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Wheel Running™


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Running is a type of locomotion for humans and animals to achieve rapid movement on the ground. Running can refer to any range of speeds from jogging to sprinting. Running is characterized by an aerial phase in which all feet are above the ground (though there are exceptions in certain birds). In contrast, walking is characterized by one foot in contact with the ground at all times (and there is a period of double support). As we discussed earlier in the ‘Inverted Pendulum’ model of walking, the point-mass COM vaults over the massless legs during walking. The legs are typically kept straight in the model. Compared to the model for walking, the viewpoint of spring-mass mechanics has been widely used to explain fast locomotion. In the ‘Spring Mass’ model for running, like a pogo stick, the movement of the COM happens through the changes in kinetic and potential energy. This occurs within a stride simultaneously when the energy is stored and released by springy tendons and passive muscle elasticity.

In a study on walking and running in reduced gravity simulations, the authors concluded that we humans are using different mechanisms (Farley CT, McMahon TA. 1992. Energetics of walking and running—insights from simulated reduced-gravity experiments. Journal of Applied Physiology 73:2709-2712). They saw that the running had much more reduction of energy requirement compared to walking in the reduced gravity simulations. Because of the traditional views of human locomotion from the ‘Inverted Pendulum’ model for walking and the ‘Spring-Mass’ model for running, many studies were done to explain the differences between these two types of human locomotion. Other studies were done to explain the transitions between the two: ‘Walk-to-Run’ and ‘Run-to-Walk‘. In contrast, a study of ostriches by Jonas Rubenson et al (Jonas Rubenson · Denham B Heliams · David G Lloyd · Paul A Fournier (2004). Gait selection in the ostrich: mechanical and metabolic characteristics of walking and running with and without an aerial phase. Proceedings of the Royal Society of London B: Biological Sciences, 271(1543), 1091–1099) showed that there was no abrupt transitions in the mechanical parameters or the metabolic cost of locomotion when ostriches adopted an aerial-running gait at faster speeds.

When we use different models for walking and running, using the same musculoskeletal structures of the body, we may get conflicting results as we study the energetics and mechanics of human locomotion. The different types of locomotion at different speeds still serve one purpose of action – distance movement. A simple hypothesis is needed to explain both types of locomotion. The hypothesis also has to be able to explain the transition patterns between walk-to-run and run-to-walk.

When the stance leg is functioning as a part of a wheel, it has to withstand a large force from the velocity and mass of the COM. Withstanding the large force during running will be an important issue for any type of fast locomotion.

Furthermore, during forward movement of the COM during the stance phase of running, the stance leg has to undergo initial flexion of the knee and hip joints in order to absorb the force of impact and minimize the braking force. This is followed by the extension of those same joints which is accomplished by the stored energy in the elastic components of tendons and muscles. Extensions of the ankle, foot, and toes will eventually add to the total length of the stance leg by the end of the phase. This increase in effective length of the limb between the ground and the hip joint will help accelerate forward speed of the COM through the torque energy over the hip joint caused by gravitational force (see the picture – acceleration diagram w/ the increase of leg length).

diagram1-2If the height of the COM from the ground is maintained relatively the same during stance phase, the rotational torque energy about the hip joints from the influence of the gravity will remain constant during forward advancement of the COM (see diagram 1). When the proper stiffness of the stance leg between the ground and the hip joints is maintained, the speed at the ground contact point (foot/toes) will be the speed of the COM over the hip joints. We can feel the difference of speeds while sitting in the seats in the same row of a vehicle when the vehicle is making a quick turn around a street corner (see diagram 2).

Effects of Toe Length and Contact Time on Running

Consequently, longer toes can help accelerate the speed of the COM by increasing the contact time with the ground a bit longer during fast running (sprinting). When there is a proper stiffness of the entire body during sprinting, longer toes will help accelerate the speed of the COM through this mechanism. In a study by Lee and Piazza (Sabrina S. M. Lee, Stephen J. Piazza. Built for speed: musculoskeletal structure and sprinting ability. Journal of Experimental Biology 2009 212: 3700-3707), 12 collegiate sprinters and 12 non-athletes of the same height were recruited. Besides the shorter lever arm of the Achilles tendon (25 % shorter) seen in sprinters, they found that sprinters had longer toes (about 9 mm longer). It should be noted that the shorter lever arm on ankle joints will help lift the body faster during initial acceleration before the sprinter reaches their optimal height. They concluded that longer toes prolonged the time of contact with the ground, giving greater time for forward acceleration. This acceleration caused by longer toes can only be explained by the ‘Wheel Running’ mechanism.

Lateral Displacement

diagram3As explained in the chapter on friction energy of the foot, during running, humans need to control the lateral displacement of the body. Initial lateral displacement of the body by the landing leg can be compensated for by an immediate inward rotation of the forefoot as it makes contact (see diagram 3). The following forward and vertical counter-angular momentum from the swing leg will be balanced by a toe-out angle at the end of the stance phase. Arm swing will assist with lateral balance on the angular torque of the vertical (yaw) axis. Certainly the arms need to respond quickly for the fast moving legs during running and sprinting. The arms effective lever length has to be shortened by elbow flexion to keep up with the speed of the legs. The flexion of the elbow (along with further upward elevation of shoulders) will help raise the height of the COM during running creating longer airtime. In a study by Richard Hinrichs (Hinrichs, R. (1987). Upper extremity function in running. II. Angular momentum considerations. Int. J. Sport Biomech. 3, 242-263) on upper body angular momentum during running, the author found that the arms made a meaningful contribution mainly to the vertical component. He suggested that the arms and upper trunk provided the majority of the angular force about the vertical axis needed to put the legs through their alternating strides in running.

Airtime and Running

As speed increases in running, airtime increases. The proper amount of airtime will be important for fast running. Stance period is always accompanied by a collision with the ground which will automatically cause loss of energy. If there is no air resistance, the falling objects of same height will reach the ground at the same time even if they have different weights. This is due to the same acceleration effect by Earth’s mass on relatively small objects.

When we apply this principle to the physics of running, we can see that the runner with a higher COM during the flight phase will have a longer air time. Several methods can be implemented to increase airtime during flight phase. Raising the arms and shoulders will be one method. Moving the chin up slightly can also help. Placing COM just over the hip joint without tilting the upper body forward will be prevent the loss of height during running. Raising the swing leg higher will be the most significant factor. This was discussed in the ‘Hamstring Pulley’ chapter. We can observe this in school children while they are running or even in a professional baseball game – certain players seem to run slower often missing a split second opportunity for base advancement.

In a study on walking and running in reduced gravity, the authors observed that the energy expenditure was much less for running compared to walking (Farley CT, McMahon TA. 1992. Energetics of walking and running—insights from simulated reduced-gravity experiments. Journal of Applied Physiology 73:2709-2712). When we use the ‘Hamstring Pulley’ mechanism for energy efficiency, gravity helps transfer the weight energy of the swing leg and the COM to the stance leg for energy efficient leg extension. When we walk in a reduced gravity field like in the study simulations, we will not get the benefit of gravity’s effect on weight energy shifting to the stance leg extension through the ‘Hamstring Pulley’ mechanism.

diagram4-5If the height of the COM from the ground is maintained relatively the same during stance phase, the rotational torque energy about the hip joints from the influence of the gravity will remain constant during forward advancement of the COM (see diagram 4). When the proper stiffness of the stance leg between the ground and the hip joints is maintained, the speed at the ground contact point (foot/toes) will be the speed of the COM over the hip joints. We can feel the difference of speeds while sitting in the seats in the same row of a vehicle when the vehicle is making a quick turn around a street corner (see diagram 5).