van Soest A J, Casius L J
Faculty of Human Movement Sciences, Free University, Amsterdam, The Netherlands.
Med Sci Sports Exerc. 2000 Nov;32(11):1927-34. doi: 10.1097/00005768-200011000-00017.
Mechanical power output in sprint cycling depends on pedaling rate, with an optimum at around 130 revolutions per minute (rpm). In this study, the question is addressed if this optimal pedaling rate can be understood from a Hill-type description of muscular dynamics. In particular, it is investigated how 1) the power-velocity relationship that follows from Hill's force-velocity relationship and 2) activation dynamics (from the perspective of which the optimal pedaling rate is near-zero) affect the optimal pedaling rate.
A forward dynamics modeling/simulation approach is adopted in this study. The skeletal model is a 2D linkage of rigid segments; it is actuated by eight Hill-type "muscles." Input of the model is the neural stimulation of the muscles, output is the resulting movement and variables dependent thereupon, such as pedal forces. For a wide range of isokinetic pedaling rates, the neural stimulation is optimized with respect to the average mechanical power output.
Correspondence between experimental data and simulation results regarding 1) the (pedaling-rate dependent) muscle phasing, 2) pedal forces, and 3) the power-pedaling rate relationship is good. At the optimal pedaling rate predicted by the model (120 rpm), muscles contract at velocities well below those that maximize their power output. Finally, when a model is considered that lacks activation dynamics, it is found that both the optimal pedaling rate and the maximal power output increase substantially.
From the results pertaining to the standard model, it is concluded that the optimal pedaling rate is not uniquely specified by the power-velocity relationship of muscle, as suggested in literature. From the results pertaining to the model lacking activation dynamics, it follows that activation dynamics plays a surprisingly large role in determining the optimal pedaling rate. It is concluded that the pedaling rate that maximizes mechanical power output in sprint cycling follows from the interaction between activation dynamics and Hill's power-velocity relationship.
短跑自行车运动中的机械功率输出取决于蹬踏频率，最优频率约为每分钟130转（rpm）。在本研究中，探讨了能否从肌肉动力学的希尔型描述来理解这一最优蹬踏频率。具体而言，研究了以下两点如何影响最优蹬踏频率：1）由希尔力-速度关系推导得出的功率-速度关系；2）激活动力学（从该角度看最优蹬踏频率接近零）。
本研究采用正向动力学建模/模拟方法。骨骼模型为刚性节段的二维连杆机构；由八块希尔型“肌肉”驱动。模型的输入是肌肉的神经刺激，输出是由此产生的运动及相关变量，如踏板力。对于广泛的等速蹬踏频率范围，针对平均机械功率输出对神经刺激进行优化。
关于以下方面，实验数据与模拟结果的对应性良好：1）（取决于蹬踏频率的）肌肉相位；2）踏板力；3）功率-蹬踏频率关系。在模型预测的最优蹬踏频率（120 rpm）下，肌肉收缩速度远低于使其功率输出最大化的速度。最后，当考虑一个缺乏激活动力学的模型时，发现最优蹬踏频率和最大功率输出均大幅增加。
从与标准模型相关的结果得出，最优蹬踏频率并非如文献中所暗示的那样由肌肉的功率-速度关系唯一确定。从与缺乏激活动力学的模型相关的结果可知，激活动力学在确定最优蹬踏频率方面起着惊人的重要作用。得出结论：短跑自行车运动中使机械功率输出最大化的蹬踏频率源于激活动力学与希尔功率-速度关系之间的相互作用。
