# Density Distribution in Wood of European Birch (Betula pendula Roth.)

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

^{3}) by using energy-transmission gamma 59.5 keV (Amerycium

^{241}Am). The diameter of used radiation collimator was 5 mm. The distance of the radiation source from the detector was 150 mm. The time of a single measurement was 30 s. The result of a single measurement was subject to an error ±10 kg/m

^{3}[27]. The diagram of the isotope X-ray density meter MGD-05 is given in Figure 1.

## 3. Results and Discussion

#### 3.1. Determining the Proportion of Juvenile and Mature Wood

#### 3.2. Wood Density Distribution Analysis

^{3}.

#### 3.3. Density Distribution of Silver Birch Wood on the Cross Section

- ●
- geographical direction (north–south) did not have a statistically significant effect on the distribution of average densities across the entire birch log;
- ●
- distance from the pith had a statistically significant effect on the distribution of average densities across the entire birch log;
- ●
- there was no significant interaction of geographical direction and distance from the pith.

^{3}was obtained for measuring lines 10 and 12 cm away from the pith, while the lowest average density of 591 kg/m

^{3}was obtained for the measuring line 2 cm away from the pith. The relationship between wood density and tree was also confirmed during studies on silver birch growing at the lower altitude of the Czech Republic region [7] and the Lativian plantation on post-agricultural lands [24].

#### 3.4. Density Distribution on the Longitudinal Section of a Birch Log

^{3}.

#### 3.5. Density Map

^{3}) appeared in the butt part (dark yellow). The correlation between the wood density and the maturity of cells was observed. It was noticed that between the measuring lines spaced 4 cm from the pitch, there was a strip of wood with a density of 550 to 599.9 kg/m

^{3}(light blue). The density of wood behind this area was from 600 to 649.9 kg/m

^{3}(green). This part around the pitch with a radius of about 8 cm formed a zone of juvenile wood with a lower density visible in the form of blue and green colors. Behind the measuring lines spaced 8 cm from the pith (mature wood), there was wood with a density in the range of 650 to 700 kg/m

^{3}(light yellow stripes). Around 11 m in height, near the peripheral parts, a reduced density area appeared (dark blue and navy blue). This phenomenon could be explained by the occurrence of wedges and cracks. At two heights: 18.0 and 21.6 m, wood density was found to be 750 to 899.9 kg/m

^{3}(orange and red). The increase in density in these areas was caused by a significant number of high-density knots. The occurrence of defects, mainly in the form of knots, had a statistically significant effect on the average density of the large-dimensioned birch wood tested. The average density of wood with defects was higher by approximately 5 kg/m

^{3}compared to the density of wood without defects. The slight difference is due to the significant share of large-sized wood in the knotless zone.

^{3}(Table 13), over 22% of average density measurement results ranged from 500 to 599.9 kg/m

^{3}, and over 75% of average density measurement results ranged from 600 to 699.9 kg/m

^{3}.

## 4. Conclusions

- The place where wood was tested, both in cross-section and longitudinal section of the trunk, had a statistically significant effect on the average density of birch wood.
- The average density of whole logs was statistically significantly higher than the average density at breast height, while the average density at ¼ height did not differ statistically significantly from the average density of the whole log.
- On the cross-section, the distribution of average densities determined at breast height, as well as on ¼ of the log height, properly depicted the distribution of average densities on the cross-section determined for the whole logs. The distribution of average densities in the cross-section can be described by a second degree polynomial in the juvenile wood area and two straight lines (in the mature wood areas); in the juvenile wood area, the average wood density increased significantly along the radius of the tree; in the mature wood areas, there was a slight density fluctuation.
- On the longitudinal section of the tested birch wood, the average density decreased going from the tree butt to 20% of the log height. In the crown area, the average wood density increased as it moved to the top of the tree. In both areas, a statistically significant correlation was obtained between the average density of wood and its location at the height of the trunk.
- The geographical direction (north–south) along which the density was determined did not have a statistically significant effect on the distribution of average densities on the cross-section of the tested birch logs.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Diagram of the isotope X-ray density meter MGD-05, where Z—source of radiation (241Am), SS—scintillation probe, A—amplifier of pulses, E1–discrimination threshold of automatic gain control, E2—measurement path discrimination threshold, PL1—pulse counter of the measuring path, PL2—impulse counter of automatic gain adjustment, uP—microprocessor, DAC—digital to analog converter, ZWN—high voltage power supply, ZNN—low voltage power supply, RS—serial port, USB—USB interface, AK—accumulator, PAK—charging rectifier.

**Figure 5.**Distribution of average densities on the cross-section of a birch log at ¼ of the log height.

**Figure 8.**Distribution of average densities on the longitudinal section of a birch log below and above 0.2 log height.

Feature | Log Number | ||||
---|---|---|---|---|---|

I | II | III | IV | V | |

Age * (years) | 71 | 72 | 72 | 70 | 70 |

Diameter at breast high in bark (cm) | 42 | 42 | 42 | 42 | 42 |

High (m) | 22.8 | 21.5 | 22.0 | 21.5 | 21.5 |

Crown index ** | 0.3 | 0.3 | 0.3 | 0.3 | 0.3 |

Feature | Value |
---|---|

Average width | 2.6 mm |

Coefficient of variation | 47% |

Minimal width | 0.4 mm |

Maximal width | 6.5 mm |

Average number of annual rings | 68 |

Feature | Value |
---|---|

Average length | 1279 μm |

Coefficient of variation | 20% |

Minimal length | 440 μm |

Maximal length | 2032 μm |

Number of measurements | 1380 |

**Table 4.**Results of tests on average density of tested silver birch (Betula pendula Roth.) at 12% moisture content.

Density | |
---|---|

Average density (kg/m^{3}) | 623 |

Standard deviation (kg/m^{3}) | 58 |

Variability coefficient (%) | 9.3 |

Average density at breast high (kg/m^{3}) | 608 |

Average density at ¼ high of the log (kg/m^{3}) | 630 |

Minimal value of density (kg/m^{3}) | 318 |

Maximal value of density (kg/m^{3}) | 895 |

Difference between maximal and minimal value of density (kg/m^{3}) | 577 |

Number of measurements | 8320 |

**Table 5.**Two-sided t-test of the difference between average densities (at significance level p = 0.05) for density distribution in birch wood.

Parameter | Empirical Statistics t | Critical Statistics t_{0.05/2; v} | Number of Degrees of Freedom v |
---|---|---|---|

Average density of all logs/Average density at breast height | 2.413 | 1.960 | 8401 |

Average density of all logs/Average density at ¼ high of the log | 0.860 | 1.993 | 73 |

**Table 6.**Two-factor analysis of variance (at the significance level p = 0.05) for the distribution of average densities across the entire birch log.

Source of Variation | Sum of Squared Deviations | Number of Degrees of Freedom | The Mean Square of Deviations | Empirical Statistics F | Test Probability p |
---|---|---|---|---|---|

Intercept | 2,039,755,000 | 1 | 2,039,755,000 | 784,716 | 0.000 |

Geographical direction | 299 | 1 | 299 | 0.115 | 0.735 |

Distance from the core | 3,709,976 | 7 | 529,997 | 203.896 | 0.000 |

Direction⋅Distance | 22,208 | 7 | 3173 | 1.221 | 0.287 |

Error | 19,786,270 | 7612 | 2599 | - | - |

**Table 7.**Tukey test of the factor “distance from the core” for the distribution of average densities over the cross-section of the entire birch log.

Distance from the Core (cm) | Average Density (kg/m^{3}) | Test Probability p | |||||||
---|---|---|---|---|---|---|---|---|---|

2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | ||

2 | 591 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | |

4 | 613 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | |

6 | 630 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.004 | |

8 | 643 | 0.000 | 0.000 | 0.000 | 0.000 | 0.004 | 1.000 | 1.000 | |

10 | 653 | 0.000 | 0.000 | 0.000 | 0.000 | 1.000 | 0.007 | 0.289 | |

12 | 653 | 0.000 | 0.000 | 0.000 | 0.004 | 1.000 | 0.026 | 0.411 | |

14 | 643 | 0.000 | 0.000 | 0.000 | 1.000 | 0.007 | 0.026 | 1.000 | |

16 | 644 | 0.000 | 0.000 | 0.004 | 1.000 | 0.289 | 0.411 | 1.000 | |

Homogeneous group number | 1 | 2 | 3 | 4 | 5 | 5 | 4 | 4. 5 |

**Table 8.**Two-sided tests of the significance of correlation coefficients between average densities across the entire birch log and average densities across the cross-section at breast height and ¼ of the height of the birch log (at the significance level p = 0.05).

Area Type | Correlation Coefficient R | Critical Values R_{0.05/2; v; k+1} | Number of Degrees of Freedom v |
---|---|---|---|

Distribution at breast height | 0.977 | 0.666 | 7 |

Distribution at ¼ of the height of the log | 0.959 | 0.666 | 7 |

Area Type | Radial Density Increase (%) |
---|---|

All logs | 11.9 |

At breast height | 17.7 |

At ¼ of the height of the log | 15.9 |

**Table 10.**One-way analysis of variance (at significance level p = 0.05) for distribution of average densities on the longitudinal section of birch logs.

Empirical Statistics F | Critical Statistics F _{0.05; u; v} | Number of Degrees of Freedom u, v |
---|---|---|

5.602 | 1.202 | 147. 8172 |

**Table 11.**Two-sided tests of the significance of correlation coefficients between the average density of birch wood and its location at the height (at the significance level p = 0.05).

Area Type | Correlation Coefficient R | Critical Values R_{0.05/2; v; k+1} | Number of Degrees of Freedom v |
---|---|---|---|

From the butt to the base of the crown | −0.291 | 0.198 | 97 |

Between the base of the crown and the top of the tree | 0.551 | 0.279 | 48 |

**Table 12.**Two-sided tests of significance of correlation coefficients between the average density of birch wood and its location at trunk height below and above 0.2 log height (at significance level p = 0.05).

Area Type | Correlation Coefficient R | Critical Values R_{0.05/2; v; k+1} | Number of Degrees of Freedom v |
---|---|---|---|

Below 0.2 log height | −0.649 | 0.355 | 29 |

Above 0.2 log height | 0.306 | 0.182 | 116 |

Feature | ||
---|---|---|

Average density (kg/m^{3}) | 623 | |

The proportion of average results of density measurements in density ranges | Density ranges (kg/m^{3}) | Proportion (%) |

0–99.9 | 0.0 | |

100–199.9 | 0.0 | |

200–299.9 | 0.0 | |

300–399.9 | 0.3 | |

400–499.9 | 0.7 | |

500–599.9 | 22.3 | |

600–699.9 | 75.4 | |

700–799.9 | 1.3 |

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**MDPI and ACS Style**

Dobrowolska, E.; Wroniszewska, P.; Jankowska, A.
Density Distribution in Wood of European Birch (*Betula pendula* Roth.). *Forests* **2020**, *11*, 445.
https://doi.org/10.3390/f11040445

**AMA Style**

Dobrowolska E, Wroniszewska P, Jankowska A.
Density Distribution in Wood of European Birch (*Betula pendula* Roth.). *Forests*. 2020; 11(4):445.
https://doi.org/10.3390/f11040445

**Chicago/Turabian Style**

Dobrowolska, Ewa, Paulina Wroniszewska, and Agnieszka Jankowska.
2020. "Density Distribution in Wood of European Birch (*Betula pendula* Roth.)" *Forests* 11, no. 4: 445.
https://doi.org/10.3390/f11040445