Gazelles v gliders: Mirinda Carfrae v Chrissie Wellington

As described in a recent post, my attempt to recover some of the speed of my youth by engaging in a lifting program to re-build my leg strength was only partially successful.  I exceeded my expectations regarding gains in strength, but so far this has not been translated into increased speed.  Unfortunately a recurrence of arthritis has confounded my immediate hopes, and at the moment I am more concerned about re-building my aerobic base.  However a recent discussion of the merits of gazelles v gliders on the Fetch efficient running thread has prompted me to re-examine the issue of my loss of speed.

The most striking thing about the change in my running style as I have grown older is the fact that my stride length has shortened.  Now, whenever I try to increase pace, my cadence automatically increases, often going well above 200 steps per minute even at a modest pace. While many recreational runners might benefit from an increase in cadence, at least up to 180-190 steps/min, I am fairly sure that in my case, the increase in cadence reflects reduced ability to get airborne, leading to a stunted stride.  I had attributed this to lack of strength but maybe strength wasn’t the main problem.

The gazelles v striders comparison provides food for thought.  Here is a good illustration (though I do not agree with all of the comments by the commentator).   The crucial difference between gazelles and gliders is that gliders do not produce as much elevation of the body on each step as gazelles. Because they produce less elevation than gazelles, their stride is shorter and they employ a higher cadence.  While I am not sure that even my mother would have ever described me as a gazelle, there is little doubt that I have become a glider as I have aged.   This is what I have been trying to correct.  However, this video clip provides at least some grounds for questioning the need to overcome my tendency to be a glider.   As the video illustrates, Chrissie Wellington, without doubt the greatest female triathlete ever, is a glider.    In the video, Chrissie’s gliding is compared with the style of one of the most elegant triathlete gazelles, Mirinda Carfrae.

The costs of gliding

Could it be that gliding is efficient?  It is tempting to think that reducing elevation costs must be more efficient, but this would be far too simplistic.  When considering efficiency, we need to consider the three major energy costs of running:

1)            Overcoming braking.  Provided a glider increases cadence to ensure that time on the ground does not increase, the braking cost per step will be the same for both but the cost per  mile will be  greater for the glider because there are more steps per mile.

2)            Limb repositioning costs: these increase with cadence and will be higher for the glider

3)            Elevation costs:  Although the video commentary  incorrectly states there are no elevation costs, in fact elevation of the centre of mass occurs before lift- off as a result of extension of hip, knee and ankle during the late stage of stance.   Furthermore due to the higher cadence, the saving in elevation cost per step is partially offset by the greater number of steps per mile.  However, the elevation cost per mile will nonetheless be somewhat lower for a glider because elevation cost increases as the square of airborne time, so the saving in elevation cost per step is relatively greater than the extra cost due to more steps per mile.

In estimating the total cost, we need to balance the three variables: braking and limb repositioning costs are greater for the glider, but elevation costs are less.  At higher speeds, repositioning costs become the dominant cost and there is no doubt that at high speed (e.g. faster than 7 min/mile) gazelles are more efficient.  At intermediate speeds (7min/mile-10 min/mile) braking costs and elevation costs are both quite appreciable and at such paces too, gazelles are almost certainly more efficient.  At very low speeds (slower than 10 min/mile) braking cost become relatively small because the leg is never far from vertical and therefore the horizontal ground reaction force that produces braking is always low.  At such paces the major goal should be minimising elevation costs.  So on balance, I think it is only at very slow paces that gliders might be more efficient than gazelles.

So why is Chrissie Wellington a glider?   I do not know, but wonder whether it might be an unconscious attempt to decrease the risk of injury when tired in the late stage of an ironman.  With regard to injury, the issue is the relative risk of a larger number of smaller impacts for the glider compared with fewer larger impacts for the gazelle.  While the phenomenon of repetitive strain injury demonstrates that repeated small impacts can be damaging, I suspect that size of the impacts plays an even bigger role in damage.  Therefore, I am inclined to think that for a tired runner, (either in the late stages of an ultra or an ironman) the risks will be lower for the glider.

Overall, there is little doubt that the gazelle style is better for medium paced and faster running, but there is reason to debate whether or not the glider style might be beneficial for tired, slow runners. I am still eager to become as much like a  gazelle as my aging limbs will allow.  While I can no longer blame lack of strength, I wonder if maybe lesser ability to capture elastic energy at foot fall is the cause of my gliding.   In a future post I will describe my plans for the attempt to recover elasticity.   But in the short term, my focus is on re-building my aerobic base, and that is what my next post will address.

Finally, it is noteworthy that on the two occasions when Chrissie Wellington and Mirinda Carfrae went head-to-head in the world ironman championship (at Kona in 2009 and 2011), on each occasion Wellington won the overall event but on both occasions Carfrae ran the faster marathon. In my opinion Wellington is the greatest female triathlete ever but Carfrae is the more efficient, and faster, marathon runner.

Added note (4^th May 2013)

In his comments below, Robert had pointed out that I have not provided adequate justification for my claims about the energy costs.   My claims are based largely on calculations based on applying Newton’s equations of motion to the simplified model of running described in my posts in January and February 2012.    At a pace of 4 m/sec, (which is close to that of Carfrae and Wellington in the world ironman championship in 2011) the calculations demonstrate that the combined cost of elevation and braking is 6% greater for a Glider than for a Gazelle, assuming that that the Glider has an increased cadence sufficient to produce a similar time on stance.  Observations suggest that Gliders do increase cadence to maintain a similar time on stance, and furthermore, if a Glider did not have increased cadence they would be even less efficient because the longer time on stance would produce an even greater increase in braking costs (as indicated by my post of February 2012).

The crucial questions is whether or not the simplifications I used in performing these calculations lead to serious errors. There are two respects in which the simplifications might lead to error.  First, I assumed a sinusoidal shape for the variation of ground reaction force with time.   Variations in the shape of this curve introduce small changes to the results of the calculations, but in the absence of force plate data for each runner, I cannot do a more precise calculation.  However, the error due to this simplification is likely to be small.

The other potential source of error is that my calculations are for the total energy expended on elevation and overcoming braking. I have not subtracted the energy saving expected via elastic recoil.  If a runner maintains greater tension in the leg muscles, as recommended in the BK running style, it is possible to recover a greater proportion of the required energy via elastic recoil.  I cannot exclude the possibility that a Glider might maintain greater tension in the leg muscles, but think that in general this is unlikely as increased tension in the leg muscles results in a greater rate of rise in ground reaction forces and potentially increases the risk of injury.  The advocates of the BK style recommend thorough preparation using plyometrics before attempting this.  I think that increasing leg muscle tension would not be a good strategy for a tired ultra runner.  Thus I doubt that Gliders make greater savings via elastic recoil than Gazelles. I suspect that the opposite might be the case, though this is speculation.  However even if equal efficiency of recovery of energy via elastic recoil is assumed, the Glider incurs a 6% greater cost for elevation and braking than the Gazelle.

Also, it should be noted that my calculations do not include limb repositioning costs. These costs are almost certainly higher for the Glider because repositioning cost increases with cadence (as discussed in my post in April 2012) and furthermore, the trajectory of the foot of a Gazelle results in a shorter lever arm of the swinging leg, further increasing efficiency.

On balance, I think it is likely that my calculations provide a fairly realistic estimate of the relative costs of elevation and braking for the two styles.

Mary Keitany, a muscle named Lady Dorothy, and the future of the women’s marathon

The past decade has seen an astounding increase in the standard of marathon running, at least in the men’s event.  Not only has the world record continued to tumble but the event has become a race from start to finish.  This was clearly evident in Wanjiru’s victory in Beijing, but was also made manifest in the London marathon a few weeks ago by Wilson Kipsang’s devastating surge beginning as he approached Tower Bridge, around the half-way mark, and continuing for more than 5 Km at 2:50 per Km (sub 2 hour marathon pace).  Abel Kirui hung on until 35 Km but the damage inflicted by Kipsang’s self-assured mid-race surge became apparent as Kirui’s pace slowed to about 4 min/Km and he dropped back from 2^nd to 6^th place over the final few Km.  Just as significant as the shift towards the mental toughness exemplified by Wanjiru in Beijing and Kipsang in London, is the manner in which the winner in most male events nowadays maintains a graceful but powerfully efficient stride similar to that we are used to seeing in a track 10,000m, all the way to the finish.   The era in which gruelling training and gritty determination took Emil Zatopek to victory in 5000m, 10000m and marathon in Helsinki is a distant memory.  The marathon is no longer merely a test of endurance, but an event that calls for tactical finesse coupled with the ability to sustain a powerful efficient gait for 42.2 Km.

How does the women’s marathon compare?  

In contrast, advance in the women’s event has been much more patchy.  Although Paula Radcliffe’s record of 2:15:25 set in London in 2003 with the assistance of two male pacers is widely regarded as phenomenal, it is not clear that it is especially outstanding when compared with the men’s record.  One might expect that in the marathon that efficiency should count for more than strength, and that women would be less disadvantaged relative to men, than in shorter events.  The evidence is ambiguous.  Across the range of distances from 100m to marathon, the female world record is slower than the male record by a margin of 9-12%.  FloJo’s time for 100m is 9.5% slower than Usain Bolt’s, though controversy lingers over FloJo’s performance.  Similarly, a cloud unfortunately hangs over Marita Koch’s 400m time, which is 10% slower than Michael Johnson’s.  Paula’s marathon record is 9.5% slower than Patrick Makau’s record of 2:03:38.  Furthermore, whereas no other woman has approached Paula’s time, at least 3 other men have demonstrated the potential to demolish Makau’s record.  Kipsang missed that mark by only a few seconds in Frankfurt last year, while both Geoffrey Mutai (2:03:02) and Moses Mosop (2:03:06) have actually recorded times faster than Makau’s record on the demanding down-hill Boston course, which unfortunately does not satisfy world record requirements.  Unlike the performances of Flo-Jo and Marita Koch, no clouds hang over Paula’s performance in London in 2003, and it is truly an outstanding performance.  But if we acknowledge that strength is less of an issue in the marathon compared with sprints, it is not clear that Paula’s female marathon record is any faster than might reasonably be expected.

More grit than grace 

When it comes to style, Paula’s head bobbing is legendary.  But it is not merely a matter of head bobbing.  She carries her shoulders high and her torso lurches.  Her victory in Chicago in 2002 when she broke Katherine Ndereba’s world record, was a triumph of gritty determination, but it was as painful as it was awe- inspiring to watch her straining virtually every muscle in the final few Km.  In London, 8 months later, as she turned into the Mall on her way to smashing her own world record, the strain in her upper body was only slightly less apparent.  Perhaps Paula Radcliffe is the Emil Zatopek of the woman’s marathon.  Katherine Ndereba is markedly different.  She is always graceful.  To my eye she swings her arm too far back and leaves her trailing foot on the ground for a little too long, resulting is a slightly delayed swing.  However the issue of how quickly the trailing foot should lift-off stance remains a controversial topic which I will return to again in a future post.    While there can be no denying that Ndereba is graceful, I think her race tactics have cost her dearly on a number of occasions, most notably in Beijing in 2008.  On previous occasions she had been prepared to let the leaders get ahead by a minute or two, only to subsequently nibble away the margin and take command in the final few Km.  In Beijing she allowed Constantina Tomescu-Dita to get away, and then she could not catch her.

Tomescu-Dita entered the stadium with arms flailing in a manner that could scarcely be described as graceful, though it was heart-warming to see a 38 year old achieve such a spirited Olympic victory.  Ndereba and Zhou entered the stadium several minutes later, and when Zhou challenged for the silver medal with less than 100 metres to go, Ndereba sprinted away elegantly.  Whether or not a more spirited performance at an earlier stage would have given her Olympic gold is unknowable.   She has indeed many memorable marathon honours to her credit, including gold medals in the world championships in the pre-Olympic years, 2003 and 2007, but on each occasion she achieved only silver in the Olympics the following year.  In their different ways the two women who dominated the marathon in the past decade might look back ruefully on the Olympics of 2004 and 2008.   Paula still has a slender chance in 2012 following a creditable 2:23:46  in Berlin last year, but Katherine now hands over the mantle of Kenya’s queen of the marathon to be shared by a handful of promising younger women, including this year’s London winner, Mary Keitany.  Might this new generation of Kenyan women do for the women’s marathon what their male compatriots have done or the men’s event?

A new era?

In contrast to the men’s event in London in April 2012, the elite women started cautiously, reaching the halfway mark in 70:53, but shortly after a new pattern emerged. It was not the male-type self-assurance of Kipsang, but rather a quiet, unassuming yet determined increase in pressure by  Keitany.  Her pace for that middle 5Km provided only a hint of her gathering speed, but she continued to accelerate, covering the 5 Km from 35 to 40km in 15:45.  Ross Tucker in Science of Sport reports that this is the fastest 5Km split ever recorded by a woman in a major marathon, faster even than Radcliffe’s 15:47 for the first 5Km in London in 2005.   In the final 2Km Keitany increased her pace even further to a pace only slightly slower than 3 min/Km.

I believe that a major factor that transformed Radcliffe from fourth placed 10,000m runner in Sydney in 2000, to a sub-2:16 marathoner in 2003 was an increase in her leg strength resulting from a program of plyometrics introduced by Gerry Hartman after the Sydney Olympics.  Maybe Paula’s 2:15:25 will only be seriously challenged when women marathoners develop the type of strength that took middle distance runner Kelly Holmes to a gold medal double in Athens, but I am inclined to think that for a marathoner efficient muscle recruitment is even more important than sheer strength.  Observing the video of Mary Keitany in VLM 2012 suggests that her efficient gait was a major factor in her ability to increase speed steadily despite accumulating exhaustion in the late stages.

Controlling rotation of the torso

Keitany swings her arms in a neatly controlled manner that sets the tone for her trunk and legs. As her arm swings down and back close to her body, the hip of her swinging leg rotates forward and the contralateral hip rotates back.  By virtue of allowing her pelvis to rotate she minimises wasteful angular rotation of the whole body around the vertical axis.  In general, her foot usually lands fairly near the midline of the body when viewed from the front (eg at 1:55:13).  In contrast, Edna Kiplagat, who vied with Keitany for the lead until around 35 Km, and Priscah Jeptoo, who eventually finished in third place to put three Kenyan women on the podium, both land more often with the foot more to the side of midline, due to lack of rotation of the pelvis. If the foot is grounded to the side of the midline, the body must rotate around the vertical axis, on account of the momentum of the torso.  The tendency for the torso to swing around can be minimised by a counter rotation of the arm.  Because a less compact body has a greater moment of inertia, if the arm displaced outwards, the angular displacement of the torso itself is reduced but the angular momentum of the torso plus arms is not.  This angular momentum must be cancelled in the next step, which wastes energy.

Lady Dorothy

The crucial link that coordinates the action of arm and opposite leg is provided not only by the motor programmes the evolved in the brains of our distant quadripedal ancestors, but also by a direct connection via the most extensive muscle of the human body: Latissimus dorsi.  The Latin name means ‘widest back muscle’.  Body builders refers to this muscle when they talk about  developing their ‘lats’, while medical students call it ‘Lady Dorothy’ to help them remember the arrangement of its attachment to the humerus in the upper arm.   The mildly bawdy mnemonic  ‘Lady Dorothy lies in a ditch between two majors’ reminds them that its tendon runs in a groove between the attachments of Pec Major and Teres Major.   However this mnemonic serves to reinforce the role of Latissimus dorsi in pulling the arm inwards and back, while distracting attention from its attachment to the thoraco-lumbar fascia (TLF).

Figure 1: Latissimus dorsi (in red) and its attachment to the iliac crest and lumbar spine via the thoraco lumber fascia (From Grays Anantomy)

When the left foot is grounded and the hip extends back, the glutes on the left side stabilise the pelvis, providing a firm anchor point for the TLF along its line of attachment to the iliac crest.  The simultaneous contraction of latissimus on the right side, pulls the arm back while rotating the lumbar spine so that the left side of the pelvis rotates forwards while the more lateral, vertically oriented muscle fibres tend to prevent it dropping as the swing leg moves forwards.  Thus the coordinated action of glutes with the latissimus stabilises the pelvis in a horizontal position as seen from the front, while allowing it to rotate about the vertical axis that facilitates the efficient passage of the swinging leg.

Figure 2: Posterior hip muscles (from Wikipedia) When the left foot is on stance, G. maximus on the left anchors the left side of the pelvis, thereby proving a firm anchor via the thoraco-lumbar facscia for right sided Latissimus dorsi as it contracts to pull the right arm down and back. Simultaneously G. medius (on the left) minimises the downwards tilt of the pelvis from left to right.

Avoiding snagging of the ITB

However this action must be quite precisely controlled.   If the swing leg rotates too far, carrying the foot too far towards the midline at foot-fall, the ilio-tibial band (ITB), which is under tension as it provides the anchor for gluteus maximus, will be dragged across the bony protrusion of bone on the lower end of the femur.  This problem will be greatly exacerbated if the pelvis has been allowed to tilt down on the side of the swinging leg.  This makes the angle between pelvis and femur even more acute, dragging the ITB closer to the femur.  This problem will also be exacerbated if the foot is prevented from pronating as the stance leg tends to twist over the grounded foot.   Thus, if risk of injury is to be minimised there is quite limited tolerance in the allowed range of rotation of the pelvis and movement of the swinging foot towards midline.  Sideways drop of the pelvis must be limited and adequate pronation of the foot allowed.    It is likely to be counter-productive to focus consciously on controlling all of these movements while running.  I believe that conscious attention to a neatly controlled arm swing, in which the hand sweeps down close to the body from a point to the side of the midline and a little above mid-chest height, towards the hip, is the best way to trigger the non-conscious motor control program that coordinates all of this.  The extent of the swing should increase a little as speed increases, but the hand should never cross the midline.

The crucial role of a stable core

Precisely controlled rotation of the pelvis about the vertical axis and minimal tilt from side to side is crucial not only for maintaining an efficient gait for the duration of a marathon, but perhaps even more importantly, for avoiding injury during the high volume training that the marathon demands.   While I believe that the program of plyometrics which Gerald Hartman introduced in 2001 to develop leg strength played a key part in the transformation of Paula Radcliffe into the most outstanding female marathoner the world has yet seen, I suspect that greater attention to the coordination of the complex system of muscles extending from shoulder to foot via Latissimus dorsi, the glutes, ITB and the lower leg muscles, might have protected her from the injuries that confounded her Olympic dreams in 2004 and 2008.

 

The future of the women’s marathon

With her victory in London in a time of 2:18:37, Mary Keitany broke the Kenyan women’s marathon record established by Catherine Ndereba in the 2001 Chicago marathon.  Ndereba’s  time of 2:18:47 was not only the Kenyan record but also the world record in 2001.   However it is noteworthy that even a decade later, Keitany shaved only 10 seconds off that time to take the Kenyan record, whereas in Chicago in 2002, Paula Radcliffe had taken possession of the world record by slicing almost a minute and a half off Ndereba’s time.  Then, the following year in London, Radcliffe took a further minute and 53 seconds off her own record.   While Keitany’s run in London in March has made her the favourite for gold in London in August 2012, Radcliffe’s world record is not threatened.  Keitany is now 30 and slightly older than Radcliffe was when she reached her peak, so the likelihood that Keitany will ever challenge Radcliffe’s record is receding.

The fact that three Kenyan women were on the podium in the World Championship in 2011 and again London in March this year confirms that Kenyan women are beginning to emulate their male compatriots’ domination of the event.  It is wild speculation to try to identify who among the current leading Kenyan women might eventually challenge Radcliffe’s record.  Nonetheless, I think that Florence Kiplagat is the one to watch – though her marathon performances so far have been erratic.  She did not finish her debut in Boston last year, but then looked very powerful and well-coordinated as she picked up speed in the final Km on her way to winning the Berlin marathon 5 months later.  However, in London in April this year, her fourth place was not enough to secure her a place in the Kenyan 2012 Olympic team.  Perhaps the intense pressure that Kenyans, both women and men, faced to achieve Olympic selection this year had taken its toll.  But it is probable that at 25, Florence is still some way from her peak.  However, if the women’s marathon is the follow the path of the men’s event, the upcoming generation will need to combine the grit of Radcliffe with the grace of Ndereba and Keitany.

The Enigmatic Benefits of Pose

My post ‘Natural Running’ posted on March 29 has so far elicited 157 comments, which at first sight might indicate that it was a topic of wide popular appeal.  While I hope there is some truth in that, the number of comments actually reflects something different.  Of the almost 4000 apparently ‘serious’ views of my blog ( not including the almost countless number of spam hits) in the past three weeks, only 288 were views of that page.  Meanwhile, in the same three week period, my post from early March, ‘Does Usain Bolt run Pose Style,’ has been viewed over 500 times, while two of my perennially popular pages (‘Why do Marathon Runners have Skinny Legs?’ and  ‘HRV during Exercise’) have drawn a few hundred views each, as is typical of any three week period.   The popularity of the Bolt post is a pointer to the explanation for the large number of comments on the ‘Natural Running’ post. The majority of the 157 comments have been discussions between Jeremy, Hans, Simon and myself on issues closely related to Pose style.

I have enjoyed participating is this lengthy discussion especially because it has yet again emphasized several of the characteristic features of Pose.  One is the issue that drew Hans in to the discussion.  As I remarked in a recent post, Hans is a runner who previously suffered a number of injuries while running with an approach based on effortful pushing.  However, apart from some transient Achilles tendon problems, has enjoyed a relaxed, injury free running since taking up Pose, under the guidance of Jeremy.  Hans has been eager to understand the physics and biomechanics of running but has been left with a dilemma: how can he explain the clear success of his current relaxed Pose style of running in light of the apparent conflict with the principles of physics and biomechanics.  He has continued to design experiments to demonstrate that gravitational torque might provide kinetic energy which can be harnessed for propulsion when running.   We have discussed his proposed experiments in some detail in the comments section of ‘Natural Running’.  Hans has a clear enough understanding to see that ground reaction forces, both horizontal and vertical, must account for forward and upward motion of the body, but is still trying to devise the experiment that will demonstrate the role of gravitational torque, for the understandable reason that his experience demonstrates that Pose works.

Simon has occasionally chipped to the discussion between Hans and myself, sometimes to re-inforce to Hans the inevitable consequences of Newton’s laws of motion, and sometimes to remind me that even though Newton’s laws clearly demonstrate that a push against the ground is required, this is a push that is largely automatic, and to warn me that my use of the term ‘push’ creates danger of misdirecting recreational runners towards a running style that emphasizes conscious push against the ground.  In fact I agree strongly with Simon that for many runners it is counterproductive and perhaps even dangerous to produce a conscious push.  Meanwhile Jeremy, who was an elite athlete with a sub-4 minute mile to his credit in the days before he took up Pose, has contributed comments reflecting the more typical position of a Pose advocate: namely that experience demonstrates Pose is unarguably the right way to run and anyone who questions this is simply wrong.

As I have pointed out several times in the past, I have been  fascinated by Pose for almost eight years on account of the fact that  many recreational runners have found it has helped them run with fewer injuries, at least once that they have got beyond the Achilles problems that are common in the early stages.  As I and others have frequently pointed out, Pose is based on a faulty understanding of physics and biomechanics, so what is the secret to its success?

The most immediately apparent answer is that by creating an illusion that gravity provides free energy, Pose encourages the runner to stop consciously pushing against the ground.  Since we are far more likely to push as the wrong time or in the wrong direction if we try to impose conscious control on the organization of a process that is better left to the non-conscious motor control system in our brain, it is not surprising that Pose often works well, at least for recreational athletes.  However, if decreasing the rate of injury is merely a matter of disengaging our conscious mind from involvement in the task, simply chatting with a running partner should work just as well.  This is probably not the case, suggesting that there are some more positive reasons why Pose works.

While it would be fatuous for an outsider to claim to understand Pose with the insight of a disciple fully imbued with the tradition and rituals of the practice,  the long and challenging discussions with Hans and Jeremy left me with a feeling that I now understand what it is about Pose that works sufficiently well to allow me to fit these beneficial features into my own approach to running, without the need to embrace the cartoon physics.   So what are the elements of Pose that might be beneficial?

 

Acceleration

First, it is important to note the role of gravity is accelerating, either at the start of a run or when changing speed.  Leaning does allow us to use gravity to generate kinetic energy which can then be re-directed to provide horizontal acceleration by means of ground reaction force.  This involves a push against the ground but this push is mainly a reflex action to stop falling on one’s face.  So there is no doubt that gravity helps acceleration, even though the work is ultimately done by the muscles.  For a sprinter, he/she consciously pushes against the starting blocks and the ground but an endurance runner rarely perceives the push.

 

Minimising time on stance

When running at a steady speed, Newton’s first law, which states that a body continues in a state of uniform motion unless acted upon by a force, tells us that we can minimise the need for any push by minimising braking.  We minimise braking by spending a small time on stance.  There are two feature of Pose that minimise braking.  The first is high cadence.  This results in a shorter gait cycle, including shorter time on stance and shorter airborne time. The shorter airborne helps reduce stance time by virtue of the fact that the impulse required to get airborne can be delivered within a shorter stance time (for a specified value of average vertical Ground Reaction Force).

The other relevant feature of Pose that helps achieve a short time on stance is the mental focus on rapidly pulling the foot from the ground.  This pull is supposedly led by a hamstring contraction (see Pose tech article 000280). In fact it is an illusion that pulling gets us airborne. It is a push that gets us airborne, though a substantial portion of the energy for this push is provided via elastic recoil.  By encouraging a mental focus on pulling the foot from the ground, Pose encourages a short time on stance. I believe this is largely achieved by producing non-conscious pre-tensioning of the hip extensors (hamstrings and gluteus maximus) in late swing, leading to a strong contraction of these muscles at foot-fall, thereby capturing impact energy as elastic energy and contributing to the build up of a strong push against the ground.  This arrests the falling body and propels it forward and upwards after mid-stance.  However, Dr Romanov argues that the hamstring contraction at the end of stance provides an upwards pull that breaks contact between foot and ground.  While there is no doubt that the push (admittedly largely automatic and powered at least in part by elastic recoil) is what generates the ground reaction force that propels the body upwards, it is nonetheless feasible that by pulling the foot towards the upwardly moving hips, a hamstring contraction might contribute to breaking contact.  To understand the role of this hamstring contraction, it is necessary to consider what happens in early swing phase

 

The mechanism of the swing

The principle role of the swing is to get the foot forwards from a position behind the torso at the end of stance to a position a short distance in front of the torso at footfall.  In early swing phase, both hip and knee flex.  The flexion of the hip causes the thigh to move forward and up while and the knee flexion causes the foot to swing upwards relative to the thigh.   In Post Tech article 000280 Dr Romanov acknowledges that both the hamstrings and hip flexors play a role in this, but he strongly emphasises that the hamstrings play the leading role.  He argues that it is preferable to focus on a hamstring contraction rather than a powerful contraction of the hip flexors because not much work is required to achieve the swing.  In Chapter 8 of Pose Method of Triathlon Techniques, he states: ‘There is no need at all to move the swing leg forcefully forward; all the runner needs to do at this point is to continue to fall forward’

His justification for this claim is based on a seriously mistaken understanding of Coriolis force, but his claim does indeed contain a germ of truth.  Coriolis force is a virtual force that is invoked to account for the path of an object viewed by an observer in a rotating frame of reference.  Neither the runner nor a stationary observer is in a rotating frame of reference.  Coriolis force might only need to be invoked to account for the trajectory of a part of the body viewed via a video camera mounted on a rotating part of the leg or arm.   And even for such an observer, the Coriolis force would not be a real force; it would simply provide a way of describing the fact that the observed body part is moving relative to the observation platform.  By invoking Coriolis force as the force involved in the swing while pointing out that it is not a real force, Dr Romanov creates an illusion that very little work is required to swing the leg.  This is simply wrong.  In fact, at high speeds, the energy cost of swinging the leg  exceeds the costs of overcoming braking and of getting airborne (as discussed in my post of  April 5^th, on cadence).

However, the germ of truth comes in the fact that in Chapter 8 of Pose Method of Triathlon Techniques, Dr Romanov explains how Coriolis force works by referring to the equation for the moment of inertia of a rotating body.  In the context of the swinging leg, this equation for moment of inertia has nothing to do with Coriolis force, but is very relevant to making the swing efficient.  The change in moment of inertia accounts for the remarkable effect obtained when the distribution of mass in a rotating objects is adjusted to make the rotating body more compact.  The effect is illustrated most dramatically by a pirouetting ice skater.  As the skater draws his or her arms in towards the torso the speed of rotation in increases. This is because for the amount of force that is required to produce rotational motion depends on both the mass of the object and the square of the distance of each part of the body from the axis about which it is rotating.   The moment of inertia of a body about a given axis is the sum of a contribution from each body part calculated by multiplying mass of the body part by square of distance of that part from the axis.   A smaller force is required to accelerate a compact rotating body on account of its relatively small moment of inertia.  If the body is already rotating, the law of conservation of angular momentum ensures that making it more compact will cause it to spin faster without requiring  input of more energy.

With regard to the swing leg, if the foot is folded up near to the buttocks as a result of knee flexion, it has a smaller moment of inertia and requires a smaller force (and less energy) to swing it.  Most coaches simply refer to this as the benefit of a short lever arm.

By spuriously invoking the concept of the virtual Coriolis force, Dr Romanov  has emphasised that it is best to avoid consciously driving the swing.  In fact, the pendular swing of the thigh around the hip and the lower leg around the knee does require exertion of force.  It is not purely driven by gravity. However much of the work of swinging the thigh is done by the psoas muscle which is buried deep in the pelvis.  Because it plays a major role in maintaining posture and in many everyday actions such a climbing stairs, psoas is a fairly strong muscle in most people.  Many runners are not aware of it, unless it is injured; and then they sometimes find themselves incapacitated for a period of months.  However most of the time psoas gets on with what we require of it without need for conscious attention.

Furthermore in late stance, the hip flexors, including psoas, are preloaded by the stretch that occurs as the torso moves ahead of the thigh, thereby extending the hip.  So at the beginning of the swing, psoas and the other hip flexors contract automatically.  If they did not, the leg and foot would drag behind the torso.   Although Dr Romanovs’ emphasis on the hamstrings as the prime mover in initiating the swing is based on erroneous physics and biomechanics, in practise it is probably best to avoid consciously driving the hip flexors.  Conscious driving is likely to lead to over-striding, in which the foot lands too far in front of the torso producing excessive braking, which wastes energy and might increase the risk of injury

 

Conclusions

Thus despite being based on erroneous physics and erroneous biomechanics, Pose does encourage the runner to engage muscles that achieve efficient running in an apparently less effortful manner, and to avoid conscious forceful contraction of muscles which are best left to contract automatically.  If we are to run well we need to avoid unnecessary or mistimed pushing.  In particular we need to avoid wasting kinetic energy by unnecessary braking and we need to learn how to capture impact energy via elastic recoil.    I therefore think that for recreational endurance runners Pose is better than a running style that is based on the mistaken belief that strong conscious pushing is required.   Elite sprinters do need to push consciously, but that is not our present topic.

However, while Pose has advantages for the recreational runner, there are two types of problem with Pose.  First, it creates the illusion that large forces are not required and this illusion does predispose to some injuries.  Secondly, for a recreational runner who wishes to achieve his/her best possible performance, there is a risk of failing do the type of training that is required.  To give one very specific example, the Change of Stance and High Knees drills involve similar movements: the flexion of hip and knee of one leg as it rises while the other leg descends to the ground.  However, CoS promotes precise timing while High Knees develops powerful hip flexors.  Pose places a disproportional emphasis on CoS at the expense of High Knees.   If we wish to achieve our peak performance we need to ensure that the hip flexors, including psoas, are powerful.

Summary

The emphasis on minimizing push against the ground avoids the dangers of a mistimed or delayed push.  In practice a push is essential to get airborne and to compensate for braking.  Nonetheless, by promoting high cadence and rapid lift-off from stance, Pose minimises the amount of braking while encouraging a non-conscious push.  Similarly, by minimising the role of the hip flexors during swing, Pose reduces the risk of harmful over-striding.  In practice, the required hip flexor contraction occurs automatically.  For the recreational runner for whom avoidance of injury is more important that achieving peak performance, Pose has several features to recommend it, including minimizing the risk of protracted push against the ground and the risk of over-striding.

Running naturally using sense and science

A few months ago I had a fairly clear idea about the content of my next few blog posts: my debate with Robert over the New Year period (recorded at length in the comments section of my Dance with the Devil article) had prompted me to tackle the issue of applying Newton’s equations of motion to running in a systematic manner, so my immediate priority at that time was a few technical articles on the mechanics of running.  After those articles, I intended to return to the issues of developing aerobic fitness; the influence of hormones such as growth hormone on tissue repair and regeneration; and some further accounts of my experiences with monitoring my heart rate.   This broad sketch is still on the drawing board but I have been waylaid by many interesting diversions. Apart from one post on the heart of the runner, that I felt could not wait too long because it was, in a way, my tribute to John Hadd, who had died while running a few months earlier, my posts this year have been heavily focussed on Newtonian mechanics, but many aspects of running mechanics remain untouched.

I anticipated that after the main article, posted on January 16^th, in which I outlined the application of Newton’s equations to the motion of the runner’s centre of gravity (COG) and demonstrated the inevitable reality that getting airborne efficiently – the essence of efficient running – demands a short, sharp push against the ground, that I would easily tie up a few loose ends: important issues such a identifying optimum cadence and more peripheral issues such as dealing with wind resistance; but I had under-estimated the magnitude of the task.  In that first article, I had alluded in passing to the energy cost of repositioning the swing leg.  However I intended to by-pass this tricky topic by focussing on low to moderate speeds where repositioning costs are a minor fraction of the total energy cost.  However, Simon, whom I had come to know, at least in cyberspace, as a kindred spirit sharing a sceptical fascination with Pose technique, would not let me get away so easily with ignoring repositioning costs.  Others have jointed the debate from various perspectives, and as a result, I am still far short of my initial goal of reviewing the implications of Newton’s equations.  I continue to ponder the issues of aerobic fitness, tissue regeneration and heart rhythms, but my planned updates on these topics have been delayed.

The conundrum of the push

However, I have not been able to ignore another issue.  The conundrum that it is almost certain that for most runners, conscious focus on delivering a short, sharp push against the ground is not the best way to run safely and efficiently, except perhaps when sprinting.  It is this conundrum that has fuelled my long-standing fascination with Pose.  Despite the ‘looney-toon’ cartoon physics proposed by Dr Romanov in his book, ‘Pose Method of Running’, and unfortunately still lingering in articles on the Pose Tech website, there is little doubt that this irrationally-inspired running technique  has helped a large number of recreational runners to enjoy safer, more satisfying running.  There have also been many individuals disillusioned by being told by Pose coaches that their Achilles tendon injuries are simply due to not doing Pose properly, and others who have been disappointed that their race performances have not improved in the way they had hoped.  However, there does appear to be some magical injury-reducing ingredients in Pose.  One of these is the necessity to cut one’s training volume while developing the skill to perform the technique.  Furthermore, the reduced stress on the knee is an easily understood consequence of the Pose emphasis on forefoot or midfoot landing, though ironically it is the forefoot landing that puts the Achilles at risk.   The recommendation of high cadence reduces the magnitude of the force required for each step.  However, I think an even more important issue is the fact that the illusion that gravity provides ‘free energy’ allows Pose runners to achieve the essential short-sharp push against the ground without trying.

The secret

Is there a secret?  Many comments that have appeared on internet discussion threads in recent years imply that the secret lies in ignoring the physics; that  it is subjective experience that counts;   that we should perhaps revert to the noble primeval state of our Palaeolithic ancestors who are thought to have engaged in persistence hunting, barefoot, on the African savannah two million years ago.  The core idea is that thinking about what you are doing gets in the way of doing it.  In fact I strongly agree that attempting to exert conscious control over skills that our unconscious brain has learned to perform is often counter-productive.  However I do not believe that the secret is to revert to a primeval Palaeolithic state.  In fact I do not believe that would be natural.  In the two million or so years that separate early members of the Homo genus, such as Homo erectus who apparently had developed the musculo-skeletal features necessary for endurance running, from Homo sapiens with his/her large skull, we have developed an extraordinary capacity to achieve our goals, a capacity residing largely in our brains.

For several millennia, this capacity was strongly shaped by spirituality.  In the video recording of persistence hunting in our own era by bushmen in the Kalahari, narrated by David Attenborough, there is a moving moment near the end, after the quarry has been killed, in which the hunter strokes the head of the dead animal in acknowledgment of the spirit with which it had eluded its pursuer in an eight hour run across the savannah.   Spirituality is a key human persisting attribute.  If we are to be truly in tune with our own nature, we need to find a way to integrate the legacy we have received from our Palaeolithic ancestors with the capacity for science that is embodied in Newtonian mechanics.  For the present discussion, we can put aside relativity, quantum mechanics, and string theory.  Our Palaeolithic ancestors, perhaps unencumbered by too much weighty remembrance of the past or planning for the future, lived much more in the present moment, in which sensations not only of sight and sound, but also the sensations of the body in its environment, dominated awareness.  Can we run in a way that utilises both sense and science?

John Woodward, a practitioner of the Alexander Technique based in the Lake District where he teaches the art of running barefoot across the Lakeland fells, summarises the challenge: ‘.. in our modern lives our thinking caps (our heads) have become disengaged from our kinesthetic (body) sense. Unlike our ancient ancestor we are rarely in the vivifying moment but we languish in some past memory or crave some future state.’

Feldenkrais

I have been diverted into this train of thought by some challenging questions and comments on my article  on Natural Running (posted  on 29^th March), especially by Hans, a Feldenkreis practitioner who had attempted various ways to escape his previous injury-prone running style before trying Pose, under the guidance of Jeremy Huffman.  Jeremy is an elite athlete with a sub-4 minute indoor mile to his credit, who has subsequently become a strong advocate of Pose, and frequently comments on this blog.  Jeremy helped Hans find the practical answer he was seeking, but left him with the challenge of understanding how Pose had worked while Feldenkrais had not.   Feldenkrais had been developed by Moshe Feldenkrais, who was an engineer who attempted to integrate a sound scientific understanding of human movement with a holistic awareness of one’s body in space.  Moshe Feldenkrias did not develop a theory of running but others, such as Feldenkrais practitioner, Jae Gruenke, have done so.  Hans concluded the emphasis on avoiding driving and pushing was a key issue in the success of Pose.  In his comments on my blog he initially questioned the necessity of the push.  After we had discussed a number of actual and hypothetical experiments that he devised, he was willing to accept that the push occurs, but proposed that the action of the leg might best be described and experienced as springy, rather than a push movement.  He agreed that that muscle work is involved in creating the springy effect, but this could happen without conscious effort

I agree that it is desirable to maximise the recovery of energy via elastic recoil, and certainly accept that it is best to let this occur with minimal conscious effort.   However, my own view is that we need a somewhat more comprehensive approach.  I think that it is best to cultivate a holistic perception of one’s body in space while applying a range of principles that are derived not only from physics and muscle physiology but also from neuroscience.

Some background

Perhaps it is time to give a little more detail about my background.  I began my scientific career as a physicist over forty years ago and subsequently have been fortunate enough to have had the opportunity do research in many different fields of science.  From physics I moved to biochemistry, or rather I integrated physics with biochemistry while holding joint academic posts in physics and biology.  Eventually, after several decades of diverse scientific and clinical experiences, I became what might be most accurately described as a neuroscientist, though I have always resisted labelling myself as a practitioner of a single discipline.  In the early 1990’s I was involved in some of the earliest investigations using modern brain imaging techniques to attempt to delineate the brain mechanism associated with willed action.  Since then I have continued to study brain function, mainly focussing on the conscious processing of information.  I am certainly not an expert in either the perceptual or motor systems in the brain.  Nonetheless, in some of my recent work using brain imaging techniques combined with electroencephalography (EEG), I have investigated the way in which the perception of bodily sensation engages the brain’s executive systems.

Although this work is exciting and high tech, it is also extremely primitive.   Indeed, while I am confident that neuroscience will furnish us with concepts that help us to understand many of the types of processes that go on in our minds and bodies, I believe it will never provide an understanding that matches the richness and diversity of personal experience.

In the days when I was doing my PhD in physics, I was also a marathon runner and a mountaineer.   Though physics, running, and spending time in the mountains were an integral part of my life, there were only a few strands that linked these activities.   Over the years, the rest of life’s activities displaced the running and, eventually, the adventurous aspects of mountaineering.  However nowadays I am once again running and also enjoying the hills and mountains, while I am still a scientist.  My forays into the intricacies of the human mind and brain have given me a slightly firmer foundation from which to try to integrate science, running and an appreciation of the natural world

The messages from neuroscience

Perhaps the most relevant message from cognitive neuroscience to the runner is that we can only focus consciously on a very small number of items of information at any one time, but the neural representation of many other aspects of a situation can be subliminally active in the background.  Furthermore, our brains are exquisitely sensitive to unexpected events. Thus we cannot focus on all of the aspects of running mechanics within a single gait cycle, but if we have practiced the actions and experienced the sensations often enough, the neural representation of most aspects of running are subliminally active, and are likely to enter into conscious awareness if the expected rhythm misses a beat.  In an attempt to instil the expectation of the pattern of activity involved in the swing of the leg from one stance to the next, I practice drills such as the Swing Drill.

The next important point emerges from our understanding of the sensori-motor systems: modern brain imaging has consolidated the observation of neurosurgeon Wilder Penfield at the Montreal Neurological Institute in the 1930’s, that the brain allocates far more of its processing resources to the hand than to the foot.   The region of the motor cortex devoted to the hand  is far greater in area than that devoted to the foot.  However, our brain can learn to integrate a complex set of muscle contraction into a single action.  Therefore, it is plausible that if we can link a set of movement of the hand to a set of movement of the leg and foot, we might be able to control this complex but integrated action more precisely.  Therefore I practice a version of the Change of Stance drill to establish in my brain a non-conscious motor program that combines a down sweep of my hand from a position near the sternum high on my chest wall towards my waist, with a quick extension of the flexed hip and knee of my elevated leg to the ground.  As I sweep my hand down, I hold forefinger and thumb lightly opposed to inculcate a sense of tidy but relaxed movement.  When I run, I rarely attend consciously to the extension of hip or knee but focus mainly on this brisk but relaxed and economical down-sweep of the hand.

This was the final sprint in a half-marathon a few years ago. I am 4449. The strain of running with a torn hip adductor, wrenched during a clumsy turn near the halfway mark, shows in the tense muscles in my neck and left shoulder, but the right hand, with forefinger and thumb lightly opposed at my waist is fairly well coordinated with the (non-conscious) push of my left leg.

The next important point to learn from the way in which our brain develops from infancy to adulthood, is that we learn how to detach unnecessary movement from a motor act.  A young child, when trying to do some intricate task with one hand, often exhibits mirror movements with the other.  Although we usually avoid this in adulthood, at times of stress, we are prone to introduce unnecessary movements.  Perhaps Paula Radcliffe’s tortuous movements of the neck during her 10,000m races in the late 1990’s were an illustration of this.  You can also see it in the picture of me.  However we have the capacity to release tension in unneeded muscles.    When I run I cultivate an awareness of the tension in my shoulder muscles, aiming for a sensation of the trapezius muscle relaxing to allowing my shoulders to relax downwards and slightly back.

I also find it helpful to maintain awareness of the pattern of pressure on the soles of my feet during stance, and to adjust this according to terrain and speed.  I do not run barefoot, except for short distances on grass, but do wear fairly light-weight shoes.

I regulate my level of energy expenditure largely by awareness of my breathing.  When breathing comfortably at a rate of one breath every six steps (about 30 breaths per minute),  I know I am in the lower aerobic zone, with minimal accumulation of acidity in my blood stream.  I can run for hours at this pace.  When my breathing rate increases to one every four steps, there has been mild accumulation of acid, but my body is dealing with it.  Nowadays I will be struggling after an hour at this pace, though a few years ago I could maintain this pace for about two hours.  When breathing rate becomes one breath every two steps, the acidity is accumulating rapidly.  This is only OK for the final stages of a race, or during high intensity intervals.

Some of these aspects of body awareness are well known to coaches and athletes; others, such as my focus on the down sweeping hand are experimental.  The over-arching principle is the cultivation of a holistic awareness of the sensations and movements involved in running, allowing for effort in the right time and place, while maintaining an overall sense of light, relaxed progress across the ground.

Final thoughts 

Here is John Woodward again, describing a workshop that he and his colleagues offer: ‘We perpetually stream down one route – the mechanical one: WE RUN MECHANICALLY. The aim of the workshop is to first and foremost stop the flow of traffic down the mechanical road the route well travelled. Like repositioning the points on the railway we want to initiate a flow down the road less travelled. This will enable the Thinking Gear to re-synchronize once more with the body. In this way we might begin to run creatively. There’s a number of key things about this invitation to re-route the traffic onto the road less travelled, the road to the present moment.’

I am not fully in tune with all of this statement.  I do not think we need to stop the traffic flow on the mechanical path.  I think the word ‘synchronise’ is the key concept. If we, as members of the species Homo sapiens, are to run truly naturally we need to find a way of synchronising the two routes: the mechanical path guided by knowledge and shaped by practice, and the path through sensations in the present moment.  I am still at the beginning of working out how this might be done.  My current experiments in running holistically might be clumsy, half-blinded attempts towards the goal.  I will value any comments.

Note added 12 April 2012

With regard to the proposal that it might be desirable develop a holistic sense of what is happening to the body, even though our attention is not focussed consciously on every aspect, there is a very informative picture in today’s Guardian newspaper, showing Prince Harry and Usain Bolt being silly for the sake of a photo-opportunity.  http://www.guardian.co.uk/uk/2012/apr/11/how-the-royals-became-cool   They are imitating a well known advertisement for Richard Branson’s company, Virgin. In the advertisement, Branson’s face is superimposed on Bolt’s body, as he mimes shooting an arrow from a bow.  In this Guardian photo of Harry and Bolt, note how the index finger of Bolt’s right hand is aligned perfectly with the index finger of his left hand.  I suspect he wasn’t consciously thinking about this as he posed for the photo.  Simply, his brain has an extremely good sense of where the ends of his limbs are at all times.  I think that is one of the reasons Bolt is the world’s fastest sprinter.  I think we can improve our running by improving our bodily awareness. In particular, awareness of the end of the index finger can probably associated with subliminal awareness of the location of the foot.

Is there a magic running cadence?

The six posts in my recent discussion of running mechanics, starting with my presentation of the equations of motion of the runner on 16^th of January, have elicited 372 comments (including my own responses to the comments of others).  I have been delighted by the vigour of the discussion, but am intrigued by the fact that of these posts, the one which elicited the least comment was my post on the increased efficiency associated with increased cadence, on 6^th February, which elicited only 5 comments.   I suspect that this relative paucity of comments reflects a widespread acceptance that increasing cadence does improve efficiency.  The major issues in the other five posts were related to the question of the push that is required to get airborne.  This appears to be a far more controversial topic.

From my own perspective, the controversy regarding push rather than cadence is a peculiar inversion of the uncertainties of running mechanics.  The fact that a large push is required to get airborne can be demonstrated by simple application of the laws of physics, and is readily confirmed by examination of force plate data.  A large vertical push makes it possible to minimise braking.  However, elastic recoil can produce at most 50% of the required energy for the push, so the vertical push is not cost free.  I suspect that the controversy about push exists because many runners, especially those who have adopted the Pose style, have found that they suffer less injury when they do not focus consciously on pushing.  Of course avoiding thinking about the push does not stop it happening.   But the evidence does suggest that avoiding thinking about it does reduce the risk of some common types of injury.  My own view is that denying the occurrence of a large push creates a different set of risks, and therefore I think that the challenging goal of developing a safe efficient running style is creating a mental image that allows a runner to avoid a mis-timed push and other associated unnecessary muscle activity, without the need to deny the existence of strong push.

The question of how to develop the optimum mental image is a question I will certainly return to in future.   The question that currently intrigues me is the apparently widespread acceptance that high cadence is generally good (a view that I myself advocate, but with reservations).  This view does not account for the clear evidence that most runners employ a relatively low cadence at low speed and increase as they increase speed.   While it is commonly believed that a cadence of 180 steps per minute (or 90 gait cycles per minute) is the optimum cacence, it is noteworthy that the representative runner depicted in figure 2 of Weyand’s paper (J appl Physiol, 89, 1991-1999, 200) increases cadence for about 144 steps per minute at a speed of 3.5 m/sec to 234 steps per minute at a speed 9.5 m/sec.  In my experience, these values are typical.   While many runners have a cadence around 140 steps /min or less when jogging, elite sprinters usually exceed 250 steps/min at top speed.   Therefore, the view that there is a target cadence of180 steps/min only corresponds very loosely with what runners do.

There is an optimum cadence for a given speed and peak vGRF

To estimate the most efficient cadence for a particular speed it is necessary to compute all three of the major costs of running: elevating the body, overcoming braking, and re-positioning the limbs.  While the combined costs of elevating the body and overcoming braking generally decrease with increasing cadence, the costs of repositioning the limbs increases with increasing cadence and also with increasing running speed (see calculations page, in the side bar, where I demonstrate that a fairly accurate estimate of the repositioing costs per Km per Kg body mass is given by 1.32CV Newton-metres where C is cadence in steps / min and V is running speed in metre/sec  ).  Therefore, for a given speed and peak value of vertical Ground Reaction Force (vGRF), there will be certain cadence at which the total energy cost will be minimised.  In other words, total energy costs decrease as cadence increases up to a certain point, but after the point at which the increasing cost of accelerating the swing leg outweighs the saving in the sum of elevation and braking costs, further increase in cadence will lead to greater costs.

Optimum cadence depends on ability to push

However, there is no single optimum value for cadence. The optimum cadence depends on one’s ability to exert a well timed strong push.  Elevation and braking costs decrease with increasing peak vGRF at a particular velocity, so the cadence at which the repositioning cost outweigh the elevation and braking costs at that velocity, will occur at a lower cadence in a runner who can exert a stronger push.  As the cost of accelerating the swing leg is lower at a lower cadence, peak efficiency will be greater in a runner who is capable of exerting a greater peak vGRF thereby achieving peak efficiency at lower cadence.  In other words, we can increase efficiency by developing the ability to exert a stronger push, provided the push is delivered at the right time and without producing unnecessary contraction of other muscles.

A comparison of age with youth

The computations that I presented on 6^th February, clearly demonstrated that at a speed of 4 m/sec, the combined cost of overcoming braking and getting airborne is less at a cadence of 200 steps per minute than at 180 steps per minute, when the peak vGRF is 3 times body weight.  In fact, I myself adopt a cadence a little over 200 steps per minute at a speed of 4 m/sec, but most runners do not adopt such a high cadence at this modest speed.  I do so because, being a 66 year old with failing muscle strength, I find it difficult to exert a push against the ground of more than 3 times my body weight without straining.   Many younger athletes can easily exceed a peak push of this magnitude without consciously trying.  I am currently trying to increase my ability to achieve a stronger, well coordinated peak push, both by means of increasing my muscle strength, and also by improving the coordination of the push.

Recently Ewen pointed out on his blog that in setting the British 3000m indoor record of 7:40.99  in Glasgow in 2009, Mo Farah exhibited a cadence of only 176 steps/min in mid-race when he was covering each Km in about 2:35 (almost 6.5 m/sec).  He did increase to a cadence of around 187 in final few laps.

It appears that Mo is able to achieve a high efficiency at a relatively low cadence.  This demonstrates that he is capable of exerting an exceptionally strong, well coordinated push.

Conclusion

In summary, while the combined cost of elevation and braking decrease with increasing cadence, the cost of accelerating the swing leg increases with increasing cadence.  The total cost of elevation, braking and accelerating the swinging leg will decrease as cadence increases up to a certain limit, but beyond the point where rate of increase in swing costs outweighs the saving in elevation and braking cost, increasing cadence results in increasing cost.   A runner who is able to deliver a well-timed large push without simultaneously contracting unnecessary muscles can achieve peak efficiency at a relatively low cadence.

Natural running

The word ‘natural’ invokes images of wholesomeness but also carries a hint that we are in danger of being hoodwinked by a snake-oil merchant.  In contrast, the word ‘technological’ has overtones of something lacking wholesomeness.  Nonetheless, on the whole, I am glad I belong to a species with the brainpower to develop technology.   Many inventions created by human wit, ranging from reading glasses to electronic devices, extend the range of activities that are accessible to me and make life more interesting.  But when it comes to running, there is good reason to ask whether we have lost our natural skill as a result of growing up a modern technological society.

Humans are in fact remarkably good endurance runners.  Although many species can outpace us in a short sprint, few can maintain a steady pace for such long distances. On the other hand, a very large proportion of us get injured each year.  In a comprehensive review of studies of injury rates among distance runners, van Ghent and colleagues found that the incidence of lower extremity injuries reported in published studies ranges from 20% to 79% (Br J Sports Med 41: 469-480, 2007).

Persistence hunting

Accumulating evidence suggests that humans became good endurance runners because evolution favoured the development of anatomical (and perhaps biochemical) adaptations that enabled our forebears to engage in persistence hunting – in which the hunter pursues his quarry to the point of exhaustion – on the African savannah around two million years ago. (Bramble and Lieberman, Nature, 432, 345-352  2004).   We do not know whether or not early persistence hunters were also prone to injury, though evolution would scarcely have favoured those who were as prone to injury as modern-day runners. Perhaps only an elite few in the tribe were able to run without injury.  Among the few remaining peoples of the Kalahari desert who continue to practice persistence hunting today, the huntsman who engages in the long chase is an elite member of the hunting group.  Nonetheless, an ability to run far with few injuries is likely to have been a fairly common skill among our early ancestors.

Bare feet v shoes

So if we wish to minimize injury, it is probably worthwhile to ask how did our forebears run.  Perhaps the first point to note is that they would not have worn shoes (though it is also noteworthy that  modern-day persistence hunters in the Kalahari do wear shoes).  The most striking difference between barefoot and shod runners is the nature of the foot-strike.  Hasegawa and colleagues demonstrated that about 75% of runners wearing modern running shoes heel-strike (J Strength Cond Res. 21(3):888-93, 2007).  In contrast, Lieberman and colleagues have demonstrated that bare-foot runners are much more likely to land on the forefoot and then transfer a portion of the load to the heel whilst on stance.  Lieberman and colleagues have demonstrated this is a systematic study comparing American habitual barefoot runners with shod runners, and confirmed it in a less systematic observation of Africans who had grown up never wearing shoes (Nature. 463(7280):531-5, 2010.   Landing on the forefoot minimises the initial sharp increase in vertical ground reaction force that is seen with heel striking.

Lieberman is firm in pointing out that there is no strong evidence that minimising this sharp increase in ground reaction force leads to lower injury risk. However, in general, the repeated application of a rapidly rising large force is stressful and might be expected to lead to stress fracture.  So it is plausible that injury risk is greater when wearing shoes. This plausibility is confirmed by Kerrigan’s demonstration of greater torques at hip and knee during shod running (PM &R: The Journal of Injury, Function and Rehabilitation, Vol. 1, pp 1058-1063, 2009).  Thus it appears that Bill Bowerman’s first experiments with a waffle iron that led to the modern running shoe, were a faltering mis-step based on the mistaken idea that putting padding between the runners foot and the ground would increase safety and efficiency.

Getting airborne

I have discussed the question of running shoes and foot-strike in a previous post, and I will probably return to it again in the future.  However my main interest today is in the question of how our forebears were equipped to deal with the cardinal challenge of running: exerting a strong enough force to get airborne.  Getting airborne is the essence of running.  It allows us to minimise the inefficient braking that is an inevitable consequence of maintaining a stationary foot on the ground during the stance phase.  To minimise braking we must spend as small a portion of the gait cycle on stance as is possible.  We can do this by landing with the foot only a short distance in front of our centre of gravity (COG), but that necessarily entails the exertion of a large push against the ground.   If we are on stance for only a third of the gait cycle, the average push against the ground during stance must be three times body weight.

A substantial part of this push is generated via elastic recoil.  But in fact, measurements suggest that at most about 50% of the required energy can be generated by elastic recoil (Alexander, R.M. Energy-saving mechanisms in walking and running. J.Exp.Biol.160,55–69,1991).  So an equally substantial portion of the work must be done by an active push.   What evolutionary development allowed early member of the homo genus to achieve this crucial push?  A clue can be found by examining the anatomical differences between ourselves and our nearest primate relative, the chimpanzee.  Chimps, like other non-human primates, are not capable of endurance running.

Differences between man and chimp

The most immediately apparent anatomical difference is man’s larger skull.  However, the larger skull is a feature of homo sapiens rather than early members of the homo genus.  Possibly we owe our large skull and brains  at least in part to a somewhat more subtle change at the lower end of the vertebral column that occurred earlier in homo evolution.  This subtle change, present in early members of the homo genus, such as homo erectus, is a substantial enlargement of the upper part of gluteus maximus.  Gluteus maximus is a hip flexor.  Although it acts with less mechanical advantage than the hamstrings, it is more massive   Could the enlargement of gluteus maximus have played a key role in the development of endurance running ability, thereby facilitating persistence hunting and providing the protein rich diet essential for the eventual development of homo sapiens’ large brain, over a million years later.

The roles of gluteus maximus

To address this question Lieberman and colleagues  examined the activity on gluteus maximus throughout the gait cycle, by recording the electrical signals from an electrode placed over the muscle, during both walking and running (Journal of Experimental Biology 209, 2143-2155, 2006.)  Their  first important  observation was that gluteus maximus is much more active during running than walking, consistent with it being an evolutionary development associated with the acquisition of capacity for endurance running.  During the running gait cycle, there are two main bursts of activity in gluteus maximus: one when the foot from the opposite side of the body is on stance and the other beginning shortly before the footfall of the foot on the same side as the muscle,  and continuing through early stance on that foot.  The activity when the opposite foot is on stance almost certainly reflects the action of arresting the forward motion of the swinging leg.   Interpretation of the role of the burst of activity in early stance on same-sided foot is more complex.  The magnitude of the activation increases with speed of running and is also correlated strongly with the velocity and timing of the forward pitch of the trunk that occurs at foot-strike.  Thus it is very likely that a major role of gluteus maximus is stabilizing the torso.

Mark Cucuzella’s resonant phrase ‘you can’t fire a cannon from a canoe’ powerfully expresses the importance of stabilization of the torso, but it also raises the question of what cannon is being fired.   Could gluteus maximus also contribute to generation of the vertical ground reaction force (vGRF) that launches the body forwards and upwards from stance?   Lieberman and colleagues  observed that the timing and magnitude of activity in gluteus maximus is also correlated with the timing and magnitude of contraction of another major hip extensor, biceps femoris, which is one of the hamstrings.    This suggests an active role in hip extension.  It is important to note this active hip extension is largely confined to the early part of the stance phase.  As the hip and knee are slightly flexed at that time, the main consequence of hip extension will be an increase in the downwards push against the ground.   Thus, this action would be expected to contribute to the initiation of the upward acceleration of the body commencing in mid-swing. Perhaps gluteus maximus also contributes to firing the cannon.

It is noteworthy that one of the early proponents of ‘natural’ running, Ken Mierke, recognised that combining contraction of gluteus maximus with the hamstrings would greatly increase the power of hip extension, thereby reducing fatigue of the relatively weak hamstrings and promoting endurance.  While I think that the essence of Ken’s proposal is sound, I would place a somewhat different emphasis on the effect of the hip extension.  Ken argues that the hip extension largely provides forward propulsion.  I do not think that fits well with the timing of the active contraction of either gluteus maximus or the hamstrings.  Even after allowing for the 40-50 millisecond delay between the electrical signal and the mechanical effect of a muscle contraction, the active contraction of gluteus maximus and the hamstrings is complete shortly after mid-stance.   I think that the main consequence of this powerful hip extension is to accelerate the body upwards thereby achieving a stance that is short – this is the key requirement for efficient running.

Other muscles also contribute, notably contraction of the gastrocnemius, which reaches its peak contraction a little later in stance.  This will generate a forward and upward GRF.  The upward component will add to the impulse that gets us airborne, while the forward component will help compensate for the braking that occurred in early stance.  Because the hamstrings cross both hip and knee, residual tension in the hamstrings in late stance might add to the upswing of the lower leg relative to the torso thereby facilitating the breaking of contact.  However it should be noted that the contribution of a hamstring to pulling the foot towards the torso cannot contribute to raising the centre of mass of the body (as is proposed in Pose theory).  That would be pulling oneself up by ones bootstraps.  The upwards acceleration of the mass of the body must be produced by a push against the ground.  (Added note: it should be acknowledged that Pose theory appears somewhat ambiguous regarding the mechanism by which the centre of mass is raised.  See the comments from Hans and Jeremy below.)

Other evolutionary developments

Development of gluteus maximus was not the only anatomical change occurring early in the evolution of the genus homo.  Freeing up of the tethering of head to shoulders that limits the independent rotation of upper torso and head in other primates, allows us to produce the counter rotation of the torso necessary to balance the swinging leg, while maintaining the head upright and forward-facing.  In addition, the development of a longer Achilles tendon that occurred at some point along the evolutionary path from our even earlier ancestor, australopithecus, to early homo species, is likely to have enhanced the efficiency of capture of impact energy as elastic energy.   But in my opinion, it was the development of gluteus maximus that was the decisive development that allowed us to get airborne efficiently.

Minimizing risk of injury

While these speculations might explain how our forebears came to be efficient endurance runners, it still leaves us with the question of how we might avoid injury in the face the inevitably large vertical ground reaction forces generated by the powerful push.  I think that Kerrigan’s  demonstration of greater torques at hip and knee during shod running is a key observation.  This suggests that the orientation of the foot on the ground during the period around mid-stance when vGRF is at its peak is likely to play a major part in determining how much torque is produced.  Drills that help develop a sharp contraction of gluteus maximus that is well coordinated with the down swing of the contralateral arm will ensure that the non-conscious brain is well appraised of just when the peak vGRF will occur.  In addition, an appropriate  sharing of weight between forefoot and heel at mid-stance facilitated by  shoes that are light enough to allow a good perception of the distribution of ground reaction forces might allow the non-conscious motor control system in our brain  to coordinate the application of the push in a way that minimises potentially damaging torque at the knee and hip.

Conclusion

We have grown to adulthood spending hours each day sitting at a desk or in an automobile seat, and even longer periods with our feet encased in rigid shoes.  If we are to run naturally, in a style similar to that which allowed our early homo ancestors to master the art endurance running, perhaps we should focus on re-training our bodies so that our non-conscious brains can once again integrate the sensory signals from the joints in our arms and legs, with those from the numerous sensory nerve terminals in our feet, to coordinate the delivery a powerful, well-timed but fairly safe push against the ground to get us airborne.

Training to increase sprinting speed

The issues raised by Klas in his comments on my recent post on Usain Bolt’s sprinting style have led me to wonder just what it is that determines peak sprinting speed and what a runner might do to increase sprinting speed.

The key relevant scientific study is the investigation of 33 physically active adults (aged between 18 and 36) of varying sprinting ability, published by Peter Weyand and colleagues from Harvard University in Journal of Applied Physiology (J Appl Physiol, 89: 1991–1999, 2000).  They measured characteristics such as cadence, time on stance, swing time and ground reaction force observed across a range of speeds up each individual’s top sprinting speed.  The range of top speeds extended from 6.2 metre/sec up to 11.1 m/sec.  They observed that the faster sprinters exerted a stronger push on the ground while on stance and concluded ‘runners reach faster top speeds not by repositioning their limbs more rapidly in the air, but by applying greater support forces to the ground’.

I agree with their conclusion, but closer inspection of their data leads me to a slight modification that might have important implications for how a runner should train to increase speed.

Limb repositioning time

First let us consider the time taken to reposition the swinging leg from its position behind the centre of gravity (COG) at lift-off from stance, to a position a little ahead of the COG at foot-fall.  This is the swing time.  It embraces two airborne intervals and a period of stance on the other leg.  Perhaps surprisingly, the swing time at top speed varies very little between runners of markedly different sprinting ability.  The average swing time of the 33 runners was 0.38 seconds with only weak evidence that faster runners have a shorter swing time.  For comparison, the average swing time of the three medal winners in the male 100m at the 1996 Olympics was 0.33 sec.  However, there is little evidence of a consistent trend across the range of sprinting ability.  For example, the slowest of the 33 individuals studies by Weyand had a swing time of 0.34 sec despite running only a little faster than half the speed of the fastest runners.

Although faster runners spend less time on stance, because their speed is greater, the foot gets left further behind during stance. Typically, a slow runner has to move the foot forward by about 85 cm relative to the COG during the swing, while the fastest runners have to move the foot forwards by about 105 cm.  Thus, the faster runners do swing their foot forwards a little faster. For an elite sprinter it is worthwhile expending some effort on improving swing dynamics, for example by flexing the knee to create a short lever arm at mid-swing.  However, this is only fine tuning – perhaps it might make the difference between a gold medal and fourth place, but it is not likely to produce the magnitude of improvement that might encourage a recreational distance runner to choose to become a sprinter instead.

It is interesting to wonder why swing time at top speed varies so little between elite sprinters and non-athletes.  It appears that most of the gain a  faster sprinter derives from increased ability to reposition the foot rapidly relative to the COG is required to compensate for the modest increase in the range of the swing required at higher speed.  It appears to be impossible to get swing time appreciably below a third of a second.  Although the swinging leg is not merely a passive pendulum it is hard to drive it much faster than its natural swinging rate

Time on stance

The strongest predictor of top sprinting speed is ability to get off stance rapidly.  In Weyand’s study, the slowest sprinters spent 0.135 sec on stance while the fastest spent about 0.09 sec on stance.  Furthermore, there was a very consistent trend for decreasing time on stance to predict faster top speed, across the full range of sprinting ability. The correlation between stance time and top speed was 0.76.

Shorter time on stance is associated with stronger push against the ground.  The average vertical ground reaction force (vGRF) during stance increased from 1.9 times body weight to 2.4 times body weight, although the relationship was not quite so consistent across the range of top speeds.  The correlation between average push and top speed was 0.62.  Thus the average vGRF while on stance was not quite such a reliable predictor of top speed as stance time.

It is of interest to note that because stance time decreases as strength of push increases, the impulse delivered (product of force by time for which the force acts) varies relatively little between the slower sprinters and the fastest.  The vertical impulse was 2.49 newton-sec at a top speed of 6.2 m/sec and 2.25 newton-sec at a top speed of 11.1 m/sec. As the vertical impulse determines how much upward momentum is imparted to the body, it determines how high the COG is elevated between mid-stance and mid-flight. .The peak elevation of the COG was marginally lower in the fastest spinters.  The precise gain in elevation from a given impulse depends on the shape of the relationship between force and time while on stance. . For a forefoot runer it is approximaltey sinusoidal and in this case, the range of vertical oscillation of the COG was 5 cm at 6.2 m/sec and 4.3 cm at 11.1 m/sec.

Estimated values for slowest and fastest runners based on linear trends across the group of 33 runners. *The calculation of peak vGRF and elevation assumes a sinusoidal variation of vGRF with time during stance – typical of a forefoot runner

Conclusion

These observations indicate that if one wants to sprint faster, one should aim to increase push and decrease time on stance.  Although these two variables are related, in fact the decrease in time on stance is a stronger predictor of peak speed than the magnitude of the push.  This is not surprising because decreased time on stance directly reduces braking, which leads not only to increased fuel efficiency, as discussed in my post on 16th January, but also to more efficient utilization of peak power.

It is necessary to have strong leg muscles to get off stance quickly, so it is worthwhile training so as to increase leg strength.  As eccentric contraction is required, plyometrics are potentially helpful. However, the fact that the ability to get off stance quickly is the strongest predictor of top speed, suggests that one requires not only adequate strength but also good coordination of the muscles so as to capture impact energy as elastic energy and then release that energy in a smoothly coordinated way.  This conclusion is similar to that reached on the basis of considering the style of Usain Bolt.  If I want to increase my sprint speed I should focus not only on increasing my strength, but also my coordination.

I suspect that genes and development during infancy play a large part in determining how quickly a person can get off stance.  Nonetheless, the fact that top speed decreases with age demonstrates that top speed is not fixed, and suggests that a training program aimed at producing changes opposite to those produced by aging might produce an increase in sprinting speed.

How might I increase my coordination?  Plyometrics are likely to increase coordination in addition to increasing strength, though they are risky, and should be performed in moderation.  A more direct focus on coordination might be worthwhile.  Coordination depends on proprioception  (the ability to sense  where ones limbs are) and the ability to send messages from the central nervous system to the muscles with the appropriate  precise timing.  I believe that drills such as ‘change of stance’ are likely to be an effective way to achieve this

Does Usain Bolt run Pose style?

The contrast between the muscular torso, arms and legs of a sprinter compared with the slight frame and skinny legs of a marathon runner tell us that the requirements for effective sprinting are not the same as for efficient long distance running.  Nonetheless, as I have grown older I am acutely aware of my loss of speed and am eager to do something to arrest this decline.  During my recent examination of the implications of Newton’s equations of motion for the mechanics for efficient running, I have pondered what these equations tell us about sprint technique.  The equations demonstrate that a high cadence and a short time on stance facilitated by a relatively large vGRF generated by a strong push, are key elements of efficient fuel consumption.  Although efficient fuel consumption is not as important for a sprinter as for a distance runner, observation of elite sprinters demonstrates that high cadence and short time on stance are also key features of fast sprinting.

How can we achieve a short time on stance? Anyone who has followed my blog for a while will probably know that I am sceptical about the claims of Dr Romanov’s Pose technique, but I am not inherently anti-Pose.  For more than eight years I have been fascinated by Pose on account of the fact that it appears to facilitate a short time on stance. I have read widely about it, talked to many Pose coaches and even attended a two-day Pose clinic conducted by Dr Romanov, in an attempt to sort out the science from the pseudo-science.  Despite the fact that Pose theory is based on questionable physics, observation of masters of the Pose technique reveals that they can achieve a very rapid lift-off from stance.  During the two-day Pose clinic the observation that impressed me most was the way in which Pose coach, Jon Port, reacted when Dr Romanov gave him a sharp sideways push on his shoulder while he was standing poised on one leg.  Instead of falling sideways, Jon managed to remain upright by getting airborne before his body had a chance to pivot sideways around his point of support.

Therefore, I have been rather intrigued by Dr Romanov’s article on the Post Tech website in which he appears to claim that Usain Bolt runs Pose style.  In an analysis of Bolt’s technique exhibited during the 100m World Championship in Berlin in 2009. Dr Romanov claims he is not “pushing off” but is “waiting”, “allowing” gravitational torque to provide the angular acceleration of the GCM’.   I do not think Dr Romanov’s description of Bolt ‘waiting’ on stance while he allows gravitational torque to provide acceleration of his centre of mass is credible.  There is no way that waiting for gravity to act, without an active push, could get him moving forwards and upwards with the required speed.  Nonetheless, could it be that Bolt’s legendary relaxed manner reflects a mental state similar to that which enables a good Pose runner to get airborne quickly without conscious awareness of a push?

My attempts to identify the features of Pose that promote a short time of stance have led me to conclude that it is achieved by two related features.  Pose drills such as ‘change of stance’ promote rapid flexion of the hip accompanied by flexion of the knee.  In addition, I believe the conscious focus on rapid lift off advocated by Pose can lead to tensioning of the major muscles of the leg at point of impact thereby facilitating efficient capture and recovery of impact energy via elastic recoil.  The combination of efficient recovery of impact energy via elastic recoil and rapid flexion of hip and knee creates a mental focus that promotes a short time on stance and an associated large vGRF.  Does Bolt achieve his powerful drive from stance by this mental focus, or does he consciously focus on a powerful push?

Tim Huntley, who writes a blog about his goal of running a fast 400m, recently posted an article in which he asks whether or not Pose is the way to go.  The responses make a very interesting debate.  Brian McKenzie replied ‘Yes, the Pose method is the only way we really run’.  In contrast, Tom Tellez, former coach of Carl Lewis, was very dismissive, saying  ‘Running action such as reaching and pulling with the hamstrings has been scientifically proven not to produce the most efficient movement. ’ Tellez quotes Peter Weyand’s evidence that  faster running speeds are achieved with greater ground forces, not more rapid leg movements (see Journal of Applied  Physiology, vol 89: pages 1991–1999, 2000)

Tim emailed Dr Romanov who replied in typically vague Pose style: ‘Sprinting or any running is the product of gravity, shaped and moulded by this universal field of the force.  The cadence and efforts of a sprinter are governed by the angle of falling.”   Tim also posted a link to a U-tube clip in which Bolt describes his own understanding of what he does.  ‘After the acceleration phase the goal is to: ‘Keep driving, driving, driving.. …. After completing the drive: ‘Get tall, knees up, dorsiflex, get your toes up, plant, push again’

Bolt’s own emphasis on driving and pushing are somewhat at odds with Dr Romanov’s  claim that he is not pushing off.  Could it be that when he runs he lets his natural instincts take-over, and what he says on the video is merely an attempt to put into words something that is too primeval for words.  I think this is very unlikely.  As Tim Huntley reports, Bolt’s coach Glen Mills makes it clear that Bolt’s style is not the product of some natural primeval intuition.  According to Mills, when he started working with Bolt ‘one of the things that stood out like a sore thumb was his poor mechanics.   We set about doing drills, then we took videos of his workouts and broke them down on the screen in slow motion to show him exactly what he was doing.’

So I think the evidence is fairly clear that Bolt achieves his powerful drive from stance as a result of a physical and mental process that focuses explicitly on a powerful push.  However, I believe that a conscious focus on pushing is only likely to be successful if you have finely tuned bodily awareness, together with rapid reactions to the sensations generated by ground contact.  Without such awareness and rapidity of reaction, it is likely that a conscious focus on pushing will result in too long a delay on stance.  Therefore, in my own attempts to arrest the decline in my speed, I practice Pose drills such as ‘change of stance’ and when running, I focus on rapid lift off from stance rather than pushing.  I would not recommend Pose for a runner with serious hopes of achieving elite status, but for a recreational runner, it has some worthwhile features.

Further reflections on running efficiency: limb repositioning , conversion of metabolic to mechanical energy, and elastic recoil

My posts on the equations of motion of the runner on Jan 16^th and Feb 6^th led to an intense discussion which included some very thought provoking comments by several readers, including Ewen, Simon, Robert, Mike, and Klas.   In essence, the discussion led to the conclusion that the calculations themselves  provide an accurate account of the mechanical energy costs of the braking that is inevitable when the point of support is in from of the centre of gravity (COG), and the cost of elevating the body to become airborne.   However, these costs are not the only costs that need to be considered.  The other main mechanical cost Is the cost of repositioning the limbs relative to the COG, In addition, possible variations in the efficiency of conversion of metabolic energy to mechanical energy, and the efficiency of recovery of energy via elastic recoil must be considered.   Furthermore, factors such as wind resistance and variation in the profile of the time course of the pressure that the foot exerts upon the ground (and the opposing ground reaction force, GRF) should be borne in mind.

A complete account of the energy costs of running needs to take account of all of these factors.   I believe it is possible to deal adequately with effects of wind residence and variation in the profile of the time course of GRF, and I plan to do this in future posts.  I am confident that these factors play only a relatively minor role under many circumstances.  Unfortunately, variation in the costs of repositioning the limbs; the efficiency of metabolic to mechanical conversion; and the efficiency of elastic recoil are difficult to estimate  precisely but would be expected to play a key role under some circumstances.   Nonetheless, I believe that for the range of time on stance, cadence and speed that I considered in my calculations, the changes in braking costs and the costs of elevating the body that are achieved by adjusting cadence and time on stance  the most important factors to consider.  A full justification of this claim would require more detailed information about repositioning costs, efficiency of metabolic to mechanical conversion and elastic recoil than are currently available.  In future posts I will also review what is known about each of these factors in detail.   My goal in this post is to provide an outline of why I think that variation in cost of braking and elevation of the body are the most important issues in the circumstances discussed in my posts on 16^th Jan and 6^th Feb,  and furthermore, to provide an indication of the range of running speeds over which  my conclusions likely to be valid.

Repositioning costs

The largest of the repositioning costs is the energy required to move the leg forward relative to the COG during the swing phase.  Muscles must do work accelerating the foot from a stationary position on the ground to a speed approaching twice the running speed by mid-swing, to allow the foot to overtake the torso and get ahead of the COG by foot-fall.    Factors such as elastic recoil of the hip flexors which were stretched in late stance will contribute to the forward propulsion of the leg.  After mid-swing, the leg decelerates so some of the energy imparted initially might be recovered as the leg pulls the torso forwards.   Nonetheless, due to inefficiency neither elastic recoil of the hip flexors nor the momentum of the swinging leg will meet all of the cost.  We can obtain a crude estimate of the magnitude of repositioning costs by applying Newton’s laws of motion estimate the mechanical cost of accelerating the leg forwards during the first half of swing.

The work that is done in accelerating an object is proportional to the integral  of force times velocity over the time period for which the force acts.  If we assume that the acceleration is uniform, it can readily be demonstrated using Newton’s laws, that the work done is proportional to  the square of the running speed and inversely proportional to the duration of the swing.  Thus the repositioning cost will increase rapidly as running speed increases. It will also increase as cadence increases since  swing time decreases as cadence increases, assuming a constant proportion of time is spent on stance (which is the case if the peak vertical GRF is fixed).   Furthermore, at fixed cadence, swing time decreases as time on stance increases, so increasing stance time will result in greater repositioning cost.

For the situation considered in my post on Feb 6^th, in which cadence increased from 180 to 200 steps per minute, while both velocity peak vGRF and hence proportion of timer spent on stance remained constant, the repositioning cost would be expected to increase by 11 per cent (20/180).   For the situation considered in my post on Jan 16^th, running speed averaged over the gait cycle remained constant and cadence remained constant at 180 steps per minute, while peak vGRF/Kg increased from 2g to  4g.  Time on stance decreased from 262 milliseconds to 131 milliseconds while swing time increased from 404 milliseconds to 535 milliseconds.  Thus, repositioning costs would be expected to decrease by 32% (131/404).   Although the assumption of uniform acceleration is an approximation that would make any estimate of actual energy cost unreliable, the estimate of the proportional change is likely to be a reasonably reliable guide for our present purpose.  The  most important issue is the direction of change in repositioning costs: namely at constant cadence, the repositioning costs decrease as peak vGRF increases and stance time decreases; while at constant vGRF, the repositioning costs increase as cadence increases.

What  proportion of the total mechanical costs can be attributed to repositioning the limbs when running speed is 4 m/sec?   As we have seen repositioning cost increase as the square of the running speed.  This was confirmed by Cavagna and Kaneko (J. Phy8iol. (1977), 268, pp. 467-481) by direct measurement  of the motion of the limbs recorded on cine films.  Furthermore, C&K demonstrated that for runners who were running using their preferred running style at various speeds, that  the repositioning costs were equal to the sum of braking and elevation costs at a speed of 20 Km/hour (5.5 m/sec).  At 4 m/sec, the cost of repositioning the limbs was 37% of the total mechanical costs.    Thus, when vGRF is kept constant while cadence increases from 180 to 200 steps per minute, the repositioning costs would be expected to increase the total mechanical work costs by about 4% (11% of 37%).   In my computation presented on Feb 6^th, I demonstrated that the combined cost of braking and elevation diminished by about 10% (ie about 6.3% of total mechanical costs) as cadence increased from 180 to 200 steps per minute (at speed of 4 m/sec and peak vGRF/Kg = 3g).  Thus the gain in mechanical efficiency achieved by increasing cadence is only a little greater than the added repositioning cost.  It is clear that at speeds much faster than 4 m/sec, the gain in mechanical efficiency obtained by increasing cadence is likely to be obliterated by the increased repositioning costs.  On the other hand, at slower speeds the gains from increasing cadence  would be expected to be appreciable.   Furthermore, at lower vales of peak vGRF which are associated with longer times on stance, the gains from increasing cadence would also be greater.  So, in summary, at a speed of 4 m/sec and vGRF/Km = 3g, a small gain in mechanical efficiency would be expected when cadence increases from 180 to 200 steps per minute.  However at higher speed or higher peak vGRF the gain from reduced braking would be offset by the increased repositioning  costs.   (Although I have not done the relevant calculations, even at 5.5 m/sec, where reposition cost is equal to the sum of braking and elevation cost, a net gain might  be expected from increased cadence but it would be very small).   In contrast, at lower speeds and/or lower peak vGRF, worthwhile gains in efficiency might be expected as cadence increases.

In the situation considered in my post on Jan 16^th, there was a 21% decrease in the braking and elevation costs as peak vGRF/Kg increases from 2g to 4g at constant cadence of 180.  Based on Cavagna and Kaneko’s data, this represents a 13% saving in total mechanical cost.  As we have seen in the above estimate, repositioning costs will be expected to decrease by about 32%.  Since the C&K data indicate that repositioning cost are 37% of total mechanical costs at this speed, the reduced repositioning cost would be expected to produce a 12% saving in total mechanical costs.  Thus when vGRF increases (and stance time decreases), the gain in efficiency for reduced braking is augmented by a gain of similar magnitude from reduced repositioning costs.  At higher speeds, an even greater proportional gain in efficiency would be expected from increasing vGRF.

Although the numbers employed in these calculations are only approximate estimates, the general conclusions are likely to be valid.   At 4 m/sec, increasing vGRF (and decreasing time on stance) at constant cadence produces an appreciable gain in efficiency due to reduced braking costs accompanied by reduced repositioning costs.  Increasing cadence from 180 to 200 steps /minute produces  only a small improvement in efficiency due to the counter-productive increase in repositioning costs.   At higher speeds, the gains from increasing vGRF would be expected to be even greater, while the gains from increasing cadence would be minimal.  In contrast at lower speeds the gains from increasing cadence would be expected to be appreciable.

Effect of increasing vGRF at very slow speeds.

As discussed in my post on Jan 16, as vGRF increases at constant cadence, braking costs decrease while elevation costs increase.  At 4 m/sec, the gain from reduced braking cost is substantially greater than the extra elevation cost, so the combined mechanical cost of braking and elevation decreases as vGRF increases.  However, at very slow speeds, the distance travelled while on stance is very small and the work that must be done to compensate or braking is much less, so braking costs are a lesser proportion of total mechanical costs.  However, elevation costs (per step) for a given peak vGRF are almost independent of speed.  (This emerged from the equations of motion and was confirmed experimentally by C&K.)   This at very low speed, the combined cost of braking and elevation will actually increase as vGRF decreases.   For example, in my response on 27^th Feb to a comment by Klas on my post of Jan 16^th, I presented results demonstrating that at a speed of 2.5 m/sec, combined cost of braking and elevation is actually greater when vGRF/Km =4g compared with 2g.  Furthermore, at such a low speed, repositioning cost are very small.  Therefore, at speed as slow as 2.5 m/sec, increasing vGRF produces no appreciable gain in mechanical efficiency.

I should also be noted that even at higher speeds, once stance time becomes extremely short, braking costs will be low compared with elevation costs and further reduction in time on stance will result in an increase in the combined cost of braking and elevation.

Efficiency of conversion from metabolic to mechanical energy.

The efficiency with which muscle contraction converts metabolic energy to mechanical energy is typically around 20% or even less in some circumstances.  The largest contribution to this is the inefficiency of the biochemical process by which fuel is burned to produce the energy molecule  ATP which proves energy to the contractile machinery of the muscle fibre.  This process has an efficiency of only 40%.  Unfortunately, no adjustment of running style can improve this biochemical inefficiency.  However the efficiency of processes by which the molecular machinery within muscle fibre generates force  is potentially amenable to change.   Muscles contract by a ratcheting action between filamentous  actin and myosin molecules  within the muscle fibre.   The efficiency of this ratcheting depends on the rate of shortening of the muscle.  There is a certain fairly narrow range of contraction speeds at which the interaction between actin and myosin is optimally efficient.

Efficiency falls away rapidly when contraction speed is less the optimal range, and falls away somewhat less rapidly as contraction speed increases above the optimal.  Different fibre types have different optimal speeds.  As might be expected, slow twitch (type 1) fibres are optimally efficient at slower speed of contraction than fast twitch (type 2) fibres.  The optimal contraction speeds for these two fibre types differ by a factor of about two.  There appears to be a neural mechanical hat ensures that type of fibres that are recruited for a task depends on the demands of the task.  Hence, at least for a professional athlete who has the opportunity to train whichever type of fibre is most relevant to his/her event, it would appear that the best strategy is to train the fibres that are most suited to achieving optimal mechanical efficiency.  Maybe a recreational runner might be better advised to adjust factors such as peak vGRF to match the fibres that are available for the task.

Furthermore, the efficiency of metabolic to mechanical efficiency conversion diminishes as a muscle becomes fatigued (C.J.Barclay, Journal of Physiology (1996), 497.3, pp.781-794).   Therefore, at least for a recreational runner, it might be better to adjust vGRF to a somewhat lower value than that which provides  optimal mechanical efficiency,  so as to increase the recruitment of the more fatigue resistant slow twitch fibres.  The tendency for marathon runners to increase time on stance in the later stage of the race might reflect the need to rely almost entirely on slow twitch fibres in the later stages of the race.

In summary, it seems to me that preferred strategy is to train to produce adequate fatigue resistance in the fibres that are best suited to achieving optimal mechanical efficiency. However if one has less opportunity to train, or when racing over a distance that is longer than usual, it might make sense to increase time on stance to maximise the efficacy of conversion of metabolic energy to mechanical work  despite some loss of mechanical efficiency.

Elastic recoil

The elasticity of tendons increases as the rate of application of force increases, so in general, the efficiency of elastic recoil of the tendon itself would be expected to be greater at shorter times on stance, though the as the rate of application of force increases a plateau would eventually be reached.  However, perhaps more important than the plateau at high loading rates is the fact that recoil is a product of the concerted action of muscle and tendon.  Tension is only created if the muscle contracts as the muscle-tendon unit is stretched.  Therefore, if the rate of application of force is potentially too great for the muscle to bear without damage, it is likely that a protective mechanism will limit the amount of tension that is developed.  Thus, it would be expected that the efficiency of elastic recoil will increase as time on stance decreases, but beyond a certain point the strength of the muscle contraction will cease to increase, and tension will no longer rise in proportion to the applied force.  Thus elastic recoil will capture a smaller proportion of the energy of impact.   I do not know of any measurements that establish the rate of loading that achieves maximum efficiency of elastic recoil during running.  However, as in the above consideration of metabolic to mechanical conversion efficiency, it would appear that the ideal strategy for optimal efficiency is to develop muscle strength to the level required to cope with the loading rate required to give maximum mechanical efficiency.

These considerations suggest that the optimum strategy is to develop both strength and fatigue resistance of muscle fibres to a sufficient degree to allow the achievement of optimum mechanical efficiency.  However in practice this might not be feasible, especially for recreational runners.  In such situations it might be more efficient to adopt a somewhat longer time on stance even it this results in sacrifice some mechanical efficiency.

Conclusion

At running speeds around 4 m/sec or higher, the greatest mechanical efficiency is likely to be achieved by aiming for a relatively short time on stance, achieved by employing a greater peak vGRF. Furthermore, increasing cadence from 180 to 200 steps per minute would also be expected to produce a small some gain in efficiency, but the increased cost of repositioning the limbs nullifies some of the potential gain from reduced braking cost.  At higher speeds, this antagonism of the potential benefit of increased cadence becomes even more marked.

The increased in peak vGRF required to achieve a shorter time on stance (at constant cadence) comes the price of greater stress on the muscles.  At least for the recreational runner, and perhaps even for professional athletes running very long distances, it might be preferable to sacrifice some of the potential gain in mechanical efficiency by employing a somewhat longer time on stance.

The equations of motion of the runner: efficiency increases with increasing cadence

The story so far

In my post of 16^th  Jan I presented results of a calculation of the work required between mid-stance and the achievement of peak height in the subsequent airborne phase to elevate the body from it’s low point at mid-stance, and to overcome the effect of braking in the first half of stance.  These calculations were based on a precise solution of the equations of motion for the centre of gravity (COG) of the runner’s body derived from Newton’s Laws of motion.  The comments by Ewen, Simon, Robert and Mike led to an extensive discussion of issues related to my calculations and the conclusions that I drew.   Here I will attempt a summary of the major issues that we discussed, including the evidence for validity of the calculations.

There are two assumptions implicit in my calculations.  First, that the time course of the vertical component of ground reaction force varies sinusoidally with time during stance (as shown in fig 1 of that post).  As can be seen by comparing figure 1 with force plate data (eg Figure 1c in the paper by Daniel Lieberman and colleagues, Nature, Vol 463,p 531, January 2010) this is a fairly good approximation to force plate data for a forefoot runner.    Secondly, that the tension in the leg muscles is adjusted to ensure that the total ground reaction force acts in the direction of the line form point support to the centre of gravity (COG).  This assumption is also supported by observational data, as outlined in the discussion between Simon and myself in the final few comments on that posting  (dated 31^st Jan).

There were also two energy costs that I had ignored in my calculations: the effect of wind resistance and the effect energy consumed in re-positioning the limbs during the gait cycle.  In his comment on 22^nd Jan, Robert kindly provided a fairly realistic estimate of the effect of wind resistance and demonstrated that for the examples that I was considering, the effect of wind resistance due to the runner’s own velocity through still air, as likely to be small.  I myself carried out some crude experiments to determine the energy cost of re-positioning the limbs, and demonstrated that these costs were fairly small and unlikely to alter the conclusions that I had drawn.  However the cost of repositioning limbs does increase with running velocity and the energy cost of repositioning the limbs is likely to be appreciable at higher running velocities. I will discuss this issue in more detail later in this posting.

Overall, the outcome of quite intensive discussion arising from comments by Robert, Simon and Mike is that the computation is likely to be a fairly good representation of the displacements, velocities and energy required to elevate the body and overcome braking in the case of a forefoot runner.  The main conclusion I had drawn was that the energy costs (for a given velocity and cadence) are lower when the time on stance is shorter.  In general a shorter time on stance can be achieved by maintain greater tension in the leg muscles so that the amount of flexion at hip and knee is reduced.  The intense discussion in the comment section helped consolidate my confidence that this is a valid conclusion.

It should be noted that my calculations of energy costs do not provide an estimate of the proportion of the required energy that can be recovered from elastic recoil.  However, because muscle and tendons are visco-elastic in the sense that their elasticity is greater when forces are applied my rapidly, it is likely that the amount of energy recovered via elastic recoil will be greater when time on stance is shorter, because the rate of increase in load is greater (as illustrated in fig 1 of my post on 16^th  Jan)

The discussion included debate about two other less clear-cut issues.  First, I had initially argued that the greater forces and also the greater rate of increase in loading associated with a shorter time on stance presents a greater risk of injury.  I still believe that this is plausible, but both Simon and Robert pointed out that this is not necessarily the case.  It is necessary to compute the actual forces and shearing effects acting on particular joints and muscles to determine the risk of injury.  My calculations apply only to the motion of the COG and to the overall energy costs, but do not directly allow an estimate of forces acting at particular points in the body.  I think that my calculations might be informative regarding the stress on the legs, but further exploration of that issue is a topic for another day.  In particular, I think that the this topic has something useful to add to the debate about the merits of bare-foot running

The most hotly debated issue in the comments on my post was the implications of my calculations for rotational effects occurring during the gait cycle, and in particular for the controversial concept of gravitational torque.  In fact my model does provide a very clear answer regarding rotational effects.  There is indeed an increase in the angular momentum about a pivot point at the point of support in a head forward and down direction during the second half of stance, though the question of whether these should be described a consequence of gravitational torque is more debateable.  In the absence of wind resistance, this effect is cancelled by an opposite effect in the first half of stance, and I do not believe that this issue is of major importance in understanding running mechanics.  However, because it has been a bone of contention in relation to the theory underlying the Pose technique, I will devote a post to that topic in the near future.

Meanwhile, in this post I wish to deal with two issues.  First is the issue of cadence.  The second is a discussion of the energy costs of repositioning the limbs.

Cadence

It is widely believed that increased cadence is associated with greater efficiency.  The energy cost (per mile or Km) of elevating the body to the peak height in the airborne phase decreases with increasing cadence.  This is because the duration of each gait cycle decreases as cadence increases.  The amount of gravitational potential energy lost when a body falls is proportional to the square of the duration of the fall.  Even though the number of steps per mile (or Km) increases linearly as cadence increases, because the energy saving is proportional to the change in the square of the duration, the energy saving more than offsets the increase cost due to an increase in number of steps.

As demonstrated in my post of 16^th Jan, the equations of motion of the runner’s body provide a precise estimate of the elevation that occurs from mid-stance to peak height, and hence provide a precise estimate of the energy cost of elevating the body  These equations also provide a good estimate of the  energy required to overcome braking in early stance, provided data for hGRF is available as a result of either direct measurement or estimation based on vGRF (equation 5 on the calculations page).   In this post, I report the result of using these equations to examine the effect of increasing cadence, while maintaining a specified peak vGRF.

I have performed the calculation assuming a peak value of vGRF of 3g per Kg.  This value is midway between the two different values of peak vGRF I considered in my previous post, and is likely to be a fairly realistic estimate form many runners when running at 4 m/sec.   Figures 3 to 5 (numbered sequentially from the figures in my post of  16th Jan) illustrate  the braking effect and also the vertical displacement of the COG during the entire gait cycle, for the case where peak vGRF is 3g per Kg, for a cadence of 180 steps/sec and 200 steps/sec.  As expected, the vertical displacement is less at higher cadence.  There is a 19% reduction in the vertical displacement (and hence a 19% reduction in energy required to elevate the body in each stride), whereas the number of strides per mile (or Km) increases by only 11%.  Thus the energy consumption per mile (or Km) is about 8% less at 200 steps per minute compared with 180 steps per minute.

Fig. 4: Change in height of the COG from mid-airborne phase (in metres) when peak vGRF= 3*g Newton/Kg, for cadence 180 steps/minute (ochre) and 200 steps per minute (blue), at velocity 4 m/sec. Vertical blue lines indicate mid-airborne phase for cadence 200.

Fig. 5: Change horizontal velocity from mid-airborne phase (in metres/sec) due to braking when peak vGRF= 3*g Newton/Kg, for cadence 180 steps/minute (ochre) and 200 steps per minute (blue), at velocity 4 m/sec. Vertical blue lines indicate mid-airborne phase for cadence 200.

There is also a saving in the energy required to overcome the braking effect.  The duration of braking is shorter, due to the shorter overall gait cycle and associated shorter time on stance.  Furthermore, the leg is less oblique at footfall when cadence is greater and consequently the horizontal component of GRF is less.  As a result of both of these factors, the braking effect is less.   Table 2 gives the energy costs  of braking, elevation and total costs for a forefoot runner, running at 4 m/sec and peak vGRF = 3g per Kg for a cadence of 180 and 200 steps/min. The energy at the higher cadence saving amounts to approximately 14%.

Table 2: Mechanical work per Km per Kg required to overcome braking and to elevate the body, when peak vGRF=3*g per Kg, velocity = 4 m/sec.

A similar calculation performed for the situation where peak vGRF = 2g /Kg indicates reduction in energy cost from  1309 Nm/Km at cadence 180 steps per minute to 1186 Nm per Km at 200 steps per minute. Thus the saving is even greater when peak vGRF is lower (relatively longer time on stance) because the increased braking with greater obliquity of the leg at footfall is even greater at lower values of peak vGRF.

How do the estimated energy costs compare with directly measured metabolic costs?

It is of interest to compare these estimates of the costs of overcoming braking and elevating the body with evidence regarding the metabolic cost of running at 4 m/sec, though there are two uncertain quantities in determining the metabolic cost of achieving a specified amount of mechanical work to metabolic costs.  The first is the fact that muscle contraction is a relatively inefficient way of converting metabolic energy to mechanical energy.  It is generally accepted that during activities such as running and cycling, muscle contraction has an efficiency of approximately 20% (i.e the consumption of metabolic energy by muscle contraction is 5 times the amount of mechanical work done).   Secondly, when running a proportion of the energy required to overcome braking and elevate the body is derived via elastic recoil of muscles and tendons.  I am not aware of any data for the proportion of energy recovered by elastic recoil.  For present purposes, I assume that 50% of the energy can be obtained via elastic recoil.  Because the elasticity of tendons in greatest when that are loaded rapidly, this proportion is likely to be higher when the rate of loading of the muscles and tendons in early stance is highest.

According to the data published by McArdle in 2000 (Essentials of Exercise Physiology, USA: Lippincott Williams and Wilkins, 2nd ed. p170) the total metabolic energy cost of running at 4 m/sec is 62.2 Kcal/Km or 0.99 Kcal/Km per Kg (4142 Nm/Km per Kg). It is usually considered that this cost varies relatively little with variation in gait. While my calculation show that energy costs do vary appreciably with duration of time on stance, for the purpose of obtaining an approximate estimate of the relative proportion of total energy spent on elevating the body and compensating for braking, we only require an approximate estimate of total cost.  If we assume the efficiency of conversion of metabolic energy to mechanical work is 20%, while 50% of the energy can be recovered by elastic recoil, McArdle’s data indicates that the mechanical work done 1656 Nm/Km/Kg.  This is of course a crude estate and makes no allowance for the fact that time and stance and cadence produce modest but appreciable changes in energy cost.

Alternatively, using Daniels’ formula for oxygen consumption at paces in the aerobic zone, it can readily be shown that for a runner with VO2max of 51 ml/min/Kg, running at 4 m/sec (which is in the upper aerobic zone where energy is largely provided by metabolism of glucose (derived from glycogen) oxygen consumption is consumption 188 ml/Km per Kg.  When glucose is the fuel, 1 litre of oxygen provides 5.05 Kcal, giving a metabolic cost of 0.95 Kcal/Km per Kg, and corresponding mechanical energy cost of 1589 Nm /Km/Kg .  Thus Daniels’ data indicates a metabolic cost about 4% lower than that derived from McArdle’s data, but this difference is trivial in light of the uncertainties in estimating mechanical cost from metabolic cost.

The important conclusion is that whether one uses an estimate based on Daniels or McArdle, it is clear from the data shown in tables 1 and 2  (which indicate mechanical costs in the range 1180 Nm to 1400 Nm per Km per Kg)  that elevating the body and overcoming braking, make a major contribution to the energy cost of running,   Provided one starts with accurate data for GRF, it is possible to compute the mechanical work required to overcome braking and to elevate the body quite precisely, using Newton’s laws of motion (as indicated in my calculations page).   Assuming a sinusoidal time course of vGRF, the results are as presented in this posting and my post on  16^th.   Nonetheless, the comparison with the data derived from McArdle or Daniels does indicate that there is some minor but nonetheless appreciable energy cost in addition to elevating the body and overcoming braking.

Repositioning the limbs

As mentioned above, the other appreciable energy cost of running is the energy required to re-position the limbs, especially the legs.  The foot must be accelerated from a stationary position on stance to a velocity somewhat greater than the velocity of the torso, so that it overtake the torso, by mid-swing, and then decelerates during late swing so that is near to zero relative to the ground at foot-fall.  In the discussion following my posting of 16 Jan, I described a crude estimate of the energy required to reposition the limbs based on estimate of the increased metabolic demand, based on measurement of increased heat rate, when I executed the arm and leg movements associated with repositioning the limbs,   The estimated cost of repositioning the limbs at pace of 4 m/sec and cadence 180 steps per minute was 0.28 Nm per step (208 Nm per Km) to achieve the range of motion required when maximum vGRF of 2g /Kg and 0.20Nm.Kg per step (or 150 Nm/Kg per Km) to achieve the range of motion required for a maximum  vGRF of 4g /Kg.  Thus , at a pace of 4 m/sec  the repositioning cost is only a minor fraction of total energy cost and, furthermore decreases as time on stance decreases, strengthening the conclusion that a short time on stance is more efficient.  The decrease in re-positioning cost when time in stance is shorter reflects a smaller range of motion and a longer airborne time in which to achieve repositioning thereby allowing a lesser acceleration.   I have not performed the corresponding measurements for cadence 180 and 200 steps per minute at maximum vGRF = 3g /Kg.  Although range of motion is less when cadence is higher, airborne time proportionately reduced demanding higher acceleration so it unlikely that the smaller range of motion required at higher cadence will offset the effect of a greater number of steps per Km.  I will perform further measurements of the costs of limb repositioning in the near future.  Whatever the outcome of these measurements, the fact that repositioning costs are only a minor proportion of the total at a speed of 4 m/sec makes it unlikely that further measurements will appreciably alter the strength of the conclusion that it is more effect to run at a higher cadence.

In an article in the Journal of Physiology in 1977 (volume 268, p467), Cavagna and Kaneko estimated the energy required to reposition the limbs based on measurement of limb movement derived from video recordings of runners. They conclude that it exceeds the energy associated with overcoming external forces at speeds above 20 Km/hr (5.55 m/sec). However, they acknowledge that there are many uncertainties in their calculations. Nonetheless when estimating energy costs at high speed it is likely to be important to take account of re-positioning of the limbs.   Actions such as flexing the knee of the swinging leg so that the lever arm is short would be expected to have an appreciable effect at high speed, but probably matters little at speeds of 4 m/sec or lower.

What determines the upper limit of cadence?

While, I am confident that the mechanical work required to overcome braking and elevate the body decreases as cadence increases, this does not prove that metabolic efficiency will continue to increase with increasing cadence.  In estimating the relationship between mechanical work and metabolic cost of running, we had to take account of two variables: the efficiency with which muscles convert metabolic energy to mechanical work, which is typically about 20%, and the proportion of energy that can be recovered via elastic recoil.  As cadence increases, there will come a point at which the contraction becomes less efficient, and in addition, it might also be expected that recovery of energy via elastic recoil will also diminish.  Hence there will be an upper limit to the optimum cadence.  I suspect that the upper limit will be determined by the peak rate at which muscle can generate the tension required to capture kinetic energy and convert it to elastic energy.   The observation that elite  5Km and 10Km runners tend to exhibit a cadence in the range 180 to 200 steps per minutes suggest that the peak is around 200 steps per minute.

Interim conclusions and issues for future analysis

Overall, my calculations indicate that efficiency is greatest when time on stance is short and cadence high.  It is current folk lore among runners that you should land under the COG.  That is impossible, when running at constant speed except when running into a strong wind, because the push from hGRF when the point of support is behind the COG would inevitably cause continued acceleration.   However the twin principles of short time on stance and high cadence are the principles that allow the runner to minimise the amount the foot is ahead of the COG at footfall.   These calculations simply use the principles of physics to explain why Tirunesh Dibaba runs like this.

In the near future I will address three further issues:

1)      How much does a change in the time course of vGRF from that typical of a forefoot runner to that typical of a heel-striker affect the energy costs.

2)      Does the increase in angular momentum around the pivot at the point of support, due to the effect of gravity, play an appreciable role in the presence of wind resistance.

3)      What are the implications of these calculation for risk of injury and in particular, for the potential benefits or costs of barefoot running?