Wind-Induced Bending Characteristics of Crop Leaves and Their Potential Applications in Air-Assisted Spray Optimization

Abstract

Crop leaves naturally exhibit a curved morphology and primarily display bending deformation and vibrational responses under wind load. The curved surface structure of leaves plays a critical role in the deposition and retention of pesticide droplets. In this study, wind tunnel experiments combined with high-speed photography and digital image analysis were conducted to systematically investigate the curvature and flexibility distributions of three typical crop leaves: walnut, peach, and pepper, across a range of wind speeds. The results indicate that with increasing wind speed, all three types of leaves gradually transition from smooth, uniform bending to a multi-peak pattern of pronounced local curvature, with increasingly prominent nonlinear deformation characteristics. Moreover, once the wind speed exceeds the critical threshold of 6 m/s, the primary deformation region generally shifts from the leaf base to the tip. For example, the maximum curvature of walnut leaves increased from 0.018 mm⁻¹ to 0.047 mm⁻¹, and that of pepper leaves from 0.031 mm⁻¹ to 0.101 mm⁻¹, both more than double their original values. In addition, all three types of leaves demonstrated a distinct structural gradient characterized by strong basal rigidity and high apical flexibility. The tip flexibility values exceeded 1.5 × 10⁻⁵, 4 × 10⁻⁴, and 5.6 × 10⁻⁴ mm⁻²·mN⁻¹ for walnut, peach, and pepper leaves, respectively. These findings elucidate the mechanical response mechanisms of non-uniform flexible crop leaves under wind-induced bending and provide a theoretical basis and data support for the optimization of air-assisted spraying parameters.

1. Introduction

With the increasing demand for efficient and precise pesticide application in modern agriculture, air-assisted spraying technology has emerged as a vital approach for field pesticide delivery. Airflow not only drives the movement and deposition of droplets [1,2,3,4,5,6] but also markedly disturbs crop leaves, inducing complex structural responses such as bending deformation, vibration, and even local instability [7,8,9]. These wind-induced deformations alter the spatial orientation and structural configuration of leaves, thereby profoundly influencing the behavior of droplet deposition [10,11,12]. Therefore, investigating the structural response characteristics of leaves under wind-induced loading is of great significance for improving pesticide utilization efficiency and optimizing air-assisted spraying parameters.

In existing studies on the structural response of leaves under external forces, leaves are often simplified as uniform planar thin plates or idealized beam structures, with most research focusing on macro-level responses such as overall leaf tilt and rotation. For example, Bhosale et al. [13] and Lauderbaugh et al. [14] investigated changes in the overall tilt angle of leaves caused by droplet impacts. Tadrist et al. [7,15] and Zhang et al. [16] examined leaf oscillation, pitching, and rotation under airflow. While these studies provide important insights into the global deformation and motion of leaves under external loading, they often fail to capture the heterogeneity and complex structural characteristics of different local sections of real leaves. As a result, the nuanced and localized response of leaves, which is critical for understanding their actual behavior in field environments, remains insufficiently explored.

The complex structural features of real leaves, especially their curved surfaces, play a critical role in governing the deposition kinetics of liquid droplets. For example, Liu et al. [17] found that droplets impacting the curved surface of Echevaria leaves exhibit directionally asymmetric bouncing and spreading behaviors. Zheng et al. [18] demonstrated that variations in curvature radius across different regions of rice leaves can significantly modulate droplet spreading and splitting processes. Moreover, Han et al. [19] and Long et al. [20] confirmed, using artificial curved surfaces such as superhydrophobic cylinders and spheres of varying diameters, that surface curvature markedly affects droplet spreading dynamics. Collectively, these studies highlight that the natural surface characteristics of leaves strongly influence droplet deposition behavior. Building on this, the present study seeks to further elucidate the localized bending deformation patterns of leaves under external force disturbances, which is essential for accurately evaluating pesticide deposition efficiency and runoff risks.

In fact, the structural response and mechanical mechanisms of real leaves at the local scale have long attracted significant attention. For instance, Niklas [21] conducted static loading tests and identified pronounced differences in the distribution of bending stiffness among various plant petioles, revealing substantial spatial heterogeneity in stiffness across different petiole segments. Moulia et al. [22] applied beam theory to investigate the bending resistance of different regions of corn leaves through single-point loading experiments, demonstrating that the leaf midrib plays a dominant role in bending response, with its structural stiffness contributing over 80% of the total leaf stiffness. More recently, Tang et al. [23] systematically analyzed the regulatory effects of leaf length, leaf width, and deformation parameters on the bending characteristics of rice leaves using digital curvature measurements and statistical analysis. These studies have established a theoretical foundation for understanding the deformation mechanisms of leaves subjected to static or localized loading. However, during air-assisted spraying operations, airflow not only transports droplets but also exerts direct mechanical forces on the leaf. To date, there has been a lack of systematic and quantitative analysis regarding the deformation characteristics of various local regions of the leaf under wind loading and their contributions to the overall bending response. Addressing this gap is essential for accurately evaluating leaf behavior and optimizing spraying strategies in agricultural practice.

Therefore, this study systematically investigates the bending morphology and mechanical response of real crop leaves under wind loading by means of wind tunnel experiments, high-speed photography, and digital image analysis. By comparing different wind speeds and leaf types, the critical wind speed at which the primary deformation region of the leaf transitions is identified, revealing the structural adaptation mechanisms of non-uniform flexible leaves under wind-induced loading. These research findings are expected to provide a theoretical foundation and quantitative data support for the optimization of precision pesticide application parameters in the field and for improving pesticide utilization efficiency.

2. Materials and Methods

2.1. Experimental Materials

In this study, mature, intact, and pest-free leaves from three common crops, namely walnut, peach, and chili pepper, were selected as experimental materials, as shown in Figure 1. All leaves used in the experiments were collected from the campus of Jiangsu University in Zhenjiang City, Jiangsu Province, China. For each crop, at least 15 leaves were randomly selected to ensure the reliability of the experimental data. Immediately after collection, the leaves were placed in water at room temperature to maintain moisture, and the time interval between collection and the start of the experiment was kept within 30 min. No wilting was observed in any sample during testing, indicating that their mechanical properties remained essentially unchanged.

To examine the structural response and local mechanical properties of crop leaves under wind loads, geometric parameters, including length, width, and area, were measured using ImageJ image analysis software (Version 1.53e, National Institutes of Health, Bethesda, MD, USA). Three-point bending tests were then conducted on the leaf midrib from base to tip using a texture analyzer (TA.XTplus, Stable Micro Systems Ltd., Godalming, Surrey, UK) (Figure 2a). Each midrib was divided into 20 mm segments with a width extension of 1–2 mm beyond the main vein to preserve structural integrity, and each segment was tested three times. Test parameters were set to a downward speed of 1 mm/s, loading speed of 0.5 mm/s, retraction speed of 3 mm/s, maximum displacement of 5 mm, and a support span of 10 mm, ensuring a smooth and controlled loading process. Force–displacement curves were recorded in real time (Figure 2b).

To evaluate the bending resistance of leaf veins in different crops, the bending stiffness EI of each vein segment was calculated from the peak load F and the corresponding maximum deformation δ obtained in the three-point bending tests. Assuming small-deformation linear elasticity, the bending stiffness of a simply supported beam loaded at its midpoint can be estimated using the following equation [24]:

$$EI={\displaystyle \frac{F{L}^3}{48\delta }}$$

(1)

where EI (N·mm²) is the bending stiffness, F (N) is the peak load in the elastic stage, L (mm) is the support span, and δ (mm) is the maximum deformation of the leaf midrib.

Using this method, both the structural parameters of the three crop leaves and the local bending stiffness of each vein segment were determined. The results showed that vein bending stiffness decreased monotonically along the axial direction from the leaf base to the tip. To illustrate this trend, the test data for two representative positions—the leaf base and the leaf tip—are reported in the format “mean ± standard deviation,” as presented in

Table 1. Physical parameters of the leaf.

Crop Species		Walnut Leaf	Peach Leaf	Chili Pepper Leaf
Parameter Value
Geometric dimensions	Leaf length (mm)	141.51 ± 8.93	128.39 ± 4.28	84.16 ± 3.87
	Leaf width (mm)	97.57 ± 3.59	42.05 ± 1.99	55.88 ± 2.15
	Leaf area (mm2)	9872.71 ± 184.24	4226.56 ± 109.82	3441.42 ± 79.94
Bending stiffness	Leaf base region (N·mm2)	33.64 ± 4.45	6.36 ± 3.17	4.39 ± 2.41
	Leaf tip region (N·mm2)	0.43 ± 0.54	0.56 ± 0.28	0.68 ± 0.29

.

2.2. Experiment Setup

Figure 3 presents a schematic diagram of the experimental system used in this study, which comprises three main components: the wind tunnel system, the force measurement system, and the image acquisition system. The wind tunnel provides a controllable and stable airflow environment, with wind speed regulated by a speed controller to ensure uniform airflow distribution within the test section. The test section is a rectangular channel constructed from acrylic panels, with dimensions of L_t = 1150 mm, W_t = 436 mm, and H_t = 436 mm. The airflow is directed along the x-axis. Wind speed is measured using a Pitot tube positioned at the center of the test section, with an accuracy of ±0.1 m/s. To minimize the influence of airflow fluctuations, the wind speed is stabilized for 3 s before each measurement, after which image acquisition is performed to ensure quasi-steady flow conditions.

To systematically describe the spatial arrangement of the experimental setup, an o-xyz coordinate system is established, as shown in Figure 3b. The origin (o) is defined at the contact point between the sleeve fixture and the leaf. The negative x-axis corresponds to the direction of airflow, the y-axis is aligned with the force sensor, and the z-axis is determined according to the right-hand rule.

The force measurement system consists of a sleeve fixture, leaf samples, a force sensor, and a flat-jaw clamp, as illustrated in Figure 3b. Prior to each experiment, the leaf sample was trimmed with a leaf to retain a stalk length of 10–15 mm from the leaf base. The remaining leaf stalk was securely clamped at one end of the sleeve fixture, while the opposite end was connected to the force sensor. The force sensor was mounted above the wind tunnel test section using the flat-jaw clamp. During testing, the leaf surface was oriented toward the airflow direction (negative x-axis), and the leaf stalk was firmly fixed to ensure that only the leaf lamina was free to deform under the influence of the airflow.

The image acquisition system comprises a high-speed camera (model: SH 6~109, DeepVision Intelligent Technology Co., Ltd., Shenzhen, China), an LED light source (JINBEI EFII 200W), and a laptop computer. The high-speed camera is mounted along the z-axis to capture the side view of the leaf, and a background panel is used for image calibration. To avoid obstruction and reflection, the LED light source is positioned at an appropriate angle relative to the camera, with both the intensity and direction of the illumination carefully adjusted to optimize image quality. The camera is set to a frame rate of 120 fps with a resolution of 512 × 288 pixels, enabling dynamic recording of the leaf deformation process under different wind speeds. This setup allows for visual analysis of the aerodynamic response of the leaf across varying wind conditions and provides foundational data for subsequent analysis of the mechanical properties of local leaf regions.

3. Results and Discussion

3.1. Aerodynamic Response of Crop Leaves

To investigate the adaptive mechanisms and wind resistance of different leaf types in response to wind disturbances, and to provide data support for subsequent studies on droplet deposition and distribution on leaf surfaces during air-assisted spraying, this study conducted aerodynamic response tests on leaves using a wind tunnel system. Although the airflow velocity at the fan outlet in field air-assisted spraying operations can often exceed 30 m/s, the actual airflow velocity acting on crop leaves is typically reduced to a range of 2 to 12 m/s due to distance and canopy obstruction effects [25,26,27]. Therefore, the wind speed range in this study was set at 0 to 12 m/s to accurately reflect the wind conditions experienced by crop leaves during field spraying operations.

Figure 4 presents the aerodynamic response of three types of plant leaves under different wind speeds, specifically walnut leaves, peach leaves, and chili pepper leaves. Each row displays a different leaf type: walnut leaves (a–e), peach leaves (f–j), and chili pepper leaves (k–o). Each column corresponds to one of five wind speeds: 0 m/s, 3 m/s, 6 m/s, 9 m/s, and 12 m/s. The superimposed leaf contours are used to visually illustrate the differences in deformation amplitude and patterns among the three crop leaves under the same wind load. The experimental results indicate that all three leaf types exhibit significant bending deformation and vibrational responses across varying wind speeds. Previous studies [16,28,29] have also shown that plant leaves often adjust their structure through active reconfiguration mechanisms such as overall bending, periodic vibration, and local curling when subjected to wind loads. These adaptive responses help disperse wind forces and reduce the risk of damage. The findings from these studies highlight the importance of leaf morphological restructuring in enhancing crop wind resistance. Accordingly, this study further investigates the mechanisms of bending deformation and the mechanical differences among the three leaf types under wind loading.

As shown in Figure 4, each crop leaf demonstrates a characteristic pattern of mechanical behavior and aerodynamic response under wind loads, which directly influences its performance in air-assisted spraying. Walnut leaves maintain structural stability even at high wind speeds (up to 12 m/s), with deformation primarily involving moderate bending and spatial twisting. This stability allows them to preserve a consistent orientation in the airflow, supporting steady droplet interception. Peach leaves exhibit nonlinear bending and localized curling beginning at moderate wind speeds (6–9 m/s), progressing to complex posture changes at higher speeds; these motions can cause frequent shifts in local wind-facing angles, reducing the uniformity of droplet deposition. Pepper leaves, due to their high flexibility, display substantial deformation at low wind speeds, and may develop localized instabilities at higher speeds, increasing the potential for droplet loss from the surface. The observed behaviors are strongly influenced by each leaf’s geometry and local vein stiffness, and together define the droplet deposition efficiency and distribution pattern achievable under air-assisted spraying.

3.2. Distribution of Leaf Curvature

The experimental results of Moulia et al. [22] indicate that the leaf midrib plays a dominant role in the overall bending response, with its structural stiffness contributing more than 80 percent of the total leaf stiffness. To quantify the curvature distribution across different regions of the leaf, this study uses the bending behavior of the midrib to represent the deformation characteristics of the entire leaf. Figure 5 demonstrates the procedure for determining the curvature of walnut leaves at a wind speed of 12 m/s. First, the experimental images were digitized using Engauge Digitizer 4.1 software, as shown in Figure 5a. The midrib curve was traced with 50 to 70 digitized points, with the coordinate system and scale established based on the background plate. The measurement results are presented in Figure 5b. The coordinates of these digitized points were then imported into Origin software (Version 2022 SR1 b9.5.1.195, OriginLab Corporation, Northampton, MA, USA), where a high-order polynomial (typically of fifth order or higher) was fitted using the least squares method to obtain the fitting function f(x) that characterizes the shape of the leaf midrib, as shown in Figure 5c. It should be noted that f(x) has inherent limitations due to natural variability among individual leaves; each leaf’s centerline differs, leading to unique polynomial models. Therefore, f(x) serves as an approximate representation of the curvature profile for each specific leaf rather than a universally applicable model for all leaves of the same species. To evaluate the accuracy of the fitted function, the agreement between the fitted curve (red line in Figure 5d) and the original data points (blue line in Figure 5d) was compared, providing a visual demonstration of how well different orders of polynomial functions describe the complex deformation characteristics of the leaf.

Based on the differential geometry of planar curves, the local curvature κ(i) at each position along the leaf is calculated using the polynomial fitting function f(x) obtained from the leaf centerline, as follows:

$$\kappa \left(i\right)={\displaystyle \frac{\left|d^{2}f(x_i)/d{x}^2\right|}{{\left\{1+{\left[df(x_i)/dx\right]}^2\right\}}^{3/2}}}$$

(2)

where f(x_i) is the function value at the i-th point on the leaf midrib, x_i is the x-coordinate of the i-th point, and κ(i) (mm⁻¹) is the curvature at the i-th point on the leaf midrib.

The curvature results at different positions along the midrib of walnut leaves under various wind speeds were calculated using Equation (2), as shown in Figure 6. The y-axis represents both the vertical coordinates of the digitized points along the midrib and the corresponding curvature values, while the x-axis represents the horizontal coordinates of these points. The function f(x) denotes the fitted curve for the midrib.

As shown in Figure 6a,b, at low wind speeds (≤6 m/s), the leaves predominantly display smooth, overall bending, characterized by few curvature extrema and relatively small amplitude values. This indicates that deformation at this stage is largely compliant and uniform. As wind speed increases to 9–12 m/s (Figure 6c,d), the amplitude of local deformation rises markedly, and the curvature distribution evolves from a few peaks to a multi-peak pattern, with certain regions exhibiting pronounced curvature extremes. These features reflect a clear shift toward localized severe bending, suggesting more pronounced nonlinear deformation and the formation of stress concentration zones that may trigger local instability or complex vibration. Similar trends are observed for peach and chili pepper leaves (Figure 7), where the number of curvature extrema progressively increases with wind speed.

Further analysis showed that at low wind speeds (≤6 m/s), bending deformation in all three leaf types was concentrated mainly near the leaf base. As wind speed increased, however, curvature at the leaf tip rose sharply, becoming the primary deformation region. For walnut leaves, tip curvature increased from approximately 0.004 mm⁻¹ at low wind speeds to over 0.04 mm⁻¹ at high wind speeds—a nearly tenfold rise. Peach and chili pepper leaves also exhibited significant tip curvature growth, increasing by about twofold and more than threefold, respectively. These results indicate a clear shift in the dominant bending region from the leaf base toward the tip as wind speed rises. While earlier studies have observed similar aerodynamic response trends, the underlying mechanism of this transition has yet to be explicitly clarified.

Specifically, Shao et al. [28] found that at low Reynolds numbers (Re ≤ 3.4 × 10⁴), the petiole of the plane tree leaf bends, causing the base of the leaf to curl and adopt a stable posture. At high Reynolds numbers (Re ≥ 9.0 × 10⁴), the vibration of the leaf tip becomes dominant, with its amplitude far exceeding that of the base. Jiang et al. [29] demonstrated that at low Cauchy numbers (≤1.76), birch leaves primarily exhibit static bending of the petiole and base. However, at high Cauchy numbers (≥12.40), the leaf tip experiences high-frequency vibrations with further increased amplitude. Zhang et al. [16] reported that pear leaves show increasing petiole bending as wind speed increases below the first critical wind speed (2.5–3.5 m/s), with the base serving as the primary deformation region. Once the wind speed surpasses the second critical value (3.0–5.0 m/s), high-frequency vibrations at the leaf tip intensify significantly, and displacement changes far exceed those at the base. While previous studies have primarily focused on the aerodynamic properties of the whole leaf—such as drag coefficients and vortex-induced vibrations—this study emphasizes the deformation characteristics of local leaf regions. By quantifying curvature distribution, it further reveals the process by which the primary deformation region of the leaf shifts with wind speed, providing quantitative evidence that supplements the qualitative descriptions in the existing literature.

In summary, the response of leaves from different species to wind generally follows the pattern of predominantly basal deformation at low wind speeds and pronounced tip deformation at high wind speeds. This phenomenon can be attributed to the spatial variation in structural stiffness along the leaf. The base of the leaf, including the petiole and midrib, possesses a robust structure with high stiffness, allowing it to bear loads through stable deformation at lower wind speeds. In contrast, the tip region of the leaf has a finer structure and lower stiffness. As wind speed increases and aerodynamic loads exceed the deformation capacity of the base, the tip region becomes the primary deformation region, dissipating energy through large deflections to reduce the risk of overall structural damage.

Table 2. Curvature results for three leaf types.

Leaf Curvature	Walnut Leaf (mm−1)	Peach Leaf (mm−1)	Chili Pepper Leaf (mm−1)
Wind Speed Value
0 m/s	0~0.018	0~0.061	0~0.027
3 m/s	0~0.010	0~0.043	0~0.030
6 m/s	0~0.014	0~0.047	0.002~0.031
9 m/s	0.003~0.047	0~0.095	0.007~0.101
12 m/s	0.007~0.037

summarizes the curvature variations of the three types of leaves (walnut, peach, and chili pepper) under different wind speeds. The reported curvature ranges, from minimum to maximum values, reflect the local and overall bending behavior of each leaf type under varying wind loads.

As shown in Table 2, the curvature results reveal distinct differences in the response of each leaf type to airflow. Walnut leaves exhibit only a small range of curvature changes at wind speeds from 0 to 6 m/s, with maximum values not exceeding 0.018 mm⁻¹, resulting in a generally gentle bending profile. As wind speed increases to 9 and 12 m/s, the maximum curvature values rise to 0.047 mm⁻¹ and 0.037 mm⁻¹, respectively, indicating that local bending in walnut leaves intensifies at wind speeds above 6 m/s. Peach leaves display strong bending characteristics, with an initial maximum curvature of 0.061 mm⁻¹ at 0 m/s. The curvature remains relatively stable below 6 m/s, but increases markedly to 0.095 mm⁻¹ at 9 m/s, suggesting that peach leaves are also prone to severe local bending above 6 m/s. At the highest wind speed tested (12 m/s), peach leaves show structural instability and severe deformation, making valid curvature measurements difficult to obtain. Chili pepper leaves show minimal curvature changes within the 0 to 6 m/s range, with a maximum value of only 0.031 mm⁻¹, indicating mild structural deformation. However, as wind speed rises to 9 m/s, the maximum curvature value surges to 0.101 mm⁻¹, demonstrating pronounced deformation, curling, and even instability.

Overall, as wind speed increased from 6 m/s to 9 m/s, the maximum curvature of all three leaf types showed a marked rise. For both walnut and chili pepper leaves, the curvature increased by more than two times, while for peach leaves, the increase was nearly twofold. This pattern indicates a transition of the primary deformation region from the base to the tip of the leaf. Accordingly, this study defines the 6–9 m/s range as the critical wind speed interval for the transition of the primary deformation region. Although the exact critical wind speed varies slightly among leaf types, within this interval, the primary deformation region generally shifts from the leaf base to the tip.

3.3. Distribution of Leaf Flexibility

The curvature distribution of the leaf reveals the actual deformation process under wind load. As bending stiffness is a key parameter influencing leaf reconfiguration [30], this study utilizes local flexibility to investigate the structural role of each segment in the overall bending response. The leaf midrib is simplified as a segmented, non-uniform flexible beam, and its mechanical properties are evaluated using a local flexibility analysis approach. Flexibility analysis is conducted at lower wind speeds (≤6 m/s), as the leaf margin remains intact within this range, allowing for accurate wind load calculation and minimizing the effects of instability or severe twisting, making the structure suitable for analysis. The bending morphologies of leaves at different wind speeds (0, 3, and 6 m/s) are obtained through image acquisition and digital processing, as shown in Figure 8a. Several digital feature points are selected at equal intervals along the length of the leaf midrib, which is then divided into multiple segments to accurately capture the leaf’s deformation state, as shown in Figure 8b. The spatial position of each segment is determined by the endpoint coordinates (x_i, y_i), the arc length is calculated using adjacent endpoints, and the angle α_i between the segment and the horizontal direction is determined through trigonometric relationships.

$$\sin {\alpha }_i={\displaystyle \frac{\left(\left|y_i-y_{i-1}\right|\right)}{l_i}}$$

(3)

where l_i (mm) is the chord length corresponding to the arc of the i-th segment of the leaf, x_i and y_i (mm) are the horizontal and vertical coordinates, respectively, of the endpoint of the i-th segment; x_i−1 and y_i−1 (mm) are the horizontal and vertical coordinates of the endpoint of the (i − 1)-th segment, and α_i is the angle between the chord of the i-th segment and the wind direction (x-axis).

The wind loads acting on the leaf model are considered as uniformly distributed loads, denoted by q, on the windward surface of the leaf, as illustrated in Figure 8c. Due to the spatial orientation and deformation of the leaf centerline, the wind force on each segment must be adjusted according to its instantaneous wind angle. Therefore, after dividing the leaf centerline into multiple segments, the actual normal wind load F(i) acting on the i-th segment can be expressed as follows:

$$F\left(i\right)=q·A_i·\sin {\alpha }_i$$

(4)

where F(i) (mN) is the normal force acting on the i-th segment, q (mN/mm²) is the distributed load per unit area on the leaf surface, and A_i (mm²) is the windward area corresponding to the i-th segment of the leaf midrib.

The leaf area A_i corresponding to the i-th segment is determined using ImageJ software, as shown in Figure 8d. To ensure that the total force on all leaf segments matches the total wind load F_d measured by the force sensor, it is necessary to normalize and correct the distributed load q. The theoretical wind loads for all segments are summed to obtain the total theoretical wind load, and the actual distributed load q is then calculated by using the total wind load measured by the force sensor (ZF350-1AA-W, ZEMIC, Hanzhong, China). This process can be described as follows:

$$q={\displaystyle \frac{F_d}{A}}={\displaystyle \frac{F_d}{{\displaystyle \sum _{i=1}^n\left(A_i·\sin {\alpha }_i\right)}}}$$

(5)

where F_d (mN) represents the total wind load acting on the leaf, A (mm²) is the total leaf area, and n is the number of segments into which the leaf is divided.

To determine the stress state of each segment of the leaf midrib under wind load, it is necessary to calculate the bending moment of each segment relative to the fixed end of the leaf. For any given segment, the total bending moment Mz(i) on its cross section is obtained by summing the products of the wind forces acting on all segments from the tip up to that segment and their respective lever arms. The lever arm for each segment is calculated using the spatial coordinates of the segment endpoints. The specific expression is as follows:

$$Mz\left(i\right)={\displaystyle \sum _{j=i+1}^n{F}_j·\left[\left(\frac{y_j+y_{j-1}}{2}\right)-\left(\frac{y_{j-1}+y_{j-2}}{2}\right)\right]}$$

(6)

It is important to note that due to the natural curvature of the leaf, the initial curvature is not zero prior to bending deformation. Therefore, flexibility is characterized by the change in curvature, Δκ(i), for each segment of the leaf’s midrib before and after deformation, based on the local curvature change under a unit bending moment. In this context, the flexibility of the i-th segment can be expressed as follows:

$$S\left(i\right)={\displaystyle \frac{\Delta \kappa \left(i\right)}{Mz\left(i\right)}}$$

(7)

where S(i) (N⁻¹·mm⁻²) is the flexibility of the i-th segment of the leaf, Δκ(i) (mm⁻¹) is the change in curvature of the i-th segment before and after deformation, and Mz(i) (N·mm) is the bending moment acting on the i-th segment.

Flexibility S(i) characterizes the deformation capability of a local segment of the leaf. Greater flexibility indicates a reduced ability of that segment to resist external disturbances, making it more susceptible to deformation. Figure 9 presents the curvature changes Δκ(i), bending moment distribution Mz(i), and flexibility S(i) response at different positions along the walnut leaf midrib at wind speeds of 3 m/s and 6 m/s. By normalizing the midrib coordinates ξ_i (with 0 representing the leaf base and 1 representing the leaf tip), the structural performance of different local positions along the midrib can be directly compared.

As shown in Figure 9a, under both wind speeds, the base of the walnut leaf (ξ_i = 0) experiences the highest bending moment but exhibits the smallest curvature change, indicating high stiffness and strong resistance to bending, which enables it to effectively withstand wind-induced disturbances. As the position shifts from the base toward the tip of the leaf (ξ_i = 1), the bending moment gradually decreases, while the amplitude of curvature fluctuations increases. Notably, curvature changes in the leaf tip region often show negative values (Δκ < 0), indicating that this area is more sensitive to external disturbances and prone to reverse curling or flattening under wind loads. These features are similar to the mechanical adaptation mechanisms observed in Calliarthron algae under fluid loading (such as waves). Martone et al. [31,32] reported that Calliarthron algae reduce resistance by bending in water flow, with the basal joint bearing most of the load and therefore exhibiting higher stiffness to minimize stress concentration, while the distal joint, supporting less load, has lower stiffness. This illustrates that plant leaves adopt a structural gradient—rigid at the base and flexible at the tip—to effectively distribute loads, reduce fluid resistance, enhance overall stability, and minimize the risk of mechanical damage [33,34,35].

As shown in Figure 9b, the flexibility distribution of walnut leaves under both wind speeds exhibits a similar pattern, with local peaks appearing in the middle (ξ_i ≈ 0.4) and tip (ξ_i ≈ 0.8) regions. In particular, flexibility at the leaf tip is markedly higher than in other segments, indicating that these regions are the most sensitive to wind-induced disturbances. At the leaf base (ξ_i = 0), flexibility values are extremely low, making significant deformation unlikely even under substantial bending moments. This spatial distribution of flexibility closely aligns with the regions of maximal curvature change, further confirming that flexibility is an effective mechanical indicator for evaluating the deformation capacity and structural response sensitivity of local leaf segments. The flexibility calculation results for peach tree leaves and chili pepper leaves are presented in Figure 10.

As shown in Figure 9b and Figure 10, all three types of leaves exhibit a spatial gradient in flexibility, characterized by high rigidity at the base and high flexibility at the tip. However, notable differences exist in the overall flexibility levels and the specific regions that are most sensitive. Specifically, walnut leaves (Figure 9b) have the lowest overall flexibility, with local peaks observed only in the middle (ξ_i ≈ 0.4) and at the tip (ξ_i ≈ 0.8), where flexibility in the tip region exceeds 1.5 × 10⁻⁵ mm⁻²·mN⁻¹. Peach tree leaves (Figure 10a) display higher overall flexibility than walnut leaves, with a multi-peak distribution—most notably at ξ_i ≈ 0.5 and ξ_i ≈ 0.8—with tip flexibility exceeding 4 × 10⁻⁴ mm⁻²·mN⁻¹. Chili pepper leaves (Figure 10b) show the highest flexibility peak, with the tip region (ξ_i ≈ 0.8) sharply increasing to over 5.6 × 10⁻⁴ mm⁻²·mN⁻¹. Overall, walnut leaves possess a more rigid structure and exhibit greater wind resistance, while peach tree leaves and chili pepper leaves are more sensitive to wind loads and more prone to local deformation. This is especially evident at high wind speeds, where severe bending and instability are most likely to occur.

Combined analysis of curvature and flexibility demonstrates that the leaf tip is an “active zone” for deformation, where pesticide droplets are prone to accumulate in significant quantities [36]. Wang et al. [37] further confirmed that leaf elasticity is a critical factor influencing the preferential deposition of pesticides at the leaf tip. When the elasticity coefficient of the leaf is less than 5 N/m, pesticide deposition within 10 mm of the leaf tip increases markedly, reaching 1.55–1.58 times the average deposition on the entire leaf. This phenomenon is closely associated with the high flexibility and deformability of the leaf tip. A lower elasticity coefficient (i.e., higher flexibility) enables the leaf tip to absorb impact energy through self-deformation when struck by droplets, thereby reducing droplet rebound and fragmentation, and improving retention efficiency.

Notably, the curvature analysis conducted previously reveals that when the wind speed exceeds the critical value of 6 m/s, the primary deformation region of the three types of leaves generally shifts from the base to the tip. This critical wind speed not only signifies an abrupt transition in the aerodynamic response of the leaves, from a state of slow change to violent deformation, but also indicates that the tip region possesses high flexibility and the potential to retain pesticide droplets under moderate deformation. However, excessive deformation or instability of the leaf tip directly impairs the preference for droplet deposition and elevates the risk of pesticide loss. Therefore, to enhance the deposition and retention of pesticide droplets, it is advisable to keep the wind speed parameters during spraying below 6 m/s as much as possible. Within this range, leaf deformation, particularly at the tip, remains moderate, maintaining favorable flexibility to facilitate droplet deposition while avoiding pesticide loss caused by severe deformation.

4. Conclusions

This study used wind tunnel experiments with high-speed photography and image analysis to examine how the mechanical behavior of walnut, peach, and chili pepper leaves influences air-assisted pesticide application. Walnut leaves, with high bending stiffness, maintain integrity up to 12 m/s, providing a stable interception surface that supports coverage uniformity but may reduce canopy penetration. Peach leaves, with moderate flexibility, show nonlinear bending and curling at moderate wind speeds, causing posture changes that affect droplet deposition uniformity. Chili pepper leaves, being highly flexible, deform even at low wind speeds and may develop instabilities at higher speeds, increasing droplet loss.

The curvature distribution results show that with increasing wind speed, the deformation patterns of all three leaf types shift from smooth overall bending to multi-peak localized severe bending, with nonlinear deformation becoming increasingly prominent. Moreover, once wind speed exceeds 6 m/s, the primary moves markedly from the leaf base toward the tip. Specifically, the maximum curvature of walnut leaves rises from 0.018 mm⁻¹ to 0.047 mm⁻¹, peach leaves from 0.061 mm⁻¹ to 0.093 mm⁻¹, and chili pepper leaves from 0.031 mm⁻¹ to 0.101 mm⁻¹, all representing substantial increases over the initial values. Accordingly, this study identifies 6 m/s as the critical wind speed at which the primary deformation region of leaves transitions toward the tip.

The flexibility distribution analysis reveals that all three crop leaves exhibit a structural gradient of “high rigidity at the base and high flexibility at the tip.” For instance, the base of walnut leaves shows low flexibility (<0.03 mm⁻²·mN⁻¹), whereas the tip exceeds 1.5 × 10⁻⁵ mm⁻²·mN⁻¹; for peach and chili pepper leaves, tip flexibility reaches 4 × 10⁻⁴ and 5.6 × 10⁻⁴ mm⁻²·mN⁻¹, respectively. Moderate tip deformation promotes droplet deposition and retention, while excessive deformation reduces droplet adhesion and increases pesticide loss. Based on these findings, a spray wind speed of no more than 6 m/s is recommended to achieve moderate tip deformation—maintaining sufficient flexibility for effective deposition while avoiding losses caused by over-bending.