# Analysis of Movement Law and Influencing Factors of Hill-Drop Fertilizer Based on SPH Algorithm
## 2 Methodology
### Fertilizer Motion Simulation
The start time was set when the opener touched the soil, and the simulation ended when it left the soil completely. The fertilizer movement in the three directions of X, Y, and Z is shown in Figure 2. Figure 2a,d,g shows state diagrams when the time was 0.35 s. The hill-drop fertilizer device started to contact the fertilizer. Figure 2b,e,h shows state diagrams when the time was 0.60 s. The soil was damaged by shearing and squeezing from the opener and cover, which caused large disturbance. The fertilizer was displaced by gravity and the surrounding soil. Figure 2c,f,i shows state diagrams when the time was 0.85 s. With the increase of time, the contact between the opener and soil increased, and the disturbance range of the fertilizer and soil became larger, and the deformation degree of the fertilizer increased. In order to visualize the overall displacement and deformation of the fertilizer, 24 points on the four vertical edges of the fertilizer cube were taken for tracking analysis. The height of the fertilizer cube in the vertical direction was 100 mm, and the length in the forward direction was 40 mm before covering with soil. As shown in Figure 3, a schematic diagram of the overall fertilizer deformation based on the simulation results was drawn. In Figure 3a, the fertilizer state is shown before covering with soil. In Figure 3b, the fertilizer state is shown after covering with soil. In Figure 3, \(\widehat{GA}\) is the planter's forward direction, \(\widehat{FA}\) is the vertical direction, and \(\widehat{MA}\) is perpendicular to the planter's forward direction. Through LS-PREPOST's tracking function of particles, 12 points of two vertical edges (AF and MR) of the fertilizer cube were tracked and shown to study the movement and displacement of fertilizer results. Figure 4 shows the movement process of fertilizer in the three directions of X, Y, and Z from the top to the bottom (A-F) on the right side of the opener. Because the simulation results on the left and right sides of the opener are similar, Figure 5 only shows the results of fertilizer displacement from the top to the bottom (M-R) on the left side of the opener. The soil and fertilizer were disturbed and displaced during the process of fertilization. The displacement and deformation of the fertilizer were important indexes for evaluating the effect and quality of fertilization. Based on the movement process and the displacement results of fertilizer, the following could be concluded:  
1. The time of displacement change was short, and it remained stable 0.3 s after the start of disturbance. The main reason was that under the limitation of the cover, the soil discharged by the opener cannot continue to move to both sides. The opener accelerated the soil backflow and shortened the time of fertilizer movement;
2. In 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 trend of fertilizer displacement was decreasing from top to bottom. The main reason was that the cover increased the disturbance of the upper soil;
3. In the vertical direction, all of the fertilizer moved downward, and the falling displacement was close. It is mainly affected by gravity, which caused the fertilizer to move downwards;
4. In the direction perpendicular to the planter's forward direction, the direction of fertilizer displacement on both sides of the opener was opposite, and it all moved toward the opener with smaller displacement. It was mainly squeezed by the surrounding soil and moved towards the ditch. Figure 4: A–F movement process: **(a)** in the X direction; **(b)** in the Y direction; and **(c)** in the Z direction.