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

Abstract This paper presents a simple mechanical model capable of evaluating a running effectiveness index $$\epsilon _{EI}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ϵ</mml:mi> <mml:mrow> <mml:mi>EI</mml:mi> </mml:mrow> </mml:msub> </mml:math> 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 $$\epsilon _{EI}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ϵ</mml:mi> <mml:mrow> <mml:mi>EI</mml:mi> </mml:mrow> </mml:msub> </mml:math> calculated by a detailed running model. To assess the accuracy of the proposed model in estimating RE, we computed the $$\epsilon _{EI}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ϵ</mml:mi> <mml:mrow> <mml:mi>EI</mml:mi> </mml:mrow> </mml:msub> </mml:math> 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 $$\epsilon _{EI}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ϵ</mml:mi> <mml:mrow> <mml:mi>EI</mml:mi> </mml:mrow> </mml:msub> </mml:math> values calculated by the two models. The regression analysis results of the $$\epsilon _{EI}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ϵ</mml:mi> <mml:mrow> <mml:mi>EI</mml:mi> </mml:mrow> </mml:msub> </mml:math> values obtained from the two models yielded significant F-statistics ( $$p &lt; 0.01$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>&lt;</mml:mo> <mml:mn>0.01</mml:mn> </mml:mrow> </mml:math> ) for all four participants, demonstrating that the proposed model can sufficiently represent the running economy index calculated by the detailed model.