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Articles containing the keyword 'taper curve'.

Category: Article

article id 7332, category Article
M. Lappi-Seppälä. (1936). Tutkimuksia männyn ja koivun runkomuodosta. Acta Forestalia Fennica vol. 44 no. 4 article id 7332. https://doi.org/10.14214/aff.7332
English title: Studies on stem forms of Scots pine and Betula sp.

The stem form influences the value and volume of the stem. Sample trees in homogenous mixed stand of Scots pine (Pinus sylvestris L.) and Betula sp. were measured to define the stem form of the trees, and to develop research methods. The height of butt swelling and the turning point of taper curve varies greatly. In Scots pine and Betula sp. it was typically between the 2/10 and 3/10 height of the tree. Consequently, the theoretical normal curves describing stem form, where the turning point of taper curve is situated under the breast height diameter, are not entirely generally applicable. There was a correlation between the base curve and the form of actual taper curve of the stem. The form of the top of the stem depends on the structure and dimensions of the crown. The most reliable measuring point to define taper curve would be a diameter that is above butt swelling, near the turning point of the taper curve. Length of the crown can be used to deduce the form of the top of the stem. According to the study, the volume tables could be based on diameter on breast height, slenderness of the stem (D0,25h:h) and length of the crown. Age of the tree and position in the stand influence stem form, but the forest site type seemed not to have clear effect on the stem form.

The PDF includes a summary in German.

  • Lappi-Seppälä, ORCID ID:E-mail:
article id 5496, category Article
Aatos Lahtinen. (1993). On the construction of shape preserving taper curves. Silva Fennica vol. 27 no. 1 article id 5496. https://doi.org/10.14214/sf.a15657

There exists an algorithm for construction interpolating quadratic splines which preserves the monotony of the data. The taper curves formed with this algorithm, QO-splines, have many good qualities when a sufficient number of measured diameters of a tree is available. In fact, they may even be superior to certain shape preserving taper curves, MR-splines. This algorithm can be modified to preserve also the shape of the data. In the present paper, the quality of taper curves constructed by a new shape preserving from of the algorithm is examined. For this purpose, taper curves are formed for different sets of measurements and their properties are compared with the ones of QO-splines and MR-splines. The results indicate that these new shape-preserving taper curves are in general better than QO-splines and MR-splines even if the differences may be small in many cases. The superiority is the clearer the less measurements are available.

The PDF includes an abstract in Finnish.

  • Lahtinen, ORCID ID:E-mail:
article id 5187, category Article
Fuhe Luo. (1983). Determination of stem value. Silva Fennica vol. 17 no. 3 article id 5187. https://doi.org/10.14214/sf.a15170

A dynamic programming approach toward stem value estimation for standing Scots pine (Pinus sylvestris L.) trees was developed. The determination of the saw log value was based on the sawing pattern and on the final products composition. The combination of taper curve models and bark models providing taper curves both over bark and under bark, which constituted the basis of the optimum stem scaling. A computer program was developed to determine the optimum log sequence of the stem aiming at maximizing the value of the final products. To examine the reliability of the computation system, 445 Scots pine sample trees from 29 stands were used as a test material. The stem values of sample trees were calculated in two ways: 1) with 12 measured diameters, and 2) with 12 estimated diameters derived from measured tree characteristics. In both cases the values of the intermediate diameters were calculated via cubic spline interpolation.

The PDF includes a summary in Finnish.

  • Luo, ORCID ID:E-mail:
article id 5047, category Article
Pekka Kilkki, Martti Varmola. (1979). A nonlinear simultaneous equation model to determine taper curve. Silva Fennica vol. 13 no. 4 article id 5047. https://doi.org/10.14214/sf.a14904

In the original set of equations derived by regression analysis, relative-height diameters (endogenous variables) are presented as nonlinear functions of the other relative-height diameters and of the height of the tree (an exogenous variable). Any of the original equations can be replaced by an interpolation formula which links a measured diameter to the four closest relative-height diameters. The solution of the simultaneous equation model yields 10 relative-height diameters. Intermediate values are obtained to avoid biases due to the nonlinearity of the simultaneous model equations.

The PDF includes a summary in Finnish.

  • Kilkki, ORCID ID:E-mail:
  • Varmola, ORCID ID:E-mail:
article id 4995, category Article
Pekka Kilkki, Matti Saramäki, Martti Varmola. (1978). A simultaneous equation model to determine taper curve. Silva Fennica vol. 12 no. 2 article id 4995. https://doi.org/10.14214/sf.a14849

A simultaneous equation model to determine taper curve for Scots pine is presented. The diameters at relative heights are endogenous variables and height an exogenous variable. Any equations may be substituted by the measured value of diameter. Solution of the system of equations yields 11 diameters at relative heights. Intermediate values are obtained by interpolation. Interpolation allows the use of diameters measured at absolute heights, too.

The PDF includes a summary in Finnish.

  • Kilkki, ORCID ID:E-mail:
  • Saramäki, ORCID ID:E-mail:
  • Varmola, ORCID ID:E-mail:
article id 7650, category Article
Aatos Lahtinen. (1988). On the construction of monotony preserving taper curves. Acta Forestalia Fennica no. 203 article id 7650. https://doi.org/10.14214/aff.7650

A monotony preserving taper curve can be constructed by using a quadratic spline. An algorithm is presented which is suitable for this purpose. It is used to the construction of a taper curve when several measured diameters of a tree are available. These taper curves are formed for different sets of measurements and their properties are evaluated. It appears that the monotony preserving quadratic spline can give a better taper curve than the usual cubic spline.

The PDF includes a summary in Finnish.

  • Lahtinen, ORCID ID:E-mail:
article id 7621, category Article
Pekka Kilkki, Martti Varmola. (1981). Taper curve models for Scots pine and their applications. Acta Forestalia Fennica no. 174 article id 7621. https://doi.org/10.14214/aff.7621

Taper curve models based on simultaneous equations were derived. The data consisted of 492 Scots pines (Pinus sylvestris L.) from Southern Finland. Two systems of simultaneous equations were constructed, one without the crown ratio and the other with the crown ratio as an exogenous variable. The endogenous variables consisted of 24 relative-height diameters and the height of the tree. The parameters of the model were derived by the ordinary least squares method.

In most applications, the height of the tree was exogenised. The logarithmically linear relationships between the relative-height diameters were utilized in the solution algorithm. The algorithm included both standard matrix operations and an iterative part in which the taper curve was fitted to any measured diameters by the natural cubic spline interpolation formula.

The models were applied to the derivation of taper curves, stem volumes, timber assortment percentages, and stem values. An experiment was also made to derive diameter and height increments from the taper curve model.

The reliability of the models was tested on the original data.

The PDF includes a summary in Finnish.

  • Kilkki, ORCID ID:E-mail:
  • Varmola, ORCID ID:E-mail:
article id 7621, category Article
Pekka Kilkki, Martti Varmola. (1981). Taper curve models for Scots pine and their applications. Acta Forestalia Fennica no. 174 article id 7621. https://doi.org/10.14214/aff.7621

Taper curve models based on simultaneous equations were derived. The data consisted of 492 Scots pines (Pinus sylvestris L.) from Southern Finland. Two systems of simultaneous equations were constructed, one without the crown ratio and the other with the crown ratio as an exogenous variable. The endogenous variables consisted of 24 relative-height diameters and the height of the tree. The parameters of the model were derived by the ordinary least squares method.

In most applications, the height of the tree was exogenised. The logarithmically linear relationships between the relative-height diameters were utilized in the solution algorithm. The algorithm included both standard matrix operations and an iterative part in which the taper curve was fitted to any measured diameters by the natural cubic spline interpolation formula.

The models were applied to the derivation of taper curves, stem volumes, timber assortment percentages, and stem values. An experiment was also made to derive diameter and height increments from the taper curve model.

The reliability of the models was tested on the original data.

The PDF includes a summary in Finnish.

  • Kilkki, ORCID ID:E-mail:
  • Varmola, ORCID ID:E-mail:

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