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Visualization of the spatial variation of wood density in Western Hemlock Henze, Kim-Jana 2006

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VISUALIZATION OF THE SPATIAL VARIATION OF WOOD DENSITY IN WESTERN HEMLOCK by KEvI-JANA HENZE Dipl.-Ing. (FH), University of Applied Sciences Rosenheim, 2003 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in The Faculty of Graduate Studies (Forestry) THE UNIVERSITY OF BRITISH COLUMBIA October 2006 © Kim-Jana Henze, 2006 ABSTRACT Previous studies of the within tree variation in density of western hemlock have constructed 2 dimensional maps of the variation in wood density from pith to bark and longitudinally within the tree, and have concluded that wood from the outer part of the stem is denser than wood found near the centre of the tree, and wood density decreases with tree height. Based on such information it should be possible to segregate wood from the outer, basal, parts of the tree stem following primary conversion and allocate it to end uses requiring hardness and higher strength. This premise assumes that circumferential variation in wood density in hemlock is insignificant, and such information is not available for western hemlock. This study mapped the density of the lower 5 m of four second-growth western hemlock stems in the x, (radial), y, (longitudinal) and circumferential (0) directions to determine their relative contributions to the overall pattern of density variation in hemlock stems. Computational and advanced visualization techniques were used to create 3-dimensional models of the spatial distribution of density in the hemlock stems. Circumferential variation in density was not significant, and previously established wood density trends from pith to bark and with height in the stem were confirmed. 3-dimensional images showed higher density wood in the outer part of the stem but the highest density wood did not form a continuous sheath in this part of the stem. Nevertheless, it should still be possible to utilize denser wood from the outer part of the tree for end uses requiring higher strength and hardness. Two novel and previously unreported features were observed. Firstly it appeared that the shape of the lower density juvenile wood core was cylindrical irrespective of the external shape of the stem. Secondly in one tree there was circumferential, helical variation in wood density with increasing height in the tree. It would be desirable to confirm whether these features are commonly found in western hemlock by examining greater numbers of trees. ii TABLE OF CONTENTS Abstract ii Table of Contents iiList of Tables v List of Figures vi Acknowledgements viDeclaration viiCHAPTER ONE 1 1 Introduction1.1 Introductory Remarks 1 1.2 Western Hemlock 2 1.3 Aims 4 1.4 Scope and Importance 5 1.5 Study Outline 6 CHAPTER TWO 7 2 Literature Review2.1 Introduction2.2 Tree Information2.3 Wood Characteristics and Utilization 8 2.3.1 Juvenile Wood 10 2.3.2 Compression Wood 1 2.4 Wood density 4 2.4.1 Variation in wood density in western hemlock 18 2.4.2 Circumferential variation in wood density 26 2.5 Methods of estimating spatial variation in density in three-dimensions 31 2.5.1 Computed Tomography 32.5.2 Image Processing using Volume Rendering; 37 2.6 Summary 38 CHAPTER THREE 40 3 Density Variation within Individual Western Hemlock Stems 40 3.1 Introduction3.2 Materials and Methods 42 3.2.1 Logs and samples3.2.2 Measurements of specific gravity 44 3.2.3 Scanning Electron Microscopy 6 3.2.4 Statistical Analysis 47 iii 3.3 Results : 48 3.3.1 Mean density 43.3.2 Scanning Electron Microscopy 54 3.4 Discussion ...55 3.5 Conclusions 59 CHAPTER FOUR 60 4 Visualization of Density Variation within Western Hemlock Stems 60 4.1 Introduction4.2 Material and Methods 62 4.2.1 3-dimensional modelling of density using Drishti 64.2.2 Computed Tomography '. 64 4.2.3 Calibrating CT Density 67 4.2.4 3-dimensional modelling of CT data with VGStudio .. 69 4.3 Results 72 4.3.1 Preliminary considerations 74.3.2 Three-dimensional reconstruction of gravimetric data using Drishti 74 4.3.3 Three-dimensional reconstruction of CT data using VGStudio 78 4.4 Discussion 89 4.5 Conclusion 93 CHAPTER FIVE .' 94 5 General Discussion, Conclusions and Suggestions for Further Research 94 5.1 General Discussion5.2 Conclusions 100 5.3 Suggestions for further research 10REFERENCES .' 101 APPENDICES 108 LIST OF TABLES Table 1. Global figures for wood density in western hemlock 19 Table 2. Summary of literature on the variation in density of western hemlock 28 Table 3. Dimensions of logs obtained from sampled trees 43 v LIST OF FIGURES Figure 1. Applications for western hemlock lumber 9 Figure 2. Average ring density trends from pith to bark for various softwood species 23 Figure 3. Principle of CT scanning 32 Figure 4. Location of Malcolm Knapp Research Forest 4Figure 5. Sampling of stems for density measurements 4 Figure 6. Segmentation of the western hemlock disks prior to density measurements 45 Figure 7. Disk showing the tracing of pie-shaped segments and density samples 45 Figure 8. Effect of tree height on density of western hemlock 49 Figure 9. Variation in wood density from pith to bark in western hemlock stems 50 Figure 10. Cross-sectional wood density map at breast height for tree # 1 52 Figure 11. Western hemlock stems 53 Figure 12 SEM photomicrographs of samples with densities of 0.56 g/cm3 (a, RLS) and 0.46g/cm3 (b,TS).... 4 Figure 13. 5 mm grid used to read off density values for each disk 63 Figure 14. Colour code for different wood density levels 64 Figure 15. Scanning planes used for CT analysis of hemlock disks 65 Figure 16. Western hemlock disk prior to CT scanning showing the orientation of density phantoms 67 Figure 17. Cross-section of a disk showing the phantoms used to calibrate density 68, Figure 18. Linear regression between CT grey value and density 69 Figure 19. Grey value segmentation for visualizing wood density distribution in an image stack 71 Figure 20. Cross-sectional view of 3D data of one disk at breast-height in western hemlock (left) and the distribution of gravimetric density in the same disk (right) 2 Figure 21. Density-related profile of CT image '. 73 Figure 22. 3D reconstruction of wood density classes for western hemlock log #2 75 Figure 23. 3D reconstruction of spatial distribution of low and medium density wood (0.35-0.40 g/cm3) in log # 2 : .76 Figure 24. 3D reconstruction of the spatial distribution of high density (0.45-0.50 g/cm3) wood in log #2 77 Figure 25. Grey-scale image of a western hemlock disk obtained by CT 78 Figure 26. Low density wood (0.30 g/cm3) highlighted at each height for tree #1 80 Figure 27. Medium density wood (0.40 g/cm3) highlighted at each height for tree #2.. 81 Figure 28. Medium/high density wood (0.45 g/cm3) highlighted at each height for tree #3 83 Figure 29. High density wood (0.50 g/cm3) highlighted at each height for tree #3 84 Figure 30. Low (0.30 g/cm3) and high (0.50 g/cm3) density wood highlighted at stump height for all four trees sampled 86 Figure 31. High density wood (0.45 and 0.50 g/cm3) at each height for tree #5 87 Figure 32. 3D reconstruction of a scanned disk highlighting low (>0.30 g/cm3) and high . (>0.50 g/cm3) density wood 88 Figure 33. Section within in log with different wood qualities 9vi ACKNOWLEDGEMENTS I would like to thank following individuals and organizations: Dr. Philip D. Evans, thank you for your guidance, your knowledge of scientific research and your assistance with the preparation of this thesis Dr. Simon Ellis and Dr. Stavros Avramidis, for their patience and for being members of my committee Dr. Ajay Limaye for his work in developing the algorithm for 3-D visualization of gravimetric density data Mr. Ross Cunningham for statistical analysis of gravimetric density data All of the faculty and staff in the Department of Wood Science and Centre for Advanced Wood Processing Robert Fiirst for his never-ending support, understanding and motivation throughout my study The graduate students in the wood surface science research group Coast Forest Products Association (CFPA) for funding Forintek Canada Corporation for allowing me to use their CT scanner and providing me with all necessary data and for introducing me to the software VGStudio Malcolm Knapp Research Forest in Haney, B.C. for supplying western hemlock logs vii DECLARATION This thesis is my own work, except as follows: The statistical analysis of the gravimetric density data was performed by Mr. R.B. Cunningham of the Statistical Consulting Unit (The Australian National University, Canberra, Australia), but I interpreted the results of the analysis. The development of 3-dimensional models using Drishti and specifically the creation of a customized algorithm to visualize gravimetric density data was undertaken by Dr. A.J. Limaye, Visualization Laboratory, Supercomputing Facility (The Australian National University, Canberra, Australia). viii CHAPTER ONE 1 Introduction 1.1 Introductory Remarks Wood is an extremely versatile material with a wide range of physical and mechanical properties and it is still the raw material of choice for a large number of products, despite the existence of competing materials such as new metal alloys, ceramics, plastics and composite materials (Haygreen and Bowyer 1996). Recently there have been large shifts in the supply of wood and the ways it is utilized. For example, trends in global industrial roundwood supply show a significant increase in the availability of wood from fast-grown short-rotation plantations in the southern hemisphere (FAO 2006), and it is estimated that 35 percent of the World's wood in the future will be grown in industrial plantations (Teischinger 2005). The importance of this plantation resource as well as the increasing use in countries with managed 'natural' forests of wood from second-growth forests is altering the nature of wood on the market. Hence, there is a pressing need to investigate and evaluate the properties of wood produced from plantations and second growth forests in order to better understand the extent of variability in properties and how this affects the processing and end uses of lumber products. The variation in wood properties and interactions of silvicultural practices and environmental factors on wood properties and final product attributes are very complex (Teischinger 2005). Thus efficient measurement of wood properties usually has to take 1 into account many features such as forest stand composition, tree species, stem form, wood age and chemical composition and many more. Tsoumis (1991), however, suggested that variability in the anatomical structure and properties of wood, within and between trees and species may not cause problems during the utilization of wood provided such variability is known and taken into consideration when the various products are made. Wood density is a composite measure of wood's properties and is directly related to its mechanical properties. Hence, it is an important index of wood quality for many end-uses particularly sawn wood, and all studies of variability in wood properties of western hemlock have measured its density (Wangaard 1950). .1.2 Western Hemlock Western hemlock (Tsuga heterophylla (Raf.) Sarg.) is the most important commercial tree species in coastal British Columbia. The volume of mature standing timber within coastal British Columbia was estimated in 1998 to be 1,681 million cubic meters. Harvest levels totaled approximately 8.0 million cubic meters that year, accounting for almost 40% of the region's total sawlog production (COFI 2000). Western hemlock is highly valued for its strength, pulping and treating characteristics (Jozsa et al. 1998). The wood is light and uniform in color, even-grained, lacks pitch and has excellent machining properties (Mullins and McKnight 1981, Jozsa et al. 1998). Western hemlock is widely used in all types of construction such as in framing, millwork and joinery, doors, windows, paneling, mouldings and architectural trim (Gonzalez 1996) with markets in the United States, S.E. Asia, China and Europe, principally for post and beam construction in 2 Japan (COFI 2000). Western hemlock is also used for veneer to manufacture Parallam and decorative overlays and is pulped to produce a variety of pulp grades (Gonzalez 1996). Second-growth western hemlock remains a small proportion of the harvested volume at present but will be a major resource in the future with different properties than old-growth (Middleton and Munro 2001). The variation of wood density within western hemlock trees has been the subject of several investigations and information on the variation in wood density from pith-to-bark and with height within trees is available (Megraw 1985, Jozsa et al. 1998). Information on the influence of silvicultural practices and environmental factors on density is also available (Gonzalez 1996, Fabris 2000, Middleton and Munro 2001). Many studies have looked at the effect of growth rate and ring width on the wood density of western hemlock (Jozsa and Kellogg 1986, Jozsa et al. 1998, Fabris 2000), and have observed that density tends to decrease with increasing ring width. According to Tsoumis (1991), however, the position of wood in the tree has a greater effect on density than ring width. Furthermore, he stated that rings of the same width do not always have the same density because they may contain reaction wood. Nevertheless, within trees of the same species it has generally been concluded that wood density follows a consistent pattern in the horizontal and vertical directions (Panshin and de Zeeuw 1980, Tsoumis 1991). 3 1.3 Aims Previous studies of the variation in wood density in western hemlock have mainly taken samples in one or more radial directions in the stem and have described within-tree variation in density based on these samples. Two dimensional maps of the within tree variation in density have been constructed (Jozsa and Middleton 1994, Jozsa et al. 1998). Most studies, however, have largely neglected possible circumferential variation in density or have assumed that it is captured by taking two or four (pith-to-bark) samples around the circumference of the stem. In many other fields increasing attention is being given to the spatial variation in morphology and properties in geometrically complex objects (Kamal et al. 1982, O'Dell and McCulloch 2000). The development of computed tomography has opened up new possibilities for the determination of internal property variation in logs. Accordingly, the more intensive measurement of wood density within trees that this technique permits should allow for a better understanding of spatial variation in density in trees and logs than has been possible based on assessment using increment cores. Using CT and advanced visualization software it should be possible to better visualize within tree variation in density and capture variability in density caused by local changes in wood structure or due to the presence of branch and reaction wood, knots or pockets of decay. It is hypothesized here that these features will alter the established pattern of density variation in western hemlock. The aim of this thesis is to examine the spatial variation in wood density in western hemlock, and specifically to quantify variation in density in the x, y and circumferential 4 directions, and use advanced visualization and computational techniques to better depict spatial variation in density in western hemlock stems. 1.4 Scope and Importance Due to the variability of wood, manufacturers often face problems in converting the raw material into products with consistent material properties and levels of performance. To some extent established methods of grading mitigate such variability; however, 'recent trends in mass-production have been towards greater uniformity' (Teischinger 2005). Therefore greater knowledge of the variability of density in western hemlock is important for the development of products that meet current market demands for high quality, uniformity and consistent levels of performance. As western hemlock is now one of the most important commercial tree species within British Columbia, it is essential for industry to improve its utilization so it can compete with other species, materials or products. The visualization of the spatial variation in density distribution within logs to better identify the location of wood of different density, could allow for improved utilization of western hemlock. More specifically this could make it possible to differentiate and utilize wood with defined density for particular end-uses, which could lead potentially to increases in both volume and grade recovery. A more refined approach to the selection and different uses of western hemlock may become increasingly important in future as the current timber resource is replaced with second growth wood. This study examined the spatial variation of wood density in western hemlock. Experimentation focussed on the lower five metres of the tree as this is the part of the stem that has the greatest variation in 5 wood density from end-to-end and has potential for segregation and conversion into higher value products (Panshin and de Zeeuw 1980). 1.5 Study Outline Following this Introduction, Chapter 2 reviews relevant literature on western hemlock wood and its use for the manufacture of wood products. The literature on wood density variation in western hemlock is reviewed and techniques for visualizing internal wood density variation in tree stems in three dimensions are described. Chapter 3 is an experimental chapter which examined basic wood density within four western hemlock trees in the x (pith-to-bark), y (height in the stem) and 8 (circumferential) directions within the first 5 m of the merchantable trunk. Wood density was determined gravimetrically and statistical modelling was used to determine the effects of position within the tree stem on density. The aim of Chapter 4 was to visualize the variation in wood density in three dimensions within western hemlock logs using a range of sophisticated modelling techniques. Measurements of wood density presented in Chapter 3 provided the numerical data for graphical analysis and 3-D modelling using the software Drishti. In addition, 2-dimensional radiographs obtained through CT scanning of log sections provided data that was used to construct three dimensional models of wood density variation at different heights in the tree stems. Chapter 5 discusses the results of the experimental chapters, presents final conclusions and makes suggestions for further research. 6 CHAPTER TWO 2 Literature Review 2.1 Introduction Western hemlock is an important tree species in the Pacific Northwest that is extensively utilized for a wide range of wood products (USDA 1984). Increasingly, the western hemlock used by industry in British Columbia is being derived from managed second-growth forests and hence it is important to better understand the properties of the wood from this resource to help industry optimize conversion and marketing strategies (Jozsa et al. 1998). 2.2 Tree Information Western hemlock is a member of the family Pinaceae, which includes other genera that are important for the forest industry including Pseudotsuga, Larix, Abies, Picea and Cedrus in the sub-division of the Abietoideae. It is a large tree that frequently grows to heights of 50 m (160 ft) and diameters exceeding 100 cm (3.5 ft) (Mullins and McKnight 1981). Maximum ages are typically between 400 and 500 years (Gonzalez 1996). Its distribution extends along the Pacific coast from Alaska southward along the whole of coastal British Columbia. It also grows in the inland and sub-alpine forest regions of British Columbia where abundant rainfall is available (Mullins and McKnight 1981). As a shade-tolerant species, it can regenerate well under a closed canopy. 7 Western hemlock is now one of the most valuable (by volume) commercial tree species in the Pacific Northwest and especially coastal British Columbia (Watson et al. 2003). It is very important for primary lumber products, and also pulp and secondary wood products. In coastal British Columbia, the harvest of western hemlock logs ranked first in 1998 followed by western red cedar (Thuja plicata Donn.), Douglas-fir (Pseudotsuga menziesii (Mirbel) Franco), true firs (Abies spp.) and spruce (Picea spp.) (COFI 2000). In 1999, almost 68% of total log exports from British Columbia were hemlock, followed by Douglas fir with less than 20% of the total. HemFir (western hemlock and amabilis fir (Abies amabilis (Dougl.) Forbes)) lumber production accounted for nearly 46% of the total produced in coastal British Columbia in 1999; however, it only represented 12.6% of the lumber production in the province. According to Middleton and Munro (2001), second-growth western hemlock represents a small proportion of the harvested volume, but it will become increasingly important in the future. For many years western hemlock was considered the least desirable commercial conifer species in the Pacific Northwest because it warps excessively during drying (Jozsa et al. 1998). However, methods have been developed to reduce the distortion of hemlock during drying and in principle it can be used for many of the purposes for which Douglas fir is employed, although it lacks the durability of Douglas fir. 2.3 Wood Characteristics and Utilization Western hemlock wood has a medium to fine texture and is straight and even grained. It is fairly light in colour and has a pinkish to reddish-brown tinge with little 8 difference in colour between sapwood and heartwood (Gonzalez 1996). The wood is normally free of resin and the annual rings are quite distinctive with a subtle transition from earlywood to latewood. Dark streaks which are caused by bark maggots occur frequently along the annual rings and are a good feature for its identification. Its density is moderate at 480 kg/m3 when air-dry (Gonzalez 1996). It takes finishes well, holds nails and screws well and is less inclined than Douglas fir to split during nailing (Mullins and McKnight 1981). Figure 1. Applications for western hemlock lumber As mentioned in Chapter 1, western hemlock is widely used in all types of construction, both residential and industrial. It is the most important pulpwood species in British Columbia and makes excellent mechanical and sulphite pulp and newsprint. It is a good framing lumber due its strength and nailing properties (Gonzalez 1996). Other uses for western hemlock are ladder stock, boxes, interior mouldings and treated railway ties (Gonzalez 1996). It is an important raw material in millwork and joinery manufacturing, (an industry traditionally oriented towards hardwood) because it is straight grained and finishes well. It is widely used for the manufacture of doors, windows, staircases, cabinets, spindles and paneling, moldings and architectural trim where its light color can be 9 enhanced by the use of natural finishes. The wood is only slightly resistant to decay and thus should be treated with a preservative when used in moist conditions or external applications (Gonzalez 1996). 2.3.1 Juvenile Wood The differences between wood properties of old growth trees and those from rapidly grown intensively managed forests are associated with the short rotation and the resulting high proportion of juvenile wood in the latter trees. There are many factors which influence the growth of individual trees on a given site, however, these will not be discussed in detail in this thesis. Generally, juvenile wood can be defined as the portion of the xylem first laid down near the centre of a tree. It forms a cylindrical column around the pith as a result of the prolonged influence of the apical meristem in the active crown on the wood formed by the vascular cambium (Panshin and de Zeeuw 1980). As the crown moves further upward in a growing tree, the influence of the apical meristem on the vascular cambium decreases and mature wood is formed. There are major differences in the wood properties of juvenile and mature wood. The former exhibits rapid changes in wood properties over space whereas mature wood is more uniform (Zobel and Sprague 1998). In general, juvenile wood has a lower mean density, shorter tracheids, thinner cell walls, lower proportion of latewood, lower cellulose and higher lignin content (Panshin and de z^eeuw 1980, Haygreen and Bowyer 1996, Zobel and Sprague 1998). The duration of the juvenile period in trees is quite variable between species, ranging from 5 to 20 years (Panshin and de Zeeuw 1980) with an abrupt termination of 10 juvenile growth in some wood species (Jozsa and Middleton 1994). Middleton and Munro (2001) found that increased proportions of juvenile wood in western hemlock were associated with significant reductions in MOE and MOR of structural lumber, but the properties of the juvenile core were a poor predictor of lumber strength. In their study the depression in wood density associated with juvenile wood formation extended for 10 to 15 annual rings (from the pith) for trees from southern Vancouver Island. In trees from northern Vancouver Island the juvenile zone extended for 25 to 30 years from the pith (Middleton and Munro 2001). Middleton and Munro (2001) also argue that pith-to-bark density trends vary greatly from tree to tree, thus a weak estimation of variation in the juvenile period is obtained when it is based on the depression of wood density. Wood juvenility can also be determined by examining fibre length, fibril angle, longitudinal shrinkage and lignin and cellulose content (Haygreen and Bowyer 1996). However, most literature uses the average ring, disk or stem density to define the juvenile period. Western hemlock shows a relatively long juvenile wood period compared to other conifers, which Jozsa and Middleton (1994) attributed to its shade tolerance due to a longer influence by the active crown. 2.3.2 Compression Wood Compression wood is formed on the lower side of the trunk of gymnosperms (Tsoumis 1991) as a response to a displacement from the vertical orientation (Panshin and de Zeeuw 1980, Timell 1986). It develops most frequently and extensively in vigorous, fast-growing trees (Timell 1986) and is common in western hemlock. It is darker than the surrounding 'normal' wood and has a reddish-brown color which makes it conspicuous, especially in species that do not possess colored heartwood (Tsoumis 1991). Severe 11 compression wood is readily recognized, by the presence of eccentric growth rings which contain larger proportions of latewood in the region of fast growth. Severe compression wood often occurs continuously over a large area of stem cross section, however, it can also be present in concentric, crescent-shaped zones which are normally concentrated in the latewood and are more characteristic of mild and moderate forms of compression wood (Timell 1986). Anatomically, compression wood differs from normal wood as it contains shorter and more distorted tracheids with thicker walls. Under the microscope, tracheids in cross-section appear rounded. Due to their circular shape, the tracheids are not tightly connected and intercellular spaces occur between them. The walls of the cells are thick, even in earlywood. Compression wood has a higher microfibril angle than normal wood (Siripatanadilok and Leney 1985), which causes the wood to shrink considerably in the longitudinal direction, resulting in warping and cracking across the grain. Microscopic checks and ridges of cell wall material are found in tracheids, both of which follow the microfibril angle of the S2 layer. Compression wood tracheids lack the inner (S3) layer of the secondary wall and the outer (Si) layer is thicker than normal (Timell 1986). Compression wood contains more lignin and less cellulose than normal wood. Furthermore, the distribution of lignin is different from normal wood and high concentrations of lignin are found in the outer portion of the S2 layer. Compression wood is up to 40% denser than normal wood and it exhibits remarkably high longitudinal shrinkage, which can reach levels of 5 - 10%. In contrast, its radial and tangential shrinkage are less than that of normal wood. Its higher specific gravity may be explained by the higher percentage of tracheids with thicker walls, 12 whereas high longitudinal shrinkage is due to its high microfibril angle in the secondary-cell wall. There is little information in the literature about compression wood in western hemlock and its distribution within trees. Kellogg and Warren (1979) observed streaks of compression wood in western hemlock that were associated with knots or the formation of branches and not, as is normally the case, with deformation of the stem. They also observed that these streaks varied greatly in size within the stem from a few centimeters to up to 4 meters in length. Siripatanadilok and Leney (1985) examined the variation in tracheid length and microfibril angle in western hemlock stems with different degrees of lean. They found that microfibril angle increased rapidly as the displacement of the stem from the vertical increased from 0 to 20°. Thereafter, as lean increased, microfibril angle remained constant. Tracheid length showed an inverse relationship to the lean angle, decreasing in length with increasing lean angle and reaching an almost constant level when lean exceeded 20°. However, there was large variation in microfibril angle and tracheid length between the trees examined. Compression wood is regarded as a serious defect since it is weaker than normal wood and its shorter tracheids make it less desirable for the manufacture of pulp. The wood is hard and brittle, has low stiffness and bending strength, and breaks with characteristic brash failures. Severe warping, distortion, and cross-checking occurs frequently when lumber that contains both normal and compression wood is dried. In normal wood most strength properties increase rapidly with increasing specific gravity, but this relationship does not apply to compression wood. 13 2.4 Wood density Wood quality is defined by Jozsa and Middleton (1994) as the attributes that make logs and lumber valuable for a particular end use. It can be characterized using a number of different properties, depending on their importance to the end use of the product. Wood density, defined as the weight of the cell wall contained in a unit volume, is considered by many as the best single measure of wood quality (Jozsa et al. 1989) because it is closely correlated with the physical and mechanical properties of wood (Brown et al. 1952). It is also a reliable indicator of the actual amount of cell wall in a tree (Smith 1970). The density of wood is directly related to its porosity which is the proportion of void volume in a given volume of wood (Haygreen and Bowyer 1996). As mentioned in Chapter 1, wood density is known to vary greatly within trees according to height, radial position from the pith, age of the annual ring, and other factors, and variation in wood density within trees is often greater than that between trees (Spurr and Hsiung 1954). Megraw (1985) claims that within a given tree, relative density varies in an organized, consistent, and reasonably predictable manner. In general, the terms specific gravity and density are often used interchangeably, however they have different meanings, as follows: Density (D) is defined as the mass of any substance per unit of volume (1). It is usually expressed in kilograms per cubic meter (kg/m3), grams per cubic centimetres (g/cm3) or pounds per cubic foot (lb/ft3). Density = mass (at a defined moisture content) (1) volume 14 Since wood is a hygroscopic material whose weight and volume vary with changes in moisture content, it is important to specify wood's moisture content at the time of measurement. The density of green wood for example decreases as its moisture content decreases, but below the fibre saturation point (FSP) the density of a sample decreases at a slower rate as the moisture content decreases. This occurs because decreases iii dry weight are smaller than decreases in volume as the wood dries further. With most methods, the weight and the volume are determined under the same conditions. Specific gravity (SG) is the ratio of the density of a material to the density of water at 4°C (Haygreen and Bowyer 1996) (2). This is also referred to as relative density. maSSoVendn Relative Density = volume (volume at any specified MC) (2) density of water Wood density based on green volume and oven dry weight is termed basic density or basic specific gravity (3). This measure of density is the one that is most commonly used because its two components, green volume and oven dry weight are almost constant and reproducible (Haygreen and Bowyer 1996). volume Basic Density = (oven-dry mass and green volume) (3) density of water Variations in the density of wood are due to differences in the amounts of cell wall and extraneous materials present per unit of volume (Brown et al. 1952). The amount of cell wall in wood is mostly determined by the sizes and proportional amounts of the 15 different cell types present in wood and the thickness of the cell walls, the latter having the greatest effect on density. Regular patterns of variation in wood density have been found within the stems of many commercial softwood species and excellent reviews of within tree variation in wood density have been written by Panshin and de Zeeiiw (1980), Megraw (1985), Zobel and van Buijtenen (1989) and Kennedy (1995). It is often reported that density decreases with height in the tree, primarily as a result of the increasing proportion of lower density juvenile-wood in the upper part of the stem (Panshin and de Zeeuw 1980). According to Tsoumis (1991) there is vertical variation (from base to the top of a tree) and horizontal variation (from pith to bark) in wood density within trees. In the vertical direction, density decreases with tree height and in the horizontal direction, density increases from pith to bark. In general, the specific gravity of most softwoods increases with distance from the pith and decreases with height (Brown et al. 1952, Haygreen and Bowyer 1996). This trend is clearer if only the merchantable trunk below the crown is considered (Panshin and de Zeeuw 1980). Megraw (1985) also claims that density is highest at the base of the tree and decreases much faster with increasing height within the first 5 m than at higher levels. In the horizontal direction, density generally increases outwards from the pith at all stem levels in softwoods. The inner lower density zone of wood represents the juvenile core. The extent of this juvenile wood core varies between species and even between trees, and the causes of this are highly debated by many researchers. 16 The horizontal variation in wood density in trees is strongly correlated with ring number from the pith, but weakly correlated with growth rate (Megraw 1985, Jozsa and Middleton 1994, Jozsa et al. 1998). According to Spurr and Hsiung (1954) who reviewed the effects of growth rate on the variation in specific gravity in conifers, the density of wood at a given point in trees is a function of the stresses placed upon it. They also described trends in specific gravity with distance from the pith; however, they questioned whether the trends observed were related to position of the wood in the tree or age. Spurr and Hsiung (1954) concluded that age or horizontal position had a much greater effect on specific gravity than ring width in a given cross-section and they asserted that the rate of growth of trees has far less effect on specific gravity than position in the tree and age of the wood. They also showed that low taper in stems was associated with a decrease in wood density with height. In summary the variation in specific gravity with position in tree including height and distance from pith (age) is considerable. Spurr and Hsiung (1954) also claimed that the volume of a growth ring with defined density and not its width.along the tree radius are important in assessing lumber production. This leads to the conclusion that it is essential to know the final use of the product and select the lumber accordingly, i.e. fast-grown tree may have a lower average specific gravity than a slow-grown tree because of its low density core wood, but it will actually produce a greater volume of high density wood in later years due to the increase in circumference of the stem. It is difficult to ascribe variability in wood density to a single factor or even to a combination of factors since density is affected by so many different variables, such as location in a tree, site conditions, nutrient supply, silvicultural practices, climate and 17 geographic location or genetic source (Haygreen and Bowyer 1996). Haygreen and Bowyer (1996) explain that factors such as age, vitality of the tree and location of wood within the tree are more closely correlated with density than rate of growth, however, they state that density is directly related to the percentage of latewood in a growth ring. Many of these factors influence density in combination, thus it is difficult to separate independent effects. There is abundant scientific literature dealing with the effect of these external factors on density and therefore they are not reviewed in detail here (Cown 1976, Panshin and de Zeeuw 1980, Smith 1980, Megraw 1985, Fabris 2000). The subsequent focus of this review is on within tree variation in density, which, as mentioned above, is greater than the between tree variation in density (Spurr and Hsiung 1954). In addition, the review focuses on the effects of macro-structural features, such as growth rings on density, rather than the influence of microscopic elements such as tracheids dimensions on density. For obvious reasons the focus of the review is on density variation in western hemlock. 2.4.1 Variation in wood density in western hemlock The average basic density of western hemlock wood has been variously reported to be 0.409 g/cm3 (Jessome 1977), 0.423 g/cm3 (Smith 1970) and 0.427 g/cm3 (Kennedy and Swann 1969). Gonzalez (1990) reported a basic wood density range for western hemlock of 409 to 436 kg/m3. 18 Table 1. Global figures for wood density in western hemlock Density (g/crri3) Date Author 0.41 1950 Stephenson 0.42 1965 U.S. Forest Products Laboratory 0.427 1969 Kennedy and Swann 0.423 1970 Smith 0.409 1977 Jessome 0.40-0.43 1998 Jozsa, Munro and Gordon Most of the research done on variation in density of second-growth western hemlock trees has examined the effect of growth rate, position in the tree, latewood and earlywood percentage, ring width and influences of stand conditions and silvicultural practices on density. Wellwood (1960) studied density variation in 60-year-old hemlock trees with site indices from 90 to 160. He found that rate of growth had the greatest effect on density. Data on density was obtained using wedge-shaped samples taken from disks cut at the base of trees, at about one-third tree height, and at the 5-inch top. Wellwood (1960) observed that rapid growth in western hemlock depressed wood density. He also reported a consistent negative correlation between density and the site index of sampled trees. Kennedy and Swann (1969) also observed a negative correlation between density (obtained from increment cores) and growth rate in western hemlock. Their results were obtained during a comparative study of the specific gravity and strength of more than 600 western hemlock trees from British Columbia. They also found that wood density was lower in trees from more northerly latitudes and increased with altitudes. Smith (1980) measured latewood width in rings 3 to 15 in increment cores obtained at breast height from 29 western hemlock trees in a 20-year-old spacing trial. He showed that rapid growth resulted in reduced wood density and percentage of latewood. The 19 effects of initial spacing and age upon ring widths and percentage latewood were shown to be highly significant. Watson et al. (2003) examined the wood and fibre properties of 38-year-old coastal western hemlock planted at five different stocking densities and found that wood density was not affected by spacing. A survey of wood density in western wood species conducted by the U.S. Forest Products Laboratory (1965) also showed a negative correlation between specific gravity (from increment cores) and average width of growth rings. 2.4.1.1 Variation in density from pith to bark One of the earliest studies of radial variation in wood density of western hemlock was performed by Wellwood and Smith (1962). Breast-height increment cores were obtained from rapidly grown 94-year-old trees located in the Malcolm Knapp Research Forest of the University of British Columbia and the density of the samples was measured at 5-year intervals. Density was highest (0.471 g/cm3) in the first five growth rings adjacent to the pith. It then declined in rings 16-20 before gradually recovering to 0.417 g/cm3 at ages 26-29. Kvarv (1964) studied density variation in western hemlock trees from different locations in British Columbia using increment cores, which were sub-divided into samples containing 10 growth rings. He found that density was highest near the pith, decreasing to a minimum 21 to 30 rings from the pith, and then slowly increased. A rather unexpected finding was that geographic location of trees had no effect on density (Kvarv 1964). Krahmer (1966) examined the relationships between some growth characteristics and density of 12 (34 to 243 year-old) western hemlock trees. He also found that density was highest in wood adjacent to the pith. His findings were based on measurements made 20 on radial strips, which were then subdivided into increments of 1 to 20 rings. The density of wood from cross-sectional disks taken at 8-ft-intervals along the stem was also measured. He observed a significant negative correlation between wood density and average width of rings beyond the core zone (radius 5 cm). Wood density was highest in the first growth ring and there was a subsequent decrease in density radially for 5 cm (with age not specified), after which density levelled off and displayed only a minimal gradual increase. Krahmer (1966) noted a significant negative relationship between density and rate of growth beyond his defined juvenile zone of 5 cm radius. Furthermore, he observed that a regular decrease in specific gravity from the base to the top of the tree was associated with growth rates of 10 or more rings per inch. Generally, density had decreased considerably at a height of 8 ft (2.4 m), but faster growth (less than 10 rings per inch) resulted in an increase in density from the base to the top of the tree. Jozsa and Kellogg (1986) studied the variation in density in 10 fast-grown western hemlock trees from British Columbia. Increment core samples were obtained from five different heights along the stem. They found that density decreased from the stump to a position representing 40% of the height of the tree and then increased to 80% of the trees height. Their results showed that wood formed in the first 10 years of growth was relatively dense (0.40 - 0.55 g/cm3). Wood formed subsequently (ages 10 to 20) was less dense and thereafter there was a rapid and steady increase in density from age 20 to about 40. They concluded that the pith-to-bark trends in wood density were age-related, and not a function of distance from the pith. DeBell et al. (1994) investigated the effect of ring width on wood density in breast-height increment cores within the confines of a similar age cohort (rings 20-24 from the 21 pith). They found that wood density averaged over the 5 years for each strip was negatively correlated with ring width (radial growth rate). Mean wood density dropped from 0.47 to 0.37 g/cm3 as average ring width increased from 2 to 8 mm. They found that the width of latewood was relatively constant regardless of growth rate resulting in lower latewood percentage and decreased density in the wider rings. They concluded that a decrease in latewood percentage was the primary reason for the negative correlation between ring width and density. Jozsa et al. (1998) undertook a comprehensive assessment of the wood properties of various softwood species including second-growth western hemlock (Figure 2). Density measurements were made on radial strips cut from disks at 12 different heights on thirteen 90-year-old western hemlock trees from coastal British Columbia. They observed. that high-density wood (>0.43 g/cm3) was located near the pith and in the outer mature wood. Density declined rapidly in the first years of growth until a minimum value was reached approximately 12 years from the pith. Thereafter density increased gradually until age 80 when it approached a value similar to that of wood adjacent to the pith. 22 Relative density at breast height 0.55 0.50 -{ 0.45 0.40 0.35 0.30 H 0.20 Douglas-fir W. larch ,W. hemlock Yellow cedar Lodgepole pine Sitka spruce , " • ^ .. • * Interior spruce — • - Subalpine fir W. redcedar Juvenile Mature wood • 1 i i i wood 10 20 30 Age (years) 40 50 60 (Graph adapted from Jozsa et al. 1998) Figure 2. Average ring density trends from pith to bark for various softwood species Middleton and Munro (2001) examined the effect of stand density on the wood properties of two hundred, 90-year-old second-growth western hemlock trees selected from three different locations on Vancouver Island, British Columbia. Trees from southern Vancouver Island, growing at stand densities of 930 stems per hectare (sph), showed only a brief and shallow juvenile wood depression with a minimum density (0.43 g/cm3) occurring between 10 and 15 rings from the pith. In contrast, trees from the northern site and at the same stand density, exhibited a much more pronounced and prolonged juvenile depression in wood density. In general, they concluded that differences in wood density were much more dependent on cambial age than on growth rate (ring width). Most recently, DeBell et al. (2004) measured the effects of ring age, stand conditions and silvicultural practices on the wood density of fifty-six western hemlock trees from 23 stands. They measured the density of radial strips of wood obtained from 23 disks taken at breast height. Wood density was highest (0.49 g/cm3) near the pith and there was a rapid decline in density at age 10 (0.40 g/cm3) and a gradual increase from age 20 until it remained fairly constant from age 38 and beyond (0.43 - 0.44 g/cm3). A negative influence of rapid growth on whole ring density was greatest when the trees were young, and diminished with time, becoming insignificant beyond age 30. Overall, DeBell et al. (2004) concluded that wood density displayed a relatively uniform trend in young-growth western hemlock. 2.4.1.2 Variation in density with tree height Kellogg and Keays (1968) studied density distribution in western hemlock and concluded that wood density was higher at the base of the tree and at the top, and there was little variation in between. This finding was subsequently confirmed by Jozsa and Middleton (1994). Farr (1973) also confirmed the aforementioned pattern of vertical variation in wood density within 75 to 186 year-old western hemlock trees. He showed that basic density declined from breast to mid height, and then generally increased toward the tip, with changes being relatively small over most of the stem except at breast height and near the top of the trees. Farr's findings were based on measurements of the basic density of increment cores as well as 2-inch thick wedges cut at 1-foot intervals from the stump to the top of the trees. He obtained significant correlations between the density of single increment cores and whole tree specific gravity, but when the specific gravity of breast-height wedge samples was included in analyses, correlations were greatly improved. He found considerably less variation in specific gravity among wedge samples than among the single increment cores taken at breast-height. His findings are similar to those of Krahmer (1966) who observed relatively little change in density over most of the 24 stem length in 12 (34 to 243 year-old) trees, but found that density was higher nearer the base and top of the trees. Wellwood (1960) also noted that density decreased with height in his study of specific gravity and tracheid length variation in second-growth (56 to 78 year-old) western hemlock. Pong et al. (1986) examined the variation in green and basic density in 54 year old-growth western hemlock trees based on disk and increment core samples. A minimum of five disks were obtained from each of 29 trees and increment cores were also taken from the same trees. They found that basic density remained fairly constant with height in the tree. The highest values were found at the stump and thereafter density decreased slightly through mid-bole and then increased slightly again in the upper bole. Jozsa and Middleton (1994) studied the variation in density of 90-year old western hemlock trees and found that density ranged from 0.44 g/cm at the stump to 0.40 g/cm' at the top, reaching a minimum value of 0.35 g/cm at 20% and 40% of the height of the trees. In the radial direction, they found that wood density decreased from a high near the pith and reached a minimum 5-8 cm from the pith. Wood density then gradually increased again until it reached a more or less constant level. This pattern was observed at all heights within the stems except at the stump where the increase was not as large after the minimum density was reached. Jozsa and Middleton (1994) also found that there was an inverse relationship between ring width and density after about the age 8-10 years. They also stated that mature wood was formed in western hemlock when its density exceeded a fixed value of 430 kg/m", which occurred after approximately 35 years (Jozsa and Middleton 1994). Jozsa et al. (1998) found that average wood density varied with height in the tree. The highest density wood was found at the base of the tree. Density decreased 25 with height, but increased towards the crown (at 90% of tree height). Differences in density within the bole were greatest between samples obtained from the stump and 10% of the height of the tree. 2.4.2 Circumferential variation in wood density • There is no consistent pattern in the tangential or angular variation in wood density either across or within species according to Tsoumis (1991), or it is insignificant, and thus can be ignored (Nicholls 1986). These conclusions, however, are based on very few studies and, for example there are no studies of the circumferential variation in wood density in western hemlock. In an unpublished survey of plantation grown Douglas-fir trees in New Zealand cited by Cown (1976), it was observed that the circumferential variation in density could contribute significantly to the overall variation in density of wood. In accord with this finding, Gonzalez (1989) concluded that circumferential variation in wood density was unpredictable in Douglas fir. Gonzalez (1989) also examined the circumferential variation in density of lodgepole pine (Pinus contorta Dougl. var. latifolia Engelm.) to determine if the method of assessing wood density using opposite radial strips was accurate enough to estimate mean disk density. The testing was done on eight disks taken at breast height with pie-shaped segments cut from within the disks. The number of segments in each disk varied from 12 to 17 and each segment was divided further at mid-radius into inner and outer samples to obtain an estimation of the variation in the density of both juvenile and mature wood. Her results showed that circumferential variation in density was generally lower in juvenile than in the mature wood. Although she observed large variation in density in some disks, a 26 systematic trend was apparent in that 'density gradually increased and decreased circumferentially reaching high and low values on opposite sides of the disk'. Nicholls (1986) examined.the within-tree variation in wood characteristics of radiata pine (Pinus radiata D. Don), including the circumferential variation in density. However, he found no significant circumferential variation in wood density in the trees that he sampled. Table 2 summarizes the results of previous studies of variation in wood density of western hemlock trees. 27 Table 2. Summary of literature on the variation in density of western hemlock General Year Author Material Testing Results for Density 1965 U.S. Forest Products Laboratory 142 western hemlock trees from 5 different locations Increment cores Negative correlation between specific gravity and average width of growth rings 1969 Kennedy, R.W. and Swann, G.W. 600 western hemlock trees from British Columbia Increment cores at breast-height Wood density was lower in trees from more northerly latitudes and increased with sites at higher altitudes 1980 Smith, J.H.G. 29 western hemlock trees, 20-year-old Latewood width measurements in rings 3-15 of increment cores at breast-height Effects of initial spacing and age upon ring width and percentage of latewood were highly significant. Rapid growth results in reduced wood density and percentage of latewood Pith to bark 1962 Wellwood, R.W. and Smith, J.G.H. 94-year-old western hemlock from UBC Research Forest Increment cores at breast-height and measurements taken of 5-year intervals Highest wood density (0.471) in first 5 rings, declines to minimum in ring 16-20, gradually recovering (0.417) at 26-29 years 1964 Kvarv, E. Western hemlock from different locations in B.C. Increment cores, sub divided into 10 growth ring samples Highest wood density at pith, decrease to minimum 21-30 years from pith and a slowly increase thereafter. Geographic location had no effect on wood density 1966 Krahmer, R.L. 12 western hemlock trees (34 to 243-year-old) Radial strips, sub divided into 1-20 rings and cross-sectional disks at 8-ft-intervals along the stem Highest adjacent to pith, subsequent decrease for 5cm (age not specified), after which density levelled off, and minimal gradual increase. Negative correlation between tree density and average width of rings beyond core zone (of 5cm radius). Highest near base and top of tree. Decrease in wood density from base to top associated with growth rates of 10 or more rings per inch density decreased considerably at 8-ft, but faster growth (< 10 rings per inch) resulted in increase from base to top of tree. Negative correlation between density and rate of growth beyond core zone (5 cm radius) 28 Pith to bark 1986 Jozsa, L.A. and Kellogg, R.M. 10 fast grown trees from B.C. averaged over 2 sites Increment cores from 5 different heights along stem Density decrease from stump to 40% height of tree, then increase to 80%. Growth rings 1-10 relatively dense (0.55-0.4), then low density wood (10-20), then rapid and steady increase 20-40. Conclusion: Density trends are age-related and not function of distance from pith 1994 DeBell, J.D., Tappeiner, J.C. and Krahmer, R.L. 30 29-year-old and 27 38-year-old western hemlock trees from two commercial thinning trials Increment cores at breast-height, measurements on similar age cohort (rings 20-24) Average over 5 years show negative correlation between wood density and ring width (radial growth rate). Decrease in wood density from 0.47-0.37 with increasing ring width from 2-8mm. Width of latewood relatively constant regardless of growth rate, resulting in lower percentage of latewood and decrease in wood density in wider rings. Conclusion: decrease in latewood percentage primary reason for decreasing wood density with increasing ring width 1998 Jozsa, L.A., Munro, B.D., and Gordon, J.R. 13 90-year-old western hemlock trees from coastal B.C. Radial strips cut from disks at 12 different heights along stem High density wood >0.43 adjacent to pith and in outer mature wood. Rapid decline in first years with minimum approximately 12 years from pith. Gradual increase until 80 years, approaching value similar to wood adjacent to pith. Highest at base with decrease to crown but increase at 90% of height. Differences in bole were greatest between base and 10% of height 2001 Middleton, G.R., and Munro, B.D. 200 90-year-old western hemlock trees from 3 different locations and stand densities from Vancouver Island, B.C. 5mm increment cores at breast-height for each sample tree 930 stems per hectare (sph) from southern site show only brief and shallow juvenile zone depression with minimum between 10-15 years 930 sph from northern site show much lower and more prolonged juvenile depression Differences in wood density much more dependent on age than growth rate (ring width) 2004 DeBell, D.S., Singleton, R., Gartner, B.L., and Marshall, D.D. 56 western hemlock trees from 23 stands Radial strips at breast height Highest (0.49) near pith, rapid decline at age 10 (0.40), gradual increase from age 20 and reaches fairly constant level from age 38 and beyond (0.43-0.44) Negative influence of rapid growth on whole ring density was greatest when trees were young and become insignificant beyond age 30 when wood density displayed relatively uniform trend 29 Height 1960 Wellwood, R.W. 56-78-year-old western hemlock trees site indices 90-160 Wedge-shaped samples cut from disk at base, midbole and at 5 inches from the top Density decreases with height 1968 Kellogg, R.M., and Keays, J.L. 3 (59-92-year-old) western hemlock trees from UBC research forest Disks taken from 10-ft stumps along stem and from each stump at 1 -ft height and at the base Higher at base and at top of tree with little variation in between 1973 Farr, W.A. Western hemlock trees from 20 even-aged stands in southeast Alaska 75 to 186 year-old Increment cores at breast-height plus 2 inches thick wedges cut at 1 -ft intervals from stump to top Decline from breast-height to mid height, increase to top with small changes over most of stem except breast-height and near top. Significant correlation between density of single increment cores and tree density, however, even more significant with wedges. Less variation among wedge samples than increment cores 1986 Pong, W.Y., Waddell, D.R., and Lambert, M.B. 29 54-year-old western hemlock trees Disk and increment cores. Minimum of 5 disks per tree and increment cores from each tree. Measurement of green and basic density Basic density remained fairly constant with height. Density was highest at stump and decreased slightly through midbole and slightly increased in upper bole 1994 Jozsa, L.A., and Middleton, G.R. 26 90-year-old western hemlock Stump height density was high (0.44) then decreased to top (0.40) and was at a minimum (0.35) at 20% and 40% height Radial pattern of density variation observed almost at all heights, except stump, (increase not as large after minimum was reached). Mature wood formed at values > 430 kg/m3, which was reached approx. after 35 years Circumferential 1976 Cown, D.J. Plantation Douglas-fir in New Zealand Circumferential variation could contribute significantly to overall variation, but Gonzalez later concluded it was unpredictable 1986 Nicholls, J.W.P. Pinus radiata D. Don Radial strips No significant variation around circumference 1989 Gonzalez, J.S. Lodgepole pine 8 disks at breast-height cut into wedge-shaped segments (12-17 segments) which were subdivided into an outer and inner sample Circumferential variation generally lower in juvenile than mature wood Trend: density gradually increased and decreased circumferentially reaching high and low values on opposite sides of disk 30 2.5 Methods of estimating spatial variation in density in three-dimensions Most previous studies did not describe the variation in wood density of trees in three dimensions, but displayed density data in two dimensional graphs (see Figure 2). There is, however, great interest in developing technologies to obtain 3-dimensional images of the internal structure of logs as a means of increasing lumber yield during sawmilling (Bhandarkar et al. 1999). The technologies being developed for this application show promise as a means of increasing our understanding of spatial variation in wood density within trees. 2.5.1 Computed Tomography Computed Tomography (CT) is a non-destructive method of obtaining accurate 2-dimensional images of the internal structure of any object, and the technique has been used to analyze the characteristics of logs (Oja and Temnerud 1999) and power poles (McCarthy and Greaves 1990). From these 2-D images the internal structure of the log can be reconstructed in three dimensions. X-ray CT is one of the systems being considered for the imaging of objects. Computerized Axial Tomography (CAT) is the most promising and most widely used technology, although tangential scanning is an alternative described by Gupta et al. (1999). CT scanning of logs uses an X-ray tube as a source of X-rays which penetrate the log perpendicular to its longitudinal axis. X-rays transmitted through the log are captured by an image receptor and their energy is measured. X-rays characteristically have short 31 wavelengths between 5 x 10"9 and 1CJ12 meters and X-ray tubes are operated at a potential of between 6 KeV and 1 MeV (Hailey and Morris 1987). The basic principle of CT scanning is illustrated in Figure 3. Usually, the X-ray tube and the image receptor are mechanically coupled together and rotate around the object to yield a series of projections through the same plane. The image receptor detects changes in attenuation as the rays pass through the object, and a computer capable of interpreting and recording the x-ray signals is connected to the receptor. Higher density wood, increasing log dimensions or distance from the x-ray source cause fewer photons to pass through the log (Rinnhofer et al. 2003). Graph adapted from http://www.birinc.com/Digital_Radiography.asp) Figure 3. Principle of CT scanning The projected image of the wood is the sum of the energy transmitted through the log. This is used to reconstruct 2- dimensional images (tomography) on a slice-by-slice basis along the length of the log. These images can either be used to identify internal features, measure the geometry of the log, or characterize its material properties. The 32 sliced images can also be assembled to provide highly accurate 3-dimensional models of the object. CT-scanners produce density maps, which are generally displayed as images of varying grey-scale intensity (Funt and Bryant 1984). The pixel grey level in a CT image represents the X-ray attenuation coefficient, which is proportional to the amount of X-ray energy absorbed (Bhandarkar et al. 1999). According to Oja and Temnerud (1999) a "CT-image is a grey scale image where each picture element (pixel) represents the average CT-number in the corresponding part of the CT-scanned object". Thus, if an object is scanned, the CT-image will be an x-ray attenuation map describing the variation in density of the material within a cross section of the object. The X-ray attenuation of a material is a function of its density, chemical composition and photon energy (Rinnhofer et al. 2003). Objects are defined by shape and X-ray attenuation (CT-number) with dark pixels having low CT-numbers and bright pixels high CT-numbers. A material like water moderately attenuates x-rays; objects like bone show higher attenuation and spongy tissues have very low attenuation coefficients (Burgess 1984). Thus, higher density materials attenuate x-rays to a greater extent (higher CT-number), whereas lower density materials have lower attenuation coefficients (and lower grey-level pixel value). Accordingly, in CT-images of wood, dark pixels represent wood of low density such as earlywood, and the light pixels, wood with high density such as latewood or knots. The procedures used for the analysis of logs using CT are more exacting than those involved in the traditional analysis of wood quality using disks or increment cores (Varem-Sanders and Campbell 1996). 33 There have been a number of studies of CT imaging of wood, particularly logs, power poles and standing trees (Funt and Bryant 1984, Hailey and Morris 1987, McCarthy and Greaves 1990, Lindgren 1991, Gupta et al. 1999, Awoyemi and Wells 2003, Cruvinel et al. 2003, Rinnhofer et al. 2003). One of the first studies using X-ray imaging was conducted by Maloy (1930) on standing trees. A brief description of the computational principle underlying CT and its application to wood are given by McMillin (1982) and Burgess (1984). Detailed explanations of the development of different types of medical and industrial CT scanners are found in Gupta et al. (1999) who state that most existing industrial CT scanners are designed for quality control inspections in offline situations. There have been numerous reviews of CT scanning, for the assessment of defects and wood quality in solid wood product industries (Hailey and Morris 1987, Schad et al. 1996, Niemz et al. 1997, Muller and Teischinger 2001). Benson-Cooper et al. (1982) demonstrated that internal wood features such as decay pockets, knots, cracks, annual rings, insect cavities, pruned branches, sapwood/heartwood boundary, bark and resin inclusions and moisture pockets could be detected and differentiated using CT. From their study it is apparent that CT scanning can display the cross-sectional structure of a log in considerable detail and in a form which is suitable for aiding decisions on subsequent processing. However, they also found that there was an unsatisfactory relationship between CT number and basic density because of the confounding effect of log moisture on x-ray attenuation. The use of CT-scanning to detect internal log defects has also been described in detail in reviews by Hailey and Morris (1987) and Bhandarkar et al. (1999). They mention 34 that the density of wood within a cross section of a log in a given species varies significantly as a result of variability in growth ring structure and the presence of moisture. Hailey and Morris (1987) also reported on the confounding effects of wood moisture content on density. Schad et al. (1996) state that additional problems in the interpretation of CT images are caused by knots because their density and moisture content is higher than that of the surrounding wood. Thus, it is difficult to delineate the boundary between areas of high moisture content and knots. This problem may be resolved, however, by increasing the scanning resolution of CT as this results in knots and high moisture content areas having different CT-numbers. The drawback of CT that are mentioned by Schad et al. (1996) are the time it takes to acquire sufficient numbers of scans to produce a representative set of images and the high costs of CT equipment. Other studies have used CT images of wood to assess spiral grain (Sepulveda et al. 2002, Ekevad 2004), automatically detected the location of the pith within logs (Longuetaud et al. 2004), estimated volume of resin pockets (Oja and Temnerud 1999), and evaluated the density profiles of wood samples (Lindgren et al. 1992). Miiller and Teischinger (2001) argue that one drawback of generating 3D models from CT images is that the crook of the stems is not accounted for, and they also emphasize the need to carefully evaluate the cost benefits of investing in CT technology. The latter point was also made by Rinnhofer et al. (2003), while Oja and Temnerud (1999) stress the limitations of CT scanning imposed by scanner resolution. They claimed that the scanners that were then available would obtain incorrect, smoothed, estimates of earlywood and latewood density due to their limited resolution. 35 The literature on CT scanning to determine wood density, excluding densitometry, is mainly associated with the research undertaken to detect defects in logs, as mentioned above. One of the most cited studies on the use of CT scanning to evaluate wood density examined the relationship between the X-ray absorption coefficient and CT-number (Lindgren 1991). Lindgren (1991) calculated CT-numbers for dry and wet wood containing different amounts of cellulose, hemicellulose and lignin, and showed that normal variations in the chemical composition of wood had a small influence on its mass attenuation coefficient. Because of this, it was claimed, CT-scanning could be used for precise and non-destructive measurements of wood density. Lindgren (1991) also examined the relationship between CT-numbers and the density of wood containing water. He measured the dry and wet density of wood with accuracies of ± 4 kg/m3 and ±13.4 kg/m3 respectively, but noted that the relationship between dry and green wood density and CT-number was not the same. Since water significantly influences measurement of wood density using CT scanning, it is difficult to accurately estimate the density of wood when it contains water. He also stressed that results obtained using CT scanning could also be affected by variation in scanner technology between manufacturers and even between scanners from the same manufacturer. Macedo et al. (2002) studied the calibration of CT images when assessing wood density at three different X- and gamma-ray energies. They found that measured attenuation coefficients for eight wood species did not vary significantly, but they confirmed that attenuation coefficients varied with material composition and density. They also reported that at low energies the former had a significant influence, but at high energies density had a more significant effect on attenuation. 36 Overall, Computed Tomography is one of the most significant advances in X-ray imaging, since it allows the internal structure of an object to be reconstructed from multiple projections of the object. The horizontal location of any included defects can be determined, however, the vertical spatial location cannot be determined from a single transmission. For this purpose, advanced software can be used to process CT-images and reconstruct 3-dimensional data sets which then assist in the assessment of the quality of the lumber. 2.5.2 Image Processing using Volume Rendering Volume rendering, also called Volume Graphics, is a specialty of 3D computer graphics and refers to the visualization of volumetric data given as a set of scalar or vectorial samples. It applies to the representation and visualization of objects represented as sampled data in three or more dimensions (Volume Graphics 2005). Volume visualization has possible applications in estimating the spatial variation in wood density of logs based on different data sources. The sources for volume data can be classified into three main groups: (1), data sampled from analytical functions; (2), data acquired from scanning real world objects, such as computed tomography (CT) or magnetic resonance imaging (MRI); or (3), data derived from computational simulation such as that obtained in the field of computational fluid dynamics. Volume visualization methods display volumetric datasets by either indirectly or directly rendering the data (Limaye 2005). Indirect volume rendering first involves the conversion of the data into a set of polygon iso-surfaces and subsequently rendering these into approximate contour surfaces (Mattausch 2003). Direct volume rendering refers to computing ah image directly from the 37 volume data without decomposing it into geometric primitives . The advantage of indirect volume rendering is that surface rendering techniques can be used that have been extensively studied and refined in computer graphics. Furthermore, specialized hardware has been developed for these applications. However, most of the information contained in the data is not utilized to its full capability and the complexity of the intermediate step of conversion into polygons is less predictable and may exceed the capacity of the hardware in terms of memory requirements. Direct volume rendering on the other hand, produces semi-transparent cloud-like images which are a representation of the entire volume since all samples contribute to the final image to a certain degree and give a better insight into the data. The main drawback of direct volume rendering is the amount of data that has to be processed and this method is therefore considered to be relatively slow, which has limited its applications in the recent years. In this thesis direct volume rendering is used since large amounts of data needed to be processed and the volumetric datasets were obtained on cubic and uniform rectilinear grids by CT scanning or alternatively through the transfer of gravimetric data into a grid. 2.6 Summary As lumber from naturally.regenerated second-growth western hemlock forests now represents the majority of the wood available from B.C.'s coastal forests (Jozsa et al. 1998), information on the quality of this resource is needed to support its processing and marketing. Accelerated growth and earlier harvest leads to a greater proportion of lower 1 Geometric Primitives consist of a box, sphere, cone and cylinder and may be created to represent the boundary of an object and may be positioned arbitrarily in three-dimensional space. Currently, all primitives are Cartesian aligned with the subject geometry. 38 density juvenile wood in the lumber. Thus the wood properties of western hemlock are changing and need to be understood in detail as they affect the utilization of the material in many important ways. This chapter reviewed previous studies of the variation in wood density of western hemlock, which is a key indicator of the quality of the resource. The literature describes in detail the horizontal and vertical variation in density in western hemlock trees, but there is little or no information available on the circumferential variation in density within trees. Furthermore, the spatial variation in density is presented in 2-dimensional density maps. In general, circumferential variation in density in conifers is considered insignificant (Nicholls 1986), and thus the literature provides little information on 3-dimensional distribution of density in trees. Thus, visual or graphical information that may assist in understanding the spatial distribution of wood density within western hemlock trees is lacking. It is anticipated that the results of this study, which employs advanced imaging technology such as Computed Tomography and sophisticated software to create 3-dimensional density maps, will lead to a more complete understanding of density distribution in western hemlock and may assist with the development of better methods of utilising this important species. 39 CHAPTER THREE 3 Density Variation within Individual Western Hemlock Stems 3.1 Introduction Variation in wood properties is a major challenge for the forest products industry (Teischinger 2005) as the market demands uniform wood products with predictable properties. It is widely known that density is highly correlated with most of the mechanical properties of wood (Panshin and de Zeeuw 1980), and is an important factor in determining the suitability of wood for many end uses. Wood density is related to the amount of cell wall and extraneous materials present per unit volume (Brown et al. 1952). Cell wall thickness has the greatest effect on density, because the density of the cell wall is constant (1.5 g/cm3). Wood density varies significantly between species, between trees of the same species and within individual trees. The magnitude of within tree variation in wood density may exceed the between tree variation. Within-tree variation of wood properties can be grouped into three components: (1) radial; (2) longitudinal (height); and (3) tangential (circumferential) (Tsoumis 1991). Studies on wood density variation in western hemlock have shown that density varies with stem height (Jozsa and Kellogg 1986) and radially from pith to bark as described in Chapter 2. According to Jozsa and Middleton (1994) density, is highest at the base of the tree and higher at the top with little variation in between. In most studies basic 40 density has been shown to decrease from a high near the pith, then decrease and then gradually increases again towards the bark. As wood density varies within western hemlock in both vertical (longitudinal) and horizontal (radial) directions, previous studies have been able to construct 2-dimensional maps showing the variation in wood density in trees of western hemlock (Jozsa and Middleton 1994, Jozsa et al. 1998). These maps more clearly show that wood from the area adjacent to the pith and from the outer and basal part of the stem is denser than wood formed between these two zones. Based on such information it should be possible to segregate wood from the inner juvenile or outer, basal parts of the tree stem and allocate them to end uses requiring higher wood density. This assumes that circumferential variation in wood density in hemlock is insignificant; however, information on such within tree variation in density in western hemlock is not available. The aim of this Chapter was to investigate the spatial variation of basic density of second-growth western hemlock in coastal British Columbia and to map the density of hemlock stems in radial, longitudinal and circumferential directions to determine their relative contributions to the overall pattern of density variation in hemlock stems. The density within the lower (<5m), more commercially valuable part of four western hemlock stems was examined and the density of wood samples cut from the entire cross-section was quantified. This approach was adopted instead of using the more commonly used method of single line densitometry on increment cores. As a result it was possible to obtain a more complete understanding of the spatial variation of density in western hemlock. 41 3.2 Materials and Methods 3.2.1 Logs and samples Six western hemlock trees in the age range of 65 to 79 years and located in a southerly site at an elevation of 155 m in UBC's Malcolm Knapp Research Forest (MKRF) were sampled (Figure 4). The trees that were selected were similar in their age and size, and representative of the second-growth western hemlock resource, but larger on average than the trees on the site. The sampled trees originated as natural regeneration following a fire in 1924. The composition of the stand was primarily western hemlock (73%) and western redcedar (Thuja plicata Donn.) (23%) with Douglas-fir (Pseudotsuga menziesii (Mirbel) Franco) making up the balance (4%). The stand density was 650 nr/ha, and the average height of the trees was 30 meters with a mean diameter of 0.25 meters at breast height. (Map adopted from http://www.for.gov.bc.ca/mof/maps/regdis/ndck.htm) Figure 4. Location of Malcolm Knapp Research Forest 42 The six hemlock trees were felled in October 2003 and the lower five meters of each tree was removed from the forest and transported to the Centre for Advanced Wood Processing (CAWP) at the University of British Columbia. However, only four logs (1. 2. 3 and 5) were comprehensively sampled to assess spatial variation in wood density. The dimensions of each log are shown in Table 3. Table 3. Dimensions of logs obtained from sampled trees Log Length Diameter butt Diameter top Diameter mean No. Growth No. [cm] • [cm] [cm] [cm] rings at butt 1 500 40.7 36.5 38.6 70 2 504 48.0 40.3 44.2 72 3 508 54.0 41.8 47.9 72 4 506 41.3 38.5 39.9 61 5 505 58.5 47.9 53.2 70 6 506 44.0 40.8 42.4 61 The logs were manually debarked using a bark spud and bucked into 14 segments with a chain saw according to the scheme shown in Figure 5. A total of five thin and five thick cross-sectional disks were cut from each stem at almost equal intervals over their total length. The thinner disks were used for measurement of the density variation of the wood within the stems. The larger disks were used for computed tomography. 43 [ Bottom j Figure 5. Sampling of stems for density measurements The exact location and code allocation for each of the sampled disks is shown in Figure 5. Each disk was air dried for 2 weeks and they were then conditioned at 20° ± 1° C and 65 ± 5 % relative humidity for 10 weeks. 3.2.2 Measurements of specific gravity Each disk was subdivided into 12 equal pie-shaped sectors using the cardinal points as the basis for allocating each wedge position (Figure 6). The pie-shaped sectors were numbered clockwise starting at north. 44 N S Figure 6. Segmentation of the western hemlock disks prior to density measurements The thin disks were leveled and machined to the same thickness using a Precix Minirouter and a 63.5 mm surface cutter. The disks were then sanded using a wide belt sander to obtain their final thickness of 25 mm. The numbers of growth rings were counted on each disk and groups of five growth rings were then traced onto the end grain of the surface of the disk orientated closest to the crown of the tree (Figure 7). \ Figure 7. Disk showing the tracing of pie-shaped segments and density samples The 5-year density sample next to the pith was designated as sample A, the adjacent 5-year sample was listed as sample B, and so on by alphabetical notation until the bark 45 was reached. The surface maps of growth ring samples and segments were transferred onto transparencies to facilitate subsequent identification of samples. The disks were cut into wedges with a band saw, and a thin kerf (0.5 mm) scroll saw was used to sub-divide each wedge into smaller specimens containing 5 growth rings. Specimens were oven dried at 105°C overnight to a constant weight and their weights were recorded on an electronic balance to a resolution of 1/1000 g. The specimens were then submerged in water for 4-5 days until they were fully saturated and their volume (cm3) was measured by displacement (ASTM 1996). The basic density (3) of each sample was determined as the ratio of oven dry weight to green volume. Weighty ^ Basic density = ^-2. (3) VolumeGrem The density of all pith-to-bark samples at each sampling height for four trees (trees 1-3, 5) was measured. 3.2.3 Scanning Electron Microscopy Small samples, 5x5 mm in cross-section and 15-20 mm in length, which were representative of wood samples cut from the stems were examined by scanning electron microscopy (SEM). Specimens were cut from the transverse, tangential and radial surfaces of each sample and were placed in a beaker containing distilled water for 3-4 days. When the specimens were saturated, thin sections were sliced off the surface of interest to obtain a perfectly smooth faces for microscopy. The prepared samples were then stored in a desiccator for approximately 3 days and a small specimen measuring 5x5 mm was cut from each sample. The specimens were fixed onto aluminium stubs with double sided 46 adhesive tape and then sputter coated with a gold-palladium alloy (Au 60%-Pd 40%). Specimens were examined using a variable pressure Scanning Electron Microscope (SEM) (Hitachi S-2600 VPSEM). Images of the radial, tangential and transverse surfaces were digitally recorded. 3.2.4 Statistical Analysis The density of 3156 samples from four logs was measured. Statistical analysis of density data was performed to assess the effects of stem, height, section (sample orientation) and sample position (radial distance from the pith) on density. Log number was regarded as a random effect. Preliminary analysis of data revealed that sample orientation had no' significant (p=0.557) effect on density. Data for density were unbalanced because the disks at each sampling height contained unequal number of samples due to differences in tree age. Therefore, analysis of data was by weighted least squares following estimation of variance components by Restricted Maximum Likelihood (REML) (Searle et al. 1992). This methodology was chosen because it is particularly suitable and efficient for modelling unbalanced data with both fixed and random effects. All data analysis was performed using GENSTAT (Lawes Agricultural Trust 1994). Results are presented graphically and least significant difference (LSD) bars (p<0.05) on each graph can be used to estimate the significance of differences between individual means. The relevant data files and output from the statistical analyses are appended to this thesis (Appendix 1). 47 3.3 Results 3.3.1 Mean density The density of individual samples varied from 0.31 (low density juvenile wood) to 0.7 g/cm3 (knot). Statistical analysis revealed that the effects of height and radial position within the tree on wood density were highly significant (p<0.001), but there was no significant interaction (p=0.628) between these two effects. Hence, density results for height and radial position were averaged across all samples in accord with the factorial design of the experiment. 3.3.1.1 Variation in density with height The effect of tree height on within tree variation in density in western hemlock stems is shown in Figure 8. Wood from the base of the tree at 0.25 m was significantly (p<0.05) denser than wood from the upper four disks (1.45m, 2.65m, 3.85m and 5.05m). The density of the wood in the basal disk averaged 0.4519 g/cm whereas the comparable value for wood from the uppermost disk was 0.4085 g/cm3. Wood density was at a minimum (averaging 0.4034 g/cm3) at 3.85m height. The density of wood at this level was significantly (p<0.05) lower than that of wood at sample heights of 0.25m and 1.45m (0.4232 g/cm3). However, its density was not significantly (p>0.05) lower than that of wood in the adjacent disks at 2.65m (0.4139 g/cm3) and 5.05m (0.4085 g/cm3) from the ground. There was no significant variation (p>0.05) in the density of the wood in between the top three disks. 48 p < 0.001 ,0 0.47 0.46 0.45 -0.44 -w 0.43 (D Q u 0.42 H w 03 m 0.41 -0.40 -0.39 LSD = 0.01624 0.00 1.00 2.00 3.00 4.00 5.00 Height, distance from base of tree (m) 6.00 Figure 8. Effect of tree height on density of western hemlock 3.3.1.2 Pith-to-bark density trends Figure 9 shows the effect of distance from pith (growth ring number) on wood density of the sampled stems. Density decreased from the pith (from rings 5, 10 and 15) and then increased towards the bark. The core-wood (rings 1-5) was as dense as wood in rings 40 to 50. Wood at the pith (0.4309 g/cm3) was significantly denser than that of samples in rings 10 to 35, but there was no significant difference between the density of wood adjacent to the pith and that of samples from ring 40 and beyond. Low density wood (in this study subjectively defined as <0.39 g/cm3) was present from growth rings 5 to 20. Results indicated that there was a significant difference in wood density between samples at growth ring number 10 (0.3788 49 g/cm ) and 40 and beyond. The lowest wood density occurred 15 rings from the pith (0.3681 g/cm ) on average and wood at this position was significantly (p<0.05) less dense than other samples except for the ones immediately adjacent to this zone. Between rings 20 and 40, density increased slightly but differences between sample means were not significant (p>0.05). The densities of the samples at a distance of 20 to 35 rings from the pith were significantly (p<0.05) lower than those of samples located more than 40 rings from the pith. p < 0.001 0.46 n 0.36 -j 1 1 1 1 1 1 1 0 10 20 30 40 50 60 70 Distance from pith (growth ring number) Figure 9. Variation in wood density from pith to bark in western hemlock stems From ring 40 to 50, density increased significantly, and thereafter showed a slight, but insignificant (p>0.05) decline. The average wood density of samples 40 rings from the 50 pith was significantly (p<0.05) lower than that of wood located 50 rings from the pith. There was no significant (p>0.05) difference in the densities of the samples located 45 to 65 rings from the pith. Figure 10 shows the density distribution within the disk at breast height in tree #1. The x-axis represents the west to east direction while north-south is represented by the y-axis. Different colors are used to depict wood in five density classes (from 0.30 to 0.50 g/cm ). It is very noticeable that low density wood forms a core at the centre of the stem while higher density wood envelops this. In accord with results shown in Figure 9 it is also clear that wood immediately adjacent to the pith is denser than the surrounding wood. The highest density wood appeared to be located at the periphery of the stem. 51 3.3.1.3 Visualization of effect of tree height and distance from pith The effect of tree height and distance from the pith on the wood density of the western hemlock stems is shown in Figure 11. Since there was no significant interaction of these two effects, wood density was averaged over each log, disk height and sample. 52 Figure 11. Western hemlock stems Figure 11 confirms the trends observed previously (Figure 8 and Figure 9), but makes it easier to visualize them. Clearly wood density decreases with height in the tree and reaches a minimum at a midpoint between the pith and the bark. The wood adjacent to the pith is as dense as the wood formed later in growth at all levels. 53 3.3.2 Scanning Electron Microscopy Figure 12 shows scanning electron photomicrographs of samples with densities of (a), 0.56 g/cm' and (b), 0.46 g/cm". Sample (a) clearly contained compression wood as Figure 12 (a) clearly shows checks in the cell walls, which is a diagnostic feature of compression wood. Sample (b) showed rounded tracheids with intercellular spaces. The S3 layer was absent and deep helical checks extend from the lumen through the S2 layer. It is clear that this sample also contained compression wood even though its density was close to the overall sample mean of 0.42 g/cm'. Figure 12 SEM photomicrographs of samples with densities of 0.56 g/cm3 (a, RLS) and 0.46 g/cm3 (b,TS) 54 3.4 Discussion Results obtained here clearly reveal that the density of the wood in the four western hemlock stems did not vary circumferentially in a systematic way. Statistical analysis of density data from four trees showed that there was no significant (p>0.05) effect of sample orientation on wood density. This accords with previous studies of the circumferential variation in wood density in Douglas-fir, lodgepole pine and radiata pine (Cown 1976, Nicholls 1986, Gonzalez 1989). The lack of systematic circumferential variation in density here and in previous studies is probably related to the way in which secondary growth occurs in trees. Such growth occurs through divisions in the vascular cambium and subsequent increases in the size of derivatives of cambial mother cells (Megraw 1985). Circumferential variation in sizes of cambial mother cells or subsequent increases in size or cell wall thickening would be needed to cause systematic circumferential variation in wood density. As mentioned above, statistical analysis of data here did not show a significant effect of 'circumference' on density, but there was still considerable random variation in wood density circumferentially. Data obtained experimentally in this Chapter are used in the next chapter to visualize circumferential density variations within the stems of hemlock trees. The basic density of the hemlock logs (averaged across four logs, five heights within the tree and all sections) was 0.42 g/cm". This value is in good agreement with the findings of the Canadian Wood Density Survey (0.423 g/cm3) (Smith 1970) and the U.S. Western Wood Density Survey (0.42 g/cm3) (U.S. Dept. of Agriculture 1965). However, it 55 is higher than the value obtained by Jessome (1977) who indicated that the basic density 3 3 of hemlock was 0.409 g/cm . Other studies obtained wood density values of 0.427 g/cm (Kennedy and Swann 1969) or 0.41 g/cm3 (Stephenson 1950). Gonzalez (1990) reported that the basic density of coastal western hemlock varies from 409 to 436 kg/m3. A study conducted by Kvarv (1964) obtained a higher density value of 0.492 g/cm3 for hemlock from the same location as the material sampled here. Kvarv (1964) also showed that specific gravity was highest in wood close to the pith and decreased thereafter, before slowly increasing towards the bark, in accord with findings here. Jozsa and Kellogg (1986) obtained average density values for coastal western hemlock of 0.425 g/cm3 averaged over two sites and also observed that high density core-wood was formed for the first 10 years of growth. Low density wood was evident from age 10 to 20, but there was a rapid increase in density up to about age 40 (Jozsa and Kellogg 1986). All studies have found that the density of juvenile wood defined as the inner most wood close to the pith differed from wood formed subsequently. Annual rings close to the pith tend to be wide and contain relatively high density wood, which was also observed here (0.50-0.57 g/cm ). Jozsa and Kellogg (1986) found that low density juvenile wood in western hemlock was formed from the 11th to 20th rings (from the pith), which is similar to the results observed here. Contrary to the findings of Krahmer (1966) as well as Wellwood and Smith (1962) who found no evidence of a continuous increase or decrease in specific gravity beyond the zone of "juvenile wood", results here show significant changes (p<0.001) in density from about 40 to 50 years of age. This pattern was evident at all heights in each tree. 56 Josza and Middleton (1994) reported that the mature wood region in western hemlock was reached at a point where relative density exceeded a fixed value of 430 kg/m (in their study this was reached after approximately 35 years). If this value was applied here then mature wood formation would not commence until after 45 years of growth. Krahmer (1966) observed that decreases in specific gravity from the base of the tree to the top in Western hemlock was associated with growth rates of 10 or more rings per inch, but faster growth (less than 10 rings per inch) resulted in specific gravity increases. According to Krahmer (1966) there is a strong relationship between wood density and ring width. Accordingly, he found that the highest specific gravity wood was found adjacent to the pith and there was a significant decrease occurring within 2 inches of the pith and at stump level, and a considerable decrease at a height of 8 feet. He also analyzed the higher density core-wood under the microscope and confirmed the presence of compression wood. The presence of compression wood in conifer stems is extremely undesirable for solid wood processing. It causes warping problems such as excessive shrinkage along the grain because of the large microfibril angle in compression wood tracheids, or twist because of spiral grain. Furthermore, both of these features also result in reduced lumber strength (Jozsa and Middleton 1994). Wood density may also be influenced by the presence of compression wood. Most previous studies of within tree variation in density in conifers deliberately avoid parts of the stem that contains compression wood. In this study the density of all of the wood in cross sectional disks in 5 m butt log segment was measured. As Megraw (1985) pointed out when investigating specific gravity variation in loblolly pine, the 5 m butt log segments have a much greater specific gravity gradient 57 from one end to the other than upper log segments. Hence, research here makes it possible to create an accurate picture of how density can vary in hemlock stems. The method used to measure relative wood density in this, study is less economical than analysing wood density through increment cores. A further advantage of measuring the density of increment cores is that the process is non-destructive. Gonzalez (1989) analyzed different methods of determining circumferential variation in the density of lodgepole pine and her results showed that two samples taken opposite each other would give a better approximation of the mean density of the disk than simply using one core. The sampling method used to assess density here, however, provides a means of understanding and visualizing wood density distribution in three dimensions. Because wood is anisotropic and e.g. shrinkage is unequal in the three axial directions, this is of technological interest. 58 3.5 Conclusions Based on the four western hemlock logs studied here, which were examined from pith to bark at five sampling heights, the following conclusions may be drawn. There was no systematic effect of circumferential position within hemlock stems on wood density, but density appears to vary randomly around the circumference. This could possibly be due to the presence of compression wood. Distance from the pith and height within the tree had significant effects on wood density, as others have found. The average basic wood density value for hemlock (0.42 g/cm3) obtained in this study is in good agreement with figures obtained by previous studies using different sampling methods (single increment core, multiple cores or wedges) and methods of measuring density. It is possible that the value obtained in this study may have been inflated slightly because samples containing compression wood were measured whereas most other studies have avoided sampling compression wood. The method of estimating within tree variation in wood density by segmenting the disks into equal pie-shaped pieces and then five growth-ring classes was time consuming but provided insights into circumferential variation in wood density and also provided data which will enable density to be visualized in 3 dimensions in the Chapter that follows (Chapter 4). 59 CHAPTER FOUR 4 Visualization of Density Variation within Western Hemlock Stems 4.1 Introduction The basic density of wood influences most aspects of the conversion, properties, and end-use of wood products and detailed knowledge of the spatial distribution of wood density in tree stems prior to their conversion into wood products would greatly increase the efficiency of many wood processing systems. Previous studies have shown that wood density varies significantly in the x (radial) and y (longitudinal) directions in western, hemlock, and results in Chapter 3 generally accord with the findings of these previous studies. Results in Chapter 3 also showed no significant variation in density tangentially around the circumference of the stem. As mentioned in Chapter 2, CT has great potential to describe the spatial variation in wood density in tree stems. When CT is coupled with sophisticated visualization software it should be possible to create 3-dimensional models of density variation within tree stems, which should be superior to the 2-dimensional models developed to-date. The primary objective of this Chapter was to create 3 dimensional models of density variation in hemlock stems using gravimetric data obtained for the study described in Chapter 3, and data obtained through CT scanning. Advanced computational and visualization techniques were used to create 3-dimensional models of density variation in hemlock stems. 60 It is hypothesized that visualizing wood density distribution in 3 dimensions will give an improved understanding of the amount and distribution of high density wood in western hemlock stems, and may reveal spatial patterns of density variation that cannot be captured using conventional 2-dimensional models of density. 61 4.2 Material and Methods Density data for 3-dimensional modelling was obtained from four western hemlock trees ranging between 65 and 79 years of age, as described in Chapter 3. 4.2.1 3-dimensional modelling of density using Drishti Among several rendering techniques for volumetric data, direct volume rending has become a very valuable visualization technique for a wide variety of applications, as mentioned in Chapter 2. The technique utilized here is the hardware-based volume rendering software Drishti, which is a tool to explore regular-grid based scalar volumetric data sets. This software system provides multi-resolution zooming that allows the user to view arbitrarily large data-sets by visualizing sub-volumes from the data-sets. The innovative features of the software include data splitting and volume sculpting facilities to gradually remove portions of the volumetric data for exploring internal structure. Sculpting has been shown to be useful in volumetric applications (Limaye 2005) because it is sometime important to explore the inner structures of the sampled datasets by gradually removing material to gain better insights into internal structure. Direct mapping, involves the assignment of optical properties such as opacity and color to voxels . Volumetric data described with voxels represents the result of some sampling process of three dimensional object or structure such as that obtained from CT images. 2 The term voxel (portmanteau of the words volumetric and pixel) is used to characterize a volume element; it is a generalization of the notion of pixel that stands for a picture element. 62 Drishti is being heavily used in The Australian National University (ANU) at the Department of Applied Mathematics and by the paleontologists at the Department of Earth and Marine Sciences. Itrequires highly developed and advanced computer hardware. Wood density values were obtained from measurements on samples containing 5 growth rings, which were cut from disks at pre-defined positions within the trees as described in Chapter 3. These density values were transferred onto transparencies which overlaid each disk before they were cut into samples. To ensure accurate representation of density distributions within each disk, values were read off a 5 mm grid, which was applied to the actual disk contour and entered into a matrix. Figure 13.5 mm grid used to read off density values for each disk 63 This procedure produced a 3 dimensional data set because the thickness of the gravimetric samples described the Z-values for each disk. The density data was then imported as text-files into the software Drishti. Values within the density matrix were assigned a colour as shown in Figure 14 to discriminate wood of different densities. > 0.30 (g/cm3) > 0.35 (g/cmJ) > 0.40 (g/cm5) > 0.45 (g/cm3) > 0.50 (g/cm3) Figure 14. Colour code for different wood density levels Missing data for wood between the disks were interpolated by applying custom-built algorithms that recognized the connection between different wood densities. Large portions of the volume were sectioned out through volume segmentation before rendering to reduce the quantity of calculations that had to be preformed. Full 3D movies were generated to show the distribution of wood density (with predefined levels) within the four western hemlock stems. 4.2.2 Computed Tomography Larger disks cut from each log, approximately 140 mm in thickness, were used for computed tomography and for further image analysis. The thick disks were air dried and then conditioned at 20° ± 1° C and 65 ± 5 % relative humidity for 20 months and disks were then levelled to same height using a wood mizer horizontal bandmill. The CT scanner that was used to analyze disks was specifically designed for the non-destructive evaluation of large dimension specimens. Its X-ray capacity (up to 3.5 64 MeV) is approximately 30 times greater than that of conventional medical equipment and it can be used for any material and sizes up to 5 m in length. The X-ray source provides a fan beam geometry and is stationary along with the detector array. Five large disks per log (Figure 5), adjacent to the thinner disks that were used for specific gravity measurements in Chapter 3, were scanned at different horizontal planes within each disk (Figure 15). 2 mm scanning Interval f 10 mm scanning Interval Figure 15. Scanning planes used for CT analysis of hemlock disks Density samples measured gravimetrically in Chapter 3 were obtained from a disk located above the larger disk that was used for CT measurements. The upper 10 mm of the larger disks were scanned at 2 mm intervals followed by 10 mm scanning intervals down through to the bottom of the disk. This approach was chosen so as to better compare the density values measured gravimetrically with those obtained by CT. The thick disks were placed individually into the CT scanner. A marker was placed at a line on each disk as a point of reference that assisted identification and orientation of the disk in their x- and y-directions, as well as the vertical orientation of consecutive disks. A total of 20 disks were scanned in the Industrial CT scanner in its translate - rotate mode. This mode of operation required the disk to be moved through the X-ray beam during data 65 collection, rotate a few degrees and then translate back through the beam in the opposite direction. In translate-rotate mode the electronic data is corrected by the translate position. After this correction, the attenuated x-ray signals are captured by the detectors and pre-processed by CT-software, in 'backprojection mode'. Backprojection projects each view of the disk back along a line corresponding to the direction in which the projection data were collected. Hence, a faithful reconstruction of the disk can be obtained, which is then saved as a 16 bit image. Two different kinds of density reference materials or phantoms were used during the scanning process to calibrate samples. Line pair phantoms were used for height orientation. These consisted of several disks made of steel and polypropylene, polypropylene and air and polypropylene only with known densities. A line pair phantom was placed on top of each sample to calibrate the machine before each scan, and to determine the exact height of the disk and ensure it was aligned horizontally (Figure 16). Eight other density phantoms were placed adjacent to the disk (Figure 16). These phantoms were composed of materials with densities ranging from 0.8 to 1.38 g/cm3, which were used for image calibration. The phantoms were composed of polypropylene (0.896 g/cm ), ultra-high molecular weight polyethylene (0.923 g/cm ), low density polyethylene (0.923 g/cm3), Nylon (1.146 g/cm3), acrylate polymer (1.18 g/cm3), polyvinyl chloride (1.377 g/cm3), acetal (1.405 g/cm3) and water (1.0 g/cm3). 66 Figure 16. Western hemlock disk prior to CT scanning showing the orientation of density phantoms The resolution of scanning was 0.635 mm using the fastest possible translate-rotate scanning parameters with a 600 mm field of view. Each scan section was 2 mm thick and each disk was scanned in cross-section every 2 or 10 mm (Figure 15). A 600 mm diameter scan circle was selected to fit the largest disk. The scan time per section was 6.25 mins and a total of 400 reconstructed images were recorded and stored for further analysis. 4.2.3 Calibrating CT Density In order to calculate wood densities from CT images, the images must be calibrated using appropriate reference materials of known density (ASTM 2003). For this reason, each hemlock disk was scanned with several density phantoms of known density, as described above. 67 The average grey-scale value of the known materials were determined using image analysis (BIR viewer 1.0.4.0) which enabled grey values to be measured at any point on the image (Figure 17). Figure 17. Cross-section of a disk showing the phantoms used to calibrate density Several scans were used to obtain average grey values for each density phantom, and the averages were plotted against the known densities of the phantoms (Figure 18). The density calibration of images was performed using the linear regression between X-ray attenuation and grey values and the density of calibrated phantoms (Figure 18). 68 CT Grey Value - Density Reference Chart y = 3875.7x+ 1439.1 onnn 7nnn 3 3 / UUU finnn • OUUU ^nnn o ouuu _ CO > ^ Ar\r\r\ 4UUU u ouuu onnn *iUUU -i nnn 1 uuu n u c 0 c 3 U 0 c 3 C 3 C 0 -5 3 C 3 U 3 C 3 C 1- U 3 C 3 U 3 U 3 C 3 C 3 <J 3 C 3 U 3 Ci 3 C 3 C 3 r-3 C 3 U - 1-3 C 3 C - 0 3 C 3 U 0 0 3 C De 3 C 0 c 3 C isity 3 U 15 C 3 C (g/c 3 C 15 C m3) 3 U 3 C 3 C 3 t 3 U 3 C - C 3 U VJ C 3 C VI c 3 U 0 C 3 C 0 T 3 u t "5 3 C 1- U Figure 18. Linear regression between CT grey value and density The linear regression between grey value and density was used to calibrate specific grey values in the CT images. These were used to estimate wood density values within the western hemlock disks. 4.2.4 3-dimensional modelling of CT data with VGStudio The direct volume rendering system VGStudio (Volume Graphics 2005) was used to create density models from CT data. VGStudio is a highly sophisticated image visualization software package that supports the interactive visualization of volumetric data. In contrast to the Drishti, VGStudio uses rendering technology that can process the largest volume data sets on a personal computer (PC). VGStudio differs from traditional 3D graphics in that the latter primarily deals with the representation of object surfaces, 69 whereas VGStudio allows the representation of the object surfaces and the interiors, and can gradually remove material (like Drishti) to reveal internal information. A wide variety of data files and types can be imported into the software for visualization, and these can be processed as single data files or stacks of several image data files. Images from CT scanning were utilized in this Chapter to analyze the interior structure of wooden disks. The CT images contained very large amounts of data because 2048 x 2048 pixels images with a pixel depth of 16 bits were generated. The specific software that was used to reconstruct 3 dimensional images from the raw data collected was VGStudio 1.2.1 Build 348 distributed by Volume Graphics. For each disk section (Figure 15), raw data files were imported into VGStudio. This was repeated for each section within a disk. All images within a disk were then combined, and image stacks for the different disks were combined for each stem. The combined image stacks were merged into one file which contained all the images, but allowed them to be moved freely and to be enhanced individually. Each disk was rotated around its vertical axis so that all the disks' cardinal points were orientated, in the same direction. To differentiate different density levels within individual disks and all disks within a log, a classification tool provided by VGStudio was used. This tool separated or segmented data within a volume data set by grey value thresholds (Figure 19). The tool also allowed manipulation of the opacity and colour of areas with different grey-scale values and it could also be used to reduce or remove noise, air or unwanted segments within a CT image. 70 •Preset selection —•——— •—•—-—• : —— j—,:' ' i';,., — —_—;,,.,.....„...„.,•••...-; j calibrated density • Object overview --• —-—- —. '-. ; ^_..„„. 1 C>inr-rtv nwnin lintinrv «r«A - -Segment 1 mm JmwmWm I, JHHL MaKWWUBm 1 1 j t/ttumti' 1 / 1 — — _ — - •.! Figure 19. Grey value segmentation for visualizing wood density distribution in an image stack For each stack of images the grey value range was divided into five sections representing the different wood density categories of interest, and colours were assigned to each category to make it possible to differentiate between them within disks (Figure 14). The grey value for each density category was estimated using the linear regression above (Figure 19). To reduce visual clutter, grey values representing noise and air were disabled and then separated from coloured wood density zones. Three dimensional models of the two dimensional density maps for each disk were created with VGStudio, and images in high resolution were exported to allow ease of interpretation and illustration. Photographs of disks were taken and compared to the CT images. This ensured correct alignment of the CT scan slices with the corresponding wood disk when creating the 3 dimensional images. 71 4.3 Results 4.3.1 Preliminary considerations Comparison of 2-dimensional representations of gravimetric density data with 3D models show a number of similarities, as expected. The areas of higher density wood discernable in 2-D plots could also be seen in the CT models (Figure 20). Small differences between the two are probably due to the difference in spatial resolution used in data acquisition. CT scanning operated at a spatial resolution of 0.623 mm, whereas the gravimetric measurements were taken at 5 mm intervals over the entire cross-section, which blurrs the boundaries between wood of different density. Figure 20. Cross-sectional view of 3D data of one disk at breast-height in western hemlock (left) and the distribution of gravimetric density in the same disk (right) The location, amount and shape of low density wood core (juvenile wood) were also discernible in both types of images (Figure 20). 72 On most 3D images obtained through CT scanning, it was quite noticeable that some image stacks were surrounded by a thin layer of material (Figure 21). This is caused by the transition between material and air. As seen in Figure 21, the red graph represents the density related profile which depends on technical parameters, energy source and the material. Figure 21. Density-related profile of CT image 73 Grey values are assigned to the ordinate while the abscissa represents the distance in mm. When a grey value threshold is applied for instance in-between the blue lines, then the 3D image will illustrate every value within this range including the value for the transition between material and air. This effect can be eliminated partly by segmentation within the software tool. However, since the stems were neither circular in shape nor of the same size, automation of this procedure was not possible and segmentation would have to be applied individually, which would be very time-consuming. Knowledge of this phenomenon is essential for correct interpretation of the 3D images that follow in Section 4.3.3. 4.3.2 Three-dimensional reconstruction of gravimetric data using Drishti As mentioned above (Section 4.2.1), 3-dimensional reconstructions of gravimetric wood density data for each western hemlock log were exported into video files. The distribution of wood in different density classes can be visualized from still frames taken from these animations. The full animations are contained in a CD appended to this thesis (Appendix 2) Results for only one log (log # 2) will be presented here. Red and green arrows represent north and west, respectively, while blue indicates the vertical axis of the log (pointing to the base of the tree). The wood density ranges are indicated to the left using the same colours employed to depict density classes obtained by CT. 74 Figure 22. 3D reconstruction of wood density classes for western hemlock log # 2 In Figure 22, all wood density classes are displayed to give an overall impression of the spatial variation in density within stem 2. To gain a better insight into the distribution of wood density, unwanted density ranges (<0.30 and >0.55 g/cm3) are disabled. Low density wood is mainly located close to the pith. Figure 23 only depicts wood in the density class 0.35-0.45 g/cm3 to facilitate better visualization of the internal distribution of wood with this density range. From this visualization it appears that wood of medium density (0.40 g/cm-) envelops the lower density wood, although medium density wood is also found near the pith. 75 0.3 0.35 i 0.4 0.45 flM5 r Figure 23. 3D reconstruction of spatial distribution of low and medium density wood (0.35-0.40 g/cm3) in log # 2 The 3D reconstruction obtained using Drishti reveals that the wood of different density classes varies with height and also circumferentially. Imaging also shows that the medium density wood is discontinuous in its distribution. The spatial distribution of wood in the higher density classes are shown in Figure 24. Wood with a density of 0.45 g/cm' encases the less dense material (not depicted) and increased quantities of this higher density class occur at the side of the log facing east and towards the base with scattered pieces located along the western side. The densest wood (>0.50 g/cm3) is only visible on the side facing east. This higher density wood extends almost along the entire length of the log. Scattered strands are found around the periphery 76 with increased amounts at the base of the log. The amount of wood with a density of 0.45 g/cm' appears to be much greater than wood of other density classes because it is located in the part of the stem with the largest diameter. Figure 24. 3D reconstruction of the spatial distribution of high density (0.45-0.50 g/cm3) wood in log # 2 In general, it was noted that low density wood (0.35 g/cm3) was located in the juvenile core pith and its quantity increased with height as expected. Medium density wood (0.40 g/cm3) encloses the lower density wood while itself being wrapped around by higher density wood that seem to occur mostly in the outer layers of the tree. Wood of these predefined density classes are for most parts discontinuous over the length or across the diameter of the stem. Imaging reveals that higher density wood is more prevalent than 77 lower density wood. A regular pattern of the effect of the cardinal points on wood density could not be discerned. 4.3.3 Three-dimensional reconstruction of CT data using VGStudio CT scanning provided good two-dimensional density maps, which are displayed as images of varying greyscale intensity. Figure 25 shows one of the cross-sectional images obtained, with the density calibration phantoms on the left. The dark areas in the image represent wood of low density, and the light areas wood of high density. In the CT scan, the growth rings are clearly visible because of the contrast in density between earlywood and latewood. Figure 25. Grey-scale image of a western hemlock disk obtained by CT Since the variation of wood density within tree stems is complex, 3-dimensional imaging and rendering has the potential to allow easier comprehension of the spatial variation in density within tree stems. The 3D images of the western hemlock disks shown 78 below depict the spatial variation in density within logs much better than the 2D graphs that summarized density data in Chapter 3. The high resolution images of the disks display some interesting features. Segmentation of wood with low and high wood density within the disks reveals that density varied significantly with height in the tree and radially across the stem. Each tree showed a low density core at the centre of the stems at all heights (as depicted in Figure 26 for one tree). It is also noticeable that this zone of low density wood mainly consists of earlywood and seems to be quite consistent at all heights within the stems. 79 Figure 26. Low density wood (0.30 g/cm3) highlighted at each height for tree #1 Low density wood forms cylindrical sheets (earlywood) within the log and the zone of low density wood appears to be quite circular in shape independent of the overall shape of the log. Small areas of low density wood are also visible outside of the central core. 80 Figure 27. Medium density wood (0.40 g/cm3) highlighted at each height for tree #2 Figure 27 shows medium density wood of 0.40-0.45 g/cm3 in log number 2. Clearly the amount of medium density wood in the stem decreases with increasing height. The difference in the proportion of the stem sections occupied by medium density wood is not pronounced at higher sample heights, but the two lower stem sections contain much more wood of this density class than those taken from the upper part of the stem. Additionally, medium density wood (0.40 g/cm3) is only evident in the outer layers of the upper part of 81 the stem while it appears to be more evenly distributed over the entire stem cross-section in the lower part of the stem. Medium density wood is also found in the region adjacent to the pith and the knots extending from the pith to the bark also appeared to be composed of medium density wood. A tangential arrangement of medium density wood following growth rings is apparent, and the wood also forms continuous sheets around the pith at lower sample heights. In the upper part of the stem there are a few scattered strands of medium density wood in the center of the log and at the periphery. Figure 28 highlights wood with a density between 0.45-0.50 g/cm3 (medium to high density wood) for log number 3. It is noticeable that much less wood in this density class is present in the stem than low or medium density wood. The quantity of medium to high density wood decreases with increasing height in the stem. Medium to higher density wood is visible immediately around the pith, but it is more fragmented. It is also found as scattered strands at the periphery of disks sampled at the top of the stem, but greater quantities occur adjacent to the pith at the base of the stem. Delineation of wood with a density of 0.45 g/cm3 is very effective at highlighting knots. 82 Figure 28. Medium/high density wood (0.45 g/cm3) highlighted at each height for tree #3 83 Figure 29. High density wood (0.50 g/cm3) highlighted at each height for tree #3 Figure 29 highlights wood with a density ranging from 0.50 to 0.55 g/cm3 for log number 3 at five heights. Such higher density wood was much more scattered than wood in lower density classes. A density threshold of > 0.50 g/cm3 reveals a significant decline in the amount of high density wood towards the top of the stem. In the upper part of the stem, high density wood forms discontinuous strands whereas at the base of the tree it is more continuous and is present in greater amounts. Knots, represented by a high 84 proportion of high density wood which could be due to compression wood, extending radially from the pith, are easily discernible at all heights. There are also small strands of high density wood immediately adjacent to the pith. In general, 3D visualization showed varying amounts of high and low density wood within the disks of all trees (Figure 30). All four logs show the same inverse relationship between proportion of high density wood and increasing tree height. However, the amount of wood within each density class varies considerably within the disks and between the sampled stems, suggesting that the average stem density for each log differs significantly. 85 Figure 30. Low (0.30 g/cm3) and high (0.50 g/cm3) density wood highlighted at stump height for all four trees sampled A regular pattern of circumferential variation in wood density was not apparent in the 3-dimensional images of the stems; however, in tree 5 a zone of high density wood spirals from south-west to north-east located midway in the disk radius (circled blue in Figure 31). Such a pattern of circumferential variation in wood density was not observed in any of the other stems. 86 Figure 31. High density wood (0.45 and 0.50 g/cm3) at each height for tree # 5 Through the allocation of different colours to wood of different density, discrimination between the zones of high and low density wood could be enhanced. In Figure 32, only low (>0.30 g/cm3) and high (>0.50 g/cm3) density wood are selected for 3D visualization. It appears as though high wood density and low wood density regions are discontinuous. High density wood only forms a contiguous zone in the outer layers of 87 the stem near ground level. This is evident in all 3D images of the four western hemlock trees. Figure 32. 3D reconstruction of a scanned disk highlighting low (>0.30 g/cm3) and high (>0.50 g/cm3) density wood 88 4.4 Discussion Established techniques for the evaluation of the spatial distribution and variation in wood density in conifer trees including western hemlock are usually based on measurement of the density of increment cores collected at breast-height. Invariably only one, two or four increment cores are taken from each stem, and the figures obtained have been used to develop 2-dimensional maps of the variation in density within trees. No literature was found that examined the variation in density in western hemlock in 3 dimensions. Results here show that voxel-based 3D models of density variation in hemlock stems are superior to these 2-dimensional maps in some respects. Firstly, they enable the log sample to be viewed from any user-specified viewpoint or cutting plane. Hence, it is possible to analyse variation in density within the stem more completely, and features such as knots and the pith are readily discernible. Furthermore, 3-D images can graphically simplify complicated concepts such as the variation in wood density within stems and visualize the relationship among the different density levels. Large numbers of features that affect wood density can be combined and presented simply in a concise manner which assists in understanding why density varies within stems spatially. There was little evidence from 3-dimensional models to suggest that there is systematic circumferential variation in wood density in western hemlock. Various positions in the tree were examined graphically, but no consistent pattern of circumferential variation density within the four trees could be observed. Areas of high density wood that spiralled around the tree from west to east could only be seen in one tree. Further studies of the effect of circumferential position within western hemlock trees 89 on wood density using a larger number of samples would need to be undertaken to fully evaluate whether wood density in western hemlock varies around the circumference of the stem in a systematic way. Both of the 3-D models, however, confirmed that wood density was higher at the base of the tree and that low wood density (juvenile wood) formed a core near the centre of the stem. Thresholding of wood of different density within the disks revealed that regions of high density wood varied extensively with height in the stem and also around the circumference of the tree. It was noted that wood density decreased with increasing height, as others have noted (Krahmer 1966, Fair 1973, Jozsa and Middleton 1994, Jozsa et al. 1998). Wood densities greater than 0.40 g/cm' were found in the outer part of the stem which validates the assumption that lumber cut from the periphery of the stem will be denser and more suitable for structural applications or end uses that require hardness. Findings here suggest that the internal distribution of wood density within western hemlock stems can be described quite accurately through 3D imaging. The 3D nature of this information allows improved visualization of relationships between different density classes and provides a better understanding of the amount and distribution of high density wood within the tree. In general, CT scanning provided quantitative densitometric images of thin cross sections through the material, and the density models derived from these images were easy to visualize, since they were sympathetic to the way the human mind perceives three-dimensional structures (ASTM 2005). Because CT images are digital, they can be enhanced and analyzed, and with proper calibration, accurate determination of wood density can be achieved. However, it is important to mention that grey values obtained 90 using CT are only applicable to the equipment and specific calibration performed using density controls (phantoms). Furthermore, fluctuations in wood moisture content will change the different thresholds for each of the density values (Hailey and Morris 1987, Lindgren 1991). In this study wood samples were conditioned" for 20 months and had an approximate equilibrium moisture content of 11%. Hence, density models were largely unaffected by variation in wood moisture content. When defining a grey value threshold for different density values, it is important to take into consideration the resolution of the scanner utilized. The scanner used here had a spatial resolution of 0.623 mm and according to Hailey and Morris (1987); 1 mm resolution is more than sufficient for industrial forest products applications. However, this scale may not be adequate for detailed discrimination of early- and latewood density because the size of growth rings may be less than 1 mm. Tracheids in western hemlock average 30-40 pm in diameter and about 3-4 mm in length (Gonzalez 1996), and hence the spatial resolution of CT scanners are clearly not sufficient to examine the variation in wood density caused by local variation in wood cell wall thickness. In addition, scanning at small resolutions as used here increases the time for data acquisition and reconstruction of images'. In general, scanning times used to obtain density information were long because very large amounts of data had to be collected to eliminate the risk of artifacts. Hence, the approach used here to obtain density data and to reconstruct images is far too time-consuming for routine assessment of within tree variation in density. The high costs of CT scanners also preclude their use for the routine assessment of wood density variation in wood quality and processing studies. 91 In this Chapter two methods were used to create 3-D models of internal variation in density of western hemlock. The 3-D reconstruction of gravimetric density data using Drishti shows similar results to those obtained by CT scanning. However, the visualization obtained using Drishti is much more schematic. This may be due to the wide separation of data points used for the model since gravimetric density data for each height were spaced almost 1 m apart, and the sample thickness was only 25 mm. The number of data points in the horizontal plane was also much higher than those obtained with height in the tree. Wood density classes are displayed as surfaces due to the amount of data that had to be processed in the horizontal plane and reduced for visualization. Thus, only larger areas of homogenous density were connected by the custom-written algorithm. This leads to a simplified reconstruction of the gravimetric data and only gross spatial relationships between different density classes can be observed such as the discontinuity of high density wood over the length of the bole and the presence of an area of high wood density enveloping wood of lower density. The 3-D imaging undertaken here, however, revealed the relationship between wood of different density classes within western hemlock and confirmed previous findings of the variation in wood density in the x and y directions. Wood density variation can be evaluated quite accurately by image analysis and with the use of 3-dimensional modelling density variation within western hemlock stems can be better visualized. 92 4.5 Conclusion The following conclusions can be drawn based on the 3-D modelling of density distributions in western hemlock undertaken in this Chapter. 3D visualization and direct rendering can display the spatial distribution of wood density within a log in great detail. The external form and internal density distribution of the sampled disks can be constructed and accurately described by image analysis. The combination of successive CT-scan slices to form complete 3-dimensional wood density maps within a log can be used to reveal the location of high and low density wood and improves our understanding of the amount distribution of high density wood in western hemlock. The spatial resolution of CT impedes analysis of the effect of growth rings and cell wall thickness on wood density. Utilization of advanced visualization software such as Drishti enhances the 3-D visualization of wood density in stems and is particularly useful in demonstrating the discontinuous nature of wood density distribution over the entire length of the stem; however, limitations imposed by data volume and processing capacity of computers cause the models to be quite schematic. 3-D modelling did not reveal a systematic effect of circumferential position on wood density, but revealed random variation of wood density around the circumference and validated findings from previous studies that distance from the pith and height in the tree had significant effects on wood density. 93 CHAPTER FIVE 5 General Discussion, Conclusions and Suggestions for Further Research 5.1 General Discussion In general, it cannot be concluded that from either statistical analysis of gravimetric data or 3-D modelling of gravimetric or CT data that wood density of western hemlock varies circumferentially around the stem. The density values obtained gravimetrically for western hemlock, however, were in good agreement. with those obtained in previous studies. Furthermore, the finding that wood density in western hemlock does not vary circumferentially accords with previous studies that examined circumferential variation in wood density in Douglas-fir, lodgepole pine and radiata pine (Cown 1976, Nicholls 1986, Gonzalez 1989). However, 3-dimensional modelling of density in Chapter 4 showed evidence of circumferential variation in wood density in one tree where a zone of high density wood spiralled around the circumference of the stem. In addition, the presence of knots and compression wood appeared to perturb the normal pattern of density variation within stems. Due to the scanning resolution employed in this study it was not possible to examine the influence of wood cell wall thickness within growth rings on wood density. However, higher density wood was observed in areas of the stem associated with knots, and low wood density was associated with the juvenile wood core. 94 This thesis has used industrial CT at its highest resolution (2048 x 2048) and demonstrated the usefulness of this technique in visualizing the spatial distribution of wood density within trees even though it did not reveal the effect of cell wall thickness on wood density. The observation of the occurrence of higher density wood at the periphery of stems agrees with previous studies of the within tree variation in density of western hemlock (Wellwood and Smith 1962, Jozsa and Kellogg 1986, Jozsa et al. 1998). CT modelling also revealed that wood in the highest density class was located in discrete areas and was not connected radially or longitudinally. These findings indicate the potential for this technique to provide valuable information about the internal distribution of wood density and possibly other properties within tree stems. Wood density is a key index for wood quality and its suitability for a variety of industrial applications. The within-tree variation in wood density in western hemlock has been studied extensively (Krahmer 1966, Jozsa et al. 1998, DeBell et al. 2004). These studies have examined the variation in density of wood radially from pith to bark (x-direction) and with height in the tree (y-direction). Visualizing such composite measures of density has been assumed to be rather difficult although this study showed that it could be achieved using advanced analytical techniques. Chapter 3 analyzed the effect of radial (x), longitudinal (y) and circumferential positions within the trees on wood density. There were statistically significant effects of the x and y positions on density which accorded with the findings of previous studies (Krahmer 1966, Jozsa and Kellogg 1986, Jozsa et al. 1998). In Chapter 4, 3-dimensional models of the spatial variation in density in western hemlock were developed using data obtained gravimetrically and through x-ray CT. In general the models developed 95 supported findings in Chapter 3 that high density wood (>0.45) was found close to the pith and in the outer part of the stem. The 3-D models also confirmed the previously observed trend that wood density decreases with height in the stem. The 3-D models did not reveal systematic variation in density around the circumference of the stem, except, as mentioned above, for tree # 5 where a region of high density wood was found at each sample height translating in a spiral fashion around the stem with increasing height. There was a reasonable correlation between the density values obtained gravimetrically and those generated by CT. In most cases, however; figures obtained gravimetrically were slightly lower than those obtained using CT, which may be attributed to differences in resolution of the testing techniques. Basic density values obtained in this study were obtained by measuring the mass and volume of wood samples containing 5 growth rings. Material from the earlywood or latewood was removed when samples were cut from the stem using a thin kerf scroll saw. The samples removed from the stem varied considerably in size, and even though the saw kerf was very small, removal of wood by the sawblade could lead to under or over-estimation of wood density depending on whether the saw cut was placed in latewood or earlywood. Overall, however, average wood density obtained here was in good correlation with figures for western hemlock' reported in the literature considering that the entire cross-sections was utilized including compression wood, which is usually avoided in studies of within-tree variation in wood density. Findings from Chapter 4 showed the scattered distribution of high density wood within the cross-section, mainly in the outer mature wood (as mentioned above) and displayed the intricate relationship between wood of different density classes that 96 influence the global average wood density figure for western hemlock. Differences between growing conditions, sampling methods and techniques used to analyze and calculate wood density make it difficult to compare and relate figures here with those obtained in previous studies; however, common trends were observed and general understanding is improved through advanced visualization and density modelling. The advantage of visualizing wood density in 3-D lies in its ability to reveal the complex pattern of density variation in stems which is, in turn, is influenced by characteristics such as knots, compression wood or the cylindrical zone of 'juvenile wood'. The utilization of industrial CT at high resolution and advanced visualization techniques has the potential to increase our understanding of the variability in wood density in western hemlock and other species. The CT equipment used here, however, is too slow for in-line scanning in sawmills. Many authors have claimed that CT scanning shows great potential to improve the conversion and timber grade recovery during sawmilling (Muller and Teischinger 2001, Rinnhofer et al. 2003). These authors claim that an optimum sawing pattern could be developed based on higher resolution imaging of logs, taking into consideration defect placement, growth distribution (density gradient), and external geometry. Based on such data the actual sawing instruction could then be fed automatically in real time to the headrig saw. However, if such a goal is to be realized much better computational hardware and software is required to process 2D radiographs. It is clear that higher resolution images of the type obtained during this study could assist in developing the best cutting pattern when sawing a log, but the cost of scanning logs at high resolution would have to offset by improved recovery (both volumetric and grade recovery). 97 When segregating western hemlock logs into lumber, the stem is divided into several circular sections around the pith. According to lumber grading standards (NLGA 2001), the cross-section of a log is divided into three zones of different quality (Figure Figure 33. Section w'thin in log with different wood qualities The outer section comprising the sapwood is relatively free from branches which are referred to as 'Clear' lumber, as it is comparatively free from large defects. The lumber obtained from this area is suitable for high quality products such as flooring, ceiling and siding. The wood from the second section inside the 'Clear' lumber may be utilized as 'Factory and Shop' lumber that contain knots but can be cut into shorter and narrower boards to obtain clear pieces which can then be used for sash and doors or for general joinery purposes. The inner zone in which many branches occur is the lowest grade, referred to as 'Construction Lumber' as its wood may be converted into general construction and structural types of lumber such as boards, shiplaps or posts (NLGA 2001). 98 The results here indicate that these rules apply only to the basal parts of second-growth western hemlock stems arid even in these areas, knots and compression wood are commonly found. The benefits of CT scanning to assess logs quality have been widely reported and the technique has been used to a limited extent in log yards to allocate logs to an appropriate end-use (Rinnhofer et al. 2003). One unfortunate feature of current CT technologies from a product quality control point of view is their rather slow processing speeds. Even if scan times were in the range of a few seconds to produce an image, it would still be too slow for production use. For online industrial application, it would be necessary for the image reconstruction system to keep pace with the data acquisition system. It should also be noted that optimization using true 3-D images of logs would be very complex, even though this approach appears to be feasible. From results here it can be concluded that information on internal log structure obtained from CT and the potential benefits of such information for process optimization must be carefully weighed against the high cost of the technology. If a consistent pattern of the effect of log diameter on the amount and location of high density wood could be found, it might be possible to significantly increase the lumber yield from logs by imposing new cutting patterns that allocate the outer mature wood to higher value-added uses while using the inner low density wood for pulp or engineered wood composites. 99 5.2 Conclusions There was no systematic effect of circumferential position within western hemlock stems on wood density. Distance from pith and height within the tree had significant effects on wood density in accord with results from previous studies. CT modelling revealed that wood in the highest density class was located in discrete areas and was disconnected radially and longitudinally whereas the juvenile core was quite homogenous. 3-dimensional visualization facilitates better understanding of the contribution of wood in different density classes and features such as knots and compression wood to the overall pattern of spatial variation in density in western hemlock stems. Spatial resolution limits analysis of the effect of wood cell wall thickness on wood density. 5.3 Suggestions for further research Results from this study are based on the intensive sampling of four trees. Another area worthy of additional research would be a study of the effect of stem diameter on the amount and location of lower and higher density wood within logs. 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Wood density data for statistical analysis (1-5) ction Sample Density Log Height Section Sample Density (pith- (pith--XII) bark) [g/cm3] 2 (1-5) (I-XII) bark) [g/cm3] I 5 0.39 2 1 I 5 0.40 I 10 0.35 2 1 I 10 0.32 I 15 0.35 2 1 I 15 0.32 I 20 0.40 2 1 I 20 0.34 I 25 0.42 2 1 I 25 0.33 I 30 0.44 2 1 I 30 0.35 I 35 0.43 2 1 I 35 0.37 I 40 0.46 2 1 I 40 0.41 I 45 0.51 2 1 I 45 0.46 I 50 0.46 2 1 I 50 0.41 I 55 0.45 2 1 I 55 0.44 I 62 0.45 2 1 I 60 0.40 II 5 0.40 2 1 I 64 0.39 II 10 0.35 2 1 II 5 0.42 II 15 0.36 2 1 II 10 0.33 II 20 0.39 2 1 II 15 0.32 II 25 0.41 2 1 II 20 0.34 II 30 0.42 2 1 II 25 0.35 II 35 0.44 2 1 II 30 0.36 II 40 0.48 2 1 11 35 0.39 II 45 0.53 2 1 II 40 0.42 II 50 0.47 2 1 II 45 0.44 II 55 0.47 2 1 II 50 0.45 II 62 0.46 2 1 II 55 0.44 111 5 0.45 2 1 II 60 0.40 III 10 0.34 2 1 II 64 0.39 III 15 0.34 2 1 III 5 0.41 III 20 0.37 2 1 111 10 0.33 III 25 0.42 2 1 III 15 0.33 III 30 0.42 2 1 III 20 0.35 III 35 0.45 2 1 III 25 0.36 III 40 0.42 2 1 III 30 0.37 III 45 0.50 2 1 III 35 0.38 III 50 0.45 2 1 III 40 0.41 III 55 0.47 2 1 III 45 0.41 III 62 0.47 2 1 III 50 0.44 IV 5 0.43 2 1 III 55 0.43 IV 10 0.34 2 1 III 60 0.38 108 IV 15 0.35 2 1 III 64 0.36 IV 20 0.41 2 1 IV 5 0.41 IV 25 0.42 2 1 IV 10 0.34 IV 30 0.41 2 1 IV 15 0.34 IV 35 0.42 2 1 IV 20 0.36 IV 40 0.42 2 1 IV 25 0.36 IV 45 0.45 2 1 IV 30 0.38 IV 50 0.44 2 1 IV 35 0.38 IV 55 0.49 2 1 IV 40 0.41 IV 62 0.49 2 1 IV 45 0.42 V 5 0.39 2 1 IV 50 0.42 V 10 0.34 2 1 IV 55 0.44 V 15 0.36 2 1 IV 60 0.40 V 20 0.40 2 1 IV 64 0.38 V 25 0.41 2 1 V 5 0.42 V 30 0.41 2 1 V 10 0.36 V 35 0.43 2 1 V 15 0.32 V 40 0.46 2 1 V 20 0.36 V 45 0.50 2 1 V 25 0.35 V 50 0.46 2 1 V 30 0.38 V 55 0.47 2 1 V 35 0.37 V 62 0.51 2 1 V 40 0.42 VI 5 0.41 2 1 V 45 0.41 VI 10 0.35 2 1 V 50 0.41 VI 15 0.37 2 1 V 55 0.41 VI 20 0.41 2 1 V 60 0.38 VI 25 0.42 2 1 V 64 0.37 VI 30 0.43 2 1 VI 5 0.39 VI 35 0.44 2 1 VI 10 0.34 VI 40 0.44 2 1 VI 15 0.32 VI 45 0.53 2 1 VI 20 0.36 VI 50 0.48 2 1 VI 25 0.35 VI 55 0.48 2 1 VI 30 0.36 VI 62 0.48 2 1 VI 35 0.37 VII 5 0.70 2 1 VI 40 0.40 VII 10 0.69 2 1 VI 45 0.40 VII 15 0.50 2 1 VI 50 0.42 VII 20 0.46 2 1 VI 55 0.40 VII 25 0.44 2 1 VI 60 0.39 VII 30 0.46 2 1 VI 64 0.37 VII 35 0.46 2 1 VII 5 0.39 VII 40 0.45 2 1 VII 10 0.33 VII 45 0.51 2 1 VII 15 0.32 VII 50 0.49 2 1 VII 20 0.34 VII 55 0.49 2 1 VII 25 0.34 VII 62 0.48 2 1 VII 30 0.35 VIII 5 0.53 2 1 VII 35 0.34 VIII 10 0.43 2 1 VII 40 0.38 VIII 15 0.39 2 1 VII 45 0.40 VIII 20 0.40 2 1 VII 50 0.43 109 VIII 25 0.41 2 1 VII 55 0.43 VIII 30 0.42 2 1 VII 60 0.38 VIII 35 0.43 2 1 VII 64 0.37 VIII 40 0.45 2 1 VIII 5 0.38 VIII 45 0.50 2 1 VIII 10 0.32 VIII 50 0.47 2 1 VIII 15 0.31 VIII 55 0.46 2 1 VIII 20 0.33 VIII 62 0.47 2 1 VIII 25 0.33 IX 5 0.41 2 1 VIII 30 0.34 IX 10 0.35 2 1 VIII 35 0.34 IX 15 0.34 2 1 VIII 40 0.40 IX 20 0.37 2 1 VIII 45 0.42 IX 25 0.42 2 1 VIII 50 0.47 IX 30 0.41 2 1 VIII 55 0.50 IX 35 0.42 2 1 VIII 60 0.42 IX 40 0.42 2 1 VIII 64 0.43 IX 45 0.49 2 1 IX 5 0.39 IX 50 0.45 2 1 IX 10 0.32 IX 55 0.43 2 1 IX 15 0.31 IX 62 0.45 2 1 IX 20 0.35 X 5 0.40 2 1 IX 25 0.38 X 10 0.35 2 1 IX 30 0.35 x 15 0.34 2 IX 35 0.37 x 20 0.36 2 IX 40 0.41 X 25 0.42 2 IX 45 0.46 X 30 0.42 2 IX 50 0.51 X 35 0.42 2 IX 55 0.56 x 40 0.42 2 IX 60 0.48 X 45 0.46 2 IX 64 0.48 x 50 0.45 2 X 5 0.42 X 55 0.43 2 X 10 0.32 X 62 0.44 2 X 15 0.31 XI 5 0.37 2 X 20 0.35 XI 10 0.33 2 X 25 0.32 XI 15 0.35 2 X 30 0.33 XI 20 0.38 2 X 35 0.33 XI 25 0.42 2 X 40 0.38 XI 30 0.42 2 X 45 0.40 XI 35 0.43 2 X 50 0.42 XI 40 0.43 2 X 55 0.51 XI 45 0.46 2 X 60 0.39 XI 50 0.46 2 X 64 0.35 XI 55 0.48 2 XI 5 0.40 XI 62 0.46 2 XI 10 0.33 XII 5 0.38 2 XI 15 0.32 XII 10 0.34 2 XI 20 0.36 XII 15 0.34 2 XI 25 0.34 XII 20 0.38 2 XI 30 0.35 XII 25 0.42 2 XI 35 0.37 XII 30 0.44 2 XI 40 0.42 1 XII 35 0.43 2 1 XI 45 0.41 1 XII 40 0.43 2 1 XI 50 0.43 1 XII 45 0.48 2 1 XI 55 0.43 1 XII 50 0.46 2 1 XI 60 0.40 1 XII 55 0.45 2 1 XI 64 0.40 1 XII 62 0.47 2 1 XII 5 0.40 2 I 5 0.43 2 1 XII 10 0.34 2 I 10 0.35 2 1 XII 15 0.33 2 I 15 0.36 2 1 XII 20 0.35 2 I 20 0.41 2 1 XII 25 0.35 2 I 25 0.44 2 1 XII 30 0.36 2 I 30 0.45 2 1 XII 35 0.38 2 I 35 0.45 2 1 XII 40 0.43 2 I 40 0.43 2 1 XII 45 0.44 2 I 45 0.48 2 • 1 XII 50 0.44 2 I 50 0.48 2 1 XII 55 0.43 2 I 55 0.45 2 1 XII 60 0.42 2 I 60 0.47 2 1 XII 64 0.41 2 I 64 0.47 2 2 I 5 0.39 2 II 5 0.41 2 2 I 10 0.33 2 II 10 0.34 2 2 I 15 0.33 2 II 15 0.35 2 2 I 20 0.35 2 II 20 0.39 2 2 I 25 0.35 2 II 25 0.40 2 2 I 30 0.36 2 II 30 0.41 2 2 I 35 0.38 2 II 35 0.42 2 2 I 40 0.42 2 II 40 0.41 2 2 I 45 0.43 2 II 45 0.49 2 2 I 50 0.46 2 11 50 0.50 2 2 I 55 0.44 2 II 55 0.48 2 2 I 60 0.42 2 II 60 0.48 2 2 I 65 0.40 2 II 64 0.51 2 2 II 5 0.42 2 III 5 0.43 2 2 II 10 0.33 2 III 10 0.34 2 2 II 15 0.33 2 III 15 0.34 2 2 II 20 0.35 2 III 20 0.39 2 2 II 25 0.35 2 III 25 0.39 2 2 II 30 0.37 2 III 30 0.40 2 2 II 35 0.41 2 III 35 0.42 2 2 II 40 0.43 2 III 40 0.40 2 2 II 45 0.45 2 III 45 0.51 2 2 II 50 0.47 2 III 50 0.49 2 2 II 55 0.44 2 III 55 0.44 2 2 II 60 0.41 2 III 60 0.46 2 2 11 65 0.38 2 III 64 0.50 2 2 III 5 0.45 2 IV 5 0.42 2 2 III 10 0.36 2 IV 10 0.34 2 2 III 15 0.36 2 IV 15 0.33 2 2 III 20 0.41 2 IV 20 0.38 2 2 III 25 0.41 2 IV 25 0.39 2 2 III 30 0.38 2 IV 30 0.40 2 2 III 35 0.40 2 IV 35 0.43 2 2 III 40 0.44 2 IV 40 0.40 2 2 III 45 0.44 2 IV 45 0.46 2 2 III 50 0.46 2 IV 50 0.45 2 2 III 55 0.45 2 IV 55 0.44 2 2 III 60 0.43 2 IV 60 0.46 2 2 III 65 0.40 2 IV 64 0.48 2 2 IV 5 0.46 2 V 5 0.42 2 2 IV 10 0.36 2 V 10 0.35 2 2 IV 15 0.35 2 V 15 0.35 2 2 IV 20 0.37 2 V 20 0.39 2 2 IV 25 0.38 2 V 25 0.40 2 2 IV 30 0.38 2 V 30 0.41 2 2 IV 35 0.38 2 V 35 0.43 2 2 IV 40 0.42 2 V 40 0.41 2 2 IV 45 0.43 2 V 45 0.47 2 2 IV 50 0.44 2 V 50 0.47 2 2 IV 55 0.44 2 V 55 0.44 2 2 IV 60 0.42 2 V 60 0.46 2 2 IV 65 0.38 2 V 64 0.46 2 2 V 5 0.57 2 VI 5 0.44 2 2 V 10 0.41 2 VI 10 0.36 2 2 V 15 0.37 2 VI 15 0.35 2 2 V 20 0.38 2 VI 20 0.39 2 2 V 25 0.37 2 VI 25 0.40 2 2 V 30 0.39 2 VI 30 0.41 2 2 V 35 0.40 2 VI 35 0.42 2 2 V 40 0.43 2 VI 40 0.42 2 2 V 45 0.46 2 VI 45 0.48 2 2 V 50 0.44 2 VI 50 0.46 2 2 V 55 0.43 2 VI 55 0.44: 2 2 V 60 0.41 2 VI 60 0.46 2 2 V 65 0.39 2 VI 64 0.46 2 2 VI 5 0.45 2 VII 5 0.43 2 2 VI 10 0.35 2 VII 10 0.35 2 2 VI 15 0.34 2 VII 15 0.35 2 2 VI 20 0.36 2 VII 20 0.38 2 2 VI 25 0.37 2 VII 25 0.41 2 2 VI 30 0.37 2 VII 30 0.40 2 2 VI 35 0.38 2 VII 35 0.42 2 2 VI 40 0.41 2 VII 40 0.42 2 2 VI 45 0.42 2 VII 45 0.49 2 2 VI 50 0.44 2 VII 50 0.47 2 2 VI 55 0.42 2 VII 55 0.45 2 2 VI 60 0.41 2 VII 60 0.46 2 2 VI 65 0.37 2 VII 64 0.47 2 2 VII 5 0.40 2 VIII 5 0.40 2 2 VII 10 0.34 2 VIII 10 0.35 2 2 VII 15 0.34 2 VIII 15 0.35 2 2 VII 20 0.35 112 2 VIII 20 0.37 2 2 VII 25 0.36 2 VIII 25 0.41 2 2 VII 30 0.35 2 VIII 30 0.40 2 2 VII 35 0.37 2 VIII 35 0.41 2 2 VII 40 0.39 2 VIII 40 0.40 2 2 VII 45 0.40 2 VIII 45 0.48 2 2 VII 50 0.42 2 VIII 50 0.47 2 2 VII 55 0.42 2 VIII 55 0.43 2 2 VII 60 0.38 2 VIII 60 0.44 2 2 VII 65 0.36 2 VIII 64 0.44 2 2 VIII 5 0.40 2 IX 5 0.39 2 2 VIII 10 0.33 2 IX 10 0.34 2 2 VIII 15 0.33 2 IX 15 0.33 2 2 VIII 20 0.33 2 IX 20 0.36 2 2 VIII 25 0.33 2 IX 25 0.45 2 2 VIII 30 0.33 2 IX 30 0.48 2 2 VIII 35 0.35 2 IX 35 0.45 2 2 VIII 40 0.37 2 IX 40 0.42 2 2 VIII 45 0.40 2 IX 45 •0.48 2 2 VIII 50 0.42 2 IX 50 0.48 2 2 VIII 55 0.49 2 IX 55 0.45 2 2 VIII 60 0.41 2 IX 60 0.43 2 2 VIII 65 0.38 2 IX 64 0.44 2 2 IX 5 0.38 2 X 5 0.39 2 2 IX 10 0.33 2 X 10 0.34 2 2 IX 15 0.32 2 X 15 0.34 2 2 IX 20 0.33 2 X 20 0.38 2 2 IX 25 0.32 2 X 25 0.47 2 2 IX 30 0.33 2 X 30 0.43 2 2 IX 35 0.34 2 X 35 0.43 2 2 IX 40 0.38 2 X 40 0.40 2 2 IX 45 0.44 2 X 45 0.44 2 2 IX 50 0.47 2 X 50 0.44 2 2 IX 55 0.55 2 X 55 0.44 2 2 IX 60 0.47 2 X 60 0.44 2 2 IX 65 0.45 2 X 64 0.46 2 2 X 5 0.38 2 XI 5 0.40 2 2 X 10 0.33 2 XI 10 0.34 2 2 X 15 0.32 2 XI 15 0.34 2 2 X 20 0.33 2 XI 20 0.40 2 2 X 25 0.33 2 XI 25 0.46 2 . 2 X 30 0.34 2 XI 30 0.45 2 2 X 35 0.35 2 XI 35 0.46 2 2 X 40 0.39 2 XI 40 0.42 2 2 X 45 . 0.42 2 XI 45 0.46 2 2 X 50 0.43 2 XI 50 0.47 2 2 X 55 0.54 2 XI 55 0.44 2 2 X 60 0.46 2 XI 60 0.44 2 2 X 65 0.43 2 XI 64 0.49 2 2 XI 5 0.42 2 XII 5 0.43 2 2 XI 10 0.34 113 2 XII 10 0.35 2 2 XI 15 0.34 2 XII 15 0.34 2 2 XI 20 0.36 2 XII 20 0.39 2 2 XI 25 0.37 2 XII 25 0.45 2 2 XI 30 0.38 2 XII 30 0.44 2 2 XI 35 0.38 2 XII 35 0.45 2 2 XI 40 0.41 2 XII 40 0.43 2 2 XI 45 0.42 2 XII 45 0.49 2 2 XI 50 0.43 2 XII 50 0.50 2 2 XI 55 0.50 2 XII 55 0.46 2 2 XI 60 0.40 2 XII 60 0.46 2 2 XI 65 0.40 2 XII 64 0.47 2 2 XII 5 0.41 3 I 5 0.43 2 2 XII 10 0.35 3 I 10 0.42 2 2 XII 15 0.33 3 I 15 0.41 2 2 XII 20 0.35 3 I 20 0.40 2 2 XII 25 0.35 3 I 25 0.45 2 2 XII 30 0.37 3 I 30 0.45 2 2 XII 35 0.37 3 I 35 0.47 2 2 XII 40 0.41 3 I 40 0.44 2 2 XII 45 0.43 3 I 45 0.49 2 2 XII 50 0.44 3 I 50 0.49 2 2 XII 55 0.42 3 I 55 0.46 2 2 XII 60 0.41 3 I 60 0.46 2 2 XII 65 0.41 3 I 65 0.46 2 3 I 5 0.44 3 II 5 1.11 2 3 I 10 035 3 II 10 0.68 2 3 I 15 0.32 3 II 15 0.48 2 3 I 20 0.33 3 II 20 0.45 2 3 I 25 0.35 3 II 25 0.46 2 3 I 30 0.33 3 II 30 0.46 2 3 I 35 0.36 3 II 35 0.47 2 3 I 40 0.40 3 II 40 0.46 2 3 I 45 0.42 3 II 45 0.48 2 3 I 50 0.46 3 II 50 0.51 2 3 I 55 0.45 3 II 55 0.49 2 3 I 60 0.44 3 II 60 0.50 2 3 I 67 • 0.39 3 II 65 0.48 2 3 II 5 0.44 3 III 5 0.44 2 3 II 10 0.36 3 III 10 0.41 2 3 II 15 0.32 3 III 15 0.39 2 3 II 20 0.35 3 III 20 0.41 2 3 II 25 0.37 3 III 25 0.42 2 3 II 30 0.36 3 III 30 0.42 2 3 II 35 0.36 3 III 35 0.44 2 3 II 40 0.40 3 III 40 0.44 2 3 II 45 0.42 3 III 45 0.47 2 3 II 50 0.44 3 III 50 0.49 2 3 II 55 0.43 3 III 55 0.48 2 3 II 60 0.43 3 III 60 0.45 2 3 II 67 0.38 114 3 III 65 0.48 2 3 III 5 0.42 3 IV 5 0.40 2 3 III 10 0.35 3 IV 10 0.36 2 3 III 15 0.32 3 IV 15 0.37 2 3 III 20 0.34 3 IV 20 0.39 2 3 III 25 0.38 3 IV 25 0.40 2 3 III 30 0.38 3 IV 30 . 0.42 2 3 III 35 0.38 3 IV 35 0.44 2 3 III 40 0.41 3 IV 40 0.45 2 3 III 45 0.43 3 IV 45 0.44 2 3 III 50 0.44 3 IV 50 0.48 2 3 III 55 0.43 3 IV 55 0.47 2 3 III 60 0.44 3 IV 60 0.46 2 3 III 67 0.37 3 IV 65 0.48 2 3 IV 5 0.40 3 V 5 0.40 2 3 IV 10 0.36 3 V 10 0.35 2 3 IV 15 0.32 3 V 15 . 0.37 2 3 IV 20 0.35 3 V 20 0.38 2 3 IV 25 0.38 3 V 25 0.41 2 3 IV 30 0.37 3 V 30 0.42 2 3 IV 35 0.38 3 V 35 0.43 2 3 IV 40 0.41 3 V 40 0.42 2 3 IV 45 0.44 3 V 45 0.43 2 3 IV 50 0.44 3 V 50 0.46 2 3 IV 55 0.43 3 V 55 0.46 2 3 IV 60 0.44 3 V 60 0.47 2 3 IV 67 0.39 3 V 65 0.46 2 3 V 5 0.41 3 VI 5 0.44 2 3 V 10 0.36 3 VI 10 0.38 2 3 V 15 0.33 3 VI 15 0.41 2 3 V 20 0.37 3 VI 20 0.44 2 • 3 V 25 0.38 3 VI 25 0.47 2 3 V 30 0.39 3 VI 30 0.45 2 3 V 35 0.39 3 VI 35 0.47 2 3 V 40 0.41 3 VI 40 0.46 2 3 V 45 0.43 3 VI 45 0.51 2 3 V 50 0.45 3 VI 50 0.51 2 3 V 55 0.45 3 VI 55 0.49 2 3 V 60 0.44 3 VI 60 0.48 2 3 V 67 0.40 3 VI 65 0.46 2 3 VI 5 0.41 3 VII 5 0.47 2 3 VI 10 0.36 3 VII 10 0.38 2 3 VI 15 0.35 3 VII 15 0.39 2 3 VI 20 0.36 3 VII 20 0.42 2 3 VI 25 0.39 3 VII 25 0.44 2 3 VI 30 0.38 3 VII 30 0.44 2 3 VI 35 0.38 3 VII 35 0.46 2 3 VI 40 0.42 3 VII 40 0.44 2 3 VI 45 0.44 3 VII 45 0.47 2 3 VI 50 0.43 3 VII 50 0.48 2 3 VI 55 0.44 115 3 VII 55 0.46 2 3 VI 60 0.42 3 VII 60 0.46 2 3 VI 67 0.39 3 VII 65 0.45 2 3 VII 5 0.41 3 VIII 5 0.47 2 3 VII 10 0.35 3 VIII 10 0.35 2 3 VII 15 0.33 3 VIII 15 0.36 2 ' 3 VII 20 0.34 3 VIII 20 0.40 2 3 VII 25 0.37 3 VIII 25 0.43 2 3 VII 30 0.38 3 VIII 30 0.46 2 3 VII 35 0.37 3 VIII 35 0.44 2 3 VII 40 0.38 3 VIII 40 0.42 2 3 VII 45 0.41 3 VIII 45 0.45 2 3 VII 50 0.45 3 VIII 50 0.46 2 3 VII 55 0.42 3 VIII 55 0.45 2 3 VII 60 0.43 3 VIII 60 0.47 2 3. VII 67 0.39 3 VIII 65 0.46 2 3 VIII 5 0.39 3 IX 5 • 0.44 2 3 VIII 10 0.35 3 IX 10 0.35 2 3 VIII 15 0.33 3 IX 15 0.35 2 3 VIII 20 0.32 3 IX 20 0.41 2 3 VIII 25 0.34 3 IX 25 0.47 2 3 VIII 30 0.36 3 IX 30 0.50 2 3 VIII 35 0.36 3 IX 35 0.47 2 3 VIII 40 0.38 3 IX 40 0.44 2 3 VIII 45 0.41 3 IX 45 0.48 2 3 VIII 50 0.43 3 IX 50 0.49 2 3 VIII 55 0.41 3 IX 55 0.46 2 3 VIII 60 0.44 3 IX 60 0.47 2 3 VIII 67 0.39 3 IX 65 0.48 2 3 IX 5 0.42 3 X 5 0.40 2 3 IX 10 0.37 3 X 10 0.35 2 3 IX 15 0.35 3 X 15 0.38 2 3 IX 20 0.34 3 X 20 0.42 2 3 IX 25 0.36 3 X 25 0.49 2 3 IX 30 0.35 3 X 30 0.48 2 3 IX 35 0.38 3 X 35 0.47 2 3 IX 40 0.39 3 X 40 0.46 2 3 IX 45 0.43 3 X 45 0.48 2 3 IX 50 0.45 3 X 50 0.48 2 3 IX 55 0.45 3 X 55 0.46 2 3 IX 60 0.47 3 X 60 0.46 2 3 IX 67 0.45 3 X 65 0.46 2 3 X 5 0.47 3 XI 5 0.39 2 3 X 10 0.37 3 XI 10 0.33 2 3 X 15 0.34 3 XI 15 0.36 2 3 X 20 0.33 3 XI 20 0.42 2 3 X 25 0.37 3 XI 25 0.46 2 3 X 30 0.39 3 XI 30 0.47 2 3 X 35 0.39 3 XI 35 0.44 2 3 X 40 0.40 3 XI 40 0.44 2 3 X 45 0.43 116 3 XI 45 0.46 2 . 3 X 50 0.45 3 XI 50 0.49 2 3 X 55 0.49 3 XI 55 0.46 2 3 X 60 0.49 3 XI 60 0.47 2 3 X 67 0.45 3 XI 65 0.47 2 3 XI 5 0.48 3 XII 5 0.39 2 3 XI 10 0.35 3 XII 10 0.35 2 3 XI 15 0.32 3 XII 15 0.37 2 3 XI 20 0.32 3 XII 20 0.40 2 3 XI 25 0.38 3 XII 25 0.44 2 3 XI 30 0.34 3 XII 30 0.45 2 3 XI 35 0.36 3 XII 35 0.45 2 3 XI 40 0.39 3 XII 40 0.42 2 3 XI 45 0.42 3 XII 45 0.48 2 3 XI 50 0.44 3 XII 50 0.49 2 3 XI 55 0.50 3 XII 55 0.45 2 3 XI 60 0.45 3 XII 60 0.46 2 3 XI 67 0.40 3 XII 65 0.48 2 3 XII 5 0.44 4 I 5 0.42 2 3 XII 10 0.35 4 I 10 0.37 2 3 XII 15 0.32 4 I 15 0.37 2 3 XII 20 0.32 4 I 20 0.37 2 3 XII 25 0.36 4 I 25 0.41 2 3 XII 30 0.33 4 I 30 0.42 2 3 XII 35 0.35 4 I 35 0.43 2 3 XII 40 0.38 4 I 40 0.45 2 3 XII 45 0.41 4 I 45 0.46 2 3 XII 50 0.45 4 I 50 0.48 2 3 XII 55 0.44 4 I 55 0.47 2 3 XII 60 0.42 4 I 60 0.47 2 3 XII 67 0.40 4 I 67 0.48 2 4 I 5 0.42 4 II 5 0.40 2 4 I 10 0.36 4 II 10 0.36 2 4 I 15 0.34 4 II 15 0.36 2 4 I 20 0.36 4 II 20 0.37 2 4 I 25 0.39 4 II 25 0.42 2 4 I 30 0.38 4 II 30 0.44 2 4 I 35 0.37 4 II 35 0.45 2 4 I 40 0.42 4 II 40 0.45 2 4 I 45 0.45 4 II 45 0.44 2 4 I 50 0.46 4 II 50 0.50 2 4 I 55 0.48 4 II 55 0.49 2 4 I 60 0.46 4 II 60 0.48 2 4 I 65 0.42 4 II 67 0.47 2 4 I 69 0.41 4 III 5 0.40 2 4 11 5 0.45 4 III 10 0.35 2 4 II 10 0.37 4 III 15 0.34 2 4 II 15 0.35 4 III 20 0.37 2 4 II 20 0.36 4 III 25 0.42 2 4 II 25 0.39 4 III 30 0.42 2 4 II 30 0.40 117 4 III 35 0.43 2 4 II 35 0.39 4 III 40 0.45 2 4 II 40 0.40 4 III 45 0.44 2 4 II 45 0.44 4 III 50 0.48 2 4 II 50 0.46 4 III 55 0.48 2 4 11 55 0.46 4 III 60 0.47 2 4 11 60 0.46 4 III 67 0.48 2 4 II 65 0.41 4 IV 5 0.40 2 4 II 69 0.39 4 IV 10 0.36 2 4 III 5 0.46 4 IV 15 0.34 2 4 III 10 0.39 4 IV 20 0.38 2 4 III 15 0.35 4 IV 25 0.41 2 4 III 20 0.37 4 IV 30 0.42 2 4 III 25 0.41 4 IV 35 0.44 2 4 III 30 0.40 4 IV 40 0.45 2 4 III 35 0.40 4 IV 45 0.45 2 4 III 40 0.41 4 IV 50 0.51 2 4 III 45 0.46 4 IV 55 0.48 2 4 111 50 0.47 4 IV 60 0.46 2 4 III 55 0.45 4 IV 67 0.47 2 4 III 60 0.48 4 V 5 0.44 2 4 III 65 0.44 4 V 10 0.39 2 4 III 69 0.41 4 V 15 0.34 2 4 IV 5 0.50 4 V 20 0.41 2 4 IV 10 0.50 4 V 25 0.43 2 4 IV 15 0.50 4 V 30 0.42 2 4 IV 20 0.49 4 V 35 0.43 2 4 IV 25 0.46 4 V 40 0.45 2 4 IV 30 0.44 4 V 45 0.43 2 4 IV 35 0.43 4 V 50 0.48 2 4 IV 40 0.45 4 V 55 0.47 2 4 IV 45 0.46 4 V 60 0.47 2 4 IV 50 0.46 4 V 67 0.47 2 4 IV 55 0.45 4 VI 5 0.46 2 4 IV 60 0.46 4 VI 10 0.39 2 4 IV 65 0.43 4 VI 15 0.35 2 4 IV 69 0.40 4 VI 20 0.39 2 4 V 5 0.42 4 VI 25 0.41 2 4 V 10 0.38 4 VI 30 0.42 2 4 V 15 0.37 4 VI 35 0.46 2 4 V 20 0.39 4 VI 40 0.46 2 4 V 25 0.42 4 VI 45 0.45 2 4 V 30 0.42 4 VI 50 0.48 2 4 V 35 0.38 4 VI 55 0.47 2 4 V 40 0.41 4 VI 60 0.49 2 4 V 45 0.43 4 VI 67 0.48 2 4 V 50 0.34 4 VII 5 0.44 2 4 V 55 0.45 4 VII 10 0.37 2 4 V 60 0.43 4 VII 15 0.36 2 4 V 65 0.42 4 VII 20 0.39 2 4 V 69 0.41 118 4 VII 25 0.43 2 4 VI 5 0.40 4 VII 30 0.44 2 4 VI 10 0.35 4 VII 35 0.43 2 4 VI 15 0.35 4 VII 40 0.45 2 4 VI 20 0.37 4 VII 45 0.42 2 4 VI 25 0.41 4 VII 50 0.50 2 4 VI 30 0.40 4 VII 55 0.46 2 4 VI 35 0.38 4 VII 60 0.47 2 4 VI 40 0.42 4 VII 67 0.46 2 4 VI 45 0.45 4 VIII 5 0.41 2 4 VI 50 0.44 4 VIII 10 0.36 2 4 VI 55 0.45 4 VIII 15 0.36 2 4 VI 60 0.44 4 VIII 20 0.36 2 4 VI 65 0.41 4 VIII 25 0.45 2 4 VI 69 0.40 4 VIII 30 0.43 2 4 VII 5 0.40 4 VIII 35 0.43 2 4 VII 10 0.36 4 VIII 40 0.46 2 4 VII 15 0.37 4 VIII 45 0.45 2 4 VII 20 0.36 4 VIII 50 0.52 2 4 VII 25 0.37 4 VIII 55 0.47 2 4 VII 30 0.40 4 VIII 60 0.46 2 4 VII 35 0.37 4 VIII 67 0.47 2 4 VII 40 0.40 4 IX 5 0.41 2 4 VII 45 0.42 4 IX 10 0.36 2 4 VII 50 0.45 4 IX 15 0.36 2 4 VII 55 0.44 4 IX 20 0.36 2 4 VII 60 0.42 4 IX 25 0.41 2 4 VII 65 0.41 4 IX 30 0.47 2 4 VII 69 0.40 4 IX 35 0.44 2 4 VIII 5 0.40 4 IX 40 0.43 2 4 VIII 10 0.36 4 IX 45 0.47 2 4 VIII 15 0.35 4 IX 50 0.53 2 4 VIII 20 0.34 4 IX 55 0.49 2 4 VIII 25 0.37 4 IX 60 0.48 2 4 VIII 30 0.36 4 IX 67 0.48 2 4 VIII 35 0.37 4 X 5 0.43 2 4 VIII 40 0.38 4 X 10 0.36 2 4 VIII 45 0.43 4 X 15 0.36 2 4 VIII 50 0.45 4 X 20 0.36 2 4 VIII 55 0.46 4 X 25 0.43 2 4 VIII 60 0.50 4 X 30 0.50 2 4 VIII 65 0.41 4 X 35 0.45 2 4 VIII 69 0.40 4 X 40 0.43 2 4 IX 5 0.39 4 X 45 0.43 2 4 IX 10 0.39 4 X 50 0.48 2 4 IX 15 0.36 4 X 55 0.47 2 4 IX 20 0.34 4 X 60 0.46 2 4 IX 25 0.36 4 X 67 0.48 2 4 IX 30 0.36 4 XI 5 0.49 2 4 IX 35 0.37 4 XI 10 0.42 2 4 IX 40 0.41 119 4 XI 15 0.40 2 4 IX 45 0.45 4 XI 20 0.40 2 4 IX 50 0.45 4 XI 25 0.44 2 4 IX 55 0.48 4 XI 30 0.50 2 4 IX 60 0.50 4 XI 35 0.46 2 4 IX 65 0.42 4 XI 40 0.45 2 4 IX 69 0.44 4 XI 45 0.44 2 4 X 5 0.44 4 XI 50 0.51 2 4 X 10 0.56 4 XI 55 0.47 2 4 X 15 0.56 4 XI 60 0.46 2 4 X 20 0.45 4 XI 67 0.49 2 4 X 25 0.49 4 XII 5 0.42 2 4 X 30 0.43 4 XII 10 0.37 2 4 X 35 0.45 4 XII 15 0.38 2 4 X 40 0.45 4 XII 20 0.38 2 4 X 45 0.46 4 XII 25 0.42 2 4 X 50 0.48 4 XII 30 0.41 2 4 X 55 0.50 4 XII 35 0.44 2 4 X 60 0.53 4 XII 40 0.45 2 4 X 65 0.48 4 XII 45 0.45 2 4 X 69 0.46 4 XII 50 0.50 2 4 XI 5 0.46 4 XII 55 0.46 2 4 XI 10 0.47 4 XII 60 0.46 2 4 XI 15 0.44 4 XII 67 0.46 2 4 XI 20 0.42 5 I 5 0.55 2 4 • XI 25 0.46 5 I 10 0.44 ' 2 4 XI 30 0.41 5 I 15 0.40 2 4 XI 35 0.41 5 I 20 0.47 2 4 XI 40 0.41 5 I 25 0.47 2 4 XI 45 0.46 5 I 30 0.48 2 4 XI 50 0.46 5 I 35 0.46 2 4 XI 55 0.46 5 I 40 0.47 2 4 XI 60 0.49 5 I 45 0.46 2 4 XI 65 0.43 5 I 50 0.51 2 4 XI 69 0.42 5 I 55 0.50 2 4 XII 5 0.45 5 I 60 0.47 2 4 XII 10 0.40 5 I 65 0.48 2 4 XII 15 0.37 5 I 70 0.47 2 4 XII 20 0.38 5 II 5 0.51 2 4 XII 25 0.41 5 II 10 0.43 2 4 XII 30 0.39 5 II 15 0.39 2 4 XII 35 0.40 5 II 20 0.46 2 4 XII 40 0.41 5 II 25 0.50 2 4 XII 45 0.46 5 II 30 0.47 2 4 XII 50 0.48 5 II 35 0.44 2 4 XII 55 0.49 5 II 40 0.46 2 4 XII 60 0.47 5 II 45 0.46 2 4 XII 65 0.44 5 . II 50 0.51 2 4 XII 69 0.44 5 II 55 0.49 2 5 I 5 0.43 5 II 60 0.46 2 5 I 10 0.40 120 5 II 65 0.47 2 5 I 15 0.40 5 11 70 0.48 2 5 I 20 0.41 5 III 5 0.47 2 5 I 25 0.43 5 III 10 0.42 2 5 I 30 0.43 5 III 15 0.40 2 5 I 35 0.43 5 III 20 0.41 2 5 I 40 0.45 5 III 25 0.43 2 5 I 45 0.45 5 III 30 0.47 2 5 I 50 0.47 5 III 35 0.43 2 5 I 55 0.51 5 III 40 0.46 2 5 I 60 0.47 5 III 45 0.45 2 5 I 65 0.48 5 III 50 0.49 2 5 I 72 0.42 5 III 55 0.49 2 5 II 5 0.41 5 III 60 0.47 2 5 II 10 0.40 5 III 65 0.49 2 5 II 15 0.40 5 III 70 0.49 2 5 II 20 0.41 5 IV 5 0.46 2 5 II 25 0.41 5 IV 10 0.41 2 5 II 30 0.47 5 IV 15 0.39 2 5 II 35 0.47 5 IV 20 0.41 2 5 II 40 0.43 5 IV 25 0.44 2 5 II 45 0.47 5 IV 30 0.45 2 5 II 50 0.48 5 IV 35 0.44 2 5 II 55 0.50 5 IV 40 0.47 2 5 II 60 0.47 5 IV 45 0.46 2 5 II 65 0.48 5 IV 50 0.48 2 5 II 72 0.42 5 IV 55 0.47 2 5 III 5 0.45 5 IV 60 0.46 2 5 III 10 0.53 5 IV 65 0.48 2 5 III 15 0.57 5 IV 70 0.49 2 5 III 20 0.52 5 V 5 0.44 2 5 III 25 0.44 5 V 10 0.39 2 5 III 30 0.48 5 V 15 0.39 2 5 III 35 0.53 5 V 20 0.41 2 5 III 40 0.48 5 V 25 0.44 2 5 III 45 0.50 5 V 30 0.45 2 5 III 50 0.50 5 V 35 0.45 2 5 III 55 0.51 5 V 40 0.46 2 5 III 60 0.49 5 V 45 0.45 2 5 III 65 0.49 5 V 50 0.46 2 5 III 72 0.46 5 V 55 0.50 2 5 IV 5 0.44 5 V 60 0.48 2 5 IV 10 0.42 5 V 65 0.48 2 5 IV 15 0.48 5 V 70 0.47 2 5 IV 20 0.48 5 VI 5 0.46 2 5 IV 25 0.48 5 VI 10 0.39 2 5 IV 30 0.47 5 VI 15 0.39 2 5 IV 35 0.48 5 VI 20 0.41 2 5 IV 40 0.49 5 VI 25 0.44 2 5 IV 45 0.51 5 VI 30 0.44 2 5 IV 50 0.51 121 5 VI 35 0.42 2 5 IV 55 0.55 5 VI 40 0.45 2 5 IV 60 0.51 5 VI 45 0.44 2 5 IV 65 0.52 5 VI 50 0.47 2 5 IV 72 0.48 5 VI 55 0.50 2 5 V 5 0.44 5 VI 60 0.49 2 5 V 10 0.41 5 VI 65 0.48 2 5 V 15 0.40 5 VI 70 0.50 2 5 V 20 0.41 5 VII 5 0.47 2 5 V 25 0.42 5 VII 10 0.41 2 5 V 30 0.42 5 VII 15 0.38 2 5 V 35 0.40 5 VII 20 0.41 2 5 V 40 0.40 5 VII 25 0.44 2 5 V 45 0.44 5 VII 30 0.46 2 5 V 50 0.46 5 VII 35 0.42 2 5 V 55 0.50 5 VII 40 0.44 2 5 V 60 0.47 5 VII 45 0.44 2 5 V 65 0.49 5 VII 50 0.50 2 5 V 72 0.45 5 VII 55 0.51 2 5 VI 5 0.45 5 VII 60 0.49 2 5 VI 10 0.41 5 VII 65 0.50 2 5 VI 15 0.43 5 VII 70 0.49 2 5 VI 20 0.44 5 VIII 5 0.47 2 5 VI 25 0.43 5 VIII 10 0.40 2 5 VI 30 0.42 5 VIII 15 0.37 2 5 VI 35 0.42 5 VIII 20 0.38 2 5 VI 40 0.41 5 VIII 25 0.44 2 5 VI 45 0.46 5 VIII 30 0.44 2 5 VI 50 0.48 5 VIII 35 0.42 2 5 VI 55 0.50 5 VIII 40 0.44 2 5 VI 60 0.45 5 VIII 45 0.45 2 5 VI 65 0.48 5 VIII 50 0.46 2 5 VI 72 0.44 5 VIII 55 0.50 2 5 VII 5 0.51 5 VIII 60 0.47 2 5 VII 10 0.57 5 VIII 65 0.47 2 5 VII 15 0.53 5 VIII 70 0.48 2 5 VII 20 0.46 5 IX 5 0.47 2 5 VII 25 0.46 5 IX 10 0.40 2 5 VII 30 0.44 5 IX 15 0.39 2 5 VII 35 0.45 5 IX 20 0.40 2 5 VII 40 0.46 5 IX 25 0.45 2 5 VII 45 0.47 5 IX 30 0.44 2 5 VII 50 0.50 5 IX 35 0.47 2 5 VII 55 0.51 5 IX 40 0.47 2 5 VII 60 0.46 5 IX 45 0.44 2 5 VII 65 0.48 5 IX 50 0.50 2 5 VII 72 0.47 5 IX 55 0.47 2 5 VIII 5 0.49 5 IX 60 0.47 2 5 VIII 10 0.45 5 IX 65 0.53 2 5 VIII 15 0.45 5 IX 70 0.53 2 5 VIII 20 0.43 122 5 X 5 0.52 2 5 VIII 25 0.42 5 X 10 0.42 2 5 VIII 30 0.43 5 X 15 0.41 2 5 VIII 35 0.41 5 X 20 0.41 2 5 VIII 40 0.41 5 X 25 0.42 2 5 VIII 45 0.44 5 X 30 0.45 2 5 VIII 50 0.47 5 X 35 0.46 2 5 VIII 55 0.49 5 X 40 0.50 2 5 VIII 60 0.48 5 X 45 0.46 2 5 VIII 65 0.46 5 X 50 0.53 2 5 VIII 72 0.44 5 X 55 0.48 2 5 IX 5 0.57 5 X 60 0.47 2 5 IX 10 0.47 5 X 65 0.49 2 5 IX 15 0.43 5 X 70 0.52 2 5 IX 20 0.42 5 XI 5 0.48 2 5 IX 25 0.41 5 XI 10 0.44 2 5 IX 30 0.40 5 XI 15 0.41 2 5 IX 35 0.38 5 XI 20 0.43 2 5 IX 40 0.41 5 XI 25 0.44 2 5 IX 45 0.45 5 XI 30 0.47 2 5 IX 50 0.49 5 XI 35 0.46 2 5 IX 55 0.52 5 XI 40 0.48 2 5 IX 60 0.50 5 XI 45 0.46 2 5 IX 65 0.48 5 XI 50 0.51 2 5 IX 72 0.45 5 XI 55 0.59 2 5 X 5 0.53 5 XI 60 0.37 2 5 X 10 0.44 5 XI 65 0.48 2 5 X 15 0.40 5 XI 70 0.48 2 5 X 20 0.39 5 XII 5 0.49 2 5 X 25 0.41 5 XII 10 0.43 2 5 X 30 0.41 5 XII 15 0.40 2 5 X 35 0.40 5 XII 20 0.43 2 5 X 40 0.43 5 XII 25 0.45 2 5 X 45 0.45 5 XII 30 0.47 2 5 X 50 0.45 5 XII 35 0.47 2 5 X 55 0.48 5 XII 40 0.47 2 5 X 60 0.50 5 XII 45 0.45 2 5 X 65 0.47 5 XII 50 0.50 2 5 X 72 0.45 5 XII 55 0.49 2 5 XI 5 0.46 5 XII 60 0.46 2 5 XI 10 0.42 5 XII 65 0.49 2 5 XI 15 0.41 5 XII 70 0.49 2 5 XI 20 0.40 2 5 XI 25 0.41 2 5 XI 30 0.42 2 5 XI 35 0.39 2 5 XI 40 0.41 2 5 XI 45 0.44 2 5 XI 50 0.46 2 5 XI 55 0.48 2 5 XI 60 0.48 123 Log Height Section Sample Density (pith-3 (1-5) (I-X1I) bark) [g/cm3] 3 1 1 5 0.50 3 1 I 10 0.47 3 1 I 15 0.41 3 1 I 20 0.38 3 1 I 25 0.38 3 1 I 30 0.44 3 1 I 35 0.40 3 1 I 40 0.40 3 1 I 45 0.43 3 1 I 50 0.41 3 1 I 55 0.41 3 1 I 62 0.42 3 1 II 5 0.51 3 1 II 10 0.51 3 1 II 15 0.44 3 1 II 20 0.41 3 1 II 25 0.39 3 1 II 30 0.38 3 1 II 35 0.39 3 1 II 40 0.41 3 1 II 45 0.42 3 1 11 50 0.42 3 1 II 55 0.41 3 1 11 62 0.42 3 1 III 5 0.53 3 1 III 10 0.47 3 1 III 15 0.41 3 1 III 20 0.40 3 1 III 25 0.39 3 1 III 30 0.38 2 5 XI 65 0.45 2 5 XI 72 0.44 2 5 XII 5 0.43 2 5 XII 10 0.40 2 5 XII 15 0.40 2 5 XII 20 0.39 2 5 XII 25 0.40 2 5 XII 30 0.39 '2 5 XII 35 0.38 2 5 XII 40 0.43 2 5 XII 45 0.46 2 5 XII 50 0.48 2 5 XII 55 0.51 2 5 XII 60 0.50 2 5 XII 65 0.46 2 5 XII 72 0.41 Log Height Section Sample Density (pith-5 (1-5) (I-XII) bark) [g/cm3] 5 1 I 5 0.40 5 1 I 10 0.33 5 1 I 15 0.35 5 1 I 20 0.37 5 1 I 25 0.35 5 1 I 30 0.35 5 1 I 35 0.37 5 1 I 40 0.34 5 1 I 45 0.41 5 1 I 50 0.44 5 1 I 55 0.39 5 1 I 60 0.42 5 1 I 64 0.47 5 1 II 5 0.40 5 1 II 10 0.34 5 1 II 15 0.34 5 1 II 20 0.36 5 1 II 25 0.36 5 1 II 30 0.36 5 1 II 35 0.36 5 1 II 40 0.35 5 . 1 II 45 0.39 5 1 II 50 0.44 5 1 II 55 0.38 5 1 II 60 0.41 5 1 II 64 0.46 5 1 III 5 0.39 5 1 III 10 0.33 5 1 III 15 0.34 5 1 III 20 0.35 124 3 1 III 35 0.39 5 1 III 25 0.34 3 1 III 40 0.40 5 1 III 30 0.36 3 1 III 45 0.41 5 1 III 35 0.35 3 1 III 50 0.41 5 1 111 40 0.34 3 1 III 55 0.39 5 1 III 45 0.41 3 1 III 62 0.41 5 1 III 50 0.44 3 1 IV 5 0.49 5 1 III 55 0.38 3 1 IV 10 0.43 5 1 III 60 0.41 3 1 IV 15 0.42 5 1 III 64 0.44 3 1 IV 20 0.40 5 1 IV 5 0.37 3 1 IV 25 0.60 5 1 IV 10 0.33 3 1 IV 30 0.40 5 1 IV 15 0.34 3 1 IV 35 0.41 5 1 IV 20 0.35 3 1 IV 40 0.40 5 1 IV 25 0.34 3 1 IV 45 0.40 5 1 IV 30 0.35 3 1 IV 50 0.40 5 1 IV 35 0.35 3 1 IV 55 0.38 5 1 IV 40 0.34 3 1 IV 62 0.40 5 1 IV 45 0.42 3 1 V 5 0.47 5 1 IV 50 0.46 3 1 V 10 0.39 5 1 IV 55 0.42 3 1 V 15 0.37 5 1 IV 60 0.43 3 1 V 20 0.36 5 1 IV 64 0.45 3 1 V 25 0.36 5 1 V 5 ' 0.44 3 1 V 30 0.39 5 1 V 10 0.40 3 1 V 35 0.39 5 1 V 15 0.38 3 1 V 40 0.40 5 1 V 20 0.38 3 1 V 45 0.40 5 1 V 25 0.36 3 1 V 50 0.39 5 1 V 30 0.35 3 1 V 55 0.38 5 1 V 35 0.34 3 1 V 62 0.40 5 1 V 40 0.33 3 1 VI 5 0.49 5 1 V 45 0.38 3 1 VI 10 0.41 5 1 V 50 0.43 3 1 VI 15 0.38 5 1 V 55 0.40 3 1 VI 20 0.39 5 1 V 60 0.43 3 1 VI 25 0.36 5 1 V 64 0.45 3 1 VI 30 0.38 5 1 VI 5 0.41 3 1 VI 35 0.40 5 1 VI 10 0.34 3 1 VI 40 0.39 5 1 VI 15 0.34 3 1 VI 45 0.41 5 1 VI 20 0.35 3 1 VI 50 0.40 5 1 VI 25 0.34 3 1 VI 55 0.39 5 1 VI 30 0.36 3 1 VI 62 0.41 5 1 VI 35 0.35 3 1 VII 5 0.48 5 1 VI 40 0.34 3 1 VII 10 0.42 5 1 VI 45 0.41 3 1 VII 15 0.39 5 1 VI 50 0.42 3 1 VII 20 0.38 5 1 VI 55 0.39 3 1 VII 25 0.38 5 1 VI 60 0.42 3 1 VII 30 0.38 5 1 VI 64 0.43 3 1 VII 35 0.38 5 1 VII 5 0.41 3 1 VII 40 0.39 5 1 VII 10 0.34 125 3 1 VII 45 0.43 5 1 VII 15 0.34 3 1 VII 50 0.41 5 1 VII 20 0.36 3 1 VII 55 0.40 5 1 VII 25 0.37 3 1 VII 62 0.41 5 1 VII 30 0.39 3 1 VIII 5 0.59 5 1 VII 35 0.38 3 1 VIII 10 0.44 5 1 VII 40 0.38 3 1 VIII 15 0.37 5 1 VII 45 0.41 3 1 VIII 20 0.36 5 1 VII 50 0.44 3 1 VIII 25 0.37 5 1 VII 55 0.40 3 1 VIII 30 0.39 5 1 VII 60 0.42 3 1 VIII 35 0.38 5 1 VII 64 0.43 3 1 VIII 40 0.40 5 1 VIII 5 0.40 3 1 VIII 45 0.42 5 1 VIII 10 0.33 3 1 VIII 50 0.40 5 1 VIII 15 0.33 3 1 VIII 55 0.40 5 VIII 20 0.34 3 VIII 62 0.40 5 VIII 25 0.35 3 IX 5 0.50 5 VIII 30 0.37 3 IX 10 0.39 5 VIII 35 0.37 3 IX 15 0.36 5 VIII 40 0.35 3 IX 20 0.35 5 VIII 45 0.39 3 IX 25 0.35 5 VIII 50 0.43 3 IX 30 0.38 5 VIII 55 0.38 3 IX 35 0.38 5 VIII 60 0.42 3 IX 40 0.40 5 VIII 64 0.43 3 IX 45 0.42 5 IX 5 0.39 3 IX 50 0.40 5 IX 10 0.33 3 IX 55 0.40 5 IX 15 0.33 3 IX 62 0.40 5 IX 20 0.36 3 X 5 0.44 5 IX 25 0.36 3 X 10 0.38 5 IX 30 0.38 3 X 15 0.36 5 IX 35 0.36 3 X 20 0.36 5 IX 40 0.37 3 X 25 0.36 . 5 IX 45 0.39 3 X 30 0.39 5 IX 50 0.42 3 X 35 0.40 5 IX 55 0.38 3 X 40 0.41 5 IX 60 0.40 3 X 45 0.42 5 IX 64 0.45 3 X 50 0.40 5 X 5 0.37 3 X 55 . 0.39 5 X 10 0.33 3 X 62 0.39 5 X 15 0.34 3 XI 5 0.45 5 X 20 0.36 3 XI 10 0.40 5 X 25 0.36 3 XI 15 0.37 5 X 30 0.37 3 XI 20 0.37 5 X 35 0.37 3 XI 25 0.38 5 X 40 0.36 3 1 XI 30 0.39 5 X 45 0.41 3 XI 35 0.39 5 X 50 0.42 3 I XI 40 0.42 5 X 55 0.40 3 1 XI 45 0.44 5 X 60 0.42 3 1 XI 50 0.41 5 1 X 64 0.44 126 3 1 XI 55 0.40 3 1 XI 62 0.40 3 1 XII 5 0.48 3 1 XII 10 0.40 3 1 XII 15 0.39 3 1 XII 20 0.38 3 1 XII 25 0.39 3 1 XII 30 0.40 3 1 XII 35 0.40 3 1 XII 40 0.41 3 1 XII 45 0.43 3 1 XII 50 0.41 3 1 XII 55 0.40 3 1 XII 62 0.42 3 2 I 5 0.40 3 2 I 10 0.36 3 2 I 15 0.33 3 2 I 20 0.36 3 2 I 25 0.37 3 2 I 30 0.38 3 2 I 35 0.40 3 2 I 40 0.40 3 2 I 45 0.40 3 2 I 50 0.41 3 2 I 55 0.39 3 2 I 60 0.41 3 2 I 64 0.41 3 2 II 5 0.41 3 2 II 10 0.37 3 2 II 15 0.34 3 2 II 20 0.37 3. 2 II 25 0.36 3 2 11 30 0.35 3 2 II 35 0.38 3 2 II 40 0.40 3 2 II 45 0.41 3 2 II 50 0.42 3 2 II 55 0.40 3 2 II 60 0.42 3 2 11 64 0.41 3 2 III 5 0.40 3 2 III 10 0.36 3 2 III 15 0.34 3 2 III 20 0.37 3 2 III 25 0.34 3 2 III 30 0.35 3 2 111 35 0.38 3 2 III 40 0.39 3 2 III 45 0.40 3 2 III 50 0.41 5 1 XI 5 0.38 5 1 XI 10 0.33 5 1 XI 15 0.34 5 1 XI 20 0.36 5 1 XI 25 0.41 5 1 XI 30 0.39 5 1 XI 35 0.37 5 1 XI 40 0.34 5 1 XI 45 0.39 5 1 XI 50 0.43 5 1 XI 55 0.39 5 1 XI 60 0.41 5 1 XI 64 0.45 5 1 XII 5 0.38 5 1 XII 10 0.33 5 1 XII 15 0.34 5 1 XII 20 0.37 5 1 XII 25 0.37 5 1 XII 30 0.37 5 1 XII 35 0.37 5 1 XII 40 0.35 5 1 XII 45 0.42 5 1 XII 50 0.45 5 1 XII 55 0.40 5 1 XII 60 0.43 5 1 XII 64 0.45 5 2 I 5 0.39 5 2 I 10 0.34 5 2 I 15 0.35 5 2 I 20 0.36 5 2 I 25 0.35 5 2 I 30 0.34 5 2 I 35 0.35 5 2 I 40 0.34 5 2 I 45 0.42 5 2 I 50 0.45 5 2 I 55 0.40 5 2 I 60 0.42 5 2 I 65 0.45 5 2 II 5 0.37 5 2 II 10 0.33 5 2 II 15 0.34 5 2 II 20 0.36 5 2 II 25 0.35 5 2 11 30 0.34 5 2 II 35 0.35 5 2 II 40 0.34 5 2 II 45 0.41 5 2 II 50 0.45 5 2 II 55 0.40 127 3 2 III 55 0.40 3 2 III 60 0.41 3 2 III 64 0.41 3 2 IV 5 0.41 3 2 IV 10 0.35 3 2 IV 15 0.32 3 2 IV 20 0.36 3 2 IV 25 0.34 3 2 IV 30 0.35 3 2 IV 35 0.39 3 2 IV 40 0.39 3 2 IV 45 0.39 3 2 IV 50 0.42 3 2 IV 55 0.39 3 2 IV 60 0.40 3 2 IV 64 0.41 3 2 V 5 ' 0.42 3 2 V 10 0.33 3 2 V 15 0.33 3 2 V 20 0.36 3 2 V 25 0.35 3 2 V 30 0.35 3 2 V 35 0.38 3 2 V 40 0.39 3 2 V 45 0.39 3 2 V 50 0.40 3 2 V 55 0.38 3 2 V 60 0.39 3 2 V 64 0.40 3 2 VI 5 0.44 3 2 VI 10 0.35 3 2 VI 15 0.34 3 2 VI 20 0.36 3 2 VI 25 0.35 3 2 VI 30 0.35 3 2 VI 35 0.37 3 2 VI 40 0.38 3 2 VI 45 0.39 3 2 VI 50 0.40 3 2 VI 55 0.38 3 2 VI 60 0.37 3 2 VI 64 0.34 3 2 VII 5 0.43 3 2 VII 10 0.36 3 2 VII 15 0.35 3 2 VII 20 0.36 3 2 VII 25 0.36 3 2 VII 30 0.35 3 2 VII 35 0.38 3 2 VII 40 0.38 5 2 11 60 0.42 5 2 II 65 0.45 5 2 III 5 0.37 5 2 III 10 0.35 5 2 III 15 0.35 5 2 III 20 0.36 5 2 III 25 0.35 5 2 III 30 0.36 5 2 III 35 0.36 5 2 III 40 0.34 5 2 III 45 0.39 5 2 III 50 0.46 5 2 III 55 0.41 5 2 III 60 0.43 5 2 III 65 0.46 5 2 IV 5 0.39 5 2 IV 10 0:35 5 2 IV 15 0.34 5 2 IV 20 0.35 5 2 IV 25 0.34 5 2 IV 30 0.35 5 2 IV 35 0.37 5 2 IV 40 0.35 5 2 IV 45 0.37 5 2 IV 50 0.44 5 2 IV 55 0.39 5 2 IV 60 0.41 5 2 IV 65 0.43 5 2 V 5 0.38 5 2 V 10 0.34 5 2 V 15 0.34 5 2 V 20 0.35 5 2 V 25 0.35 5 2 V 30 0.36 5 2 V 35 0.36 5 2 V 40 0.35 5 2 V 45 0.38 5 2 V 50 0.44 5 2 V 55 0.40 5 2 V 60 0.41 5 2 V 65 0.42 5 2 VI 5 0.38 5 2 VI 10 0.32 5 2 VI 15 0.33 5 2 VI 20 0.37 5 2 VI 25 0.42 5 2 VI 30 0.40 5 2 VI 35 0.37 5 2 VI 40 0.35 5 2 VI 45 0.39 128 3 2 VII 45 0.41 3 2 VII 50 0.41 3 2 VII 55 0.39 3 2 VII 60 0.39 3 2 VII 64 0.40 3 2 VIII 5 0.45 3 2 VIII 10 0.36 3 2 VIII 15 0.35 3 2 VIII 20 0.36 3 2 VIII 25 0.36 3 2 VIII 30 0.40 3 2 VIII 35 0.39 3 2 VIII 40 0.39 3 2 VIII 45 0.43 3 2 VIII 50 0.41 3 2 VIII 55 0.39 3 2 VIII 60 0.41 3 2 VIII 64 0.40 3 2 IX 5 0.42 3 2 IX 10 0.36 3 2 IX 15 0.35 3 2 IX 20 0.36 3 2 IX 25 0.36 3 2 IX 30 0.36 3 2 IX 35 0.38 3 2 IX 40 0.39 3 2 IX 45 0.43 3 2 IX 50 0.42 3 2 IX 55 0.39 3 2 IX 60 0.41 3 2 IX 64 0.40 3 2 X 5 0.45 3 2 X 10 0.37 3 2 X 15 0.34 3 2 X 20 0.36 3 2 X 25 0.36 3 2 X 30 0.35 3 2 X 35 0.37 3 2 X 40 0.39 3 2 X 45 . 0.41 3 2 X 50 0.41 3 2 X 55 0.39 3 2 X 60 0.39 3 2 X 64 0.41 3 2 XI 5 0.43 3 2 XI 10 0.35 3 2 XI 15 0.34 3 2 XI 20 0.35 3 2 XI 25 0.36 3 2 XI 30 0.36 5 2 VI 50 0.44 5 2 VI 55 0.40 5 2 VI 60 0.40 5 2 VI 65 0.42 5 2 VII 5 0.38 5 2 VII 10 0.32 5 2 VII 15 0.34 5 2 VII 20 0.43 5 2 VII 25 0.46 5 2 VII 30 0.42 5 2 VII 35 0.39 5 2 VII 40 0.38 5 2 VII 45 0.39 5 2 VII 50 0.41 5 2 VII 55 0.38 5 2 VII 60 0.38 5 2 VII 65 0.42 5 2 VIII 5 0.39 5 2 VIII 10 0.34 5 2 VIII 15 0.35 5 2 VIII 20 0.41 5 2 VIII 25 0.43 5 2 VIII 30 0.38 5 2 VIII 35 0.39 5 2 VIII 40 0.38 5 2 VIII 45 0.40 5 2 VIII 50 0.45 5 2 VIII 55 0.38 5 2 VIII 60 0.42 5 2 VIII 65 0.45 5 2 IX 5 0.38 5 2 IX 10 0.34 5 2 IX 15 0.34 5 2 IX 20 0.42 5 2 IX 25 0.45 5 2 IX 30 0.41 5 2 IX 35 0.41 5 2 IX 40 0.38 5 2 IX 45 0.39 5 2 IX 50 0.48 5 2 IX 55 0.40 5 2 IX 60 0.45 5 2 IX 65 0.47 5 2 X 5 0.38 5 2 X 10 0.33 5 2 X 15 0.34 5 2 X 20 0.38 5 2 X 25 0.38 5 2 X 30 0.35 5 2 X 35 0.39 129 3 2 XI 35 0.38 3 2 XI 40 0.40 3 2 XI 45 0.41 3 2 XI 50 0.41 3 2 XI 55 0.39 3 2 XI 60 0.39 3 2 XI 64 0.39 3 2 XII 5 0.43 3 2 XII 10 0.36 3 2 XII 15 0.33 3 2 XII 20 0.35 3 2 XII 25 0.35 3 2 XII 30 0.37 3 2 XII 35 0.39 3 2 XII 40 0.41 3 2 XII 45 0.40 3 2 XII 50 0.40 3 2 XII 55 0.39 3 2 XII 60 0.40 3 2 XII 64 0.41 3 3 I 5 0.39 3 3 I 10 0.36 3 3 I 15 0.34 3 3 I 20 0.39 3 3 I 25 0.37 3 3 I 30 0.37 3 3 I 35 0.40 3 3 1 40 0.41 3 3 I 45 0.42 3 3 I 50 0.41 3 3 I 55 0.40 3 3 I 60 0.42 3 3 I 65 0.43 3 3 II 5 0.51 3 3 II 10 0.57 3 3 II 15 0.53 3 3 II 20 0.47 3 3 II 25 0.43 3 3 11 30 0.41 3 3 II 35 0.46 3 3 II 40 0.47 3 3 11 45 0.49 3 3 II 50 0.46 3 3 II 55 0.43 3 3 II 60 0.44 3 3 II 65 0.44 3 3 III 5 0.40 3 3 III 10 0.37 3 3 III 15 0.35 3 3 III 20 0.37 5 2 X 40 0.36 5 2 X 45 0.37 5 2 X 50 0.42 5 2 X 55 0.39 5 2 X 60 0.43 5 2 X 65 0.45 5 2 XI 5 0.36 5 2 XI 10 0.32 5 2 XI 15 0.34 5 2 XI 20 0.36 5 2 XI 25 0.34 5 2 XI 30 0.34 5 2 XI 35 0.37 5 2 XI 40 0.35 5 2 XI 45 0.39 5 2 XI 50 0.44 5 2 XI 55 0.38 5 2 XI 60 0.41 5 2 XI 65 0.46 5 2 XII 5 0.35 5 2 XII 10 0.33 5 2 XII 15 0.34 5 2 XII 20 0.36 5 2 XII 25 0.35 5 2 XII 30 0.35 5 2 XII 35 0.35 5 2 XII 40 0.35 5 2 XII 45 0.41 5 2 XII 50 0.44 5 2 XII 55 0.40 5 2 XII 60 0.42 5 2 XII 65 0.46 5 3 I 5 0.38 5 3 I 10 0.35 5 3 I 15 0.34 5 3 I 20 0.36 5 3 I 25 0.35 5 3 I 30 0.36 5 3 I 35 0.37 5 3 I 40 0.36 5 3 1 45. 0.36 5 3 I 50 0.45 5 3 I 55 0.43 5 3 I 60 0.41 5 3 I 67 0.43 5 3 II 5 0.38 5 3 II 10 0.35 5 3 II 15 0.33 5 3 II 20 0.35 5 3 II 25 0.35 130 3 3 III 25 0.35 3 3 III 30 0.36 3 3 III 35 0.40 3 3 III 40 0.39 3 3 III 45 0.43 3 3 III 50 0.42 3 3 III 55 0.40 3 3 III 60 0.40 3 3 III 65 0.42 3 3 IV 5 0.40 3 3 IV 10 0.36 3 3 IV 15 0.35 3 3 IV 20 0.35 3 3 IV 25 0.36 3 3 IV 30 0.37 3 3 IV 35 0.38 3 3 IV 40 0.39 3 3 IV 45 0.40 3 3 IV 50 0.41 3 3 IV 55 0.39 3 3 IV 60 0.40 3 3 IV" 65 0.41 3 3 V 5 0.42 3 3 V 10 0.38 3 3 V 15 0.36 3 ' 3 V 20 0.36 3 3 V 25 0.35 3 3 V 30 0.36 3 3 V 35 0.38 3 3 V 40 0.38 3 3 V 45 0.40 3 3 V 50 0.40 3 3 V 55 0.38 3 3 V 60 0.40 3 3 V 65 0.40 3 3 VI 5 0.44 3 3 VI 10 0.41 3 3 VI 15 0.41 3 3 VI 20 0.42 3 3 VI 25 0.42 3 3 VI 30 0.42 3 3 VI 35 0.44 3 3 VI 40 0.45 3 3 VI 45 0.48 3 3 VI 50 0.47 3 3 VI 55 0.44 3 3 VI 60 0.44 3 3 VI 65 0.43 3 3 VII 5 0.42 3 3 VII 10 0.38 5 3 II 30 0.36 5 3 II 35 0.37 5 3 II 40 0.37 5 3 II 45 0.37 5 3 II 50 0.46 5 3 II 55 0.43 5 3 II 60 0.42 5 3 II 67 0.45 5 3 III 5 0.36 5 3 III 10 0.35 5 3 III 15 0.33 5 3 III 20 0.36 5 3 III 25 0.37 5 3 III 30 0.37 5 3 III 35 0.36 5 3 III 40 0.36 5 3 HI 45 0.36 5 3 III 50 0.43 5 3 III 55 0.42 5 3 III 60 0.41 5 3 III 67 0.43 5 3 IV 5 0.44 5 3 IV 10 0.41 5 3 IV 15 0.36 5 3 IV 20 0.40 5 3 IV 25 0.41 5 3 IV 30 0.37 5 3 IV 35 0.36 5 3 IV 40 0.35 5 3 IV 45 0.35 5 3 IV 50 0.41 5 3 IV 55 0.40 5 3 IV 60 0.38 5 3 IV 67 0.42 5 3 V 5 0.41 5 3 V 10 0.35 5 3 V 15 0.34 5 3 V 20 0.43 5 3 V 25 0.45 5 3 V 30 0.41 5 3 V 35 0.38 5 3 V 40 0.37 5 3 V 45 0.35 5 3 V 50 0.42 5 3 V- 55 0.41 5 3 V 60 0.41 5 3 V 67 0.42 5 3 VI 5 0.39 5 3 VI 10 0.34 5 3 VI 15 0.33 3 3 VII 15 0.38 3 3 VII 20 0.37 3 3 VII 25 0.36 3 3 VII 30 0.35 3 3 VII 35 0.39 3 3 VII 40 0.38 3 3 VII 45 0.43 3 3 VII 50 0.40 3 3 VII 55 0.39 3 3 VII 60 0.39 3 3 VII 65 0.40 3 3 VIII 5 0.42 3 3 VIII 10 0.36 3 3 VIII 15 0.36 3 3 VIII 20 0.36 3 3 VIII 25 0.36 3 3 VIII 30 0.35 3 3 VIII 35 0.38 3 3 VIII 40 0.39 3 3 VIII 45 0.44 3 3 VIII 50 0.42 3 3 VIII 55 0.39 3 3 VIII 60 0.39 3 3 VIII 65 0.40 3 3 IX 5 0.41 3 3 ' iX 10 0.35 3 3 IX 15 0.34 3 3 IX 20 0.35 3 3 IX 25 0.36 3 3 IX 30 0.35 3 3 IX 35 0.37 3. 3 IX 40 0.38 3 3 IX 45 0.42 3 3 IX 50 0.43 3 3 IX 55 0.40 3 3 IX 60 0.39 3 3 IX 65 0.40 3 3 X 5 0.48 3 3 X 10 0.43 3 3 X 15 0.38 3 3 X 20 0.39 3 3 X 25 0.38 3 3 X 30 0.38 3 3 X 35 0.40 3 3 X 40 0.41 3 3 X 45 0.43 3 3 X 50 0.43 3 3 X 55 0.40 3 3 X 60 0.40 3 3 X 65 0.41 5 3 VI 20 0.41 5 3 VI 25 0.46 5 3 VI 30 0.41 5 3 VI 35 0.40 5 3 VI 40 0.38 5 3 VI 45 0.35 5 3 VI 50 0.42 5 3 VI 55 0.38 5 3 VI 60 0.38 5 3 VI 67 0.41 5 3 VII 5 0.39 5 3 VII 10 0.36 5 3 VII 15 0.35 5 3 VII 20 0.38 5 3 VII 25 0.46 5 3 VII 30 0.39 5 3 VII 35 0.40 5 3 VII 40 0.39 5 3 VII 45 0.40 5 3 VII 50 0.46 5 3 VII 55 0.40 5 3 VII 60 0.40 5 3 VII 67 0.48 5 3 VIII 5 0.40 5 3 VIII 10 0.38 5 3 VIII 15 0.47 5 3 VIII 20 0.47 5 3 VIII 25 0.43 5 3 VIII 30 0.40 5 3 VIII 35 0.40 5 3 VIII 40 0.40 5 3 VIII 45 0.39 5 3 VIII 50 0.48 5 3 VIII 55 0.44 5 3 VIII 60 0.44 5 3 VIII 67 0.47 5 3 IX 5 0.37 5 3 IX 10 0.35 5 3 IX 15 0.35 5 3 IX 20 0.37 5 3 IX 25 0.35 5 3 IX 30 0.36 5 3 IX 35 0.36 5 3 IX 40 0.36 5 3 IX 45 0.36 5 3 IX 50 0.43 5 3 IX 55 0.38 5 3 IX 60 0.40 5 3 IX 67 0.44 5 3 X 5 0.37 3 3 XI 5 0.41 3 3 XI 10 0.41 3 3 XI 15 0.38 3 3 XI 20 0.37 3 3 XI 25 0.37 3 3 XI 30 0.38 3 3 XI 35 0.41 3 3 XI 40 0.41 3 3 XI 45 0.43 3 3 XI 50 0.42 3 3 XI 55 0.40 3 3 XI 60 0.41 3 3 XI 65 0.42 3 3 XII 5 0.39 3 3 XII 10 0.36 3 3 XII 15 0.34 3 3 XII 20 0.36 3 3 XII 25 0.37 3 3 XII 30 0.36 3 3 XII 35 0.40 3 3 XII 40 0.40 3 3 XII 45 0.42 3 3 XII 50 0.41 3 3 XII 55 0.40 3 3 XII 60 0.40 3 3 XII 65 0.42 3 4 I 5 0.45 3 4 I 10 0.37 3 4 I 15 0.36 3 4 I 20 0.37 3 4 I 25 0.40 3 4 I 30 0.39 3 4 I 35 0.39 3 4 I 40 0.42 3 4 I 45 0.44 3 4 I 50 0.44 3 4 I 55 0.44 3 4 I 60 0.43 3 4 I 68 0.45 3 4 II 5 0.48 3 4 II 10 0.39 3 4 II 15 0.36 3 4 II 20 0.37 3 4 II 25 0.38 3 4 II 30 0.37 3 4 II 35 0.38 3 4 II 40 0.41 3 4 II 45 0.42 3 4 II 50 0.43 3 4 II 55 0.44 5 3 X 10 0.34 5 3 X 15 0.34 5 3 X 20 0.37 5 3 X 25 0.37 5 3 X 30 0.38 5 3 X 35 0.37 5 3 X 40 0.38 5 3 X 45 0.37 5 3 X 50 0.45 5 3 X 55 0.42 5 3 X 60 0.41 5 3 X 67 0.45 5 3 XI 5 0.39 5 3 XI 10 0.35 5 3 XI 15 0.34 5 3 XI 20 0.36 5 3 XI 25 0.38 5 3 XI 30 0.38 5 3 XI 35 0.36 5 3 XI 40 0.37 5 3 XI 45 0.37 5 3 XI 50 0.44 5 3 XI 55 0.42 5 3 XI 60 0.42 5 3 XI 67- 0.47 5 3 XII 5 0.38 5 3 XII 10 0.35 5 3 XII 15 0.34 5 3 XII 20 0.37 5 3 XII 25 0.37 5 3 XII 30 0.38 5 3 XII 35 0.37 5 3 XII 40 0.38 5 3 XII . 45 0.38 5 3 XII 50 0.46 5 3 XII 55 0.43 5 3 XII 60 0.43 5 3 XII 67 0.46 5 4 I 5 0.41 5 4 I 10 0.36 5 4 I 15 0.35 5 4 I 20 0.37 5 4 I 25 0.37 5 4 I 30 0.37 5 4 I 35 0.37 5 4 I 40 0.38 5 4 I 45 0.37 5 4 I 50 0.45 5 4 I 55 0.44 5 4 I 60 0.42 133 3 4 II 60 0.42 3 4 II 68 0.44 3 4 III 5 - 0.46 3 4 III 10 0.37 3 4 III 15 0.36 3 4 III 20 0.37 3 4 III 25 0.37 3 4 III 30 0.37 3 4 III 35 0.38 3 4 III 40 0.40 3 4 • III 45 0.42 3 4 III 50 0.43 3 4 III 55 0.43 3 4 III 60 0.40 3 4 III 68 0.43 3 4 IV 5 0.44 3 4 IV 10 0.47 3 4 IV 15 0.58 3 4 IV 20 0.46 3 4 IV 25 0.44 3 4 IV 30 0.41 3 4 IV 35 0.41 3 4 IV 40 0.43 3 4 IV 45 0.43 3 4 IV 50 0.44 3 .4' IV 55 0.46 3 4 IV 60 0.42 3 4 IV 68 0.42 3 4 V 5 0.45 3 4 V 10 0.46 3 4 V 15 0.55 3 4 V 20 0.49 3 4 V 25 0.44 3 4 V 30 0.45 3 4 V 35 0.44 3 4 V 40 0.44 3 4 V 45 0.44 3 4 V 50 0.48 3 4 V 55 0.45 3 4 V 60 0.43 3 4 V 68 0.48 3 4 VI 5 0.44 3 4 VI 10 0.39 3 4 VI 15 0.37 3 4 VI 20 0.36 3 4 VI 25 0.37 3 4 VI 30 0.35 3 4 VI 35 0.38 3 4 VI 40 0.40 3 4 VI 45 0.41 5 4 I 68 0.44 5 4 II 5 0.40 5 4 II 10 0.35 5 4 II 15 0.34 5 4 II 20 0.39 5 4 II 25 0.37 5 4 II 30 0.37 5 4 II 35 0.37 5 4 11 40 0.37 5 4 II 45 0.35 5 4 II 50 0.44 5 4 II 55 0.45 5 4 II 60 0.42 5 4 II 68 0.45 5 4 III 5 0.42 5 4 III 10 0.37 5 4 III 15 0.35 5 4 III 20 0.43 5 4 III 25 0.43 5 4 III 30 0.41 5 4 III 35 0.38 5 4 111 40 0.39 5 4 III 45 0.36 5 4 III 50 . 0.43 5 4 III 55 0.43 5 4 III 60 0.40 5 4 III 68 0.43 5 4 IV 5 0.42 5 4 IV 10 0.39 5 4 IV 15 0.37 5 4 IV 20 0.45 5 4 IV 25 0.50 5 4 IV 30 0.45 5 4 IV 35 0.41 5 4 IV 40 0.41 5 4 IV 45 0.37 5 4 IV 50 0.44 5 4 IV 55 0.43 5 4 IV 60 0.39 5 4 IV 68 0.43 5 4 V 5 0.43 5 4 V 10 0.38 5 4 V 15 0.34 5 4 V 20 0.37 5 4 V 25 0.41 5 4 V 30 0.37 5 4 V 35 0.35 5 4 V 40 0.38 5 4 V 45 0.36 5 4 V 50 0.41 3 4 VI 50 0.42 3 4 VI 55 0.42 3 4 VI 60 0.39 3 4 VI 68 0.40 3 4 VII 5 0.43 3 4 VII 10 0.38 3 4 VII 15 0.38 3 4 VII 20 0.37 3 4 VII 25 0.37 3 4 VII 30 0.36 3 4 VII 35 0.36 3 4 VII 40 0.40 3 4 VII 45 0.40 3 4 VII 50 0.43 3 4 VII 55 0.42 3 4 VII 60 0.40 3 4 VII 68 0.40 3 4 VIII 5 0.43 3 4 VIII 10 0.38 3 4 VIII 15 0.36 3 4 VIII 20 0.37 3 4 VIII 25 0.38 3 4 VIII 30 0.36 3 4 VIII 35 0.37 3 4 VIII 40 0.40 3 4 VIII 45 0.41 3 4 VIII 50 0.43 3 4 VIII 55 0.43 3 4 VIII 60 0.41 3 4 VIII 68 0.41 3 4 IX 5 0.44 3 4 IX 10 0.39 3 4 IX 15 0.39 3 4 IX 20 0.40 3 4 IX 25 0.42 3 4 IX 30 0.41 3 4 IX 35 0.41 3 4 IX 40 0.43 3 4 IX 45 0.45 3 4 IX 50 0.49 3 4 IX 55 0.47 3 4 IX 60 0.44 3 4 IX 68 0.44 3 4 X 5 0.43 3 4 X 10 0.41 3 4 X 15 0.47 3 4 X 20 0.55 3 4 X 25 0.56 3 4 X 30 0.47 3 4 X 35 0.46 5 4 V 55 0.40 5 4 V 60 0.39 5 4 V 68 0.42 5 4 VI 5 0.42 5 4 VI 10 0.37 5 4 VI 15 0.34 5 4 VI 20 0.37 5 4 VI 25 0.37 5 4 VI 30 0.37 5 4 VI 35 0.37 5 4 VI 40 0.36 5 4 VI 45 0.35 5 4 VI 50 0.44 5 4 VI 55 0.40 5 4 VI 60 0.41 5 4 VI 68 0.43 5 4 VII 5 0.41 5 4 VII 10 0.37 5 4 VII 15 0.33 5 4 VII 20 0.35 5 4 VII 25 0.36 5 4 VII 30 0.38 5 4 VII 35 0.39 5 4 VII 40 0.37 5 4 VII 45 0.36 5 4 VII 50 0.46 5 4 VII 55 0.42 5 4 VII 60 0.45 5 4 VII 68 0.46 5 4 VIII 5 0.41 5 4 VIII 10 0.36 5 4 VIII 15 0.33 5 4 VIII 20 0.36 5 4 VIII 25 0.40 5 4 VIII 30 0.40 5 4 VIII 35 0.38 5 4 VIII 40 0.37 5 4 VIII 45 0.37 5 4 VIII 50 0.40 5 4 VIII 55 0.40 5 4 VIII 60 0.41 5 4 VIII 68 0.45 5 4 IX 5 0.40 5 4 IX 10 0.36 5 4 IX 15 0.33 5 4 IX 20 0.36 5 4 IX 25 0.43 5 4 IX 30 0.41 5 4 IX 35 0.38 5 4 IX 40 0.38 135 3 4 X 40 0.48 3 4 X 45 0.47 3 4 X 50 0.47 3 4 X 55 0.44 3 4 X 60 0.43 3 4 X 68 0.43 3 4 XI 5 0.43 3 4 XI 10 0.39 3 4 XI 15 0.37 3 4 XI 20 0.36 3 4 XI - 25 0.38 3 4 XI 30 0.38 3 4 XI 35 0.38 3 4 XI 40 0.42 3 4 XI 45 0.46 3 4 XI 50 0.45 3 4 XI 55 0.44 3 4 XI 60 0.43 3 4 XI 68 0.42 3 4 XII 5 0.45 3 4 XII 10 0.36 3 4 XII 15 0.34 3 4 XII 20 0.34 3 4 XII 25 0.40 3 4 XII 30 0.40 3 4 XII 35 0.40 3 4 XII 40 0.43 3 4 XII 45 0.43 3 4 XII 50 0.44 3 4 XII 55 0.43 3 4 XII 60 0.41 3 4 XII 68 0.43 3 5 I 5 0.53 3 5 I 10 0.45 3 5 I 15 0.42 3 5 I 20 0.39 3 5 I 25 0.41 3 5 I 30 0.39 3 5 I 35 0.38 3 5 I 40 0.40 3 5 1 45 0.44 3 5 I 50 0.50 3 5 I 55 0.53 3 5 I 60 0.47 3 5 I 65 0.46 3 5 I 72 0.46 3 5 II 5 0.50 3 5 II 10 0.54 3 5 II 15 0.52 3 5 II 20 0.44 5 4 IX 45 0.39 5 4 IX 50 0.40 5 4 IX 55 0.43 5 4 IX 60 0.42 5 4 IX 68 0.44 5 4 X 5 0.40 5 4 X 10 0.36 5 4 X 15 0.34 5 4 X 20 0.37 5 4 X 25 0.40 5 4 X 30 0.37 5 4 X 35 0.37 5 4 X 40 0.38 5 4 X 45 0.39 5 4 X 50 0.42 5 4 X 55 0.45 5 4 X 60 0.42 5 4 X 68 0.45 5 4 XI 5 0.41 5 4 XI 10 0.34 5 4 XI 15 0.34 5 4 XI 20 0.36 5 4 XI 25 0.37 5 4 XI 30 0.35 5 4 XI 35 0.36 5 4 XI 40 0.38 5 4 . XI 45 0.38 5 4 XI 50 0.43 5 4 XI 55 0.44 5 4 XI 60 0.42 5 4 XI 68 0.46 5 4 XII 5 0.41 5 4 XII 10 0.35 5 4 XII 15 0.34 5 4 XII 20 0.37 5 4 XII 25 0.36 5 4 XII 30 0.39 5 4 XII 35 0.38 5 4 XII 40 0.40 5 4 XII 45 0.39 5 4 XII 50 0.47 5 4 XII 55 0.46 5 4 XII 60 0.43 5 4 XII 68 0.46 5 5 I 5 0.41 5 5 I 10 0.43 5 5 I 15 0.44 5 5 I 20 0.48 5 5 I 25 0.42 5 5 I 30 0.39 136 3 5 II 25 0.44 3 5 II 30 0.43 3 5 II 35 0.44 3 5 11 40 0.45 3 5 II 45 0.45 3 5 II 50 0.46 3 5 II 55 0.47 3 5 II 60 0.43 3 5 II 65 0.45 3 5 II 72 0.47 3 5 III 5 0.56 3 5 III 10 0.52 3 5 III 15 0.67 3 5 III 20 0.60 3 5 III 25 0.52 3 5 III 30 0.48 3 5 III 35 0.46 3 5 III 40 0.48 3 5 III 45 0.50 3 5 III 50 0.49 3 5 III 55 0.49 3 5 III 60 0.46 3 5 III 65 0.46 3 5 III 72 0.48 3 5 IV 5 0.50 3 5 IV 10 0.43 3 5 IV 15 0.42 3 5 IV 20 0.43 3 5 IV 25 0.40 3 5 IV 30 0.38 3 5 IV 35 0.39 3 . 5 . IV 40 0.39 3 5 IV 45 0.44 3 5 IV 50 0.45 3 5 IV 55 0.45 3 5 IV 60 0.45 3 5 IV 65 0.44 3 5 IV 72 0.47 3 5 V 5 0.51 3 5 V 10 0.47 3 5 V 15 0.50 3 5 V 20 0.47 3 5 V 25 0.41 3 5 V 30 0.39 3 5 V 35 0.41 3 5 V . 40 0.42 3 5 V 45 0.45 3 5 V 50 0.44 3 5 V 55 0.47 3 5 V 60 0.48 5 5 I 35 0.38 5 5 I 40 0.41 5 5 I 45 0.40 5 5 1 50 0.43 5 5 I 55 0.46 5 5 I 60 0.43 5 5 I 65 0.42 5 5 I 70 0.46 5 5 II 5 0.46 5 5 II 10 0.45 5 5 II 15 0.45 5 5 II 20 0.48 5 5 II 25 0.45 5 5 II 30 0.40 5 5 II 35 0.39 5 5 II 40 0.41 5 5 II 45 0.40 5 5 II 50 0.45 5 5 II 55 0.47 5 5 II 60 0.44 5 5 II 65 0.40 5 5 II 70 0.46 5 5 III 5 0.46 5 5 III 10 0.41 5 5 III 15 0.37 5 5 III 20 0.43 5 5 III 25 0.45 5 5 III 30 0.44 5 5 III 35 0.40 5 5 III 40 0.39 5 5 III 45 0.40 5 5 III 50 0.46 5 5 III 55 0.47 5 5 III 60 0.42 5 5 III 65 0.45 5 5 III 70 0.46 5 5 IV 5 0.44 5 5 IV 10 0.40 5 5 IV 15 0.37 5 5 IV 20 0.40 5 5 IV 25 0.41 5 5 IV 30 0.38 5 5 IV 35 0.36 5 5 IV 40 0.37 5 5 IV 45 0.37 5 5 IV 50 0.41 5 5 IV 55 0.45 5 5 IV 60 0.41 5 5 IV 65 0.41 5 5 IV 70 0.42 137 3 5 V 65 0.45 3 5 V 72 0.47 3 5 VI 5 0.53 3 5 VI 10 0.49 3 5 VI 15 0.59 3 5 VI 20 0.53 3 5 VI 25 0.50 3 5 VI 30 0.42 3 5 VI 35 0.39 3 5 VI 40 0.42 3 5 VI 45 0.44 3 5 VI 50 0.44 3 5 VI 55 0.46 3 5 VI 60 0.46 3 5 VI 65 0.46 3 5 VI 72 0.47 3 5 VII 5 0.51 3 5 VII 10 0.43 3 5 VII 15 0.41 3 5 VII 20 0.40 3 5 VII 25 0.39 3 5 VII 30 0.40 3 5 VII 35 0.42 3 5 VII 40 0.41 3 5 VII 45 0.40 3 5 VII 50 0.42 3 5 VII 55 0.46 3 5 VII 60 0.46 3 5 VII 65 0.45 3 5 VII 72 0.45 3 5 VIII 5 0.49 3 5 VIII 10 0.44 3 5 VIII 15 0.41 3 5 VIII 20 0.39 3 5 VIII 25 0.40 3 5 VIII 30 0.40 3 5 VIII 35 0.41 3 5 VIII 40 0.40 3 5 VIII 45 0.42 3 5 VIII 50 0.44 3 5 VIII 55 0.49 3 5 VIII 60 0.47 3 5 VIII 65 0.45 3 5 VIII 72 0.44 3 5 IX 5 0.48 3 5 IX 10 0.60 3 5 IX 15 0.65 3 5 IX 20 0.50 3 5 IX 25 0.47 3 5 IX 30 0.40 5 5 V 5 0.50 5 5 V 10 0.44 5 5 V 15 0.39 5 5 V 20 0.39 5 5 V 25 0.41 5 5 V 30 0.37 5 5 V 35 0.36 5 5 V 40 0.37 5 5 V 45 0.36 5 5 V 50 0.39 5 5 V 55 0.43 5 5 V 60 0.40 5 5 V 65 0.42 5 5 V 70 0.43 5 5 VI 5 0.43 5 5 VI 10 0.41 5 5 VI 15 0.37 5 5 VI 20 0.38 5 5 VI 25 0.40 5 5 VI 30 0.39 5 5 VI 35. 0.37 5 5 VI 40 0.38 5 5 VI 45 0.38 5 5 VI 50 0.44 5 5 VI 55 0.45 5 5 VI 60 0.42 5 5 VI 65 0.43 5 5 VI 70 0.44 5 5 VII 5 0.41 5 5 VII 10 0.40 5 5 VII 15 0.36 5 5 VII 20 0.37 5 5 VII 25 0.38 5 5 VII 30 0.38 5 5 VII 35 0.40 5 5 VII 40 0.41 5 5 VII 45 0.36 5 5 VII 50 0.35 5 5 VII 55 0.50 5 5 VII 60 0.46 5 5 VII 65 0.46 5 5 VII 70 0.50 5 5 VIII 5 0.42 5 5 VIII 10 0.39 5 5 VIII 15 0.37 5 5 VIII 20 0.38 5 5 VIII 25 0.41 5 5 VIII 30 0.44 5 5 VIII 35 0.40 5 5 VIII 40 0.40 3 5 IX 35 0.42 3 5 IX 40 0.43 3 5 IX 45 0.48 3 5 IX 50 0.50 3 5 IX 55 0.52 3 5 IX 60 0.51 3 5 IX 65 0.50 3 5 IX 72 0.47 3 5 X 5 0.57 3 5 X 10 0.56 3 5 X 15 0.50 3 5 X 20 0.44 3 5 X 25 0.44 3 5 X 30 0.41 3 5 X 35 0.41 3 5 X 40 0.44 3 5 X 45 0.46 3 5 X 50 0.49 3 5 X 55 0.51 3 5 X 60 0.49 3 5 X 65 0.50 3 5 X 72 0.49 3 5 XI 5 0.54 3 5 XI 10 0.46 3 5 XI 15 0.41 3 5 XI 20 0.40 3 5 XI 25 0.41 3 5 XI 30 0.43 3 5 XI 35 0.41 3 5 XI 40 0.45 3 5 XI 45 0.49 3 5 XI 50 0.49 3 5 XI 55 0.49 3 5 XI 60 0.47 3 5 XI 65 0.48 3 5 XI 72 0.47 3 5 XII 5 0.51 3 5 XII 10 0.46 3 5 XII 15 0.41 3 5 XII 20 0.39 3 5 XII 25 0.39 3 5 XII 30 0.43 3 5 XII 35 0.42 3 5 XII 40 0.42 3 5 XII 45 0.46 3 5 XII 50 0.48 3 5 XII 55 0.47 3 5 XII 60 0.46 3 5 XII 65 0.46 3 5 XII 72 0.47 5 5 VIII 45 0.38 5 5 VIII 50 0.37 5 5 VIII 55 0.44 5 5 VIII 60 0.42 5 5 VIII 65 0.42 5 5 VIII 70 0.43 5 5 IX 5 0.44 5 5 IX 10 0.39 5 5 IX 15 0.37 5 5 IX 20 0.37 5 5 IX 25 0.40 5 5 IX 30 0.38 5 5 IX 35 0.37 5 5 IX 40 0.40 5 5 IX 45 0.40 5 5 IX 50 0.38 5 5 IX 55 0.44 5 5 IX 60 0.40 5 5 IX 65 0.42 5 5 IX 70 0.47 5 5 X 5 0.44 5 5 X 10 0.41 5 5 X 15 0.37 5 5 X 20 0.37 5 5 X 25 0.40 5 5 X 30 0.37 5 5 X 35 0.37 5 5 X 40 0.42 5 5 X 45 0.40 5 5 X 50 0.39 5 5 X 55 0.46 5 5 X 60 0.41 5 5 X 65 0.42 5 5 X 70 0.48 5 5 XI 5 0.48 5 5 XI 10 0.41 5 5 XI 15 0.36 5 5 XI 20 0.39 5 5 XI 25 0.38 5 5 XI 30 0.38 5 5 XI 35 0.40 5 5 XI 40 0.43 5 5 XI 45 0.39 5 5 XI 50 0.42 5 5 XI 55 0.47 5 5 XI 60 0.43 5 5 XI 65 0.46 5 5 XI 70 0.48 5 5 XII 5 0.42 5 5 XII 10 0.42 139 5 5 XII 15 0.40 5 5 XII 20 0.44 5 5 XII 25 0.42 5 5 XII 30 0.39 5 5 XII 35 0.42 5 5 XII 40 0.46 5 5 XII 45 0.43 5 5 XII 50 0.47 5 5 XII 55 0.50 5 5 XII 60 0.45 5 5 XII 65 0.46 5 5 XII 70 0.49 140 Appendix IB. Data and statistical output used in Chapter 3 REML variance components analysis Response variate: TrimDensity (NOTE: 19 data points have been excluded as they appeared to be inconsistent with the bulk of data) Fixed model: Constant + height + sample Random model: log + log.height + log.height.section + log.height.sample + log.height.section.sample Number of units: 3137 (19 units excluded due to zero weights or missing values) log.height.section.sample used as residual term Non-sparse algorithm with Fisher scoring Estimated variance components Random term component s.e. log 0.0003079 0.0002729 log.height 0.0000835 0.0000536 log.height.section 0.0001802 0.0000201 log.height.sample 0.0003828 0.0000393 Residual variance model Term Factor Model(order) Parameter Estimate s.e. log.height.section.sample Identity Sigma2 0.000391 0.0000107 Approximate stratum variances Stratum variance effective d.f. log 0.2569743. 3.00 log.height 0.0200000 12.00 log.height.section 0.0027411 219.99 log.height.sample 0.0049519 224.00 log.height.section.sample 0.0003909 2654.02 Matrix of coefficients of components for each stratum: log 7.69E+02 1.54E+02 1.28E+01 1.19E+01 log.height 0.00E+00 1.53E+02 1.27E+01 1.19E+01 log.height.section 0.00E+00 0.00E+00 1.30E+01 4.59E-05 log.height.sample 0.0OE+O0 0.00E+00 0.00E+00 1.19E+01 log.height.section.sample 0.00E+00 O.00E+O0 0.00E+00 0.00E+00 log 1.00E+00 log.height 1.00E+0log.height.section 1.00E+00 log.height.sample 1.00E+0log.height.section.sample 1.00E+00 Wald tests for fixed effects Sequentially adding terms to fixed model Fixed termWald statistic d.f. Wald/d.f. chi pr height 48.664 12.17<0.001 sample 426.57 19 22.45<0.001 NOTE: Both height and sample (distance from core/pith) are highly statistically significant, but no interaction (see below) Table of predicted means for Constant 0.4202 Standard error: 0.00930 Table of predicted means for height height 1 0.4085 2 3 0 .4034 4 5 0.4139 0 .4232 0 .4519 Standard errors of differences Average Maximum Minimum 0 . 008120 0 .008159 0 .008091 Table of predicted means for sample sample 5 10 15 20 25 30 35 40 0.4309 0.3788 0.3681 0.3852 0.3971 0.3966 0.3998 0 .4088 sample 45 50 55 60 62 64 65 67 0.4291 0.4493 0.4437 0.4364 0.4337 0.4464 0.4344 0 .4452 sample 68 69 70 72 0.4440 0.4087 0.4505 0.4168 Standard errors of differences Average Maximum Minimum 0 . 01254 0.02585 0 . 006445 Average variance of differences: 0.0001886 Wald tests for fixed effects Sequentially adding terms to fixed model Fixed term Wald statistic d.f. Wald/d.f. chi pr height 47.894 11.97<0.001 sample 419.62 19 22.09<0.001 height.sample 45.2149 0.92 0.628 142 "Table of predicted means for Constant 0.4209 Standard error: 0.00959 Table of predicted means for height height All values in table missing: due to missing factor combinations in higher order interactions. Table of predicted means for sample sample 5 0.4309 0 .4088 10 15 0 .3788 20 25 0 .3681 30 35 0 .3852 40 0 .3971 0 .3966 0 .3998 sample 4 5 0.4291 50 55 0.4493 60 62 0 .4437 64 65 0 .4367 67 sample 68 69 70 72 Standard errors of differences Average: Maximum: Minimum: 0 . 006557 0 . 006840 0 . 006498 Table of predicted means for height.sample sample height 10 15 20 25 30 35 1 0 4256 0 3626 0 3545 0 3705 0 3745 0 3846 0 3883 2 0 4076 0 3457 0 3404 0 3700 0 3787 0 3783 0 3908 3 0 4167 0 3658 0 3601 0 3797 0 3960 0 3924 0 3999 4 0 4281 0 3827 0 3652 0 3829 0 4074 0 4043 0 4023 5 0 4765 0 4370 0 4203 0 4228 0 4289 0 4234 0 4176 sample height 1 0.4000 2 0.3922 3 0.4038 4 0.4161 5 0.4317 40 45 0 0 0 0 50 55 60 62 64 4346 4267 4229 4228 0.4388 0 .4348 0 .4429 0 .4491 0 .4565 0 .4629 0 .4264 0 .4229 0 .4310 0 .4510 0.4875 0 .4272 0 .4225 0 .4321 0 .4430 0 .4586 0.4219 0.4369 * 0.4272 sample height 1 * * 2 0.4280 3 0.4282 65 67 68 0 .4360 69 70 72 143 4 0.4226 0.4542 0.4472 0.4110 * 5 0.4647 * * * 0.4822 0.4485 Standard errors of differences Average: 0.01741 Maximum: 0.03000 Minimum: 0.01453 Average variance of differences: 0.0003104 Standard error of differences for same level of factor: height sample Average: 0.01624 0.01672 Maximum: 0.03000 0.02668 Minimum: 0.01453 0.01616 Average variance of differences: 0.0002722 0.0002833 144 Appendix 1C. Visualization data and images (Chapter 4) Figure C3. Log 1, >0.45 g/cm3 147 Figure C4. Log 1, >0.50 g/cm3 149 Figure C6. Log 1, Disk 1 150 11 30 0.30 0.45 Figure C7. Log 1, Disk 1 151 Figure C8. Log 1, Disk 2 152 Figure CIO. Log 1, Disk 3 154 1 3 -30 -20 -10 0 10 20 30 X Data 0.30 •1 0.35 0.45 | 0.50 Figure CI 1. Log 1, Disk 3 155 Figure CI2. Log 1, Disk 4 156 1 4 30 -i -30 -I , 1 1 1 1 1 -30 -20 -10 0 10 20 30 X Data 0.30 0.35 nn 0.40 Warn® 0.45 wm 0.50 Figure CI3. Log 1, Disk 4 157 158 Figure CI5. Log 1, Disk 5 ure C16.Log 2, >0.30 g/cm Figure CI8. Log 2, >0.45 g/cm3 162 Figure C19. Log 2, >0.50 g/cm Figure C20. Log 2 164 Figure C21. Log 2, Disk 1 165 2 1 0.30 0.35 •i 0.40 0.45 mm 0.50 Figure C22. Log 2, Disk 1 166 Figure C23. Log 2, Disk 2 167 2 2 Figure C25. Log 2, Disk 3 Figure C26. Log 2, Disk 3 171 172 173 2 5 30 -30 -20 -10 0 10 20 30 X Data 0.30 0.35 0.40 0.45 •• 0.50 Figure C30. Log 2, Disk 5 174 Figure C32. Log 3, >0.40 g/cm3 176 Figure C33. Log 3, >0.45 g/cm Figure C35. Log 3 179 Figure C37. Log 3, Disk 1 Figure C38. Log 3, Disk 2 182 3 2 20 A 10 A res ro Q -10 H -20 H -30 -20 -10 0 10 20 30 X Data 0.30 0.35 0.45 Figure C39. Log 3, Disk 2 183 Figure C40. Log 3, Disk 3 184 33 Figure C41. Log 3, Disk 3 Figure C42. Log 3, Disk 4 186 34 Figure C43. Log 3, Disk 4 Figure C44. Log 3, Disk 5 35 30 -30 4 1 1 1 , 1 1 -30 -20 -10 0 10 20 30 X Data 0.30 0.35 MR 0.40 0.45 wm 0.50 Figure C45. Log 3, Disk 5 189 190 Figure C47. Log 5, >0.40 g/cm3 Figure C48. Log 5, >0.45 g/cm3 192 A* \ si 0.3 0.35 0,4 0.45 Figure C49. Log 5, >0.50 g/cm3 193 194 195 Figure C52. Log 5, Disk 1 Figure C53. Log 5, Disk 2 197 52 30 1 20 A 10 A -io A -20 i -30 A 1 1 1 1 1 1 -30 -20 -10 0 10 20 30 X Data 0.30 0.35 0.40 MB 0.45 0.50 Figure C54. Log 5, Disk 2 198 199 53 Figure C56. Log 5, Disk 3 200 Figure C57. Log 5, Disk 4 201 54 30 -30 -20 -10 0 10 20 30 X Data 0.30 0.35 •1 0.40 0.45 •i 0.50 Figure C58. Log 5, Disk 4 202 Figure C59. Log 5, Disk 5 203 55 -30 -20 -10 0 10 20 30 X Data 0.30 •H 0.35 0.45 mm 0.50 Figure C60. Log 5, Disk 5 204 Appendix 2. CD including 3D movies 205 

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