Running: a dance with the devil
This page contains a series of articles that attempt to cover the major physical, biological and psychological factors involved in running. The first of these was an introduction and overview posted on 18th March 2008. As each new article in the series is posted on the blog, it will be appended so as to provide a single continuous record of the series.
This series updates and extends the page entitled ‘Mechanics of Efficient Running’ published in January 2008. That page remains on this site, but a few of the ideas expressed on that page have been modified by my subsequent thoughts and discussions.
Furthermore, this page was edited in April 2012 to take account of the results on computations performed as a result of my discussion with Robert Osfield over the New Year period, 2011-2012 (reported in the comments section below). The results of these computations were presented and discussed in several blog postings in the period January to April 2012.
RUNNING: A DANCE WITH THE DEVIL
Running is becoming airborne.
The essence of running is becoming airborne. When a human wants to increase speed while walking, he or she can increase stride rate or stride length. Beyond a certain stride rate, muscle contraction becomes inefficient because force is generated by a ratchet-like interaction between actin and myosin molecules within the muscle fibre, and the speed of this ratchet action is limited by the time it takes to make and break chemical bonds. Furthermore, it can be shown that the energy cost of swinging the leg forward rises in proportion to the produce of velocity times cadence (at least while running and a similar effect would be anticipated during walking) so at high speed, the energy cost of a high cadence becomes large. Beyond a certain stride length, efficiency falls due to poor leverage of muscles on awkwardly angled legs. The oblique forward angle of the leg in the period immediately after footfall gives rise to a large braking force that slows the body while increasing risk of injury. So the only practical option for further increase in speed is to increase stride length by becoming airborne for part of each stride. Thus we make the transition from walking to running.
Becoming airborne requires energy to propel us upwards against gravity. Once we are airborne, our body inevitably experiences a downwards acceleration of 9.8 metres/sec/sec (32 feet/sec/sec) due to gravity. The energy used to raise the body is now converted to kinetic energy that must be dissipated on impact with the ground. While a single impact following a fall of a few inches is unlikely to do much damage, minor impact repeated thousands of times creates a risk of repetitive strain injuries to connective tissue or even to stress fracture of bones such as the metatarsals in the feet or the tibia (shin bone). Thus, while running can be both graceful and efficient, it is also an energetic and risky form of locomotion. Not surprisingly, many runners suffer injury.
The deal with the devil
Thus running is a dance with the devil – gravity. We spend energy raising ourselves against this demon and then are at risk of injury as we are flung back to earth. However, in the force of impact, there is the sniff of a deal with the devil. If instead of dissipating the impact energy destructively at foot-fall we can capture it as elastic potential energy by the stretching of muscles and other connective tissues, this elastic energy might subsequently be recovered to propel us upwards at lift-off. The muscle contraction energy required to lift our bodies is reduced and the jarring effect of impact is diminished.
The process of capturing impact energy as elastic energy and sustaining it as we prepare for lift-off requires exquisitely controlled tensioning of muscles and angling of joints. Releasing it at the right moment and in the correct direction requires exquisite timing. Fortunately our brains learn to do this automatically in infancy and childhood, so for the most part, we can run tolerably well without thinking about it. However, whether due to bad habits of posture acquired sitting in an office chair, to de-conditioning of the muscles of the feet due to wearing shoes, or simply the fact that nothing in either the evolution of the species or the experiences of childhood prepared us for the monotonous repetitive impacts produced by running for miles on a paved surface, few people run naturally with optimum efficiency or adequate safety. Therefore, we need to learn how to run. This is the introduction to a series of three articles that will address the question of how to run efficiently and safely.
The laws of the dance
In our dance with the devil both he and we are constrained by the laws of motion. We cannot violate these laws. If we try to we are likely to waste energy and/or injure ourselves. In this article we will examine the physical mechanics of running. We will identify the constraints imposed by the laws of Newtonian physics. These laws are immutable (at least for bodies of human scale moving at running speed) and therefore, they provide a clearly defined framework that must be taken into account irrespective of personal choice or opinion.
The steps of the dance
In the second article, we will examine the biodynamics of running; that is, the optimum way to use of muscles, connective tissues and joints to execute the movements required to become airborne, to maintain forward momentum and move our legs forward to provide support at footfall; and to avoid injury on impact. Because of the complexity of the human body, it is virtually impossible to take into account all of the factors that might determine the outcome of a particular action, so the proposals are more speculative. They should be tested against experience, but it is not easy to generalise from a single test because individual differences in body constitution and in circumstances can lead to different outcomes. Therefore, the proposals in this section should be taken with a pinch of salt
The mind of the dancer
The third section will deal with the psychodynamics of running: the intentions, beliefs and perceptions that allow us to perform the steps of the dance. It is impossible, and in any case counterproductive to try to consciously manage each muscle contraction when running. We can only attend consciously to a single perception at one time, so we need to identify the aspects of our running on which it is most helpful to focus consciously. Fortunately, as we shall see when we consider the constraints imposed by the laws of mechanics, the magnitude and direction of the impulses delivered at lift-off place tight constraints on the location and impact of footfall. Furthermore, we have well developed automatic mechanisms that regulate footfall. Therefore, most of our conscious focus should be on the lift-off.
Perception is a product of sensory information entering the brain and of predictions generated within the brain. The predictions are shaped by prior beliefs. What we perceive does not necessarily correspond exactly with what an external observer or a video camera might record. We ourselves can shape our perceptions. Some schools of running technique, such as Pose (Pose Method of Running, Nicholas Romanov, Pose Tech Corp 2002) appear to encourage perceptions that are contrary to the laws of physics, and in particular encourage the perception that freely available propulsive energy is provided by gravity. The Pose Method provides many valuable insights into good running style. The perception that gravity provides freely available energy for propulsion might be beneficial insofar as it might discourage unnecessary and wasteful muscular effort, but in my opinion, it leads to internal contradiction and confusion in the mind of the runner. Therefore, the goal of this article is to develop perceptions that are consistent with the biomechanics of running based on physical laws and biodynamics.
The conversion of intention into action is guided not only by perception but also by a more tenuous but crucial mental attribute: confidence. It is confidence that allows conscious perception to be integrated with automatic processes to produce the exquisite control of force and timing necessary to run well. One way to acquire confidence is to place faith in a guru. The other is to place faith in principles derived from understanding of the laws of physics and from sound biodynamic theory. The ambitious goal of this set of articles is to provide a foundation for such confidence. However, it should be emphasised that the material presented is a preliminary effort at assembling such principles. The main direct evidence supporting them is my own experience as a runner. I am not a coach. My experience should not be assumed to apply to others and before changing one’s running style it is advisable to consult a qualified coach.
THE LAWS OF THE DANCE
As discussed in the introduction, the essence of running is locomotion in which the length of stride is increased by becoming airborne for a part of each stride. In this article we will consider the constraints that the laws of Newtonian mechanics place on how we run. These laws apply whatever running style we adopt. The laws do not tell us which muscles we should use to achieve our goal, but they do provide guidance to help answer questions about optimum cadence and stride length and the relative proportion of each stride that should be spent airborne for optimum efficiency and safety. Before starting, we should define a few of the terms we will use.
The gait cycle
The full gait cycle covers the period from the time at which one foot contacts the ground (foot-fall) to the next time point at which that same foot contacts the ground. For ease of description, we will assume that this foot is the right foot. During the cycle, there are several phases. At first, the right foot remains stationary on stance while the torso passes forwards over it. Once the torso has passed over the point of support (usually located under the forefoot) which happens at mid-stance, the hip extends backwards until the point of lift-off is reached, initiating the swing phase for the right leg. The first airborne phase continues until foot fall of the left leg. While the left leg is on stance, the right leg continues to swing forwards. Shortly after the left leg lifts from the ground, the right leg reaches it forward most point of travel relative to the torso and then drops to the ground. At footfall of the right foot, the full cycle is completed. It contains one period of stance for each foot and two airborne phases. Note that the swing phase for one leg includes two airborne phases and also the period while the other leg is on stance.
Stride length is the distance on the ground from where the right foot contacts the ground to the point where the left foot contacts the ground. Cadence is the number of strides per minute. (Note that some people define cadence as number of gait cycles per minute, giving numerical values half as large as the values we will quote.) Speed is obtained by multiplying stride length by cadence. For most runners, cadence is approximately constant through the much of their range of speeds, and is typically 180 strides per minute. At this cadence, a stride length of 1 metre corresponds to a speed of 180 metres per minute (which is a little slower than 1Km in 5 minutes or 1 mile in 8 minutes.) Speed can be increased at constant cadence by increasing stride length. At a cadence180, a stride length of 2.2 metres corresponds to 4 minute mile pace.
Efficiency and safety
We run more efficiently when we consume less energy per kilometre at a given speed. Efficiency can be quantified as the energy required to run a fixed distance at a particular speed. The higher the efficiency the lower the energy required.
Safety refers to running with low risk of injury. In general, risk of injury increases with increasing magnitude of forces applied to body tissues, though factors such as the direction of application of force, and the rate at which forces are applied play a large part. Also, in light of the fact that running often involves thousands of repeated impacts, that it is important to note that repeated application of relatively small forces than are well below the level required to break a bone or tear a muscle can cause stress fractures of bones or repetitive strain injures to muscles and other connective tissues. Nonetheless, if our goal is running safety, in general we are aiming to minimise the size of forces exerted on body tissues and the abruptness with which they are applied.
The tasks of running
Running at constant speed on a level surface demands the execution of three main tasks:
1) Maintaining forwards velocity that is constant when averaged over the gait cycle
2) Propelling the body upwards to initiate each airborne phase
3) Moving the legs forward to provide support on landing.
Maintaining constant forwards velocity
Newton’s first law of motion a states that a body will continue in a state of uniform motion at constant velocity unless acted upon by a force. That is, the body maintains constant forward directed momentum unless acted upon by external forces. To influence forward momentum, these forces must have a component acting the either the forwards or backwards direction.
The external forces that act on a running body are:
Although gravity acts on each part of the body, for the purpose of estimating the overall effect of gravity on the body, the force of gravity can be treated as acting through the general centre of mass (gcm) of the body, which is also called the centre of Gravity (COG). Although the anatomical location of the gcm moves slightly within the body as the legs move relative to the torso, the COG is always in the vicinity of the midpoint of the line that joins the iliac crests (the prominent curved bony ridge above the hip and just below the waist level on each side of the body); it is the top edge of the side of the pelvis.) Because gravity act downwards, it cannot directly produce acceleration or deceleration of the body in a forwards or backwards direction. Thus, gravity does not directly produce any change in forward momentum.
Vertical ground reaction force
The vertical ground reaction force (vGRF) arises as a reaction by the ground to the downwards forces exerted by the body via the legs and feet on the ground. The downwards forces exerted by the body arise from the body’s weight; from active contraction of muscles pushing down; and from elastic recoil of stretched muscles and connective tissues. The upwards vGRF is due to elastic reaction by the ground as it resists compression by the body. Upwards ground reaction force is equal and opposite to the downwards force exerted by the body according to Newton’s third law. By virtue of acting vertically, vGRF cannot directly alter the forwards momentum of the body.
Horizontal ground reaction force along the y axis
When the legs are directed obliquely forwards and down as is the case in the early part of the stance phase, the ground reaction has a backward directed horizontal component (hbGRF) that exerts a braking effect on the body. The horizontal component of the force that the body exerts on the ground arises from muscle contraction pushing obliquely and/or from elastic recoil forces acting obliquely. The ground reaction force is generated by the resistance of the ground to compression by the pressure of the foot.. Similarly, when the legs are directed obliquely down and back as in the latter part of stance, the ground reaction generates a forward directed hfGRF, that tend to accelerate the body forwards. By convention, we regard the direction from front to back of the body as the direction of the y axis. Relative to this axis, hbGRF has positive values while hfGRF has negative values. When the foot is on the ground, it is assumed to be stationary. This implies that there is no friction force (the retarding force generated when one surface slides over another) though it can be helpful to consider that the vertical pressure of the foot on the ground generates a property called stiction holds the foot in place. This stiction is sometimes described as static friction but it does no work to either propel or retard the motion of the body.
Figure 1 is a diagrammatic illustration of typical force plate data demonstrating the ground reaction forces along the y axis for a mid-foot runner.
The figure shows that in the early part of stance hbGRF rises initially and, after a brief drop at around 20 milliseconds, continues to rise to a peak at around 50 milliseconds and then falls to zero at 90 milliseconds after footfall. The drop at around 20 milliseconds is due to the fact that usually for a mid-foot runner, the point of support at foot fall is on the lateral edge of the foot a little in behind the ball of the foot. During the first 10 milliseconds the foot rolls inwards and the point of support moves towards the centre of the foot before the heel descends to the ground and the point of support moves backwards. As the point of support moves backwards, there is a brief drop in the forward component of force exerted by the foot and GRF exhibits the notch observed around 20 milliseconds, Then the point of support shifts forwards to the ball of the foot as the COG passes over it (at around 90 milliseconds). At that point the GRF is purely vertical and hbGRF is zero. In the remaining period before lift-off, the leg is angled down and backwards as the runner’s hip extends, and a hfGRF rises to a peak before finally falling to zero at lift-off. A more complete description of ground reaction forces is provided in the paper by Cavanagh and LaFortune (Journal of Biomechanics, 1980)
Horizontal GRF along the x axis
Because the foot must be angled inwards if the point of support is to be under the centre of mass, the foot exerts a sideways (x axis) force on the ground that elicits an opposing sideways ground reaction force, hxGRF. However, assuming symmetry, the sideways forces exerted by one foot exactly balance those exerted by the other foot so there is no net sideways impulse averaged over the full gait cycle. In any case, because it acts sideways, hx GRF cannot affect forwards momentum.
Except when running with a strong following wind, wind resistance mainly acts in a backwards direction on the body and tend to produce deceleration. Movement of the body in the vertical direction and movement of the limbs will also generate air drag, but these forces are usually very small, and in any case, tend to be reversed and therefore to cancel out over the duration of the gait cycle.
The other forces that act during running, naming the forces generated by muscle contraction, and the elastic recoil forces generated when muscles, tendon and ligaments are passively stretched, do not act on the body. Rather than act either within the body or they act on the ground thereby generating the GRF. Because they do not act on the body, they do not directly cause acceleration or deceleration of the body.
If a force F acts for a time t, then it can readily be shown from Newton’s second law of motion (F=ma) that the force produces a change in momentum given by Ft. This product of force and time is known as the impulse delivered by the force.
Balance of forces
When running at a constant velocity, Newton’s first law requires that the impulse due to forward directed forces acting over the duration of each gait cycle must exactly balance the impulse due to backwards directed forces. (It should be noted that within a single cycle, the body is often off balance. Being off balance is probably one of the major stimuli to automatic movement of the legs to stop a face down crash.)
Backward directed forces are wind resistance and the backward component of ground reaction, hbGRF, which acts while the leg is directed obliquely forwards and down between footfall and the point at which the COG passes over the point of support. The only forward directed force is the forward directed component, hfGRF, which acts when the leg is directed obliquely down and back after the COG has passed over the point of support until lift-off.
These considerations reveal two important principles.
a) In the absence of wind resistance, the impulse due to backwards directed GRF must equal that due to forwards directed GRF. The period that the foot is on the ground before COG passes over the point of support must be approximately equal to the period after the COG passes over the point of support.
If one lands with point of support directly under the COG, impulse due to hfGRF will not be balanced by a braking impulse, and the body will accelerate out of control. Thus, except in the presence of a substantial head wind, the advice to aim to land under the COG, commonly given by advocates of efficient running, is misleading. In fact, video recording of runners demonstrate that the foot does land in front of the COG even in individuals who aim to land under the COG. However, because of the different angles at the joints in early stance compared with late stance, vGRF rises more rapidly in early stance than the rate at which it decreases in late stance, to the period between mid-stance and lift off is usually appreciably longer than the period between footfall and mid-stance.
b) In the presence of wind resistance, the drag due to the wind must be compensated for hfGRF which is a reaction to a downwards and backwards push by the leg on the ground. The push against the ground must be provide either by elastic recoil of muscles and connective tissues muscle releasing energy stored as elastic potential energy following the impact of footfall, or by active muscle contraction.
When the long axis of the body is leaning forwards (i.e. when the COG is in front of the point of support) gravity acts obliquely relative to the axis of the body. Therefore, there is a component of gravity at a right angle to the long axis of body that can be considered to be acting on the COG. If the body is on stance with the foot fixed, the component of gravity at right angles to the body is will exert a torque that tends to cause the body to rotate in a face forwards and downwards direction. This situation exists during the latter half of the stance phase. However this torque does not directly facilitate forward propulsion. In fact, there is not even an increase in the speed of rotation of the body in a face-forward direction about the pivot at the point of support, on account of the opposite rotational effect of the upward vGRF acting during stance.
To appreciate this point it is helpful to consider three hypothetical situations. If the torso passes over a pivot at the point of support at constant velocity, the line from point of support to COG rotates around the pivot point in a face-forwards direction. If a net downwards vertical force acts on the COG after it has passed over the point of support, the speed of face-forward rotation would be expected to increase as the downward acceleration adds to the speed of rotation. However, if a net upwards vertical force acts, the upward acceleration of the COG makes the line from point to support to COG more vertical and thereby slows the rate at which this line rotates in a face-forward direction. Throughout most of the stance period, the net vertical force is upward. The speed of face-forward rotation about the point of support slows after mid-stance. The proposal that gravitational torque might provide free energy that facilitates forward propulsion is ill-founded.
However, to determine the effect on angular momentum one must also consider the moment of inertia. Moment of inertia resists the tendency of a body to resist rotational acceleration when acted upon by a torque. Angular momentum is the product of rotational velocity by moment of inertia. Moment of inertia is greater for a less compact object. When a pirouetting ice skater extends his/her arms the moment of inertia increases and the speed of rotation slows, while angular momentum remains constant. As the mass of the runner’s body moves further from the point of support, the moment of inertia around that pivot point increases, and as a result, it is possible for the angular momentum in the face-forward direction to actually increase even as the speed of rotation slows. Thus, in some circumstances it is true to say that angular momentum in a face-forward direction does increase after mid-stance but this effect has no forward propulsive effect. In the absence of wind resistance, an oppositely direct change in angular momentum occurred before mid-stance. In the presence of wind resistance, it is true that leaning forwards, to increase ‘gravitational torque’ about the pivot point does help oppose the oppositely directed torque exerted by the pressure of a head-wind on the body.
Running on Ice
When the coefficient of friction between two surfaces is low, and a force is applied obliquely to the interface, the ratio of vertical pressure (which promotes stiction) and the horizontal force (which promotes sliding) must be high to prevent slipping of one surface over the other. The coefficient of friction is minimal for a foot on ice. Therefore, in order to run on ice, it is essential to spend a very short time on stance, so that the long axis of the body never becomes more than very slightly oblique while on stance. This demands a very short time on stance. As well shall see in the next section, very short time on stance is associated with large vertical ground reaction forces. Nonetheless, running on ice is possible, though it is a stringent test of the ability to lift the foot from stance quickly.
While forward momentum can be maintained fairly easily provide the braking forces in the first half of stance are kept within reasonable limits, getting airborne is both consumptive of energy and risky.
Acceleration upwards requires a vertically directed force. The only external force that acts upwards on the body is vGRF (apart from a trivial contribution from air drag as the body falls). As discussed above, vGRF is the reaction of the ground as it resists compression by the vertical downwards force exerted by the body via the legs. These vertically downwards forces are body weight, and downwards push by contracting muscles or elastic recoil of stretch tissues.
How large is vGRF. When running on a level surface, the body is at the same height at the end of each gait cycle as it was at the beginning. Therefore, the net impulse due to vertical forces acting on the body must be zero. Apart from a trivial contribution from air drag as the body rises, the only external force acting downwards on the body is gravity (i.e. body weight). If Ta denotes airborne time and Ts denotes time on stance, while W denotes body weight, the downwards directed impulse arising from gravity during each stride is W(Ta+Ts). vGRF acts only during stance. vGRF is not constant during the time on stance. Nonetheless, the upwards directed force is the product of average vGRF during stance by Ts. Thus, the requirement that net vertical impulse over the entire gait cycle is zero requires that:
average(vGRF) . Ts = W.(Ts+Ta).,
Therefore, average (vGRF) = W. (Ts+Ta)/Ts
If time on stance is equal to time airborne, average vGRF is twice body weight.
If time on stance is 66 milliseconds, as is recommended in the Pose Method while cadence is 180 strides per minute (corresponding to stride duration (Ta+Ts) = 333 milliseconds, average vGRF is five times body weight. Peak vGRF will be even greater
Conclusion: If time on stance is only a small fraction of total stride duration, average vGRF is many times greater than body weight.
The central challenge of the dance with the devil
To elicit such a vGRF, a powerful downwards push by the leg on the ground is required. At least some of this downward push can be supplied by elastic recoil of tissues that were stretched at impact. However, it is likely that capture of energy impact and its subsequent recovery can only be performed efficiently if time on stance is quite short.
The improvement in efficiency with decreased time on stance presents us with the central challenge of the dance with the devil. When time on stance is short, vGRF is high. Exerting a push that is several times body weight is likely to demand strong muscles and is very consumptive of energy unless a substantial proportion of the energy released by the impact at foot fall can be stored as elastic potential and recovered in late stance to help generate the vGRF required to propel the body upwards. However, efficient capture of the impact energy and its subsequent recovery is likely to place substantial stress on muscles, tendons and ligaments, unless it is done very skilfully.
If forces many times body weight are applied very abruptly, the risk of injury is likely to be high. What is required is a finely controlled foot fall that results a large rise in vGRF over a relatively short time while avoiding a very abrupt rise.
Strictly speaking, this principle is not a direct consequence only of Newtonian mechanics, but also depends on the science of materials. The way in which structures fail when stress is applied is determined in part by the intrinsic properties of the material. For example, kangaroo tail tendon is more capable of absorbing stress without failure than any other material, but all mammalian tendon is fairly tough due to the properties of the collagen protein. The failure of a structure under load is also determined by extrinsic design of the structure. The way in which load can be transferred from the lateral edge to the medial arch of the foot in the first 20-30 milliseconds after foot fall provides increased ability to absorb stress. In the subsequent section on biodynamics we will address the question of what specific orientation of joints and tensioning of muscles might facilitate a relatively slow rate of rise of stress on foot fall. Another major factor to consider is cadence.
Because a freely falling body accelerates steadily under the constant influence of gravity, the downwards speed of the body at the end of the airborne period is much greater for a longer airborne duration. Thus, the total distance of fall during a series of many short duration airborne periods is less than that for a series of fewer longer duration airborne period of the same total duration, (This is demonstrated mathematically in the calculations page on the side bar of this blog). Thus a high cadence requires less energy expenditure in raising the body and less severe impact forces.
It is most efficient to run with a high cadence and short period on stance relative to airborne time, but the risk of injury is likely to be high unless joints are positioned and muscles tensioned at foot fall in a way that avoids very abrupt rise in vGRF
Moving the legs forwards to provide support on landing
The foot and leg must be accelerated forwards relative to the torso (and relative to the ground) in the early part of the swing phase, but then decelerated in the second half of swing so that at footfall the foot is travelling backwards relative to the torso. Once the foot is on stance, speed of the foot relative to the ground must be zero. Thus, during each gait cycle, the foot is accelerated from rest to a speed somewhat greater than the speed of the torso and then decelerated to rest once again.
The acceleration and deceleration can in principle be performed either by external forces acting on the foot (horizontal GRF) or by internal forces. Unless the body is on stance for an infinitesimally small time (which would necessarily be associated with huge values of vGRF) the legs must be angled obliquely forward and down during the first part of stance, resulting in a braking force acting on the foot and similarly, obliquely backwards and down during the second half of resulting in forward acceleration of the foot. Therefore at least some of the impulse required to accelerate and decelerate the foot and leg will be provided by external forces.
As discussed in the previous section, a short time on stance is preferable with a view to efficient capture of the energy of impact as elastic energy and the subsequent re-use of that energy to help propel the body upwards for the next airborne phase. When time on stance is short compared to airborne time, the amount of acceleration of the foot and leg necessary to allow the foot to overtake the torso in mid-swing is lower than when time on stance is a large part of total stride duration. For example, if time on stance is half of stride duration the average velocity of the foot must be twice that of the torso if the foot by the time the swinging foot passes under the COG, whereas if the time on stance is one fifth of total stride duration, the average velocity of the swinging foot during the first part of swing need only be about 20% greater than the velocity of the torso.
Thus, if speed and cadence are fixed, the energy cost of repositioning the swing leg is less when time on stance is short. However, at higher speed, the COG moves a greater distance forward while the foot is on stance, necessitating a larger range of motion of the foot during the subsequent swing phase. It can readily be shown that the energy cost of the swing for each step increases as the square of the speed. However, because the number of steps per unit distance travelled decreases as speed increases, the swing cost per unit distance travelled increases only linearly with increasing speed. On the other hand, the number of steps per unit distance (at a given speed) increases in proportion to cadence, the swing cost increases in proportion to cadence. Thus, the overall effect is that the energy cost of repositioning the swing leg increases in proportion to both speed and cadence.
Overall conclusions derived from the implications of Newtonian physics:
1) High cadence is beneficial
2) Time on stance should be small compared with airborne time (though at very slow speeds total energy cost actually increases as time on stance decreases while high cadence is maintained)
3) If time on stance is substantially shorter than airborne time, vGRF will be at least several times body weight
4) The impulse require to lift the body against gravity must be provided by a downwards push of the leg against the ground.
5) Skilful orientation of joints and tensioning of muscles at foot fall is required to minimize abrupt rise in vGRF
6) Landing in front of the COG is inevitable to balance the effects of the forward directed hGRF acting in the second half of stance.
7) The energy cost (per unit distance) of repositioning the swinging leg increases with increasing running speed and also with increasing cadence.
These principles are essential for efficient running irrespective of the specific running style adopted. In the next section, we will address the question of which specific muscle actions are mostly likely to achieve these principles efficiently and safely.