<p>This paper presents a simple mechanical model capable of evaluating a running effectiveness index <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40648_2025_315_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">\(\epsilon _{EI}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>ϵ</mi> <mrow> <mi mathvariant="italic">EI</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> based on mechanical energy. We extended a spring-loaded inverted pendulum model, considering the biomechanical determinants of running economy (RE), to develop a simplified mechanical model that can accurately represent the <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40648_2025_315_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">\(\epsilon _{EI}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>ϵ</mi> <mrow> <mi mathvariant="italic">EI</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> calculated by a detailed running model. To assess the accuracy of the proposed model in estimating RE, we computed the <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40648_2025_315_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">\(\epsilon _{EI}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>ϵ</mi> <mrow> <mi mathvariant="italic">EI</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> using both the proposed and detailed models, based on data obtained from running experiments. A linear regression analysis using the least squares method was performed to analyze the relationship between the <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40648_2025_315_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">\(\epsilon _{EI}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>ϵ</mi> <mrow> <mi mathvariant="italic">EI</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> values calculated by the two models. The regression analysis results of the <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40648_2025_315_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">\(\epsilon _{EI}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>ϵ</mi> <mrow> <mi mathvariant="italic">EI</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> values obtained from the two models yielded significant F-statistics (<InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40648_2025_315_Article_IEq6.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="62" /> </InlineMediaObject> <EquationSource Format="TEX">\(p &lt; 0.01\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>&lt;</mo> <mn>0.01</mn> </mrow> </math></EquationSource> </InlineEquation>) for all four participants, demonstrating that the proposed model can sufficiently represent the running economy index calculated by the detailed model.</p>

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Development of a simple mechanical model to evaluate running economy for designing running augmentation suits

  • Hiromu Mori,
  • Takayuki Tanaka,
  • Akihiko Murai,
  • Takashi Kusaka,
  • Yumeko Imamura

摘要

This paper presents a simple mechanical model capable of evaluating a running effectiveness index \(\epsilon _{EI}\) ϵ EI based on mechanical energy. We extended a spring-loaded inverted pendulum model, considering the biomechanical determinants of running economy (RE), to develop a simplified mechanical model that can accurately represent the \(\epsilon _{EI}\) ϵ EI calculated by a detailed running model. To assess the accuracy of the proposed model in estimating RE, we computed the \(\epsilon _{EI}\) ϵ EI using both the proposed and detailed models, based on data obtained from running experiments. A linear regression analysis using the least squares method was performed to analyze the relationship between the \(\epsilon _{EI}\) ϵ EI values calculated by the two models. The regression analysis results of the \(\epsilon _{EI}\) ϵ EI values obtained from the two models yielded significant F-statistics ( \(p < 0.01\) p < 0.01 ) for all four participants, demonstrating that the proposed model can sufficiently represent the running economy index calculated by the detailed model.