### Experimental design

The study was carried out in a plantation of two poplar hybrids (*Populus deltoides* × *nigra* and *Populus trichocarpa* × *deltoides*) belonging to GreenWood Resources, Inc. The plantation is situated south of the Columbia River a few kilometres from the city of Boardman in eastern Oregon, USA (45.77° N, 119.54° W). Plots were located within 8- or 13-year-old forest blocks with a stand density of approximately 750 stems ha^{-1}. The criteria for the location of the plots in the stands took into account the variability of the curvature of the trees so as to have some plots with predominantly straight stems and some plots with stems with very pronounced curvatures.

A total of 15 plots were located in the plantation with four of these selected based on the severity of the curvature of the trees; two had more pronounced curvature than average and, two had less pronounced curvature. The remaining eleven plots were randomly located. The plots were circular with an 8 m radius, yielding between 13 and 16 trees per plot.

In each plot, a hemispherical laser scan was made using a Faro Focus 3D (Faro Technologies Inc. Lake Mary, Florida, USA). The scanner resolution was set such that a 6.1 mm gap would be obtained between points hitting an object at a range of 10 m from the scanner. Particular attention was paid to the positioning of the scanner in order to avoid a plot tree being hidden behind another and not being measured by the scanner. The stress wave velocity of every tree in each of the 15 plots was measured using the ST300 tool (Fibre-gen Ltd., Christchurch, New Zealand). Stress wave velocity was measured at breast height (1.3 m above the ground) and parallel to the maximum curvature (convex side, see Figure 1). The diameter at breast height (DBH) was also measured. The curvature of the stem was mainly located below or directly at breast height. A second measurement was made at breast height perpendicular to the angle of curvature, i.e. at 90 degrees relative to the first measurement. A flag was installed on the first tree that was located to the east of north of the plot. Acoustic measurements were then gathered systematically on each tree within the plot in a clockwise direction. The flagging of the first tree and clockwise measurement procedure facilitated accurate linking of the scanner data and the individual tree velocity measurements.

The speed with which the mechanical wave travels depends on the type of wave generated, the properties of wood in the direction of wave propagation and the diameter of the tree (Wang et al., Wan 2007). The depth of the probes has an influence on the propagation time since the deeper the probe the shorter time taken by the transmitted wave to reach wood with a lower moisture content (heartwood), so allowing a faster propagation of mechanical waves. Therefore, insertion depth of the probes was kept constant at 3 cm to minimise the influence of this parameter. During the measurement, the probes were separated by a distance of 50 ± 5 cm.

The ST300 was tested using a standard brass bar and calibration procedure prior to use in the field. The velocities obtained during the calibration procedure (3.95 to 4.10 km s^{-1}) were always higher than the value specified in the calibration manual (3.75 km s^{-1}), meaning that the device used provided overestimates of velocity compared with a factory calibrated instrument. The error is a fixed difference in the time of flight which would result in a 6 to 13% overestimate of velocity; larger percentage differences being associated with larger true velocities. Velocities should not, therefore, be directly compared with values from other studies.

### Data processing

The data collected by the scanner were pre-processed using “Autostem” software (Treemetrics Ltd., Cork, Ireland) to obtain three dimensional stem profiles in an appropriate form for making a more thorough analysis of the curvature of the tree. The information generated by “Autostem” does not give the maximum value of the curvature but rather specifies the distance between a vertical axis and the centreline of the tree. Since the data collected by the scanner is very accurate (in the order of a millimetre), it is possible to measure the centreline, and therefore, the curvature of a tree regardless of the orientation of the curve relative to the scanner.

The stem profiles from “Autostem” were then processed using "Sweep Extractor", a program written specifically for this task, to obtain the maximum curvature of a log according to a predetermined length and a predetermined position in the tree. Curvature can be expressed in a number of ways, including the maximum deflection from a straight-line joining the centre points of the two ends of the log. The calculation of the maximum deflection of a log often requires the rotation of the x and y coordinates when the vertical axis is z (Figure 2).

“Sweep Extractor” generated the data necessary to conduct a detailed study on the relationship between the curvature of the tree and the acoustic velocity. The analysis was applied to two lengths of logs; one extending 3.0 m above the stump (10 cm from the ground) and the other extending 6.0 m from the stump.

### Statistical analysis

Analyses were conducted to compare the stress wave velocities measured using the ST300 at different positions on the tree. The Tukey Honestly Significant Difference test available in the R package (R Development Core Team 2009) was used for all comparison tests. The velocities measured parallel to the curvature (from the convex face) were compared with those measured at 90 degrees to the first measurement. A test for normality of the distribution of the data was performed for this analysis with the Shapiro-Wilk test for normality. The test confirmed that the data were normally distributed (w = 0.9927 and p = 0.2427). It is noted, however, that samples whose speed exceeded 7.5 km s^{-1} were excluded because the ST300 was very sensitive to temperature, tending to overestimate the speed when the outside air temperature was less than 10°C. This resulted in a reduction in the number of sample trees from 146 to 128.

A comparison was also made between the velocities obtained from the 50 samples having the smallest curvatures and the velocities obtained from the 50 samples having the largest curvatures. For this analysis the average of the two velocities measured on the tree (parallel and perpendicular to the curvature) were used. The data were shown to be normally distributed for both the 3 m log length (w = 0.988 and p = 0.50) and the 6 m log length (w = 0.991 and p = 0.74). The threshold curvatures for the 3 m log lengths were <63 mm and >84 mm. The thresholds for the 6 m log length curvatures were <79 and >107 mm.

A linear regression analysis was applied to the results for the two log lengths. Acoustic velocity was considered to be the independent variable, and curvature and DBH were considered to be the dependent variables. For these two regressions, the averages of the two velocities measured on the tree (parallel and perpendicular to the curvature) were used since no significant difference was found between them.