# Analysis of Movement Law and Influencing Factors of Hill-Drop Fertilizer Based on SPH Algorithm
## 4 Conclusions  
In the present paper, the SPH method and a 3D model were used to simulate fertilizer movement and analyze influencing factors. The method and model were shown by a field experiment to be of generally good accuracy and effect in simulating the fertilizer movement process. By using the method and the model, the movement process and deformation of the fertilizer in three directions of X, Y, and Z under the action of a hill-drop fertilizer device were analyzed. According to the simulation results, the following observations were made: (1) Along the planter's forward direction, the fertilizer displacement in the upper layer was larger, the fertilizer displacement in the lower layer was smaller, and the fertilizer displacement decreased from top to bottom; (2) In the vertical direction, the fertilizer overall moved downwards, and the falling displacement was close; (3) In the direction perpendicular to the planter's forward direction, the fertilizer located on both sides of the opener moved toward the opener, and the displacement was small.  
We then used the orthogonal simulation method to study the key factors affecting the overall deformation and displacement of the fertilizer, and used the range analysis method to analyze the simulation results of each index. The following conclusions were drawn: (1) The most important factors affecting the deformation coefficient in the vertical direction, the deformation coefficient in the forward direction, and the average point displacement were the forward speed of the planter, the cover depth, and the distance between the cover and the opener, respectively; (2) The optimal scheme was when the forward speed of the planter was 1.6 m/s, the cover depth was 100 mm, the distance between the cover and the opener was 140 mm, and the cover and the fertilizer pipe aligned from the center.  
Validated by a field experiment, the results demonstrate the following: (1) As the soil depth increased, the offset distance of the fertilizer decreased; (2) The offset distance was large along the planter's forward direction, and the offset distance perpendicular to the forward direction was small; (3) The distribution distance of the fertilizer was concentrated at 60 to 80 mm, which was lower than the theoretical distribution distance. Comparing the simulation results with the experiments, we concluded that although there were small differences between the fertilizer displacement calculated based on the SPH algorithm and the measuring results in the field experiment, they had the same variation trend. This means we can use this SPH method to analyze fertilizer movement law and influencing factors effectively.  
In conclusion, our work demonstrates that there are merits to using the SPH method to analyze movement law and influencing factors. These merits are as follows: (1) The SPH method avoids the misconvergence caused by mesh distortion and increases the accuracy of the simulation; (2) The orthogonal simulation method considerably reduces the number of experimental groups under different working parameters and provides a theoretical foundation for optimizing working parameters; (3) This work proves that the factors that affect the movement of fertilizer in soil can be studied by simulation rather than by real experiments. This avoids the laborious experimental process and substantially reduces work time and cost.  
**Author Contributions:** All authors contributed to the work. [PERSON] established the 3D model and performed the data analysis; [PERSON] guided the research work and designed the experiment; [PERSON], [PERSON], and [PERSON] performed the experiment; [PERSON] edited the paper; [PERSON], [PERSON], and [PERSON] proof-read the paper. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research work is supported by the National Key Technology Research and Development Program of China (No. 2015 BAD23B02).  
**Conflicts of Interest:** The authors declare no conflict of interest.