The steps of the dance: 3. Swing Phase

SWING PHASE

The goal of early swing is to get airborne and accelerate the leg forwards on a trajectory that will allow it to overtake the torso by mid-swing. While it is essential that the foot should accelerate in early swing, it should be borne in mind that it must decelerate in late swing if it is to have zero horizontal velocity relative to the ground at foot-strike. It might seem at first sight that the need to match an energy consumptive acceleration with a deceleration that will also consume energy should encourage us to be conservative in the generation of acceleration. However, this would be a very misleading conclusion. Our ability to generate adequate forward acceleration of the foot in early swing determines our ability to maintain a particular target speed.

The crucial role of acceleration of the leg in early swing
To understand why forward acceleration of the leg in early swing is crucial, we need to return to basic biomechanical principles. In the earlier posts in this series in which we considered the implications of Newtonian physics we reached the conclusion that cadence should be high and time on stance should be short. Except at very slow speeds, cadence should be near the limit determined by the optimum speed of contraction of muscles. Observation of elite runners suggests the optimum is a cadence in the range 180-200 strides per minute. Elite athletes employ a cadence in this range for all except very slow paces.

Furthermore, time on stance should be as short as can be tolerated, after allowing for the fact that ground reaction forces and risk of tissue damage increase dramatically as time on stance becomes very short. Elite athletes tend to spend only about 50-100 milliseconds on stance, with the longer times being applicable in long events where protection of muscles from damage due to repetitive impacts in important. Apart from these relatively small variations, cadence and time on stance are fairly consistent over a range of paces extending from 1500K pace to marathon pace. Therefore, over this range of paces, the major variable that increases as pace increases is stride length.

As shown on the calculations page accessed via the side bar, the work that must be done against gravity (per unit of time) is determined by cadence, time on stance and body weight. The energy required to lift the body is not directly influenced by stride length. However, increase in stride length must be matched by an increase in the amount of acceleration required to bring the foot forward fast enough to support the body at foot fall. Thus, it is ability to accelerate the leg in early swing phase (and then decelerate it again in late swing phase), that is the main determinant of our ability to maintain a high pace. So how should we do this?

Breaking contact with the ground
In late stance the elastic recoil of quadriceps, augmented by concentric contraction, has imparted an upward impulse to raise the centre of gravity and hip extension has preloaded the hip flexors (e.g. psoas). As the body rises, an active contraction of hamstrings lifts the foot from the ground. Contraction of the hamstring alone, when the hip is already extended, will produce flexion at the knee, pulling the foot up wards behind the line from foot to hip. While this is the path of the foot observed in many athletes, if the main goal is to accelerate the leg forwards, the hamstring contraction should be accompanied by hip flexion.

Accelerating the leg
Fortunately, the preloading of the hip extensors (i.e stretching associated by eccentric contraction) during hip extension in late stance can be utilized to facilitate a powerful recoil associated with concentric contraction of the hip flexors that accelerates the leg forwards.

Deceleration of the leg
However, the price paid for this powerful forward acceleration is the need for a powerful deceleration in late swing, provided by an eccentric contraction of the hip extensors. This is stressful for the hamstrings, and suggest that exercises such as hip swings might play a useful role in conditioning the body during training.

As the hip extensors decelerate the leg, the lower leg and foot should be allowed to swing down to that the knee is only mildly flexed, in preparation for footfall. The combination of contraction of hip extensors and relaxed un-flexing of the knee present a challenge. Because the hamstrings cross both hip and knee joint, pure hamstring contraction to decelerate the leg would prevent the relaxed swinging of the knee. Therefore it is essential to use gluteus maximus to assist in the deceleration of the leg. In addition, some contraction of the quadriceps might also be used to un-flex the knee, but this should be done very sparingly, as vigorous contraction of quadriceps at this stage is likely to result in over-striding.

In summary

Contraction of the hamstrings will help break contact with the ground as the body rises under the influence of the upwards impulse generated by recoil and quadriceps contraction in late stance. However, the ability to accelerate the leg forwards in early swing phase (and then decelerate it again in late swing phase), is the main determinant of our ability to maintain a high pace. Rapid forward acceleration of the leg in early swing might be achieved by employing the preloading of the hip flexors (e.g. psoas) that occurred during late stance to facilitate a powerful contraction of the hip flexors. However, this must be matched by a deceleration produced by contraction of hamstrings and gluteus maximus in late swing, allowing the foot to drop to the ground with the knee slightly flexed and travelling with approximately zero horizontal velocity relative to the ground.

The Steps of the Dance: 2. Stance

Preamble

The early articles in this series examined the constraints that Newton’s laws of motion place on the way in which we run. The most recent article, posted on 31^st March examined the question of how we should orient the joints and tension the muscles at foot fall in order to capture the energy of impact as elastic potential energy, while minimizing the risk of damage to muscles and other tissues. This article examines the actions that occur during stance.

STANCE

Following foot fall the foot remains stationary on the ground, anchored by friction, while the COG passes over the point of support. Then as the COG continues forwards the hip extends until lift-off. We will use the term early stance to describe the period from foot fall to point where COG passes over point of support, and late stance for the period from the passing of the COG over point of support to lift off.

The preceding article in this series discussed the mechanisms by which a substantial portion of the energy of impact at footfall is converted to elastic potential energy, stored in quadriceps, calf muscles and the connective tissues of the foot. During late stance the elastic potential energy is recovered and contributes to the generation of the impulse required to get airborne at lift off.

 

While the main task that must be performed during stance is the generation of the upwards impulse required to get airborne, there are also a number of important subsidiary actions, including:

- generation of horizontal GRF.

- subjecting the hip flexors to eccentric contraction preparing them for the task of accelerating the leg forwards in early swing phase

- subjecting the hip rotators to eccentric loading in preparation for the rotation around the long axis of the body during swing phase

- preventing the unsupported hip from dropping and tilting the pelvis.

These actions are mostly performed automatically when running, but understanding them is important to allow us to develop strength and resilience in the muscles and other connective tissues, and to identify faults that might cause injuries. In particular, it is important to identify the muscles that undergo a large change in length during the gait cycle, as flexibility exercises might profitably be employed to maintain as these muscles and their tendons in a pliant state. In contrast, those muscles which exert large forces over relatively short distances are generally better maintained in a stiffer state.

 

Generation of the upwards impulse.
The only upwards directed external force acting on the body is the vertical component of Ground Reaction Force (vGRF) and hence this force is responsible for lifting the body. vGRF is a reaction by the ground as it resists compression by a downwards directed force exerted though the foot. It should be noted that pulling the foot towards the hip (like pulling on ones own boot-straps) cannot lift the body.

About 50% of the energy required to become airborne might be derived from elastic recoil of quads and calf muscles. The knee had been initially slightly flexed at footfall and then flexed even more as the impact energy was absorbed in early stance; as this flexion occurs the quadriceps undergo a moderate eccentric contraction , then in late stance, recoil augmented by the concentric contraction of the quadriceps straightens the leg, and imparts an upwards impulse to the body.

Similarly, the recoil in the calf abolishes the mild dorsiflexion of the ankle that had developed by midstance and re-establishes the mild degree of plantar flexion present at footfall. The pronation of the foot in mid-stance is replaced by slight supination.

 

Generation of horizontal impulse
As the hip extends in late stance, the predominantly downwards directed forces exerted by the leg on the ground inevitably have a small backward directed component, which is resisted by friction, thereby generating a forward directed horizontal GRF. This will propel the body forwards against wind resistance – but unless there is a strong head wind, this forward propulsion is usually excessive and the excess must be matched by braking in early stance (as discussed when we addressed the question of where the foot must land at footfall). Apart from the contribution that overcomes wind resistance, the impulse due to horizontal GRF does not achieving any useful purpose. Therefore this impulse should be minimized as far as is feasible by lift-off from stance which is as rapid as possible (bearing in mind that stance must be long enough to allow the generation of adequate vertical impulse without necessitating very high and potentially damaging vGRF

 

Preloading the hip flexors
Immediately after foot fall the hip extensors (mainly gluteus maximus and the hamstrings) will undergo a degree of eccentric contraction as impact forces are absorbed. In mid and late stance, the elastic energy stored during eccentric contraction will be released in conjunction with moderate concentric contraction of the hip extensors. In addition there will be a strong impetus to passive extension of the hip as momentum carries the COG forwards beyond the anchored foot. Thus there is an almost effortless extension of the hip which stretches the hip flexors, priming them for a powerful concentric contraction in early swing phase that will help propel the foot and leg forwards to overtake the torso. Because the hip flexors, predominantly psoas undergo a major change in length, these muscles should be maintained in flexible, pliant state. The hip flexors are perhaps the most important muscles for a runner to maintain in a flexible, pliant state.

Preloading the hip rotators
In late stance, as the torso moves forwards leaving the support foot behind, not only is there passive extension of the hip but there is also a passive (external) rotation of the hip about the long axis of the body because the hip on the supported side is tethered via the leg to the ground while the other hip is free to move with the torso. Thus the internal rotators of the hip are subjected to an eccentric contraction which primes them for an internal rotation after lift-off that will help increase stride length.

 

Supporting the pelvis
The unsupported hip tends to drop, causing the pelvis to tend swing inwards towards the supporting leg. This adduction of the hip must be opposed by the hip abductor muscles of the supporting leg. The main abductors are gluteus medius and gluteus minimus, assisted by tensor fascia lata (TFL), a long muscle running down the outside aspect of the thigh from the rim of the pelvis to attach to the tibia via the iliotibial band (ITB). If gluteus medius is weak, TFL is called upon to bear too much of the load in prevent the pelvis from tilting. Excessive tension of the iliotibial band creates a risk of friction at the point where the ITB passes adjacent to the bony protrusion (femoral condyle) on the lateral aspect of the knee. Excessive eversion of the ankle, which tilts the tibia (shin bone) outwards at the knee also increases the friction on ITB. Increased friction may lead to painful inflammation (ITB syndrome).

 

 

In summary

The quads and calf muscles undergo eccentric contraction in early stance thereby storing much of the energy of impact as elastic energy. In late stance, recoil of these muscles, aided by moderate concentric contraction provides the impulse required to accelerate the body upwards against gravity. The other major muscle action during stance is hip extension. Some of the impact energy is absorbed in an eccentric contraction of the hip extensors (gluteus maximus and hamstrings) which subsequently recoil while undergoing concentric contraction in late stance. Hip extension is further promoted by passive extension generated by the momentum of the torso. The resulting hip extension pre-loads the hip flexors preparing them for a powerful hip flexion to accelerate the leg forwards after lift-off. Other important actions are external rotation of the hip that preloads the internal rotators, and hip abduction that prevents tilt of the pelvis.

In the next article in this series we will examine the actions occurring at lift-off and during swing phase.

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 22^nd 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.

The laws of the dance: part 2

Preamble

This posting is a continuation of the article examining the constraints that the laws of Newtonian physics place on how we run. In the introduction to this series of articles, posted on 18th March 2008, it was pointed out that being airborne for part of each stride is the defining feature of running. A posting on 21st March examined the nature of the forces acting on the body of a runner, and in particular, addressed the question of what is required to maintain forwards momentum. This posting addresses the implications of Newtonian physics for how a runner gets airborne.

The full series of postings is assembled in order of posting in the page ‘Running: a dance with the devil’ accessible via the side bar of this blog.

 

 

Getting airborne

While forward momentum can be maintained fairly easily provided 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 form 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 the energy of impact and its subsequent recovery can only be performed efficiently if time on stance is quite short .

It should be noted at very slow speed, if we attempt to maintain a high cadence (eg 180 /min or more) the increasing energy cost of raising the body against gravity as time on stance decreases and airborne time increases, results in an increased net energy cost with shorter time on stance. Therefore at slow speed, it is inefficient to spend only a very short time on stance. (The calculations that demonstrate this are complex, and must take account of the energy required to generate horizontal GRF in addition to the energy costs of lifting the body ; I will post an example of such calculations in the calculation page accessed via the side panel in the near future).

The improvement in efficiency with decreased time on stance (at all except very slow speeds) 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 hep 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.

 

Optimum 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.

 

Interim conclusion

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 in 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 during the time from lift off to mid-swing when 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.

 

These consideration demonstrate that despite the fact that some of the acceleration and deceleration of the foot and leg must be done by hGRF (which is a reaction to the horizontal component of push upon the ground during stance) it is preferable that the majority of the acceleration and deceleration should be done by contraction of muscles so as to pull the foot towards the torso. In the first half of swing, such a pull will accelerate the foot and leg; in the second half of swing, such a pull will decelerate the leg. It is also important to note that just as the magnitude of the forward impulse by external forces (hfGRF) must be equal to the backward directed impulse by external forces (nbGRF), similarly , the acceleration due to pull in the first half of swing must be matched by an equal deceleration by pull of the foot back towards the torso in the second half of swing.

 

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 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 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

Dancing with the devil: the laws of the dance, part 1

As discussed in the introduction to this series (posted on 18th March 2008) 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 e 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), 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 is .

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 constant forwards velocity

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:

Gravity
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 cgm 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 force of friction, which we assume for the present discussion is adequate to stop the foot slipping. 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 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

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)

Horizonatal 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.

Wind resistance
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.

Other forces
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.

Impulse
If a force F acts for a time t, then it can readily be shown from Newtons 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 GOG 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.

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.

Gravitational torque
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 right angle to the body that can be considered to be acting at the site of the COG. If the body is on stance the foot is 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.

If a face-down crash is to be avoided, this rotation must be reversed at some other point in the gait cycle. Torque can only be applied by an external force acting on the body. The only tow such forces that might reverse the rotation are wind resistance and the oppositely directed gravitational torque that will be generated when the COG is behind the point of support.

We have already seen that in order to avoid uncontrolled acceleration in the absence of a strong head wind, it is essential to land in front of the COG. The need to cancel rotation provides an additional reason why we must land in front of the COG.

Running on Ice
Horizontal ground reaction force is due to friction which arises in reaction to the horizontal component of forces acting obliquely down the leg . Friction is minimal 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.

This article will be continued in a subsequent post.

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. Beyond a certain stride length, efficiency falls due to poor leverage of muscles on awkwardly angled legs. 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.

(Subsequent articles in this series will be posted over the next few days)

Time on stance; recovery of elastic energy; and risk of stress fracture

On Jan 5^th, I discussed the question of how long should be spent on stance, and reached the tentative conclusion that it is best to be fast enough off stance to avoid unnecessary waste of energy sustaining the isometric contraction of calf and quadriceps muscles, but not so fast as to cause dangerously high vertical ground reaction forces. Today, I want to return to this issue and attempt to make an estimate of the minimum time on stance to allow efficient and safe recovery of elastic energy. This requires a consideration of the processes by which elastic energy is distributed within the foot, and also the risks associated with metatarsal stress fracture when vertical ground reaction force (GRF) is high.

First, why do we need to spend any time in stance at all? The essence of running (in contrast to walking) is that when running we are airborne for part of the gait cycle. This allows a longer stride length and hence, for a given cadence, a faster pace. However, being airborne comes at a price. While airborne, we fall freely under the influence of gravity and therefore must use energy to recover the height lost while falling. Furthermore, if we let our bones absorb the impact force arising from the free-fall, we would produce heavy jarring and inevitable damage to bones and joints. Fortunately the human body has a well developed mechanism for absorbing energy of impact in muscles and ligaments in early stance, and then releasing this in late stance, thereby improving efficiency and lowering the risk of injury. I believe that one the major goals of developing an efficient running style is adjusting the time on stance to optimise this process of storing and recovering the energy of impact efficiently and safely.

 

Absorbtion of the energy of impact

If we land with slightly flexed knee and with the heel off the ground, impact will stretch the quadriceps and the calf muscles. If we are to avoid risk of tearing these muscles, and the tendons that attachments them to bone, the impact force must be absorbed gradually. Furthermore, to avoid too much stress on the Achilles tendon, it is almost certainly necessary to let the heal touch the ground in mid-stance so that part of the energy can be stored in the ligaments that maintain the longitudinal arch of the foot. Impact tends to occur on the outer edge of the foot, because of the inclination of the leg necessary to ensure the foot is near the mid-line at foot strike, so the first action after foot-strike is pronation, a rolling the foot so that the weight is transferred towards the inner edge and onto the longitudinal arch. Then the heel drops allowing the arch to take some of the load. How long does this take? The force plate data for mid-foot runners collected by Cavanagh and LaFortune (Journal of Biomechanics, 1980) indicates that this process takes somewhere in the order of 40-50 milliseconds.

Preparation for lift-off

How long does it take to recover this stored elastic energy in the latter part of stance? One way to answer this question is to invoke the principle that we need to maintain GRF as near to constant as is possible while on stance to avoid sharp and potentially injurious peaks in GRF. As the amount of upward impulse delivered in the latter part of the stance period must equal the downward impulse that follows foot-strike, if we want to maintain near constant GRF, then the time spent developing the impulse that promotes lifting-off should be similar to the time spent absorbing the energy at impact. (Impulse is given by the product of force by time. If force is to be near constant, the time interval should be similar). So the minimum time for the second phase of stance should also be around 40-50 milliseconds. This limit might be over-ridden by a very sharp pull from the hamstrings but if we do this, we might fail to use elastic recoil fully.

Ground reaction forces

So far, we have estimated that we should aim to spend a total of at least 80-100 milliseconds on stance (It should be noted that these estimates are only approximate, but they allow is us to explore the principles.) However, we must also consider the influence of time on stance on the average value of the vertical GRF. As discussed on my article on the mechanics of running (see the side bar) the average GRF over the entire gait cycle must be at least equal to the body weight, if the body is to be supported. Therefore, the average GRF over the time on stance must be greater than body weight by the ratio of total duration of the gait cycle to the time on stance. At a cadence of 180 strides per minute, the stride duration is 333 milliseconds, so a time on stance of only 100 milliseconds would generate an average GRF of over three times body weight, and the peak GRF might be somewhat higher unless the force was maintained at a very uniform level throughout stance.

Stress fracture

What are the likely consequences of such high values of GRF? One issue to consider is the risk of metatarsal stress fracture. Metatarsal stress fracture is a relatively common injury in army recruits (‘march fracture’), dancers and runners.

It is instructive to consider march fracture. Traditionally, this was observed in new recruits to the army who are required to march for long distance carrying a backpack. In a soldier marching with a back-pack of 50 lbs, his effective weight is increased by about one third. When marching, one foot is always on the ground, so peak GRF is unlikely to rise by more than about 30-50% compared with standing still. Therefore, overall GRF is probably no more than twice that when standing still on one leg without a back-pack. A force of this magnitude applied briefly on one occasion would not be expected to cause a fracture of a metatarsal. So why is the new recruit at risk of march fracture?

The major issue is that stress fracture occurs from repeated application of a force that is substantially less than that required to break the bone during single impact. In this respect, it is analogous to the metal fatigue that caused ships in the Atlantic convoys during World War Two to break up and sink in mid-Atlantic. It was the repeated application of the relatively minor forces associated with bucking over the ocean waves that did the damage. Bone also suffers fatigue and fracture after repeated relatively minor stress.

The first important conclusion is that GRF of no more than twice body weight might cause stress fracture, at least in new recruits, when it is applied repetitively during a long march. However, it is recognised in military circles, that it is the new recruits who are most at risk, not the seasoned veterans. It is probable that for new recruits, muscles such as the peroneal muscles became less able to sustain the arches of the foot as they become more tired, so the ability of the foot arch to distribute the load is diminished. Perhaps even more important is the fact that bone can adapt to repeated stress by redistribution of bone mass, thereby effectively providing internal struts that increase the capacity of the bone to bear weight. Thus it is probable that seasoned soldiers are less at risk from march fracture because they have developed greater muscle and bone strength.

This discussion of march fracture makes it clear that we would be very unwise to attempt to run long distance with GRF much greater than twice body weight until we have developed strong muscles and bones. At cadence 180 strides per minute, this would require a time on stance of about 165 milliseconds. This is at least 60 milliseconds longer than the minimum we estimated for the distribution and recovery of elastic energy in the foot, while on stance. During this extra 60 milliseconds, the quadriceps and calf muscles will consume energy maintaining isometric contraction, thereby decreasing efficiency. We could of course decrease GRF for a given duration on stance by increasing cadence, but maintaining a very high cadence fro a long period will require well developed muscles.

Conclusion

So where does this leave us. First of all, it is clear that aiming for times on stance of less than around 165 milliseconds for long distances is likely to create a substantial risk of metatarsal stress fracture unless muscular strength and bone strength have been developed. Maybe no sensible runner would attempt this, so this cautionary tale might appear unnecessary. However, at this stage, we know very little of how much training is required to develop adequate muscle and bone strength to sustain repeated impacts of three times body weight or more over long distances. Almost certainly we can afford to spend less than 165 milliseconds on stance once we have acquired reasonable fitness. What target should we aim for?

A reasonable goal for Pose Method runners is sometimes suggested to be around 132 milliseconds (4 video frames at 30 frames per second). As the members of the PoseTech forum (http://posetech..com) will be aware, one of the most experienced Pose coaches who advises on that forum suffered a stress fracture despite several years of substantial training and drilling. Maybe in this case there was some incidental factor that is unknown to me. However, this instance, together with the fact that metatarsal stress fractures are recognised to be a relatively common injury amongst runners would suggest that we should be cautious about aiming for time on stance less than 130 milliseconds when running long distances, unless we are confident that we have very well developed strength in muscles and bones. We might pay a small price in extra energy consumed in maintaining isometric contraction in quads and calf muscles, but in my opinion, this price is probably worth paying. Furthermore, it should be borne in mind that if time on stance is much shorter than this, we might suffer inefficiency due to failure to fully recover stored elastic through recoil. In my view, a simple recommendation to spend as little time on stance as possible without consideration of these issues is misleading and potentially dangerous.

Why elite runners land in front of their COG

One of the strong beliefs within most of the schools of efficient running that developed subsequent to the ground breaking attempts of Gordon Pirie to understand how to run efficiently, is the belief that one should aim to land with the foot travelling backwards relative to the centre of gravity of the body (COG) so that the foot is travelling at zero velocity relative to the ground at foot-strike. This would be expected to avoid a braking action that is both wasteful of energy and also raises the risk of injury. Pirie is emphatic: ‘Over-striding is one of the most common technical afflictions of runners and is one of the most dangerous’ (Pirie, Running Fast and Injury Free, p18). However, observation of elite athletes reveals that at footfall the point of contact is in fact usually in front of the COG.

Some coaches have tended to relax the demand to land under the COG and have suggested that it might be best if the foot lands a little in front of the COG. For example, in a comment on my blog ‘Where should the foot land’ posted on January 2^nd, Pose runner Bill McGuire, said:

‘Jack Becker, who is the main guiding voice on the Pose forum, has suggested a few times that landing a little in front of the COG is acceptable. I can’t say for sure, but I suspect his reasons are based on his formidable intuitive feel for Pose more than on mathematics.’

I too have a great respect for Jack Becker, and I believe his intuition is correct. My reasons are based on the principles of rotational motion. The issue can be discussed without mathematical formula, but it does require at least an intuitive understanding of Newtonian mechanics. Fortunately, at least with the hind-sight available to us in the modern world, most of Newtonian mechanics appears intuitively correct. Certainly Newtonian mechanics appears more in tune with common-sense that Einstein’s relativistic mechanics which superseded it. The reality is that for human-sized objects moving at running speed on the surface of the earth, Newtonian mechanics provides an excellent description of reality. So, let us re-examine the issue that I addressed in my blog on January 2^nd in a little more detail

In the language of Newtonian mechanics, the arrest of the foot on the ground at foot-strike interacts with the impetus of the forward momentum of the torso to create a torque (a ‘twisting effect’) that results in rotational motion. That is, when the torque is applied, the angular momentum of the body increases. It is crucial to appreciate that a torque can only be applied by contact with an external object such as the ground. Re-arrangements of the relative placement of limbs without leverage on the ground cannot change the angular momentum. When the moving body contacts the ground, angular momentum can be imparted to the body. The angular momentum of the body will then remain constant unless another external torque acts on it. This is the law of conservation of angular momentum (see http://en.wikipedia.org/wiki/Angular_momentum).

If the initial torque is uncorrected, this rotational motion will result in a face-down crash within a few strides. In conclusion, during the period of stance, there must be an initial period in which the foot is arrested and a ‘head forwards and down’ rotation is generated, and this must be followed by a subsequent time interval in which an opposite torque is applied.

The angular momentum imparted will only be appreciable if the torque is applied for an appreciable length of time. In theory we might avoid the problem of rotation if we could support ourselves using only an instantaneous touch down. But an instantaneous period on stance would result in infinite vertical ground reaction force to ensure that the weight of the body can be supported. Therefore, we must remain on stance for an appreciable time. If vertical GRF is to remain less than three times body weight, we must be on the ground for at least one third of the gait cycle.

Where must the foot fall? The first thing that must happen during stance is the foot must be arrested. To achieve this, the ground reaction force must be directed backwards. This can be achieved by landing slightly in front of the COG, so the downwards pressure of the impact is directed downwards and slightly forwards. This induces a backwards directed ground reaction force (GRF) that arrests the foot and the lower leg. Once the COG has passed over the point of support, the downwards force exerted by the body on the ground is directed obliquely backwards, generating a forwards directed component of GRF. As discussed in my post earlier today, the impulse imparted to the foot by this forward directed ground reaction force is almost adequate to accelerate the foot and lower leg to a forward velocity matching that of the torso. Angular momentum is conserved. Rotation is corrected and very little energy is lost. Nonetheless, it is crucial to appreciate that unless we land in front of the COG, a face down crash will eventually occur. These considerations suggest that attempting to land immediately beneath or behind the COG is not only pointless, it is potentially injurious.

What observational evidence supports this conclusion? As mentioned previously, elite athletes such as Haile Gebreselassie tend to land with their foot in front of the COG. What happens in elite athletes who employ the Pose style? Recently Jeremy Huffman, elite sub-4 minute miler who has subsequently adopted Pose (and generously offers expert advice on the PoseTech forum and elsewhere) posted some excellent pictures of himself taken during early and mid-stance, on the Fetcheveryone website (http://www.fetcheveryone.com). In the picture taken very slightly after mid-stance (when the leg is bearing the maximum load) the point of support (the ball of the foot) is slightly behind the COG. However, in the earlier pictures, the point of contact of the foot with the ground is clearly in front of the COG. We cannot easily estimate how much ground reaction force is being exerted in the period before the COG passes over the point of support from these pictures. However, force plate data acquired by Cavanagh and LaFortune (Journal of Biomechanics, 1980) provide a strong clue. In the runners who landed on mid-foot there was a horizontal backward directed ground reaction force acting during the period from first contact with the ground until the point of maximum load bearing. After that time, the horizontal ground reaction force is reversed. A similar phenomenon was observed in heel strikers, though the shape of the GRF curve was somewhat different. As predicted in light of the law of conservation of angular momentum, in both mid-foot strikers and heel strikers, the average value of the backward directed GRF in the first part of stance was approximately equal to the average value of the forward directed horizontal GRF acting in the final part of the stance phase.

If we accept that it is inevitable that we must experience a braking force early in the stance phase, how can this be done safely? As recently suggested in the Fetcheveryone discussion of efficient running by coach emjaybee, the really important goal is having the knee flexed so that the point of foot contact is behind the knee joint. This will facilitate absorption of much of the impact energy in the quadriceps muscles, allowing for subsequent recovery of the energy at lift-off, and minimizing injurious jarring of the knee and other joints. (http://www.fetcheveryone.com).

Does leaning help us run faster?

In my blog of Jan 10^th I discussed the fact that we cannot obtain free energy from gravity while running on a level surface. Both the Pose Method of Running (http://posetech.com) and Chi running (http://www.chirunning.com) advocate a forward lean from the ankles, on the grounds that such a lean promotes unbalancing which supposedly helps the runner capture the hypothetical supply of free gravitational energy. The reality of this source of energy appears to be confirmed by the experience that you can speed up if you lean more. So, if gravitational free energy is an illusion, do we go faster if we lean more, and if so, why?

Initial acceleration
The first point is than lean certainly helps us get started from rest. A sprinter driving from the blocks leans forward in a seriously unbalanced position and is forced to swing the legs forward powerfully to prevent a face down crash. Even when a long distance runner starts from a standing position, it is probable that a transient forwards lean creates the initial unbalancing that evokes the commencement of forward movement.

Maintaining a steady velocity
Once we are moving forwards at a steady velocity, momentum ensures that the torso continues forwards relative to the foot while the foot is on stance, so an unbalancing rotation of the body forwards and downwards will occur without the need for input from gravity. The second calculation on the calculations page (see the side bar) demonstrates that at least during the early part of the time on stance, when the amount of lean is small, and the hip is not far from a neutral position, any contribution from gravity to the rotational motion associated with unbalancing is much less than the contribution from forwards momentum in a runner moving at a moderate speed. I suspect that this will remain true even up to the largest degree of lean occurring in a long distance runner running at steady pace. Irrespective of whether the unbalancing arises primarily from the effect of linear momentum or from gravity, the forward and downwards rotation will result in lean and raises the question of whether or not deliberately accentuating the lean will cause us to go faster.

Lean might lead to increased speed by two mechanisms.

 

The impulse from horizontal ground reaction force.

In the final part of the stance phase, lean will result in the leg pressing down obliquely on the ground. This oblique push will have a backward directed horizontal component that will in turn lead to a forward directed ground reaction force (GRF). Force plate measurements confirm this, revealing a forward directed GRF typically lasting around 100 milliseconds before the completion of lift-off and reaching a peak value that is typically 0.45 times body weight (Cavanagh and LaFortune, (Journal of Biomechanics, 13, 397-406, 1980). This forward directed GRF will impart an impulse to the foot that will tend to propel the foot and lower leg forwards.

On the calculations page (see side bar) I have estimated the increase in forward momentum of the foot and lower leg after lift-off from stance, and compared this with the impulse imparted by the horizontal component of GRF measured by Cavanagh and LaFortune. This computation is only intended to provide an imprecise estimate of the acquired momentum. It reveals that the horizontal GRF observed in runners who land on the mid-foot is sufficient to generate about 90% of the forward momentum attained by the foot and lower leg following lift-off from stance. It should be noted that runners using different running styles might generate differing amounts of horizontal GRF, though in fact Cavanagh and LaFortune found very similar forward directed GRF in heel-strikers during this late part of the stance. (As expected, during early stance, the heel-strikers showed an additional sharp peak of vertical GRF suggesting a sharp and potentially damaging loading of the structures of the leg).

Thus it appears plausible that the forward directed horizontal GRF generated when the leg presses obliquely downwards in the late part of the stance delivers a sufficient impulse to the foot to provide for the majority of the momentum gained by foot and lower leg during lift-off.

 

Reflexive pull
The unbalancing associated with leaning will elicit a reflex that pulls the leg forwards to prevent a face-down crash. Thus, any additional force required might be generated by a reflex action, or indeed by a voluntary pull . In particular contraction of the hamstrings, supported perhaps by some action of hip flexors, will pull the foot towards the hip, thereby proving both horizontal propulsion of the foot and lower leg and also vertical elevation.

 

It should be noted that in addition to gaining forward momentum, the foot and lower leg will gain gravitational potential energy as they are lifted vertically. This lift will be generated by an upwards force supplied in part by the vertical component of GRF (which will include a contribution from the reaction to elastic recoil by achilles and calf muscles) and also by the vertical component of the active pulling of foot towards the hip.

Conclusion
Increasing the lean will increase both of these two effects (the impulse derived form the from horizontal GRF and the tendency for unbalancing to elicit an active reflexive pull). Thus deliberately increasing the lean should result in the legs moving forwards powerfully enough to sustain a higher speed of running.

 

Does gravitational torque matter?

When the foot is on stance, the body becomes unbalanced due to two effects:

1) Inertia due to the forward linear velocity of the body will cause the body to lean forwards.

2) As the body begins to lean, the downwards force of gravity is now acting at an angle to the axis of the body, and will exert a torque that increases the speed of rotation (that is, an increase in angular momentum)

 

According to the theory of the Pose technique developed by Dr Romanov (http://www.posetech.com) this gravitational torque provides useful forwards propulsion. However, as discussed in my blog on 2 Jan, if this forward acceleration is not corrected at some point in the gait cycle by a torque acting in the opposite direction, the angular momentum will continue to increase with each stride. If the effect is of substantial magnitude, a face down crash would be expected after a few strides. On Jan 2, I speculated that it might be necessary to land in front of the COG to avoid this problem.

 

However, an alternative possibility is that the effect of gravitational torque is negligibly small and can be ignored. On the calculation page, I have posted a calculation of the magnitude of the increase in angular momentum during a single stride, for a runner travelling at 5 metres/sec (corresponding to a marathon time of about 2 hours 21 min). The calculation is the second of the calculations presented on the calculation page in the side bar of this blog.

 

The increase in angular momentum during a single stride is 0.2 per cent of the angular momentum arising from inertia associated with forward linear motion. This calculation assumed that the runner remains on stance long enough to increase lean by 6 degrees. If the time on stance is long enough to increase lean by 10 degrees, the increase in angular momentum will be about 0.4 per cent per stride. This suggests that it is mainly linear momentum that keeps us going (provided we move our legs forward quickly enough) and that gravitational torque will have a minor effect compared with other factors such as wind resistance. Therefore, we need not be too concerned about the need to reverse this torque at some other stage in the gait cycle.

 

While this is re-assuring, it appears to me to raise concerns about the role of gravitational torque in the theory of the Pose technique.