2023-12-09T06:18:06Z https://mie-u.repo.nii.ac.jp/oai
oai:mie-u.repo.nii.ac.jp:00003509 2023-11-09T05:43:10Z 143:144:262:272
A nonlinear regression model for distance-velocity curve of 100m sprint HAGIWARA, Katsuyuki 萩原, 克幸 SUGITA, Masaaki 杉田, 正明 application/pdf Position data during a 100m sprint are usually recorded by using the LABEG(LAser VElocity Guard) system. The recorded position data is transformed into a velocity course by a certain method and a distance-velocity property is often focused in analyzing a 100m sprint. The transformed velocity data is noisy in general if we apply a simple numerical differentiation. Therefore, we need a device for extracting a smooth distance-velocity property from the raw velocity data. In this paper, we proposed a nonlinear regression model for this purpose. The nonlinear function in our model is composed of a sum of two functions which represent a velocity increase in the early stage of a 100m sprint and a velocity decrease in the later stage respectively. The former function is an exponential function to represent a rapid speed increase at a sprint start and the latter function is a polynomial function to represent a gradual decrease due to fatigue in the later state of a sprint. We apply this model to analyze collected LABEG data of students in elementary and junior high school under an appropriated pre-processing for position data. The model parameters were estimated by the gradient descent method for the least squares estimation. As a result, we verified that this model can well represent distance-velocity properties of the collected data. By the analysis based on the estimated curves, we clarified that the maximum velocity is the most important factor for a 100m sprint time. This is consistent with the well known speculation. We also found that the start acceleration and velocity decrease at the later stage are also related to the 100m sprint time. Furthermore, we introduced a derivative of the estimated distance-velocity curve and found that it's values at around sprint start are well related to a sprint time. Fortunately, we could confirm that the similar insights were obtained by estimated parameter values. This is because we have assumed a structured model in which the parameters directly reflect characteristics of each phase of a 100m sprint. departmental bulletin paper 三重大学教育学部 2014-03-31 VoR application/pdf 三重大学教育学部研究紀要, 自然科学・人文科学・社会科学・教育科学 65 5 17 1880-2419 AA12097333 https://mie-u.repo.nii.ac.jp/record/3509/files/20C17039.pdf eng