The dynamics of bicycle pedalling

Abstract

According to recent developments in the theory of muscular action, the average external force exerted during a muscular movement, carried out with maximal effort, may be regarded as equal to a constant theoretical force diminished by an amount proportional to the speed of movement. As a deduction from this, the relation between certain quantities involved in a specified type of muscular exercise can be expressed in the form of a mathematical equation. The equation can then be tested by experiment. Certain kinds of human limb movements have already been subjected to this form of analysis (5), (6), (7), (8). In the present paper is described a similar investigation of the movements of pedalling a bicycle. Consider the case of a subject pedalling a bicyle against a constant resistance. The resistance might be due to a hill of constant slope, or, in the case of laboratory experiments with a bicycle ergometer, to the friction of a band applied to the wheel. Let P be the maximum force (averaged over the whole range of foot movement) that can he exerted by the leg at right angles to the pedal crank when the rate of pedalling is such that one foot movement ( i. e. , half a complete revolution of the crank) is completed in t seconds. Then according to the theory, the relation between P and t should be capable of expression in the form, P = P 0 (1 - k/t ), where P 0 kind k are constants, represents the maximum force that could be exerted at right angles to the pedal crank, and would be attained only if the movement could take place infinitely slowly; while k represents the shortest time in which the movement could be completed, and would be attained only if no external work were done. The constants have a theoretical meaning only, and cannot be measured directly. If the theory holds, they should be characteristic for a given subject in a given bodily condition.