Mathematics and Sports: Biomechanics of Running and Walking

Abstract Running and walking are integral to most sports and there is a considerable amount of mathematics involved in examining the forces produced when a foot contacts the ground. In this paper we discuss biomechanical terms related to running and walking. We use experimental ground reaction force data to calculate the impulse of running, speed-walking, and walking. We mathematically model the vertical ground reaction force curves for both running and walking, successfully reproducing experimental data. Finally, we discuss the biological implications of the mathematical models and give suggestions for classroom or research projects. Introduction Running speed is essential for many sports, whether it is the ability to beat a defender, run faster than an opponent, or develop enough take-off velocity to achieve distance or height on a jump. Running tends to occur at faster speeds than walking, although speed walkers can achieve speeds of up to 4.6 meters per second using an unusual gait in which the hip is dropped each step. Running is defined as a gait in which there is an aerial phase, a time when no limbs are touching the ground. Aside from wind resistance and gravity, there are no external forces applied to the body during this aerial phase. Therefore, it is the stance phase (the time when a limb is in contact with the ground) of running that must be modified in order to change speed.