DIMENSIONAL ANALYSIS MODEL FOR ANALYTICAL EVALUATION OF PROPULSION FORCE IN SPORTS ACTIVITIES
DOI:
https://doi.org/10.15330/fcult.40.97-104Keywords:
propulsive force, velocity, body mass, running distance, ageAbstract
Aim. The dimensional analysis model is used to analytically express a physical quantity dependent on a number of physical parameters observed experimentally. Thus, using the method of dimensional analysis products, in this paper, the expression of the propulsion force of the human body, in sports activities, was analytically determined. Methods. Analytical modeling using experimental observations. Results. The experi-mental observations, both by the authors and from the specialized literature, have identified as the main parameters that influence the propulsion force, the speed of movement, the distance over which the movement is made, the duration of time for the movement, the mass of the human subject and the age of the individual. The method involves the choice of independent or fundamental dimensions, with the help of which dimen-sionless proportions are formed, both for the propulsion force and for the other physical parameters whose dimensions depend on the fundamental dimensions. For the case analyzed in this paper, the fundamental quantities were the distance traveled, the time duration for the movement and the mass of the human subject. With the help of the product method, the analytical expression of the propulsion force was obtained as a product between the physical parameters whose dimensions are fundamental and a function defined with the help of the dependent physical parameters and some of the independent ones, a function that is determined experimentally. Based on the specialized literature, the dependence function of the dependent and independent physical parameters was determined, so that the numerical simulation is possible. Conclusion. Te product method presented in this paper can also be used in the field of sports, when a physical quantity dependent on a number of experimentally observed physical parameters is desired to be expressed in a calculation expression.
References
2. K. A. Boyer, T. P. Andriacchi. (2009). Changes in running kinematics and kinetics in response to a rocke-red shoe intervention. Clin. Biomech. 24(10): 872-876.
3. V. Tessutti, F. Trombini-Souza, A. P. Ribeiro, A. L. Nunes, I. de C. N. Sacco. (2010). In-shoe plantar pres-sure distribution during running on natural grass and asphalt in recreational runners.J. Sci. Med. Sport. 13(1): 151-155.
4. M. Damavandi, P. C. Dixon, D. J. Pearsall. (2012). Ground reaction force adaptations during cross-slope walking and running. Hum. Mov. Sci. 31(1): 182-189.
5. P. O. Riley, G. Paolini, U. Della Croce, K. W. Paylo, D. C. Kerrigan. (2007) A kinematic and kinetic com-parison of overground and treadmill walking in healthy subjects. Gait Posture. 26(1): 17-24.
6. HaoYuan Hsiao, Brian A. Knarr, J. S. Higginson, S.A. Binder-Macleod. (2015). Mechsnisms to increase propulsive force for individuals poststroke. Journal of NeuroEngineering and rehabilitation, 12(40), doi: 10.1186/s12984-015-0030-8.
7. Michael G. Browne, Jason R. Franz. (2017). Does dynamic stability govern propulsive force generation in human walking?. Royal Society Open Science. https://royalsocietypublishing.org/doi/10.1098/rsos.171673.
8. S. J. Dixon, A. C. Collop, M. E. Batt. (2000). Surface effects on ground reaction forces and lower extremity kinematics in running. Med. Sci. Sport.Exerc. 32(11): 1919-1926.
9. N. A. A. Abdul Yamin, M. N. Ali Amran, K. S. Basaruddin, A. F. Salleh, W. M. R. Rusli. (2017). Ground reaction force response during running on different surface hardness. ARPN Journal of Engineering and Applied Sciences, 12(7). https://www.researchgate.net/publication/316935106.
10. Wannop, J. W., Worobets, J. T., Stefanyshyn, D. J.(2012). Normalization of ground reaction forces, joint mo-ments, and free moments in human locomotion. J. Appl. Biomech. 28, 665–676. doi: 10.1123/jab.28.6.665.
11. Horsak, B., Slijepcevic, D., Raberger, A. M., Schwab, C., Worisch, M., Zeppelzauer, M. (2020). GaitRec, a large-scale ground reaction force dataset of healthy and impaired gait. Sci. Data 7:143. doi: 10.1038/s41597-020-0481-z.
12. Colyer, S. L., Graham-Smith, P., Salo, A. I.(2019). Associations between ground reaction force waveforms and sprint start performance. Int. J. Sport. Sci. Coach. 14, 658–666. doi: 10.1177/1747954119874887.
13. Mei, Q., Gu, Y., Xiang, L., Baker, J. S., Fernandez, J. (2019). Foot pronation contributes to altered lower extremity loading after long distance running. Front. Physiol. 10:573. doi: 10.3389/fphys.2019.00573.
14. Hendry, D., Leadbetter, R., McKee, K., Hopper, L., Wild, C., O’sullivan, P., et al. (2020). An exploration of machine-learning estimation of ground reaction force from wearable sensor data. Sensors (Switzerland) 20:740. doi: 10.3390/s20030740.
15. Williams, L. R., Standifird, T. W., Creer, A., Fong, H. B., Powell, D. W. (2020). Ground reaction force profiles during inclined running at iso-efficiency speeds. J. Biomech. 113:110107. doi: 10.1016/j.jbiomech.2020.110107.
16. Logan, S., Hunter, I., Hopkins, J. T., Feland, J. B., Parcell, A. C. (2010). Ground reaction force differences between running shoes, racing flats, and distance spikes in runners. J. Sport. Sci. Med. 9, 147–153.
17. Soares, D. P., De Castro, M. P., Mendes, E. A., Machado, L. (2016). Principal component analysis in ground reaction forces and center of pressure gait waveforms of people with transfemoral amputation. Prosthet. Orthot. Int. 40, 729–738. doi: 10.1177/0309364615612634.
18. Deluzio, K. J., Wyss, U. P., Zee, B., Costigan, P. A., Sorbie, C. (1997). Principal component models of knee kinematics and kinetics: normal vs. pathological gait patterns. Hum. Mov. Sci. 16, 201–217. doi: 10.1016/S0167-9457(96)00051-6.
19. Lever, J., Krzywinski, M., and Altman, N. (2017). Points of Significance: Principal component analysis. Nat. Methods 14, 641–642. doi: 10.1038/nmeth.4346.
20. Cushion, E. J., Warmenhoven, J., North, J. S., Cleather, D. J. (2019). Principal component analysis reveals the proximal to distal pattern in vertical jumping is governed by two functional degrees of freedom. Front. Bioeng. Biotechnol. 7:193. doi: 10.3389/fbioe.2019.00193.
21. Lin Yu, Qichang Mei, Liangliang Xiang, Wei Liu, Nur Ikhwan Mohamad, Bíró István, Justin Fernandez, Yaodong Gu. (2021). Principal component analysis of the running ground reaction forces with different speeds. Front. Bioeng. Biotechnol., vol. 9, https://doi.org/10.3389/fbioe.2021.629809.
22. Ullah, S., Finch, C. F. (2013). Applications of functional data analysis: a systematic review. BMC Med. Res. Methodol. 13:43. doi: 10.1186/1471-2288-13-43.
23. Ain A. Sonin. (2001). The physical basis of dimensional analysis. Department of Mechanical Engineering MIT, Cambridge, MA, https://web.mit.edu/2.25/www/pdf/DA_unified.pdf.
