# Predicting Field Efficiency of Round-Baling Operations in High-Yielding Biomass Crops

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

- C
_{m}= material capacity sometimes referred to as throughput, Mg/h - v = field speed, km/h
- W = implement working width, m
- E
_{f}= field efficiency, decimal - Y = unit yield of the field, Mg/ha
- K
_{1}= 10 km-m/ha.

_{f}, ha/h) or of material processed per unit time (C

_{m}, Mg/h), and these two capacities are related by the following:

_{m}) of the machine; these are capacity-limited machines. For a given C

_{m}, W, and Y, Equation (1) can be used to find the allowable or effective travel speed.

_{mx}) is introduced into the machine. The yield (Y

_{c}) at which the maximum throughput is achieved can be expressed as:

_{mx}= 30.8 Mg/h) is reached.

_{f}, ha/h) and is a product of the processing width and effective speed of the machine. Since width and speed are easily measured, field capacity measurements are not complex. For forage machines, such as mowers, rakes, mower-conditioners, or windrowers, the material handling capacity may not be as critical and only the field capacity is measured. The key issue is to better understand the machine’s maximum throughput limits. Maximum throughput has not been advertised by the manufacturers because the value is impacted by crop characteristics and operator skill, however this value is a critical parameter to properly assess machine performance in high-yield conditions [6].

_{mx}) that can be accommodated on a sustained basis. This typically is a design limitation of the machine. For example, the feed mechanism of a chopper is adjusted so that it is sequenced with the forward speed. Forage harvester throughput is the product of mass processed per unit travel distance (for example, kg/m) times the forward speed of the harvester (km/h). The product of these two parameters then gives capacity in kg/h. The mass per unit distance can be measured before the material enters the harvester or as it leaves. One method uses the crop yield and effective machine width to obtain an estimate of the feed rate into the machine per unit of forward travel. With the second method, the processed material is caught in a container for a given travel distance and then weighed. Feed rate can be determined for a baler by measuring the average time required to produce a bale and weighing to determine the mass in an average bale [11]. When the machine operates in a field with a high yield, the field capacity (ha/h) decreases because of a reduction in field efficiency (more bales dropped per unit area), and because the operator is reducing the forward speed to limit the amount of material flowing through the machine. If the equipment is operating at maximum throughput (C

_{mx}) in a field with yield (Y), the effective travel speed with an operating width (W), is given by:

_{e}= the effective field speed, including a consideration of field efficiency, km/h.

#### Impact of Higher Yield on Round Balers

_{m}) is impacted by how the baler is operated. This factor is not addressed here. The time to form a bale and the time to wrap/eject the bale can be easily measured. The achieved field capacity (C

_{fa}) is given by:

- B
_{m}/C_{m}= the time to form a bale, h - t
_{w}= time to wrap/eject a bale, s - K
_{2}= 3600 s/h.

_{m}), with wrap/eject time, can be used to calculate an “achieved” capacity:

_{s}= E

_{f}× E

_{e}) can be represented by 2 terms, E

_{f}dealing with the productivity issues and E

_{e}representing the wrap/eject process, Equation (6) can be rewritten as:

_{e}, the wrap/eject efficiency, is given by:

_{m}, with v, W, and E

_{f}) that are typically used in machinery management and cost models. The new functions that are required for round bales is the time to wrap/eject per bale (t

_{w}), the mass of an average bale (B

_{m}), and the yield (Y). The yield can be an average for a given field or the annual average for all fields harvested, thus it is a known input to the model. While the two efficiencies could remain together, one component is a function of yield and may reinforce that additional modelling consideration is warrantied especially when yields are high.

## 3. Results

#### 3.1. Example Use of Relationships

_{f}) of 74%. The baler has a maximum throughput of 30.8 Mg/h, thus the critical yield at the transition (Y

_{c}) is 5.6 Mg/ha. The baler creates bales with a mass (B

_{m}) of 0.51 Mg and the time (t

_{w}) to wrap/eject a bale is 32 s. When field data is added in Figure 3, the curves show the impact of both the maximum throughput restriction and bale warp/eject time (Figure 4). Grisso et al. [3] provide measured field performance data, and this is shown in Figure 4 for comparison.

#### 3.2. Impact on Cost Calculations

_{mx}at 71 Mg/h, and 75% effective field efficiency. The round bales weighed 0.52 Mg and took (t

_{w}) 31 s to wrap/eject.

_{mx}).

## 4. Summary and Conclusions

_{mx}) on baler field efficiency and field capacity (ha/h). The assumption used in most prior biomass harvest modeling studies that capacity is negligibly impacted by yield is incorrect. Subsequently the number of machines required and the cost of round baler operations has often been underestimated. Impacts are shown for the round baler since a wrap/eject time is required for this baler. Relationships for the bale wrap/eject times were developed. In the round baler example, the impact of wrap/eject time was a 50% reduction in capacity. After the maximum throughput is reached, the cost of the round-baler operation (3.23 USD/Mg) is double that of the large-square-baler operation (1.63 USD/Mg). The round baler achieved throughput capacity is 50% less (32.7 Mg/h compared to 71.0 Mg/h) than the large-square baler.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Results obtained by assuming that speed and capacity are constant for all yields. Equations (1), (2) and (4) are used assuming operating parameters: W = 6.7 m, v = 10.9 km/h, E

_{f}= 0.74, and Y

_{c}= 5.6 Mg/ha.

**Figure 2.**The impact of maximum throughput, showing how achieved field capacity and speed decrease as yield increases. Equations (1), (2) and (4) are used and assumed operating conditions are: W = 6.7 m, v = 10.9 km/h, E

_{f}= 0.74, C

_{mx}= 30.8 Mg/h, Y

_{c}= 5.6 Mg/ha.

**Figure 3.**Impact of bale wrap/eject time on achieved field capacity, speed, and achieved throughput. Using Equations (1), (2), (4) and (6) and assuming operating conditions of: W = 6.7 m, v = 10.9 km/h, E

_{f}= 0.74, C

_{mx}= 30.8 Mg/h, Y

_{c}= 5.6 Mg/ha, B

_{m}= 0.52 Mg, and t

_{w}= 32 s.

**Figure 4.**Data from field observations [3] compared with Equations (1), (2), (4) and (6) and assuming operating conditions of: W = 6.7 m, v = 10.9 km/h, E

_{f}= 0.74, C

_{mx}= 30.8 Mg/h, Y

_{c}= 5.6 Mg/ha, B

_{m}= 0.52 Mg, and t

_{w}= 32 s.

**Figure 5.**Number of round balers required to supply a 3000 Mg/day biorefinery. The solid red line is the theoretical throughput capacity of the baler and the dashed line is the baler-achieved throughput after adjustment for the bale wrap/eject time.

**Figure 6.**The impact of the number of large-square balers required to supply a 3000 Mg/day biorefinery. The solid red line is the theoretical capacity of the baler (no consideration of design maximum throughput) and the dashed line is the baler-achieved throughput after accounting for throughput restrictions.

**Figure 7.**The cost per Mg to operate the square and round balers for annual use of 1200 h. The solid red line is the theoretical capacity of the baler and the dashed line is the baler-achieved throughput after accounting for throughput restrictions.

**Table 1.**Machinery cost factors for the balers using the notation and definitions given in ASABE Standard [10].

Cost Factors | Round | Large-Square |
---|---|---|

Purchase price (USD) | 45,000 | 112,000 |

Design life (h) | 1500 | 3000 |

Interest rate (%) | 8% | 8% |

Tax rate: | 1.00% | 1.00% |

Housing: | 0.75% | 0.75% |

RF_{1} | 0.43 | 0.1 |

RF_{2} | 1.8 | 1.8 |

Labor cost (including benefits) (USD/h) | 15 | 15 |

Salvage value | 10% | 10% |

**Table 2.**Cost factors for balers as a function of annual use. (n = number of useful yrs of design life).

Round Baler | Large-Square Baler | |||||
---|---|---|---|---|---|---|

h | n | USD/h | USD Annual | n | USD/h | USD Annual |

1200 | 1.3 | 105.37 | 126,445 | 2.5 | 116.06 | 139,271 |

960 | 1.6 | 106.02 | 101,781 | 3.1 | 117.68 | 112,973 |

720 | 2.1 | 107.11 | 77,118 | 4.2 | 120.38 | 86,676 |

480 | 3.1 | 109.28 | 52,454 | 6.3 | 125.79 | 60,379 |

240 | 6.3 | 115.80 | 27,791 | 12.5 | 142.01 | 34,081 |

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**MDPI and ACS Style**

Grisso, R.“.; Cundiff, J.S.; Webb, E.G.
Predicting Field Efficiency of Round-Baling Operations in High-Yielding Biomass Crops. *AgriEngineering* **2020**, *2*, 447-457.
https://doi.org/10.3390/agriengineering2030030

**AMA Style**

Grisso R“, Cundiff JS, Webb EG.
Predicting Field Efficiency of Round-Baling Operations in High-Yielding Biomass Crops. *AgriEngineering*. 2020; 2(3):447-457.
https://doi.org/10.3390/agriengineering2030030

**Chicago/Turabian Style**

Grisso, Robert “Bobby”, John S. Cundiff, and Erin G. Webb.
2020. "Predicting Field Efficiency of Round-Baling Operations in High-Yielding Biomass Crops" *AgriEngineering* 2, no. 3: 447-457.
https://doi.org/10.3390/agriengineering2030030