# 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

- Cui, E. Design and Research of the Qiaohua Orchard Operation Vehicle. Master’s Thesis, Northwest Agriculture and Forestry University of Science and Technology, Xianyang, China, 2018. [Google Scholar]
- Zhang, H.F.; Xu, L.Y. Current status and outlook of orchard sprayer development. China J. Agric. Chem.
**2014**, 35, 112–118. [Google Scholar] - Tu, J. Experimental Research on the Design and Optimization of Key Operational Parameters of Tower-Type Air-Fed Spraying System. Master’s Thesis, Chinese Academy of Agricultural Sciences, Beijing, China, 2020. [Google Scholar]
- Zhao, Y.; Xiao, H.; Mei, S.; Song, Z.Y.; Ding, W.Q.; Jing, Y.; Xia, X.; Yang, G. Current situation and development strategies of mechanized orchard production in China. J. China Agric. Univ.
**2017**, 22, 116–127. [Google Scholar] - Zhang, L.; Wang, J.; Ye, Y.; Yang, D.; Yuan, H.; Tian, H.; Xia, C. Preliminary observations on the attenuation of droplet deposition distribution on maize plants in high pole spraying technology: Public Plant Protection and Green Control. In Proceedings of the 2010 Annual Conference of the Chinese Society for Plant Protection, Hebi, China, 28–31 November 2010. [Google Scholar]
- Qin, W.; Xue, X.; Zhou, L.; Zhang, S.; Sun, Z.; Kong, W.; Wang, B. Influence of spray parameters of unmanned helicopters on the distribution of droplet deposition in maize canopies. J. Agric. Eng.
**2014**, 30, 50–56. [Google Scholar] - Gaskin, R.E.; Manktelow, D.W.; Cook, S.; May, W.A. Effects of canopy density on spray deposition in kiwifruit. N. Z. Plant Prot.
**2013**, 66, 194–198. [Google Scholar] [CrossRef][Green Version] - Zhu, Y.K.; Zheng, Y.M.; Wang, J.; Xiao, X.M.; Wang, K.Y. Effect of spraying method and spray volume on the deposition distribution of pirimicarb and acetamiprid in cotton fields and the control effect of cotton aphids. J. Insects
**2013**, 56, 530–536. [Google Scholar] - Kong, X.; Wang, G.; Ji, J.; Xu, D.; Yuan, H. Study on the distribution of droplet deposition and pesticide utilization rate of seven plant protection machines in maize field spraying: Green ecological sustainable development and plant protection. In Proceedings of the 12th National Members’ Congress and Annual Conference of the Chinese Society for Plant Protection, Changsha, China, 9–10 November 2017. [Google Scholar]
- Zhai, C.; Zhao, C.; Ning, W.; Long, J.; Wang, X.; Weckler, P.; Zhang, H. Research progress on precision control methods of air-assisted spraying in orchards. Trans. Chin. Soc. Agric. Eng.
**2018**, 34, 1–15. [Google Scholar] - Zhou, L.; Xue, X.; Zhou, L.; Zhang, L.; Ding, S.; Chang, C.; Zhang, X.; Chen, C. Research situation and progress analysis on orchard variable rate spraying technology. Trans. Chin. Soc. Agric. Eng.
**2017**, 33, 80–92. [Google Scholar] - Cross, J.V.; Walklate, P.J.; Murray, R.A.; Richardson, G.M. Spray deposits and losses in different sized apple trees from an axial fan orchard sprayer: 1. Effects of spray liquid flow rate. Crop Prot.
**2001**, 20, 13–30. [Google Scholar] [CrossRef] - Cross, J.V.; Walklate, P.J.; Murray, R.A.; Richardson, G.M. Spray deposits and losses in different sized apple trees from an axial fan orchard sprayer: 2. Effects of spray quality. Crop Prot.
**2001**, 20, 333–343. [Google Scholar] [CrossRef] - Cross, J.V.; Walklate, P.J.; Murray, R.A.; Richardson, G.M. Spray deposits and losses in different sized apple trees from an axial fan orchard sprayer: 3. Effects of air volumetric flow rate. Crop Prot.
**2003**, 22, 381–394. [Google Scholar] [CrossRef] - Xue, X.; Song, S.; Chen, J.; Hong, T.; Li, Z.; Dai, Q. Experimental study on spraying effectiveness and droplet penetration of a wide spraying width wind-driven sprayer in fruit tree canopies. Guangdong Agric. Sci.
**2014**, 41, 155–158. [Google Scholar] - Duga, A.T.; Ruysen, K.; Dekeyser, D.; Nuyttens, D.; Bylemans, D.; Nicolai, B.M.; Verboven, P. Spray deposition profiles in pome fruit trees: Effects of sprayer design, training system and tree canopy characteristics. Crop Prot.
**2015**, 67, 200–213. [Google Scholar] [CrossRef] - Sun, C.; Qiu, W.; Ding, W.; Gu, J. Parameter optimization and experiment of air-assisted spraying on pear trees. Trans. Chin. Soc. Agric. Eng.
**2015**, 31, 30–38. [Google Scholar] - Sun, C.; Liu, C. Construction and application of droplet canopy penetration model for air-assisted spraying pattern. Trans. Chin. Soc. Agric. Eng.
**2019**, 35, 25–32. [Google Scholar] - Miranda-Fuentes, A.; Rodríguez-Lizana, A.; Gil, E.; Agüera-Vega, J.; Gil-Ribes, J.A. Influence of liquid-volume and airflow rates on spray application quality and homogeneity in super-intensive olive tree canopies. Sci. Total Environ.
**2015**, 537, 250–259. [Google Scholar] [CrossRef] [PubMed] - Endalew, A.M.; Debaer, C.; Rutten, N.; Vercammen, J.; Delele, M.A.; Ramon, H.; Nicolaï, B.M.; Verboven, P. Modelling pesticide flow and deposition from air-assisted orchard spraying in orchards: A new integrated CFD approach. Agric. For. Meteorol.
**2010**, 150, 1383–1392. [Google Scholar] [CrossRef] - Hong, S.-W.; Zhao, L.; Zhu, H. CFD simulation of airflow inside tree canopies discharged from air-assisted sprayers. Comput. Electron. Agric.
**2018**, 149, 121–132. [Google Scholar] [CrossRef] - Chen, S.; Lan, Y.; Bradley, K.F.; Li, J.; Liu, A.; Mao, Y. Effect of Wind Field below Rotor on Distribution of Aerial Spraying Droplet Deposition by Using Multi-rotor UAV. Trans. Chin. Soc. Agric. Mach.
**2017**, 48, 105–113. [Google Scholar] - Salcedo, R.; Granell, R.; Palau, G.; Vallet, A.; Garcerá, C.; Chueca, P.; Moltó, E. Design and validation of a 2D CFD model of the airflow produced by an airblast sprayer during pesticide treatments of citrus. Comput. Electron. Agric.
**2015**, 116, 150–161. [Google Scholar] [CrossRef] - Wang, B. Study on Flow Field and Resistance Characteristics of Three-Dimensional Microscopic Canopy Structure. Master’s Thesis, Donghua University, Shanghai, China, 2016. [Google Scholar]
- Wu, S.; Pan, F. SPSS Statistical Analysis; Tsinghua University Press: Beijing, China, 2014. [Google Scholar]
- Wang, L. Multivariate Statistical Analysis: Model, Case and SPSS Application; Economic Science Press: Beijing, China, 2010. [Google Scholar]

**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