One-Dimensional Mathematical Model for Kayak Propulsion

The displacement of a sprint kayak can be described by a one-dimensional mathematical model, which, in its simplest case, is analogous to the free-fall problem with quadratic drag and constant propulsion. To describe realistic cases, it is necessary to introduce a propulsion capable of reproducing t...

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Autores principales:	Diego Delgado, Camilo Ruiz
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	kayak propulsion analytic model mathematical model Fourier series periodic propulsion reduced dimensionality models Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999
Acceso en línea:	https://doaj.org/article/862b736ad0a548db9d99b1bd5d3568e1
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id	oai:doaj.org-article:862b736ad0a548db9d99b1bd5d3568e1
record_format	dspace
spelling	oai:doaj.org-article:862b736ad0a548db9d99b1bd5d3568e12021-11-11T15:23:57ZOne-Dimensional Mathematical Model for Kayak Propulsion10.3390/app1121103932076-3417https://doaj.org/article/862b736ad0a548db9d99b1bd5d3568e12021-11-01T00:00:00Zhttps://www.mdpi.com/2076-3417/11/21/10393https://doaj.org/toc/2076-3417The displacement of a sprint kayak can be described by a one-dimensional mathematical model, which, in its simplest case, is analogous to the free-fall problem with quadratic drag and constant propulsion. To describe realistic cases, it is necessary to introduce a propulsion capable of reproducing the characteristics of the kayak stroke, including periodicity, average force and effects of stroke frequency, among others. Addressing the problem in terms of a Fourier series allows us to separate the equation into two parts, one of which is equivalent to the constant propulsion case and results in an asymptotic expression, while the second accounts for the periodic contributions. This approach allows us to solve several cases of interest: to propose a quadrature rule for the asymptotic part that allows fast estimations; to compare results with the literature; and finally to propose a general mathematical method for this problem which could help to understand some key strategies in the kayak race.Diego DelgadoCamilo RuizMDPI AGarticlekayak propulsionanalytic modelmathematical modelFourier seriesperiodic propulsionreduced dimensionality modelsTechnologyTEngineering (General). Civil engineering (General)TA1-2040Biology (General)QH301-705.5PhysicsQC1-999ChemistryQD1-999ENApplied Sciences, Vol 11, Iss 10393, p 10393 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	kayak propulsion analytic model mathematical model Fourier series periodic propulsion reduced dimensionality models Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999
spellingShingle	kayak propulsion analytic model mathematical model Fourier series periodic propulsion reduced dimensionality models Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999 Diego Delgado Camilo Ruiz One-Dimensional Mathematical Model for Kayak Propulsion
description	The displacement of a sprint kayak can be described by a one-dimensional mathematical model, which, in its simplest case, is analogous to the free-fall problem with quadratic drag and constant propulsion. To describe realistic cases, it is necessary to introduce a propulsion capable of reproducing the characteristics of the kayak stroke, including periodicity, average force and effects of stroke frequency, among others. Addressing the problem in terms of a Fourier series allows us to separate the equation into two parts, one of which is equivalent to the constant propulsion case and results in an asymptotic expression, while the second accounts for the periodic contributions. This approach allows us to solve several cases of interest: to propose a quadrature rule for the asymptotic part that allows fast estimations; to compare results with the literature; and finally to propose a general mathematical method for this problem which could help to understand some key strategies in the kayak race.
format	article
author	Diego Delgado Camilo Ruiz
author_facet	Diego Delgado Camilo Ruiz
author_sort	Diego Delgado
title	One-Dimensional Mathematical Model for Kayak Propulsion
title_short	One-Dimensional Mathematical Model for Kayak Propulsion
title_full	One-Dimensional Mathematical Model for Kayak Propulsion
title_fullStr	One-Dimensional Mathematical Model for Kayak Propulsion
title_full_unstemmed	One-Dimensional Mathematical Model for Kayak Propulsion
title_sort	one-dimensional mathematical model for kayak propulsion
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/862b736ad0a548db9d99b1bd5d3568e1
work_keys_str_mv	AT diegodelgado onedimensionalmathematicalmodelforkayakpropulsion AT camiloruiz onedimensionalmathematicalmodelforkayakpropulsion
_version_	1718435376302915584

One-Dimensional Mathematical Model for Kayak Propulsion

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