superphosphate (18% P₂O₅, 16% Ca and 10% S), granulated urea (46% N) and granulated red potassium chloride (60% K₂O) (Figure 2). The choice of these fertilizers is justified by their widespread use in N–P₂O₅–K₂O mineral fertilization practices, both in agriculture and silviculture. The aim of this stage was to characterize the average values of the main physical properties, which were then used in the correlation analyses (Section 2.6—Statistical analyses) and the results are presented in Appendix A.1.

To determine the physical characteristics, four 500 g samples of each mineral fertilizer were randomly collected directly from the commercial packages, which were packed in airtight plastic bags to avoid physical and hygroscopic changes and then sent to the laboratory for analysis. The initial samples were homogenized and divided into sub-samples for the experimental replicates. Six replicates of 100 g per fertilizer were used for the analyses of the granule dispersion index, percentage of granules ≤ 106 µm, water content and relative density. For the angle of repose, six repetitions of 4 kg per fertilizer were used. Sphericity was determined from granules collected at random in each repetition of the previous analyses.

The Granule Dispersion Index (GSI) was determined according to the Manual of Official Methods for Fertilizers and Correctives [58], using standardized sieves (3.55 mm to 63 µm). Samples of 100 g were shaken for 10 min, and the retained fractions were weighed to calculate the percentage distribution and the GSI; the fraction ≤ 106 µm was expressed as the percentage by mass of the material passing this sieve. The water content was determined according to Alcarde et al. [41], by drying sub-samples at 50 °C for 48 h until constant mass, and calculated by the percentage difference between the wet and dry masses. The relative density was obtained in accordance with ISO 3944:1992 [59], using 100 g of sample transferred without compaction to a graduated cylinder, calculated using the mass/volume ratio (g cm⁻³).

The angle of repose was determined according to Reynaldo [60], by forming a mound in a glass box, and the angle was calculated trigonometrically from the height and radius of the base of the cone formed. Finally, sphericity was measured in 100 intact granules per fertilizer, by measuring the triaxial dimensions (length, width and thickness) using a digital caliper (0.001 mm), calculated by the ratio between the equivalent diameter and the length of the granule, according to Sun et al. [61]. The formulas used to calculate each variable are shown in

Table 1. Physical variables of mineral fertilizers, citations and equations used in the calculations and definition of the terms used.

Variable/Reference	Formula Used	Description of Terms
Granule dispersion index (GSI) [58]	GSI = ((D16 − D84)/(2 × D50)) × 100	D16, D84 and D50 = diameter of the sieve corresponding to 16, 84 and 50% of the accumulated mass, respectively.
Granules ≤ 106 µm (%)	% ≤ 106 µm = (m≤106/mtotal) × 100	m≤106 = mass of the material that has passed through the 106 µm sieve; mtotal = total mass of the sample (100 g).
Water content (%) [41]	T = [((mu − ms))/ms] × 100	T is the water content in the fertilizer (%); mu is the weight of the fertilizer’s wet mass (g); ms is the weight of the fertilizer’s dry mass (g).
Relative density (g cm−3) [59]	ρ = m/V	m = sample mass (g); V = volume occupied in the cylinder (cm3).
Angle of repose (°) [60]	θ = arctan (Co/Ca)	θ = angle of repose (°); Co = height of the pile (opposite side, cm); Ca = horizontal distance from the base to the center of the pile (adjacent side, cm).
Sphericity (%) [61]	De = $\sqrt[3]{(C\times L\times E)}$	C = granule length (mm); L = width (mm); E = thickness (mm); De = equivalent diameter (mm).
	φ = (De/C) × 100	φ = sphericity (%); De = equivalent diameter (mm); C = granule length (mm).

.

2.4. Determination of the Cross-Sectional Distribution Profile of Mineral Fertilizers

The cross-sectional distribution profile was evaluated by collecting the fertilizers in the field. However, as this was an experiment conducted with the DJI Agras T50 RPA (DJI, SZ DJI Technology Co., Ltd., Shenzhen, China), some methodological adaptations were necessary, as suggested by Zhang et al. [62], Liu et al. [46] and Wang et al. [55] in the distribution of fertilizers. The adaptations involved reducing the number of collectors, adjusting the distances between them and changing the dimensions of the collectors, without compromising the reliability of the experimental results.

To collect the fertilizers, 50 pyramid-shaped polyethylene collectors were used, measuring 34.50 cm high × 34.50 cm wide × 52.10 cm long. Galvanized metal structures painted safety yellow, measuring 1.10 m high × 0.50 m wide, were made to keep the collectors standardized and structured at a height of 1.0 m above the ground in the experimental area (Figure 3), in order to withstand the wind generated by the RPA’s propellers.

Before the experimental treatments were applied, the structures and collectors were tested in the field to check for any ricocheting of particles after impact. No effects were observed, which validated the use of these structures for the collection stages of the experimental treatments.

Before each application, each mineral fertilizer was calibrated individually in the RPA. The distribution system’s rotating disk was removed to keep the outflow in a fillet, allowing the material to be collected and returned to the bag. For the ground calibration, the aircraft was supported on boxes and kept at a height of approximately 40 cm from the ground. Initially, calibration was carried out with an empty tank, followed by checking the Hall effect and weight sensors. At the start of each experimental day, 45 kg of fertilizer was inserted into the tank, selecting the large outlet opening according to the physical characteristics of the material, and the calibration was carried out automatically by the on-board system.

2.4.1. Experimental Design

This stage was carried out separately for each mineral fertilizer evaluated (simple superphosphate, urea and potassium chloride). The experiment was structured in a randomized block design with a 3 × 3 × 3 factorial scheme: three fertilizers (simple superphosphate, urea and potassium chloride), three flight heights (4, 6 and 8 m) and three speeds (16, 18 and 20 km h⁻¹), with four repetitions. The 27 experimental treatments were previously configured in the RPA control system before each application.

Each repetition corresponded to one day of application, with the variation between blocks represented by the different days of application, applied at the same times. The treatments were standardized in order to guarantee the sources of variation established in the study. The following operating parameters were previously adjusted in the RPA control and kept constant for all treatments: theoretical application range of 8 m and centrifugal disc rotation of 800 rpm as suggested by Wang et al. [22]; application rate of 400 kg ha⁻¹, aiming for greater collection volume; and flight path perpendicular to the wind direction, as recommended in RPA operations [63].

In the experimental area, with a tape measure, the structures equipped with the collectors were distributed in two parallel lines, spaced 15.0 m apart, with 25 units in each line, arranged 0.50 m apart (Figure 4). The lines with the collectors were previously identified (1 to 25) and aligned with the prevailing wind direction and perpendicular to the direction of the RPA’s flight path. The treatments were carried out on a total area of 5000 m² (50 m × 100 m); however, the useful area of the experimental unit (area occupied by the collectors) was approximately 375.0 m² (15 m × 25 m).

Considering the 27 experimental treatments and four replications (blocks, represented by the application days), the experiment totaled 108 experimental units. Each experimental unit corresponded to one flight and was composed of two subsamples (collection lines), whose values were later converted into means for statistical analyses (Topic 2.6. Statistical analysis). The application was started approximately 20 m before the collector line in order to activate the centrifugal disc, stabilize the height and flight speed, and start spreading the fertilizer.

In the RPA control system, the theoretical application range was kept at 8 m for all treatments, and the aircraft only covered one route line. This procedure made it possible to determine the total range and the effective range of application, isolating the performance of the spreading system according to the characteristics of each fertilizer, without interference from overlaps. This approach is fundamental for accurately assessing the lateral distribution of fertilizers applied by RPAs [39]. Figure 5 shows the experimental scheme used.

After the application of each treatment, the fertilizer deposited in each collector was removed using a brush and transferred to collection containers, identified according to the sampling point and packed in double zip-lock plastic bags with airtight seals. They were then immediately sent to the Laboratory of Mechanization and Agricultural Defensives (LMDA) at the North University Center of Espírito Santo, Federal University of Espírito Santo, in São Mateus ES, Brazil.

In the laboratory, the samples were transferred to Petri dishes and weighed on a precision analytical balance (0.001 ± 0.001 g). The same collection points were used in all experimental replications, ensuring that the final averages per collection line were obtained at the end of the experiment.

2.4.2. Variables Relating to the Total Application Range

The sum of the granule deposition in the total range was calculated from the sum of the individual fertilizer depositions in each collector distributed along the total application width, in which the presence of non-zero granules was recorded, expressing the results in grams per square meter. The width of the total application range was defined as the total transverse distance at which the presence of granules in the collectors was observed, with non-zero deposition. The equations relating the variables of the total application range are shown in

Table 2. Variables related to the total application range; equations used in the calculations and definition of the terms adopted.

Variable	Formula Used	Description of Terms
Sum of granule deposition of granules in the total range	${\mathrm{D}\mathrm{E}\mathrm{P}}_{\mathrm{F}\mathrm{T}}={\displaystyle \sum _{i=1}^n}\left({\displaystyle \frac{Q_{g,i}}{A_c}}\right)$	DEPFT is the sum of the deposition of granules in the total range (g m−2); Qg,i corresponds to the mass of granules collected in the ii-collector (g); Ac is the collector area, a constant value of 0.180 m−2, and n is the total number of collectors evaluated.
Total range application width	${\mathrm{L}\mathrm{A}\mathrm{R}\mathrm{G}}_{\mathrm{F}\mathrm{T}}=n_d\times e$	LARGFT is the total range application width (m); nd refers to the number of collectors that showed granule deposition (DFi > 0.0); and corresponds to the spacing between the collectors, a constant value of 0.50 m.

.

2.4.3. Response Variables for the Effective Application Range

The coefficient of variation (CV) was adopted as a statistical measure for assessing the uniformity of application distribution over the effective application range [64]. To do this, simulations of successive overlays were carried out based on the accumulated deposition values in the collectors, with the CV calculated for each simulated overlay condition according to studies carried out by Song et al. [52] and Wang et al. [22,55] using RPAs for mineral fertilization.

The analyses were carried out using the software Adulanço^® version 4.0 [65], developed by the Mechanization and Precision Agriculture Group (GMAP) of Escola Superior de Agricultura Luiz de Queiroz at the University of São Paulo (ESALQ/USP, Brazil) [66], which allows successive overlays to be simulated in order to calculate the coefficient of variation. Similar studies have used Adulanço^® to analyze the cross-sectional distribution of fertilizer and corrective applicators [5,67,68,69].

The software made it possible to simulate three application systems: an alternating system (right and left) and a continuous system. In this study, for the following variables related to the effective application range, the continuous system was adopted, as it simulates the overlap between the right and left sides of the machine’s deposition, and vice versa, minimizing possible imbalances resulting from asymmetry in the deposition pattern [70,71]. This procedure more realistically represented the operating conditions of the study, in which the back-to-back route system, commonly used in commercial operations with RPAs, is predominantly used [13].

For each overlap width considered in each experimental treatment, the software recalculated the accumulated transversal distribution along the application range and determined the coefficient of variation (CV) of the deposition. Based on these simulations, the effective application range was defined as the greatest width with a CV ≤ 20%, a value widely adopted for granular fertilizers [72,73]. Based on the width of the effective range identified in each treatment, the collectors located within the lateral limits of this range (±width/2 in relation to the center of the application range) were selected, from which the response variables shown below were determined.

The average deposition of granules in the effective range was determined by the arithmetic mean of the depositions recorded in the collectors located within the limits of the effective range, according to Song et al. [53]. The effective range width was defined as the maximum cross-sectional length of the application with a CV ≤ 20%.

Based on the effective width and operational flight speed of each treatment, the theoretical operational capacity of the effective range was estimated, according to Antuniassi and Boller [74], with the unit adapted to ha h⁻¹. As this is a theoretical estimate, operating losses, maneuvers, overlaps, interruptions or unproductive times were not taken into account, as discussed by Ferreira and Matuo [75]. The equations relating the variables of the effective application range are shown in

Table 3. Variables related to the effective application range, citations and equations used in the calculations and definition of the terms adopted.

Variable/Reference	Formula Used	Description of Terms
Average deposition of granules in the effective range [53]	${\mathrm{D}\mathrm{E}\mathrm{P}}_{\mathrm{F}\mathrm{E}}={\displaystyle \frac{1}{{\mathrm{n}}_{\mathrm{e}}}}{\displaystyle \sum _{i=1}^{n_e}}\left({\displaystyle \frac{Q_{g,i}}{A_c}}\right)$	DEPFE is the average deposition of granules in the effective range (g m−2); Qg,i corresponds to the mass of granules collected in the ii-ac is the area of the collector, a constant value of 0.180 m−2, and ne is the number of collectors included in the effective range.
Effective range application width	${\mathrm{L}\mathrm{A}\mathrm{R}\mathrm{G}}_{\mathrm{F}\mathrm{E}}=n_d\times e$	LARGFE is the application width of the effective range (m); ne refers to the number of collectors included within the limits of the effective range (CV ≤ 20%); and corresponds to the spacing between the collectors, a constant value of 0.50 m.
Theoretical operating capacity of the effective range [74]	${\mathrm{C}\mathrm{O}\mathrm{T}}_{\mathrm{F}\mathrm{E}}={\displaystyle \frac{{\mathrm{L}}_{\mathrm{F}\mathrm{E}}\times \mathrm{V}}{10}}$	COTFE is the theoretical operational capacity of the effective range (ha h−1); LFE is the width of the effective application range (m); V is the operational flight speed of each experimental treatment (km h−1).

.

2.4.4. Application Efficiency and Relative Error

Application efficiency was determined as the ratio between the deposition retained in the effective range and the total deposition collected in the application range, expressing the fraction of fertilizer effectively used and the lateral losses associated with the process (

Table 4. Variables related to application efficiency and relative error, equations used in the calculations and definition of the terms adopted.

Variable	Formula Used	Description of Terms
Application efficiency	$\mathrm{E}\mathrm{F}\mathrm{A}={\displaystyle \frac{{\sum }_{\mathrm{i}\in \mathrm{f}\mathrm{a}\mathrm{i}\mathrm{x}\mathrm{a}\mathrm{e}\mathrm{f}\mathrm{e}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{a}}{\mathrm{D}}_{\mathrm{i}}}{{\sum }_{\mathrm{i}=\mathrm{n}}^{\mathrm{n}}{\mathrm{D}}_{\mathrm{i}}}}\times 100$	EFA = application efficiency (%); is the fertilizer deposition on the ii-ism collector (g m−2); n is the total number of collectors distributed along the total application range; ${\sum }_{\mathrm{i}\in \mathrm{f}\mathrm{a}\mathrm{i}\mathrm{x}\mathrm{a}\mathrm{e}\mathrm{f}\mathrm{e}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{a}}{\mathrm{D}}_{\mathrm{i}}$ = sum of the fertilizer deposition on the collectors located within the limits of the effective range; ${\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{D}}_{\mathrm{i}}$ = sum of the total fertilizer deposition on all the collectors.
Relative error of total deposition mass	${\mathrm{E}\mathrm{R}\mathrm{R}\mathrm{O}}_{\mathrm{S}\mathrm{O}\mathrm{M}\mathrm{A}}={\displaystyle \frac{\left|{\mathrm{Q}}_{\mathrm{o}\mathrm{b}\mathrm{s}}-(\mathrm{G}\times \mathrm{L})\right|}{\mathrm{G}\times \mathrm{L}}}\times 100$	${\mathrm{E}\mathrm{R}\mathrm{R}\mathrm{O}}_{\mathrm{S}\mathrm{O}\mathrm{M}\mathrm{A}}$ = relative error of the total deposition mass (%); Qobs = total amount of fertilizer observed in the effective range (g); G = programmed theoretical dose (g m−2), with a constant value of 40 g m−2 (corresponding to 400 kg ha−1); L = width of the effective application range (m).

). The relative error, considered in this study as the relative error of the total mass deposited, was used to quantify the percentage deviation between the amount of fertilizer actually deposited and the programmed theoretical dose, based on an adaptation of the equations proposed by Su et al. [6] and Zhou et al. [54] as described in Table 4.

2.5. Monitoring Weather Conditions

All the experimental treatments were applied in the afternoon between 1:00 PM and 4:00 PM. Throughout the experiment, relative humidity, air temperature, wind speed, direction and average gust were recorded automatically at hourly intervals. This information was obtained from the automatic weather station model A616 of the National Institute of Meteorology (INMET), manufactured by Vaisala^® (Vantaa, Uusimaa, Finland), equipped with various internal and external sensors, located approximately 650 m from the experimental area. Table S1 shows the complete meteorological data for each day of application.

2.6. Statistical Analysis

Initially, the averages of two independent groups regarding the deposition of granules (g) in the collection lines (Line 1 and Line 2) were compared using Student’s t-test for two independent samples, assuming equivalent variances, for each experimental treatment involving the fertilizers evaluated—urea (Table S2), potassium chloride (Table S3) and simple superphosphate (Table S4). There were no statistically significant differences between the means (two tailed p-value > 0.05). Once this assumption had been met, the data from both lines was grouped and converted into average values, which were then used to analyze the variables associated with the total application range and the effective application range.

The variables related to topic 2.4 (Determination of the cross-sectional distribution profile of fertilizers) were previously assessed for compliance with the assumptions of the analysis of variance. Next, the variables related to the total application range, effective application range, application efficiency and relative error were submitted to analysis of variance (Appendix A.2) and when significant differences were identified, the means were compared using the Tukey test, adopting a significance level of 5%.

The association between the variables obtained in topics 2.3 (Determination of the physical characteristics of fertilizers) and 2.4 (Determination of the transversal distribution profile) was estimated by means of Spearman’s correlation, using its coefficient (Spearman’s rho—ρ_s) to interpret and classify the results, considering the guide proposed by Mukaka [76]. The choice of this method was justified by the lack of normality of some variables, even after applying transformations to the data (logarithmic transformation [log (x + 1)] for variables containing zero values and [log(x)] for strictly positive variables). In addition, Spearman’s coefficient does not assume normality or a strict linear relationship, but is based on the ordering of values (ranks), which makes it more robust to the presence of extreme values (outliers).

Different graphic resources were used to present the results of the analyses described above, including bar and scatter graphs, violin-type boxplots and heatmaps, allowing integrated visualization of the trends and relationships between the variables evaluated. All statistical analyses and the preparation of graphs were carried out in the RStudio software version 4.5.0 [77], using specific packages appropriate to each analytical procedure.

2.7. Artificial Intelligence Tools

In the development of this study, tools based on artificial intelligence were used as auxiliary support in specific stages of the research. The Litmaps and LeapSpace platforms were used to systematically prospect, organize and map scientific literature, making it possible to identify relationships between studies, gaps in knowledge and trends regarding the subject of the study. In addition, the DeepSeek V3 and ChatGPT 5.2 tools were used to support the conceptual organization of the content, to improve textual clarity, cohesion and precision and to review the computational scripts of the statistical analyses, including suggestions for optimizing and standardizing codes. It should be emphasized that the use of these tools was exclusively auxiliary and did not replace the critical analysis of this study.

3. Results

3.1. Variables Related to the Total Application Range

The sum of the deposition of granules in the total range was significantly influenced by the type of mineral fertilizer and was not affected by height or flight speed alone (Figure 6; Appendix A.2). In general, there was a consistent trend towards greater deposition of granules within the total range for potassium chloride (KCl), followed by urea—statistically similar—and, lastly, simple superphosphate (SS). KCl showed significantly higher deposition, being 5.63% higher than urea and 14.42% higher than SS, within the total application range.

Although the total mass deposited did not vary with height or speed alone, the width of the total range of application responded strongly to the three-way interaction between the fertilizer, height and speed factors (

Table 5. Mean values ± standard error of total range application width (m). Breakdown of the three-way interaction between the flight speed factors (16, 18 and 20 km h⁻¹), flight height (4, 6 and 8 m) and type of mineral fertilizer (urea, potassium chloride—KCl, and simple superphosphate—SS).

Fertilizers	16.0 km h−1
	4 m	6 m	8 m
Urea	8.50 ± 0.08 a	10.5 ± 0.15 a	11.50 ± 0.21 a
Potassium chloride	7.50 ± 0.07 b	9.0 ± 0.14 b	10.50 ± 0.15 b
Simple superphosphate	6.0 ± 0.09 c	8.50 ± 0.16 c	10.0 ± 0.22 c
Fertilizers	18.0 km h−1
	4 m	6 m	8 m
Urea	9.0 ± 0.10 a	9.0 ± 0.14 a	11.0 ± 0.13 a
Potassium chloride	7.50 ± 0.15 b	9.0 ± 0.15 a	11.0 ± 0.17 a
Simple superphosphate	7.0 ± 0.11 c	9.0 ± 0.08 a	10.5 ± 0.17 b
Fertilizers	20.0 km h−1
	4 m	6 m	8 m
Urea	7.5 ± 0.13 a	9.50 ± 0.16 a	10.5 ± 0.04 a
Potassium chloride	6.50 ± 0.12 b	8.5 ± 0.15 b	10.0 ± 0.13 b
Simple superphosphate	6.50 ± 0.09 b	8.50 ± 0.13 b	10.5 ± 0.22 a

Means ± standard error, followed by distinct lowercase letters in the column, indicate significant differences according to Tukey’s test at the 5% significance level (p ≤ 0.05).

; Appendix A.2). Urea showed the greatest total range width, regardless of the flight parameters. 16 km h⁻¹ and 6 m high, the application range was 10.5 m (urea), 9.0 m (KCl) and 8.5 m (SS), representing differences of 14.28% in relation to KCl and 19.04% in relation to SS. This pattern was repeated in all operating combinations, showing greater lateral dispersion of the urea.

The effect of speed depended on the fertilizer and height (

Table 6. Mean values ± standard error of total range application width (m). Breakdown of flight speeds (16, 18 and 20 km h⁻¹) within each level of mineral fertilizer (urea, potassium chloride—KCl, and simple superphosphate—SS) and flight height (4, 6 and 8 m).

Flight Speed (km h−1)	Potassium Chloride
	4 m	6 m	8 m
16.0	7.50 ± 0.07 aC	9.0 ± 0.14 aB	10.5 ± 0.15 bA
18.0	7.50 ± 0.15 aC	9.0 ± 0.15 aB	11.0 ± 0.17 aA
20.0	6.50 ± 0.12 bC	8.50 ± 0.15 bB	10.0 ± 0.13 cA
Flight Speed (km h−1)	Simple Superphosphate
	4 m	6 m	8 m
16.0	6.0 ± 0.09 cC	8.50 ± 0.16 bB	10.0 ± 0.22 bA
18.0	7.0 ± 0.11 aC	9.0 ± 0.08 aB	10.50 ± 0.17 aA
20.0	6.5 ± 0.09 bC	8.50 ± 0.13 bB	10.50 ± 0.22 aA
Flight Speed (km h−1)	Urea
	4 m	6 m	8 m
16.0	8.5 ± 0.08 bC	10.5 ± 0.15 aB	11.50 ± 0.21 aA
18.0	9.0 ± 0.10 aC	9.0 ± 0.14 cB	11.0 ± 0.13 bA
20.0	7.5 ± 0.13 cC	9.5 ± 0.16 bB	10.5 ± 0.04 cA

Means ± standard error, followed by different lowercase letters in the column and uppercase letters in the row, indicate significant differences using the Tukey test at a 5% significance level (p ≤ 0.05).

). For KCl, the variation between 16 and 18 km h⁻¹, there was little change, especially at heights of 4 and 6 m, with no statistical difference. For simple superphosphate, the influence was reduced, with differences between 18 and 20 km h⁻¹ at 4 and 6 m and no differences at 8 m. For urea, there was greater variation: at 4 m it increased between 16 and 18 km h⁻¹, reducing at 20 km h⁻¹; at 6 and 8 m, the differences were smaller.

In general, for all fertilizers, increasing the flight height from 4 to 8 m led to a significant increase in total range, regardless of flight speed. On the other hand, increasing the flight speed to 20 km h⁻¹ resulted in a slight reduction in the width of the total range, especially for KCl and urea at the lowest flight heights, although this reduction was less than 1.0 m in most combinations (Table 5). The joint analysis of the granule distribution profiles along the total range (Figure 7, Figure 8 and Figure 9) confirms that flight speed acted as a secondary factor in relation to flight height, modulating the response of each mineral fertilizer, with urea being more sensitive to operational variations.

3.2. Variables Related to the Effective Application Range

Deposition in the effective range was influenced by the interaction between height and operational flight speed (Figure 10; Appendix A.2). Speed had a less pronounced effect than height (Figure 10a). At 4 m, the greatest deposition occurred at 20 km h⁻¹, 5% higher than at 16 km h⁻¹ (similar) and 16.3% at 18 km h⁻¹ (different). At 6 and 8 m there were no statistical differences between speeds, restricting the effect to the lower heights.

Deposition in the effective range decreased consistently with increasing height (Figure 10b). At 4 m, the highest values were recorded; at 6 m, an intermediate decrease; at 8 m, lower results between 8.61 and 9.63 g m⁻¹. Raising the height from 4 to 8 m led to a reduction of more than 35% in average deposition, regardless of speed.

The average deposition of granules in the effective range differed significantly between fertilizers, regardless of height and flight speed (Figure 11). Potassium chloride (KCl) had the highest average deposition value, followed by simple superphosphate and urea. There was also greater dispersion of the data for simple superphosphate, evidenced by the greater amplitude, while KCl showed a more concentrated distribution around the average, indicating greater regularity in deposition.

The effective range was influenced by the interaction between fertilizer, height and operational flight speed (Figure 12; Appendix A.2). Height increased significantly from 4 to 8 m in most combinations. Urea showed higher values than the other fertilizers. Speed only promoted specific variations in height, with differences restricted to specific combinations, without altering the order between fertilizers. A similar trend was observed for the width of the total application range (Table 5).

When analyzing each mineral fertilizer separately, different operational behaviors were observed (Figure 13). For urea, the width of the effective range was determined predominantly by flight height, with a significant increase of approximately 37.5% when raising the height from 4 to 8 m, while speed did not alter this pattern, with no statistical differences between 16 and 20 km h⁻¹ within each flight height. For potassium chloride, flight height also significantly widened the range, but flight speed began to modulate the response at higher flight heights: at 6 m, increased speed significantly reduced the width, while at 8 m, the range increased with increased flight speed. Simple superphosphate, on the other hand, showed greater variability between operational combinations, with significant reductions in some conditions—such as at 6 m at 20 km h⁻¹—indicating greater sensitivity between the operating conditions evaluated.

The theoretical operating capacity of the effective range was significantly affected by the interaction between mineral fertilizer, height and flight speed (Figure 14; Appendix A.2). It was observed that the lowest values were concentrated at a flight height of 4 m, while raising the height to 8 m led to a consistent increase in operational yield, reaching up to 16.0 ha h⁻¹ for urea at 20 km h⁻¹. The effect of speed became more evident at greater heights: at 8 m, the transition from 16 to 20 km h⁻¹ resulted in increases of around 20% for urea and around 25.7% for simple superphosphate. In practically all operational combinations, urea had the highest capacities, followed by potassium chloride and simple superphosphate.

When analyzed separately, the fertilizers showed different responses (Figure 15). For urea, the variation in flight height was the main determinant of performance, establishing three well-defined operational levels (4 < 6 < 8 m), while flight speed only extended the values within each range. With potassium chloride, in addition to the effect of flight height, flight speed made an additional contribution, especially at 8 m, where the difference between 16 and 20 km h⁻¹ reached approximately 3.6 ha h⁻¹. Simple superphosphate showed the lowest performance at the lowest flight heights, but gradually increased under higher conditions, especially at 20 km h⁻¹, confirming different responses between the fertilizers under the same operating conditions.

3.3. Variables Related to Application Efficiency and Relative Application Error

The application efficiency showed an interaction among mineral fertilizer, flight height, and flight speed (

Table 7. Mean values ± standard error of application efficiency (%). Breakdown of the triple interaction among the factors flight speed (16, 18, and 20 km h⁻¹), flight height (4, 6, and 8 m), and type of mineral fertilizer (urea, potassium chloride—KCl, and single superphosphate—SS).

Fertilizers	16.0 km h−1
	4 m	6 m	8 m
Urea	90.7 ± 3.19 ab	85.00 ± 2.28 b	93.47 ± 0.75 a
Potassium chloride	89.86 ± 2.58 b	94.48 ± 0.48 a	83.79 ± 0.63 b
Simple superphosphate	95.69 ± 1.43 a	94.30 ± 0.44 a	89.41 ± 0.72 a
Fertilizers	18.0 km h−1
	4 m	6 m	8 m
Urea	79.16 ± 2.72 c	91.07 ± 0.92 a	93.45 ± 1.07 a
Potassium chloride	98.40 ± 0.52 a	88.31 ± 0.44 a	90.51 ± 0.90 ab
Simple superphosphate	90.81 ± 0.88 b	93.21 ± 2.18 a	85.65 ± 1.42 b
Fertilizers	20.0 km h−1
	4 m	6 m	8 m
Urea	95.47 ± 0.41 a	92.45 ± 1.05 a	95.31 ± 1.68 a
Potassium chloride	94.34 ± 0.79 a	88.89 ± 1.23 a	90.17 ± 0.94 ab
Simple superphosphate	91.79 ± 2.09 a	87.37 ± 1.33 a	86.21 ± 2.70 b

Means ± standard error, followed by distinct lowercase letters in the column, indicate significant differences according to Tukey’s test at the 5% significance level (p ≤ 0.05).

; Appendix A.2). This interaction revealed wide variability among fertilizers, with no consistent linear trend. At 16 km h⁻¹, single superphosphate (SS) showed the highest efficiency at 4 m, with a progressive reduction as height increased. At 18 km h⁻¹, KCl showed the best performance at 4 m, whereas urea presented increasing values with increasing height. At 20 km h⁻¹, differences occurred only at 8 m, establishing the following order: urea > KCl > SS.

The circular heat map (Figure 16) confirms the pattern observed in the breakdown of the triple interaction (Table 7), indicating that application efficiency depends on the simultaneous adjustment of flight height and flight speed. Urea showed the highest application efficiency at 20 km h⁻¹, regardless of flight height. Potassium chloride exhibited greater contrast among the operational combinations, with the highest efficiencies concentrated under intermediate conditions and showing an inverse relationship with flight height at 16 km h⁻¹. For single superphosphate, greater spatial heterogeneity was observed, with a significant trend of gradual decrease in application efficiency as flight height increased, particularly at flight speeds of 16 and 20 km h⁻¹.

The relative error of the total mass of granule deposition showed no triple interaction among the evaluated factors (Figure 17; Appendix A.2). For fertilizers (Figure 17a), the following significant order was observed: urea > single superphosphate > KCl. For the flight speed factor (Figure 17b), no statistical differences were detected among the evaluated speeds. Flight height significantly influenced the relative error of the total mass (Figure 17c), showing a directly proportional relationship: as height increased, the error also increased. Specifically, the 4 m condition presented the lowest mean values, whereas increasing the height to 8 m resulted in an increase of approximately 19.3% compared to the lowest height.

3.4. Spearman Correlation Between the Variables

The Spearman correlation analysis (Figure 18) revealed consistent relationships between the physical characteristics of fertilizers and the application quality variables associated with the total application swath, effective swath, relative error, and application efficiency. The significance levels were determined based on the critical values of ρ_s, as follows: *** p ≤ 0.001 (|ρ_s| ≥ 0.312); ** p ≤ 0.01 (|ρ_s| ≥ 0.247); * p ≤ 0.05 (|ρ_s| ≥ 0.189); and ns: not significant (|ρ_s| < 0.189). The classification of the magnitude of ±ρ_s followed the guideline proposed by Mukaka [76].

The mean granule deposition in the effective swath (Dep_FE) showed a significant, very high, and negative correlation with the relative error of the total mass (Erro_soma), indicating a consistent association between higher deposition values and lower application errors. Dep_FE also showed a significant negative correlation with the effective swath width (Larg_FE) and the total swath width (Larg_FT), whereas the theoretical operational capacity of the effective swath (Cot_FE) showed a very high and significant positive correlation with Larg_FE and a significant negative correlation with Dep_FE. These results indicate a direct association between increasing operational swath width and greater operational capacity, accompanied by a reduction in deposition per unit area.

The coefficient of variation of the effective swath (CV) showed a positive correlation with Larg_FE and Cot_FE, suggesting an increase in non-uniformity as the operational width expanded. Although of low magnitude, the granulometric dispersion index (Indice_GSI) showed a significant negative correlation with Erro_soma, indicating a partial association between the granulometric heterogeneity of the material and the magnitude of the deposition error. Although positive, the correlation with Dep_FE was weak and not significant, indicating no direct relationship with effective deposition.

Relative density (Dens_rel) showed a very high, positive, and significant correlation with the angle of repose (Ang_rep). The moisture content (Teor_agua) was negatively and significantly correlated with Dens_rel, Ang_rep, and Indice_GSI. In turn, the fraction of fine particles ≤ 106 µm (Menor_106) showed a significant positive correlation with these variables and a significant negative correlation with Teor_agua, indicating an association between a higher proportion of fines and changes in the physical properties of the material. Particle sphericity (Esferic) showed predominantly low to moderate correlations with some operational variables (EFA, Cot_FE, Larg_FE, Larg_FT, and CV), which were not significant (|ρ_s| < 0.189), indicating a reduced direct association between sphericity and the overall indicators of application quality. However, a significant negative correlation was observed with Dep_FT, Indice_GSI, and Menor_106, and a significant positive correlation with Dens_rel, Teor_agua, and Ang_rep.

4. Discussion

The results indicated that flight height acted as the dominant factor, while speed had a modulating effect, and that the physical properties of the fertilizers (mainly density, sphericity and GSI) had a significant influence on lateral dispersion, confirming a dynamic air-particle distribution behaviour. The quality of the aerial application of fertilizers by RPAs stems from the interaction between the aerodynamics of the flight, the physical properties of the particles and the environmental conditions [46,78,79], this interaction being consistent with the interpretation of the distribution as a two-phase system called coupled gas–solid [38], in which the trajectory of the granules is governed by the interaction between the air flow and the particulate material [48,80].

Increasing the flight height led to a consistent widening of the total application range, accompanied by a reduction in deposition per unit area in the effective range and an increase in relative error. This effect is from the longer suspension time of the particles in the air, which intensifies their interaction with the downwash of the RPA and with atmospheric turbulence during application, a behavior typical of particle launches in a turbulent regime. Zhou et al. [54] observed that greater heights reduce the central concentration of the profile and increase the area covered, but with greater spatial variability, while Song et al. [53] reported an increase in the transverse width of the urea associated with a loss of uniformity.

As the distance between the rotors and the ground increases, the speed gradients and lateral vortices generated by the multi-rotors [20,49,81], modulated by the flight speed [22,82], intensify the lateral redistribution of the particles. Thus, the expansion of the total range does not result in a proportional increase in the effective range, generating residual deposition on the margins and a higher coefficient of variation after overlapping. As highlighted by Antuniassi et al. [83] and Carvalho et al. [13], the pass spacing should be defined in the RPA remote controller based on the effective application swath, rather than on the maximum particle distribution (total application swath). Therefore, the most appropriate operational height is the one that minimizes the coefficient of variation within the effective application swath (CV ≤ 20%), ensuring acceptable uniformity after overlap.

The operational flight height had a primary effect on most of the variables evaluated, while speed acted as a secondary modulating factor. The influence of speed mainly affected the system’s longitudinal distribution and flow rate, with a significant effect on transverse distribution at lower flight heights (4 m), when the downwash remains more concentrated. The highest speed evaluated (20 km h⁻¹) resulted in greater deposition of granules under certain conditions, due to the increase in the flow rate released by the system [84], reaching approximately 106.66 kg min⁻¹ under the operating conditions adopted (400 kg ha⁻¹, 20 km h⁻¹ and theoretical range of 8 m). In addition, the speed influences the transport distance and the sedimentation pattern of the particles, since higher speeds tend to increase the horizontal displacement [80]. Although Li et al. [85] observed increased deposition and effective range at lower heights and higher speeds, Han et al. [39] point out that speed predominantly affects longitudinal distribution, while transverse distribution remains largely controlled by the rotor’s aerodynamic field.

The differences observed between the fertilizers indicate that the operational performance of aerial application depends not only on the equipment’s settings, but mainly on the aerodynamic response of the particles to the flow field generated by the aircraft. Materials with a lower relative density tend to have a lower terminal fall speed and, consequently, a longer residence time under the action of the downward flow of the rotors, making them more susceptible to aerodynamic drag and lateral transport [86,87,88]. This mechanism explains why materials such as urea with a lower relative density (0.77 g cm⁻³), even with a more regular sphericity (88.26%) (Appendix A.1), show greater operational sensitivity in RPA applications, while denser fertilizers—such as potassium chloride (1.06 g cm⁻³) and simple superphosphate (1.16 g cm⁻³) (Appendix A.1)—tend to concentrate the deposition of granules in the central region of the range.

Xia et al. [47] showed that fertilizers with a moisture content of less than 0.5%, a sphericity of more than 95% and a relative density of between 1.2 and 1.4 g cm⁻³ have superior operational performance in RPA applications, in contrast to lower quality fertilizers that exhibit greater distribution variability and uneven deposition. In the laboratory, Zhao et al. [89] observed greater flow instability for KCl due to its lower sphericity; however, under field conditions, the aerodynamic action of the rotor becomes dominant over the internal flow dynamics of the material. Song et al. [23] also reported an increase in the coefficient of variation in fertilizers with heterogeneous granulometry, due to the difference in trajectories between particles.

The granule dispersion index (GSI) was associated with application errors, indicating that granular fertilizers with greater particle size heterogeneity tend to have greater deposition variability and greater susceptibility to segregation during distribution [90]. Smaller diameter particles, because they have a higher drag coefficient, remain in suspension for longer and suffer greater lateral displacement under the action of the downward flow generated by the rotors, distorting the transverse distribution profile [55,91]. In this sense, the very high and positive correlation between the GSI index and the fraction of particles ≤ 106 µm indicates that the increase in the proportion of fines is directly associated with an increase in granulometric heterogeneity—a condition observed mainly for KCl (2.59%) and simple superphosphate (1.46%) with regard to the fraction of particles ≤ 106 µm—although the actual drift in the field of these granules was not directly measured in this study. In addition, Gimenez and Giosa [92] point out that mixtures such as urea and potassium chloride tend to segregate due to differences in particle size.

Application efficiency remained high (>83%) under different operating conditions, indicating a greater relationship with the mass recovered than with spatial distribution, justifying the fact that the sum of deposition varied only between fertilizers, with higher values for urea and potassium chloride (>155 g m⁻²) and lower for simple superphosphate. The negative correlation between effective deposition and relative error indicates that higher depositions reduce variability, showing that the best operating condition is the one that minimizes the error in the effective range, and not necessarily the highest operating yield [6,54].

Although the results showed the influence of the physical characteristics of fertilizers commonly used as basic sources of NPK—urea (N), potassium chloride (K₂O) and simple superphosphate (P₂O₅)—on range widths (total and effective) and granule deposition, confirmed by Spearman’s correlation in an RPA equipped with a centrifugal distribution mechanism using a hopper-type discharge device (DJI Agras T50), further studies are still needed involving other single fertilizers and commercial formulations. In addition, evaluations related to the effectiveness of root absorption in target crops are recommended, as well as comparisons between different application methods and mechanisms.

Considering that flight height and speed are operational parameters that influence the quality of granule application, the investigation of other operational factors—such as application rate, flight path, distributor rotation and different hopper configurations in centrifugal spreading systems—is also necessary to consolidate technical recommendations. In addition, it is important to compare the performance of RPAs with that of conventional land-based fertilizer distribution methods.

5. Conclusions

The results of this study provide a comprehensive understanding of the operational factors and material properties that influence the spatial distribution of granule deposition during the application of mineral fertilizers using remotely piloted aircraft. This understanding was achieved through the integration of operational analyses and statistical approaches, allowing the identification of relationships between the physical properties of the fertilizer, flight parameters, and application quality indicators. The main conclusions are summarized below:

• The quality of aerial fertilizer application by remotely piloted aircraft was determined by the interaction between the type of fertilizer, height and flight speed, showing that operational performance depends on the joint adjustment of flight parameters for each material applied.
• The physical properties of the fertilizers were correlated with the application quality variables, influencing granule deposition, range widths (total and effective) and relative error.
• Increasing the flight height led to an increase in range widths (total and effective), but this was accompanied by a reduction in deposition per unit area and an increase in application errors in the following order: 8 m > 6 m > 4 m.
• Flight speeds of 18 and 20 km h⁻¹, associated with flight heights of 4 and 6 m, maintained adequate average deposition in the effective range and increased the theoretical operational capacity, showing lower relative error compared to the 8 m height.
• Fertilizers that are less dense and more susceptible to aerodynamic drag, such as urea, showed greater lateral dispersion, lower average deposition in the effective range and greater relative error, requiring greater rigour in operational adjustment.
• Although the recommendation for the use of each mineral fertilizer depends on specific technical guidelines for each crop, based on the cross-sectional distribution profile, the effective range and the relative error observed, suggested operating intervals for application using the DJI Agras T50 RPA equipped with a centrifugal distribution system were defined for each mineral fertilizer studied:
  • Urea: operate between 4 and 6 m high and 16–18 km h⁻¹, adopting an effective range of 5–7 m.
  • Potassium chloride: operate between 4 and 8 m and 18–20 km h⁻¹, with an effective range of 5.5–7 m.
  • Simple superphosphate: operate at 4 m and 16–18 km h⁻¹, with an effective range of 4–6.5 m.