# Research on the Wood Density Measurement in Standing Trees through the Micro Drilling Resistance Method

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## Abstract

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## 1. Introduction

^{2}= 0.943 between drill resistance and wood density [27]. Isik et al. revealed strong correlations between average drilling resistance values and wood density, indicating strong genetic control at the family level. However, individual phenotypic correlations were observed to be relatively weak [34]. Downes et al. found determination coefficients of the linear models between the average drill resistance and wood density of each tree in various plots ranging from 0.662 to 0.868 [35]. Due to the significant differences in the parameters and determination coefficients among various linear models, the universality of these models was poor. Therefore, researchers needed to establish a mathematical model for every tree species, and the modeling workload was enormous. In addition, the scatter plots of drill needle resistance and wood density were relatively scattered, and some data points had a large distance from the fitting curve. Therefore, the reliability of this method needs further verification.

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## 2. Materials and Methods

#### 2.1. Core Sampling and Drill Resistance Measurements

#### 2.2. Basic Density and Moisture Content Measurements of the Cores

_{0}) of the core was calculated using an electronic balance. The diameter of the core was 5.15 mm. The volume of fresh cores was calculated using the following formula.

^{2}l

^{3}), and l denotes the length of the fresh core (cm).

_{1}) was measured using an electronic balance. The basic density of the core was calculated using the following formula.

_{1}/V

^{3}), and m

_{1}is the mass of the dry core (g). The moisture content of the cores was calculated using the following formula.

_{0}− m

_{1})/m

_{1}

#### 2.3. Calculation Method for Average Drill Resistance of Each Test Tree

_{1}= F

_{0}− (f

_{0}− f

_{i})L

_{0}/L

_{1}is the drill resistance after removing drill shaft friction, F

_{0}denotes the original drill resistance, f

_{0}represents the average drill resistance after the drill exited the tree, f

_{i}is the average drill resistance before the drill penetrated the tree, L

_{0}is the real-time drilling depth, L denotes the total drilling depth. The complete drill needle resistance curve and the schematic of removing the drill shaft friction are shown in Figure 3.

#### 2.4. Statistical Analysis, Modeling, and Testing

_{i}is the true value of the ith data, σ is the standard deviation.

## 3. Results

#### 3.1. Results of Removing Outliers

#### 3.2. Modeling Results

#### 3.2.1. Mathematical Model for the Three Tree Species

#### 3.2.2. Mathematical Model for Each Tree Species

#### Mathematical Model for Pinus massoniana

#### Mathematical Model for Cunninghamia lanceolate

#### Mathematical Model for Cryptomeria fortunei

#### 3.3. Test Results

## 4. Discussion

^{2}> 0.60) [41], lumber and the linear regression model for agarwood (R

^{2}= 0.25) [42]. However, owing to the exponential relationship between wood strength and wood density, the relationship between drill resistance and wood density does not follow a linear pattern. The results of this study revealed that except for Cryptomeria fortunei, the natural logarithm of drill resistance significantly influenced the wood density model. Figure 5 shows a comparison between the linear and logarithmic fitting curves of the average drill resistance and wood density on the modeling dataset. Table 7 displays the linear and logarithmic fitting equations of the average drill resistance and wood density.

## 5. Conclusions

- The use of the micro drilling resistance method for measuring the wood density of standing trees was feasible;
- The relationship between wood density and drill resistance did not follow a linear pattern; in some tree species, this relationship exhibited a logarithmic pattern;
- The establishment of a mathematical model for each tree species was considered essential.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 5.**Comparison between the linear and logarithmic fitting curves of the average drill resistance and wood density. (

**a**) Total modeling data. (

**b**) Pinus massoniana. (

**c**) Cunninghamia lanceolate. (

**d**) Cryptomeria fortunei.

Species | Number of Original Data Records | Number of Data Records after Removing Outliers |
---|---|---|

Pinus massoniana | 111 | 101 |

Cunninghamia lanceolate | 60 | 57 |

Cryptomeria fortunei | 60 | 56 |

Total | 231 | 214 |

**Table 2.**p-values of each parameter in the linear model for basic wood density, the natural logarithm of the average drill resistance, and absolute moisture content.

Parameter | Parameter Value | p-Value |
---|---|---|

Intercept | −1279.480 | <0.001 |

The natural logarithm of average drill resistance | 335.320 | <0.001 |

Absolute moisture content | −97.400 | <0.001 |

**Table 3.**p-values of each parameter in the linear model for Pinus massoniana, involving basic wood density, the natural logarithm of the average drill resistance, and absolute moisture content.

Parameter | Parameter Value | p-Value |
---|---|---|

Intercept | −656.000 | <0.001 |

The natural logarithm of average drill resistance | 229.190 | <0.001 |

Absolute moisture content | −147.320 | 0.001 |

**Table 4.**p-values of each parameter in the linear model for Cunninghamia lanceolate, involving basic wood density and the natural logarithm of the average drill resistance without intercept.

Parameter | Parameter Value | p-Value |
---|---|---|

The natural logarithm of average drill resistance | 66.958 | <0.001 |

**Table 5.**p-values of each parameter in the linear model for Cryptomeria fortunei, involving basic wood density and average drill resistance.

Parameter | Parameter Value | p-Value |
---|---|---|

Intercept | 208.746 | <0.001 |

Average drill resistance | 0.791 | <0.001 |

Spieces | Total Model | Sub Model | Average Basic Density of Each Tree Species | |||
---|---|---|---|---|---|---|

Estimated Standard Error/(kg∙m^{−3}) | Mean Estimated Accuracy (%) | Estimated Standard Error/(kg∙m^{−3}) | Mean Estimated Accuracy (%) | Estimated Standard Error/(kg∙m^{−3}) | Mean Estimated Accuracy (%) | |

Pinus massoniana | 58.646 | 91.401 | 47.393 | 93.248 | 47.669 | 92.639 |

Cunninghamia lanceolate | 46.505 | 88.491 | 27.062 | 93.263 | 31.138 | 92.260 |

Cryptomeria fortunei | 44.238 | 89.337 | 18.087 | 95.540 | 36.172 | 91.360 |

Total | 50.599 | 90.070 | 35.639 | 93.865 | 39.776 | 92.195 |

Species | Linear Model | Logarithmic Model | ||
---|---|---|---|---|

Equation | Adjusted R^{2} | Equation | Adjusted R^{2} | |

Pinus massoniana | y = 285.499 + 0.965x | 0.506 | y = −766.910 + 234.970lnx | 0.521 |

Cunninghamia lanceolate | y = 219.332 + 0.759x | 0.256 | y = −283.580 + 123.220lnx | 0.270 |

Cryptomeria fortunei | y = 208.746 + 0.791x | 0.347 | y = −335.230 + 132.510lnx | 0.336 |

Total | y = 91.366 + 1.692x | 0.733 | y = −1370.740 + 341.840lnx | 0.746 |

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**MDPI and ACS Style**

Yao, J.; Zhao, Y.; Lu, J.; Liu, H.; Wu, Z.; Song, X.; Li, Z.
Research on the Wood Density Measurement in Standing Trees through the Micro Drilling Resistance Method. *Forests* **2024**, *15*, 175.
https://doi.org/10.3390/f15010175

**AMA Style**

Yao J, Zhao Y, Lu J, Liu H, Wu Z, Song X, Li Z.
Research on the Wood Density Measurement in Standing Trees through the Micro Drilling Resistance Method. *Forests*. 2024; 15(1):175.
https://doi.org/10.3390/f15010175

**Chicago/Turabian Style**

Yao, Jianfeng, Yabin Zhao, Jun Lu, Hengyuan Liu, Zhenyang Wu, Xinyu Song, and Zhuofan Li.
2024. "Research on the Wood Density Measurement in Standing Trees through the Micro Drilling Resistance Method" *Forests* 15, no. 1: 175.
https://doi.org/10.3390/f15010175