Modeling of Droplet Deposition in Air-Assisted Spraying

Abstract

Air-assisted spraying is the primary method of plant protection in orchards, and precision spraying according to the canopy characteristics of fruit trees can reduce waste and pollution due to pesticide drift. To facilitate targeted pesticide application in the canopy of fruit trees, this study employed a newly developed wind-speed-adjustable orchard sprayer and established a prediction model for deposition based on data from orthogonal trials using a central composite design accounting for the coupling effect of three-dimensional spatial parameters. The experimental design systematically quantified the interaction effects of spray distance (1.5–2.5 m), fan wind speed (10–20 m/s), and deposition height (0.5–3 m) on the spatial distribution of droplets. Model significance was p < 0.0001 and the misfit term was significant (p = 0.2193), supporting its validity. The research found that wind speed and distance significantly interact in influencing deposition. By adjusting fan speed and spray distance, variable applications can be achieved in different canopy zones during plant protection operations. The response surface model developed in this study can be applied to variable-rate spraying control systems, thus providing a quantitative basis for dynamic droplet control guided by canopy characteristics. Validation tests revealed that the model’s accuracy was lower in high canopy regions and upwind spraying scenarios, indicating areas for further research.

1. Introduction

Air-assisted spraying is currently the main method of pest control in orchards. It offers key advantages over alternative approaches in spraying uniformity, droplet penetration, operational efficiency, and other aspects. However, traditional air-assisted spraying ignores differences in orchard canopies and applies pesticides at a uniform wind speed and distance. This results in substantial pesticide drift and low pesticide utilization, causing environmental pollution and the wasting of resources [1]. As precision agriculture has become more prevalent, improving the efficiency of air-assisted spraying and reducing pesticide drift has become a significant area of interest for scholars.

Extensive research has focused on enhancing the deposition of air-assisted spraying, and targeted application methods have been proposed. For example, Gu et al. [2] designed a canopy-meshing profile characterization method based on light detection and ranging (LiDAR) point–cloud data and achieved an accuracy of 93.3% for the measured canopy volume. Dou et al. [3] found that a canopy with a leaf area of 2.54–5.08 m² requires an effective air speed of 18.12–37.05 m/s. They also developed a decoupled air speed and air volume adjustment system to satisfy the differential airflow requirements of fruit tree canopies. Hocevar et al. [4] designed an ultrasound measurement system for orchard sprayers capable of evaluating canopy density based on the intensity of reflected ultrasound signals and verified its feasibility for detecting the target positions of fruit trees. Kise et al. [5] employed a stereovision sensing method to reconstruct a 3D field of fruit trees, which yielded a maximum error of 0.09 m between the reconstructed values and ground truth data for tree height and a root mean squared error of only 0.04 m. The stereovision system can achieve centimeter-level accuracy in height measurements, providing an effective means of monitoring fruit tree growth, as well as estimating canopy size and volume. In terms of droplet deposition effects, Zhang et al. [6] investigated the patterns of droplet deposition within a wind tunnel environment under different wind speeds and pulse–width modulation (PWM) working parameters. Excessive wind speeds increased in the droplet deposition distance, and there was a greater deviation from the target area of pesticide application. Liu et al. [1] examined the droplet deposition performance of profile spraying in a tea plantation and established a calculation model for droplet deposition density and distribution uniformity.

With the continuous advancement of precision pesticide application technologies in recent years, a growing number of studies have focused on the optimization of spray parameters and the modeling of droplet deposition. For example, Gil et al. [7] showed that a rise in wind speed increases droplet drift significantly. Using wind tunnel experiments, Wei et al. [8] demonstrated that electrostatic spraying technology effectively reduces droplet drift. Balan et al. [9] studied the variation in spray deposition under different meteorological conditions and found that wind speed and humidity are important determinants of droplet deposition. Li et al. [10] proposed a prediction model for droplet deposition states based on leaf surfaces, providing a theoretical basis for precise spraying in orchards. Holterman et al. [11] developed an empirical model for orchard pesticide deposition and drift prediction depending on the growth stages of fruit trees based on experimental data accumulated over more than 20 years. By applying a continuous decision-making model to an orchard sprayer, Escolà et al. [12] adjusted the application rate in real time according to the canopy volume, thereby achieving a consistent amount of pesticide deposited per unit leaf area. Their results indicated that 71% of cases were over-sprayed when treated using conventional pesticide spraying, whereas only 16% were over-sprayed when using a variable-rate application. In variable-rate spraying, it is necessary to match the pesticide dose applied to the canopy structure. Hence, Walklate et al. [13] recommended a generalized model for selecting the pesticide dose for spraying and experimentally verified the strong adaptability of this model for evaluating the effective pesticide utilization rate of sprayers. Gu et al. [14] employed an orthogonal experimental design to investigate the effects of spray parameters (e.g., spray fan speed and spray distance) on the distribution of pesticide deposition in kiwifruit orchards and established regression equations to optimize and validate the parameters.

Spray volume, airflow velocity, and spray distance were identified as the three most important technical parameters affecting the deposition amount of air-assisted spraying on fruit trees [15]. Liu et al. [16] developed a PWM-integrated controller to adjust different spray nozzles for different applications using complex spray systems. Jiang et al. [17] modeled the relationship between the duty cycle and spray flow rate based on Kalman filtering; the coefficients of determination for the model were above 0.995 under different pressure conditions. Many other researchers have evaluated the atomization performance of PWM-based variable-rate spraying systems [18,19]. These studies have shown that spray volume increases with an increase in duty cycle, the distribution decreases in uniformity, and droplet size decreases gradually, while droplet velocity increases with the increase in duty cycle. During the air-assisted spraying of fruit trees, canopy-matched airflow (airflow speed, airflow volume, and airflow direction) will ensure effective pesticide application, with insufficient airflow hampering the canopy penetration of droplets and excessive application causing difficulties in droplet deposition, thus resulting in substantial pesticide drift [20]. Balsari et al. [21] achieved a higher rate of droplet deposition and more uniform distribution when the working airflow reached the canopy of fruit trees at 5 m/s. Landers [22] installed a louver structure at the sprayer air outlet, which allowed for the adjustment of the spray airflow between 0–100% by altering the cross-sectional area of the air outlet through the louver. Experimental results showed that this structure can effectively increase droplet deposition in the canopy, thus providing new ideas for airflow control. However, the sensitivity and reliability of such methods require further improvements. Spray distance is a key technical parameter affecting the spraying effect. Osterman et al. [23] designed an online adjustment device and control algorithm for the geometric positioning of an air-assisted sprayer; this system enhanced the effective utilization of pesticides and reduced pesticide drift significantly. Song et al. [24] designed a flexible targeted sprayer prototype for orchards and tested the droplet deposition rate under different control modes, indicating a maximum droplet deposition rate of 88.4%.

The design and optimization of spraying machinery are also important directions for improving the spraying effect. Li et al. [25] designed a spraying device with an air-assisted annular nozzle and optimized its spraying performance through experiments. Zhang et al. [26] investigated the effects of the nozzle pore diameter and spraying pressure on the size and deposition distribution of droplets, which revealed that a smaller nozzle pore diameter and higher spraying pressure improved the uniformity of droplets. Musiu et al. [27] examined the effects of the spray volume rate, airflow rate, and target location on spray deposition and distribution, showing that increases in the spray volume rate and airflow rate improve the number of droplets deposited in the target area. Bahrouni et al. [28] studied the effects of sprayer parameters and wind speed on pesticide foliage and soil deposition. They showed that anti-drift nozzles were more effective than conventional nozzles and recommended selecting a medium droplet size, medium pressure, and reduced wind speed to minimize the environmental impact and improve efficiency. Deng et al. [29] constructed a direct nozzle injection pesticide spraying system based on a solenoid valve, which mainly involved designing a fast-response valve based on electromagnetic principles, to accurately alter the amount of pesticide injected and the concentration of liquid sprayed by PWM.

Despite extensive research on target detection, requirement calculation models, variable control systems, and droplet spatial deposition patterns, further investigations are still needed to explore models for quantitatively calculating the spatial distribution of droplet deposition. In particular, is there a quantitative pattern in droplet deposition distribution under varying wind speeds, spray distances, and deposition heights? Therefore, this study aimed to examine the effects of spray distance, fan wind speed, and deposition height on the spatial distribution of droplet deposition through an orthogonal experimental design and to establish corresponding mathematical models, thereby providing theoretical support for variable-rate spraying based on the canopy characteristics of fruit trees.

2. Materials and Methods

2.1. Orchard Sprayer

The air-assisted sprayer used in the experiment was designed by the Research Center of Intelligent Equipment, Beijing Academy of Agricultural and Forestry Sciences, as shown in Figure 1a, with overall dimensions of 2.30 × 0.75 × 1.05 m and a tank capacity of 350 L. The machine has a double petrol engine design. The front engine drives the rotation of the fan, the rotating speed is controlled by the throttle, and the wind speed at the air outlet is adjustable between 10 and 20 m/s. The rear engine drives the movement and spraying action of the machine, with a spraying pressure of 0.5–1.2 Mpa and a plunger pump flow rate of 18–22 L/min.

2.2. Meteorological Monitoring

To monitor the natural wind speeds and wind directions within the testing environment, a small weather station developed by the Research Center of Intelligent Equipment, Beijing Academy of Agriculture and Forestry Sciences was used, as shown in Figure 1b. The anemometer had a measurement accuracy within ±0.3 m/s for wind speed and ±1° for wind direction, and the frequency of data acquisition was set to 0.5 Hz.

2.3. Tracers and Analytical Instruments

The experiment was conducted using rhodamine(Kemio Chemical Reagent Co., Ltd., Tianjin, China) as a substitute for pesticides [30,31,32]. Droplets were collected using a 9-cm-diameter filter paper(Hangzhou Special Paper Co., Ltd., Hangzhou, China), and the deposition amount was measured using a Trilogy spectrophotometer (Turner Designs, San Jose, CA, USA), as shown in Figure 1c.

2.4. Solution Preparation and Instrument Calibration

Firstly, 10.5 g of rhodamine was dissolved in 6 L of distilled water, added to a sprayer tank containing 294 L of water, and mixed well. Then, 500 µL of the solution was obtained from the sprayer tank and diluted with 49.5 mL of distilled water. The theoretical concentration of the diluted solution was 350 µg/L. The solution was further diluted to 175, 87.5, 43.75, and 21.875 µg/L, respectively, and these solutions were used to calibrate the spectrophotometer.

2.5. Orthogonal Experimental Design

To explore the effects of spray distance, wind speed, and deposition height on spatial patterns of deposition, a three-factor, five-level orthogonal experimental design was adopted. Spray distances were based on the common row spacing of fruit trees, with a minimum value of 1.5 m and a maximum value of 2.5 m. Wind speeds were based on the adjustable wind speed range of the sprayer, with a minimum value of 10 m/s and a maximum value of 20 m/s. Deposition heights were based on the common height of densely planted dwarf fruit trees, with a minimum value of 0.5 m and a maximum value of 3 m.

The central composite design (CCD) method was adopted with α = 1.682 to achieve rotatability and orthogonality. We designed a total of 14 non-center-point trials to ensure the robustness of the model and 9 center-point trials, which resulted in a total of 23 trials. The factor levels are shown in

Table 1. Factor levels.

Level	Factor
	Distance (m)	Wind Speed (m/s)	Height (m)
−1.682	1.50	10.00	0.50
−1	1.70	12.03	1.01
0	2.00	15.00	1.75
1	2.30	17.97	2.49
1.682	2.50	20.00	3.00

, and the orthogonal experimental scheme is shown in

Table 2. Orthogonal experimental scheme.

No.	Factor
	Distance (m)	Wind Speed (m/s)	Height (m)
1	1.70	12.03	1.01
2	1.70	12.03	2.49
3	1.70	17.97	1.01
4	1.70	17.97	2.49
5	2.30	12.03	1.01
6	2.30	12.03	2.49
7	2.30	17.97	1.01
8	2.30	17.97	2.49
9	1.50	15.00	1.75
10	2.50	15.00	1.75
11	2.00	10.00	1.75
12	2.00	20.00	1.75
13	2.00	15.00	0.50
14	2.00	15.00	3.00
15	2.00	15.00	1.75
16	2.00	15.00	1.75
17	2.00	15.00	1.75
18	2.00	15.00	1.75
19	2.00	15.00	1.75
20	2.00	15.00	1.75
21	2.00	15.00	1.75
22	2.00	15.00	1.75
23	2.00	15.00	1.75

.

The spray collection frame is shown in Figure 2a. During the experiment, three water-sensitive papers were arranged horizontally at heights of 0.75, 1.25, 1.75, 2.25, and 2.75 m to calculate the total deposition. For each orthogonal trial, six water-sensitive papers were arranged horizontally with equal spacing at the target height to measure the deposition amount at the given height. During the spray test, the wind speed of the sprayer fan was adjusted to the target wind speed for the given trial and the spray distance was set to the target distance. The sprayer was held parallel to the collection frame and the experimenter advanced at a uniform walking speed while spraying. The experimental procedure is shown in Figure 2b. After the spray test, the water-sensitive papers were collected, and the amount of rhodamine deposition was determined using a spectrophotometer.

2.6. Data Analysis

In each orthogonal trial, the deposition amounts on three water-sensitive papers arranged horizontally with equal spacing were averaged for heights of 0.75, 1.25, 1.75, 2.25, and 2.75 m. The sum over all heights was then used as an index of the total deposition on the spray collection frame. The total deposition for each trial was normalized to 100, and the normalization coefficient was obtained by dividing 100 by the total deposition in each trial. The deposition amounts on the six water-sensitive papers at the corresponding height were averaged in each of the 23 orthogonal trials and multiplied by the normalization coefficient to obtain the normalized deposition for a given trial, which served as the main evaluation indicator in this study.

After the experiment was completed, a model of the relationships between the three factors (spray distance, fan wind speed, and deposition height) and normalized deposition was established through an orthogonal analysis using Design Export. The data transformation method was set to “None”, “Coding for Analysis” was selected as “Coded”, and “Process order” was chosen as “Quadratic”.

2.7. Validation of the Experimental Design

To further verify the reliability of the model, validation trials were conducted, with randomly selected factor values deviating from the levels in the orthogonal trials. The spray distances were 1.83 and 2.17 m; fan wind speeds were 13.30, 16.70, 13.30, and 16.70 m/s; and deposition heights were 1.00, 1.50, 2.00, and 2.50 m. After combining the factors, 16 validation trials were designed. The experimental scheme is shown in

Table 3. Scheme of validation trials.

No.	Factor
	Distance (m)	Wind Speed (m/s)	Height (m)
1	1.83	13.30	1.00
2	1.83	13.30	1.50
3	1.83	13.30	2.00
4	1.83	13.30	2.50
5	1.83	16.70	1.00
6	1.83	16.70	1.50
7	1.83	16.70	2.00
8	1.83	16.70	2.50
9	2.17	13.30	1.00
10	2.17	13.30	1.50
11	2.17	13.30	2.00
12	2.17	13.30	2.50
13	2.17	16.70	1.00
14	2.17	16.70	1.50
15	2.17	16.70	2.00
16	2.17	16.70	2.50

.

3. Results

3.1. Recovery Rate

A volume of 100 µL of solution obtained from the sprayer tank was diluted with 49.9 mL of distilled water, and its concentration, as measured using a spectrophotometer, was 75.138 µg/L. In addition, 100 µL of the solution was obtained from the sprayer tank and dripped onto a filter paper. After repeated washing with 49.9 mL of distilled water, its concentration was measured using a spectrophotometer. The test results are shown in

Table 4. Recovery rates.

Treatment	1st Concentration (µg/L)	2nd Concentration (µg/L)	3rd Concentration (µg/L)	Mean (µg/L)	Recovery Rate
Repeated washing after dripping on filter paper	62.61	60.55	60.72	61.29	81.57%

, which indicates a recovery rate of 81.57%.

3.2. Measurement Results for Sprayer Travel Speed and Nozzle Flow

The sprayer traveled at a constant speed on a fixed gear for 30 m. A stopwatch was used for timing, and the measurement was repeated three times. The average speed of the sprayer at uniform traveling operation was 0.526 m/s, and test results are shown in

Table 5. Travel speed measurements for spraying operations.

	1st	2nd	3rd	Mean
Distance (m)	30	30	30	30
Time (s)	56.68	57.59	56.95	57.07
Speed (m/s)	0.529	0.521	0.527	0.526

. The nozzle flow test was carried out at a pressure of 0.7 MPa, which is commonly used for orchard air-assisted spraying. The spray volume of four nozzles on one side were collected for a duration of 1 min, and the test was repeated three times. The mean flow rates of the four nozzles were calculated as 0.96, 1.10, 0.92, and 1.08 L/min. The test results are shown in

Table 6. Measurements of nozzle flow.

		Flow (mL)	Time (min)	Flow Rate (L/min)	Average Flow Rate (L/min)
Nozzle 1	1st	950	1	0.95	0.96
	2nd	980	1	0.98
	3rd	950	1	0.95
Nozzle 2	1st	1110	1	1.11	1.10
	2nd	1090	1	1.09
	3rd	1110	1	1.11
Nozzle 3	1st	920	1	0.92	0.92
	2nd	930	1	0.93
	3rd	920	1	0.92
Nozzle 4	1st	1110	1	1.11	1.08
	2nd	1080	1	1.08
	3rd	1050	1	1.05

.

3.3. Results of Orthogonal Trials

The trials were conducted in October 2022 under breezy conditions. The natural wind speed, measured using an anemometer, was 0.56–0.86 m/s during the trials. The results for 23 orthogonal trials are shown in

Table 7. Results of orthogonal trials.

No.	Distance (m)	Wind Speed (m/s)	Height (m)	Deposition Amount (µg/L)	Total Deposition (µg/L)	Normalization Coefficient	Deposition Amount Normalized Value (%)
1	1.70	12.03	1.01	159.66	487.73	0.2050	32.74
2	1.70	12.03	2.49	67.87	487.73	0.2050	13.92
3	1.70	17.97	1.01	194.83	561.26	0.1782	34.71
4	1.70	17.97	2.49	62.91	561.26	0.1782	11.21
5	2.30	12.03	1.01	94.34	378.35	0.2643	24.93
6	2.30	12.03	2.49	53.28	378.35	0.2643	14.08
7	2.30	17.97	1.01	92.70	421.89	0.2370	21.97
8	2.30	17.97	2.49	64.62	421.89	0.2370	15.32
9	1.50	15.00	1.75	116.18	604.39	0.1655	19.22
10	2.50	15.00	1.75	76.37	330.69	0.3024	23.09
11	2.00	10.00	1.75	116.05	346.52	0.2886	33.49
12	2.00	20.00	1.75	120.57	538.07	0.1858	22.41
13	2.00	15.00	0.50	57.29	587.01	0.1704	9.76
14	2.00	15.00	3.00	73.45	587.01	0.1704	12.51
15	2.00	15.00	1.75	123.46	478.99	0.2088	25.77
16	2.00	15.00	1.75	115.29	492.86	0.2029	23.39
17	2.00	15.00	1.75	150.70	540.64	0.1850	27.87
18	2.00	15.00	1.75	147.59	608.88	0.1642	24.24
19	2.00	15.00	1.75	174.38	638.34	0.1567	27.32
20	2.00	15.00	1.75	137.90	520.21	0.1922	26.51
21	2.00	15.00	1.75	119.64	404.35	0.2473	29.59
22	2.00	15.00	1.75	126.29	497.20	0.2011	25.40
23	2.00	15.00	1.75	160.10	594.58	0.1682	26.93

.

A cubic polynomial was used to describe the relationships between normalized deposition and spray distance, fan wind speed, and deposition height. The analysis of variance (ANOVA) results for the regression equation are shown in

Table 8. Regression analysis.

Source	Sum of Squares	Degrees of Freedom	Mean Square	F	p
Model	1100.3722	13	84.6440	21.8490	<0.0001
A	7.4921	1	7.4921	1.9339	0.1978
B	61.4103	1	61.4103	15.8518	0.0032 **
C	3.7908	1	3.7908	0.9785	0.3484
AB	0.1242	1	0.1242	0.0321	0.8619
AC	76.9764	1	76.9764	19.8698	0.0016 **
BC	0.0297	1	0.0297	0.0077	0.9321
A2	37.6069	1	37.6069	9.7074	0.0124 *
B2	11.8240	1	11.8240	3.0521	0.1146
C2	410.3855	1	410.3855	105.9322	<0.0001 **
ABC	9.8622	1	9.8622	2.5457	0.1451
A2B	29.5767	1	29.5767	7.6346	0.0220 *
A2C	228.1383	1	228.1383	58.8890	<0.0001 **
AB2	33.5961	1	33.5961	8.6721	0.0164 *
Residual	34.8663	9	3.8740
Misfit term	6.3355	1	6.3355	1.7765	0.2193
Pure error	28.5309	8	3.5664
Total	1135.2385	22

“*” indicates significant p-value < 0.1, “**” indicates significant p-value < 0.01.

, and the significance level was p < 0.0001. The misfit term was p = 0.2193, indicating that the model was highly significant and misfit was not significant.

Y = 26.31 + 1.15A − 3.29B + 0.82C − 0.12AB + 3.10AC − 0.06BC − 1.54A² + 0.86B² −

5.08C² + 1.11ABC + 2.99A²B − 8.30A²C − 3.18AB²

As shown in Table 8, the effects on normalized deposition were highly significant for B, AC, C², and A²C. The significance of these effects was ranked as C², A²C, AC, and B, corresponding to the effects of height², distance² × height, distance × height, and wind speed. The effects of A², A²B, and AB² were also relatively significant.

After inserting the values for the orthogonal trial factor levels into the regression equation, the data shown in

Table 9. Results after value substitution in the regression equation.

No.	Distance (m)	Wind Speed (m/s)	Height (m)	Normalized Deposition (%)	Calculated Normalized Deposition (%)	Error	Relative Error
1	1.70	12.03	1.01	32.74	32.17	0.57	1.73%
2	1.70	12.03	2.49	13.92	13.35	0.57	4.07%
3	1.70	17.97	1.01	34.71	34.15	0.56	1.62%
4	1.70	17.97	2.49	11.21	10.65	0.56	4.98%
5	2.30	12.03	1.01	24.93	24.37	0.56	2.26%
6	2.30	12.03	2.49	14.08	13.51	0.57	4.06%
7	2.30	17.97	1.01	21.97	21.43	0.54	2.47%
8	2.30	17.97	2.49	15.32	14.77	0.55	3.57%
9	1.50	15.00	1.75	19.22	20.02	−0.80	4.14%
10	2.50	15.00	1.75	23.09	23.89	−0.79	3.44%
11	2.00	10.00	1.75	33.49	34.28	−0.79	2.35%
12	2.00	20.00	1.75	22.41	23.21	−0.80	3.57%
13	2.00	15.00	0.50	9.76	10.56	−0.80	8.20%
14	2.00	15.00	3.00	12.51	13.32	−0.81	6.43%
15	2.00	15.00	1.75	25.77	26.31	−0.54	2.08%
16	2.00	15.00	1.75	23.39	26.31	−2.92	12.48%
17	2.00	15.00	1.75	27.87	26.31	1.56	5.61%
18	2.00	15.00	1.75	24.24	26.31	−2.07	8.54%
19	2.00	15.00	1.75	27.32	26.31	1.01	3.69%
20	2.00	15.00	1.75	26.51	26.31	0.20	0.75%
21	2.00	15.00	1.75	29.59	26.31	3.28	11.08%
22	2.00	15.00	1.75	25.40	26.31	−0.91	3.58%
23	2.00	15.00	1.75	26.93	26.31	0.62	2.29%

were obtained, with a maximum relative error of 12.48% and a variance of 1.52.

For a constant deposition height, the effects of fan wind speed and spray distance on normalized deposition are shown in Figure 3.

As shown in Figure 3a, at a deposition height of 1.00 m, normalized deposition exhibited an initial decrease, followed by an increase with the increase in spray distance, reaching its minimum value at a distance of 2.10 m and a maximum at 1.70 m. As the wind speed increased, when the spray distance was >2.10 m, normalized deposition showed a decreasing trend, and maximum deposition was observed at a wind speed of 12 m/s; when the spray distance was <2.10 m, normalized deposition showed an initial increase, followed by a decrease.

As shown in Figure 3b, at a deposition height of 1.75 m, when fan wind speed was <17 m/s and kept constant, normalized deposition exhibited an initial increase, followed by a decrease with the increase in spray distance. When fan wind speed was >17 m/s and kept constant, normalized deposition exhibited a decreasing trend with the increase in spray distance; however, the effect was not significant. As wind speed increased, normalized deposition showed an overall decreasing trend at a deposition height of 1.75 m; however, the effect was not significant.

As shown in Figure 3c, at a deposition height of 2.50 m, normalized deposition exhibited an initial increase, followed by a decrease with the increase in spray distance, and the effect was significant. Normalized deposition was highest at a spray distance of 2.0 m. Normalized deposition showed a decreasing trend with the increase in wind speed.

For a constant fan wind speed, the effects of deposition height and spray distance on normalized deposition are shown in Figure 4.

As shown in Figure 4a, at a wind speed of 12 m/s, when the deposition height was <1.3 m, normalized deposition showed an initial decrease, followed by an increase with the increase in spray distance. When deposition height was >1.3 m, normalized deposition exhibited an initial increase, followed by a decrease with the increase in spray distance. The extrema in both cases were detected at a spray distance of 2–2.1 m.

As shown in Figure 4b, at a wind speed of 15 m/s, when the deposition height was <1.7 m, normalized deposition exhibited an initial decrease, followed by an increase with the increase in spray distance. When the deposition height was >1.7 m, normalized deposition exhibited an initial increase followed by a decrease with the increase in spray distance. The extrema in both cases were detected at a spray distance of 2–2.1 m.

As shown in Figure 4c, at a wind speed of 18 m/s, when the deposition height was <1.85 m, normalized deposition exhibited an initial decrease, followed by an increase with the increase in spray distance. When the deposition height was >1.85 m, normalized deposition exhibited an initial increase, followed by a decrease with the increase in spray distance.

For a constant spray distance, the effects of deposition height and fan wind speed on normalized deposition are shown in Figure 5.

As shown in Figure 5a, when the spray distance was 1.70 m, normalized deposition exhibited a decreasing trend with the increase in deposition height. At the same deposition height, normalized deposition exhibited an initial decrease, followed by an increase with the increase in wind speed, reaching its minimum at 15 m/s.

As shown in Figure 5b, at a spray distance of 2.00 m, normalized deposition exhibited an initial increase, followed by a decrease with the increase in deposition height, reaching its maximum at a height of 1.80 m. At the same deposition height, normalized deposition exhibited a decreasing trend with the increase in wind speed.

As shown in Figure 5c, at a spray distance of 2.30 m, normalized deposition exhibited a decreasing trend with the increase in deposition height. At the same deposition height, normalized deposition exhibited an initial increase, followed by a decrease with the increase in wind speed, reaching its maximum at a wind speed of 15 m/s.

In summary, when the spraying distance is around 2.00–2.10 m, droplets are more likely to deposit in the middle and upper canopy regions. If the spraying distance is greater or smaller than this range, droplets will predominantly deposit in the lower canopy region. This phenomenon may occur because, at longer spraying distances, gravity causes more droplets to settle in the lower canopy, while at shorter distances, insufficient diffusion by the fan’s airflow results in greater deposition in the lower canopy. Changes in wind speed have a relatively minor impact on the normalized deposition values in the middle canopy region but significantly affect the normalized deposition values in the upper and lower canopy regions. This may be because, under the combined influence of wind force and gravity, the increase or decrease in deposition in the upper canopy region compensates for the middle canopy region, while changes in deposition in the middle canopy region compensate for the lower canopy region. As a result, the deposition in the middle canopy region remains relatively stable despite variations in wind speed.

3.4. Results of Validation Trials

Validation trials were conducted under breezy conditions. The natural wind speed, measured using an anemometer, was 0.56–1.17 m/s during the trials. The results of the 16 validation trials are shown in

Table 10. Results of validation trials.

No.	Distance (m)	Wind Speed (m/s)	Height (m)	Deposition Amount (µg/L)	Total Deposition (µg/L)	Normalization Coefficient	Deposition Amount, Normalized Value (%)
1	1.83	13.30	1.00	175.56	566.72	0.1765	30.98
2	1.83	13.30	1.50	160.87	566.72	0.1765	28.39
3	1.83	13.30	2.00	76.75	566.72	0.1765	13.54
4	1.83	13.30	2.50	26.14	566.72	0.1765	4.61
5	1.83	16.70	1.00	148.11	551.43	0.1813	26.86
6	1.83	16.70	1.50	184.45	551.43	0.1813	33.45
7	1.83	16.70	2.00	125.99	551.43	0.1813	22.85
8	1.83	16.70	2.50	63.30	551.43	0.1813	11.48
9	2.17	13.30	1.00	141.05	616.57	0.1622	22.88
10	2.17	13.30	1.50	182.30	616.57	0.1622	29.57
11	2.17	13.30	2.00	102.63	616.57	0.1622	16.64
12	2.17	13.30	2.50	59.98	616.57	0.1622	9.73
13	2.17	16.70	1.00	98.19	248.29	0.4028	39.55
14	2.17	16.70	1.50	43.34	248.29	0.4028	17.46
15	2.17	16.70	2.00	9.36	248.29	0.4028	3.77
16	2.17	16.70	2.50	10.76	248.29	0.4028	4.33

.

After inserting the values for the factor levels in the validation trials into the original regression equation, the data shown in

Table 11. Results after value substitution in the regression equation for validation trials.

No.	Distance (m)	Wind Speed (m/s)	Height (m)	Normalized Deposition (%)	Calculated Normalized Deposition (%)	Error	Relative Error
1	1.83	13.30	1.00	30.98	25.36	5.62	18.13%
2	1.83	13.30	1.50	28.39	27.83	0.55	1.95%
3	1.83	13.30	2.00	13.54	25.66	−12.12	89.49%
4	1.83	13.30	2.50	4.61	18.86	−14.25	308.92%
5	1.83	16.70	1.00	26.86	23.57	3.29	12.24%
6	1.83	16.70	1.50	33.45	25.51	7.94	23.73%
7	1.83	16.70	2.00	22.85	22.81	0.04	0.16%
8	1.83	16.70	2.50	11.48	15.47	−3.99	34.78%
9	2.17	13.30	1.00	22.88	22.73	0.14	0.63%
10	2.17	13.30	1.50	29.57	27.09	2.48	8.37%
11	2.17	13.30	2.00	16.64	26.81	−10.17	61.08%
12	2.17	13.30	2.50	9.73	21.89	−12.17	125.06%
13	2.17	16.70	1.00	39.55	19.33	20.22	51.12%
14	2.17	16.70	1.50	17.46	24.13	−6.67	38.23%
15	2.17	16.70	2.00	3.77	24.29	−20.52	544.52%
16	2.17	16.70	2.50	4.33	19.81	−15.48	357.19%

were obtained, with a maximum error of 544.52%, a mean error of −3.44, and a variance of 115.17.

4. Discussion

(1) Through orthogonal experiments, this study established a model describing the effects of spray distance (1.5–2.5 m), fan wind speed (10–20 m/s), and deposition height (0.5–3 m) on the spatial distribution of droplets. This model can provide a quantitative basis for dynamic droplet control guided by canopy characteristics. Furthermore, the quantitative calculation of the droplet spatial deposition offers the possibility for online analyses of pesticide deposition in agricultural products.

(2) In validation trials, mean relative errors corresponding to deposition heights of 1.00, 1.50, 2.00, and 2.50 m were 20.53%, 18.07%, 173.81%, and 206.49%, respectively, clearly demonstrating that model accuracy was lower in high canopy areas. This may have been because the deposition amount was smaller at higher deposition positions, resulting normalized deposition in larger errors.

(3) The validation trials consisted of 16 sets of data, with 4 sets forming one group, resulting in 4 groups of trials. The mean relative errors for the four groups were 104.62%, 17.73%, 48.79%, and 247.77%, and the corresponding natural wind speeds were 0.71, 0.64, 0.56, and 1.17 m/s, respectively. Group 4 had the highest natural wind speeds, resulting in a maximum relative error of 544.52% and the largest mean error observed, which was most likely due to the impact of natural wind on prediction accuracy. The natural wind direction in Group 1 was 301.05° and the natural wind speed component in the direction of spraying was −0.61 m/s, indicating upwind spraying, which may have resulted in a relatively large error.

(4) To better apply the model to practical operations, further investigations should evaluate deposition in high canopy areas and the impact of weak natural wind on droplet distribution.

5. Conclusions

(1) At a height of 1.00 m, wind speed had no significant effect on the deposition, whereas spray distance had a significant effect on deposition, showing a trend of initial decrease, followed by an increase, reaching its minimum at a distance of 2.10 m and its maximum at 1.70 m. At a height of 1.75 m, both the spray distance and wind speed had a relatively small impact on deposition. At a height of 2.50 m, both the spray distance and wind speed had significant effects on deposition; an increase in wind speed reduced deposition significantly at this height, with maximum deposition observed at a spray distance of 2.00 m, and increasing or decreasing spray distance reduced deposition significantly at this height.

(2) Wind speed and distance had significant interaction effects on deposition. When the spray distances were 1.70 m and 2.30 m, deposition was greater at higher positions. When the spray distance was 2.00 m, maximum deposition was observed at a height of 1.80 m. During plant protection operations, the precise control of deposition in different canopy areas can be achieved by adjusting the fan wind speed and spray distance according to canopy characteristics.

(3) The interaction effects of spray distance (1.5–2.5 m), fan wind speed (10–20 m/s), and deposition height (0.5–3 m) on the droplet spatial distribution were modeled. The significance of the effects of each factor on the deposition ratio was ranked as follows: deposition height, spray distance, and fan wind speed. The response surface model established in this study can be directly integrated into variable-rate spraying control systems. By analyzing actual canopy characteristics (e.g., height and volume) of fruit trees, the optimal spray distance and fan speed parameters can be selected, thereby providing a quantitative basis for dynamic droplet control guided by canopy characteristics.