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

My posts on the equations of motion of the runner on Jan 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.

Conclusion

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

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

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

  1. Simon Says:

    Cannute,

    This all looks very interesting, unfortunately I’ve only had time to read the introduction and the piece on repositioning.

    Are you sure repositioning costs are proportional to the square of the runner’s speed? That would obviously be true for a separated object needing to attain double the speed of the main object, but when the object is physically connected like a leg to the torso, it does not seem quite right.

    If the runner did no work at all with leg muscles and allowed only connectivity and elasticity to effect the leg, it would at least trail and match the speed of the torso and possibly have a faster speed than the torso from elasticity. So if connectivity alone is utilised to some degree to match leg speed to torso speed, then the work done by the muscles would just be co-ordination and an impulse to make the leg overtake the torso in a timely manner (plus a similar impulse to reverse swing to some degree).

    I’m not sure what effect that would have on the relationship between pace and swing cost, but thought it worth consideration.

    Does the pendular nature of the movement make any difference as well?

  2. canute1 Says:

    Simon,

    Thanks for your comment.

    The Cavagna and Kaneko data provide strong support for an increase in repositioning costs proportional to the square of velocity. Whether or not the leg is connected to the torso, the energy required to accelerate within a particular time period it will be determined by the mass and the required increase in speed. The estimate that the foot must achieve a speed of twice running speed is only approximate. Provided the velocity achieved by the foot has a similar ratio to running speed over the range of speeds under consideration, the estimate of proportional increase in repositioning costs will be reasonable. However, this only an assumption, so the important fact is that the experimentally observed rate of increase in repositioning cost is proportional to the square of running speed.

    I agree that elasticity will allow recovery of some of the energy, and also that the momentum of the swinging leg will return some of the energy to the torso in late swing. That is why I only estimate proportional costs and then refer to the C&K data to provide a reference speed at which repositioning cost is equal to cost of braking plus elevation.

    Pendular motion also matters. I have only dealt with linear acceleration but a full calculation should also take account of rotational motion. I think this will consume less energy than the linear acceleration, but the arguments in favour of flexing the knee to provide a shorter lever arm suggest that rotational effects are appreciable.

    I do not wish to claim that my estimates provide an accurate estimate of repositioning costs, but I think they provide a useful insight into the direction of the relationship and furthermore, give an estimate that is in line with the experimental observations of C&K.

  3. Simon Says:

    Canute,

    Thanks, I took a look at the C&K paper to see what they had discovered.

    As you say, the total cost increases with the square of pace.

    Also of interest in that paper, is that they estimate the elasticity covers 45% of the cost at slow running speeds and that goes up to 80% at high running speeds. So although the overall cost increases with the square of pace, the specific cost of muscular contraction is a fraction of the total cost meaning that the real cost to the runner of an increase in cadence is not so high.
    It would be interesting to incorporate the figures for elastic return to see the relationship between muscular work and repositioning.
    Or did you do that already when you used the C&K data for a reference point to a speed at which repositioning cost is equal to cost of braking plus elevation?

  4. canute1 Says:

    Simon,
    Thanks for your comment. The question of variation of efficiency of elastic recoil with time on stance, cadence and speed is important, and as outlined in my post, not easy to deal with.

    I did not use the estimates of elastic recoil from C&K because their estimate is based on approximations which seem to me implausible. Their estimate is based on the assumption that metabolic to mechanical conversion efficiency is 25% under all circumstances and also on an assumed value for total metabolic energy consumption. Their estimates of elastic recoil efficiency which range from 0.45 to 0.80 cover a far wider range that published values from other studies. See for example, Asmussen, E. & Bonde-Petersen F. (1974). Apparent efficiency and storage of elastic energy in human muscles during exercise. Acta physiol. scand. 92, 537-545. As you know, in the deliberations on Pistorius’ blades, the values for typical runners were taken to be less than 50%.

    In contrast to the C&K estimate of elastic recoil, their estimates of costs of repositioning (what they call internal work) and braking together with elevation (which they call external work) were based on actual measurements. While they acknowledge the potential inaccuracies, I nonetheless regard these as the best available published values. My estimates of proportional change in the mechanical cost of repositioning with variation in speed are based on their estimates of internal and external work and do not depend on efficiency of elastic recoil.

    What can we conclude about elastic recoil? I suspect that elastic recoil is most effective in recovering impact energy, rather than the energy required for repositioning. Perhaps the greatest influence of recoil on repositioning is the recoil of hip flexors that are stretched at the end of stance. The extent of stretching of hip flexors is less at higher cadence. As I state in the above discussion, the elasticity of tendons increases as the rate of application of force increases. When running at slow speed and long time on stance (as in the video of Ken Bob which Robert posted in a comment on my post of 16th Jan) I suspect elastic recovery is low, and will almost certainly increase with increased speed, but would also increase with shorter time on stance at the same speed. So the estimation of variation with speed must also take account of variation in time on stance. I certainly intend to look into the issue of elastic recoil in greater detail.

    In conclusion, I suspect that elastic recovery does increase appreciably with speed, though probably not as much as suggested by C&K. It might also with decrease time on stance at constant speed. These possibilities do not affect my estimate of repositioning cost, but do suggest that the greatest efficiency will be achieved with a short time on stance and fairly high running speed.

  5. Simon Says:

    Canute,

    Its not clear from the abstract of ‘Apparent efficiency and storage of elastic energy in human muscles during exercise’ whether they are considering just repositioning costs or all stretch-shortening throughout the gait? I cannot access the whole paper.
    The Pistorius figures were concerned with elastic recoil in the vertical plane rather than repositioning of the swing leg as far as I know.
    To date, the C&K paper is the only one I know that has considered recovery costs alone.

  6. canute1 Says:

    Simon,

    C&K estimate the elastic recovery by comparing the mechanical costs (the sum of elevation, braking and repositioning) with metabolic costs, together with the assumption that metabolic to mechanical conversion is 25% efficient under all circumstances. In my opinion, this not a reliable way to compute elastic recovery, but nonetheless, to the extent that it is valid, it is an estimate of total elastic recovery, including recovery of impact energy.

    Nonetheless I have always been a bit concerned about C&K’s estimate of repositioing cost at high speed, as you might remember for our three way discussion with Peluko some time ago. It never really made sense to me that repositioning costs should become so high as speed increases, as this would seem to make sprinting a rather inefficient form of locomotion. At this stage, I wonder whether they have properly computed the cost of rotation of the swing leg about the COG. The formula they use is of course the basic formula that is derived from Newtonian mechanics, but there are several potential weaknesses in their computation (based on measurements from cine film), including uncertainty in the estimation of the location of the COG within the torso. Clearly as the knee of the swinging leg flexes in early swing, the COG moves upwards relative to the iliac crest. There may also be other inaccuracies in their computation

    I was initially re-assured that my crude estimate of the cost of linear acceleration of the swinging leg was in agreement with their finding that repositioning costs increase in proportion to square of the running speed. However, it may be that the crucial contribution to repositioning cost is the cost of rotation around the COG. If so, it becomes crucial to know whether or not C&K’s estimation of the cost of this rotation is correct. It is widely believed that flexing the knee in early swing reduces the cost of repositioning appreciably, and perhaps C&K have not dealt adequately with this.
    .
    If repositioning cost is less than C&K estimate, that would strengthen my main conclusions based on the computation of braking and elevation cost.

  7. Simon Says:

    Canute,

    I did not appreciate the C&K computations concerned recovery of impact energy too, apologies.

    Yes, estimating COG positions via film is a weakness in the C&K method and as we have seen in other studies (Romanov & Fletcher), the failure to get the COG position right can make the results useless.

    My suspicion is that the costs of repositioning are less than the C&K estimates. My reasons for this are; pendulum arm shortening (as you mentioned), pendulum forces (much of swing happens with one grounded leg, so classic pendulum forces apply, plus differentials in momentum that add to the effect) and an uncertain amount of elasticity.

    If the cost of recovery is less, does that increase the potential gains of increasing cadence from 180 to 190?

  8. canute1 Says:

    Simon
    Yes according to my calculations, increasing cadence from 180 to 190 will increase efficiency.
    I note that elite 10K runners often exceed 200 in the final lap, and sprinters exceed 250. I understand Bolt’s cadence in Berlin was 257.
    I am still a little puzzled by the fact that novices almost always have a cadence much below 180, but maybe it requires good coordination to achieve optimum efficiency. As far as I remember, in their EMG study, Priluksky and Gregor showed that the consistency of coordination of the firing of the hams and gastrocnemius was correlated with improved efficiency.

  9. Simon Says:

    Maybe it is just counter intuitive to take more steps as each step is associated psychologically with effort? I expect co-ordination comes into it too.

  10. Klas Says:

    I strongly believe the reason why novice adult runners have low cadence is because they view running as based on a forceful push-off, and their shoes reduce the sense of ground contact. Most of them can quickly learn to increase cadence simply by pushing off less. Some of them also need to improve their ability to react quickly in the stretch-shortening cycle of landing and pushing off.

    • Klas Says:

      It is worth mentioning that it is much easier to push off too much at slow speed when the ground contact time is longer.

    • canute Says:

      Klas
      Thanks for your comment. It is an important issue for those who coach runners with a wide range of experience including novices, and I value you opinion.
      I agree that a conscious focus on pushing off might result in the novice failing to focus on increasing cadence. In general exerting greater pressure on the ground leads to greater efficiency, though it is likely to increase the risk of injury, so it is definitely better to encourage a novice to think about increased cadence rather than make a stronger push against the ground. Another approach, employed by many Pose coaches, is to encourage the runner to focus on getting the foot off the ground quickly. This leads to increased efficiency, but the reduced stance time is associated with increased pressure on the ground. In recent years, Dr Romanov has claimed that short time on stance defines the Pose standard. It is not of course unique to Pose. It is a consequence of any strategy that leads to increased pressure on the ground. As it is not without at least some risk, it is only safe to do this with a novice if you encourage drills together with keeping total volume of training relatively small.
      I believe there are several factors that prompt novices to run with relatively low cadence. While I emphasized poor coordination in my discussion with Simon a few days ago, I think that over-striding is another important factor.. I remember as youngster, about 57years ago when I was aged 9 (and had I had been running to and from school without any thought about running style for about 4 years) I decided that I wanted to increase my speed. So I deliberately increased stride length. As far as I remember this was my first conscious attempt to modify my running style and it was almost certainly a mistake.

      • Klas Says:

        I suggest we don’t get side-tracked by discussing interpretations of the Pose method.

        It is actually very hard in practice to push off more without decreasing cadence, especially for a recreational runner. The common view of running as based on a forceful push-off is directly associated with the view that longer strides generate speed. It tends to increase rather than decrease ground contact time, and lead directly to overstriding.

        Poor coordination might well be a factor preventing runners from increasing cadence, hard to distinguish from the inability to react quickly in the stretch-shortening cycle.

      • canute1 Says:

        Klas,
        The fact that the average of vGRF/kg over the gait cycle must be equal to g means that a short time on stance is associated with a large vGRF. Focussing on getting off the ground quickly produces a short time on stance and a large vGRF. vGRF is what provides the push. So a strong push is associated with short time on stance. I find that when I focus on a short time on stance I also tend to increase cadence. Therefore I do not agree with your statement that a strong push is associated with a low cadence.

        I think that the best mental approach to achieving a short time on stance, together with a strong push and a high cadence, is to focus on getting off the ground quickly rather than focussing on pushing. I think the reason this works well is because it is likely to promote increase in tension in the leg muscles an instant before foot-fall, thereby assisting in capture of impact energy as elastic energy. The elastic recoil contributes to a strong push.

      • Klas Says:

        Canute,

        I did not talk about a runner attempting to reduce time on stance. I agree that focusing on the pull can do that, although it does not happen easily. (And I agree of course that it increases vGRF.)

        What I’m saying is that a runner who attempts to run with long strides based on a forceful push-off, which is a very common view, will typically generate a greater impulse, increasing both stance and air time. In other words, it is hard to generate a greater vGRF without generating a greater impulse.

      • canute1 Says:

        Klas
        I agree that attempting to achieve a long stride by a more sustained push off is likely to be inefficient.

        As I stated in my response to your comment, I do not agree with your statement that it is very hard in practice to push off more without decreasing cadence, Efficiency is increased by increasing the force of the push off (ie the force that creates vGRF) and by increasing cadence. It is desirable to generate as much of the push off via elastic recoil as possible, and this can be facilitated by focus on a rapid take-off.
        In fact a short duration powerful push off when combined with a large forward momentum produces a long stride, but that should not be the primary focus of attention of the novice.
        I think we are in partial agreement, though I would place more emphasis on the value of a strong push off. However if a novice lacks the coordination and power to get airborne with a short push-off it is best to focus first on increasing cadence, while encouraging drills that increase coordination and power.

      • Klas Says:

        I suspect that we are mainly talking about it from different contexts. My context is giving advice to people who are not technique nerds. My experience is that the vast majority put very little effort into learning running technique. When I say “very hard” I mean that it requires more discipline and dedication than most people are willing to put in. I think it is a high probability that someone who attempts to increase vGRF will in reality increase the impulse, ending up less efficient.

        I also suspect that the advice to increase vGRF is not necessary in practice, as long as we have high cadence. The range of motion will automatically make time on stance shorter as speed increases. (Top speed is limited by our ability to generate enough vGRF in the short time available.) Simply focusing on a relaxed stride where the knee is allowed to fold freely in leg recovery is in my experience enough to get a short stance time at high speed, when we have high cadence.

    • canute1 Says:

      Klas,

      We agree that the most important advice for novices is to increase cadence. Indeed even for more experienced runners, the advice to press harder on the ground can be counter-productive.
      I am interested in your statement that focusing on a relaxed stride where the knee is allowed to fold freely in leg recovery is enough to get a short stance time at high speed, in the presence of high cadence. I find that focus on a rapid lift- off is an effective way to decrease time on stance. Maybe what I perceive as a rapid lift-off is related to what you describe as allowing the knee to fold freely. In contrast, elite sprinters such as Usain Bolt, aim for a strong conscious push from stance (see http://www.youtube.com/watch?v=JAlpH911YKU ) . However this focus on the push requires exquisite bodily awareness and rapid reactions, and I believe it is not sensible for those of us with no expectation of becoming elite sprinters.

      However one achieves a short time on stance, I believe that it is important to be aware that a decrease time on stance at a particular cadence is associated with increased vGRF and greater elevation of the COG. For many years I have been intrigued by Pose because it tends to promote a short time on stance. I have discussed this with several Pose coaches, and I learned a lot that I believe is helpful with regard to achieving a short time on stance by examination of Pose technique and drills, despite the fact that key aspects of Pose theory make little sense. However, it is important to appreciate the risks associated with short time on stance. There was time a few years ago, shortly after Jack Becker suffered a metatarsal stress fracture, when some Pose coaches in the UK refused to accept that short time on stance was associated with large vGRF. Such a refusal fosters the tendency to claim that any injury with Pose is the fault of the student, without examining which aspects of the technique might present risks.

      • Klas Says:

        It sounds like we agree. As I wrote before, I agree that focusing on the pull can decrease time on stance within a cadence. However, I find it most effective at slow speeds when it is actually counterproductive. I don’t think relaxed knee is directly related to focusing on the pull as such. But both things are part of how Pose teaches the pull. IMHO, Pose places too much emphasis on reducing braking, at the expense of vertical oscillation. I agree that it is risky, but I also suspect it is inefficient. And I think your work is very interesting in trying to tease this out.

        I have also seen Bolt say in interview that the most important thing to focus on in sprinting is to be relaxed.

        I believe that we are designed to run. For various reasons, many of us need to get rid of tension in the run. I see no real danger that we will have too little tension in the run, except due to poor training. The tension we need comes automatically with speed, if we have the strength and elasticity.

  11. Ewen Says:

    Canute, your conclusions seem reasonable. There’s a point of diminishing returns from increasing cadence (which presumably would be at a different point for each runner). A cadence of 195 for example, might have the same energy cost as a cadence of 190, and a cadence of 200 for that runner might have a higher energy cost. So, the ideal cadence fo that runner might be 190.

    On a different subject, there was an article in Runner’s World that basically said ‘running in light shoes is more efficient than running barefoot’. Your thoughts? Mine are that if the shoes are light enough, there’s minimal energy cost with repositioning limbs, but the runner can land with more force than they could barefoot and therefore produce more elastic recoil.

    • canute Says:

      Ewen
      Thanks for posting that link. I am not surprised by this evidence that it is more efficient to run in shoes provided that they light weight.
      I agree with you. Wearing light cushioned shoes makes it less stressful for the runner to exert a greater force on the ground. A greater vGRF at constant cadence leads to shorter time on stance and less braking, so efficiency is likely to be greater, provided the shoes are not so heavy that the increased work in repositioning of the limbs becomes larger than the saving from sorter time on stance.

  12. Ewen Says:

    Sorry, here’s the link to that article: http://sweatscience.runnersworld.com/2012/02/barefoot-versus-running-shoes-which-is-surprisingly-more-efficient/

  13. Robert Osfield Says:

    Hi Canute,

    Thanks for another excellent essay on efficiency.

    It would be great to get an actual model of the repositioning costs and drag costs put into the overall model of the running mechanics in a way that you could adjust the efficiency of recoil and work done by the muscles/tendons. In such a model if we could get in the cost of the weight of the legs and especially the foot + shoes would be very useful in fleshing out what might be most efficiency cadence and time on stance for different speeds. I’d love to get to putting such a model together, but am rather wrapped up in training to do the Highland Fling this spring to spare mindshare for esotric maths :-)

    My expectations in efficiency is that shoe weight makes a big difference in the cost of repositioning the foot and what the optimum cadence and time on stance will be. The lighter the shoe the faster the turn over that could be managed without incurring such a great cost, which would lead to a faster optimum cadence, but make it less critical in cutting time on stance. If one goes to the extreme of light weight footwear i.e barefoot you’ll certainly have the most efficient configuration for low cost of repositioning the foot and shift the most efficiency cadence higher.

    Even if you scale back from barefoot and wear lightweight shoes you’ll feel the benefits – I certainly do feel much more nibble and quicker with light shoes, speed feel far less effort. Getting numbers for just how much more efficient is something that would be useful to do.

    Another thing I’d expect is that optimum cadence and time on stance will vary hugely with speed, both from an efficiency standpoint and speed endurance standpoint. I don’t think it’s a co-incidence that sprinters hit cadence in the mid 200’s, and also don’t believe that someone running at 10 minute/mile pace needs to ever a high cadence, even 180 is likely excessive for joggers. I strongly believe cadence should increase with speed for best efficiency. I also don’t believe that short time in stance is best is universally good advice, nether for efficiency or injury prevention – short time on stance is needed for high speed running not low speed. I’m pretty sure if we get a decent model together this will fall out of the analysis.

    Thanks again for your efforts on this Canute.

    • canute1 Says:

      Robert,

      Thanks for your comment.

      I agree that optimum cadence and time on stance will vary with speed, both from an efficiency standpoint and speed endurance standpoint, and furthermore, that optimum cadence increases with speed. The evidence from observing sprinters confirms that conclusion at the high end, but understanding what is best at the low end of the speed range is also important, both for coaching novices and for ultra-marathon running.

      About six weeks ago you pointed out that the cost of braking and elevation during each step must be equal to the sum of change in kinetic energy and the loss of gravitational potential energy between mid-flight to mid-stance. In the limit of extremely slow speed, the loss of kinetic energy will become very small compared with the loss of gravitational potential energy, so the energy cost per step will approach mgh where h is the difference in height of the COG during the between mid-airborne and mid-stance. This height will be a constant for a given vGRF. Since the number of steps per Km increases as cadence increases, the cost per Km will increase with increasing cadence if peak vGRF remains constant. Thus at very low speed, high cadence is not efficient.

      Good luck in the Highland Fling. Have you run Ultras of that length previously?

      • Robert Osfield Says:

        Hi Canute,

        > Have you run Ultras of that length previously?

        Furthest I’ve run before is the 41 mile River Ayr Way Challenge, but this was back in September 2010. Last year I did the Glen Ogle Ultra (31 miles) and Lochalsh Dirty 30 (30 miles;-) as well as the Kielder Marathon and mountain marathon in training, but nothing close to the 53miles I’ll be attempting with the Fling.

        I’ll be on my feet for at least 10 hours so it’s an interesting task to work out how to be most efficient for this length of time. Run/walk looks to be the most efficient strategy. It’s a bit hard as a “runner” to plan to walk though, need to go over my ego and dial properly into the task.

      • canute1 Says:

        Robert,
        It is clear that you are well beyond the novice stage of ultra running, but this will take you to a new level. It is hard to imagine a better course than the West Highland Way: spectacular scenery, reasonable paths and tracks (for much of the way), and a couple of challenging ascents. I know the WHW as a walker rather than as a runner, and I am more familiar with the northern section, but if ever I take up ultras, the Highland Fling will be high on my priority list.

  14. Klas Says:

    Canute,

    I would like to get back to the topic of the limits of cadence. I still suspect that you are wrong in your reasoning that the cost of repositioning grows significantly with cadence at constant running speed.

    The cost of accelerating the foot to running speed is included in the cost of overcoming braking, since the foot is a part of the body. As Simon pointed out Feb 29 above, the foot will get the same speed as the body without repositioning. The hGRF that propels the runner forwards will also propel the foot forwards.

    The way I see it , increasing cadence is not more rapid leg movements, when running at constant speed. It is more frequent leg movements. When stride time decreases by increased cadence, the range of motion decreases by the same factor.

    • Robert Osfield Says:

      Hi Klas,

      Perhaps I can add another perspective on how to understand what is happening to the foot when it’s in flight, when vary cadence and a constant average speed.

      The way I think about it is the higher the cadence the shorter the time between landings and proportionally the shorter the distance between each foot plant. The average speed of the foot during flight will be higher than the body as the foot is behind the body on toe off and in front of the body on landing. The maths of this relationship is that the foot has (60/cadence)*2-time_on_stance to cover two strides worth of distance, while the body has (60/cadence)*2 to cover the same distance.

      So while the feet on average have the same speed as the rest of the body over the whole gait cycle, when the foot is off the ground it’s average speed is higher than the body. Now if we up the cadence whilst keeping the same max vGRF the time on stance will go down proportionally so I’d expect that the % difference between speed of the foot in the air vs body will remain the same. However, given the less time to accelerate from 0 to above the average speed and back down to zero the accelerations involved will be higher. I wouldn’t expect these higher accelerations to be entirely free so I would expect there to be cost associated with increasing cadence.

      Also for a fixed cadence, the % difference in speed of the foot in the air vs speed of the body will also be lower when time_on_stance is lower which is achieved by increase the vGRF. Given a lower % in difference one would then expect the cost of repositioning the foot+ leg to lower for the higher vGRF.

      I believe this is essentially what Canute is trying to convey. Perhaps calculating and publishing the actual numerical difference in speed of the foot in flight vs average speed of the body for the examples given would help clarify things.

      • Klas Says:

        Robert and Canute,

        I agree that it is worth looking at the cost of repositioning separately from overcoming braking, and I agree of course that it involves acceleration.

        If we look at it relative to the COG, which I agree we should, the movement is indepedent of running speed (except for air resistance). For the purpose of this calculation, the COG has zero speed.

        If you talk about accelerating the foot from zero relative to COG, I’m ok with that. However, relative to the COG, the foot will not accelerate to or beyond running speed. Relative to the COG, the speed of repositioning is the same if I’m standing still doing leg swings.

    • canute1 Says:

      Klas,

      By cost of repositioning I mean the cost of repositioning the limbs relative to the COG. This is what Cavagna and Kaneko meant by cost of repositioning. It is separate from the cost of accelerating the body as a whole (including the foot) to overcome the slowing of the average speed of the whole body due to braking.
      .
      One reason why it is useful to consider the work required to accelerate body parts relative to the COG separately from the work required to accelerate the COG relative to an external observer is that Newton’s first law of motion specifies that acceleration of the COG can only be achieved by the application of an external force to the body. We can compute the acceleration of the COG accurately if we have accurate knowledge of the external forces acting on the body. In principle we can obtain this information using a force plate.

      My computations of the work required to overcome braking provide an estimate of the work required to accelerate the COG, but do not include what C&K describe as internal work, required to reposition body parts relative to the COG.

      • Klas Says:

        Please see my response to Robert just above.

      • canute1 Says:

        Klas,
        At lift off,he foot is going backwards relatve to the COG at running speed. It passes COG at mid-swing and therfore must accelerate relative to the COG to a speed greater than running speed. The amount of work required to do this will increase in propostion to the square of running speed

      • Klas Says:

        If we observe the foot in the air, it accelerates from zero to beyond running speed, relative to the ground. But that view is misleading for the purpose of the separate calculation of repositioning cost, because the foot is a part of the body which is already at running speed.

        Yes, the foot is in fact moving slightly backwards relative to COG. And it must move from behind the body to in front of the body, just like when standing still doing leg swings.

        But we are looking at the internal movement of the limbs of the body as system that is already at running speed. It is as if the runner has been propelled into outer space (ignoring air resistance).

        We should analyse the foot in relation to the COG, and the COG gravity obviously has zero speed in relation to itself.

  15. Klas Says:

    I would like to expand on the relation between stance time and range of motion. You mentioned elsewhere that you regard range of motion as a consequence of stance time and speed, at a fixed cadence. That is true. However, given a certain stance time, range of motion increases with speed alone.

    Range of motion substantially constraints stance time in efficient running above jogging speed. The reason is that limb repositioning is more efficient with a relaxed knee, allowing the knee to fold during the first half of swing. The “price” we pay for that is that the knee must be higher up at take-off in order for the two legs to balance each other. The consequence is that more air time is required before we can land – we must let knee swing down first. This effect is greater the faster we run.

    So, efficient leg recovery constraints stance time to decrease when speed increases. If you look at videos of runners with high cadence at different speeds, I think you will see that the constraint is substantial.

    Before we jump to any conclusions, I would like to get your feedback on this description of the constraint on stance time.

    • canute1 Says:

      Klas,
      Yes, at higher speed, the foot gets left further behind the torso during a fixed stance time and hence must move through a greater range during swing, so I agree that range of motion increases with speed.
      .
      I also agree that the swing is more efficient with a flexed knee. However I think greater flexion of the knee occurs at greater speed because elastic recoil of the extended hip at lift-off results in a more rapid flexion of the hip producing more rapid forward motion of the knee, I believe that iliopsoas plays a bigger role than the quads in the forward swing. EMG reveals that the vasti are quiescent. In the absence of contraction of the quads the knee will flex as the hip flexes because of residual tension in the hams.

      Because the swing is driven by a stronger recoil of hip flexors aided by a shorter lever arm, the knee swings further forward, balancing the greater backward extension of the stance leg. I believe that this series of events results in a slightly faster swing, rather than a slower swing. This is confirmed by Weyand’s data.

      As a consequence of the slightly faster swing, cadence tends to rise somewhat as speed rises. If cadence were deliberately held constant, I think that there would actually be a very small increase stance time and a very small decrease in the required push, purchased by the increased efficiency of capture of elastic energy by hip extension in late stance. However, in practice that is not what happens. The runner pushes as hard or even harder, stance time decreases and cadence increases due to a slight decrease of swing time and a modest decrease in stance time.

    • Klas Says:

      I agree with you on how the swing works. But I think that if cadence is held constant as speed increases, then stance time is reduced and swing time is increased. This is confirmed by Weyand’s data Fig 2, which shows a constant cadence from 2-4 m/s.

      I think stance time must decrease if cadence is held constant, due to the range of motion, including the rising of the knee. Unless the runner forces the swing, which does not happen.

      When I say that vGRF must increase with speed, I mean assuming that the runner has an efficient swing. In principle it could be possible to force a reduction of swing time such that stance time would increase with increased speed, but that would not be efficient, if possible at all.

    • canute1 Says:

      Klas,

      I agree that at very slow speeds that swing time can actually become longer as speed increases (as shown in Weyands figure 2) and consequently, at constant cadence, time of stance must necessarily decrease. However Weyand’s figure 2 shows that swing time decreases as speed increases from 4m/sec to peak sprinting speed for this runner (9 m.sec) I was speculating on what would happen at speeds at which the swing time decreases.

      Weyand’s data clearly shows that over substantial part of the speed range (ie from 4 m/sec to that runners top speed of 9 m/sec) swing time does decrease appreciably as speed increases despite the fact that the range of motion increases substantially over this speed range.

      • Klas Says:

        4 m/s is not slow for us non-elite runners.

        I don’t think there is any inherent change in how the parameters change as a function of speed over the interval. If this runner would hold cadence constant at higher speed, he would have the same change in air time and stance time.

        The reason why there is such a dramatic change in the functions here is that most runners try to push off more than they should, and it is easier to push off too much at slower speed, since stance time is longer. At top speed, it is impossible to push off too much.

        This runner has a constant cadence of around 150 from 2-4 m/s. The effective impulse (excl bw) is much too high from the beginning, and he increases the impulse more than he should as speed increases in this range. People tend to maintain the rhythm and to increase the push-off (impulse) more than they should when speed increases. The net result is constant cadence while stance is constrained to decrease.

        Above 4m/s, the stance time is constrained to be so low that he is no longer able to increase the impulse despite increasing vGRF. The result is increased cadence and therefore shorter swing time. Above 6m/s the impulse decreases despite increasing the vGRF.

        If this runner would be able to hold cadence constant above 6 m/s, it would be by increasing the impulse as he did from 2-4 m/s.

        Swing time includes stance time on the other foot. The only way to reduce swing time while increasing stance time is to drastically reduce air time. The only way to do that is to adopt a more walking-like stride. That is not possible at sprint speed.

      • canute1 Says:

        Klas,

        I think you are over interpreting my speculation that there would actually be a small increase in stance time with increasing speed at constant cadence. The main point I was drawing attention to is that swing time decreases at high speed and therefore in the unnatural circumstance that cadence is held constant, stance time would have to increase. However I emphasized that this is not what happens in practice. We are in danger of getting lost in a debate about details of a hypothetical situation.

        As I understood it, you proposed that the greater range of motion is the constraint on stance time at high speed. As I see it the main consequence of the greater range of motion is a greater extension of the hip at lift off which produces greater recoil and a somewhat faster swing.

      • Klas Says:

        Thanks. I agree that we can skip this hypothetical question.

        The greater range of motion is one constraint. The greater momentum is another. I should have mentioned that as well. The torso passes more quickly over support, so there is less time available for generating vGRF, especially when considering what is a good angle for generating vGRF.

        I’m not sure how big a role the hip flexor recoil plays. I don’t think it is an important question.

        Do you agree that in order to balance the legs with a relaxed knee, the COM has to rise more, which in practice requires a stronger push?

    • canute1 Says:

      Klas,

      As explained in my response to your comment on my post on ‘natural running’ I consider that if the flexion of hip of the leading leg and the knee of the trailing leg result in the COG being located higher in the torso at mid flight than at mid-stance, when the stance leg is only moderately flexed, then he torso will exhibit a lesser vertical oscillation than the COG. However I consider it is more informative to say that this would allow for a lesser elevation of the torso rather than saying it requires a greater elevation of the COG.

      The magnitude of the elevation of the COG is determined by the airborne time because the COG must fall by a distance that determined by the product of g/2 by the square of airborne time. Although airborne time is related to the time required to reposition the limbs, the greater flexion of hip and knee at mid flight does not cause a longer airborne time. In fact high speeds (above 6 m/sec), flexion of knee and hip at mid-flight are greater than at low speed, yet airborne time is less.

      As I see it, the main reason we spend time airborne is that it allows us to minimise braking and, as shown by the calculation I presented in Jan 16th, under typical circumstances it is more economical to spend more energy getting airborne because the extra cost of getting airborne is less than the saving in braking cost. We can reduce the cost of getting airborne by increasing cadence, because we fall less far during two small hops than one large hop of the same totals duration. However there appears to be a limit on how short it is feasible to make airborne time because there is a limit on how quickly we can reposition the legs. The duration of a pendulum swing is almost perfectly constant independent of the magnitude of the swing. Although the swinging leg is not a passive pendulum, it appears that there is an upper limit to how fast we can force the swing to occur that is almost independent of the magnitude of the swing.

      • Klas Says:

        Thanks. It is good that you agree that the range of motion of a proper swing itself requires more elevation of the COM at higher speed.

        The reason why I think this point of view is valuable, is that explains why we don’t need to deliberately focus on reducing stance time with increasing speed. That will happen as a consequence of good posture and a proper swing.

        I agree that reducing braking is important at high speed. My point is that we don’t need to focus on that, because of how our gait changes as a consequence of speed.

        In my experience, a focus on short stance time leads to overdoing it.

    • canute1 Says:

      Klas

      I do not agree that the range of motion of a proper swing itself requires more elevation of the COM at higher speed. Rather, the vertical motion of the legs relative to the torso allows the torso to oscillate less than the COM.

      As you have acknowledged elsewhere, the magnitude of vertical oscillation if the COM is determined by the vertical impulse. In fact vertical oscillation of the COM decreases slightly at high speed because vertical impulse decreases due to shorter time on stance.

      It might not be necessary to focus consciously on short time on stance if we have developed this habit, but I personally find it helpful to focus my attention on checking that I am achieving a short time on stance at least some of the time when running at moderate or high speed (relative to my unimpressive range of speeds)

      • Klas Says:

        Canute,

        I am writing of course in the context of a runner who (consciously or subconsciously) attempts to push off as little possible.

        He will still push off more and reduce stance time at higher speed, to maintain stability with the greater range of motion, since the flexed knee requires a higher COM compared to the corresponding gait at lower speed.

        Do you agree?

        I think this is very important, so I don’t mind clarifying further if needed.

      • canute1 Says:

        Klas

        I agree in part. However when you refer to a higher COM. I am not sure whether you mean higher relative to the ground or higher relative to the torso. I do not believe that flexing the knee demands a higher COM relative to the ground. In ‘Groucho’ running the knee is quite flexed in both stance and air-borne phases. Time on stance is long, vGRF is low, and I suspect that the vertical oscillation of the COM is not higher than typical of more normal gaits.

      • Klas Says:

        (I thought I made this reply but it seems to be lost)

        I mean higher COM relative to the ground.

        Thanks for pointing out the extreme of groucho running. Running with equal flexion of both knees is like walking, and assumes that the swing knee is not allowed to fold during the first half of swing. (I suspect that this more than the knee bend explains why groucho runners have less vertical force.)

        Let me rephrase to avoid that.

        A runner who attempts to push off as little as possible for the speed, allows the knee to fold during the first half of swing, and keeps good posture including a perception of running tall, will raise the swing knee more and thus elevate the COM higher above the ground when the range of motion increases due to speed.

        Do you agree?

      • canute1 Says:

        Klas,

        Thanks for persisting.

        I am inclined to think that we agree only in part. I agree that when the range of motion increases due to speed the swing knee will rise higher in late swing phase. However, the elevation of the COM above the ground is determined by the impulse during the preceding stance phase and this tends to decrease at high speed because time on stance usually decreases relatively more that average vGRF at high speed.

        I do not think that flexing either hip or knee in itself raises the COM relative to the ground. Rather, flexion that brings the foot near to the height of the torso tends to raise the COM relative to the hip (ie the COM is located higher in the torso), so the torso rises somewhat less than the COM. In fact I think that runners who achieve a lesser than average vertical oscillation of the torso achieve this by greater flexion of the leading leg during the airborne phase. Because the COM rises to a higher point in the torso, the torso itself rises less high.

        However I think that a large hip flexion in late swing will stretch gluteus maximus and thereby promote a stronger contraction of gluteus maximus at foot strike. This stronger reflexive push would be expected to decrease the energy expenditure required in early stance to initiate the subsequent airborne phase – though of course energy had been spent in accelerating the swing leg forwards in the preceding swing. Thus there can be transfer of energy between different phases, and hence there is a sense in which a high swing in the preceding swing phase promotes elevation of the COM in the next airborne phase.

      • Klas Says:

        Thanks for questioning.

        I did not imply that the knee flexing by itself would raise the center of mass. Only that it requires a rising COM, since lowering the torso would require a gait change.

        Can you explain why and how the runner would lower the torso at higher speed?

      • Klas Says:

        If I stand on one leg and raise my knee, I will increase vGRF without being aware of it. That is what I think happens when the runner is balancing the legs.

      • canute1 Says:

        Klas,

        Once a specified impulse has been delivered during stance, the height to which the COM will rise is now determined. If there is flexion of hip and/or knees at mid-flight such that the combined weight of the two legs is located nearer to the height of the hips than at mid-stance, then COM will be located at a higher location relative to any fixed anatomical feature within the torso than at mid-stance. Therefore any fixed feature of the torso does not rise as high as the COM does.

        To give a hypothetical example, let us assume the impulse is enough to elevate the COM by 5cm. Let us also assume at mid-stance, the COM is at the level of the iliac crest. At midflight, let is assume that the COM of the thigh of the leading leg is raised by 8 cm relative to the height of the hips compared with its location at it swung past the leg. The COM of the lower part of that leg and foot will be at approximately the same distance below hip height as when it swung past the stance leg. At mid flight, the thigh of the trailing leg will have risen slightly nearer to the height of the hips than at mid-stance, while the COM of the lower leg and foot will have swung up to a position about 20 cm closer to hip height compared with its position at mid-stance. Thus roughly speaking the average of the two thighs will be about 4 cm nearer to the height of the hips while the average of the two lower legs and feet will be about 10 cm closer to the height of the hips. The lower leg and foot is a little lighter than the thigh, so let us say (very approximately) that the combined COM of the two legs is now 6.5 cm closer to the height of hips (and to the height of the iliac crest). If we assume that the two legs together account for 25% of body mass, the COM will have risen relative to the iliac crest by about 1.7 cm. Therefore, if the COM rises by 5 cm from mid-stance to mid-flight, the iliac crest and the rest of the torso, will rise by about 3.3 cm. This estimate is very crude, but demonstrates that provided flexion of hips and knees brings the combined mass of the legs nearer to the height of the hips at midflight compared to mid-stance, the vertical oscillation of the torso is less than that of the COM
        .
        As stated previously, the COM does not need to rise higher to accommodate the elevation of the legs relative to the hips. Instead, the torso rises less than the COM.

        With regard to the issue of increase of awareness of vGRF when standing on one foot, if I stand barefoot on concrete I am very aware of the increased vGRF compared with standing on two feet. Similarly, when running in light-weight shoes over stony ground I am very aware of the increased vGRF when I decrease time on stance. However this is not the same as focusing on pushing.

      • Klas Says:

        Canute,

        thanks for the very detailed example, but it sounds to me like you are neglecting the fact that the hip flexion happens on stance.

        My point is that the runner does not lower the torso on stance at higher speed, but he raises the knee, on stance.

        I should mention a sprinter can probably reach maximal range of motion before top speed, but that is a special case.

      • Klas Says:

        It may be interesting to note that when standing on one leg and raising the other knee, the glutes will indirectly generate a vGRF. If the pelvis is kept stable, the rising of the knee will in fact generate a vGRF.

      • canute1 Says:

        Klas
        First of all, as a matter of clarity, when you refer to raising the knee on stance, I presume you mean flexing the knee on stance.

        With regard to my crude calculation of the change between mid-stance and mid-flight of the vertical distance between hips and the centre of mass of the legs, I am not sure what you mean by hip flexion at mid-stance as there is only a small flexion of both hips at this time. I had taken account of the flexion of the swinging knee at mid-stance in my calculation. My statement that there was very little change in the height of the COM of the lower leg and foot of the swinging leg between stance (on the other leg) and the middle of the subsequent flight was based on the observation that at high speed the COM of the lower leg and foot (located slightly near the ankle than mid-calf) of the swing leg is about 2/3 of a thigh length below hips when the knee is flexed at mid-stance, while it is a similar distance below the hip when the hip is flexed in mid-flight. However this is only a crude estimate, and it does not matter to my argument if the error is substantial. The point I was making is that if the vertical distance between the centre of mass of both legs combined (including thigh, lower leg and foot) and the hips is less at midflight than at mid-stance, the torso will exhibit a smaller range of vertical oscillation than the COM. In fact I do not consider that this is very important, though many commentators have stated that efficient athletes exhibit a small range of oscillation of the torso. As far as my computations of the energy cost of elevating the COM are concerned, the possibility that the torso might oscillate less than the COM is a red herring.

        This discussion began when you asked if I agree that ‘He will still push off more and reduce stance time at higher speed, to maintain stability with the greater range of motion, since the flexed knee requires a higher COM compared to the corresponding gait at lower speed.’ Because you had not stated that you were referring to knee flexion on stance, I had addressed the question of the effect of joint (knee and hip) flexion during swing. Now I know that you are referring to knee flexion on stance, I am happy to accept that the COM is a little higher at mid-stance in a runner with a larger degree of knee flexion of the swing leg, assuming no greater flexion of the stance leg. However, when computing the cost of elevating the COM, the relevant range of vertical oscillation is from mid-stance to mid-flight. The runner needs to elevate the COM to allow for free fall when in flight. Simply starting with the COM at a higher point above the ground at mid-stance in itself neither increases nor decreases the amount of vertical impulse required to elevate the COM to recover the loss of height during free fall.

        With regard to your statement that raising a knee while standing generates vGRF. I disagree with your use of ‘indirectly’ regarding the action of the glutes. One might say that the flexion of hip and knee of the raised leg ‘indirectly’ generate the additional vGRF. The glutes together with other muscle of the stance leg directly generate the vGRF. I accept that in this situation you might be more aware of flexing of the raised leg than the greater isometric tension in the muscles of the stance leg. I also accept that when running it might be useful to visualise pulling rather than pushing. However, the point I was addressing in my post, is what muscles do the pushing. As I have stated many times, I do not think it is helpful to focus on a deliberate push, except perhaps for an elite sprinter.

      • Klas Says:

        “when you refer to raising the knee on stance, I presume you mean flexing the knee”. I meant raising the knee, as in flexing that hip joint (but as given by the context, with a flexed knee).

        I am not really referring to the increase in knee flexion that can happen as a consequence of speed. That is relevant too, but not all runners do that very well. My point is that since the swing leg is a shorter lever, the swing hip needs to flex more than the stance hip extends. And therefore the COM must rise more, on stance, when the stance hip extends more due to higher speed. I thought we already agreed on that.

        Please look at Bolt in the video if my picture is not clear. He raises the knee (flexes the hip) more and more all the way until the end of stance. With greater range of motion due to higher speed, he would need to do that even more. Because this happens (only) on stance, it generates a higher vGRF.

        I don’t think we need to discuss what happens in flight. I’m talking about why the runner generates more vGRF.

        To rephrase: “He will still push off more and reduce stance time at higher speed, to maintain stability with the greater range of motion, since the flexed swing leg must swing up higher while on stance”.

        OK?

        I accept that it would be correct to say that the glute directly generates a higher vGRF even when standing up straight on one leg and then raising the knee, since it is really the combination of contractions that does it, including those that seem to merely stabilize.

    • canute1 Says:

      Klas,
      Thanks for making it clear that you are discussing what happens between mid-stance and lift-off.

      I still think we agree only partially. I think that most likely explanation for the greater elevation of the thigh of the swing leg after mid-swing (which coincides with mid-stance of the other leg) is the greater preloading if the hip flexors during the latter part of preceding stance phase. I think this accounts for the observed greater elevation of the thigh while the other leg is on stance. (incidentally, it also accounts for the observation that greater extension of the stance leg in late stance is accompanied by a greater elevation of the thigh of the swing leg)

      Whatever the cause of the greater magnitude of the swing, if by greater elevation of the COG you mean greater elevation from mid-stance to the end of stance, I disagree. The vertical impulse decreases at high speed. Because the vertical impulse is less, there is no reason to propose that the elevation of the COG during the period from mid-stance to end of stance should be greater. It is true that the thigh rises more. Greater elevation of the thigh is not necessarily associated with greater elevation of the COM if the elevation of the thigh causes the COM to be located higher within the torso.
      Because the COG is not a visible feature, I think we could only settle this definitively by detailed cinematic analysis to estimate the location of the COG. However I consider that in view of the evidence that vertical impulse decreases at high speed, it very unlikely that the elevation of the COG between mid-stance and end of stance increases at high speed.

    • Klas Says:

      Thanks. I’m glad you are beginning to see what I mean. Thanks for your patience.

      You believe that the greater counterbalancing swing is explained by greater preloading of hip flexors. I have not said anything about what causes the hip flexors to shorten. You may be right. Since elasticity is not 100%, I suspect there is more to it. But that is a totally different question. I suggest we skip that for now.

      Even if the forward swing on stance is fully explained by preloading, it causes a vGRF unless the torso is lowered at the same time. I don’t think that lowering the torso would be a useful strategy, since it would have to be lower and lower for each step.

      You say the vertical impulse decreases at high speed. I guess you are referring to Weyand’s data. As I have explained, that data clearly seem to be the sign of a runner who tries to push off more than he should. Approaching top speed he is then constrained to reduce the impulse more than an efficient runner would. As I suggested just above, another factor that might play a role near top speed is that the runner reaches maximal range of motion. When that happens, the mechanism I describe would not happen.

      The mechanism I described can in combination with a drastic increase of cadence result in no increase of impulse. However, I guess it would still result in an increase in the air time ratio.

      The reason why I’m using Bolt as an example is that his torso does not oscillate, and yet we know that he generates a massive vGRF. It seems to be completely explained by the need to counterbalance the legs like I described, in combination with the short time available due to momentum.

    • canute1 Says:

      Klas,

      The Weyand data demonstrates not only that the individual athlete depicted in figure 2 shows a diminishing vertical impulse with increasing spewed, but also the data depicted in figure 5 derived from all 24 subjects shows that the faster runners develop a lower vertical impulse. The higher impulse is not due to a stronger push. The slower runners generate a smaller average vGRF. The reason for the larger impulse is that they the spend longer on stance. As I have continued to emphasize, one of the most important things to aim for when trying to improve efficiency is reducing time on stance.

      Whether we look at individual an individual athlete or at a group of athletes of differing ability, we find evidence that vertical impulse (and therefore elevation of the COM) tends to decrease slightly with increasing speed. In fact this a straightforward consequence of the fact that most runners exhibit a higher cadence at greater speed.

      Your suggestion that according to my account, the torso would get lower on successive steps misses the point. In my account, the torso does not get lower after mid-stance. I argue that the elevation of the torso is less than the elevation of the COM when the swinging thigh rises higher. Bolt illustrates this quite clearly. You can easily demonstrate by observing the proportion of the gait cycle that he spends on stance that his COM must rise by something between 4 and 5 cm between mid-stance and mid flight, yet as you yourself have noted, his torso illustrates little vertical oscillation. This must mean that at mid flight the weight of his legs is nearer to the height of his hips than at mid-stance, such that his COM is located higher in his torso. Thus, despite his COM oscillating by between 4 and 5 cm, his torso oscillates somewhat less.

      Both the Weyand’s data for the individual runner depicted in fig 2 and the entire group of 24 depicted in fig5, together with the video or Bolt support my claim that the greater elevation of the thigh after mid swing at higher speed does not lead to a greater elevation of the COM.

      As I have concluded several times, we agree in part. For example, we agree that an efficient runner exhibits relatively little vertical oscillation of the torso at high speed. We also agree that elastic recoil of the hip flexors only provides part of the energy required for the swing. In fact I believe that energy cost of the swing becomes one of the major energy costs of running at high speed. However I do not agree with your statement that ‘the flexed knee requires a higher COM compared to the corresponding gait at lower speed’ (where by ‘flexed knee’ you mean the flexion of the swinging knee in the second half of stance on the other foot).

    • Klas Says:

      When I say stronger push I usually mean a bigger impulse. You are right that it is often simply a longer push, but it is hard for a runner to perceive the difference.

      The decrease in impulse with speed happens at very high speeds. I think it is explained by the factors I mentioned and you have not argued against that. Nevertheless, it is a very different topic. We can agree to disagree about that.

      Increasing cadence is definitely a way to avoid the increase in impulse that I claim the range of motion otherwise calls for. I agree that there should be an increase in cadence with speed. In my opinion it should be a small but steady increase beginning at relatively low speed. In that scenario, I think we would see a an increase in air time as well. But that is a different topic.

      If we simplify this discussion by assuming that there is no increase in cadence, do you then agree that the increased elevation of the swing leg due to greater range of motion at higher speed requires a greater impulse?

    • canute1 Says:

      Klas,

      While it might be hard for a runner to perceive the difference between stronger push and a longer push, the need to make a stronger, shorter push is at the heart of what I propose for improving efficiency. As I pointed out in the title of my post on Jan 16th, there is a potential danger of injury associated with a stronger push. Finding the right mental image to achieve the short, strong push is not easy unless the runner has very good proprioception and muscle control.

      We agree that the need for a larger impulse can be removed by increasing cadence. Up to a certain point, increasing cadence improves efficiency. That was the main point of my post of Feb 6th. I still do not fully understand what sets the limit for the peak cadence. It is probably determined by the elastic properties of muscles and tendons and by the energy costs of repositioning the limbs. Those were the some of the main issues motivating by post of Feb 27th.

      I do not see any justification for your proposal that the increased elevation of the swing leg due to greater range of motion at higher speed requires a greater impulse. I believe that the greater elevation of the swinging arises from greater elastic recoil of the hip flexors together with a more effortful flexion of the hip flexors.

      In the hypothetical situation in which a constant cadence is maintained as speed increases, the runner could maintain a constant vertical impulse. The range of motion of the swing would increase with increasing speed, the energy cost of the swing would increase and the thigh would rise higher after mid-swing, but there would be no necessity to increase vertical impulse. The torso would exhbit a smaller range of vertical oscllation but the vertcial oscillation of the COM would remain the same. In the presence of wind resistance the need for a greater horizontal impulse at higher speed would make things a little more complex but I do not think the vertical impulse would have to increase.

    • Klas Says:

      Thanks.

      Now I see what you mean. I forgot to mention that I’m talking about the ideal to run with no oscillation of the torso. It is then not possible to compensate by reducing the oscillation of the torso.

      Thanks for forcing me to make that assumption explicit.

      Imagine a runner who runs with no oscillation at jogging pace, and then increases to high speed. Do you agree that the greater range of motion and an efficient swing will force him to increase the air time ratio with speed? At constant cadence, this would require a greate impulse. But it is really the increase in air time ratio that I’m interested in, not the increase in impulse which is also affected by cadence.

    • canute1 Says:

      Klas,

      Minimal oscillation of the torso can only be achieved by bringing the centre of mass of the legs nearer to the torso as the airborne body falls. It is only possible to have a smaller oscillation of the torso than the COM by employing a swing that elevates the leg.

      I do not believe that the large range of motion at high speed is the cause of increase in the proportion of airborne time. The proportion of the gait cycle that is spent airborne is (mean vGRF/g). Usually vGRF increases substantially with speed, and range of motion also increases, but it seems to me misleading to claim that the large range of motion ‘forces’ the increase in proportion of airborne time. A runner with stronger hams and glutes, who can create a greater vGRF and shorter stance time at a given speed is likely to be more efficient despite a smaller range of motion of legs relative to the torso, than a runner with weaker hams and glutes.

    • Klas Says:

      Canute,

      I’ve been too busy with other things lately, but I would like to pick this up, I don’t think your last response is in conflict with what I try to convey.

      My reasoning is that at slow speed (e.g. 2.5 m/s), we should keep the oscillation very low by minimizing the airborne time with a high cadence. It does not eliminate oscillation, but it makes it very small.

      As speed increases, the increasing range of motion combined with the relaxed folding swing necessitates an increase in air time ratio. The direct cause of the increase in air time ratio is of course an increase in GRF. It would be more accurate to say that the range of motion promts the runner to make this increase.

      A runner who gradually increases speed in this way, from slow jog to elite sprint speed will have to gradually increase air time ratio and GRF to the level of an elite sprinter at top speed, and this level will be dictated by the range of motion.

      If we assume that elite sprinters have optimal ground/air time ratio for their speed, then the range of motion could potentially dictate the optimal ground/air time ratio at any running speed. If humans are adapted by evolution for efficient running, then this hypothesis seems plausible to me.

    • canute1 Says:

      Klas
      It is good to hear from you again. I hope the calf injury you suffered while skiing has healed.

      With regard to your proposal that range of motion could potentially dictate the optimal ground/air time ratio at any running speed, I agree that the relationship between the variables that determine the energy cost of running could be expressed this way. If we assume a fixed trajectory of the swing leg and also a particular time course for vGRF, the energy cost of running at a given speed is determined by any two of a set the variables: average cadence, vertical impulse, swing duration or stance duration (which corresponds to what I understand by your term range of motion (ie the distance relative to the COG through which the foot must move during swing, which is determined by the product of stance time and speed) My choice of key variables cadence and vertical impulse as these two variables can be altered by a combination of training and deliberate choice while running. For any given speed there is a combination of values of cadence and vertical impulse that minimises the energy cost. Since cadence and stance time together can be used to calculate mean vGRF and hence vertical impulse, it is clear that if it was helpful to do so, we could regards cadence and stance time as the two variables that determined energy cost. Since speed and stance time allow us to calculate range of motion, we could even regard cadence and range of motion as the two variable s that determine energy cost at a given speed. So, from the computational point of view, there several different choice of pairs of variables that determine energy cost.

      It seems to me that the question of which variables should be regarded as determining the other variables depends on the question we are asking. As already stated, I think that if we are concerned about what we can adjust by training and/or deliberate choice, cadence and vertical impulse are the two primary variables. However one might ask, how can we estimate the best combination of vertical impulse and cadence at any given speed. I intend to compute this relationship at some time in the future, but before spending time doing this, I want to develop a more realistic description of the time course of vGRF. In fact I do not think the exact time course will make much difference to the conclusions, but I nonetheless think it is best to do this first. The time course can be estimated of real force plate data, but when using real data it is necessary to include air drag in the calculations. I know how to do this, but still have to find time to do it.

      Inspection of real data suggests to me that if the goal is to minimise energy cost, the optimum choice of cadence and vertical force will be the values to satisfy the relationship: vertical force = (A*cadence) where A is approximately constant across a wide range of speeds, for an individual runner. Furthermore, I think that faster runners will have a larger value of A. However, this is only a speculation that requires confirmation by more precise computation.

      However if the question we are asking is: what determine maximum running speed, I think the most important variable is swing time (which is of course determined by stance time or by range of motion at a given cadence and speed. Thus I do think that range of motion can be regarded as a key variable in determining maximum speed.

    • Klas Says:

      Thanks. I agree that it makes most sense to look at cadence and effective impulse or stance/air time as the variables to optimize. Personally I prefer to look at stance/air time over impulse since that is easier to observe, but the impulse is what we control.

      My point is that the range of motion combined with a relaxed folding knee during swing require an increase in vertical oscillation of the swing leg with increasing speed. Combined with a minimal oscillation of the torso, this vertical oscillation of the swing leg requires an increase in air time ratio with speed. This mechanism dictates a minimum air time with a relaxed swing knee for any given speed and cadence, corresponding to a minimum effective impulse. The air time of elite sprinters is very close to this minimum air time. If they have optimal air time, then it seems plausible that the optimal air time is close to this minimum air time at any given running speed.

      If this is true, then runners don’t need to deliberately minimize stance time. It is enough to run with a relaxed swing knee and minimal oscillation of the torso, and to let that prompt an increase in push-off and air time with speed. We still need to optimize cadence, but that is a slightly different thing.

      (My calf if not quite well yet, problems with scar tissue, but treating it with deep massage and EMS seems to work.)

      • Klas Says:

        The ability to produce a high vGRF is of course still a limit on top speed and probably important for running economy slower speeds as well.

    • canute1 Says:

      Klas,
      Your hypothesis raises the interesting question about how relaxed the swing should be. Observation suggests that there is a limit as to how short swing time can be. However, for a particular athlete, swing time decreases as speed increases despite the increase in range of motion. This suggests that swing is not a passive pendulum action but is driven by muscular work. Most of this work is done by hip flexors, especially iliopsoas in early swing, with a contribution for the quads later in swing. The fact that at high speed, repositioning of the limbs makes the greatest contribution to the energy cost of running (shown by my own calculations and also by Cavanna and Kaneko) confirms that the swing is driven.
      The contraction of the hip flexors at the beginning of swing is enhanced by the extension of the hip at the end of stance. In this sense, the increasing range of motion facilitates a more powerful swing.

      I regard the small oscillation of the torso as an incidental consequence of a large elevation of the COG of the leg relative to the COG of the whole body. This allows elevation of the torso to be less than elevation of the whole body COG . Insofar as a large elevation of the swing leg is characteristic of fast running, fast runners also exhibit a small oscillation of the torso. As speed increases, elevation of the COG of the swing leg should increase, either unconsciously or perhaps consciously. Your emphasis on minimising oscillation of the torso is implicitly a recommendation to lift the swinging knee high.

      This gets us back to the question of whether we should attempt to exert conscious influence over the swing. Traditionally coaches advised consciously aiming for high knees in late swing, but this has gone out of fashion. I think the main reason that this has gone out of fashion is the risk that it might lead to over-striding. My current opinion is that we should consciously aim to get off stance quickly and let unconscious mechanisms control the swing. In fact this recommendation is similar to the recommendation of some Pose coaches, though Pose coaches tend to place the main emphasis on a pull which they believe is produced by a hamstring contraction, whereas I believe iliopsoas makes a greater contribution. I accept that it is not generally helpful to focus on driving the swing leg, but neither do I think it is good to encourage a relaxed swing, when attempting to run fast, as one actually needs to decrease swing time despite the increasing range of motion as speed increases.

      So in summary, I find it more helpful to focus on getting off stance quickly. However, the risk of this approach is that it might lead to less powerful swing. Coaches such as Steve Magness explicitly advise not trying to get off stance quickly to ensure strong pre-loading of the hip flexors

    • Klas Says:

      By relaxed swing I’m only referring to the knee extensors. I believe that hip flexors actively but subconsciously pull the swing leg forwards. It is probably partly by stretch reflex and elasticity, but muscular contraction is subconsciously added in order to keep the torso in balance when the stance foot is standing still while the torso is moving forwards. The two legs must counter-rotate. This is something we must learn at a very early age in order to keep the balance when running. It does not require conscious thought.

      I agree with you that it should probably mostly be psoas in the first half of swing. When coaches used to advocate active knee drive, I think that lead to an over-use of rector femoris and the other quads during the first half of swing, preventing a relaxed folding knee.

      For a sprinter at top speed, I think it makes sense to focus on a high knee lift in the second half of swing, when the knee has folded, since that promotes a high vGRF. I’m not sure it is needed, but I suspect it might help to achive maximum performance.

      I don’t believe the high knee lift in sprinting is due to the minimal oscillation of the torso. I think it is due to the range of motion and the flexing knee. The high knee lift is needed in order to counter-rotate the legs. I don’t think sprinters are getting of stance quickly. They seem to get of stance as late as possible, pushing off as little as possible for the speed. If they managed to reduce stance time further, their torso would oscillate.

      • Klas Says:

        I should perhaps clarify that I mean pushing off as little as possible given the constraint of the oscillation of the swing leg due to the folding knee and the range of motion.

    • canute1 Says:

      Klas

      I think we are largely in agreement about what actually happens though we tend to emphasise different features of the gait. I consider that the most useful emphasis is that which helps create the mental image that enables the individual to achieve the most efficient style. This is a subjective matter. Each person must establish what mental image works best for him/her, though the coach should make suggestions that are likely to help the runner discover what works

      The answer to the question of whether or not sprinters do in fact get off stance quickly depends on what one means by quickly. On the one hand, the data from fig 5B in Weyand et al demonstrate that the faster sprinters spend a shorter time on stance than the slower sprinters. The fastest sprinters spend about 90 ms on stance. This is very similar to my estimate of the time that Usain Bolt spent on stance during the middle part of the race in his World Championship victory (and WR) in Berlin in 2009. However it is clear that fast runners spend appreciably longer on stance after mid-stance than before mid-stance. This is possible because they exert relatively light pressure against the ground in late stance, when the gastrocnemius contracts and the ankle lifts high off the ground while the forefoot remains grounded. I think that it is this asymmetry of time on stance that led Steve Magness (and others) to advocate avoiding a rapid lift-off. However I believe that many recreational runners are unable to get stance time below 100ms at top speed and hence I believe that aiming to get off stance quickly is a helpful goal.

    • Klas Says:

      Thanks. I agree of course that aiming for shorter stance time is a helpful goal when trying to increase top speed in sprinting.

    • canute1 Says:

      Klas,

      Although I have yet to determine the energy costs over all plausible values of cadence and time of stance (or average vGRF) for all speeds, I am fairly confident that for each speed there is will a particular combination of cadence and stance time that gives the lowest total energy cost. At high speed, both short stance time and high cadence are desirable. At lower speed, the optimal values of cadence will be lower and stance time longer. Nonetheless, I suspect that for speeds in the range 3 – 4 metres per sec the optimal time on stance will be shorter than that exhibited by the majority of recreational runners and hence that for most runners in this speed range, it is beneficial to aim to decrease stance time. However, until I have done the calculations this is mere speculation.

      As outlined in my recent article on Pose, I think that two of the principle benefits of Pose are that it encourages short time on stance and high cadence, relative that the habitual values of these variables for most recreational runners.

    • Klas Says:

      I agree. The majority of recreational runners don’t run with a relaxed knee, and/or have too limited quad flexibility, The biggest error they make is pushing off too much and for too long. Both contribute to inefficiently long time on stance.

      Looking forward to seeing your calculations.

      • canute1 Says:

        Klas
        We agree only in part.
        I disagree that pushing off too strongly leads to longer time on stance. A strong push accelerates the body upwards rapidly (according to Newton’s second law) and results in a shorter time on stance. I believe that very few recreational runners push off too strongly. However I believe that many runners who try to push off consciously, push for too long with a force that is not strong enough, and hence spend too long on stance
        With regard to your recommendation that runners should have a relaxed knee, if you mean that the knee should be relaxed at footfall, this is not efficient, as the falling body will decelerate slowly resulting in a vGRF that is too low, and hence, too long a period on stance. However, it is probably safer.

      • Klas Says:

        I meant relaxed knee during swing of course.You may be right that they don’t push of too strongly but rather just for too long.

    • canute1 Says:

      Klas

      I think we are now in fairly good agreement. I agree that the knee should be relaxed during swing. I believe that a fairly powerful psoas contraction must occur early in the swing, but this psoas contraction is largely automatic. The result of psoas contraction with a relaxed knee is that both the hip and the knee flex. At high speed, the knee folds almost completely so the foot is near to the buttocks (‘shortening the lever arm’ – or in technical language, ‘decreasing the moment of inertia’) as the thigh swings forwards.

      I frequently attend consciously to the initiation of the swing. However I do not think about which muscle to use. I imagine the swing leg arching forwards gracefully and rapidly. I believe that the quads only become active just before foot fall to ensure that impact energy is captured as elastic energy

  16. Klas Says:

    It is worth mentioning that a consequence of this constraint is that vGRF must increase with speed, in order to run with a relaxed knee. So I think we agree about the causality. I guess this is partly regulated by the limb repositioning itself. We reflexively raise the swing knee higher up in order for the legs to balance. Since the swing knee is part of the body, this requires rising of the COM, which requires higher vGRF by a stronger push.

    • canute1 Says:

      Klas,
      I do not think this is the case. As explained above, I think that if we deliberately held cadence constant as speed increased, vGRF would actually diminish by a very small amount. The leg would rise higher relative to the torso, but the elevation of the torso would be less. In fact in Weyand’s study, the faster sprinters did produce a marginally smaller rise of the COG than slower sprinters, though this was due to a substantial increase in cadence, not a decrease in vGRF.

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