# Experimental Study of Disc Fertilizer Spreader Performance

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Theoretical Considerations

_{e}that ranges between 15–50 m·s

^{−1}with a maximum value that, in some case, can reach 70 m·s

^{−1}with higher speeds related to wider working widths [25]. The fertilizer particle eject speed is directly related (Figure 1) to the angular speed of the disc w

_{d}and to specific design factors of the spreader itself such as: (i) the disc radius r

_{d}; (ii) the fertilizer feed point radius r

_{0}; (iii) the angle between each vane and the corresponding radius (pitch angle β

_{0}) and (iv) the cone angle of the rotating disc.

_{e}and a smaller eject angle θ [25].

#### 2.2. Esperimental Tests

^{2}, consisted of an array of 176 collection trays, each measuring 0.5 m × 0.5 m × 0.15 m (length × width × height), arranged in 11 rows and 16 columns, separated from each other by 0.5 m (2 in Figure 2). The spreader (Sipma RN 410-Antek, Lublin, Poland) was located almost in the middle of the first row, 0.7 m from the right lower edge of the first tray in Column 9 (1 in Figure 2). The center of the rotating disc was taken as the origin from which the fertilizer range was measured.

^{3}) with a dosing outlet and a stirrer, a disc (diameter 0.43 m, concavity angle 6°) mounted 0.67 m from the ground, two electric motors (to drive the disc and the stirrer) and controls. The design allowed the parameters, such as the fertilizer feed point on the disc, the angular velocity of the disc and the pitch of the vanes, to be readily modified.

- n: number of testing field rows;
- m: number of testing field columns;
- ${m}_{ij}$: mass of fertilizer collected by tray at row i column j of testing field, kg;
- ${r}_{ij}$: distance between center of tray at row i column j of the testing field and center of disc, m.

^{2}was used to explain the variability of the dependent variable in the model. A multiple regression analysis with R version 4.0.2 software (R Foundation for Statistical Computing) was used to assess the relationships between the different variables.

- ${\left(\overline{R}\right)}_{ijklm}$: m-th result of calculations of the mean fertilizer spread radius for the i-th fertilizer, the j-th angular velocity of disc, the k-th point of fertilizer feed onto the disc and the l-th vane configuration, m;
- μ: general average of the population of fertilizer spread radius measurements, m;
- FT: main effect of the i-th fertilizer;
- DS: main effect of the j-th angular velocity of the disc;
- FP: main effect of the k-th fertilizer feed point on the disc;
- VC: main effect of the l-th vane configuration on the disc;
- Ij: interaction effect of the i-th fertilizer with the j-th angular velocity of the disc;
- ik: interaction effect of the i-th fertilizer with the k-th fertilizer feed point;
- il: interaction effect of the i-th fertilizer with the l-th vane configuration;
- jk: interaction effect of the j-th angular velocity of the disc with the k-th fertilizer feed point;
- jl: interaction effect of the j-th angular velocity of the disc with the l-th vane configuration;
- kl: interaction effect of the k-th fertilizer feed point with the l-th vane configuration;
- ${e}_{ijklm}$: random experimental error, m.

^{2}was used to explain the variability of the dependent variables by a constant model; T-Tukey confidence intervals were used to assess the significance of the differences in individual parameters. The relationships between the dependent variables (parameters of the average fertilizer distribution field) and independent variables were described by first-degree multiple regression equations. Model parameters were estimated using the least squares method [27]. Statistical verification of the model was carried out by the Fisher–Snedecor F test.

## 3. Results and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 4.**Spreading disc showing the location of the fertilizer feed points A and B: (

**a**) the L3 vane configuration; (

**b**) the L0 vane configuration.

Property | Fertilizer | ||
---|---|---|---|

Urea | CAN | AS | |

Bulk density (loose), $\mathrm{kg}\xb7{\mathrm{m}}^{3}$ | 758 | 1029 | 1018 |

Bulk density (sieved), $\mathrm{kg}\xb7{\mathrm{m}}^{3}$ | 789 | 1062 | 1104 |

Specific density, $\mathrm{kg}\xb7{\mathrm{m}}^{3}$ | 1340 | 1800 | 1780 |

Mass powdery fraction $\left(<1\xb7{10}^{-3}\text{}\mathrm{m}\right)$, % | 10.350 | 0.030 | 52.500 |

Median diameter ${d}_{50}$, ${10}^{-3}\text{}\mathrm{m}$ | 0.830 | 2.100 | 0.490 |

Variation | DoF | Sum of Squares | Mean of Squares | F Function Value | Pr > F |
---|---|---|---|---|---|

Model | 14 | 123.82 | 8.84 | 783.26 | <0.0001 |

Error | 57 | 0.64 | 0.01 | ||

Total | 71 | 124.46 | |||

${R}^{2}=0.9948$ | |||||

Average mean radius of fertilizer spread = 4.10 m | |||||

Standard Estimation Error = 0.103 m | |||||

Coefficient of Variation = 0.0248 | |||||

FT | 2 | 63.44 | 31.72 | 2809.03 | <0.0001 |

DS | 1 | 34.24 | 34.24 | 3032.2 | <0.0001 |

FP | 1 | 0.01 | 0.01 | 0.94 | 0.337 |

VC | 1 | 15.92 | 15.92 | 1409.65 | <0.0001 |

FT × DS | 2 | 6.16 | 3.08 | 272.55 | <0.0001 |

FT × FP | 2 | 0.05 | 0.025 | 2.16 | 0.1241 |

FT × VC | 2 | 3.02 | 1.51 | 133.76 | <0.0001 |

DS × FP | 1 | 0.05 | 0.05 | 4.21 | 0.0448 |

DS × VC | 1 | 0.89 | 0.89 | 79.54 | <0.0001 |

FP × VC | 1 | 0.05 | 0.05 | 4.12 | 0.0471 |

**Table 3.**T-Tukey’s multiple confidence intervals comparing the average mean radius of fertilizer spread.

Compared Averages for | Average Value | Number of Observations | Mean Square Error | Limit Value (α = 0.05) | Least Significant Difference |
---|---|---|---|---|---|

Fertilizer type (FT): Urea | 4.23 | 24 | 0.011 | 3.40 | 0.074 |

Fertilizer type (FT): CAN | 5.45 | 24 | 0.011 | 3.40 | |

Fertilizer type (FT): AS | 3.15 | 24 | 0.011 | 3.40 | |

angular velocity of disc (DS): 42 $\mathrm{rad}\xb7{\mathrm{s}}^{-1}$ | 3.59 | 36 | 0.011 | 2.83 | 0.05 |

angular velocity of disc (DS): 63 $\mathrm{rad}\xb7{\mathrm{s}}^{-1}$ | 4.97 | 36 | 0.011 | 2.83 | |

Fertilizer feed point (FP): A | 4.26 | 36 | 0.011 | 2.83 | 0.05 |

Fertilizer feed point (FP): B | 4.29 | 36 | 0.011 | 2.83 | |

Vane configuration (VC): L0 | 3.81 | 36 | 0.011 | 2.83 | 1.86 |

Vane configuration (VC): L3 | 4.75 | 36 | 0.011 | 2.83 |

**Table 4.**Model parameter assessment of the linear multiple regression of the mean radius of fertilizer spread.

Variation | Parameter | SE | F Function Value | Pr > F | Partial Correlations |
---|---|---|---|---|---|

Constant | 0.80798 | 0.47985 | 2.84 | 0.0969 | - |

VC | −0.03483 | 0.00352 | 98.1 | <0.0001 | 0.12789 |

DS | 0.00690 | 0.00047 | 211.01 | <0.0001 | 0.31543 |

SD | 1.65821 | 0.23382 | 50.29 | <0.0001 | 0.00421 |

DF | −0.04357 | 0.00221 | 389.04 | <0.0001 | 0.85308 |

**Table 5.**Analysis of variance for the linear multiple regression model of the relationship between the mean radius of fertilizer spread and the considered parameters.

Variation | DoF | Sum of Squares | Mean of Squares | F Function Value | Pr > F |
---|---|---|---|---|---|

Model | 4 | 113.59512 | 28.39878 | 175.02 | <0.0001 |

Error | 67 | 10.87144 | 0.16226 | ||

Total | 71 | 124.46656 | |||

${R}^{2}=0.9127$ | |||||

Coefficient of Variation = 0.0942 |

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**MDPI and ACS Style**

Przywara, A.; Santoro, F.; Kraszkiewicz, A.; Pecyna, A.; Pascuzzi, S.
Experimental Study of Disc Fertilizer Spreader Performance. *Agriculture* **2020**, *10*, 467.
https://doi.org/10.3390/agriculture10100467

**AMA Style**

Przywara A, Santoro F, Kraszkiewicz A, Pecyna A, Pascuzzi S.
Experimental Study of Disc Fertilizer Spreader Performance. *Agriculture*. 2020; 10(10):467.
https://doi.org/10.3390/agriculture10100467

**Chicago/Turabian Style**

Przywara, Artur, Francesco Santoro, Artur Kraszkiewicz, Anna Pecyna, and Simone Pascuzzi.
2020. "Experimental Study of Disc Fertilizer Spreader Performance" *Agriculture* 10, no. 10: 467.
https://doi.org/10.3390/agriculture10100467