Cone Morphology as a Diagnostic Attribute of Resonant Properties of Standing Spruce Wood

The paper presents the results of dendroacoustic research and statistical and correlation analysis. The insights of heuristic identifi cation based on biotechnology law are also given with the aim of defi ning the relationship of wood resonant properties with the form of seed scales of spruce growing in the Kama-Volga region of Russia.


INTRODUCTION 1. UVOD
It is well-known that the ways to diagnose and select wood for manufacturing both musical instruments and acoustic panels for theatres and conservatories (Fedyukov et al., 2011) can be conventionally classifi ed into direct and indirect.
Direct methods are based on determining dendroacoustic indices with the help of ultrasonic and other instruments for measuring sound velocity in wood, its frequency-amplitude characteristics, and a number of other physical and mechanical properties (Bucur, 2006;Fedyukov and Makaryeva, 1992).Based on the results obtained, the main criterion of 'musicality' of the material, i.e. its acoustic constant of sound propagation K, is defi ned.In many countries, К ≥ 12 m 4 /kg•cm is accepted for resonant wood.
Direct methods involve some technical diffi culties in conducting studies in the forest and are still used primarily in the laboratory environment.
It is impossible to fi nd reliable data on the way these attributes were used by Stradivari and other masters of the Old Italian school in the selection of wood for manufacturing unique musical instruments.However, it is wrong to exclude this, as later and modern ways of visually estimating the resonance quality of standing tree wood applied the attributes mentioned above.

Visual appearance and conditions of a tree
According to modern masters, a spruce tree selected for manufacturing musical instruments should meet the following requirements: -be absolutely vertical; -have symmetric, narrow and spiry crown; -have a cylindrical trunk and branchless zone no less than 5-6 meters; -not contain other visible defects and damages.
Thicker trunks are in demand: if the diameter at breath height is less than 35 cm, i.e. at the age of less than 100-120 years, the use of such a tree as a source of resonant material is considered counterproductive.
A Rumanian scientist, V. Grapini (1967), gives more detailed data for resonant spruce: -the crown is in the form of a column, almost symmetric, gradually decreases from the basis to the top at an angle of 30-40° and is formed by thin branches oriented mainly downwards; -the branches from the third part of the middle and the bottom of a crown are attached to the trunk at an angle of 30-40°; large branches are arranged in clusters; -the second order branches are rather rare, thin, long, hanging down, ash-gray-green; -the third order branches are also rare, thin, but light green.
A lot of individual masters also consider descending branches to be an attribute of a resonant spruce.The fact that it 'is not warped' is especially valued.It is determined by attentive inspection of a tree with regard to clusters arrangement, bark cracks, etc., which requires considerable experience.

Bark structure and color
These morphological attributes of spruce are often used by masters selecting the material for manufacturing musical instruments from the root and round assortments.However, there is no general opinion about any characteristic attribute that can be undoubtedly acceptable as diagnostic.This is probably related to strong variability of the above attributes, which also correlate with biological and ecological features of individual trees (Onegin and Kuznetsova, 2012;Pat. № 2130611 RF, 1999;Pchelin, 1961;Pravdin, 1975).
Absence of a uniform method to give the diagnostics of acoustic properties of standing tree wood is caused by the elements of subjectivity in conclusions based on the results of observations by different au-thors, especially, in different soil, climate and geographical environment.
Selector Yablokov (1962) recommends to select spruce trees with smooth bark forms (low land, in his opinion) as resonant; this coincides with the opinion of Gavris (1938).Bagayev and Alexandrov (1967), who believe that smooth-barked spruce-trees with narrow crown of both Norway and Siberian species have the best resonance.Sankin (1972) conducted a thorough research on determining the relations between the variability of macrostructure, anatomical structure of wood, physical, mechanical and acoustic properties depending on spruce tree bark appearance (rhytidoma) in the environment of the Vologda Region of Russia.Having studied the trees of two groups (with platy and scaly bark), he came to a conclusion that spruce with scaly bark is preferable due to greater genetic plasticity.Meanwhile, the relationship of late wood percentage and annual ring width with wood density, dynamic modulus of elasticity and acoustical constant is equally strongly expressed in both groups.
Further to the above review of scientifi c literature, it can be concluded that hereditary genetic factors prevail in the formation of wood quality.They manifest themselves in quite a sustained way through external biomorphological features of cones, including their size and seed scale forms (Bakshayeva, 1966;Danilov, 1943;Mamayev and Nekrasov, 1968;Onegin and Kuznetsova, 2012;Pchelin, 1961;Redulescu, 1969;Yablokov, 1962).
It is necessary to bear in mind that each master chooses, at his discretion, the characteristic attributes of wood 'musicality' as a criterion for visual estimation of the resonant raw material.The criteria used by individual masters or representatives of different schools are different as a rule, with rare exceptions.
In this connection, uniform diagnostic attributes should be established for mathematical modeling and development of an objective way of selection of standing spruce trees with resonant properties in certain nature-climate environment of its growth.

MATERIJALI I METODE
Searching an objective biomorphological attribute, we chose the seed scale form from the middle part of the cone.
Danilov's (1943) and Bakshayeva's (1966) methods are taken as a basis for drawing up a matrix of initial data to differentiate the trees inside a population with respect to seed scale form, which results from their characteristic features.
Danilov's method is most detailed.It is based on the analysis of four attributes: Based on cone classifi cation according to Bakshayeva's method (1966), it was possible to establish unequivocally that 39 model trees selected were Siberian Spruce, and Danilov's classifi cation made it pos-а) degree of scale edge tapering -the main attribute ( 5classes); b) angle form of a scale edge (obtuse, acute, round); c) nature of generatrix (smooth-margined or serrated); d) outside edge type (straight, sinuous, even).
The method of tree classifi cation according to the above attributes is presented as a whole in Tab. 1.
As an example, Siberian spruce is characterized by rounded smooth-margined seed scales of cones, while the Norway spruce is characterized by lengthened, a little bit pointed hackly ones (Fig. 1).
However, hybrid forms of spruce can be met more often, and they can be classifi ed in detail using the method given.Using Bakshayeva's method of classifi cation, it is comparatively simple and easy to translate the data into mathematical language.It is based on defi ning the factor through the ratio of height Н of the seed scale top part to its width in the widest part l (Fig. 2).
All the variety of seed scales is reduced to three groups depending on the size of the factors obtained: groups I, II and III at Н / l = 1.32 (Norway spruce); = 0.09 (Siberian spruce) and = 1.0 (hybrid form).This was confi rmed by the research site.The fact of the matter is that model trees were taken from ripe spruce groves of the Kirov Region in a taiga zone.In this region, European spruce is hardly ever met in its pure form, but rather in the hybrid form (Ovechkin, 1982).
Cross-section radial cores, 4.0 mm in diameter, selected with an increment borer at breath height from 16 model trees, after being felled, were the material for the research into dendroacoustic parameters.Simultaneously, diameters of trunks at relative heights of 0.2 Н, 0.5 Н and 0.7 Н, as well as tree crown parameters (extension, fi rst alive knot fastening height, etc.) were defi ned.
The method of determining the resonance of wood in standing trees against the cores has been introduced abroad (Bucur, 2006) and in Russia (Fedyukov and Makaryeva, 1992) rather recently.
As a rule, wood structure is different along the length of a radial core and, accordingly, wood physical and mechanical parameters are also different in medullary parts and in sapwood.This distinction is obvious even with a naked eye, fi rst of all, judging from wood macrostructure: narrow annual rings are in trunk peripheral zone and wide ones are close to juvenile central zone (Fig. 3, а).
Rather homogeneous wood between undercork and near-core zones is usually taken for deck manufacturing.In view of this, the study was focused on the part of the trunk along the radius, conditionally denoted on cores as a 'working' zone (Fig. 3, b).
Basic physical and dendroacoustic properties of wood -humidity, density, macrostructure, and ultrasound velocity -were defi ned in laboratory environment.Recalculation of the results obtained against standard humidity of wood, W = 12 %, was made.The complex research is presented in Fig. 4.
The macrostructure of wood was studied with electronic dendrometer, which operates on the basis of Sound velocity in wood (С) was assessed with a pulse ultrasonic method by fi xing the time (τ) of elastic longitudinal wave propagation along the sample (l): It should be noted that the device was equipped with a 60 kHz piezoelectric transducer, which is optimal for wood study.
Based on sound velocity in the material, C, and its density, it is possible to assess Young's dynamic modulus, Е, on the basis of the following ratio: , then It is known that, today, acoustic constant of sound propagation (К), suggested by the Academician N.N.Andreyev, is accepted as the basic criterion of 'musicality' of a given material in many countries: (3) Threshold value is K ≥ 12.0 m 4 /kg•cm for resonant wood in a longitudinal direction along fi bers, and under cross-section radial measurements K ≥ 3.5 m 4 / kg•cm (Ugolev, 2001).
Small transformations and joint solution of equations 2 and 3 allow to defi ne the size of acoustical constant К through С and ρ: Thus, the physical essence of resonant wood represents a combination of incongruous properties, i.e., high parameters of rigidity, sound velocity and low density.
Processing of statistical data for determining the relationship of the cones (seed scales) form with physical, mechanical and acoustic properties of wood was supplemented with heuristic identifi cation of the results obtained with a general model (Mazurkin, 1989): where а 1 …а 7 are regression coeffi cients (model parameters); i f is cone seed scale form code (individual rank); у is theoretical value of physical, mechanical and acoustic properties of wood parameters.
According to this technique, coding of morphological attributes of cone seed scales for the specifi ed trees is developed to perform further calculations on the basis of Danilov's classifi cation.Values of attributes are classifi ed by transition from the Norway spruce to Siberian spruce.
Attribute values were classifi ed in accordance with the transition from Norway spruce to Siberian spruce.
Integer scales i f and I f are four-factorial in the given coding, scale I f = 1...40 taking into account specifi c morphological variety of spruce features in different regions of the country.
Using PC and Eureka mathematical environment, the results of corresponding parameters identification were obtained.Parameters adequacy values according to model 5 are shown in Tab. 4.
Maximal residual ε max was calculated according to the formula: where ŷ i , y i are experimental and theoretical parameter values.Maximal relative error ∆ mах was calculated using the formula: (7)

REZULTATI I RASPRAVA
Values of correlation coeffi cients (R) and correlation ratio (η) of dendroacoustic parameters and seed scales form, according to Bakshayeva (1966), are presented in Tab. 3.
According to the above table, there are certain relationships between a specifi c biomorphological attribute and the basic dendroacoustic parameters, all coeffi cients being positive because the relationships are direct.However, the reliability of these relationships is less than 95 %; e.g. the relationship of correlation coeffi cients with seed scales form for К and b is only about 90 % reliable; as for Е and υ, the reliability is much lower, and for ρ and δ it is close to zero.
The correlation ratio η against all parameters, except for b, is higher than the correlation coeffi cient R. Hence, a nonlinear relationship would be more appropriate than a linear one.
In practice, when selecting a resonant raw material (standing tree), it should be noted that the correlation between acoustic constant coeffi cient and seed scales form (0.767) appeared to be maximum with high level of reliability (0.99 %).
Parameters adequacy values according to model 5 are shown in Table 4.
The results presented in Tab. 4 confi rm that model 5 describes the relationship of scale form with parameters of physical, mechanical and acoustic properties of spruce wood, in this case with δ, ρ, υ and K, with rather small relative error ∆ mах <10 % for practical purposes.
Basically, model 5 is characterized by three kinds of biotechnology law (Mazurkin, 1989).The fi rst component describes the process of parameters δ, ρ and υ value recession in transition from Norway spruce to Siberian spruce.The width of annual rings depends on habitat conditions rather than on species diversity.
The second component of the model is characterized by stressful change of parameters δ, b and υ.Stressful infl uence of hybrid species strongly affects the width of annual rings and practically does not change the density.This fact does not mean the absence of relationship between wood density and width of annual rings; it mainly emphasizes the possibility of purposeful forming of resonant wood with specifi c macrostructure.
The third part of the model describes allometric growth of scale form infl uence.
Fig. 5 presents the graphs of parameters change depending on an integer scale i f .Parameters δ and b change under the wave law (Fig. 5, а).Values ρ and υ (Fig. 5, b) are minimal at various codes (i f = 7 and i f = 3).Such unequal extremes of the graphs require accounting for the complex parameter K, which is defi ned as the υ / ρ ratio.Since i f grows from 1 to 10, K value increases almost rectilinearly (Fig. 5, c).
Graph K =f (i f ) shows that Siberian spruce has better resonant properties than Norway spruce.Sound velocity in a radial direction at breath height increases likewise.
The analysis of these graphs disproves the opinion of some researchers about the absence of heredi- tary-genetic factor role in the formation of wood resonant properties and, accordingly, their transfer to subsequent generations of spruce trees, saying that 'a resonant spruce is usual spruce wood that happened to grow in a certain specifi c environment' (Onegin and Kuznetsova, 2012).
It is important to note that the probability of the occurrence of the best resonant properties in spruce is observed at υ> 1,400 m/s.Further modeling of υ change depending on other factors, b and δ in particular, made it possible to derive the equation: (8) Model ( 4) describes the law of aperiodic motion with fast attenuation under the infl uence of late wood as a damper of sound velocity in radial direction.Thus ε mах = 17,278 m/s; ∆ mах =11.3 %.
The constant component of sound velocity (1,376.25 m/s) and infl uence of annual ring average width are taken into account under the biotechnology law in the model (9) where ε mах = 149.92m/s; ∆ mах =9.82 %.
The graph in Fig. 6.a clearly illustrates a significant increase of sound velocity under b> 1 mm.

ZAKLJUČAK
In conclusion, the main results of the research can be summarized as follows: 1. Seed scales form of spruce is a rather significant biomorphological attribute describing genetic and, to a certain extent, phytocenotic predisposition of a tree to forming resonant wood with good acoustic properties.
2. Hybrid forms have lower acoustic parameters of wood than pure forms of Norway or Siberian spruce, resonant properties improving in the process of transition from Norway spruce to Siberian spruce.
3. Close correlation between the basic physical, mechanical and acoustic parameters of wood remain even against the background of its genetic and phytocenotic (ecological) variability.
4. Spruce seed scales form can be a characteristic attribute for non-destructive diagnostics of standing tree resonant properties.