Error predictions for average end diameter sectional formula in tree stem volume measurement

The use of the sectional formula given by the product of the cross sectional area related to the average of segment end diameters, times segment length, is a known method to estimate the volume of a tree stem segment. The whole tree stem volume can be obtained summing volumes of individual segments....

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Autores principales:	Cruz de León,Gildardo, Alfaro-Trujillo,Isaac, Bañuelos-Jiménez,Margarita
Lenguaje:	English
Publicado:	Universidad Austral de Chile, Facultad de Ciencias Forestales 2016
Materias:	sectional methods subneiloid applied mathematics
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0717-92002016000100020
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spelling	oai:scielo:S0717-920020160001000202016-05-17Error predictions for average end diameter sectional formula in tree stem volume measurementCruz de León,GildardoAlfaro-Trujillo,IsaacBañuelos-Jiménez,Margarita sectional methods subneiloid applied mathematics The use of the sectional formula given by the product of the cross sectional area related to the average of segment end diameters, times segment length, is a known method to estimate the volume of a tree stem segment. The whole tree stem volume can be obtained summing volumes of individual segments. There is not a formal study about the errors in using that method that allows comparing it to other conventional methods. In this work, following a theoretical procedure proposed recently in the forest measurement literature, those errors were computed. The method was evaluated applying it to the geometries of paraboloid, cone, and neiloid, to get the errors in tree stem volume estimation as function of a given number of segments, n. The average absolute percent errors were: ≤ 10.9 % for n ≥ 5; ≤ 5.5 % for n ≥ 10; ≤ 2.8 % for n ≥ 20; ≤ 1.9 % for n ≥ 30. Compared to known results, the method is better than Smalian and Huber methods, though it is not for the frustum of cone volume formula. Additionally, there are algebraic proves showing that the segment volume estimated by the method is lower than the volume for frustums of paraboloid and cone; in this work, the proof that it is also lower than the volume for a frustum of neiloid is provided, which completes the corresponding knowledge on the subject.info:eu-repo/semantics/openAccessUniversidad Austral de Chile, Facultad de Ciencias ForestalesBosque (Valdivia) v.37 n.1 20162016-01-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0717-92002016000100020en10.4067/S0717-92002016000100020
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	sectional methods subneiloid applied mathematics
spellingShingle	sectional methods subneiloid applied mathematics Cruz de León,Gildardo Alfaro-Trujillo,Isaac Bañuelos-Jiménez,Margarita Error predictions for average end diameter sectional formula in tree stem volume measurement
description	The use of the sectional formula given by the product of the cross sectional area related to the average of segment end diameters, times segment length, is a known method to estimate the volume of a tree stem segment. The whole tree stem volume can be obtained summing volumes of individual segments. There is not a formal study about the errors in using that method that allows comparing it to other conventional methods. In this work, following a theoretical procedure proposed recently in the forest measurement literature, those errors were computed. The method was evaluated applying it to the geometries of paraboloid, cone, and neiloid, to get the errors in tree stem volume estimation as function of a given number of segments, n. The average absolute percent errors were: ≤ 10.9 % for n ≥ 5; ≤ 5.5 % for n ≥ 10; ≤ 2.8 % for n ≥ 20; ≤ 1.9 % for n ≥ 30. Compared to known results, the method is better than Smalian and Huber methods, though it is not for the frustum of cone volume formula. Additionally, there are algebraic proves showing that the segment volume estimated by the method is lower than the volume for frustums of paraboloid and cone; in this work, the proof that it is also lower than the volume for a frustum of neiloid is provided, which completes the corresponding knowledge on the subject.
author	Cruz de León,Gildardo Alfaro-Trujillo,Isaac Bañuelos-Jiménez,Margarita
author_facet	Cruz de León,Gildardo Alfaro-Trujillo,Isaac Bañuelos-Jiménez,Margarita
author_sort	Cruz de León,Gildardo
title	Error predictions for average end diameter sectional formula in tree stem volume measurement
title_short	Error predictions for average end diameter sectional formula in tree stem volume measurement
title_full	Error predictions for average end diameter sectional formula in tree stem volume measurement
title_fullStr	Error predictions for average end diameter sectional formula in tree stem volume measurement
title_full_unstemmed	Error predictions for average end diameter sectional formula in tree stem volume measurement
title_sort	error predictions for average end diameter sectional formula in tree stem volume measurement
publisher	Universidad Austral de Chile, Facultad de Ciencias Forestales
publishDate	2016
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0717-92002016000100020
work_keys_str_mv	AT cruzdeleongildardo errorpredictionsforaverageenddiametersectionalformulaintreestemvolumemeasurement AT alfarotrujilloisaac errorpredictionsforaverageenddiametersectionalformulaintreestemvolumemeasurement AT banuelosjimenezmargarita errorpredictionsforaverageenddiametersectionalformulaintreestemvolumemeasurement
_version_	1718444218556350464

Error predictions for average end diameter sectional formula in tree stem volume measurement

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