# The Optimum Slash Pile Size for Grinding Operations: Grapple Excavator and Horizontal Grinder Operations Model Based on a Sierra Nevada, California Survey

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

_{0}), thereby suggesting that there might be an optimum size of slash pile for a grinding operation. Modeling of the excavator and grinder operations was also examined, and the constructed simulation model was observed to well-replicate the actual operations. Based on the modeling, the productivity of grinding at a landing area of 710 m

^{2}of slash pile location was estimated to be 31.24 BDT/PMH

_{0}, which was the most productive rate.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Site and Treatment

^{3}per pile [23].

#### 2.2. Description of Slash Pile and Element Operation

**Loading**means grabbing logging residues out of a slash pile and then pivoting with load;**Unloading**means releasing the residues at the conveyor of a horizontal grinder and then pivoting with no load;**Shaking**means shaking waste material off in order to facilitate the feeding of grabbed residues;**Waiting**means waiting for feeding the material; the grinding operation was carried out by the interaction of excavator and grinder, so the waiting operation was essential for the excavator;**Pushing**means pushing the material into the grinder when it could not ‘swallow’ the residues because of their bulkiness;**Reorienting or repositioning**means reorienting or repositioning the scattered material in order to increase the amount of residue per grab when the operation proceeded and the bulk volume of pile became smaller;**Loading with moving**means that the loading operation shown above was done with moving;**Unloading with moving**means that unloading operation shown above was done with moving.

^{2}were calculated as 0.171 BDT/m

^{2}(=51.41 BDT/(20 m × 15 m)), 0.170 BDT/m

^{2}(=122.66 BDT/(30 m × 24 m)), and 0.166 BDT/m

^{2}(=173.78 BDT/(35 m × 30 m)) for the Small, Medium, and Large piles, respectively, and it was thus concluded that there was no significant deviation of the amount of residues among the three piles.

## 3. Results of the Time Study and the Monitored Productivity of a Grinder

_{0}(=122.66 BDT/14,408 s × 3600 s/h). The productivity for the Small pile was 21.73 BDT/PMH

_{0}(=51.41 BDT/8519 s × 3600 s/h), and that for the Large pile was 24.49 BDT/PMH

_{0}(=173.78 BDT/25,545 s × 3600 s/h), thereby suggesting that there might be an optimum size of slash pile for a grinding operation. The Nordic guidelines state that the preferable size for a slash pile is 20–30 m long and a max. of 4 m high [24]; this guideline supports this paper’s finding about the Medium pile, of which width was 24 m.

## 4. Discussion by the Simulation Model

#### 4.1. Modeling a Grapple Excavator Operation

^{2}), 8.61 s/BDT for the Medium pile (720 m

^{2}), and 39.3 s/BDT for the Large pile (1050 m

^{2}), the relationship between the landing area of slash pile location, x (m

^{2}), and the time of reorienting or repositioning per BDT, y (s/BDT), was approximated as follows:

^{2}= 0.9992)

^{2}), 0.212 BDT/time for the Medium pile (720 m

^{2}), and 0.208 BDT/time for the Large pile (1050 m

^{2}), as follows:

^{−7}x

^{2}+ 4.292 × 10

^{−4}x + 3.184 × 10

^{−2}(r

^{2}= 1.000)

#### 4.2. Verification of the Replicability of the Model and an Optimum Slash Pile Size

^{2}(for the Small pile; 20 m long × 15 m wide) and 1050 m

^{2}(for the Large pile; 35 m long × 30 m wide) at 10 m

^{2}intervals. In the simulation of the respective landing areas, the calculation was repeated 1000 times. The productivity for each landing was determined based on the averaged total operation time. Since no significant deviation of the amount of residues among the three piles was observed in the time study, the mass of the slash pile in an initial state of simulation was calculated by multiplying 0.168 BDT/m

^{2}(=(0.171 × 300 + 0.170 × 720 + 0.166 × 1050)/(300 + 720 + 1050), which was the weighted average value of the monitored three piles) by the landing area.

^{2}of slash pile location is 31.24 BDT/PMH

_{0}, which is the highest productivity value obtained. However, the difference in the estimated productivities is small between the areas 690 m

^{2}(31.21 BDT/PMH

_{0}) and 730 m

^{2}(31.20 BDT/PMH

_{0}), and there is a range in the calculation result for each landing. It should be noted therefore that Figure 6 simply compares the average values of the 1000-times repeated calculation. Concerning the versatility of the constructed model, however, the following points should be discussed further so that the accuracy of the model can be improved:

- The shape of each landing, i.e., the ratio of its length to its width, was not considered in the simulation model;
- The theoretical formulae of (1) and (2) were both approximated from only three samples;
- The optimum size of the slash pile for a grinding operation will also depend in part on aspects of the machines used, e.g., their size, engine output, and grinding capacity.

## 5. Conclusions

- The energy (diesel fuel) expended for processing and transport was 2.5% of the biomass fuel (energy equivalent);
- Based on measurements from a large pile burn, air emission reductions of 98–99% for PM2.5, CO, NMOC, CH
_{4}, and BC, and 20% for NO_{X}and CO_{2}-equivalent greenhouse gases were observed; - The delivered cost of $70/BDT exceeds the biomass plant gate price of $45/BDT. Under typical conditions, the break-even haul distance would be approx. 48 km.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 6.**Relationship between the landing area of slash pile location and the estimated productivity of grinding.

Equipment | Grapple Excavator | Horizontal Grinder |
---|---|---|

Vendor, model | Link-Belt, 290 LX | Bandit, Beast 3680 |

Engine, horsepower | Isuzu CC-6BG1TC, 132 kW | Caterpillar C18 Tier III, 522 kW |

Length | 10.41 m | 11.89 m |

Width | 3.400 m | 2.845 m |

Height | 3.270 m | 4.115 m |

Weight | 29,211 kg | 28,122 kg |

Maximum reach | 10.54 m | - |

Maximum feed height | - | 0.890 m |

Infeed conveyor | - | 6.110 m × 1.520 m |

Element Operation | Pile | |||
---|---|---|---|---|

Small | Medium | Large | ||

Loading | Time (s) | 3484 | 5312 | 7614 |

Frequency | 359 | 550 | 802 | |

Avg. (s) | 9.70 | 9.66 | 9.49 | |

Std. Dev. (s) | 5.55 | 4.29 | 4.56 | |

Unloading | Time (s) | 3114 | 4776 | 6848 |

Frequency | 383 | 594 | 863 | |

Avg. (s) | 8.13 | 8.04 | 7.94 | |

Std. Dev. (s) | 3.09 | 3.00 | 2.73 | |

Shaking | Time (s) | 92 | 95 | 201 |

Frequency | 14 | 15 | 29 | |

Avg. (s) | 6.57 | 6.33 | 6.93 | |

Std. Dev. (s) | 3.08 | 2.50 | 2.84 | |

Waiting | Time (s) | 479 | 1314 | 1875 |

Frequency | 29 | 71 | 88 | |

Avg. (s) | 16.52 | 18.51 | 21.31 | |

Std. Dev. (s) | 18.06 | 19.95 | 19.32 | |

Pushing | Time (s) | 1013 | 1190 | 1316 |

Frequency | 132 | 168 | 180 | |

Avg. (s) | 7.67 | 7.08 | 7.31 | |

Std. Dev. (s) | 5.02 | 4.83 | 7.06 | |

Reorienting or repositioning | Time (s) | 52 | 1056 | 6826 |

Frequency | 3 | 11 | 21 | |

Avg. (s) | 17.33 | 96.00 | 325.05 | |

Std. Dev. (s) | 2.31 | 126.17 | 732.85 | |

Loading with moving | Time (s) | 100 | 201 | 284 |

Frequency | 13 | 29 | 33 | |

Avg. (s) | 7.69 | 6.93 | 8.61 | |

Std. Dev. (s) | 3.82 | 2.25 | 3.19 | |

Unloading with moving | Time (s) | 185 | 464 | 581 |

Frequency | 18 | 47 | 56 | |

Avg. (s) | 10.28 | 9.87 | 10.38 | |

Std. Dev. (s) | 6.95 | 5.44 | 9.28 | |

Total | 8519 | 14,408 | 25,545 |

Element Operation | Chi-Square Test | Theoretical Formula ^{1} | ||
---|---|---|---|---|

χ^{2} | df | p-Value | ||

Loading | 5.416 | 5 | 0.367 | e^{N}^{(2.140, 0.485)} |

Unloading | 10.985 | 5 | 0.052 | e^{N}^{(2.023, 0.370)} |

Shaking | 4.422 | 5 | 0.490 | e^{N}^{(1.825, 0.383)} |

Waiting | 6.314 | 5 | 0.277 | e^{N}^{(2.625, 0.800)} |

Pushing | 10.238 | 5 | 0.069 | e^{N}^{(1.819, 0.539)} |

Loading with moving | 8.353 | 5 | 0.138 | e^{N}^{(1.987, 0.363)} |

Unloading with moving | 8.009 | 5 | 0.156 | e^{N}^{(2.153, 0.530)} |

^{1}N(m, σ) is an operator that generates random normal numbers of which average and standard deviation are m and σ, respectively.

Pile | Monitored | Estimated Productivity | ||||
---|---|---|---|---|---|---|

Area of Landing (m^{2}) | Amount of Slashes (BDT) | Productivity (BDT/PMH_{0}) | Calculation Frequency | Avg. ± Std. Dev. (BDT/PMH_{0}) | Rate of Avg. Value to Monitored (%) | |

Small | 300 | 51.41 | 21.73 | 1000 | 21.78 ± 0.70 | 100.2 |

Medium | 720 | 122.66 | 30.65 | 1000 | 31.17 ± 0.75 | 101.7 |

Large | 1050 | 173.78 | 24.49 | 1000 | 24.27 ± 0.38 | 99.10 |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Yoshioka, T.; Sakurai, R.; Kameyama, S.; Inoue, K.; Hartsough, B.
The Optimum Slash Pile Size for Grinding Operations: Grapple Excavator and Horizontal Grinder Operations Model Based on a Sierra Nevada, California Survey. *Forests* **2017**, *8*, 442.
https://doi.org/10.3390/f8110442

**AMA Style**

Yoshioka T, Sakurai R, Kameyama S, Inoue K, Hartsough B.
The Optimum Slash Pile Size for Grinding Operations: Grapple Excavator and Horizontal Grinder Operations Model Based on a Sierra Nevada, California Survey. *Forests*. 2017; 8(11):442.
https://doi.org/10.3390/f8110442

**Chicago/Turabian Style**

Yoshioka, Takuyuki, Rin Sakurai, Shohei Kameyama, Koki Inoue, and Bruce Hartsough.
2017. "The Optimum Slash Pile Size for Grinding Operations: Grapple Excavator and Horizontal Grinder Operations Model Based on a Sierra Nevada, California Survey" *Forests* 8, no. 11: 442.
https://doi.org/10.3390/f8110442