# Assessment of Effective Wind Loads on Individual Plantation-Grown Forest Trees

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## Abstract

**:**

## 1. Introduction

## 2. Material and Methods

#### 2.1. Workflow

_{OC}) and non-oscillatory (D

_{NOC}) components using singular spectrum analysis; (3) Low-pass filtering of momentum flux data (M

_{NOC}) to match the frequency range of D

_{NOC}; (4) Applying regression analysis (significance level α = 0.05) for estimating the coefficients of D dependence on the force applied on the sample trees during non-destructive pulling tests; (5) Maximizing the local correlation between D

_{NOC}and M

_{NOC}using dynamic time warping; (6) Calculating of the effective force (F

_{eff}) from dynamically time-warped D

_{NOC}and M

_{NOC}; (7) Determining of wind load coefficients (WLC) from F

_{eff}and M

_{NOC}values; (8) Calculating of the tree-specific, instantaneous effective wind load (WL

_{eff}) using M

_{NOC}and WLC values.

#### 2.2. Research Site and Forest Characteristics

#### 2.3. Airflow Measurements

#### 2.4. Stem Tilt Measurements

_{x}, east-west) and y (t

_{y}, north-south) directions, four Tree Response Sensors (TRS) [40] were mounted to the north facing side of the stems of five sample trees (B1 to B5) at the stem base (z

_{TRS,1}= 0.1 m), 1/7 H (z

_{TRS,2}), 3/7 H (z

_{TRS,4}), and 5/7 H (z

_{TRS,5}), H is the tree height, and z is the measuring height (Table 1).

_{TRS,2}, z

_{TRS,4}, and z

_{TRS,5}, represent the antinodal points of stem vibration. The time series of stem tilt components t

_{x}and t

_{y}were used to calculate the stem displacement vector (D):

_{TRS,}

_{2}. Earlier studies show that information on the Scots pine trees’ stem response measured at one point is sufficient for the following analysis [29,32]. All stem tilt data were collected wirelessly and stored on a ground receiver using the Tree Motion Monitoring System (TreeMMoSys) [40].

#### 2.5. Non-Destructive Tree Pulling

_{a}= 0.6 H. This height was assumed to be a compromise between avoiding the effects of knots on the overall strength of the stems and being close enough to the crowns where the wind loading occurs [39].

_{a}) along the rope into the pulling direction. Three TreeQinetic elastometers were mounted to the leeward side of the stems at 1 m (z

_{PTQ,2}), 2 m (z

_{PTQ,3}), and 3 m (z

_{PTQ,4}) to measure strain in the marginal wood fibers. TRS (z

_{TRS,1}, z

_{TRS,3}) and TreeQinetic inclinometers were mounted to the stem base (0.1 m) and at 5 m height (z

_{PTQ,1}, z

_{PTQ,5}) to record t

_{x}and t

_{y}while B1 to B35 were pulled [44]. The pulling force was increased until a root plate inclination of 0.25° or 100 µm of strain in the marginal fibers were reached to prevent primary tree failure [45].

#### 2.6. Processing and Analysis of Stem Displacement Data

_{NOC}and decomposing D into D

_{OC}and D

_{NOC}through the application of singular spectrum analysis (SSA) [46,47]. The D decomposition separates motion components responding to wind loading from components that dissipate elastic energy stored in the stem and roots, such as oscillatory sway in the fundamental mode [31].

_{NOC}and D

_{NOC}were dynamically time-warped to synchronize their time series and maximize their correlation [50,51] as described in a previous study [32]. All further analyses were carried out with dynamically time-warped M

_{NOC}and D

_{NOC}. The oscillatory signal components were no longer considered.

#### 2.7. Calculation of Effective Wind Load

_{a}using a modified approach proposed in a previous study [52]:

_{a}and the rope anchorage point at the ground.

_{TRS,1}and z

_{TRS,2}were 80 and 40 for D at z

_{TRS,3}and z

_{TRS,5}, respectively. On average, the first SSA component, which represents the low-pass filtered signal component of D (D

_{LP}) and FP (FP

_{LP}), explained 97% of the variance in the FP signals and 83% (z

_{TRS,1}) to 96% (z

_{TRS,4}) in the D signals.

_{NOC}is represented by D

_{LP}because from previous studies, it is known that at the research site, the Scots pine trees’ total wind-induced reactions are dominated by sway in the fundamental mode. Vibrations in higher modes are negligible [29,30,32].

_{LP}and FP

_{LP}:

_{a}per meter of stem displacement, and has the same units as the spring constant (N/m). It is a measure of flexural tree stiffness.

_{TRS,1}:

_{1}, a

_{2}, and a

_{3}are coefficients. The strength of the functional relationships was assessed with the coefficient of determination (r

^{2}).

_{LP}and s, the effective pulling force applied at z

_{a}(F

_{ZV}) was calculated:

_{a}under natural wind conditions, s and D

_{NOC}were used to calculate the effective force (F

_{eff}).

_{NOC}and F

_{eff}, the wind load parameter (WLP) was calculated for 10 min intervals using a linear regression forced through zero:

_{NOC}, the wind load coefficient (WLC) was determined as the offset of the second phase (i.e., using all values greater than detected change points) of a two-phase regression of WLP on 10 min mean values of M

_{NOC}(M

_{NOC,mean}). WLC enables the calculation of the instantaneous, effective wind load (WL

_{eff}):

#### 2.8. Change Point Analysis

_{NOC}thresholds. We used a two-phase linear regression model for detecting these thresholds [53].

## 3. Results and Discussion

#### 3.1. Non-Destructive Tree Pulling

_{LP}, FP

_{LP}calculated at height z

_{TRS,2}= 1/7 H increased during static pulling tests. The FP

_{LP}maxima always occurred when 100 µm of strain was reached and the force application was aborted. After reaching the FP

_{LP}maximum, F

_{a}was steadily reduced, and the trees returned to their rest position. For B1 to B5, which were equipped with multiple sensors, s was calculated at heights z

_{TRS,1}to z

_{TRS,5}(Figure 4a). The vertical s profiles along the stem available are of similar shape, the highest values occurring at z

_{TRS,1}, where stem diameters were always the biggest, resulting in the greatest flexural stiffness. From z

_{TRS,1}to z

_{TRS,2}, the s values decrease by several orders of magnitude, which requires the results to be presented on a logarithmic scale. Due to the very small D

_{LP}values, s needs to be considerably larger to reach the same FP

_{LP}as at height z

_{a}.

_{TRS,1}to z

_{TRS,3}. Generally, s values are orders of magnitude higher at the stem base than at the other measuring heights due to very small D

_{LP}, ranging from 962 (B31) to 23606 (B23) kN/m at z

_{TRS,1}and 0.9 (B26) to 13.6 (B22) kN/m at z

_{TRS,3}(Figure 4b).

^{3}[55], H [17,35,54], H/DBH [35], DBH/H

^{2}[56,57], DBH

^{2}/H [58], and DBH

^{2}H [17,58,59,60,61] that have been reported in previous studies to influence tree response on static pulling and wind loading. Crown and stem mass, which also influence tree response to external loading [56,57,58], were not included in this analysis since they were unavailable.

^{2}, were established between s and DBH, mean r

^{2}= 0.86 from z

_{TRS,1}to z

_{TRS,3}. With increasing DBH, s also increases. The increase is more linear at z

_{TRS,2}= 1/7 H and z

_{TRS,3}= 5 m than at the stem base. We argue that the stronger nonlinear dependence at the stem base is due to the cable attachment height z

_{a}= 0.6 H which is higher than in other studies [35,58]. The greater cable attachment height causes stronger bending of the upper stem parts [39], which mimics the stem bending of the sample trees under natural wind conditions better than the bending with cable attachment heights below 0.5 H. Regressing s against DBH

^{3}as conducted in a previous study [58], did not raise the explained variance of DBH in s.

^{2}(mean r

^{2}= 0.83) and DBH

^{2}H (mean r

^{2}= 0.85) are only slightly weaker. As H/DBH

^{2}increases, s decreases. The decrease in s is most pronounced at z

_{TRS,1}, but curvilinear at all displayed heights. With increasing DBH

^{2}H, which is used to represent stem volume, s increases. The strength of the presented functional relationships is in the range of previous studies [54,58]. Other tree characteristics such as H, H/DBH, DBH

^{2}/H, DBH/H

^{2}, and TLS-measured CA available in different directions were tested, but their functional relationships were weaker (r

^{2}≤ 0.75) at all studied heights.

#### 3.2. Tree Response under Natural Wind Conditions

_{NOC}(D

_{NOC,mean}) of B1 to B5 along the stem at the heights z

_{TRS,5}to z

_{TRS,1}plotted against M

_{NOC,mean}values. The D

_{NOC,mean}values decrease by several orders of magnitude towards the stem base. At the same measurement heights, D

_{NOC,mean}is mostly similar for B1 to B5. The greatest inter-tree differences occur at the stem base.

_{eff}(F

_{eff,mean}) are plotted against M

_{NOC,mean}, then large differences between the sample trees become apparent, although the tree-specific D

_{NOC,mean}patterns are similar. This demonstrates that B1 to B5 were subjected to different wind loads, the wind load acting on B5 being the greatest at z

_{TRS,4}and z

_{TRS,5}. The wind load acting on B3 is always the smallest. The inter-tree differences in F

_{eff,mean}decrease from the crown space towards the stem base. There is a considerable spread of the data at the stem base resulting from the small D

_{NOC,mean}values used in the F

_{eff,mean}calculation.

_{NOC,mean}values dominate, there are change points in the relationship of F

_{eff,mean}and M

_{NOC,mean}. Below the change points, D

_{NOC,mean}was always close to zero, indicating minimal wind-induced stem displacement resulting from weak wind loading. Except for the nearest area around the coordinate origin, the dependence of F

_{eff,mean}on M

_{NOC,mean}is linear, as is demonstrated in detail for B2 (thickest tree with DBH = 28.6 cm) and B19 (thinnest tree with DBH = 19.3 cm) in Figure 7.

_{eff,mean}acting on B2 and B19 are at 0.20 (Figure 7a) and 0.60 m

^{2}/s

^{2}(Figure 7b). After passing these points, the dependence of the tree response on M

_{NOC,mean}increases linearly.

_{NOC,mean}also show a two-phase pattern with a change point. After passing these points, the WLP distributions level off and are parallel to the x-axis. The small insets highlight the WLP development as a function of M

_{NOC,mean}after the passage of the change points in a linearly scaled coordinate system.

_{NOC,mean}after crossing the change points, allows the estimation of the wind-induced tree response as a function of M

_{NOC,mean}. The WLP vs. M

_{NOC,mean}change point values are very similar (r

^{2}= 0.89) to the F

_{eff,mean}vs. M

_{NOC,mean}change point value distribution, as is illustrated by boxplots for B1 to B20 in the inset in Figure 7b. The WLP-related change points range from M

_{NOC,mean}= 0.18 m

^{2}/s

^{2}(B5) to M

_{NOC,mean}= 0.67 m

^{2}/s

^{2}(B13), with the median WLP-related change point value being 0.32 m

^{2}/s

^{2}. The medians of the F

_{eff}- and WLP-related change points show no significant difference at the 95% confidence level as indicated by the boxplot notches.

_{eff}) knowing M

_{NOC}.

_{eff}and F

_{eff}10 Hz values (300 s) as an example. The time series length is limited to highlight their similar behavior from small to some of the largest values that occurred during the study period. Calculated WL

_{eff}is strongly correlated with measured F

_{eff}(r

^{2}= 0.99). Over the entire study period, r

^{2}calculated from 2,263,673 WL

_{eff}and F

_{eff}values each per tree ranges between 0.45 (B6) and 0.94 (B5). The r

^{2}median is 0.89 (B11).

_{eff}and F

_{eff}values is shown for B4 as red points in Figure 8b. The red points are plotted together with a binned (40 × 40 bins) scatter plot including the 2,263,673 WL

_{eff}and F

_{eff}values, exceeding the tree-specific M

_{NOC}thresholds. The data from the interval shown in Figure 8a are in the range of the histogram bins that represent the total wind-induced response of B4 in the study period. The majority of all analyzed WL

_{eff}and F

_{eff}values (84%) are in the range smaller than WL

_{eff}< 0.1 kN indicating the dominance of episodes with low wind loading.

_{eff}in the study period is shown as bivariate histograms in Figure 9. The histogram bins of all trees group around the 1:1 line indicating a good approximation of F

_{eff}. This figure shows the differences in tree-specific WL

_{eff}. Lowest WL

_{eff}acted on B10 and B19, the smallest of the presented trees. The largest effective wind load acted on B2, which is the tallest tree. Common to all trees is that high WL

_{eff}values are rare. The highest share of WL

_{eff}values of 90.4% can always be found close to the origin of the coordinate system for WL

_{eff}< 0.1 kN. Due to measurement device failure, there are no data for B7 and B15.

## 4. Conclusions

^{2}H, the effective wind load can be estimated tree-specifically and used to determine the instantaneous effective wind load via the wind load coefficient WLC. The use of WLC will simplify future investigations into the Scots pine trees’ wind-induced motion behavior.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Acronyms | Description |

α | significance level |

c | above-ground tree characteristic |

CA | crown area (m^{2}) |

D | stem displacement (m) |

D_{NOC} | non-oscillatory component of stem displacement (m) |

D_{NOC,mean} | 10 min mean value of D_{NOC} |

D_{OC} | oscillatory component of stem displacement (m) |

D_{LP} | spline-smoothed stem displacement during tree pulling tests (m) |

DBH | diameter at breast height (cm) |

F_{a} | force applied along the rope into the pulling direction (N) |

F_{eff} | effective force (N) |

F_{eff,mean} | 10 min mean value of F_{eff} |

FP | horizontal component of the pulling force at pulling rope attachment height during tree pulling tests (N) |

FP_{LP} | Low-pass filtered (SSA) bending moment (N) |

F_{ZV} | effective load during pulling test (N) |

H | tree height (m) |

M | above-canopy momentum flux density (m²/s²) |

M_{NOC} | low-pass filtered component of above-canopy momentum flux (m²/s²) |

M_{NOC,mean} | 10 min mean value of M_{NOC} |

p | p-value of the applied regression analyses |

r | correlation coefficient |

r^{2} | coefficient of determination |

RA | pulling rope angle between z_{a} and anchorage point at the ground (°) |

s | slope of the regression line determined between D_{LP} and FP_{LP} during tree pulling (N/m) |

t_{x} | stem tilt in x direction (east-west) (°) |

t_{y} | stem tilt in y direction (north-south) (°) |

u | horizontal wind vector component in east-west direction (m/s) |

v | horizontal wind vector component in north-south direction (m/s) |

w | vertical wind vector component (m/s) |

WL_{eff} | effective wind load (N) |

WLC | wind load coefficient (kN/(m^{2}/s^{2})) |

WLP | wind load parameter (kN/(m^{2}/s^{2})) |

z_{a} | attachment height of the pulling rope (m) |

z_{PTQ} | measurement height above ground of TreeQinetic sensors (m) |

z_{TRS} | measurement height above ground of the Tree Response Sensor (m) |

Abbreviations | Description |

PTQ | Picus TreeQinect |

S | ultrasonic anemometer |

SSA | singular spectrum analysis |

B | sample tree |

TLS | terrestrial laser scanning |

TRS | tree response sensor |

TreeMMoSys | tree motion monitoring system |

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**Figure 2.**System used to measure airflow and stem tilt. Four ultrasonic anemometers (S1 to S4) mounted to a slender scaffold tower measured the horizontal and vertical wind vector components at 2 m, 9 m, 18 m, and 21 m. Tilt of the sample trees’ stems under natural wind conditions and during pulling tests was measured in different configurations with the Tree Response Sensor (TRS) [40] at heights z

_{TRS,1}= 0.1 m, z

_{TRS,2}= 1/7 H, z

_{TRS,3}= 5 m, z

_{TRS,4}= 3/7 H, and z

_{TRS,5}= 5/7 H, H is the tree height.

**Figure 3.**System used for measuring stem tilt of B1 to B35 during static, non-destructive pulling tests. The stem tilt was measured with five Tree Response Sensors (TRS) at heights z

_{TRS,1}= 0.1 m (stem base), z

_{TRS,2}= 1/7 H, z

_{TRS,3}= 5 m, z

_{TRS,4}= 3/7 H (only B1 to B5), and z

_{TRS,5}= 5/7 H (only B1 to B5), and two PiCUS TreeQinetic (PTQ) inclinometers at z

_{PTQ,1}= 0.1 m and z

_{PTQ,5}= 5 m. Three PTQ elastometers at z

_{PTQ,2}= 1 m, z

_{PTQ,3}= 2 m, and z

_{PTQ,4}= 3 m measured strain in the marginal wood fibers.

**Figure 4.**(

**a**) Vertical profiles of the slope (s) calculated by a linear regression (p < 0.001) between smoothed displacement (D

_{LP}) and horizontal component of the pulling force (FP

_{LP}) at TRS measurement heights z

_{TRS,1}to z

_{TRS,5}resulting from static pulling tests at sample trees B1 to B5. Due to the large s range, the x-axis is logarithmically scaled. (

**b**) Boxplots of s at z

_{TRS,1}to z

_{TRS,3}resulting from static pulling tests at sample trees B1 to B35.

**Figure 5.**Slope (s) as a function of DBH (1.3 m a.g.l.), H/DBH

^{2}, and DBH

^{2}H of the sample trees B1 to B35 at heights (

**a**,

**d**,

**g**) z

_{TRS,1}= 0.1 m, (

**b**,

**e**,

**h**) z

_{TRS,2}= 1/7 H, and (

**c**,

**f**,

**i**) z

_{TRS,3}= 5 m.

**Figure 6.**Dependence of 10 min mean values of non-oscillatory stem displacement (D

_{NOC,mean}) on low-pass filtered momentum flux (M

_{NOC,mean}) at heights (

**a**) z

_{TRS,5}= 5/7 H, (

**b**) z

_{TRS,4}= 3/7 H, (

**c**) z

_{TRS,2}= 1/7 H, and (

**d**) z

_{TRS,1}= 0.1 m. Dependence of 10 min mean effective force (F

_{eff,mean}) on M

_{NOC,mean}at (

**e**) z

_{TRS,5}, (

**f**) z

_{TRS,4}, (

**g**) z

_{TRS,2}, and (

**h**) z

_{TRS,1}along the stems of B1 to B5. The arrow in (

**g**) highlights the point where the response of B1 to B5 to wind loading systematically changes.

**Figure 7.**(

**a**,

**b**) Dependence of 10 min mean effective force (F

_{eff,mean}) on 10 min mean low-pass filtered momentum flux (M

_{NOC,mean}) of trees B2 (thickest tree with DBH = 28.6 cm) and B19 (thinnest tree with DBH = 19.3 cm). (

**c**,

**d**) Dependence of the tree-specific wind load parameter (WLP) on M

_{NOC,mean}. The red and orange lines represent the two phases of a linear regression before and after a change point. The inset in (

**b**) shows the distribution of WLP and F

_{eff}values of B1 to B20 as boxplots. The boxplot notches indicate the 95% confidence interval around the median. The insets in (

**c**,

**d**) show the relationships between WLP and M

_{NOC,mean}in a linearly scaled coordinate system.

**Figure 8.**(

**a**) Time series (300 s) of instantaneous WL

_{eff}and F

_{eff}of sample tree B4. The grey region shows the standard deviation of the residuals from WLP values of the second phase (i.e., for all values greater than detected change points) of the two-phase linear regression model. (

**b**) WL

_{eff}plotted against F

_{eff}(red dots) and bivariate histogram bins (green tiles) that represent the total wind-induced response of B4 in the study period. 84% of the displayed values are smaller than WL

_{eff}< 0.1 kN (yellow and light green bins), indicating the dominance of episodes with low wind loading in the study period.

**Figure 9.**(

**a–t**) Bivariate histograms of instantaneous WL

_{eff}and F

_{eff}of B1 to B20 in the study period. Due to measurement device failure there is no data for B7 and B15.

**Table 1.**Height (H, m), stem diameter at breast height (DBH, 1.3 m a.g.l., cm), and crown area (CA, m

^{2}) of the sample trees B1 to B35. z

_{a}is the height of pulling rope anchor point (m), RA is the pulling rope angle (°), and z

_{TRS,}

_{1}to z

_{TRS,}

_{5}are the Tree Response Sensor (TRS) stem tilt measurement heights.

Sample Tree | H | DBH | CA | z_{a} | RA | z_{TRS,1} | z_{TRS,2} | z_{TRS,3} | z_{TRS,4} | z_{TRS,5} |
---|---|---|---|---|---|---|---|---|---|---|

B1 | 18.5 | 25.1 | 26.0 | 11.2 | 18.5 | 0.1 | 2.7 | 5.0 | 8.2 | 13.7 |

B2 | 20.4 | 28.6 | 31.2 | 13.4 | 17.9 | 0.1 | 2.9 | 5.0 | 8.6 | 14.3 |

B3 | 16.7 | 23.2 | 18.0 | 9.7 | 16.6 | 0.1 | 2.6 | 5.0 | 7.8 | 12.9 |

B4 | 19.4 | 28.6 | 15.9 | 11.2 | 18.4 | 0.1 | 2.8 | 5.0 | 8.4 | 13.9 |

B5 | 18.5 | 27.7 | 27.0 | 11.9 | 22.7 | 0.1 | 2.7 | 5.0 | 8.1 | 13.5 |

B6 | 17.7 | 26.8 | 27.3 | 11.7 | 26.8 | 0.1 | 2.5 | 5.0 | ||

B7 | 19.6 | 30.6 | 40.4 | 10.6 | 19.2 | 0.1 | 2.8 | 5.0 | ||

B8 | 17.7 | 21.9 | 26.6 | 9.7 | 22.5 | 0.1 | 2.5 | 5.0 | ||

B9 | 17.5 | 22.3 | 27.0 | 9.6 | 27.9 | 0.1 | 2.5 | 5.0 | ||

B10 | 16.5 | 20.7 | 17.9 | 9.5 | 22.3 | 0.1 | 2.4 | 5.0 | ||

B11 | 18.5 | 21.4 | 24.0 | 9.8 | 19.6 | 0.1 | 2.6 | 5.0 | ||

B12 | 18.7 | 25.2 | 33.3 | 11.5 | 23.4 | 0.1 | 2.7 | 5.0 | ||

B13 | 19.6 | 28.1 | 31.4 | 11.6 | 27.8 | 0.1 | 2.8 | 5.0 | ||

B14 | 18.8 | 21.3 | 21.3 | 10.8 | 26.2 | 0.1 | 2.7 | 5.0 | ||

B15 | 19.8 | 27.2 | 24.5 | 11.5 | 27.5 | 0.1 | 2.8 | 5.0 | ||

B16 | 17.6 | 22.2 | 24.9 | 11.6 | 27.8 | 0.1 | 2.5 | 5.0 | ||

B17 | 17.4 | 20.7 | 23.5 | 10.7 | 25.9 | 0.1 | 2.5 | 5.0 | ||

B18 | 18.3 | 25.3 | 19.8 | 11.1 | 32.4 | 0.1 | 2.6 | 5.0 | ||

B19 | 16.5 | 19.3 | 18.1 | 10.7 | 29.7 | 0.1 | 2.4 | 5.0 | ||

B20 | 17.5 | 24.8 | 22.8 | 10.4 | 30.5 | 0.1 | 2.5 | 5.0 | ||

B21 | 18.2 | 30.5 | 34.5 | 10.5 | 27.5 | 0.1 | 2.6 | 5.0 | ||

B22 | 20.6 | 34.8 | 53.8 | 12.8 | 32.6 | 0.1 | 2.9 | 5.0 | ||

B23 | 18.1 | 35.5 | 47.6 | 12.3 | 39.2 | 0.1 | 2.6 | 5.0 | ||

B24 | 16.8 | 20.6 | 14.0 | 10.7 | 25.5 | 0.1 | 2.4 | 5.0 | ||

B25 | 16.7 | 21.3 | 19.4 | 11.6 | 21.1 | 0.1 | 2.4 | 5.0 | ||

B26 | 15.5 | 17.0 | 11.1 | 11.8 | 30.5 | 0.1 | 2.2 | 5.0 | ||

B27 | 18.5 | 35.4 | 40.8 | 11.9 | 29.9 | 0.1 | 2.6 | 5.0 | ||

B28 | 16.8 | 20.5 | 14.3 | 10.7 | 39.9 | 0.1 | 2.4 | 5.0 | ||

B29 | 20.1 | 31.2 | 32.1 | 10.8 | 29.0 | 0.1 | 2.9 | 5.0 | ||

B30 | 16.0 | 19.4 | 13.1 | 11.2 | 39.9 | 0.1 | 2.3 | 5.0 | ||

B31 | 17.3 | 18.9 | 14.7 | 11.5 | 35.0 | 0.1 | 2.5 | 5.0 | ||

B32 | 16.6 | 18.2 | 13.1 | 10.0 | 25.8 | 0.1 | 2.4 | 5.0 | ||

B33 | 18.6 | 28.1 | 28.5 | 11.0 | 28.8 | 0.1 | 2.7 | 5.0 | ||

B34 | 18.6 | 28.7 | 37.6 | 12.2 | 29.7 | 0.1 | 2.7 | 5.0 | ||

B35 | 19.3 | 30.9 | 40.2 | 12.0 | 36.2 | 0.1 | 2.8 | 5.0 |

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**MDPI and ACS Style**

Kolbe, S.; Rentschler, F.; Frey, J.; Seifert, T.; Gardiner, B.; Detter, A.; Schindler, D.
Assessment of Effective Wind Loads on Individual Plantation-Grown Forest Trees. *Forests* **2022**, *13*, 1026.
https://doi.org/10.3390/f13071026

**AMA Style**

Kolbe S, Rentschler F, Frey J, Seifert T, Gardiner B, Detter A, Schindler D.
Assessment of Effective Wind Loads on Individual Plantation-Grown Forest Trees. *Forests*. 2022; 13(7):1026.
https://doi.org/10.3390/f13071026

**Chicago/Turabian Style**

Kolbe, Sven, Felix Rentschler, Julian Frey, Thomas Seifert, Barry Gardiner, Andreas Detter, and Dirk Schindler.
2022. "Assessment of Effective Wind Loads on Individual Plantation-Grown Forest Trees" *Forests* 13, no. 7: 1026.
https://doi.org/10.3390/f13071026