# Droplet Penetration Model Based on Canopy Porosity for Spraying Applications

^{*}

## Abstract

**:**

^{2}) (0.9672) and the lowest root mean square error (RMSE) (5.56%). This paper provides information on optimising the spraying parameters, improving the pesticide utilisation rate, and selecting the optimum spraying conditions and application parameters.

## 1. Introduction

## 2. Determination of Canopy Porosity

#### 2.1. Point Cloud Data Acquisition

#### 2.2. Generating a Two-Dimensional Image Scatter

#### 2.3. Determination of Distance Thresholds

#### 2.4. Contour Detection and Filling

#### 2.5. Optical Porosity Calculations

_{total}is the area of the canopy (number of pixels); S is the projected area of the canopy (number of pixels).

## 3. Materials and Methods

#### 3.1. Test Set-Up

#### 3.2. Test Methods

#### 3.2.1. Canopy Laser Scanning

#### 3.2.2. Canopy Airflow Field Test

#### 3.2.3. Droplet Deposition Test

^{2}) for later analysis of droplet penetration and distribution patterns.

## 4. Results and Discussion

#### 4.1. Optical Porosity of the Test Trees

#### 4.2. Effect of Optical Porosity on Airflow

#### 4.3. Effect of Different Incoming Wind Speeds on Airflow Velocity

#### 4.4. Canopy Penetration Ratio of Droplets

^{2}; ${Q}_{i}$ is the average number of droplets per unit area at the collection point in layer i, mg/cm

^{2}.

^{2}) [23,24] as indicators to determine the fitting performance of the regression model. The RMSE represents the average prediction error, with lower values indicating a higher accuracy. The R

^{2}represents the model’s goodness of fit. It ranges from 0 to 1, with a larger R

^{2}indicating a better fit, as shown in Equations (6) and (7).

^{2}of 0.9672 and the smallest RMSE of 5.56%; therefore, the quadratic exponential regression model 7 is the optimum model for predicting the droplet penetration ratio. The coefficients of model 7 are listed in Table 3.

## 5. Conclusions

^{2}of 0.9672 and the smallest root mean square error RMSE of 5.56%.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 10.**Variation of relative wind speed with height at 0.1 m downwind of canopy of experimental tree 5.

**Figure 11.**The effects of the incoming wind speed V, optical porosity $\alpha $ and collection point depth S on the droplet penetration ratio P.

Canopy Information | Tree Number | ||||
---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | |

Tree Height/m | 1.391 | 1.386 | 1.419 | 1.439 | 1.423 |

Canopy height/m | 0.919 | 0.887 | 0.876 | 0.908 | 0.893 |

Crown width/m | 0.909 | 0.906 | 0.925 | 0.935 | 0.928 |

Maximum canopy thickness/m | 0.884 | 0.872 | 0.896 | 0.888 | 0.884 |

Optical porosity | 0.40576 | 0.34138 | 0.23287 | 0.13637 | 0.06594 |

Function Type | Model Number | Expressions | R^{2} | RMSE/% |
---|---|---|---|---|

First-order polynomial | 1 | ${a}_{1}V+{b}_{1}\alpha -{c}_{1}S+{d}_{1}$ | 0.7889 | 15.17 |

2 | $\frac{({a}_{1}V+{b}_{1})({a}_{2}\alpha +{b}_{2})}{{a}_{3}S+{b}_{3}}$ | / | / | |

Quadratic polynomial | 3 | ${a}_{1}{V}^{2}+{b}_{1}V+{a}_{2}{\alpha}^{2}+{b}_{2}\alpha -{a}_{3}{S}^{2}-{b}_{3}S+c$ | 0.7898 | 15.14 |

First-order exponential | 4 | $A{e}^{-\frac{1}{{a}_{1}V+{b}_{1}\alpha -{c}_{1}S}}$ | 0.9197 | 6.54 |

5 | $A{e}^{-\frac{{a}_{3}S+{b}_{3}}{({a}_{1}V+{b}_{1})({a}_{2}\alpha +{b}_{2})}}$ | 0.9466 | 6.08 | |

Second-order exponential | 6 | $A{e}^{-\frac{1}{{a}_{1}{V}^{2}+{b}_{1}V+{a}_{2}{\alpha}^{2}+{b}_{2}\alpha -{a}_{3}{S}^{2}-{b}_{3}S}}$ | 0.9271 | 6.52 |

7 | $A{e}^{-\frac{{a}_{3}{S}^{2}+{b}_{3}S+{c}_{3}}{({a}_{1}V+{b}_{1})({a}_{2}\alpha +{b}_{2})}}$ | 0.9672 | 5.56 |

^{2}is the coefficient of determination; RMSE is the root mean square error, %; the other letters are coefficients.

A | a1 | b1 | a2 | b2 | a3 | b3 | c3 |
---|---|---|---|---|---|---|---|

30.874 | 0.057 | 9.622 | 0.351 | 3.262 | 0.023 | 113.038 | 65.979 |

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**MDPI and ACS Style**

Ru, Y.; Hu, C.; Chen, X.; Yang, F.; Zhang, C.; Li, J.; Fang, S.
Droplet Penetration Model Based on Canopy Porosity for Spraying Applications. *Agriculture* **2023**, *13*, 339.
https://doi.org/10.3390/agriculture13020339

**AMA Style**

Ru Y, Hu C, Chen X, Yang F, Zhang C, Li J, Fang S.
Droplet Penetration Model Based on Canopy Porosity for Spraying Applications. *Agriculture*. 2023; 13(2):339.
https://doi.org/10.3390/agriculture13020339

**Chicago/Turabian Style**

Ru, Yu, Chenming Hu, Xuyang Chen, Fengbo Yang, Chao Zhang, Jianping Li, and Shuping Fang.
2023. "Droplet Penetration Model Based on Canopy Porosity for Spraying Applications" *Agriculture* 13, no. 2: 339.
https://doi.org/10.3390/agriculture13020339