Effect of knots on the flatwise bending stiffness of lumber members

In machine stress-rating of lumber where flatwise bending stiffness is used as a predictor of strength, it is customary to assume that the effect of knots is accounted for by stiffness. However, only few data in the published literature can be used to substantiate this claim. The present study was undertaken to evaluate the relationship between stiffness and knot size for lumber members loaded in bending with a test geometry similar to that used by grading machines. Experiments were carried out with spruce lumber specimens containing a single centerline knot. A theory-of- elasticity based model was derived for analysis purposes. Theory and experiments agreed in showing that the effect of knots on flatwise bending stiffness is very small. This low sensitivity may explain why correlations between strength and machine measured stiffness are rather poor for commercial lumber. Implications of this finding on the practice of machine stress-rating of lumber are discussed.     

The role of geometry on the viscoelastic materials properties: tensile and stress relaxation of the yarn

The time-dependent mechanical behavior of textiles has particular importance. One of such behaviors is stress relaxation. When strain is applied constantly, there is a decreased stress with time in viscoelastic materials, which is called stress relaxation. The aim of this study is to investigate the effect of knot’s geometry (surgeon, square and eight) and the number of knots on the tensile and stress relaxation properties of the polyester yarn. Significant differences were observed for the tensile characteristics of the yarn in the presence of the knot. Generally, the knotted yarns demonstrated lower tensile stress and strain at failure. Moreover, the results revealed that the stress relaxation behavior of the yarn is affected by the number of knots and their geometry. The yarn without knot exhibited the highest stress relaxation percent while the yarn with the surgeon’s knot displayed the least stress relaxation percent. On the other hand, increasing the number of knots led to a decrease in the percentage of yarn stress relaxation.     

Association of abnormal hind-limb postures and back arch with gait abnormality in dairy cattle

Detection of lameness in individual cows is important for the prompt treatment of this painful and production-limiting disease. Current methods for lameness detection involve watching cows walk for several strides. If clinical signs predictive of lameness could be observed more conveniently, as cows are undergoing regularly scheduled examinations while standing, detection levels could increase. The objective of this study was to assess the association between postures observed while cows are standing in stanchions and clinical lameness evaluated by locomotion scoring, and to evaluate the observation of these postures as a test for lameness. The study included 1,243 cows from 4 farms. Cows were observed while standing in stanchions for regularly scheduled management procedures and the presence of arched back and cow-hocked, wide-stance, and favored-limb postures were recorded. The same cows were locomotion-scored as they exited the milking parlor. The proportion of cows observed with arched back and cow-hocked and favored-limb postures increased with increasing severity of lameness (higher locomotion score) but did not increase for the wide-stance posture. For the presence of these postures as a test for lameness (locomotion score ≥3), sensitivity and specificity were 0.63 and 0.64 for back arch, 0.54 and 0.57 for cow hocks, and 0.05 and 0.98 for favored limb. Back-arched, cow-hocked, and favored limb postures were associated with lameness but were not highly sensitive or specific as diagnostic tests. However, observation of back arch may be useful to identify cows needing further examination.     

Technical note: A comparison of 2 methods of assessing lameness prevalence in tiestall herds

We compared 2 methods for identifying lame cows and estimating the prevalence of lameness in tiestalls. Cows (n = 320) in 9 tiestall herds were scored as lame both by the presence of limping while walking and by stall lameness scores (SLS). The SLS was based on the number of the following behaviors that the cow showed while standing in the tiestall: weight shifting, standing on the edge of the stall, uneven weight bearing while standing, and uneven weight bearing while moving from side to side. Two observers watched video-recordings of the cows. Intraobserver agreements for the 4 SLS behaviors ranged from 92 to 100%, and interobserver agreement ranged from 81 to 100%. The overall prevalence of lameness based on an SLS of ≥2 was similar to that of limping (39 vs. 40%). The sensitivity of the classification based on the SLS was 0.63 and the specificity was 0.77 in identifying cows with a limp; accuracy varied across farms from 62.2 to 80.4%, with a mean of 71.7%. A cow with an SLS of ≥2 had 4.88 times the odds of limping than a cow with an SLS of <2. The prevalence of lameness on farms based on SLS was highly correlated with the prevalence of limping (Pearson correlation = 0.88; n = 9), and prevalence estimates from the 2 methods diverged most when the mean herd prevalence was lower. The SLS method provides an estimate of the prevalence of lameness in tiestall herds comparable with traditional gait scoring, but does not require that the cows be untied. The SLS method could be used to improve lameness detection on tiestall farms and obtain estimates of lameness prevalence without the need to walk the cows.     

New insights into the association between lameness,behavior, and performance in Simmental cows

In a herd of 100 milking Simmental cows, data of performance and behavior parameters were collected automatically with different systems such as pedometers, an automatic milking system, and automatic weighing troughs for 1 yr. Performance measures were several milking-related parameters, live weight, as well as feed intake. Behavior-associated measures were feeding behavior (e.g. feeding duration, number of visits to the trough, and feeding pace) as well as activity such as lying duration, number of lying bouts, and overall activity. In the same time, lameness status of every cow was assessed with weekly locomotion scoring. According to the score animals were then classified lame (score 4 or 5) or nonlame (score 1, 2, or 3). From these data in total, 25 parameters summarized to daily values were evaluated for their ability to determine the lameness status of a cow. Data were analyzed with a regularized regression method called elastic net with the outcome lame or nonlame. The final model had a high prediction accuracy with an area under the curve of 0.91 [95% confidence interval (CI) = 0.88–0.94]. Specificity was 0.81 (95% CI = 0.73–0.85) and sensitivity was 0.94 (95% CI = 0.88–1.00). The most important factors associated with a cow being lame were number of meals, average feed intake per meal, and average duration of a meal. Lame cows fed in fewer and shorter meals with a decreased intake per meal. Milk yield and lying-behavior-associated parameters were relevant in the model, too, but only as parts of interaction terms demonstrating their strong dependence on other factors. A higher milk yield only resulted in higher risk of being lame if feed intake was decreased. The same accounts for lying duration: only if lying time was below the 50% quantile did an increased milk yield result in a higher risk of being lame. The association of lameness and daily lying duration was influenced by daily feeding duration and feeding duration at daytime. The results of the study give deeper insights on how the association between behavior and performance parameters and lameness is influenced by intrinsic factors in particular and that many of these have to be considered when trying to predict lameness based on such data. The findings lead to a better understanding why, for instance, lying duration or milk yield seem to be highly correlated with lameness in cows but still have not been overly useful as parameters in other lameness detection models.     

Routine detection of hyperketonemia in dairy cows using Fourier transform infrared spectroscopy analysis of β-hydroxybutyrate and acetone in milk in combination with test-day information

The objective of this study was to assess the quality of a diagnostic model for the detection of hyperketonemia in early lactation dairy cows at test days. This diagnostic model comprised acetone and β-hydroxybutyrate (BHBA) concentrations in milk, as determined by Fourier transform infrared (FTIR) spectroscopy, in addition to other available test-day information. Plasma BHBA concentration was determined at a regular test day in 1,678 cows between 5 and 60 d in milk, originating from 118 randomly selected farms in the Netherlands. The observed prevalence of hyperketonemia (defined as plasma BHBA ≥1,200μmol/L) was 11.2%. The value of FTIR predictions of milk acetone and milk BHBA concentrations as single tests for hyperketonemia were found limited, given the relatively large number of false positive test-day results. Therefore, a multivariate logistic regression model with a random herd effect was constructed, using parity, season, milk fat-to-protein ratio, and FTIR predictions of milk acetone and milk BHBA as predictive variables. This diagnostic model had 82.4% sensitivity and 83.8% specificity at the optimal cutoff value (defined as maximum sum of sensitivity and specificity) for the detection of hyperketonemia at test days. Increasing the cutoff value of the model to obtain a specificity of 95% increased the predicted value of a positive test result to 56.5%. Confirmation of test-positive samples with wet chemistry analysis of milk acetone or milk BHBA concentrations (serial testing) improved the diagnostic performance of the test procedure. The presented model was considered not suitable for individual detection of cows with ketosis due to the length of the test-day interval and the low positive predictive values of the investigated test procedures. The diagnostic model is, in our opinion, valuable for herd-level monitoring of hyperketonemia, especially when the model is combined with wet chemistry analysis of milk acetone or milk BHBA concentrations. By using the diagnostic model in combination with wet chemistry milk BHBA analysis, 84% of herds were correctly classified at a 10% alarm-level prevalence. As misclassification of herds may particularly occur when only a limited number of fresh cows are sampled, we suggest using prevalence estimates over several consecutive test days to evaluate feeding and management practices in smaller dairy farms.     

Model for the prediction of the tensile strength and tensile stiffness of knot clusters within structural timber

In the present paper, a model for the prediction of the local strength and stiffness properties is developed. Compared to existing models, here the local material properties are described according to their morphological characteristics; i.e. the timber boards are subdivided into sections containing knots (knot sections) and sections without knots (clear wood sections). The strains of the corresponding sections are measured during non-destructive tensile tests using an optical camera device. Based on these measurements the tensile stiffness of each particular section is estimated. For the estimation of the tensile strength, destructive tensile tests are performed. Herewith, the tensile strength of the entire timber board is measured. The strength of the other knot clusters are estimated using censored regression analysis. Taking into account the results of the experimental investigation, material models are developed to predict the tensile strength and the tensile stiffness of knot clusters.     

Including milk production,conformation, and functional traits in multivariate models for genetic evaluation of lameness

Lameness is a serious health and welfare issue that can negatively affect the economic performance of cows, especially on pasture-based dairy farms. However, most genetic predictions (GP) of lameness have low accuracy because lameness data are often incomplete as data are collected voluntarily by farmers in countries such as Australia. The objective of this study was to find routinely measured traits that are correlated with lameness and use them in multivariate evaluation models to improve the accuracy of GP for lameness. We used health events and treatments associated with lameness recorded by Australian farmers from 2002 to early 2019. The lameness incidence rates in Holstein and Jersey cows were 3.3% and 4.6%, respectively. We analyzed the records of 36 other traits (milk production, conformation, fertility, and survival traits) to estimate genetic correlations with lameness. The estimated heritability ± standard error (and repeatability ± standard error) for lameness in both Holstein and Jersey breeds were very low: 0.007 ± 0.002 (and 0.029 ± 0.002) and 0.005 ± 0.003 (and 0.027 ± 0.006), respectively, in univariate sire models. For the GP models, we tested including measurements of overall type to prediction models for Holsteins, stature and body length for Jersey, and milk yield and fertility traits for both breeds. The average accuracy of GP, calculated from prediction error variances, were 0.38 and 0.24 for Holstein and Jersey sires, respectively, when estimated using univariate sire models and both increased to 0.43 using multivariate sire models. In conclusion, we found that the accuracy of GP for lameness could be improved by including genetically correlated traits in a multivariate model. However, to further improve the accuracy of predictions of lameness, precise identification and recording incidences of hoof or leg disorder, or large-scale recording of locomotion and claw scores by trained personnel should be considered.     

New test methods to evaluate the performance of dermatological braided sutures from both the doctor and the patient sides

Test methods and instrumentations to measure suture tensile performances have been limited to single‐pull to failure and knot‐pull strength. Though useful, these tests do not thoroughly represent the stresses that sutures experience during wound healing. This paper proposes new test methods to evaluate the performance of dermatological sutures using slippage ratio and recovery deformation based on a realistic representation of suture geometry in wounds. For demonstration purposes, we compared three dermatological knots: square, surgeon’s square, and surgeon’s granny. Our results confirmed that the knot design and the generated internal forces in the knot led to significant change in suture behavior during the tying and healing process. Suture performance depended greatly on the intensity of internal forces and the ability of knot packing. Among the studied knots, the square knot had the lowest slippage ratio because it showed the best aptitude to tightening, while the surgeon’s knot exhibited the highest deformation recovery due to its lower locking ability.     

基于高光谱技术的金银花硫含量快速检测模型建立

为实现金银花硫含量的快速无损检测,利用高光谱成像技术结合化学计量学方法,建立不同浓度硫磺熏蒸金银花快速检测模型。采用硫磺使用量为鲜质量的0%、0.5%、1%、1.5%四种硫熏梯度的金银花干燥样品,首先利用高光谱成像技术采集各组金银花光谱图像数据,并采用S_G（Savitzky-Golay）卷积平滑、多元散射校正（multiple scatter correct,MSC）和标准正态变量变换（standard normal variate transformation,SNV）3 种方法对原始光谱进行预处理,得到S_G卷积平滑为最佳预处理方法。随后,对经S_G预处理后的光谱信息分别进行Fisher判别分析（Fisher discriminate analysis,FDA）与核Fisher建模分析（kernel Fisher discriminate analysis,KFDA）,得到KFDA具有更好的判别正确率（98.2%）。最后,全光谱数据具有量大、冗余信息的问题,采用了相关系数法（regression coefficients,RC）、Wilks和RC-Wilks三种方法对预处理后的数据进行特征提取,最终建立了RC-KFDA、Wilks-KFDA、RC-Wilks-KFDA三种判别模型。结果表明,经S_G卷积平滑预处理后的光谱信息,3?种方法的判别正确率均为100%,使用RC-Wilks相结合提取特征波长的方法建立KFDA模型能够实现较短的计算时间（0.69 s）和较好的类间分布。因此,所建立的S_G-RC-Wilks-KFDA模型可以实现金银花不同硫含量的快速、有效、无损检测。     

基于近红外光谱技术的赣南茶油掺假快速鉴别北大核心CSCD

为了探索基于近红外光谱技术快速无损鉴别掺假油茶籽油的可行性,以赣南茶油为研究对象,通过掺入不同植物油如玉米油、花生油、菜籽油、葵花籽油和大豆油等制备掺假油茶籽油,应用近红外光谱技术采集其光谱特征信息,对比不同预处理方法和主成分数,并结合线性和非线性建模方法建立油茶籽油掺假鉴别模型,以识别准确率(纯油茶籽油样品和掺假油茶籽油样品被正确判别的比例)、灵敏度(纯油茶籽油样品被正确判别为纯油茶籽油的比例)、特异性(掺假油茶籽油样品被正确判别为掺假油茶籽油的比例)作为模型的评价指标,优选出最佳模型。结果表明:二阶微分联合线性判别分析(SD-LDA)模型为最优线性模型,标准正态变量变换联合人工神经网络(SNV-ANN)模型为最优非线性模型,两个模型的识别准确率、灵敏度、特异性分别为97.58%、100%、97.33%和98.99%、100%、98.88%。SNV-ANN模型鉴别效果优于SD-LDA模型,说明非线性模型更适于油茶籽油掺假判别,该模型能更准确地鉴别油茶籽油是否掺假。     

Comparison of modeled sampling strategies for estimation of dairy herd lameness prevalence and cow-level variables associated with lameness

Monitoring herd lameness prevalence has utility for dairy producers and veterinarians in their efforts to reduce lameness, for animal welfare assessment programs, and for researchers. Locomotion scoring is a method used to quantify lameness and calculate prevalence. Because of the time necessary to locomotion score each cow in large dairy herds, a sampling strategy to determine herd lameness prevalence that allows scoring of fewer cows would be useful. Such a sampling strategy must be validated for accuracy compared with the lameness prevalence when all cows in a herd are locomotion scored. The purpose of this study was to assess 3 previously suggested methods of estimating lameness prevalence by strategic sampling of dairy herds. Sampling strategies tested included (1) sampling a calculated number of cows in the middle third of the milking parlor exit order for each pen, (2) sampling a calculated number of cows weighted across pens and distributed evenly within each pen, and (3) sampling all cows in the high production, low production, and hospital pens. Lactating cows on 5 dairy farms in Washington and Oregon (n = 4,422) were locomotion scored using a 5-point scale to determine herd-level lameness prevalence (percentage with locomotion score ≥3). Milking parlor exit order, order in headlocks at the feed bunk within each pen, and breed were recorded for each cow. The number of days in lactation, milk production, and parity were collected from farm computer records. Pen grouping strategy for each farm was obtained by interview with farm management. Sampling strategies were modeled using the locomotion score data set for each herd. Estimates of lameness prevalence obtained from the milking parlor exit order sample and the sample distributed across pens were within 5 percentage points of the whole herd prevalence. The third strategy estimated the lameness prevalence within 5 percentage points on 4 farms, but overestimated prevalence on 1 farm. Pen-level prevalence obtained by locomotion score of all cows in the pen was variable and not reliably predictive of herd-level prevalence. Cows of Holstein breed, parity >1, and exiting the milking parlor in the last 20% of the pen had greater odds of lameness compared with other breeds, parities, and milking parlor exit order groups in a multivariate analysis. This study indicates that the sampling strategies using the middle of milking parlor exit order and a calculated sample distributed across the herd may be used to obtain an estimate of herd lameness prevalence.     

The contribution of previous lameness events and body condition score to the occurrence of lameness in dairy herds: A study of 2 herds

It has been demonstrated that low body condition and previous occurrence of lameness increase the risk of future lameness in dairy cows. To date the population attributable fraction (PAF), which provides an estimate of the contribution that a risk factor makes toward the total number of disease events in a population, has not been explored for lameness using longitudinal data with repeated measures. Estimation of PAF helps to identify control measures that could lead to the largest improvements on-farm. The aim of this study was to use longitudinal data to evaluate the proportion of lameness that could be avoided in 2 separate herds (2 populations) through (1) reduced recurrence of previous lameness events, (2) and moving body condition score (BCS) into more optimal ranges. Data were obtained from 2 UK dairy herds: herd A, a 200-cow herd with 8 yr of data from a total of 724 cows where lameness events were based on weekly locomotion scores (LS; 1 to 5 scale), and herd B, a 600-cow herd with data recorded over 44 mo from a total of 1,040 cows where treatment of clinical cases was used to identify lameness events. The PAF for categories of BCS were estimated using a closed equation appropriate for multiple exposure categories. Simulation models were used to explore theoretical scenarios to reflect changes in BCS and recurrence of previous lameness events in each herd. For herd A, 21.5% of the total risk periods (cow-weeks) contained a lameness event (LS 3, 4, or 5), 96% of which were repeat events and 19% were recorded with BCS <2 (3 wk previously; 0 to 5 scale). When lameness events were based on 2 consecutive weeks of LS 4 or 5, 4% of risk periods were recorded as lame, of which 89.5% were repeat events. For herd B, 16.3% of the total risk periods (consecutive 30 d) contained a lameness event (72.6% were repeat events) and 20% were recorded with BCS ≤2 (0 to 120 d previously). The median PAF for all previous lameness was between 79 and 83% in the 2 herds. Between 9 and 21% of lameness events could be attributed to previous lameness occurring >16 wk before a risk period. The median PAF estimated for changes in BCS were in the region of 4 to 11%, depending on severity of lameness. Repeated bouts of lameness made a very large contribution to the total number of lameness events. This could either be because certain cows are initially susceptible and remain susceptible, due to the increased risk associated with previous lameness events, or due to interactions with environmental factors. This area requires further research.     

On-farm detection of claw lesions in dairy cows based on acoustic analyses and machine learning

Claw lesions are a serious problem on dairy farms, affecting both the health and welfare of the cow. Automated detection of lameness with a practical, on-farm application would support the early detection and treatment of lame cows, potentially reducing the number and severity of claw lesions. Therefore, in this study, a method was proposed for the detection of claw lesions based on the acoustic analysis of a cow's gait. A panel was constructed to measure the impact sound of animals walking over it. The recorded impact sound was edited, and 640 sound files from 64 cows were analyzed. The classification of animal-lameness status was performed using a machine-learning process with a random forest algorithm. The gold standard was a 2-point scale of hoof-trimming results (healthy vs. affected), and 38 properties of the recorded sound files were used as influencing factors. A prediction model for classifying the cow lameness was built using a random forest algorithm. This was validated by comparing the reference output from hoof-trimming with the model output concerning the impact sound. Altering the likelihood settings and changing the cutoff value to predict lame animals improved the prediction model. At a cutoff at 0.4, a decreased false-negative rate was generated, and the false-positive rate only increased slightly. This model obtained a sensitivity of 0.81 and a specificity of 0.97. With this procedure, Cohen's Kappa value of 0.80 showed good agreement between model classification and diagnoses from hoof-trimming. In summary, the prediction model enabled the detection of cows with claw lesions. This study shows that lameness can be detected by machine learning from the impact sound of hoofs in dairy cows.     

Die Rohdichteverteilung und deren feuchteabhängige Änderung bei astiger fichte im hinblick auf die maschinelle Holzsortierung

For the machine grading of timber by isotopic-radiation the difference in density between sections with and without knots is being used as a criterion to evaluate the knot ratio. The precondition for the general use of this method, even for wood with varying moisture contents would be to prove that there are no changes in density relationship at least up to fiber saturation. For determining the relationship and density changes in spruce, with and without knots, comprehensive investigation on 230 test groups (1600 specimens) were carried out. Evaluation of results led to the conclusion that a reliable differentiation regarding the criterion “knot ratio” is possible for moisture content up to 30%, independent of the initial data of the timber to be graded.     

Sampling strategies for assessing lameness,injuries, and body condition score on dairy farms

Our objective was to evaluate how sampling strategies (i.e., how many cows to sample and which animals to include) used in 4 dairy cattle welfare assessment programs affect the classification of dairy farms relative to thresholds of acceptability for animal-based measures. We predicted that classification performance would improve when more cows were sampled and when selecting from all lactating cows versus when some pens were excluded. On 38 freestall farms, we assessed all 12,375 cows for lameness, injuries on the tarsal (hock) and carpal joints, and body condition score and calculated the farm-level prevalence for each measure. Based on approaches used in the industry, we evaluated 6 sampling strategies generated using formulas with precision (d) of 15, 10, or 5% applied to either a single high-producing pen or all lactating cows; an additional sample was included with d = 10% applied to the entire herd, selecting lactating cows in proportion to their representation in the herd. For each sampling strategy, cow records were selected randomly (in 10,000 replicates) to calculate prevalence. The strategy of assessing all cows in the high-producing pen was also compared. Farms were classified as meeting (below) or failing to meet (above) thresholds of ≤15% moderate lameness; ≤20% moderate carpal or hock injuries; <10, <5, and ≤1% severe lameness; or injuries on the carpus or hock; and <5, <3, <1, or 0% thin cows. For each measure and threshold, we calculated pooled percent agreement, kappa, sensitivity, specificity, and positive and negative predictive value for each sampling strategy using true prevalence as the gold standard for herd classification. Across measures and thresholds, classification performance increased with the number of cows sampled [i.e., when narrower precision values (d = 5 vs. 10 vs. 15%) were used in the sample size calculation]. Because narrower precision values can dramatically increase sample size, assessment programs may need to consider both feasibility and the degree of misclassification they will accept. Applying the formula directly to lactating cows performed better than applying it to the entire herd and then selecting lactating cows in proportion to their representation in the herd. Farm classifications were similar whether cows in the hospital pen were included or excluded from the sample. Selecting all cows from the high-producing pen resulted in classifications similar to when including all lactating cows, suggesting that assessing cows from the high-producing pen may serve as an acceptable proxy for all lactating cows on the farm.     

A probabilistic neural network model for lameness detection

A 4-balance system for measuring the leg-load distribution of dairy cows during milking to detect lameness was developed. Leg weights of 73 cows were successfully recorded during almost 10,000 robotic milkings over a period of 5 mo. Cows were scored weekly for locomotion, and lame cows were inspected clinically for hoof lesions. Unsuccessful measurements, caused by cows standing outside the balances, were removed from the data with a special algorithm, and the mean leg loads and number of kicks during milking were calculated. To develop an expert system to automatically detect lameness cases, a model was needed, and a classifying probabilistic neural network model was chosen for the task. The data were divided into 2 parts and 5,074 measurements from 37 cows were used to train a classifying probabilistic neural network model. The operation of the model was evaluated for its ability to detect lameness in the validating data set, which had 4,868 measurements from 36 cows. The model was able to classify 96.2% of the measurements correctly as sound or lame cows, and 100% of the lameness cases in the validation data were identified. The number of measurements (equal to the number of milkings) causing false alarms was 1.1%. The model developed has the potential to be used as an on-farm decision aid and can be used in a real-time lameness monitoring system.     

Distribution of lignans in knots and adjacent stemwood of Picea abies

The distribution of lignans in knots, i.e., the branch bases encased in the stemwood, and in the adjacent stemwood of Norway spruce (Picea abies) was studied. Hydrophilic extracts in samples of three annual rings from the side wood of knots, as well as samples from the surrounding stemwood, were analysed by GC and GC-MS. The knots had an exceptionally high content of lignans (up to 15% w/w), compared to the stemwood (less than 0.05% w/w). The content decreased clearly in the radial direction from the knot pith towards the outerwood, to come down to the same level as in the surrounding stemwood. In the branches, the lignan content also decreased in the radial direction from the branch pith outwards. The lignan content decreased sharply outwards in the branches and came down to the same levels as in the stemwood already 20 cm outside of the stem.     

Internal distribution of sound and dead knots in Picea abies (L.) Karst.

(L.) Karst. in the south-eastern part of Norway. Distribution of sound and dead knots was evaluated as the mean and the range of the radial extension of sound knots within each whorl. The mean value was found to increase with increasing height in the lower 40% of the tree height followed by an upwards decreasing trend. It was related to diameter at breast height and annual ring width together with site index. The range of sound knot length within a whorl was calculated to 22 mm on average. It was found to be increasing up to 30% of tree height followed by a decrease upwards. The range was related to site index, diameter at breast height, eccentricity and to difference in height to the lowest living branch and the lowest living whorl.