Archive for the ‘Running Mechanics’ Category

Is there a magic running cadence?

April 5, 2012

The six posts in my recent discussion of running mechanics, starting with my presentation of the equations of motion of the runner on 16th 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 6th 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 6th 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.


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

March 29, 2012

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.


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

March 15, 2012

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


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?

March 11, 2012

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

February 27, 2012

My posts on the equations of motion of the runner on Jan 16th and Feb 6th 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 front 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 16th Jan and 6th 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 6th, 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 16th, 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 6th, 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 16th, 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 27th Feb to a comment by Klas on my post of Jan 16th, 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.


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

February 6, 2012

The story so far

In my post of 16th  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 31st 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 22nd 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 16th  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.


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 16th 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  16th.   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?

The equations of motion of the runner: is there a trade-off between mechanical efficiency and risk of injury when running?

January 16, 2012

The title of my blog reflects my initial goal: promoting discussion of issues related to running efficiency.  Perhaps the beginning of a new year is a good time to take stock of my current understanding of the topic.   An additional reason for a review at this time is the recent protracted debate between Robert and myself waged in the comment section of my page on the Dance with the Devil (see side panel).  This debate was fairly adversarial in character at times, and it prompted me to re-examine some of the issues related to the perennially thorny topic of gravitational torque.  Robert’s challenges led me to do some computations, which as a by-product revealed some findings regarding linear velocity during the gait cycle.  Because linear velocity is related to progress towards the finishing line, I think linear velocity is a more important aspect of running mechanics than the rotational motion arising from gravitational torque, which is largely about going around in circles (or preventing such motion).  So I am grateful to Robert for re-focussing my attention on running mechanics and running style.  Though first, it is important to put the issue of running style in a larger context.

Granted that races at distance ranging from 5000m to marathon are run at a paces either a little above or a little below the anaerobic threshold, the greatest determinant of efficiency is the ability to achieve a high pace at threshold so as to minimise the amount of fuel-inefficient anaerobic metabolism.    If the goal is efficiency, much of one’s training efforts should be directed at this raising the threshold pace.  Whether this goal is best achieved by emphasis on high volume or high intensity training (or both) remains a controversial topic, but that is not the question I will focus on in this post.   Instead, I will return to the less important but nonetheless intriguing question of running style.

Almost certainly, the most important issue in considering the effects of running style on efficiency is minimization of risk of injury.  Injury impairs not only performance at the time of injury but also leads to missed training and loss of aerobic fitness.  Unfortunately, the evidence suggests there might be a trade-off between mechanical efficiency and safety.  I think this can be illustrated most readily by examining solving the equations of motion of the running body (though if you are willing to accept my calculations, you do not need to do the maths yourself – I will illustrate the results pictorially).  The complete solutions of the equations describing a multiply-jointed body made of viscoelastic tissues (i.e. tissues in which change of shape depends on how rapidly the force is applied) is of course horrendously complex.  Nonetheless a great deal can be learned by focussing on the equations that describe the motion of the centre of gravity of the body (COG).  If we know the time course of the external forces acting on the body – namely gravity; ground reaction force (GRF); and wind resistance – it is possible to perform an accurate computation of the motion of the COG.

On the surface of the earth, the force of gravity is constant.  It is the product of mass multiplied by the acceleration due to gravity (g), which has the value 9.8 metres/second/second (or 32 feet/sec/sec in Imperial units).  Ground reaction force is the reaction of the ground to the push of the body against the ground.  We can measure the push of the body against the ground quite precisely using a force plate, and therefore, since action and reaction are equal and opposite, we can deduce the GRF. Estimation of wind resistance is trickier, and for the purpose of this post, I will assume that wind resistance is negligible.   I have presented the equations and a description of how I solved them, in the calculations page (see the sidebar).

Ground reaction forces

For simplicity I have assumed that the vertical component of ground reaction force (vGRF) varies sinusoidally while the runner is on stance, as shown in figure 1.   This is a moderately good approximation to real data for a forefoot runner, and is convenient from the computational point of view.   vGRF rises rapidly from zero after footfall, reaches a peak at mid-stance and then falls away to zero as the runner approaches take-off.  I do not think the main conclusions I will draw will be appreciably influenced by the exact shape of the time course of vGRF, though at the price a little more computation, I could solve the equations using real data for vGRF.

One crucial feature regarding vGRF is that the value of vGRF averaged over the entire gait cycle must equal the downward force of gravity (mg, where m is mass) since gravity acts constantly throughout the gait cycle.  Otherwise, there would be a net vertical impulse that would either cause the runner to continue to float upwards after the completion of the gait cycle if average vGRF exceeded mg, or alternatively to be pulled to the ground if average vGRF was less than mg.  One inevitable consequence is that when time on stance is short compared with the total period of the gait cycle, peak vGRF must be high (as is illustrated by the ochre dashed curve in figure 1) compared with the situation where time on stance is a large faction of the total duration of the gait cycle (as illustrated by the dashed blue line in figure 1).

Fig 1: vGRF (dashed line) and hGRF (solid line) for relatively long time on stance (blue) and short time on stance (ochre). Vertical lines denote footfall, mid- stance and take-off. (Force units are Newtons)

Once vGRF is known, the horizontal GRF (hGRF) can readily be computed assuming the total GRF acts along the line from point of support to the COG (as shown in equation 5 on the calculations page).  The hGRF associated with a sinusoidal  time course of vGRF is depicted by the solid ochre and blue lines in figure 1.   In early stance, vGRF is negative, indicating that it exerts a braking effect on the runner.   Early in the stance phase magnitude of hGRF increases as vGRF increases, but because hGRF is only appreciable when the line joining point of support to COG  is oblique, the magnitude of hGRF begins to decrease despite the continued rise in vGRF as the runner approaches mid-stance.  By mid-stance, the COG is directly above the point of support, total GRF is vertical and hGRF is zero.  After mid-stance, the line from COG to point of support is directed obliquely backwards, so hGRF is now directed forwards and has an accelerating effect on the runner that reveres the braking effect in early stance phase.   One feature of interest is that when the runner spends a long time on stance, the peak magnitude of hGRF is almost the same as when the runner spends only a short time on stance, despite the much greater peak vGRF when stance is short.  The reason is that when time on stance is short, the line from COG to point of support is never far from vertical so hGRF does not rise as high is it would if this line was more obliquely inclined.   The fact that the magnitude of peak hGRF is similar for both short and long times on stance means that the braking effect is actually much greater when time on stance is longer, because the braking force acts for a longer time.

Vertical and horizontal components of velocity

Figure 2 depicts the time course of the velocity of the body in both vertical and horizontal direction throughout the gait cycle, based on the solution of equations 1 and 2 shown on the calculation page.

Fig 2: Vertical velocity (dashed line) and change in horizontal velocity from airborne phase, V(a), due to braking and acceleration. Blue: long stance; Ochre: short stance. Running speed: 4 m/sec.

If we focus first of all on the vertical velocity in the case where time on stance is a large proportion of the total gait cycle (the dashed blue line), we see that starting from the high point at mid-flight, downwards velocity increases at a steady rate under the influence of the uniform accelerating effect of gravity.  After foot-fall, as vGRF rises, the rate of acceleration slows and once vGRF exceeds mg, the downwards acceleration ceases, though the body still continues to move downwards at a decreasing rate until mid-stance, by which time vertical velocity is zero.  After mid-stance, the body accelerates upwards under the influence of vGRF.  Once vGRF has fallen below mg, the acceleration diminishes, though the velocity remains upwards.  After the body becomes airborne, vGRF is zero and the upwards velocity continues to decrease at a constant rate as gravity retards the ascent.  By the middle of the airborne period (the end of the cycle in figure 2) the vertical velocity is zero.

In the case in which time on stance is short (the ochre dashed line in figure 2), the constant increase in downwards velocity during the airborne phase continues for a longer period than when time on stance is long (blue dashed line).  Consequently, when stance time is short, the downwards velocity is much greater at foot-fall.   As vGRF rises in the first half of the stance phase, the downwards velocity decreases reaching zero at mid-stance.  After mid-stance, the high vGRF causes a greater upwards acceleration than in the case where time on stance is longer, so that upward velocity at take off is higher.  The body rises to a greater height before its ascent is arrested by gravity in the middle of the airborne phase.  Using equation 3 to compute distances travelled, in the case where horizontal velocity at mid-stance is 4 m/sec, it can be shown that in the case when peak vGRF is 2mg, the total vertical distance travelled between mid-stance and airborne peak is 5.8 cm whereas it is 9.8 cm when peak vGRF is 4mg.

In contrast, in the case of horizontal velocity (solid lines in figure 2) the amount of slowing between footfall and mid-stance is appreciably greater when time on stance is longer, because, as we have seen, the braking force (hGRF) is of similar magnitude but acts for a longer period of time.

Implications for efficiency

What do these calculations tell us about mechanical efficiency?  It is important to note that a substantial proportion of the kinetic energy of the falling body is absorbed and stored as elastic energy during the first half of stance, and is recovered by elastic recoil after mid-stance.  The proportion that is recovered is likely to be higher when time on stance is short because tendons and muscle as viscoelastic, meaning that up to a certain point, they are more elastic when the force is applied over a shorter period of time.  In similar manner, some of the kinetic energy lost due to the braking effect of  hGRF in early stance can be stored as elastic energy and recovered after mid-stance.  Again, the proportion recovered is likely to be higher when time on stance is shorter.  However, irrespective of whether time on stance is short or long, only a proportion of the kinetic energy lost during the first half of stance can be recovered.  Thus, in general efficiency will be less when the total amount of work that must be done to reverse the braking effect and to elevate the body back to its peak height is large.  We have already seen that the braking effect is greater when time on stance is long, whereas the amount of upwards acceleration required to elevate the body to its peak height is greater when time on stance is shorter.  Which of these effects demands more energy?

Energy required

The amount of work done when a force is applied can be computed using equation 6.  The results are shown in table 1 for a running speed of 4 m/sec.

Table 1: the work done per step after mid-stance to reverse the braking effect by hGRF and to elevate the body from mid-stance to peak height in mid-flight. Less of the required energy is derived from elastic recoil at longer time on stance (i.e lower vGRFmax). Work per Km is 750 times greater.

At both short and long times on stance, the energy required to overcome braking is greater than the energy required to elevate the body from its low point at mid-stance to its high point in the airborne phase.  Thus, the sum of the amounts of energy required to overcome braking and to elevate the body is substantially greater when time on stance is longer.  Since the proportion of energy recovered by elastic recoil is likely to be less under these circumstances, it is clear that mechanical efficiency is less when time on stance is long.  It should be noted that these calculations refer to the work done to counteract the effects of external forces acting on the body.  Some additional work is also done repositioning the limbs, and at very high running speeds this can become appreciable, but is beyond the scope of this discussion.


The calculations confirm that mechanical efficiency is increased by shorter time on stance.  Although many coaches believe this, it is not universally accepted, so it is re-assuring to see that the equations provide a clear confirmation.  In practice a shorter time on stance can be achieved though stiffening the hip, knee and ankle joints by applying greater tension in the muscles that flex and extend these joints, especially the hamstrings and quads.  The BK method of running developed by Frans Bosch and Ronald Klomp focuses on decreasing time on stance via plyometric drills that develop the strength necessary to maintain adequate leg stiffness.   However, the equations also provide a clear warning regarding the increased ground reaction force.  As shown in figure 1, when time on stance is short, the peak vertical forces acting on the body are much larger, and the potential risk of injury is potentially greater.

It is noteworthy that in the late stages of a marathon, many runners automatically increase their time on stance.  This is probably due in part to the fact that as muscle strength diminishes it is harder to maintain the required tension in the hamstrings and quads, but also might be an unconscious defensive reaction to protect the body from injury at a stage where tired muscles are less able to withstand stress.

So far we have not addressed the issue of cadence.  For a given proportion of the gait cycle spent on stance, the magnitude of peak vGRF required to achieve a specified proportion of the gait cycle airborne is lower at high cadence because both airborne time and stance time decrease at higher cadence.  In my next post I will discuss cadence.  The interim conclusion is that there is a trade off between mechanical efficiency and risk of injury.  Efficiency can be increased by spending a shorter period of the gait cycle on stance, but the risk of injury is greater.  Therefore, a style which entails greater leg stiffness should be adopted cautiously, and requires careful conditioning of the muscles, tendons and joints to allow them to withstand the greater forces.


Note added 27th  Feb 2112:

In the discussion below, Simon drew attention to the fact that by emphasising the trade off between increased efficiency and increased risk of injury that appears to arise in the circumstances described in this post, I do not acknowledge that for a recreational runner who habitually runs at a cadence in the vicinity of 160, it is possible to increase efficiency with no appreciable increase in injury risk simply by increasing cadence from 160 to 180 steps per minute.  I agree that such an increase in cadence will lead to a decrease in braking cost without the need to increase vGRF.  The potential benefits of increasing cadence from 180 to 200 are less clear-cut, and are discussed in my posts of Feb 6th and Feb 27th.

Heel striking v. forefoot

September 24, 2010

A few weeks ago I had speculated on how Dathan Ritzenhein might fare in the New York marathon on 7th November.  As I described, he has been cruelly afflicted with metatarsal problems throughout his running career, and in the past year or so has taken three steps to banish these problems.  First he moved from Boulder, Colorado with it hard trail surfaces, to join the Nike team in the verdant environment of Portland, Oregon, where the trails are softer.   Secondly, Nike’s head of biomechanics, George Valiant, designed some shoe inserts which relieve the pressure on the downward protruding head of the third metatarsal of his right foot.  Thirdly, and more controversially, under the guidance of Alberto Salazar, he has adjusted his style from heel striking to a landing with the impact point nearer to the forefoot.  I think that such an adjustment must be approached cautiously by any runner, but especially by an individual with metatarsal problems.

On Saturday he returned to racing following his most recent metatarsal injury, running in the Great Northern Run.  He finished 4th in 62:35., which was disappointing in comparison with his time of 60:00 in Birmingham a year ago when he won the bronze medal at the World Half Marathon championships. In his recent blog post [1] he put a brave face on his performance in the GNR by pointing out that it was not bad for a first race after injury.  He had done only about 10 weeks of serious marathon training, though he had previously posted on his blog on Sept 9th that he felt not far off his fitness a year previously in Birmingham.  At Gateshead on 19th Sept he set out in the lead group, covering the first mile in 4:38 (on target for around 60 minutes for the HM), but dropped off the pace when Kiplimo Kimutai surged shortly after the 5Km mark, which leaders had reached in a fairly brisk 14:09.  Only the eventual winner, Haile Gebreselassie was able to stay with Kimutai after the surge and perhaps it would be expecting too much to expect Dathan to hold that pace at this stage in his training.  However, in the later stages of the race he slowed even more due to tight calf muscles.  In his blog post he reported ‘my calfs were barely working in the last 5K of the race’.  He blamed this on his light weight Streak XC shoes, which is perhaps plausible though I would also wonder whether his changed running style might  contributed. While it is currently popular to advocate a forefoot landing, even for  long distance runners,  there is little doubt that a forefoot landing places extra strain on Achilles and calf.

The good news is that Dathan suffered nothing worse that tight calf muscles.  At least his metatarsals are surviving.  I still hope he does well in New York, but after Haile G’s comfortable win in the GNR it is clear that Haile is in dominant form and he must start as the favourite in New York.  I hope his run in New York will dispel the disparaging whispers that he has shied away from the head-to-head competition in recent years, to focus only on world records on flat courses.  I think that these whispers are unfair on the greatest distance runner the world has ever seen.  So I am hoping for a great race in New York, with Haile prevailing, but others including Martin Lel, Meb Keflezighi and Dathan running really well.

Meanwhile on a much more humble stage I have been pleased with the result of my regression from my usual forefoot striking to heel striking, to deal with the recent acute exacerbation of  my own longstanding metatarsal problems. Since temporarily adopting a high cadence, heel-striking style, I have gradually increased my training volume with runs in the lower aerobic zone (HR around 120 b/min; pace around 5:45 /Km). I have had no metatarsal pain while running and only mild discomfort later in the day.  However, while the metatarsalgia has receded into the background, the knee problems that have hampered me all year are still lurking.  I am aware of the potentially greater jarring forces on the knee when heel striking and have been ensuring that I land with a ‘soft’ flexed knee so that the quad absorbs much of the impact.  I think this has been successful, because my knees have also continued to improve in the past two weeks and I no longer suffer knee pain while actually running.  However I still get some pain in the anterior compartment of the knee on standing from a sitting position, and I am also getting occasional spasms in popliteus (the small muscle running transversely behind the knee, which is responsible for unlocking the fully extended knee). The spasm of popliteus had started when there was a marked effusion in my left knee during the episode acute arthritis that afflicted me in February.  The fact that the popliteus spasms are continuing indicates that there is still something not quite right about the mechanics of my knee, so I am being very cautious in building up the training volume.  I will refrain from increasing the pace for a few weeks longer.  Overall, I think that my heel strike experiment is proving to be a success.

I remain convinced that the choice between heel and forefoot striking, at least when running slowly, should be decided by an appraisal of one’s own situation rather than being dictated by popular dogma.  For a person with metatarsal problems, heel strike might well be safer, provided one lands with moderate flexion of the knee.  Nonetheless, I anticipate returning to my habitual forefoot landing once I start increasing the pace a bit, because impact forces are greater at higher speed, and the forefoot landing helps distribute the task of absorbing the impact between structures of foot, lower leg and thigh.  However I will take care to ensure that I condition my calf muscles to cope with the extra stress.



September 6, 2010

My post on 4th September was motivated largely by Ewen’s recent question about my plans for running a half marathon this year.  My running has been disrupted by several health problems and now these have receded into the background, I am trying to build up training volume.  However, I am struggling against the re-emergence of several long standing musculo-skeletal problems.  Currently my most troublesome problem is metatarsalgia.

By way of introduction to the topic, I had devoted most of my post on 4th September to the rather tortuous history of Dathan Ritzenhein’s metatarsals. Despite a very bright career as a high school athlete and many subsequent major achievements, including a brief tenure as the 5,000m US record holder, and a bronze medal in the world half-marathon championships in 2009, his potential has frequently been hampered by metatarsal fractures.  Most dramatically, metatarsal pain led him to drop out halfway through the 10,000m at the Athens Olympics in 2004.

He is currently a member of the elite team of US distance runners participating in the Nike Oregon project.  Under the guidance of his coach Alberto Salazar he has made three major adjustments to deal with his metatarsal problems.  First, he moved from the beautiful but austere environment of Boulder Colorado, where the trails are rock-hard, to the soft moist terrain of Portland, Oregon.  Secondly, Nike’s head of biomechanics, George Valiant, deigned some shoe inserts which relieve the pressure on the downward protruding head of the third metatarsal of his right foot.  Finally, and in my opinion, most controversially, he has, abandoned heel-striking for something approaching a mid-foot landing.  I presented my reasons for questioning the wisdom of third of these changes in my post on 4th September.  Now it is time to describe the history of my own metatarsals.

The history of my metatarsals

Although by nature a forefoot runner, I have always had problems with my metatarsal heads.  Since birth, the second metatarsal head in both my right and left feet has protruded downwards.  In childhood , I used to wear out my shoes from the inside.  By the time I reached my teens, a few months after I obtained a new pair of shoes, a hole appeared in the insole as a result of abrasion by the callous on the underside of my forefoot.  Perhaps surprisingly, my feet scarcely suffered at all. I ran all of my marathons in the same pair of Onitsuka Tigers – the fore runner of today’s minimalist shoes.  Although I had to take special precautions to deal with my congenitally peculiar toes, I suffered no pain in the vicinity of the metatarsal heads.  I think that in those days my body’s ability to repair itself far outstripped the rate of tissue damage.  I simply developed thicker callous. However, that has changed as the fat pads between the metatarsal heads and the callous have disappeared with age, and my capacity for tissue regeneration has waned.

About a decade ago, I went shopping for a new pair of street shoes and was frustrated by the fact that every pair I tried caused pain in my forefoot.  I was puzzled as to why I had not had such a problem before.  Even the worn old shoes that I had worn into the shop were quite comfortable.  At first I failed to draw the obvious conclusion but later when I started to suffer serious metatarsalgia (pain beneath the metatarsal heads) while running, the answer came to me.  My old shoes were comfortable because the insole have been hollowed out by the abrasive action of my foot.

I therefore hollowed out the insole of my running shoes, in a similar manner to the way George Valiant created inserts for Ritz eight years later.  The pain diminished substantially, though unfortunately did not resolve entirely.  Perhaps I lacked George’s engineering skills but I suspect the main problem was that I had developed inflammation of the fascia on the underside of the forefoot.  Although the hollowed-out insole shifted the pressure away from the metatarsal head, stress was transferred to a different region of the fascia, which continued to tug on the inflamed area.  I think that is why orthotics rarely provide full relief from plantar fasciitis.

However as the inflammation settled, I found that I could run without pain. Nonetheless, as an extra precaution, I avoided running on hard surfaces as much as possible.  In addition I embarked on regular exercising of the intrinsic muscles of my feet – mainly variations on toe curling – with the expectation that strengthening these muscles would improve their ability to help distribute the load at foot strike thereby controlling the rise in in the tension in the fascia. Together these precautions proved quite effective. Since taking up running again three years ago, I have had minimal trouble from metatarsalgia.

The price of complacency

Eventually I became a little complacent.  I stopped doing the exercises to maintain strength in the intrinsic foot muscles and I became lackadaisical about hollowing out the insole when I obtained new shoes.  There were slowly evolving signs that all was not well: since the episode of acute arthritis in the early months of this year, I had been aware of an increase in forefoot pain, but in the setting of the various other aches and pains that afflicted me, it appeared trivial and I ignored it.  However, I suffered a rude awakening two weeks ago when I set out for my ill fated tempo run. Because I had been late home from work, I ran along a paved sidewalk rather than risk the uneven riverside path in the dark.  I am not sure what was the main culprit: lack of hollowed insole; the hard surface; the alteration of gait due to my knee problems; the effect of lingering systemic inflammation or the accumulation of stress due to my recent return to running.  Whatever the cause, the outcome was a sharp pain in the forefoot.  The metatarsalgia had returned with a vengeance.  The following morning I could scarcely bear to put my foot on the ground.  Hollowing-out the insole of my street shoes provided only slight relief. I was amazed at the ferocity of the sudden exacerbation.   I wondered whether or not it might be a stress fracture.  Focal tenderness of the second metatarsal head added weight to this possible diagnosis, though my experience of similar pain in the past indicated that it would be unwise to jump to a rapid conclusion.

An abrupt drop in high frequency Heart Rate Variability that morning confirmed that I was markedly stressed, no doubt mainly due to the widespread minor musculoskeletal trauma arising from my tempo run, to which the metatarsalgia was only one contributor.  As shown in the figure presented in my post of 30 August, HRV remained depressed for two days, but then returned to a healthy level, indicating that my recovery mechanisms had risen to the challenge and dealt with the systemic stress level.  The focal pain in my forefoot was also substantially reduced but nonetheless, still quite appreciable.  Even with a hollowed-out insole, I could not bear to take my weight on my forefoot while standing.  Running was unthinkable.

Becoming a heel-striker

Gradually the pain in my forefoot diminished and by the fourth morning after the tempo run I decided it was time to try to run.  However it was clear that landing on my forefoot was out of the question.  Circumstances dictated that I should become a heel-striker. To minimise the force at each foot fall, I adopted a quite high cadence and short stride.  To my delight, I found this high cadence, heel-striking style was actually less painful than walking.  After a few Km, the pain in my forefoot had disappeared entirely, a time course typical of pain due to chronically inflamed connective tissue, which tends to feel better once recently formed local adhesions have been remodelled and local blood flow has increased.  This is not the usual time course of pain from a fracture, which tends to increase as the distance run increases.  So I was relived to realise that stress fracture was unlikley.

I was feeling very relaxed at a pace between 5:30 and 6 min per Km.  There was no sign of the discomfort in my knee that had plagued me in recent weeks.  I had intended to run about 6Km. but was feeling so relaxed that I extended this to almost 14 Km.  Although I still felt comfortable, I stopped simply because this was several Km further than I had run in the preceding two months, and I feared that accumulating tiredness would increase the risk of further injury.  My average pace was 5:45 Km/min and average heart rate 120, confirming the previous evidence that my loss of aerobic fitness has not been severe.  Later in the day I suffered the expected aches in knee and forefoot, but on the whole, my body had coped well.

In subsequent days my forefoot has remained tender. When I stand-up from a sitting position pain from the patella-femoral joint and also from the point where the ITB rubs against the lateral femoral condyle confirms that I still have lingering irritation of tissues in these areas, but provided I run with a mild degree of heel-strike and a high cadence, both my forefoot and my knees are comfortable when running.

The future

What the next few weeks will bring remains uncertain, but I have growing optimism that conversion from forefoot striking to slight heel striking, at least during low-aerobic training runs, might be the key to building up to an adequate volume of training.  If I can achieve a reasonable volume of running, I would like to run a half-marathon before the end of the year. Currently, I have the Worksop Halloween half marathon pencilled into my diary.  However that is less than two months away, and in the intervening period I will be doing some travelling.  I am scheduled to deliver talks at conferences in both Germany and China in October.  Unfortunately attending conferences does not diminish the load of routine work, so October will be a busy month.  Therefore, it is far from clear that I will be able to get my legs adequately conditioned for a half marathon by the end of October, and it would be foolish to race if my legs are seriously ill-prepared.

Whatever happens with my own race preparations, I am of course looking forward eagerly to the outcome of Dathan Ritzhenhiem’s experiment with the transition from heel-striking to mid-foot striking.  I hope that on 7th November in New York he at least improves upon his previous best marathon time even if he does not win what promises to be a great race.  But even if his experiment has a successful outcome, I am dubious about Alberto Salazar’s belief that there is one ‘best way’ to run.  I am increasingly inclined to think that while there are indeed rational principles that govern running mechanics, each individual needs to discover how best to apply those principles to his or her own situation.  The heel-strike debate is probably one of the least important issues for most marathon runners, but for Ritz, I think that it is potentially an important issue, and that in abandoning heel-striking he is taking a risk.

Can Dathan Ritzenhein win the 2010 New York City Marathon?

September 4, 2010

After Meb Keflezighi’s victory in the New York City Marathon last year and his fifth place in Boston this year, he will start as one of the favourites this year, though it promises to be a great race.  Haile Gebreselassie will be making his New York debut, but he is in no other sense a debutante.  It will fascinating to see whether or not he still has the form that carried him to the world record in Berlin in 2008.  I understand that Tesfaye Jifar who set the course record almost a decade ago, will be back again this year.  Among the somewhat younger contenders in New York on 7th November will be Dathan Ritzenhein [1].  He made a rather disappointing New York debut in 2006 but is returning to New York after some strong performances on the track, and a bronze medal at the World Half-Marathon Championships in a time of 60:00 in Birmingham in 2009.

But really this blog post and the next will be about me almost as much as Dathan Ritzenhein, and the sub-title might well be ‘Will Canute be fit enough to run the Worksop Half marathon on Halloween?’  I am writing this in response to Ewen’s recent question about my prospects of running a half marathon this year in light of the fact that my year has been blighted by illness.  In my return to running two weeks ago, I struggled to maintain a pace of 5 min/Km during an attempted modest tempo run.   The reason for a rather far-fetched comparison of myself with one of  America’s leading  distance runners is that Ritz has also frequently been sidelined by injury, and if one digs a little deeper into the details, there are some interesting parallels, but also interesting differences in the way that we have responded to a similar problem.

My main problem this year has been an episode of arthritis that started in January and lingered for many months.  It started in my neck, and then spread to my knees, especially the left knee.  Although the acute inflammation settled several months ago, I have subsequently been plagued by a variety of irritating problems around the knee joint, especially  patello-femoral pain and also irritation of the iliotibial band.  I suspect that both of these problems can be attributed largely to a temporary  alteration of my gait to protect the femoro-tibial joint (the main load-bearing joint at the knee) during the period when the acute arthritis was resolving. However, I think the presence of acute systemic inflammation and/or my altered gait has also unsettled several of my other long-standing trouble spots, including my metatarsals.     At present my most frustrating problem is metatarsalgia.

The history of Ritz’s metatarsals

Dathan Ritzenhein  has suffered metatarsal  problems for years.  After a promising display of talent in high school athletics, culminating in a bronze medal at the IAAF World Junior Cross-Country Championships in 2001, he had went to college in Boulder, Colorado.  Following a successful freshman year, his sophomore year was blighted by two metatarsal stress fractures.   The next year he won the National Collegiate cross country championship but again suffered a stress fracture, and limped home in last place in the 10,000m trials for the 2004 Olympics.  Nonetheless due to various mishaps to the initially selected runners, he made the Olympic team, but dropped out halfway through the race in the Athens on account of pain from the stress fracture.   After the Olympics he left college athletics to become a professional and joined Brad Hudson’s coaching group in Boulder.

Boulder is a quirky university town set in awe-inspiring but austere landscape on the eastern slope of the Rockies.  I knew Boulder as it was in the days before Ritz attended college there, but I do not expect that the terrain has changed greatly in the past decade.   Within the city are many paved cycle paths, including the well known creek- side path, which at first sight appears an attractive running route,  but the concrete surface is very hard.  Extending up into the nearby foothills is a further network of unpaved trails but these are mostly hard earth and rock.    Being in the centre of the north American landmass, Boulder also happens to be more than a mile (1600m) above sea level.   It is not as high as towns such as Eldoret in the Rift Valley district of western Kenya, or the mountains near Addis Ababa in Ethiopia, where high country lying between 2000 and 3000m above sea level  has become a Mecca for athletes seeking the secrets of African distance runners.  However Boulder’s  combination of thin air, hard rocky ground and relatively few trees create an environment that is hard on the body of a serious  distance athlete.

In her account of  training in the mountains of Ethiopia,  Hilary Stellingwerff noted ‘Finally, on all my recovery runs, the Ethiopian athletes stressed the importance of running on soft ground in the forest to make sure you go slow enough to really recover. They don’t worry too much about their pace, but instead about “getting good oxygen” from the trees and “soft ground” for the body.’ [2]

I will return to the question of whether or not  the harshness of the environment makes an appreciable contribution to the risk of injury in a future post when I respond to Ewen’s other recent question about the value of monitoring Heart Rate Variability.  However I think it is plausible that the austere environment, and especially the hard trail surfaces of Boulder contributed to several of Ritz’s injuries and illnesses over the years.

Softer ground

In May 2009 Ritz left Brad Hudson to joint Alberto Salazar’s group at the Nike Oregon project in Portland.   Although I do not know Portland, I had lived for almost a decade in Vancouver, BC, and I am fairly familiar with the Pacific Northwest.  I find it hard to imagine anywhere in the world  that could be more congenial to the body and spirit of a distance runner than the moist and verdant Pacific Northwest.  Added to the idyllic natural surroundings is the high tech support provided by Nike, which includes a house with artificially thinner air.  The athletes can live and sleep in the rarefied atmosphere that encourages accumulation of red blood cells, yet avoid the stress of high altitude training by doing their rigorous training at normal atmospheric pressure.  However even in this runners’ paradise, Ritz continued to suffer injury.   So the hard surfaces of Boulder were not the only cause.

In an interview with Peter Gambaccini for the Racing News blog at Runner’s World in July of this year Salazar admitted  ‘Dathan continues to have some foot problems which he’s had for years. I had thought that just by keeping him on soft surfaces and making sure that he’s recovered that this would be taken care of.’ [3]

Shoe inserts

In an attempt to overcome the continuing problems Salazar and the Nike team have implemented two changes.  First they identified the fact that the head of Dathan’s third metatarsal on the right foot protrudes downwards.  To relieve the pressure,  Nike’s head  of biomechanics, George Valiant, produced a hollowed-out insert for his running shoe.  This produced an immediate relief  which I find understandable, because I had made a similar modification to the insoles of my own running shoes about 8 years ago, and , as I will describe in my next post, this provided a partial relief to my own problems.   In the interview reported in the Racing News blog  Peter Gambaccini also spoke to Dathan himself.  He reported ‘I feel really comfortable now. The inserts feel real good. There’s still a little bit of refining on them, but at this point, I feel like when I train daily now, it feels good and my body’s getting used to it.’

Changing  from heel-striking to mid-foot landing

Salazar’s other innovation was to encourage Dathan to change from heel-striking.  Alberto Salazar believes that there is a right way to run and that right way does not include heel-striking.   In the interview for the Racing News blog, Gambaccini asked about the change from heel striking and Dathan repliedI was definitely more of a heel-striker, so I’m definitely getting on to my midfoot more. I wouldn’t say I get all the way up to my toe. I think I’m more pretty much efficient for the marathon if I stay in more of a midfoot stance anyway. ……. Initially, the problem was we tried to focus solely on changing that without being strong enough to do it. We went back to trying to build it up from the strength side so it (the stride change) naturally took over instead of trying to think about it consciously

It is of interest to note that Ritz emphasized the necessity of building strength to support the transition from heel-strike towards the forefoot.  In that interview he did not give further details, but  I suspect he was referring largely to the greater calf strength required when running on the forefoot, though I wonder whether he was also referring to the necessity for greater strength of the intrinsic muscles of the foot, which are called upon to take a larger role in distributing the  forces of impact.  I seriously doubt Salazar’s wisdom in the decision to change from heel-striking for a runner with metatarsal problems, and will return to that issue when I focus on my own tentative approach to my metatarsal problems.

Is the heel-strike debate a red herring?

In my own speculation about running style (described in ‘Running: a dance with the devil’ in the side panel)  I have advocated forefoot landing, but I believe that even more important than forefoot landing in a high cadence and short time on stance.  A recent study by Heiderscheit and colleagues from Wisconsin [4] confirms that increasing cadence by 10% without making any conscious attempt to  change  other aspects of running style results in a substantial reduction in stress at knee and hip.   I continue to believe that if there is one change that is worth making to running style, it is increasing cadence, at least up to a rate in the range 180-200 steps per minute.  I think that above 200 there are diminishing benefits, except when sprinting.  But the nagging question remains: is it also worthwhile to change from heel-strike to forefoot strike.

There are three main arguments favouring a change.  First, it would be expected that landing on the forefoot will result in greater capture of the energy of impact as elastic energy in the muscles and tendons of the foot and calf, and that this energy might be recovered at lift-off from stance.  Secondly, the absorption of impact energy as elastic energy will prevent the sharp rise in ground reaction force immediately after foot-strike.  The jarring effect of this rise in force transmitted upwards through knee and hip might be expected to increase risk if musculo-skeletal injury, though there is little evidence supporting this.   Thirdly, from the evolutionary perspective, it is probable that the human frame evolved to facilitate barefoot running, and barefoot runners usually land on mid or forefoot.

However, the extensive anecdotal evidence of increased rate of calf injuries following transition to forefoot landing suggests that the injury risk associated with the transition is high unless the runner makes a determined effort to strengthen the muscles of foot and calf.   Studies such as the Capetown study of Pose [5] suggest that the transition can be associated with less stress at the knee, but the more recent study by Heiderscheit and colleagues [4] indicates that the reduced  stress on the knee with Pose style might be due at least in part to increased cadence. With regard to the evolutionary argument, it might well be that forefoot striking was best suited to the barefoot running on the African savannah 2 million years ago, but most of us now run on paved surfaces much of the time.  Furthermore the elegant longitudinal arch of the foot suggests to me that the human foot evolved to absorb and store impact energy efficiently when both forefoot and heel are grounded.

In principle heel -striking and forefoot striking are distinctly different, but in fact there is a continuum.  At one extreme, the entire force of impact is borne by the heel; at the other extreme the impact is taken entirely on the forefoot.  I consider that both of these extremes are likely to increase risk of injury.  In the middle of the range is mid-foot striking in which the initial impact is taken equally on forefoot and heel.  In this style, the impact forces within the foot are immediately distributed along the length of the longitudinal arch.  But of course, the runners’ stance is a dynamic event in which the peak vertical ground reaction force occurs around mid-stance, and perhaps that it the point at which it is most beneficial to have both forefoot and heel grounded.

If one is aiming to have both forefoot and heel grounded around midstance, the possibilities for ankle posture at foot-strike stance range from  plantar flexion to mild dorsiflexion, but I suspect that the factor that plays the greatest role in determining the softness of the landing is the degree of flexion of the knee.  As the knee flexes at impact, the quads, which are far bulkier than any muscles below the knee,  will absorb impact energy.  If the degree of tension in the quads is low, the landing will be soft and the risk of injury low, but the recovery of elastic energy will be relatively slow.  If higher tension is maintained in the quads, the leg will act like a stiff spring, retuning energy rapidly and promoting efficiency, at the price of somewhat greater initial rate of rise of the vertical ground reaction  force and possibly greater risk of injury.

I suspect that there is an inevitable trade-off between efficiency of energy recovery and risk of injury, determined largely by the amount of tension in the quads.  I also suspect that for a long distance runner, the orientation of the ankle matters relatively little provided it is within the moderate range that allows an equable dissipation of impact forces along the longitudinal arch by midstance.  If so, the heel-strike v fore-foot debate is largely irrelevant, unless the athlete has anatomical features that make a particular part of the foot more vulnerable.  For a runner with downward protruding metatarsal heads, I suspect that a mild degree of heel-strike might actually be preferable.

I have taken a particular interest in the way Dathan Ritzenhein has dealt with his problem because I have faced some similar issues.  By trial and error I had discovered some of the same strategies as Ritz, though in one potentially important respect I have taken a different path.  But this post is already long enough so I will defer the history of my own metatarsal problems to my next post.




[4] Heiderscheit, BC.; Chumanov, ES.; Michalski, MP.; Wille, CM.; Ryan, MB (2010) Effects of Step Rate Manipulation on Joint Mechanics during Running. Medicine & Science in Sports & Exercise: doi: 10.1249/MSS.0b013e3181ebedf4; Jun 23. [Epub ahead of print]

[5] Arendse RE Noakes TD, Azevedo LB, Romanov N, Schwellnus MP, Fletcher G.  (2004) Reduced Eccentric Loading of the Knee with the Pose Running Method. Medicine & Science in Sports & Exercise: Vol 36 pp 272-277