Theoretical evaluation of Huber and Smalian methods applied to tree stem classical geometries

Huber, Smalian and Newton methods, to estimate tree stem and log volume by sections, were theoretically evaluated applying them to the geometries of paraboloid, cone and neiloid. The study follows approximation procedures from calculus for volume estimation of solids of revolution as function of the...

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Autores principales:	Cruz de León,Gildardo, Uranga-Valencia,Luisa P
Lenguaje:	English
Publicado:	Universidad Austral de Chile, Facultad de Ciencias Forestales 2013
Materias:	sectional methods tree stem volume
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0717-92002013000300007
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spelling	oai:scielo:S0717-920020130003000072014-01-14Theoretical evaluation of Huber and Smalian methods applied to tree stem classical geometriesCruz de León,GildardoUranga-Valencia,Luisa P sectional methods tree stem volume Huber, Smalian and Newton methods, to estimate tree stem and log volume by sections, were theoretically evaluated applying them to the geometries of paraboloid, cone and neiloid. The study follows approximation procedures from calculus for volume estimation of solids of revolution as function of the number of segments and error analysis methods from forest measurement research. The errors in using Huber and Smalian methods have been determined. Additionally, it was algebraically proved that the Huber's error is exactly one half of the Smalian's error and opposite in sign. The results predict that, for any tree stem modeled classically, Huber's and Smalian's average absolute percent errors should be: less than 13.5 % and 27 %, respectively, for five or more segments; less than 7 % and 14 %, for 10 or more segments; less than 3.6 % and 7.2 %, for 20 or more segments; less than 2.5 % and 5 %, for 30 or more segments. This work provides a quantization on the classical theory of tree stem and log volume estimation. It could help to unify that theory and make it a more compact reference for forest measurement teaching and research.info:eu-repo/semantics/openAccessUniversidad Austral de Chile, Facultad de Ciencias ForestalesBosque (Valdivia) v.34 n.3 20132013-01-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0717-92002013000300007en10.4067/S0717-92002013000300007
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	sectional methods tree stem volume
spellingShingle	sectional methods tree stem volume Cruz de León,Gildardo Uranga-Valencia,Luisa P Theoretical evaluation of Huber and Smalian methods applied to tree stem classical geometries
description	Huber, Smalian and Newton methods, to estimate tree stem and log volume by sections, were theoretically evaluated applying them to the geometries of paraboloid, cone and neiloid. The study follows approximation procedures from calculus for volume estimation of solids of revolution as function of the number of segments and error analysis methods from forest measurement research. The errors in using Huber and Smalian methods have been determined. Additionally, it was algebraically proved that the Huber's error is exactly one half of the Smalian's error and opposite in sign. The results predict that, for any tree stem modeled classically, Huber's and Smalian's average absolute percent errors should be: less than 13.5 % and 27 %, respectively, for five or more segments; less than 7 % and 14 %, for 10 or more segments; less than 3.6 % and 7.2 %, for 20 or more segments; less than 2.5 % and 5 %, for 30 or more segments. This work provides a quantization on the classical theory of tree stem and log volume estimation. It could help to unify that theory and make it a more compact reference for forest measurement teaching and research.
author	Cruz de León,Gildardo Uranga-Valencia,Luisa P
author_facet	Cruz de León,Gildardo Uranga-Valencia,Luisa P
author_sort	Cruz de León,Gildardo
title	Theoretical evaluation of Huber and Smalian methods applied to tree stem classical geometries
title_short	Theoretical evaluation of Huber and Smalian methods applied to tree stem classical geometries
title_full	Theoretical evaluation of Huber and Smalian methods applied to tree stem classical geometries
title_fullStr	Theoretical evaluation of Huber and Smalian methods applied to tree stem classical geometries
title_full_unstemmed	Theoretical evaluation of Huber and Smalian methods applied to tree stem classical geometries
title_sort	theoretical evaluation of huber and smalian methods applied to tree stem classical geometries
publisher	Universidad Austral de Chile, Facultad de Ciencias Forestales
publishDate	2013
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0717-92002013000300007
work_keys_str_mv	AT cruzdeleongildardo theoreticalevaluationofhuberandsmalianmethodsappliedtotreestemclassicalgeometries AT urangavalencialuisap theoreticalevaluationofhuberandsmalianmethodsappliedtotreestemclassicalgeometries
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Theoretical evaluation of Huber and Smalian methods applied to tree stem classical geometries

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