Archive for January, 2008

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

January 19, 2008

On Jan 5th, 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

January 13, 2008

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 2nd, 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 2nd 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?

January 13, 2008

In my blog of Jan 10th 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.

 

Gravity and running

January 10, 2008

 

‘The great runner is not impervious to gravity; instead he taps it as a readily available source of free energy.’ Nicholas Romanov, founder of the Pose Method (in ‘Pose Method of Running, 2004 edition p62,)

‘All you’re doing is this (focussing on the central needle – the core of the body); gravity is doing the rest. You let gravity do its job and you get out of the way. The only thing the legs are for is for momentary support’ Danny Dreyer, founder of Chi Running,
http://www.youtube.com/watch?v=e-zrH6IOTQI

 

How should we to interpret these key statements of the theoretical foundations for Pose method and for Chi running. These statements cannot be literally true for running on a level surface. They violate the law of conservation of energy. As an object moves, the change in potential energy due to gravity is proportional to the change in height (http://en.wikipedia.org/wiki/Gravitational_potential_energy). If the height of the body’s centre of gravity at the end of each stride is the same as that at the end of the previous stride, there is no change in gravitational potential energy. The law of conservation of energy requires that any energy supplied by gravity at some part in the gait cycle must be re-paid at some other point in the gait cycle, and gravity cannot do the work required to keep us running.

My own belief, reinforced by the opinions of experts such as Dr Tim Noakes of Cape Town University, is that Dr Romanov has a remarkably good intuitive grasp of good running style, and hence his teachings should not be abandoned wholesale because one of his key theoretical statements appears mechanically unsound. So, how are we to interpret these statements about gravity?

If they cannot be accepted as literal truth, do they have any truth? Consider the saying: ‘the way to a man’s heart is via his stomach’. If this statement appeared in a training manual for aspiring cardiac surgeons, it would lead to surgical catastrophe, but in a ‘good home-makers guide’ it might lead to domestic bliss.

Dr Romanov, in an article posted in 2003 on PoseTech (http://www.posetech.com) makes it clear that he does expect the muscles to play a part: ‘By the pose method philosophy, muscles should just assist gravity in pulling us forward. Which doesn’t mean, of course, that we don’t need muscular strength, on the opposite, with the increase of the portion of gravity work we need much more skilful and powerful muscles to handle gravity.’ Maybe this implies that he intends us to adopt a mind set more analogous to that of the romantic homemaker rather that of the cardiac surgeon reading a training manual. The meaning might be in the image created rather than the literal truth. The image created might help harness muscular strength efficiently.

So what image might be created by the statement that we must get out of the way and let gravity do the work? By implying that the body will continue to progress forwards with only relatively minimal guidance from muscles, these statements encourage us to avoid pointless muscle action which is both wasteful and potentially injurious. ‘When you master the Pose method you will experience the incredible Lightness of Running’ (Pose Method of Running, 2004 edition, p 42). In fact because of Newton’s first law of motion, (a moving body will continue to move in a straight line at constant velocity unless acted upon by a force) a direct propulsive force is not required to maintain a constant pace when running on a level surface in the absence of wind resistance. However, because we run upright on two legs rather than rolling like a billiard ball, we do have to move our legs rapidly forwards in each stride if the body is to remain supported in an approximately upright orientation. The goal of efficient running is to move the legs forward rapidly enough to prevent a face-down fall in a way that uses minimal energy with minimal risk of injury. A focus on minimizing muscle action makes sense.

Dr Romanov emphasizes the incredible lightness of running – in other words, minimizing the impact of gravity which tends to pull us to earth with a thud. So if we are to achieve this incredible lightness we need to understand the points within the gait cycle at which gravity is likely to play a strong role.

Free-fall while airborne
Gravity is at its most remorseless when we are airborne. It is inevitable that we will fall freely during this time. Gravitational potential energy is converted to kinetic energy that will bring us forcefully into contact with the ground at foot-strike. At this point, some of the energy can be captured in the stretching of the quadriceps muscles, provided the knee is slightly flexed, and in the muscles and tendons of the foot and calf, provided we land on the ball of the foot. These are features of the Pose style. The stored energy can be recovered by elastic recoil as the foot is lifted from the ground at the end of stance. However, some energy will inevitably be lost, so one of the cardinal goals of efficient running is to minimise the amount of free fall. Because the speed of falling increases with longer duration of fall, less energy will be lost by a series of frequent short airborne periods than by series of fewer longer airborne periods, of the same total duration. Hence high cadence is essential. For a mathematical proof of this, see the calculations page in the side bar.

Footfall
What about the foot fall itself? Because the leg begins to fall while the body is already falling, gravity is unable to pull the foot down relative to the trunk. A very light muscular action is in fact required. However, consciously forcing the foot down creates a grave danger of excessive force. The task of applying the slight force to bring the foot down while simultaneously adjusting muscle tension in a way that establishes sufficient tension in the muscles of the thigh to stabilise the knee is beyond conscious control. Fortunately, by virtue of learning to walk in the omnipresence of gravity, we have already acquired a great deal of automatic skill in summoning the right amount of force. If we are applying too much force, foot-strike will generate a thudding sound. However, the incredible lightness of running described by Dr Romanov cannot be attained by conscious adjustment of muscle tension; rather it is done by listening to the sound of foot-strike and simply aiming to reduce the thud to a light patter. Our brain has a remarkable capacity to adjust muscular activity to produce the goals we set for it.

While on stance
Once the foot is on the ground, gravity serves one useful goal: it tends to anchor the foot in place and minimizes the risk of slipping. However, now our body will begin to rotate in a head forward and downwards direction because our trunk is carried forwards by momentum, while the foot is stationary. This rotation unbalances the body and after a short period, will stimulate a reflex action that lifts the foot from the ground and initiates the next swing forwards. This lift-off can be promoted by conscious effort, and indeed a strong intentional pull is essential if we wish to run fast.

As the long axis of the body rotates away from vertical during the early part of the stance phase, gravity will have a component at right angles to the axis of the body and therefore, will tend to increase the speed of rotation. Dr Romanov suggests that this effect of gravitational torque offers a free source of energy. However by virtue of the law of conservation of energy, any energy gained from gravity at this point of the gait cycle must be paid back at some other point in the gait cycle. Furthermore, according to the calculation presented on the calculations page (in the side panel), the amount of acceleration due to gravity is relatively small, at least until the lean becomes quite marked.

The gravitational torque induced by the transient marked lean as a sprinter drives from the starting blocks almost certainly plays an important part in generating the rotational motion that stimulates rapid and forceful lift-off from stance. However, in my opinion, during steady running at the more moderate pace of the long distance runner, the contribution of gravitational torque to destabilization is likely to be small relative to the contribution from forward momentum. Even if the degree of lean is sufficient to produce an appreciable contribution of gravitational torque to the de-stabilization, this energy would have to be paid back, and it cannot be regarded as a free source of energy. So, I suspect that gravitational torque generated while on stance plays at most a very small part in running.

Conclusion
Where does this leave the teaching of Dr Romanov and Danny Dreyer regarding gravity. The crucial importance of their contributions is their emphasis on running lightly. In practice, they offer several very useful suggestions for achieving this. In Pose Method, the recommendations are:Run with a high cadence to minimise free fall. Land with the knee flexed, and on the ball of the foot, to absorb the energy of impact in quadriceps, and the tendons and muscles of the foot and calf. (But allow the heel to touch the ground to prevent excessive load on the Achilles tendon). Spend a short time on stance to promote efficient recovery of this stored energy through elastic recoil. And if your ears tell you that you are not running lightly, simply focus your mind on achieving lightness. The brain will do the rest.

How should the foot be lifted from the ground?

January 8, 2008

When running on a level surface in the absence of wind resistance, momentum carries us forwards. According to Newton’s first law of motion, maintaining a constant velocity does not in itself require any input of energy. However, we do have to put energy into moving our legs forward quickly enough from one stance to the next to avoid a face down crash.

The process of moving the leg forward from stance to take up stance again with the foot beneath the body about 300 milliseconds later can be subdivided into three segments: lifting the foot off the ground, swinging it forward and allowing it to fall to the ground. These three phases merge into each other, but nonetheless, each has its own characteristic role in the gait cycle, and it is worthwhile to try to examine the requirement of each phase.

Because it is wasteful of energy and potentially injurious to land any more than a slight distance in front of the centre of gravity (COG) the swing forwards should be as passive as possible (though maybe when we want to run very fast, we do need to put a bit more energy into the swing). Because the foot needs to be going backwards relative to the COG at foot-strike, it is also best if the foot-fall is a passive as possible, though of course, substantial muscular contraction is required to stop the knee collapsing on impact.

The involuntary muscular effort required to prevent the knee collapsing is not directed at moving the leg forward, so the major muscular effort to move the leg forwards must be provided in the lift off phase. In this post we will consider only this phase. In later posts I will return to the question of what should happen in the other phases; though from the point of view of conscious effort, the answer is probably: ‘very little’.

There are various different ways we might use our muscles to lift our foot from the ground. Let us start with the issue of how we might lift the left foot from the ground while standing stationary. It is instructive to consider three ways in which we might do this. I will describe the intentions, sensations and results of each of the three ways of doing it:

 

(1) Start with feet side by side; then think ‘Lift the ankle to the hip’. The left foot travels almost perfectly straight up, with only a slight initial swing backwards, so that the mid-point of the left instep passes just behind the medial malleolus of the ankle of the right foot. I feel a contraction in my hamstrings, and also a weaker amount of activity is hip flexors, especially sartorius (a thin strip of muscle that runs down and across the front of the thigh.)

 

(2) Start with feet side by side, think ‘lift the knee’; The hip flexors, especially rectus femoris, the large muscle on the front of the thigh, contracts; the foot comes almost straight up, but with slight forward swing, and the instep passes just in front of medial malleolus on the right ankle.

 

(3) Start with the active foot about 12-15 inches behind the support foot, with the ankle in a neutral position; think: ‘Lift foot to hip’. The foot travels upwards just a little behind the direct line to the hip, as the hamstring contracts. This feels as if it is an almost pure hamstring action. I have no awareness of contraction of either sartorius or rectus femoris when I do this.

 

Which of these is nearest to the required action when running? We can rule out action (2) immediately. First of all, several studies in which electrodes attached to the muscles have been used to record muscular activity during running of runners reveal relatively little activity in the quadriceps during the lift-off (see for example, Pilutsky and Gregor, Journal of Experimental Biology, vol 204, pages 2277-2287, 2001); although some studies such as the ingenious study by Modica and Kram (Journal of Applied Physiology, vol 98, pages 2126-2131, 2005) do indicate that the hip flexors might play some role. While it may be that the runners who participated in these studies were not using the most efficient style, we would be unwise to try anything that is too far different from what runners typically do. We can reasonably assume that at even in modern society we are not so far removed from the natural human condition that modern man (or woman) has made a really radical shift from the optimum running style. Our goal in seeking an efficient style is largely to remove any relatively minor inefficiency that might have crept in as a result of modern life style (and shoes). Therefore, it seems sensible to assume that hip flexors play at most a relatively minor role.

So we are left to consider methods (1) and (3), both of which rely largely on the hamstrings. Brief consideration of the consequences of spending at least the minimum reasonable time on stance suggests that (3) is most appropriate.

When on stance, the body will necessarily rotate in a ‘head forwards and downwards’ direction, as a result of forward momentum that carries the body forwards while the foot is anchored. If we are moving at 4 metres per sec, immediately after foot-strike the COG will continue to move forwards at 4 metres per sec, while the foot is stationary. Assuming the COG is approximately 1 metre off the ground, the line joining COG to the foot must start rotating at 4 radians per second (a radian is the ‘natural unit’ of angle and is approximately 57 degrees). Assuming a cadence of 180 strides per minute, the total duration of each stride is 333 milliseconds. Unless we are prepared to suffer ground reaction forces exceeding 3 times our body weight, we must remain on stance for at least one third of the gait cycle in order for our weight to be supported, so we must spend at least 110 milliseconds on stance. During this time, our COG will have moved forward about 0.4 metres (somewhat more than a foot.). That is why when I described method (3), I had specified starting with the left foot about 12-15 inches behind the right foot. In fact, most runners will remain on stance longer than 110 milliseconds; the foot will be even further behind at lift off and the hip will be further extended. However, the crucial point to make at this point is that if we land with the foot under the COG (which is desirable to minimize wasteful braking), by time of lift-off from stance, the hip must be moderately extended. A pure hamstring pull without hip flexor action will now bring the foot up towards the hip without any action of the hip flexors.

In general, action of the hip flexors would increase the risk that we will over-stride at the next foot fall, unless we actively employ the hamstring in the late swing phase to arrest the swinging leg. It seems inefficient to use hip flexors at lift off, and then have to apply hip extensors in late swing to correct for this. Perhaps if we are aiming for maximum speed, we might have to be prepared to spend a bit more energy to get the swing moving forwards more quickly, at the price of needing to do extra work later in the swing to arrest it, but this appears to be an expensive way to run.

So these considerations suggest that a pure hamstring pull starting from a position of moderate hip extension is the most economical way to perform the lift off. Maybe active hip flexion is necessary if we want to run really fast, but this active flexion will come at extra cost.

I think that these considerations have led us to an action largely consistent with the proposal of Dr Romanov (founder of the Pose technique) who states that the pull should be performed by the hamstring. However, I am a little puzzled by one of the drills that Dr Romanov recommends in order to help us learn the correct direction of the pull. In the tapping drill, he recommends starting with the feet side by side, and as far as I can establish, the recommended action is very similar to what I have described in action (1). It should be noted that my knowledge of Pose comes only from Dr Romanov’s book ‘Pose Method of Running’ and from information on the PoseTech website (www.posetech.com). I am looking forward to my first workshop with Dr Romanov in March of this year, and maybe I will understand the tapping drill better after that.

So for the time being, I think that if one wants to learn the correct muscle action for economical lift-off using a drill performed when stationary, it might be more sensible to start with one foot 12-15 inches (30-40 cm) behind the other. I have previously posted (in the side bar of this blog) what I describe as the ‘swing drill’ to encourage the appropriate action for moving the leg forwards from one stance to the next when running. Today, I have modified this drill to recommend starting with one foot about 12-15 inches behind the other. I must emphasize that this suggested drill is experimental. I am still working on its development. It has not been tested on anyone apart from myself and cannot yet be recommended as a safe or useful procedure. Nonetheless, I would value any comments on this proposed drill.

More on the effects of gravitational torque

January 6, 2008

Earlier today I posted to say that my calculations indicated that the contribution of gravitational torque to running was minimal. Since then I have been engaged in an interesting discussion with Mike Stone (which you can see in the comments section at the bottom of the calculation page.) He initially challenged one of the mathematical steps in my calculation, but I think we have agreed that subject to the validity of the assumptions on which my calculations were made, that is OK. However, he is currently querying the assumptions.

My understanding of the situation is that the calculation I have done gives a reasonable good estimate of the effect of gravitational torque if the assumptions are correct. The most important of these assumptions is the assumption that the ankle, hip and shoulder remain in a straight line. This was one of the rules for good Pose running originally specified by Dr Romanov, but there is no doubt that in practice runners disobey this rule once the pace has increased beyond a fast jog. What actually happens is that the hip extends while the runner is on stance so that the leg on stance rotates through a larger angle than the torso. To do the calculation in a more realistic way, we need to treat the body as consisting of at least two elements joined by a hinge at the hips to allow for the fact that at speed, runners do flex (backwards) at the hips. This calculation could be done, but will require more complex mathematical procedures. The flexion results in the COG moving relative to the hips while the runner is on stance

So where have we got to: I still think that provided the line from the ankle to the COG at lift off from stance leans by no more than about 10 degrees, the contribution of gravitational torque to running is likely to be very small. However, there is no doubt that it would be best to do the calculation using a model in which the body is allowed to hinge at the hips. I hope that we can get this done in the not too distant future.

 

Does gravitational torque matter?

January 6, 2008

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.

How fast off stance? – a comparison of Pirie and Pose

January 5, 2008

What is the problem?
Many runners believe that they should minimize the time spent with a foot stationary on the ground. One hears statements along the lines of ‘you are going no-where when you are on stance’. In fact that statement is very misleading and needs to be re-examined. Your grounded foot might be going nowhere, but your torso continues forwards while the foot is on the ground at approximately the same speed as while you are airborne. The race is won (or at least finished) when the torso crosses the finish line, not the trailing foot. Clearly we shouldn’t stay fixed on stance for ever, but neither should we be airborne for too long either, as free-fall under the influence of gravity is inevitable while airborne, and free-fall is very wasteful of energy. The calculations section in the side bar of this blog illustrates why the airborne period should be short but frequent. Frequent airborne periods are achieved by running with high cadence (at least 180 strides per minute). High cadence also places a very tight limit on how long we can remain on stance, but it leaves unanswered the question of what proportion of each stride should be spent on stance.

What does Pirie propose?
This issue was addressed explicitly by Gordon Pirie in chapter 3 of his book ‘Running Fast and Injury free’ (http://www.gordonpirie.com). Pirie is a very strong advocate of high cadence, but he also recommends staying on stance for a substantial period. He states: ‘This low running posture allows me to stay in contact with the ground longer, and makes it possible for me to generate more power during each contact power-phase with the ground.’ (p21).

What does Pose propose?
In contrast to Pirie, some of the other schools of thought on efficient running recommend getting off stance as quickly as possible. In particular, proponents of the Pose technique developed by Dr Nicholas Romanov (http://www.posetech.com/) emphasize the importance of attempting to get off stance very rapidly, by means of a rapid pull. This pull is facilitated by the unbalancing of the body as the centre of gravity (COG) passes over the point of support. The pull itself is executed mainly by a rapid contraction of the hamstrings.

Features shared by Pirie and Pose, and differences between them
Pirie and Pose share many features, especially the emphasis on high cadence and also the emphasis on landing with the foot travelling backwards relative to the COG so that at point of contact with the ground it is stationary relative to the ground. This minimizes wasteful and potentially injurious braking. However, it appears that Pirie and Pose make opposite recommendations regarding the proportion of the gait cycle which should be spent on stance, so it is worthwhile making a close examination of what they each recommend and evaluating these recommendations in light of the physics and physiology of running. But before doing that, it is worth considering the evidence regarding the efficiency of these two styles.

The evidence for efficacy of Pirie style
The evidence regarding the efficacy of the Pirie style is largely anecdotal evidence based on Pirie’s own achievements. He was undoubtedly fast. He broke 5 world records in his lifetime, including a spectacular breaking of the 5000m and 3000m records in 1956. In ‘Running Fast and Injury Free’ he claims to have run 240,000 miles during 45 years, with very few injuries. In 1998, The Guinness Book of Records credited him with running 216,000 miles in 40 years and described this as the greatest mileage by a human being (http://www.gordonpirie.com). Thus, anecdotal evidence, confirmed by world-record breaking performances, provides good grounds for accepting that he achieved what is claimed in the title of his book: he ran both fast and (relatively) injury free.

The evidence for efficacy of Pose
In the case of Pose, there is evidence about efficiency from scientific trials, but that evidence is equivocal. The only published study of running efficiency with Pose is a study by Dallam and colleagues published in Journal of Sports Science in 2004 (volume 23, pages 757-764). In that study 8 sub-elite triathletes, who were trained using the Pose method for twelve weeks, were compared with a matched sample of 8 sub-elite triathletes, who continued training with their usual running style. Running efficiency was assessed by measuring oxygen requirements at a particular running speed, on the assumption that a more efficient style would require less oxygen. After twelve weeks the athletes trained using the Pose style had suffered a significant decrease in their efficiency, whereas those who continued to train using their usual style do not exhibit a change in efficiency. Were the athletes properly trained in authentic Pose style? One of the investigators in this study was Dr Romanov himself, so it is hard to imagine that the Pose training could have been any more authentic. Was the impaired efficiency due to unfamiliarity with the new style? Maybe, but if there was still a problem with unfamiliarity after 12 weeks, that in itself is a problem for the practicality of learning the Pose style.

With regard to risk of injury, the evidence is indirect but it is more encouraging. Several studies, including the Arendse study performed in Tim Noakes’ laboratory in Cape Town, and published in Medicine & Science in Sports & Exercise in 2004 (Volume 36. pages 272-277), demonstrate significant reduction in stressful forces at the knee joint when running Pose style compared with either mid-foot running or heel-striking. In contrast, stress at the ankle was found to be greater, raising the possibility of higher risk of injury of the Achilles tendon and calf muscles. Again Dr Romanov was a co-investigator in this study, so it is likely that the athletes received authentic Pose training. However, the average time spent learning Pose technique was only 7.5 hours and it is possible that with more training the athletes might have learned to avoid extra stress at the ankle by allowing the heel to rest briefly on the ground, so that stress is absorbed by the longitudinal arch of the foot in the latter part of the stance phase.

So, overall, the evidence does provide some support for reduced risk of knee injury with Pose, but the evidence regarding improved efficiency as assessed by oxygen consumption is disappointing.

Ground reaction forces
The first issue to consider in deciding on the optimum proportion of the gait cycle to spend on stance is the requirement that the weight of the body be supported. Body weight pressing down through the feet elicits an upwards directed ground reaction force (GRF) that supports the body. The average value of the vertical component of the GRF during the gait cycle must be equal to the body weight. When the body is airborne there is no GRF, so the average GRF during stance must be greater than the body weight by the ratio of total stride duration to time on stance. If the body is on stance for half of the stride duration, the average GRF during stance must be twice the body weight and the peak GRF might be somewhat greater. So if the time on stance is too small a proportion of the stride duration, the forces on the foot will be intolerable. Pirie’s recommendation for a relatively long time on stance will protect the foot against excessive GRF.

What can be achieved while on stance?
Pirie argues that running consists of brief bursts of activity, while on stance, interspersed with periods of relaxation while airborne. He states: ‘Correct running should feel like a series of very quick but powerful pulses, with the arms and legs working in unison, followed by a period of relaxed flying between each power phase’ (page 24). He does not state explicitly what the brief period of activity during stance involves though his use the term ‘powerful pulses’ suggests the generation of upwards and forwards forces. Some of this might be derived from recoil of the quadriceps and calf muscles and tendons, thereby recovering energy that was stored in these structures during impact at foot fall. Pirie’s choice of the word ‘power phase’ possibly implies an even more active process, and perhaps that active process was what gave him the edge in his world-record breaking performances.

Although Pose style aims for a relatively brief time on stance, Dr Romanov argues that the destabilization of the body when the COG is forward of the point of support generates a gravitational torque that promotes lift-off from stance and helps propel the body forwards. Thus Pose also proposes utilizing the time on support, but mainly to achieve unbalancing of the body. Like Pirie, Dr Romanov also emphasizes relaxation during the airborne period.

One thing that is clear about the time stance is that once the COG is ahead of the point of support the force exerted by the foot on the ground will have a backwards directed component, so there will be a forwards directed component of the GRF that tends to push the foot forwards. Thus, the latter part of the time on stance can be used to generate force in a forwards direction.

Penalties of time on stance
The gravitational torque proposed by Dr Romanov will produce acceleration of rotation in a ‘head forwards and downwards’ direction, and if this is not corrected at some other point in the gait cycle, a face-down crash will occur after a few strides. I am not sure how or when in this occurs (see my blog of 2 Jan 08). However, irrespective of how or when it occurs, reversing of this forward and downwards acceleration will consume energy, and hence, is a potential drain on efficiency. The longer the runner remains on stance after the COG has passed over the point of support, the greater the effect of gravitational torque and therefore, the greater the energy required to prevent a face-down crash.

If the footfall occurs ahead of the COG and lift-off occurs at a similar distance behind the COG, the net gravitational torque will be zero and no energy will be required to reverse the rotational acceleration. However, landing in front of the COG will result in braking that consumes energy and is also likely to increase risk of injury.

An additional issue to consider is that, as discussed in my article on the mechanics of efficient running (see side bar), the foot appears to have a very elegant mechanism for absorbing the energy of impact and conserving it so that it can drive elastic recoil. It is likely that a time of at least 50-70 milliseconds will be required for this mechanism to be engaged, so time on stance should be adequate to allow this. However, the energy can only be conserved while the calf muscles are contracted, so too long on stance will result in inefficient energy consumption by the calf, and eventual exhaustion of the muscles.

Conclusion
The evidence suggests that the proportion of time on stance should not be very short or GRF forces will be intolerable. On the other hand, it should not be too long either, or face-down crash will ensue, unless we are prepared to risk the penalties of landing in front of the COG. The one lesson that is very clear from consideration of the mechanics of running is that cadence must be high so that the absolute value of both time on stance and airborne time in each stride are small. In this respect, both Pirie and Pose are in agreement.

We still require a better understanding of the benefits and penalties of time spent on stance. However, despite the arguments in support of Pirie’s view that time on stance should be substantial, my intuitive sense is in accord with Pose. When I run I still attempt to get the foot off the ground as quickly as possible. I think the main reason why I favour a relatively short time on stance is that this allows recovery of the stored energy in Achilles and quadriceps tendon by elastic recoil at lift-off, with minimal exhaustion of the calf and quadriceps muscles as they sustain the stored energy. However, this speculation is not directly supported by evidence

Where should the foot land?

January 2, 2008

One of the key principles of efficient running advocated by Gordon Pirie, and subsequently incorporated as a major feature in other styles such as the Pose method of running developed by Dr Nicolas Romanov, is the principle that the foot should land under the body. (See p16 of Pirie’s book ‘Running Fast and Injury Free’). At first sight this makes sense since placing the foot beneath the body, with the foot moving backwards relative to the centre of gravity (COG) such that the velocity of the foot relative to ground is zero, will minimize braking which would waste energy while increasing the risk if injury.

Pirie is emphatic about the importance of avoiding landing with the foot too far forward. He warns: ‘over-striding is one of the most common technical afflictions of runners and one of the most dangerous’ (p18).

However, observation of elite athletes, such as Haile Gebrselassie (http://www.youtube.com/watch?v=_xGXPxJzeug ) reveals that they often land a little in front of the COG. An elite athlete probably does this automatically, but if we assume that one of the characteristics that makes an athlete elite is the ability to sense what is most efficient intuitively, it suggests there might be a reason why landing in front of the COG is actually more efficient.

A clue is provided by consideration of the torque that will be applied by gravity during the stance phase when the foot is on the ground. Once the COG passes in front of the point of support, the body is unbalanced and gravity will exert a torque that tends to pull the head forwards and down relative to the feet. In fact Dr Nicholas Romanov argues that this torque provides useful forward propulsion. I am dubious of this claim because gravitational torque will tend to generate angular momentum (rotational movement) rather than linear momentum (forward motion). Whatever the fact of this issue, there is an even more important issue to consider. If gravity applies torque that increases angular momentum, then this torque must be reversed at some point in the gait cycle or the rotation would continue to accelerate and the runner would end up face down on the ground after a few strides.

So, granted that once the COG has passed in front of the point of support gravitational torque promoting a face-down crash is unavoidable, we need to ask where in the gait cycle an opposite torque might be applied. One answer would be to land with the foot a little in front of the COG so that for a brief period the gravitational torque acts in the opposite direction. This might seem to provide a plausible explanation for the observation that elite athletes often land a little in front of the COG, and also emphasizes that struggling to adjust one’s style to land directly under the COG might be both pointless and possibly dangerous.

 

What image should guide lift-off from stance?

January 1, 2008

My experience in  the last two days makes me wonder again about the right mental image to use to help develop a good lift-off of the foot from stance. Video recordings of Haile Gebreselassie, such as the recording made during his world record breaking marathon run in Berlin in 2007 (http://www.youtube.com/watch?v=_xGXPxJzeug ) suggest that the ankles should rise well behind the direct line from lift-off to the hips. This is what you should expect if the lift-off from stance is executed mainly by the hamstrings with very minimal hip flexion, because the hamstrings not only flex the knee but also tend to extend the hip backwards. Unless there is a moderately active hip flexion, the ankle will rise well behind the hip, just as Haile Gebrselassie’s ankles do.

Probably Haile Gebrselassie does not even need to think about the direction of pull, because it is so habitual for him. But if we want to deliberately emulate him, what mental image should we use to guide the lift-off?

When we run, it is usually better to think of what direction of movement we are aiming for rather than thinking about which muscles to use, because the brain appears able to compute which muscles to use unconsciously, once we have decided on the desired direction of movement. In the article I posted on 29th December, I had suggested an image of lifting the ankle directly towards the hip. I based this partly my own experience and partly on the recommendation by Dr Romanov in his training session presented on the PoseTech website on 27 June 2006 (http://www.posetech.com), in which he states: ‘Our perception of the foot movement should be as of a vertical motion from the ground up under the hip (piston-like), a kind of up&down motion. In our perception the foot shouldn’t deviate from the vertical line going from the ball of the support foot on the ground to under the hips’

A piston-like action from ground to hip must entail a substantial amount of hip flexor action in addition to hamstring contraction, to counteract the fact when the hamstring flexes the knee it also tends to extend the hip. Maybe Dr Rovamov only means the piston action to be an image to guide our thoughts, rather than an actual prescription for the action, because elsewhere in his books and video recordings, Dr Romanov makes it very clear that he considers that the pull should be executed mainly by the hamstring. Nonetheless, in line with his recommendation to think of an up-and down piston action, that is the image I have been trying to employ to guide lift-off recently.

At first, this appeared to work fine. I was really pleased with the feeling of ease as I ran. However, yesterday, during my fourth consecutive longish run, I was aware that my hip flexors were becoming tired even though my hamstrings felt fine. So, I am fairly sure I have been using too much hip flexion – certainly more than Haile Gebrselassie. Maybe I have simply been too vigorous is applying the up-down piston image, but I think it is more likely that, at least for me, that piston image actually results in a true up-down piston action and as a result engages the hip flexors too much. So in the next few days I will experiment with a different image in the hope that my action looks a bit more like that of Haile Gebrselassie – though I have no illusions about achieving his speed.