The steps of the dance: foot fall

Preamble

In the first part of this series of articles (posted in mid March 2008) we examined the way in which of Newton’s laws of motion constrain the way in which we run. This section of the series will examine the ways in which we should orient our joints and contract our muscles to run efficiently and safely in accord with the constraints of Newtonian mechanics.

It should be noted that the conclusions we draw should guide the way we judge running style objectively, such as when examining a video recording, or using specialized equipment such as a force plate or electromyography. These conclusions should not dictate the way in which we attempt to control our muscles consciously when running, because it is impossible to focus simultaneously on everything that matters, and furthermore, muscle actions that require precise timing are more effective when controlled automatically via habit than by imposition of conscious control. If we have not yet acquired the required habits, drills performed with a greater degree of conscious control might help establish the required automatic control. The issue of what perceptions we should attend to when actually running will be dealt with in a subsequent section on the psychodynamics of running.

 

Summary of Newtonian principles

In the first section of the series devoted to Newtonian mechanics, we saw that the laws of conservation of conservation of momentum and angular momentum led to the following principles:

P1) On a level surface in the absence of wind resistance, no direct net propulsive force is required to keep the body moving at a constant velocity. However, energy is required to lift the body against gravity to compensate for free fall during airborne time, and also to accelerate each leg forwards in early swing phase so that it can overtake the torso and provide support at the next footfall.

P2) When the leg is angled downwards and backwards in late stance, there is a forward-directed horizontal ground reaction force (GRF) that will propel the body forwards. In the absence of wind resistance on a level surface, this must be balanced by a backward directed horizontal GRF at some other part of the gait cycle. This will generally be provided by the braking effect in the first half of stance, provide the point of support in front of the body’s centre of gravity (COG) at that stage. Unless the foot lands in front of the COG there will be no compensation for the acceleration of he body in the late stance and hence , it will be impossible to remain in control at constant velocity. A face down crash will occur.

P3) Any force that pulls the foot forwards towards the torso in early swing phase must be balanced by a compensating force that pulls the foot backwards towards the torso after the foot has passed beneath the torso. As a result, the foot will be travelling at the same speed relative to the torso (and therefore the same speed relative to the ground if torso moves at constant velocity) at foot-strike and was the case at lift-off. If velocity relative to the ground is zero at lift off, then velocity relative to the ground will be zero at foot fall.

P4) Any external torque applied to the body at some point in the gait cycles (eg gravitation torque that arises when the COG is not aligned over the point of support) must be compensated for by an oppositely directed external torque applied at some other stage of the gait cycle. (In general, gravitational torque provides angular acceleration in a face forwards and down direction in late stance, and this must be compensated by a torque producing head back and downwards directed torque in early stance.

P5) Mean vertical GRF during stance is equal to body weight x stride duration/time on stance. This equation must be satisfied to ensure that the average upwards force over the full gait cycle exactly matches body weight.

Because Newton’s laws are immutable for bodies of human scale moving at running speed, we cannot maintain a constant speed if any of these principles are violated

 

Essentials for efficient safe running

These principles led us to the following conclusions about how we should run for optimum efficiency and safety (posted 22nd March, but repeated here for convenience).

C1) High cadence is beneficial

C2) 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)

C3) If time on stance is substantially shorter than airborne time, vGRF will be at least several times body weight

C4) The impulse require to lift the body against gravity must be provided by a downwards push of the leg against the ground.

C5) Skilful orientation of joints and tensioning of muscles at foot fall is required to minimize abrupt rise in vGRF

C6) Landing in front of the COG is inevitable to balance the effects of the forward directed hGRF acting in the second half of stance.

C7) The majority of the impulse required to accelerate the legs forward past the torso and then decelerate them to provide support at foot fall, is best provided by internal muscle action that pulls the foot forward towards the torso in early swing and backwards towards the torso in late swing.

These recommendations apply whatever running style we choose to adopt. The goal of the current article is to begin to address the question of how we should orient our joints and tension our muscles to achieve these recommendations. The connective tissues of the body (muscles, tendons, ligaments) are viscoelastic, which means that their stiffness depends on the rate at which force is applied. Therefore, it is virtually impossible to make accurate predictions about the exact consequences of any specific muscular action. The conclusions reached in this section are tentative and must be tested against experience. Furthermore it is likely that what works best for one individual in one circumstance might not be best for other individuals, or indeed even for the same individual under different circumstance.

 

Assumptions regarding behaviour of musculo-skeletal tissues

In order to proceed we need to understand how musculo-skeletal tissues react to forces. There is an extensive body of knowledge from material science and physiology that provides the principles and information needed to understand the behaviour of body tissues, but in this article, we will merely present some of the principles as assumptions. In a subsequent post, we will examine the evidence justifying these assumptions. The assumptions are:

A1) Musculo-skeletal tissues are more likely to be damaged by forces that are applied abruptly. For example, Simpson and colleagues in their chapter in Exercise and Sport Science (edited by WE Garrett & DT Kirkendall) provide references to several studies that indicate that the rate of impulsive loading might determine the risk of degenerative changes to cartilage.

A2) Tissue rupture can occur after many repeated applications of a relatively small force which is below the threshold required to cause tissue rupture on a single application. This is why repetitive strain injuries arise in tendons after thousands of repetitions of the same small impact such as is generated when playing a piano, and why metal fatigue caused ships in World War 2 Atlantic convoys suddenly broke up and sank in mid-ocean after many repeated relatively minor impacts with ocean waves.

A3) Muscles develop greater force when a concentric contraction (in which the muscle shortens as it exerts force) follows an eccentric contraction (in which the muscle is stretched by an external force while the contractile process within the muscle exerts an opposing force. This is known as the stretch shortening cycle (SSC). The effectiveness of the SSC depends on the period of time between eccentric contraction and the subsequent concentric contraction (known as the amortisation time). This probably depends on circumstance such as the size of the muscle and the stiffness of the muscle during the eccentric contraction, which in turn depends on the rate at which the external force builds up, because muscle and tendon is viscoelastic.

A typical manoeuvre that illustrates the SSC is the drop jump in which the body drops from a height (typically 50-100cm) and then rebounds into the air. On initial impact, some of the energy of impact is stored as elastic energy and then recovered as the muscle recoils. As the height of the drop increases, the height of rebound increases up to a certain optimum value and then decreases. At the optimum, the maximum amount of elastic energy is recovered in the recoil. Data collected by Ishikawa and colleagues demonstrates that the duration of the eccentric contraction of the quadriceps is around 100 milliseconds when the maximum rebound is achieved. If the leg were stiffer at impact, the optimum would be achieved at a shorter time. If it were less stiff, the optimum would be achieved at longer time. Thus, we will assume that the optimum amortisation time for human leg muscles when running is in the range 50-150 milliseconds; shorter values will apply when the leg is stiffer on impact.

The muscle actions of the gait cycle are many and the relationships between them are complex. In particular, the actions we perform at lift-off from stance place strong constraints on where and how we land at the next foot-fall. We will start by considering each section of the gait cycle in isolation and than address the question of how it should all fit together

 

FOOT-FALL

The goals

There are three goals to be achieved at footfall:

1) maximizing the capture of impact energy as stored elastic energy that can be recovered at a later stage of the stance phase,

2) minimizing the risk of tissue damage; and

3) avoiding over-striding.

 

In general a stiff spring stores elastic energy more efficiently and delivers it for re-use more rapidly than a soft spring. The connective tissues of the legs are viscoelastic which means that stiffness will be greater when the tissue is subjected to a rapidly rising force. Therefore, for maximum mechanical efficiency of elastic recoil, the joints and muscles should be deployed so that impact forces are absorbed rapidly, and the time on stance should be should be correspondingly short to allow efficient recovery of the elastic energy.

However risk of tissue damage, both short and long term, is likely to be greater if vGRF rises rapidly (assumption A1 above). Impact will stretch the quadriceps and calf muscles. This stretching is likely to cause microscopic tearing of muscle fibres, which is the most likely explanation for delayed onset muscle soreness (DOMS) experienced the day after heavy exercise. Furthermore, immediately after substantial use muscles suffers a loss of power that lasts for one or two days, consistent with the possibility that microscopic tearing has weakened the muscle. In long events, such as a marathon or ultra-marathon, in which the legs will be subjected to thousands of repeated impacts, it is especially important to minimise microscopic tearing.

Furthermore, in the case of runners who have recently adjusted their running style or are currently unfit, the risk of microscopic tearing is likely to be increased because the adjustment of muscle tension and joint position is likely to be less finely tuned.

Thus there are a variety of circumstances in which minimization of risk of tissue damage might take precedence over achievement of maximal mechanical efficiency. Under such circumstances landing might be softened so as to avoid abrupt rise in vGRF. Fortunately, under such circumstances the time optimum time scale for recovery of elastic energy will be increased, so provided time on stance is adjusted appropriately, it is nonetheless possible to retain at least a moderate level of mechanical efficiency. Thus, one consequence of the viscoelastic nature of human connective tissue is the possibility of adjusting rate of rise of GRF so as to reduce risk of tissue damage without serious loss of efficiency.

The third goal to be achieved at foot fall is avoidance of over-striding. Although many experts since (and perhaps even before) Gordon Pirie have emphasized the importance of avoiding over-striding, it is not easy to define what is meant by over-striding. For the purpose of this discussion, we will define over-striding as landing further forward than is necessary to counteract the inevitable forward directed GRF that arises from the backwards angling of the leg during the second half of stance when duration on stance is optimal for the circumstances.

One consequence of the forgoing considerations is that the optimum foot fall depends on circumstances. There is no single universally applicable description of how the joints and muscles should be deployed. While this flexibility allows for adjustment according to priorities, it might seem daunting that there are many possibilities. Fortunately, as we will see in the finals section of this series of articles, most of the required adjustments are automatic provided we focus on a few essential features.

 

Orientation of the joints

The ankle and foot
The foot human is exquisitely designed for the absorption and distribution of elastic energy to structures such as the medial longitudinal arch, and it seems sensible that when running the foot should be allowed to fall in a manner that utilizes this design, except under circumstances such a sprinting, where a high degree of stiffness of the leg is required to ensure very rapid return of the stored elastic energy. Because our main concern in this article is with middle and long distance running we will focus on the mechanism for transferring the load to the medial arch.

As the foot falls the leg must be angled towards the mid-line of the body to ensure that COG advances in a straight line. Hence the foot strikes on the lateral side. The ankle should be very slightly plantar flexed and the initial point of support a little forward of mid-foot. The foot rolls inwards (pronation) so that the load is transferred towards the medial side, and the plantar flexion of the ankle is relaxed so that the heel touches the ground, to minimise the stress on the Achilles tendon. Otherwise, the Achilles tendon would be required to support a downwards force typical several time body weight via a cantilever. There is debate about the degree to which force should be transmitted to the ground via the heel. In the manual for the Pose Method, Dr Romanov states that the heel should only lightly brush the ground. My own belief is that under circumstances where avoidance of damage to tendons and muscles is a priority (eg during a marathon or ultra-marathon) it is best to allow the heel to bear appreciable weight.

As the COG passes forward of the point of support, the ankle should remain approximately neutral but because the leg is now angled backwards, the point of support moves forward in the under surface of the foot and the foot should roll outwards slightly (supination) as recoil occurs. The process of pronation followed by supination transfers weight to the medial arch and then allows recoil that employs the stored elastic energy to provide an upwards impulse. The degree of pronation should be modest to ensure that the elastic energy is not dissipated prior to recoil.

The knee
The knee should be at least slightly flexed at footfall to ensure that the quadriceps absorbs much of the energy of he impact. If the quadriceps is quite highly tensioned prior to impact, the energy of will be absorbed rapidly. This is appropriate when sprinting but for middle and long distance runners, there should be less tension in the quadriceps allowing a somewhat greater knee flexion and more gradual absorption of elastic energy.

Where should the foot fall?

Unless wind resistance is sufficient to counteract the forward directed GRF generated in the second half of stance, the point of support at foot fall must be in front of the COG in order provide adequate braking to prevent uncontrolled acceleration. As implied in the definition of over-striding given above, the point of support at foot fall should be the minimum distance necessary to compensate for that part of the forward GRF that is not counteracted by wind resistance. The longer the duration of stance the greater the horizontal GRF and the hence the further forward the point of support should be a footfall. Thus, time on stance determines where the foot should fall.

What is the optimal time on stance? It can be shown that the energy consumed in generating the forces that elicit the horizontal ground reaction forces is proportional to velocity squared multiplied by time on stance (see calculations page – to be presented early April). At moderate and high speeds the energy cost of generating these horizontal forces become appreciable compared with the energy costs of compensating for free fall when airborne, so it is desirable to keep time on stance as short as possible. However if time on stance is too small vertical GRF becomes damagingly high and furthermore there is a risk that stored elastic energy will not be recovered efficiently.

Thus, the optimum time on stance will depend on the relative priority of speed versus minimization of damage to tissue. As discussed above in the section on assumptions, the available evidence suggests that elastic energy can be recovered with times on stance ranging from around 50 to 150 milliseconds, depending on how rapidly GRF rises.

When speed is the priority, the knee should be held fairly stiffly at foot fall leading to rapid rise in GRF and rapid accumulation and then release of elastic energy. Time on stance will be as short as 50-60 milliseconds. This time on stance will generate vGRF that is 4-5 times body weight at cadence 180 /min. As approximately half of the time on stance is spent with the point of support in front of the COG, footfall should occur approximately 25 -30 milliseconds before COG passes over the point of support. This footfall should be about 10 cm in front of the COG at a speed of 4.1 m/sec (equivalent to 4 min per Km).

When minimization of tissue damage is the priority, (eg in a marathon or ultra-marathon or for a runner with less skill in controlling a rapid rise in vGRF) it would probably be prudent to land with foot fall up to 50-60 milliseconds before the COG passes over support. Provided the knee is allowed to flex somewhat more to give a relatively soft landing, the rate of uptake of elastic energy and its subsequent recovery can be slowed sufficiently to match the time on stance. Mean vGRF will only be about twice body weight.

 

Horizontal speed of the falling foot

To minimize shearing forces in the foot, horizontal speed of the foot relative to the ground at foot fall should be near to zero. In fact provided the forwards impulse delivered while the leg was angled backwards in the latter part of the previous stance was exactly matched by the braking impulse in the first part of that stance (plus wind resistance), and also providing the accelerating impulse during early swing was matched by a braking impulse during later swing, the speed of the foot will automatically be adjusted to zero at footfall. Note that swing phase and stance phases impulses must be balanced separately, since only the stance phase horizontal forces exert a net effect on the body as a whole, and these must therefore be balanced (after allowing for wind resistance) to achieve a constant forward motion of the body.

 

Summary

At foot fall, the ankle should be slightly plantar flexed, and after initial impact on the lateral side of the foot a little in front of mid-foot, the load should be transferred to the medial arch by a small degree of pronation. The location of point of support on the sole of the foot should move slightly backwards and the heel should touch the ground before the point of support moves forward again after the COG passes over it. Finally mild supination promotes recoil releasing the stored elastic energy. The degree of stiffness of the knee joint should be adjusted according to the relative priority of speed versus protection against tissue damage. At foot fall the point of support should be in front of the COG by the minimum amount needed to provide braking to compensate for the forwards impulse delivered when the leg is angled down and backwards in late stance. This amount will depend on duration of stance, but typically the time from footfall to when the COG passes over the point of support should be in the range 25-50 milliseconds, with the shorter durations being appropriate when speed in the priority and longer duration appropriate when minimizing risk of tissue damage is the priority. At foot fall, the horizontal speed of the foot relative to the ground should be zero. This will be achieved automatically if the pairs of horizontal forces acting during the various phases of the gait cycle are well matched.

The muscle actions required in late stance and during swing phase will be discussed in future blogs.

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2 Responses to “The steps of the dance: foot fall”

  1. Simon Says:

    Canute,

    I was initially a bit concerned with the assumption that a landing forward of the COG is inevitable – not because of the physics (which I agree with), but because of the perceptive danger that a runner may allow too great a forward landing and introduce an overstride.
    However, you tackled it and showed that the amount of forward landing can be as little as 10cm which fits with observations of runners at fairly fast constant pace.
    One point that may be worth considering is that when a runner accelerates, there will no longer be the need for balanced horizontal forces and we may well see the runner’s foot striking directly under the COG.

    Good work.

  2. canute1 Says:

    Simon,
    Thanks for your comment. It is important to note that what I am attempting to describe is what an external observer or video camera would record. When running we should not try to focus on all of these features, and in particular focussing on landing in front of the COG is unlikely to be helpful. On the other hand, I believe that is best to avoid trying to create perceptions that are counter to biomechanical principles (eg consciously attempting to land under the COG). In a later article, I will attempt to formulate recommendation for the perceptions that we should focus on, and will try to ensure that these do not actually conflict with biomechanical principles.

    With regard to what happens when we are actually accelerating, I agree with you. Landing under or even behind the COG will create a strong impetus to get the legs forward quickly to prevent a face down crash, and hence will help us accelerate. Acceleration is a major feature of sprinting, but in longer runs or races, the priority is on efficiency and minimization of injury at constant speed (except maybe in the final few hundred metres of a close race).

    Canute

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