Creating optimum stride length and cadence

In my post yesterday, I raised the question of the optimum ratio of stride length to cadence.   Speed is the product of stride length and cadence, but if we wish to increase speed efficiently, it is not simply a matter of increasing one or the other.   There is little doubt that efficient running requires a fairly rapid cadence.  Video recordings of elite athletes demonstrate that most run with a cadence of at least 180 steps /min (90 per foot), and many recordings of elite 10K runners demonstrate a cadence of 200 steps per minute or slightly more.  

However, there are several reasons why there is likely to be a point beyond which increase in cadence become inefficient.  First, there are factors related to the internal (molecular) mechanism of muscle contraction.  A muscle contraction involves formation and breakage of chemical cross- links as the chain-like actin and myosin molecules slide past each other. The evidence suggests that maximum efficiency is achieved when the rate of contraction is about one third of the maximum velocity of shortening of the muscle (Koushmerick and Davies, 1969).  Secondly, there are external mechanical factors that would make very high cadence inefficent.  Very rapid starting and stopping of the actions of repositioning the limbs is inefficient (Cavagna  and Franzetti, 1986).

Therefore, as speed increases there will come a point beyond which it is no longer efficient to increase cadence. Observational evidence suggests that this optimum cadence is around 180-200 steps per minute (90-100 per minute for each foot). Beyond this stage increase in stride length is essential for any further increase in speed.  It is almost certain that my current step rate of around 245 steps per minute when sprinting is inefficient.  I need to increase my stride length.

However, the issue of the most efficient way to increase stride length is a challenging question.  Reaching out with the swinging leg so that the foot lands too far in front of the centre of gravity (COG) will result in a wasteful and jarring braking action that decreases efficiency and is likely to  increase the risk of injury to knees, hips and spine.  

This might suggest that we should aim to have the point of support behind the COG throughout stance.  However, this would also present problems.  While point of support is behind the COG there will be a gravitational torque producing a head-forwards and downwards rotation.  If this is not reversed at some point in the gait cycle, we will end up flat on our face. 

It is therefore tempting to think that we should spend as little time on stance as possible.  However once we are airborne, we are subject to the downwards pull of gravity. The impulse that gets us airborne will cause us to follow an arch-like trajectory.  Gravity will nullify our ascent by mid-flight and for half of each airborne period we will accelerate earthwards at 9.8 metres/sec/sec.  If cadence has an upper limit, the duration of each step must have a lower limit.  If we spend half of this time in free fall, we must necessarily lose height and regain it in the next airborne phase.  So being airborne extracts a large energy cost.  

In addition, because the average upwards force acting throughout the gait cycle must be equal to body weight, a very short time on stance demands a very large upwards force during time on stance to provide the impulse necessary to get us airborne.

Therefore despite the immediate attraction of the proposals that we should land with the foot under the centre of gravity and that we should spend as little time on stance as possible, these proposals present serious problems.  The challenge of working out how to run most efficiently has no easy answer.

There are many things about running mechanics which cannot be described precisely in terms of either physics or physiology, but there are a few important things that can be established with confidence from the laws of physics.  Before attempting to reach a decision about the best way of increasing my stride length, it is worthwhile to step back and examine a few of the conclusions that can be drawn with confidence.  Unfortunately, this discussion does require that we grapple with some of the principles of Newtonian Mechanics.  As I remarked in the previous paragraph, there is no easy answer, but I think the intellectual effort is worthwhile if it leads to a constructive plan for the application of physical effort in training.

Gravity and getting the cost of getting airborne

First, it should be stated that despite the impression created by some recent theories, such as Pose and Chi, that emphasize the benefits of gravitational torque, gravity can provide no net energy when running on a level surface. The law of conservation of energy dictates that gravity can only provide energy if the centre of mass suffers a net fall. When running on a level surface, a fall in one part of the gait cycle must be compensated for by a rise at another phase of the cycle.  If gravitational torque plays any useful role at all, it might be that the unbalancing associated with gravitational torque triggers a reflex muscle action that gets the foot off stance and initiates the swing phase.

Although gravity does not provide net energy, it plays a major role in running because the essence of running is getting airborne.  At low speeds, walking is a very efficient form of locomotion.  A walker maintains unbroken contact with the ground and relatively little energy is spent lifting the body.  Most of the energy costs of walking are consumed by  repositioning the limbs at each step, and in compensating for the braking effect that arises when the leading leg presses obliquely against the ground at footfall.  As speed increases, the leg and foot must undergo increasingly rapid acceleration to catch up with the torso, and then suffer a corresponding deceleration in late swing phase. As a result, the energy costs of repositioning the limbs increase rapidly with increasing speed, and there comes a point where walking fast becomes inefficient.  At this point, it is better to pay the price of getting airborne.   Perhaps surprisingly, the costs (per Km) of getting airborne actually decrease with increasing speed when running.  This is because when moving at a higher speed, momentum carries us further during the arch-like trajectory of a given height.  If we maintain a trajectory of the same height on each step, we need fewer steps per Km and hence the energy cost of getting airborne (per Km) actually decreases as speed increases.   However, in considering the overall energy requirements of running we must also take account of the costs of braking and the costs of re-positioning the limbs.

  
Gravitational torque and braking

While it is tempting to think that we might eliminate the costs of braking by landing with the foot immediately under the centre of gravity (COG), as mentioned above, under most circumstances, this hope is illusory because we must reverse the head-forwards-and-downwards angular momentum generated during the second part of stance when the COG is in front of the point of contact between foot and ground.   If we ignore wind shear, the reversal this head-forwards this must occur when the foot is on the ground because the angular momentum of a body can only be changed by external torque acting on the body.   (This is illustrated, apparently paradoxically, by the fact that an airborne high-board diver spins faster as he wraps his body into compact ball.  A compact ball has a smaller moment of momentum – the equivalent of mass for a rotating body – and hence must spin faster if it cannot transfer momentum to an external object.).  Gravity cannot exert torque on a freely falling body. The wikipedia article on angular momentum states: ‘Angular momentum is conserved in a system where there is no net external torque.’ 

The observational evidence that runners land at least a short distance in front of their centre of mass suggests that most of the compensation for the head-forwards angular momentum generated by gravitational torque in the second half of stance is provided by an opposite torque acting the first half of stance.  An alternative possibility, suggested by Simbil in his comment on my blog posting on 24th February  is that a backwards push in late stance reverses the head-forwards angular momentum generated in the second part of stance.  I believe Simbil’s proposal would lead to a violation of the law of conservation of linear momentum, but for the time being, this debate between Simbil and myself has not been completely resolved.  Nonetheless, there is little doubt from observational evidence, that all runners do land with the initial point of support in front of the COG, thereby providing for at least part of the reversal of the head-forwards rotation.

Landing in front of the COG inevitably results in a braking force because the leg is angled forwards and down at the point of impact, and therefore pushes obliquely against the ground. The ground reaction force pushes back and up.  The backwards component of this push acts as a brake.   While the energy cost of braking can be reduced by spending only a short time of stance, and thereby producing less braking and angular momentum due to gravitational torque, the price is the need for a greater vertical push on the ground.  Because the upwards impulse exerted by vertical ground reaction force, averaged over the entire gait cycle must be equal to body weight, a shorter proportion of the time on stance demands a greater the vertical ground reaction force during the time on stance.  If one third of the gait cycle is spent on stance, the average vertical ground reaction force during stance must be three times body weight; the peak might be substantially higher. 

An additional crucial issue is the fact that the muscles and tendons can absorb some of the energy of impact at footfall, and this elastic energy can be recovered at lift off, thereby providing part of the energy necessary to get airborne.  Typically, about 35% of the stored energy can be recovered.   However the capture and release of elastic energy takes time as the tissues must stretch and then contract again.  It is difficult to calculate the minimum time required for this stretching and contraction because muscle and tendons are actually viscoelastic- that is, their elastic properties change as the load changes. They are quite stiff when loading is rapid but less stiff when loading is slower.  Observational evidence suggests that it is necessary to spend at least 70-80 milliseconds on stance if elastic energy is to be recovered and re-used efficiently.

The conclusion so far is that time on stance should be as short as possible down to a limit of around 70-80 milliseconds.  However, a stance time as short of this will necessitate the strength necessary to sustain high vertical forces.  If cadence is 200 steps per minute, step time is 60/200 sec (= 0.3 sec = 300 milliseconds).  If time on stance is 70 milliseconds at this cadence, the average vertical ground reaction force during stance is 300/70 (= 4.3) times body weight.  Because Newton’s third law demands that action and reaction are equal and opposite, the foot must push against the ground with a force of at least 4.3 times body weight   

Repositioning the limbs

The energy cost of repositioning the limbs will increase as running speed increases, although a full explanation requires some mathematics.  Peluko presented the mathematics in a comment on my blog a few weeks ago.  The essence of the argument is that at higher running speeds (and approximately fixed airborne time) the foot must accelerate faster to catch up with the torso because airborne body follows a longer trajectory. Rapid acceleration requires a large force.  As this larger force acts for a similar length of time, the transfer of momentum to the leg and foot will be greater and will consume a larger amount of energy.   I believe that in his calculations Peluko over-estimated the magnitude of the increase because he did not allow for the fact that the action of pulling the foot towards the torso actually slows the torso a little.  Thus some of the energy required for accelerating the foot can be extracted from the kinetic energy of the moving torso.  This kinetic energy is then returned to the torso in late swing when contraction of the hip extensors pulls the swinging leg back towards the torso.  Nonetheless, although the cost of repositioning the legs is not as large as Peluko estimated, I agree that there will be a substantial relative increase in energy cost per Km with increasing speed.

Direct observation indicates that the total energy cost of running per Km (which can be computed fairly accurately by measuring fuel consumption) remains almost constant as speed increases. This suggests that the saving on energy (per Km) required for getting airborne as speed increases is consumed in the increased energy cost of repositioning the limbs.

Conclusions

There are at least three major factors that create a demand for muscle strength and power if we wish to run fast.

1)      the ability of the extensor and flexors of the hip, knee and ankle to absorb a substantial portion of impact energy as elastic energy and to release this by a controlled approximately isometric contraction in late stance to help propel the body upwards.

2)       A powerful concentric contraction of the hamstrings (hip extensor and knee flexor) to initiate the upward swing of the foot towards the buttocks followed by powerful concentric contraction of the hip flexors to accelerate the trailing leg and foot forwards to overtake the torso in mid-swing.

3)      A powerful eccentric contraction of the hip extensors to arrest the forward swing of the leg so that at footfall the foot is only a short distance in front of the COG.

Of course we require not only strength and power, but also exquisite neuromuscular coordination to achieve these actions in a timely manner.   I believe that when we are running, we should not focus our attention on these individual actions, but instead devote our conscious attention to maintaining a sufficiently rapid cadence while relaxing all non-essential muscles. Provided we have developed the required strength, power and coordination, stride length will be adjusted automatically.  

It is clear that despite being able to run fairly efficiently at slow speeds at present, I do not have the strength, power and coordination required to maintain an adequate stride length at high speed.   I had originally intended to outline my plans for developing the required strength, power and neuromuscular coordination in this posting, but the story is already more than long enough to be digested at a single sitting, so I will defer the remainder of the story until early next week.

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83 Responses to “Creating optimum stride length and cadence”

  1. RICK Says:

    Wow i never knew running was so complicated!
    Great article Canute.
    I wonder how much body weight affects stride length?
    could losing weight be the answer?

  2. canute1 Says:

    Rick, The energy cost of getting airborne definitely increases with increasing weight, so one effective way of improving efficiency (energy cost per Km) is losing any unnecessary weight.
    With regard to the question of stride length, the push against the ground required to generate the vertical ground reaction force that lifts the body is proportional to body weight. Therefore a lighter person will require less force to get airborne and so will find it easier to increase stride length – provided the weight loss did not involve sacrificing leg muscle.
    Thanks for all your interesting comments during the past year. Have a great New Year – running ‘fast and injury free’

  3. RICK Says:

    Thanks Canute, really enjoy reading your articles.
    hope you have a very healthy and happy new year.
    by the way i think one component of your running form that might need work on is your knee drive.
    by driving your knee forward your rear leg will straighten out behind you, increasing stride length.
    Pete Magil calls the action as ‘knee popping’, a short explosive action of the knee forward.
    I’ve been using resistance cords to word on improving my hip flexor muscles.
    i agree about pulling your foot off the floor it does help increase leg speed, use the knee drive as well and you should have both fast turnover and a longer stride :]

  4. RICK Says:

    oh and check this out
    triathlon.competitor.com/2009/12/news/matt-fitzgerald-talks-about-his-new-book%E2%80%94racing-weight_6462

  5. canute1 Says:

    Rick, Knee drive is an interesting issue. I agree that it is probable that I am not bringing the knee through briskly enough at present. Among the list of things I plan to develop is hip flexor power (included in item 2 of the summary, above) This will drive the knee forwards. However consciously forcing the knee forwards might create a risk of over-striding. I hope that if I develop enough hip flexor power the knee drive will be automatic.

  6. RICK Says:

    I think as long as you do the paw back you should not overstride.
    i think it’s a good idea to concentrate on one part of the stride cycle at a time ie knee drive for one min then switch to paw back for a min then pulling the foot off the floor , maybe you could repeat this twice after a warm up on a couple of your runs each week.
    hopefully this will program the action into your nervous system and muscles and become an automatic action.
    I,ve noticed the more relaxed at speed i can be the faster I can run, the more I force it the faster i slow and get tired!
    Arthur Lydiard placed a lot of importance on knee lift but if you focus on lift you tend to bounce up and down to much, maybe it would have been better to think of driving the knee forward straight after your foot has left the floor, then the the swing upwards of the knee will happen through momentum and speed!
    I’ve just got a marathon program from marius bakken, he surggests doing what he calls ‘smart strides’ at the end of some of your key workouts, this is 20 sec fast with 20 sec recovery pepeated 5 times, the idea is to leave a memory of fast running in the muscles so with time this faster lenger stride will become automatic!

  7. Terry Hand Says:

    Hi Canute,

    Fascinating article, as usual.

    In addition to the three factors that you mention I do think that flexibility, or the lack of in my case, has a mayor part to play in limiting stride length. Some time ago on one of the forums, which have become the battleground for the efficient running debate, someone posted an article by Seb Coe on running technique. Sadly, I don’t have the link. Most of what he said was discounted, as his views were not in line with the views of the more outspoken posters, but he did emphasize flexibility as being one of the most important components. I would tend to agree.

  8. canute1 Says:

    Rick, I agree that developing the power and coordination to allow things to happen automatically, then focussing on relaxing while running, is very important. Usain Bolt appears to demonstrate that being relaxed while running is crucial for maximum speed.
    I like Marius Bakken’s idea. I think the emphasis should be on short bursts of speed (eg a few bursts of 20m at near top speed after a build-up over about 40 m) at the end of a run; otherwise there is a risk of damage when muscles are tired. I am also experimenting with including a very small amount of rapid but short two-footed hopping at the end of the warm-up to get the neuromuscular system firing quickly early in the session, while avoiding placing a great deal of stress on the muscles or joints.

  9. canute1 Says:

    Terry, Thanks for your interesting comment. Flexibility is an especially interesting topic because on the whole, stretching has become less popular in recent years following studies that have suggested risk of as much harm as benefit. However, I am particularly interested in the question of flexibility of the quads. In late stance the hip extends backwards and at lift-off the knee must flex rapidly carrying the foot up to ‘shorten the lever’ before swinging forwards. The hip extension and knee flexion both pull against the quads, while the forward swing requires contraction of quads together with psoas. It seems to me that this sequence requires quads that are both flexible and powerful

  10. Simon (simbil) Says:

    Hi Canute,

    You have stated that landing ahead is necessary to balance the angular momentum of the runner whilst on stance.

    The obvious problem with that is when a runner accelerates, they have a shorter time where the runner’s foot is ahead of support and a longer time when the runner’s foot is behind support.
    An example of a heel toe runner accelerating rapidly shows initial contact at -7* to the vertical (leaning backwards), midstance at 12* and terminal stance at 30*. For the angular momentum to balance using just your model of landing ahead, the angle of landing and the angle of terminal stance would need to be equivalent with midstance at 0* i.e. a completely symmetrical gait.
    So your model does not seem to explain what happens in heavily accelerated running and by logical extension would not seem to explain what is happening in constant pace running either as that requires some constant acceleration to overcome braking.

  11. canute1 Says:

    Simbil, Thanks for your comment.
    There are major differences between accelerated running and running at constant speed. Undoubtedly when accelerating the forwards impulse due to the strong push back against ground (or blocks) exceeds the backwards impulse due to landing ahead of the centre of gravity. As a result the body accelerates. However, if we can ignore wind resistance, at constant velocity, the backwards impulse must equal the forwards impulse – if not, acceleration would continue.
    Interestingly, during acceleration from a crouched start there will be initial rotation in a head forwards direction but this must be reversed very quickly to avoid a face down crash, yet while acceleration continues the amount of backwards push against the ground must exceed braking. There is not the symmetry of the forward and back impulses that I propose must exist during constant velocity running in order to conserve linear momentum. I am inclined to accept that at least part of the correction of rotation during accelerated running might be from the backwards push as you have proposed. However, because of the need to conserve both angular and linear momentum at constant velocity, I cannot see how it is possible that your proposed mechanism makes a major contribution during constant velocity running.
    As you know from our calculations based on the Cavanagh and Lafortune force plate data, it appears that the majority of the correction of rotation comes from landing in front of the COG, but that perhaps one third of the correction comes from the backward push in late stance. The issue is clouded by the fact the data and the calculations are not precise. I agree that the force plate data do demonstrate that the forwards impulse appears to exceed the backwards impulse by a small amount even at constant velocity – and in the absence of wind resistance, I cannot account for this. So I accept that we have not yet reached a satisfactory resolution of our debate.

  12. canute1 Says:

    Simbil, A further thought. On the treadmill there is no wind resistance, but perhaps the runner does some work against the treadmill mechanism. The load on the treadmill motor will increase when the runner is on stance with COG behind the point of support, but decrease when the COG moves in front of the COG. This might suggest that the runner exerts no net impulse on the treadmill. However, if the treadmill drive mechanism does not allow it to absorb the energy imparted to it by the runner in late stance, the runner might do net work against the treadmill. This might add heat to the environment and account for the apparent excess of forward impulse. If this does account for the imbalance of linear momentum, it would still leave the estimated one third of the correction of angular momentum to be accounted for. I can offer no better explanation than measurement inaccuracy. I am not sure about this. I will go for a run now and think about it. What do you think?

  13. canute1 Says:

    Simbil,
    As you know, I do not currently have a copy of the Cavanagh and LaFortune article published in Biomechanics in 1980. When you had sent me a copy of the data, I had mistakenly believed that it was data collected during treadmill running. I was therefore puzzled by the apparent violation of the law of conservation of linear momentum implied by the greater impulse from forward ground reaction force in the second part of stance compared with the backward force in early stance. In the absence of wind resistance, I had to hypothesize that the runner must do work against the treadmill. However, in an attempt to clarify the situation I looked at a power-point presentation by Peter Cavanagh and Mario Lafortune, in which they present data which they state was collected with a Krystal force plate located in a 40m runway.

    On inspection of the data, it is clearly identical with the data you sent me. I also note that in one of your previous comments you had in fact stated that the data was collected outdoors. My experience of the benefits of running with a 10-12 Km/hr following wind suggests that air resistance can be appreciable and might provide a plausible explanation. Air resistance will exert a backward impulse that might account for the deficit in backward linear impulse indicated by the horizontal GRF data. It would also exert a torque generating head-backwards rotation while the runner is on stance. Thus, it is no surprise that our calculation indicated that the head-backwards rotation generated by gravitational torque in the first part of stance only accounts for about two thirds of the angular impulse required to reverse the head-forwards gravitational torque generated when the COG is in front of the point of support.

    I acknowledge that in the absence of accurate estimate of air-resistance, it is not possible to be sure that air-resistance fully accounts for the ‘missing’ linear and angular impulse. None the less, as the evidence currently stands, I am inclined to think that when running at constant velocity, braking during early stance together with air-resistance balances the horizontal GRF generated in late stance, and furthermore, head-back rotation generated by gravitational torque in the first part of stance, together with head-back rotation due to air resistance, balances the head-forward GRF generated by gravitational torque when the COG is in front of the point of support.

    This has been a long discussion to address what in the end is perhaps a trivial issue. Nonetheless, it has been an interesting and enjoyable debate. Unless you offer a counter argument to the potential resolution offered by air resistance, I am happy to let things rest at this point, with the conclusion that the work performed by gravitational torque makes only a slight contribution to the mechanical work done while running at constant velocity. I accept that the sensation of unbalancing might promote a rapid swing.

  14. Simon (simbil) Says:

    Canute,

    Yes it has been a long and useful discussion and I appreciate your time.

    I believe that constant pace running is just a scaled down version of accelerated running. Braking occurs in the whole gait, a substantial part of which is airborne where losses due to wind resistance happen – so to maintain pace, stance must have net propulsion. So this is not a trivial issue, it is central to all running other than running on the spot.

    To look for obvious signs of how we accelerate, we must look at heavily accelerated running and there is some data for it here http://w4.ub.uni-konstanz.de/cpa/article/viewFile/3291/3092
    When a runner accelerates heavily, they spend more time with their foot behind their COM than infront. That simple fact can lead to a number of theories for how we actually achieve propulsion in running. I would welcome your considered views on acceleration in a future blog article.

  15. canute1 Says:

    Simbil, I will indeed think a bit more about accelerated running. Insofar as a runner needs to compensate for both braking (which I believe is inevitable except when the head wind is very strong) and wind resistance, which occurs unless the following wind exceeds running speed, we do need to provide forwards impulse in the second half of stance (i.e. after the braking has ceased), and therefore we accelerate during the second half of stance.

    I still maintain that a crucial difference between running at constant (average) velocity and accelerated running is the net horizontal impulse averaged over the full gait cycle is zero for constant velocity running but has a non-zero value in the forward direction during accelerated running. I am also prepared to accept that observation of accelerated running might provide some useful lessons about the best way to achieve the required compensatory acceleration during constant velocity running, though it is necessary to be very cautious about applying conclusions drawn from one situation to a different situation. Nonetheless I will examine the data on accelerated running carefully.

    I will of course look carefully at what accelerated running might teach us about gravitational torque. I think we both agree that when running at constant velocity the net angular impulse is zero. Furthermore, the fact that we land in front of the COG means that there will be a head-back torque in early stance. At least part of the role of the head forward torque after the COG passes over the point of support is compensating for that head-backwards rotation generated in early stance. An additional part of the role is compensating for any head-back rotation induced by air-resistance. It is credible that the head-forwards angular impulse due to gravitational torque might exceed that needed to compensate for the sum of the impulses due to GT in early stance and that due to air-resistance, at least during accelerated running. So I when I examine the data acquired during accelerated running I will look closely at this excess.

  16. Simbil Says:

    Hi Canute,

    Thanks for the replies.

    You maintain that the net horizontal impulse averaged over the full gait cycle is zero for constant velocity running, but do you accept that due to unavoidable braking in the flight phase from wind resistance, stance must be net propulsive? (The exceptions are running on the spot, treadmill, strong tail wind etc.)
    If you do agree that the stance phase in constant pace running must be net propulsive, I would be interested in your view of where the acceleration comes from and why it would be different in mechanism rather than just magnitude when compared to heavier accelerated running.
    In the meantime, I need to read and digest the interesting exchanges between Brodie and Fletcher/Romanov on this subject http://www.informaworld.com/smpp/1850797252-69641213/content~content=a902510666&db=all

  17. canute1 Says:

    Simbil,
    It looks like the debate continues.

    During the past two years I have frequently stated that in the absence of air-resistance, gravitational torque does not produce a net linear propulsive effect during running at constant velocity. Under these circumstances I believe that the head-back rotation induced when the COG is behind the point of support balances the head-forward rotation generated when COG is in front of the point of support. I still believe that to be the case. Whenever I have discussed the effects of wind-resistance, I have stated that gravitational torque must compensate for the torque exerted by air-resistance during the stance phase. I still believe that to be the case. Furthermore, if the head wind is strong enough, it is not even necessary for footfall to occur in front of the COG to ensure that angular momentum is conserved. It will be advantageous to maintain a forward lean throughout stance.

    The issue of the braking effect of air-resistance acting during the airborne phase raises a different issue. If linear momentum is to be conserved this braking effect must be balanced by a net propulsive force acting during the stance phase. This will require a backwards push against the ground to generate a forward-directed ground reaction force. Because the air-resistance does not exert a rotational impulse during the airborne phase, there is no need for any additional rotational impulse during the stance phase to compensate for the effect of air-resistance during the airborne phase. Hence there is no need to propose that gravitational torque produces any additional net rotational impulse to overcome air-resistance during the airborne phase.

    However, to address your question fully we need to consider whether or not there might be transient effects that play some role. This is of course a complex question and I would want to examine some of the data from accelerated running before drawing any definite conclusions. I would anticipate that any effect of gravitational torque related to air-resistance during the airborne phase will be trivial compared with the undisputed role of gravitational torque in balancing the torque due to air-resistance during the stance phase.

    Although we now we are getting embroiled in the minutiae of running mechanics, I appreciate that the role of gravitational torque is of conceptual importance in Pose theory and therefore I am happy to continue to think about the issues. I will look into the question of the role of gravitational torque during accelerated running in more detail at some point in the near future, and when I have had the time to do so, I will do a blog posting on the issue.

  18. Simon (simbil) Says:

    Hi Canute,

    I’m glad to see you agree that stance must be net propulsive due to wind resistance in flight. I would also suggest internal braking whilst on stance further increases the requirement for propulsion just to maintain pace.

    You say that propulsion “will require a backwards push against the ground to generate a forward-directed ground reaction force”. What is the source of that backwards push? No need to hurry to an answer, I’m happy to wait until you have time to write an article.

  19. canute1 Says:

    Simbil, I had a look at the paper by Fletcher, Dunn and Romanov describing the observations of accelerated running that led them to suggest that gravitational torque plays an important role in acceleration. I appears to me that the paper contains a number of inconsistencies and peculiarities in the mathematics. I have summarized these in the calculation page (in the side panel of this blog). At least until we can sort out these peculiarities and inconsistencies in their paper, the conclusions of FD&R should be taken with a pinch of salt. I would be grateful if you would look at my summary on the calculation page and let me know what you think.

    With regard to your more recent question about the source of the backwards push against the ground needed to overcome the loss of momentum due to wind resistance in flight, I suspect it is achieved by a small increase in the power of hip extension after mid-stance.

  20. Simon (simbil) Says:

    Hi Canute,

    Thanks for looking into that.

    I’m not really qualified to answer questions on the maths and was not really that interested in the maths part of the paper – it is the data itself rather than the maths that I found interesting.

    On the calculations page you have a number of objections, which I will quote and try to answer in turn.

    “First of all, one of the main points the authors make is that the maximum horizontal acceleration of the COM occurs before the maximum horizontal GRF. However equation 1a shows that horizontal acceleration of COM is strictly proportional to horizontal GRF. Therefore, it appears that either figure 1 and the main conclusion of the paper are wrong, or equation 1a is wrong.”

    What horizontal GRF does to the runner depends on when it is applied in stance. For example, hGRF applied whilst the runner is vertical will create a torque that causes the runner to tip backwards and hence the resultant horizontal COM velocity will decrease. So it is not really the case that hGRF will lead to COM horizontal acceleration and that’s not what they mean.
    Equation 1a is correct in the sense that an actual acceleration in the x direction will cause hGRF, as every action causes an equal and opposite reaction. It is not an equation to show what happens if/when the runner adds force but an equation to show what hGRF will be due to the runners movement alone.

    ” Secondly, even if we accept that figure 1 is correct, it appears odd to conclude that gravitational torque might cause acceleration on the grounds that horizontal GRF reaches its peak value after the point of maximum acceleration of the COM while the data also show that gravitational torque reaches its maximum even later than horizontal GRF. In fact one does not even need to look at the data; gravitational torque must be greatest at the end of stance around the time when the horizontal distance between COM and point of support is at its maximum.”

    GT causes angular motion that has the greatest horizontal component at 22.5*. If the angle is larger, then the movement is dominated by downwards rather than forwards motion.
    The more important factor though in my opinion is the correction in angular momentum that must be taking place. What I intuitively see in the data is the runner pushing to rebalance there angular momentum. So hGRF is maximum because the runner is falling via GT plus pushing to resist and reverse angular momentum plus pushing to regain height. The result is a decrease in COM acceleration.
    Prior to this correction phase, the runner is falling forwards via GT and so hGRF is made up of GT and pushing to regain height only – hence hGRF is smaller but COM horizontal acceleration is larger.

    “Thirdly [maths]”

    Your last point delves into the maths and I haven’t got time for a detailed look at it right now and may not be able to add much anyway.

    Hopefully you can see what my thinking is from the discussion of point 2. It is worth noting that this is my interpretation and is not necessarily in line with the authors’ view.

  21. Peluko Says:

    Hello Canute.

    ‘…we must reverse the head-forwards-and-downwards angular momentum generated during the second part of stance when the COG is in front of the point of contact between foot and ground…’

    Due to the discussion in the Pose forum’s long thread about your site, I’ve been thinking about ‘the head-forwards-and-downwards angular momentum’, which is something which is in conflict with what I feel when I’m running. This effect of gravitational torque only can be produced if body acts like a stick, but the body has joints, and those joints make a much more complex falling. So I’ve done a little experiment to see what happens to a two-part body with a joint in between:

    This body only has a joint, but the human body has two joints affected: the hip and the knee.

    As you can see, the body collapses, but the ‘head’ doesn’t get a forward-downward torque. So you can’t compensate for the forward rotation of the body. What happens is that the ‘hip joint’ is propelled forward by the angular movement of the ‘leg’, but the ‘head’ keeps back due to inertia. If this model could run, at the next step the ‘hip joint’ would brake due to the leg contacting the ground, but the ‘head’ would continue moving forward due to inertia, until the next forward propulsion of the ‘hip joint’ produced by the collapsing body.

    For the topic of your post, this might mean that the need to counteract the GT is, at least, unknown. This could be worse than you thought or it may be completely innecesary or anything else.

    Of course, we could translate this model to the discussion about if the GT produces a forward propulsion or not… well, this is food for the Pose forums.

    Happy new year!!

  22. SPR Says:

    Hi Canute

    Below is a link to (and the text) of what Terry was referring to, I certainty didn’t discount it, and at the time remember saying something like, i’d expect science to explain Coe’s perceptions as a world class runner with good technique not discount them because they don’t fit a model.

    http://www.fetcheveryone.com/blog_other.php?id=8835

    Putting on the style

    Everybody runs in a different way, and most runners, unless they are reaching for the heights are unlikely to modify their style very much. Activities depending upon fluent movement, like ballet and gymnastics as well as running, need the faults ironed out early on, and the correct movements practised as soon as possible. At some stage it becomes too late to start correcting ingrained faults, and for older fitness runners correction becomes so difficult that there is a danger of it becoming counter productive. But this does not mean that style is not important in running, or that it is not worth examining the the running body in detail.
    In engineering, particularly on the design side, there is an old saying that goes like this: :If it looks right, it very likely is. If it looks wrong, it certainly is.” This is equally true of running style. A good style does not guarantee that you are a great runner but a bad style almost certainly guarantees that you are not. There will always be a few exceptions to this rule, but not many.

    Head

    This should be well poised on the shoulders – not too far back, as in exaggerated effort – this restricts breathing and at the same time causes the stride to shorten. Keep it still, the head must not turn. Running head down also restricts breathing, and as the head is a heavy weight, it will alter the line of carriage just to balance the body.

    Neck

    A well poised head is easier to balance, therefore the muscles have less work to do and neck strain is considerably lessened. Neck strain soon shows with the sterno-mastoid muscles standing out like tight cords. Remember neck strain does not contribute to forward propulsion.

    Shoulders

    “To every force there is an equal and opposite reaction” In high speed running one depends more on the reaction of the arms to offset the drive of the legs, and when you are running with a fast cadence, contra rotation of the shoulders to any degree is hardly possible. Whenever the fast runner is tiring, though , he starts to labour and roll the shoulders, but at slower speeds some contra-rotation is natural because the arms cannot move with as much vigour. Again, this must not be excessive. Overstriding, which is mechanically inefficient anyway, will tend to distort shoulder movement. While running do not stick out the chest by forcing back the shoulders – it creates tension, which means wasted energy.

    Arms

    A very essential part of running. Upper-arm development is important to all runners. Sprinters need good muscular development to provide the mass for the reaction to the powerful leg drive required for their event. Middle distance runners have to attack hills, which requires a good knee lift and a vigorous arm action. Long distance runners require endurance-toughened arms that do no drop with fatigue. At any cross country event, and on hilly sections of long runs, you can hear the old party-cry “use your arms” or “drive with your arms” often directed at schoolboys and attenuated ectomorphs who have neon-tubes for arms. The under trained and/or under equipped can often be seen dropping their arms from the sheer fatique of maintaining the arm postion and action.
    Steady fast running requires a vigorous action with the elbow unlocked. The angle between the upper and lower arm should be about ninety degrees, but not with the elbow locked. During the backward motion the arm should be slightly extended, and then slightly flexed to something less than ninety degrees on the return.
    The carriage of the arms should be low, for two reasons. First, it is less strain on the shoulders if the arms swing close to the body with the upper arm hanging more or less vertically, and the elbows in rather than sticking out spicily. Secondly, arms cannot be lifted into the driving position if they are already there. In the driving position the arms are best moved in a plane parallel to your direction (the sagittal plane) but in distance running, with it’s far less robust action, the arms will want to swing slightly across the body.
    A clenched, high arm action is more tiring and mechanically does not provide the same reaction as the lower arm carriage. The wrists should be loose (though without the hand flapping wildly), fingers should be relaxed, usually with a light curl and with the thumb resting lightly on the index finger. Clenched fists betray unnecessary strain.

    Hips

    The part played by the hips is not readily seen except through the general carriage of the runner, and especially in his stride length. When runners lack flexibility in the hips they often attempt to attain a good stride length by increasing the forward lean of the body. This tends to be self-defeating, because it hinders front knee lift and toe-off comes earlier. While some rotation takes place, the accentuated hip rotation cultivated by the race walker is not desirable in a runner. It often shows as an exaggerated roll as a runner reaches for stride length, especially when tiredness sets in.

    Knees

    Seen from the front the knees should not describe a circle, but should move in an arc parallel to the sagittal plane. In an all-out drive in flat-out running, or when attacking a hill, the knees should allow the leg to straighten fully in the driving phase. A good knee-lift is an economical way of preserving stride length. It increases the flinging effect of the loose-hanging lower leg so that it flicks forward easily but not too far at the end of the recovery phase. If the leg is fully straightened, at this stage it throws a stress on the knee joint as the leg snaps out straight, and the runner over-strides. Over-striding places the foot strike too far in front of the centre of gravity of the body. This has a retarding effect, tends to promote a heavy heel strike and unnecessarily jars the body.
    Knees should also allow for a high heel lift of the swinging leg – the faster one runs, the higher the heels. When the heel is tucked up close to the buttocks the leg is folded into half its length and this brings the centre of gravity of the leg closer to the pivot point, which is the hip joint. Now the leg is a much shorter lever, and the effort required to swing the leg forward to take up the supporting phase is much reduced. Further, when the heel is dropped it falls freely under gravity and being free to swing is easily flung forward without effort. Remember, good style promotes efficiency.

    Ankles

    The requirements of the ankle exemplify the basic requirements of all athletic endeavour: strength with flexibility. The ankle is at the receiving end of heavy loads with shock, tension and bending combined. The ankle must be strong to cope with uneven ground, with slipping or with any other accident, but in the context of style our main concern is with flexibility, because of the effect it has on stride length.
    When the foot hits the ground the ideal foot-strike is the one that makes contact with the ball of the foot but allows the heel to lower and kiss the ground immediately after the touchdown, when the leg is then in the supporting phase, slightly bent at the knee. Meanwhile the body is continuing to move forward so that the runner with the greatest range of movement in the ankle will be the one who can leave the foot in flat contact with the ground the longest.
    This delays toe-off to the very last moment and extends the duration of the driving phase in which the very powerful calf muscles can contract and contribute to forward propulsion rather than pushing the body upwards.
    The fault of over-striding has been emphasised. It is in the driving phase where stride length is effectively increased.

    Toe-off

    By this we mean that as the heel begins to lift it should be driven by the forceful contraction of the calf muscles, rather than just being a foot lifted off the ground. The drive should be continued right through to the toes, which should maintain driving contact until the very last moment. Place the foot flat on the ground and note the position of the ankle bone by placing it in line with the leg of a chair or table. Then still leaving this foot flat on the ground take a stride forward. See how far you can stride with the stationary heel still in contact with the ground.
    As soon as you feel the tightness in front of the ankle or in the calf you will realise that with more flexibility the stride could be longer. Now slowly raise the heel from the ground and the ankle bone will lift and move forward. Continue this movement until the ball of the foot is off the ground and only the toes are in contact. The distance the ankle has moved horizontally from the chair leg is the distance you have added to your stride. Since this also depends upon the range of movement allowed by your ankle it is easy to see the contribution to your stride that ankle flexibility provides.

    Feet

    When running, feet seldom make contact with the ground in such a way that a line drawn across the ball of the foot makes instant contact along its whole length. The side of the foot is the first point to touch, after which the foot rolls to flat contact with the ground. This is called pronation, and is only safe and allowable over a limited range. There is a considerable risk in distance running from excessive pronation and here prevention is much better than cure. Orthotics -inserts in the shoes – may be necessary.

    The Body as a Whole

    Generally, seen front on, a runner should progress in a straight line with the knees moving smoothly in a vertical plane and not seen to move in and out across the body. The heels, too, should not be seen to move inwards during the toe-off. It is, in fact, often seen in an exaggerated form with some sprinters during the start and early acceleration – and it is wasteful. Style is not merely a matter of aesthetics, it is harmonising a series of separate movements into a single economical effective motion.
    Seen from the side, the main features we would look for would be: head well poised, trunk either erect or with just the slightest forward lean, arms held easily, hands and neck relaxed, a clean knee lift, good foot plant, with the knee nicely bent on contact under the centre of gravity (or just a few inches in front) and generally a smooth flow.

  23. canute1 Says:

    Simbil,
    It looks like we will simply have to disagree. When a horizontal force is applied to a body the centre of mass will not move in the opposite direction, even when the force is applied at point that is ‘off centre’. Equation 1a simply states that force in the x direction is equal to mass times acceleration in the x direction. This is Newton’s second law of motion. A force in the x direction acting on a unconstrained body causes acceleration in the x direction, proportional to the force applied. A force in the x direction cannot cause movement of the centre of mass in the opposite direction, though, of course, if an object is fixed at some point distant from the point of application of the force, there will be an oppositely directed reaction at the point of fixture that prevents the movement of the body in the horizontal direction and generates a torque that results in rotation. However the runner is not fixed at the centre like a mill wheel.

  24. canute1 Says:

    Peluko, Thank you for that lovely model of a sagging athlete. However I think that even on my saggiest days I manage to maintain a bit more tension in my hip flexors and extensors than your model does. However, even if the hip flexors and extensors were as saggy as shown, it would still be necessary to correct the angular rotation of the leg. As you imply, this happens at the next foot fall, similarly to what I have proposed regarding correction of the rotation due to gravitational torque but because I assume that the athlete has somewhat stiffer hip flexors and extensors I use the term head-forwards rotation rather than hip forward rotation.
    Happy New Year

    • Peluko Says:

      Hi Canute. Three questions about my model:

      First, of course this is only a model, the saggiest one, but for sure that it reflects the action of gravity on the body better than the stick model. To see how saggy can our body be, think of the joint of my model as the knee instead of the hip. In this kind of movement the knee can be a lot saggiest than the hips. Now think about the combined sagginess of the hip and knee all working at the same time. Of course, we never let our body to act like this, but you could do it if you want to crash to the ground.

      Second, and the main question. The total angular momentum of a system is the sum of the angular momentum of all their particles. In my model you could see that the body has an opposite rotation to the legs, so each part with a distinct and opposite angular momentum… what’s the total angular momentum? Is head forward? Is head backward? Is null? Angular momentum depends on mass, angular velocity and radius, so this could be tricky a lot to estimate.

      Third, of course that by the law of conservation of angular momentum you can’t change total (unknown) angular momentum of the flying body, but by repositioning your limbs you can ‘translate’ angular velocity from the upper body to the lower body and viceversa. With no change in total angular momentum. So you can compensate rotation of the body by repositioning your limbs while airborne. And we have a near perfect tool for contrarresting unbalancing forces and rotations: our sense of balance.

      (Well, and I’ve just noticed that in this example the center of mass has had a forward displacement, all done with an unknown angular momentum, which might well be 0)

  25. Simon (simbil) Says:

    Canute,

    No problem, disagreement is fine once the ideas have been discussed. On complex issues like these, it usually becomes a judgement call at the end of the day, though there is some misunderstanding that I will attempt to clear up first.

    You mentioned that an objects centre of mass will not move in the opposite direction to an applied force and from that it is clear you misinterpreted my comments about acceleration and instead took them to mean movement or velocity.
    In the case of something falling forward via GT, if the base is then pushed in the direction of the fall, the acceleration of its COM will decrease. You can see this effect readily by leaning a ruler over whilst balanced on your hand and then pushing the base along in the direction of the lean until the base is under the COM. In that case, a push (the hand horizontal movement) can cause the COM to stop accelerating.
    The affect in running is a bit more subtle, but I hope you see the basic principle and at least see the possibility even if you do not think it relevant to running.

    • canute1 Says:

      Simbil, I think that while the force continues to be applied (eg to the base of a teetering pencil) the centre of mass of the pencil will undergo linear acceleration in the direction of the applied force. The effect on the angular acceleration induced by the gravitational torque is a different issue. You can cancel the GT but having done so, if you wish to keep the pencil upright and (near) stationary, you have the challenge of slowing the linear motion that resulted from the acceleration, sufficiently slowly that you do not cause the pencil to become seriously unbalanced again

      • Simon (simbil) Says:

        Canute,

        With respect, I still don’t think you are seeing the point. The top of the ruler accelerates via GT, the base is accelerated by the hand and then you have the ruler moving vertically at constant speed with no more acceleration. Gravity has done work to displace the COM forwards and the hand has done work to correct the lean and added a little COM acceleration too.

        If you look at the acceleration of the COM of the ruler in the GT phase and then the hand moving correctional phase, you would see a comparative deceleration in the hand moving phase as you are moving mainly the base of the ruler rather than its COM.
        Once the ruler is vertical and moving at constant speed, acceleration is zero. If you drew a graph of the acceleration you would get a peak as GT develops and then lessening for the hand moving phase and flat line for the constant speed (assuming modest lean angles).
        If you looked at the horizontal GRF, it would be maximal whilst the hand is moving in the correction phase even though overall horizontal acceleration is less than that by GT alone. This is because there are 2 lots of forces creating a reaction; hGRF from the moving hand and hGRF from friction plus GT. In initial acceleration there is only GT so hGRF is smaller.

        In running it is similar, GT creates initial acceleration. The correction of the angular momentum lessens the acceleration and the foot leaving the ground ends acceleration.

        When the hand is moved in the direction of a teetering pencil (or ruler as I prefer as it has a bit more mass), you say that the COM will undergo linear acceleration. That is true, but not the whole story as you must know. Inertia of the ruler causes the whole ruler to experience a reverse torque that returns the ruler to a vertical position – if you are skillful enough, or just lean back in the other direction if you overdo it. Your statement that “the centre of mass of the pencil will undergo linear acceleration in the direction of the applied force” is only 100% true when the force is applied to the pencil’s centre of mass, which is not the case for the ruler or for a runner.
        The whole point is that there is a balance between GT followed by a correction that creates acceleration, the system is net neutral in terms of angular momentum and results in linear movement horizontally.

        I’m happy to agree to disagree, but I’d be happier if you could either agree or state why you think this is not the case.

  26. canute1 Says:

    SPR, thanks for your detailed comment. You quite rightly provide a detailed discussion of the upper body. I had not mentioned the upper body in this blog posting because I was focusing on the energy-demanding actions. I believe that the actions of the upper body are largely concerned with balance and minimization of waste, whereas the actions of the lower body perform most of the essential work when running. Iin my article ‘Running: A Dance with the Devil’ I do discuss the upper body but not in the detail you have provided. So thanks very much for that.
    With regard to knees, I agree with most of what you say, but I am cautious about describing the action of the knee as a knee lift. To me, knee lift implies hip flexion and I think it is important that this does not occur too early. As you state, when running fast it is efficient to get the foot high behind the buttocks. Therefore I think that as the foot comes up, the knee must first flex while the hip remains extended. Then a powerful (but automatic) hip flexion, brings the knee forwards.
    I am interested in your description of toe off – and at this stage I am undecided about toe off and am still seeking good evidence about its role.
    Happy New Year. I wonder if we can find some way to re-invigorate the Fetch efficient running thread this year.

  27. SPR Says:

    Canute, Happy New Year to you too.

    the comment was a quote of Seb Coe from one of his books, it was what Terry referred to above when he said he didn’t have the link. Madmike had posted it on fetch as a blog.

    I think upright posture (balanced as you say) and knee lift should get most running with good form (Seb’s last para is gold IMO). The knee lift doesn’t result in the knee rising much, which is the mistake people make when thinking knee lift I believe. In fact i’m thinking it may help to think knee lift until you feel the foot come off the ground which probably results in the knee staying slightly bent while you are on the ground and not straightening fully at any point (ala Bolt). I don’t believe you need to pull the foot off the ground with the hamstring. The foot can come up towards the buttocks as long as the quad is relaxed when the foot leaves the ground. Both Coe (implicitly) and Pirie (explicitly) seem to believe the foot loses contact with the ground which is what I believe should happen (Although you can influence how long it stays in contact with the ground by allowing more pelvis rotation and/or allowing the upper leg to go back, which a knee lift focus prevents to a certain extent, or more knee bend in initial stance which I will come to later).

    The toe-off is all passive I believe and is all ME and the loading from landing IMO. Pirie talks about something similar in his book.

    Stride length, next time you sprint or run fast try running with a little more knee bend so you are running lower, the foot can stay on the ground for a longer distance and more power can be generated, so instead of your cadence increasing as you run faster, your time on the ground stays the same you just travel faster on the ground and therefore further, same applies in the air.

  28. SPR Says:

    I think the efficient running thread is getting old and is not as active as he was in his younger days ;-). I guess there was a lot of repetition, which is inevitable on a thread like that, and people got tired of it. Once everyone had become fairly set in their ideas of efficient running the arguments just became a loop cycle with no prospect of much movement on the ideas by anyone involved.

  29. canute1 Says:

    Simbil
    I agree with some aspects of your description of the correction of the lean of the teetering ruler, but do not agree entirely. While the ruler is a poor model of a runner, the leaning ruler does provide a good illustration of some of the mechanical principles that apply when running. Here is my understanding of what happens.
    Initially the ruler is leaning (let us say away from you) and experiences a gravitational torque that would cause it to rotate in a top-away-from –you-and-down direction if unchecked. To prevent this, you exert a horizontal force (via your finger) to the bottom of the ruler, causing it to accelerate. The centre of mass (COM) will also accelerate way from you, but because of inertia, the acceleration is less than that of the bottom of the ruler, so a rotation in a top-towards-you directed is initiated. In other words angular acceleration is produced in addition to the linear acceleration of the COM away from you. Although the linear acceleration COM is less than that of the bottom, it is this acceleration that is equation the force applied via the finger, divided by the mass of the ruler. This is Newton’s second law of motion, and is represented by equation 1a in the FD&R article.
    After a brief period you cease to exert a horizontal force. Unless you actively exert a braking force, the ruler now continues to move away from you at a constant velocity and also the ruler continues to rotate in a top-towards-you direction with constant angular velocity. As the ruler approaches vertical, you exert a braking force on the bottom of the ruler. This produces line deceleration such that the horizontal motion of the ruler is arrested. Similarly, as the base decelerates faster than the COM, the rotation is canceled. If you have judged it correctly, the total amount of rotation (including that during the period of constant angular velocity between the push away and the pull back towards you is enough to correct the initial lean and the you achieve a pseudo-equilibrium with the ruler vertical and stationary. If you did not judge it correctly, you will need to continue the process a few more times until you achieve pseudo-equilibrium.

    So what conclusions follow from this description:
    1) the initial lean triggered the events but gravity did no net work – the work was done by the arm muscles that push and pull the finger. (I appreciate that were not claiming that gravity did any work, though some of the loose descriptions of Pose imply that gravity does work – in fact FD&R state that gravity does angular work – I am not sure what they mean by this, but I am confident that gravity provides no net energy to drive the movements.)
    2) the ruler undergoes linear acceleration, initially away from you, and then towards you. The amount of acceleration of the COM at any instant is the force at that instant divided by mass (Newton’s second law). While the COM accelerates less rapidly than the base of the ruler, nonetheless the acceleration of the COM is proportional to the applied horizontal force. The occurrence of rotation does not destroy the synchronization of the linear acceleration and the application of the horizontal force.
    3) angular acceleration is required to get the ruler moving towards vertical, but this angular acceleration must be reversed to prevent the ruler falling flat.
    4) The net horizontal impulse applied to the base of the ruler is zero.
    Although this rigid ruler is a poor model of a runner, similar conclusions apply to a runner (in the absence of air-resistance). The major differences from constant pace running is that the forward and back accelerations described above are superimposed on a constant underlying forward motion, and in addition, at the end of stance the runner becomes airborne as a result of vertical forces, and while airborne, re-positions the legs. This allows a correction of the lean of late stance by an opposite lean after footfall. In the absence of air-resistance, I believe that there is symmetry of both the horizontal and angular accelerations.

  30. Simbil Says:

    Hi Canute,

    Thanks for your thoughtful answer to the ruler hypothesis.
    We are doing slightly different experiments and the outcome is a bit different I think.

    When I do the experiment, the ruler leans away from me, I then push the base away from me so the ruler is vertical (not so far that it leans towards me, just enough so it becomes vertical). If anything, I need to keep my hand moving at a constant speed away from me to maintain the vertical ruler. Stopping my hand causes the ruler to lean away from me again. I think what you are doing is leaning the ruler and then moving the base beyond the COM so that the ruler leans towards you, you then need to pull your hand back to correct that lean.

    The way I do it, the ruler starts vertical and close to me and finishes vertical and further away from me i.e. the net movement is horizontally away from me.

    So gravity does horizontal work initially. The push of the base back under the COM acts against gravity, so overall gravity’s effect is neutral.

    The important part is that gravity did horizontal work (or angular work to be correct) and then the hand did work to correct the angle and return the ruler to vertical. Gravity did no net work, but gravity was responsible for the largest portion of horizontal acceleration of the COM. Nobody is saying gravity gives a free ride, but it can give you a ride you pay for, and in paying for it you continue to add to forwards motion rather than act against forward motion.

    So in answer to your conclusions:

    1) Yes gravity does no net work – the hand needs to work against gravity when it corrects the lean angle. That is not the same as saying that gravity performed no work though – gravity accelerated the ruler initially. Gravity then made the hand do work to return the ruler to vertical.

    2) We did the experiment differently so that does not apply to mine – there is no linear acceleration towards you.

    3) No, the correction of the angular motion should leave the ruler vertical if you do the experiment as I intended. It may not have zero velocity, but it should be vertical and with zero acceleration.

    4) Again, not if you do the experiment as I intended. The hand initially resists the leaning ruler (the lean produces a force on the hand that pushes it towards you as the ruler falls away from you) and so the hand has to be braced to resist that force. More force is then added to the hand to push the base of the ruler away and correct the lean so the ruler stands vertical again.

    It would be good if you try the experiment again with the aim of allowing a lean to develop and then incrementally accelerating the hand just enough so that the lean ends. At no point should the lean be towards you. Using something bigger and heavier like a broom handle makes it easier to do. The aim of the experiment is to achieve movement of the object by lean and correction of lean alone and then we can discuss the forces.

    • canute1 Says:

      Simbil
      We might be discussing different models so we need to clarify this. You have provided a model of accelerated running, insofar as the final horizontal velocity of the ruler is different from its initial velocity whereas I was describing a situation in which the final horizontal velocity is equal to the initial horizontal velocity. (The ruler might have an underlying steady velocity relative to the earth. For example you might be traveling on a bus at the time. This detail is trivial but might make the ruler model a bit more similar to constant velocity running.)

      In both of our models, the base of the ruler, and its COM, initially accelerates away from you under the influence of the horizontal force. After the horizontal force ceases, it will continue to move away at constant velocity forever in accord with Newton’s first law of motion, unless a force is applied in the opposite direction. The reason I argue that gravitational torque must be cancelled by an opposite gravitational torque in constant velocity running is that you cannot cancel gravitational torque by applying a horizontal force to the base of the ruler (in the absence of wind resistance) without producing a net increase in horizontal velocity of the ruler. Your model does not apply to running at constant speed in the absence of air- resistance. As we already agree, in the presence of air-resistance, gravitational torque does play an appreciable role in running – but even in this circumstance, it does no net work.

      There was one minor feature I left out of the description of my model – for the period of time that the ruler is leaning away it will accumulate some top-away-and-down angular momentum due to gravitational torque and therefore, it is necessary to overshoot the vertical position somewhat so that gravitational torque acts in the other direction to reverse the initial effect of gravitational torque. Gravitation does a small amount of angular work insofar as provides energy to rotate one way at first and the other way later. This is similar to running, where the head-forward GT must be cancelled by a head-back GT, in the absence of air-resistance.

      With regard to the question of the effect of air-resistance during the airborne phase, the source of the work that overcomes this is a horizontal ground reaction force, though in the presence of air-resistance you do not have to land as far in front of the COM to cancel gravitational torque. The symmetry I have described does not apply in the presence of air-resistance, but I do not think this has ever been a matter of dispute.

  31. Simon (simbil) Says:

    Hi Canute,

    As I see it, there are 2 main points to the discussion. Where does acceleration come from – so lets look at accelerated running / experiments, and how is any rotation created by gravity corrected.

    I am performing the experiment as if it were accelerated running. The ruler starts at rest and finishes moving.
    You make the point that constant pace running is different but i think that should be the discussion once we reach agreement on accelerated running.

    We know from the recent FD&R study that the accelerated runner spends much more time with a forwards lean than a backwards lean and that the midpoint of stance sees a lean as much as 15* forwards in the direction of travel. Under these conditions your landing ahead to correct the rotation theory does not seem to apply as there will be net gravitational torque acting forwards and downwards whilst on stance. I would appreciate it if you conducted the ruler experiment under these conditions.

    This statement you made is interesting, “In both of our models, the base of the ruler, and its COM, initially accelerates away from you under the influence of the horizontal force.”
    That is of course true but avoids mentioning gravity which is undoubtedly the motive force at that point. Gravity creates a ground reaction which manifests as horizontal force at the support point which is additionally braced by friction. That is a reactive force as is the friction that holds it, the motive force at that point is gravity.

  32. canute1 Says:

    Simbil,
    It is no surprise that a runner doesn’t need to land as far in front of the centre of mass (COM) during accelerated running. The ‘teetering ruler’ model illustrates clearly that a horizontal push against the bottom of the ruler can reverse the effect of gravitational torque and one would expect the same thing during accelerated running when the forward horizontal ground reaction force (GRF) must exceed backward GRF in order for acceleration to occur.

    Your statement that gravitational torque is ‘undoubtedly’ the motive force during the initial period of acceleration following application of the horizontal force in the teetering ruler model is unlikely to be true. If the teeter it to be corrected, the torque due to the horizontal push must exceed the torque due to gravitational torque. If a ruler of mass m starts inclined at an angle theta relative to vertical, and a horizontal force sufficient to correct the lean is applied, the horizontal force must exceed m*g*sin(theta). (If not the lean would continue to increase). According to Newton’s second law, the horizontal acceleration due to a horizontal force greater than m*g*sin(theta) must be greater than g*sin(theta). However, the forward and down acceleration of the COM due to gravity is g*sin(theta) Thus provided the force is adequate to reverse the lean of the ruler, the horizontal acceleration of the COM due to the applied horizontal force exceeds the forwards and downwards acceleration due to gravitational torque.

    In summary, the ruler models (either with net gain of velocity or without) demonstrates that horizontal force can correct a lean, but in so doing the horizontal force produces forward acceleration of the ruler. The model in which final velocity of the ruler is the same as the same as initial velocity illustrates that the forward impulse due to forward horizontal force must be balanced by an equal backward impulse due to backward horizontal force during constant velocity running in the absence of air-resistance. The head-forward angular acceleration generated by the forward horizontal force will be balanced by head-back angular momentum generated by the backward horizontal force. Thus the torque due to gravity after mid-stance must be balanced by the opposite gravitational torque between footfall and mid-stance. At most gravitational torque might be regarded as a trigger for muscle action.

    In the presence of air-resistance, the forward horizontal GRF will exceed the backward GRF in order to overcome the resistance, so the runner no longer needs to land as far in front of the COM

  33. Simon (simbil) Says:

    Hi Canute,

    Thanks again for the replies.

    From your second paragraph, my comments about gravity being motive were purely in the falling phase of the ruler, not the whole cycle of fall and correction. I have said that overall gravity is neutral in the experiment, but we were talking specifically about the falling phase of the experiment before the correction via the horizontal push.
    Let me put it this way, when a tree is felled, what is the motive force that displaces its COM horizontally and makes it lie on the ground?
    Your wording that I quoted in my last post carefully avoided acknowledging gravity when it is undoubtedly the motive force in a ruler falling over. Clearly the correction of angular momentum is impeded by the same force which thus makes gravity neutral overall. Perhaps we just misunderstood each other there.

    I am very pleased with your first paragraph as that is exactly what the teetering ruler experiment is designed to show; angular momentum from gravitational torque and then the correction of the angular momentum by a horizontal push to produce linear movement.
    I wonder if you will acknowledge that gravity did work in the first phase (to produce movement) and hindered work in the second phase to be overall neutral, but importantly the movement it created was not reversed.

    Now on to your summary. You do not acknowledge gravity and instead look only at horizontal GRF. That is fine, though rather side steps the issue at hand as to what gives rise to the horizontal GRF in the first place.
    A portion of horizontal GRF is certainly created by gravitational torque – that is simply a function of the support point being behind the COM of the ruler and the omnipresence of gravity.
    An additional amount of horizontal GRF will arise when the base of the ruler is pushed to correct its lean.
    The first phase of the experiment with the ruler sees a lean develop which creates a horizontal GRF on the unyielding supporting finger. Gravity does work to increase the lean supported by the finger and friction.
    The second phase of the experiment increase the horizontal GRF of the ruler and reverses the lean and also adds some more linear acceleration into the system. Gravity impedes the acceleration in this phase.
    Overall, gravity is neutral BUT the maximum COM acceleration occurs due to gravity in the falling phase. A lesser acceleration occurs in the correctional phase, although the horizontal GRF is greater – that is because of the impedance of gravity in this phase.
    I am pleased that you acknowledge that correcting the lean helps with propulsion, but still wonder if you see that the effects of gravity dominate the horizontal acceleration of the COM?

    This part of your summary deserves particular attention:

    “The head-forward angular acceleration generated by the forward horizontal force will be balanced by head-back angular momentum generated by the backward horizontal force.”

    There is no need for a backward horizontal force as you already indicated in your first paragraph.

    “Thus the torque due to gravity after mid-stance must be balanced by the opposite gravitational torque between footfall and mid-stance.”

    Gravitational torque is not symmetric in accelerated running so it is hard to see how what you state here can possibly be happening. To put it simply, your model of landing ahead to correct angular momentum does not work for accelerated running.

    “At most gravitational torque might be regarded as a trigger for muscle action.”

    I understand that is your opinion but that is really a semantic point so I’ll let it go. Suffice to say I don’t think it tells the whole story 🙂

  34. canute1 Says:

    Simbil
    My comments about the forward linear acceleration due to the horizontal push exceeding the forward and downward acceleration due to gravitational torque refer to the early phase of the horizontal push in the teetering ruler experiment. I think you might underestimate the implications of Newton’s Second law and consequently underestimate the importance of the linear acceleration produced by the horizontal force. However, in the context of our discussion, we agree on the most important aspect of accelerated running: namely that the rotation generated by the horizontal component of GRF can compensate for a substantial part of the rotation due to gravitational torque. There is a net forward GRF and the runner will spend less time with the point of support ahead of the COM than behind it. As I do not regard the initial acceleration phase of running is of much importance for the distance runner, I am quite happy to agree to differ on the minor details.

    With regard to constant velocity running in the absence of air-resistance, I consider that the ruler analogy reinforces the strength of my claim that the runner must land in front of the COM if gravitational torque is to be reversed, simply because the forward impulse delivered by forward directed horizontal GRF must be balanced by a backward impulse delivered by backward directed GRF. If this were not so, the runner would continue to accelerate. Therefore, the head forward rotational effect of GT in late stance must be compensated by the head backward rotational effect of GT when the point of support is ahead of the COM. I think you might still disagree with this

    In the presence of air-resistance, the backward directed air-resistance provides both head-back rotational impulse (during stance) which will at least partially reverses the torque due to GRF. Furthermore the air resistance provides backward directed linear impulse due to the pressure it exerts on the body throughout the gait cycle, and hence, if constant velocity is to be maintained, forward GRF must exceed backward GRF. Therefore the runner spends a greater proportion of the time on stance with the COM in front of the point of support. If the head wind is strong enough the runner might even land with point of support behind the COM. As far as I am aware, we also agree that the presence of air resistance diminishes the proportion of time that the runner spends on stance with point of support in front of the COM.

    So I think we have only one major disagreement and that is about my claim that the runner must land in front of the COM when running at constant velocity in the absence of air-resistance

  35. Simon (simbil) Says:

    Hi Canute,

    Our major disagreement is how gravity works in running, not constant pace running in the absence of wind resistance – what you say there is fine.

    Your third paragraph summarises your view of constant pace running with wind resistance and whilst I agree with much of it, it does not tell the whole story.
    The way you present balance of forward and rearward GRF does not take into account that the GRFs will produce angular as well as linear acceleration. If the running was completely symmetrical (as it would be in the absence of wind resistance) then that would not matter. But as the running is asymmetric with a longer period with foot behind the COM than infront, your summary becomes inaccurate.
    This comes back to the point that GT creates a net forward and downwards acceleration in accelerated running. Your model of landing ahead does not apply so it seems reasonable to conclude that angular momentum is corrected by a horizontal GRF as you mention in your first paragraph.
    That correction is not obliged to create any linear acceleration of the COM as it’s purpose is to create a rotation around the COM. Practically, there may be some linear COM acceleration as a by-product of the process. Empirically, we have seen that maximum horizontal GRF occurs after maximum COM horizontal acceleration – a GRF paradox. The falling and correction model agrees with that observation whilst your simple GRF model fails to explain it. That is the essence of our disagreement, your simple model does not acknowledge GT properly and hence does not account for the GRF paradox.

  36. RICK Says:

    Guys here are Coach Al Lyman, CSCS commandments for faster injury free running:
    • Begin to pull the leg back from the HIP (a PAWBACK), with a
    fairly constant knee angle, BEFORE foot-strike.
    • After follow-through, drive the knee forward powerfully, allowing
    the foot to lag well behind during leg-recovery. Use momentum,
    not muscular contractions, to raise the heel.
    • Develop your propulsion from the CORE & HIPS. Push off should
    be passive and relaxed. Incorporate the “swagger” of a rotating
    hip motion…
    • Minimize contact time between the feet and the ground. Think
    of “flicking” the ground as your feet/legs move backward before
    foot strike…
    • At any running speed, maintain approximately the same high
    turnover rate (cadence) – that is, about 180 steps per minute,
    or 90 stride “cycles.”
    • Keep the heel un-weighted throughout footstrike, landing from
    mid-foot to fore-foot. *avoid the tendency to over-exaggerate
    this by landing on the toes!
    See the full link here;
    http://teampursuitfitness.homestead.com/articles/running_better_a_guide.pdf

  37. RICK Says:

    And check this out
    http://teampursuitfitness.homestead.com/articles/Improving_Functional_Strength_and_Muscle_Elasticity_By_Coach_Al_Lyman.pdf

  38. canute1 Says:

    Rick. Thanks for this.
    I agree with many of the points made by Al Lyman, though I think his statement ‘Push off should be passive and relaxed’ needs some comment. I agree that there should be no conscious effort to push at push off. (One of the good things about Pose is that it discourages an emphasis on a conscious push though it does advocate a conscious pull). However when one examine force plate data it is clear that a large vertical force is exerted for much of the stance period. In the second half of stance, a substantial portion of this push probably comes from elastic recoil. The practical implication is that when running, one should not consciously push, as advocated by Al Lyman. However in preparing yourself for running fast you need to ensure that you have adequate leg muscle strength to sustain the non-conscious push. I think it is likely that a major factor in loss of stride length with age is loss of the strength necessary to sustain the push

    I think that his recommendation to keep the heel unweighted throughout foot strike also need comment. When the heel does not touch the ground at all during foot-strike, the shearing forces on the metatarsals and the tension on the Achilles are large. This presents little concern for a sprinter, but for a long distance runner it creates risk of either Achilles strain or metatarsal stress fracture.

  39. canute1 Says:

    Simbil. Your statement that the way I ‘present balance of forward and rearward GRF does not take into account that the GRFs will produce angular as well as linear acceleration.’ raises the possibility that you might not understand the law of conservation of momentum. That law demands that when running at constant velocity, the impulse due to forward force (forward GRF) must balance the impulse due to backward force (backward GRF + wind resistance).

    The angular momentum generated by the horizontal force might be thought of as a byproduct of the fact that when a horizontal force is applied ‘off centre,’ inertia results in a differential rate of horizontal acceleration of different parts of the object, and hence the body rotates. However the amount of horizontal linear acceleration of the COM is simply the horizontal force applied divided by the mass – according the Newton’s second law. If the body is to suffer no net gain in either linear momentum or angular momentum, both the linear acceleration and the angular acceleration due to the forward force must be balanced by the linear acceleration and the angular acceleration produced by the backward force. In other words, both linear and angular momentum must be conserved.

  40. canute1 Says:

    Simbil, It might be that you error arises from confusing the law of conservation of momentum with the law of conservation of energy. When a horizontal force is applied ‘off centre’ to achieve a given amount of linear acceleration of the COM, more work must be done than if the same force were applied directly to the COM because the ‘off centre’ point at which the force is applied moves through a greater distance than the COM. The work done is the product of force by distance, whereas the gain in momentum is the product of force by time. In the case of the accelerating teetering ruler, the work done by the off-centre horizontal force produces both linear kinetic energy due to motion of the COM and rotational kinetic energy. The work done by the horizontal force contributes to both linear kinetic energy and rotational kinetic energy.

    Linear momentum and angular momentum must be separately conserved; whereas work done by a horizontal force can produce both linear kinetic energy and rotational energy provided total energy is conserved.

  41. Simon (simbil) Says:

    Hi Canute,

    Thanks for the posts, but I do not think I am confused about these principles 😉

    I agree entirely that for constant pace running with wind resistance that the *horizontal linear* impulse due to forward force (forward GRF) must balance the *horizontal linear* impulse due to backward force (backward GRF + wind resistance).

    But, the problem is that the GRF is applied off centre (in the ruler experiment and in running).
    You state that this is not important and that the linear momentum must be effected in line with Newton’s second law and this is an oversight on your part: “However the amount of horizontal linear acceleration of the COM is simply the horizontal force applied divided by the mass – according the Newton’s second law.”
    Now, Newton’s second law only deals with linear acceleration as expressed by F=ma and so applies when the object can be assumed to be a particle or that the force is acting on the object’s COM directly.
    Those assumption are way off for our ruler and runner.
    In the runner and the ruler, the force is acting on the end of a lever, not on the COM directly. That means that depending on the angle of application, there will be a split between linear and angular momentum. The more upright the runner is, the larger the proportion of the angular momentum.
    There is little point trying to progress this discussion until you have re-examined your assumptions here.

    Finally, as an example of applying a force off centre in the real world. Imagine the case where you have a bicycle lying on its back with vertical wheels so its front wheel can spin freely.
    Now add a horizontal push to the wheel in line with the hub – if you get it right it should create a completely linear impulse that does not spin the wheel but tries to push the whole bike along.
    Secondly, apply the same force midway between the hub and the top of the wheel – a combination of linear impulse and rotational impulse are created and the wheel will spin slowly.
    Lastly, apply the same force as close to the top of the wheel as you can. The wheel experiences nearly complete rotational impulse and spins more quickly. There is little linear impulse to the bike.

    That experiment shows me that you seem not to have applied Newton’s laws properly to the runner/ruler, do you agree?

  42. canute1 Says:

    Simbil
    I am afraid I disagree with your statement: ‘Now, Newton’s second law only deals with linear acceleration as expressed by F=ma and so applies when the object can be assumed to be a particle or that the force is acting on the object’s COM directly.’

    I have not read Newton’s Principia in the original Latin, but when I last formally studied Newtonian mechanics (about 45 years ago – I must admit) I am quite sure that Newton’s second law was applicable to forces applied at any point to objects of various shapes and sizes. One recent illustration of the application of Newton’s second law to a the situation in which a force is applied off-centre to the human body is equation 1a in the article by Fletcher, Dunn and Romanov about accelerated running. (In case you are unfamiliar with the notation of calculus, dv/dt represents acceleration). I accept that is not a very reliable source because that article contains several mathematical peculiarities, but I quote it here because you regard that article as credible.

    Before we can draw any conclusion from your bicycle wheel analogy, you would need to carry out the experiment with precise measurement of the forces and movements involved. Be aware that the application of the force tangentially to the outer rim is likely to entail only a brief contact and therefore the transfer of momentum (product of force by time) will be relatively small compared with a more sustained push of similar force against the wheel hub.

    If we cannot agree on the issue of whether or not Newton’s second law applies to forces applied ‘off centre’ to a body we may have leave this line of argument – but in any case I am not really sure that this argument is the most direct way of tackling the question of whether a fall of the body under the influence of gravity after the COM has passed in front of the point of support, makes a substantial contribution to propulsion in running. Would you be prepared to accept that it does not make an appreciable contribution if it can be demonstrated that there is no appreciable fall of the COM once the COM is in front of the point of support ?

    I am not sure whether or not I can demonstrate this convincingly, but in principle it would be possible, at least for a mid-foot runner, using the Cavanagh and LaFortune force plate data. Visual inspection of that data suggests only a small amount of fall after the point of balance. I would be happy to attempt this computation, if you would be interested in the result. Following Romanov, I suggest we call the point where the COM is over support the ‘point of balance’. For the calculation I would need to apply the laws of Newtonian mechanics to vertical forces, and you would of course be free to reject my application of these laws. However it might be that you will find the application of Newton’s laws to vertical forces a little more intuitively acceptable.

  43. Simon (simbil) Says:

    Hi Canute,

    Common sense says it cannot be the way you indicate. Imagine applying a push to an Astronaut – are you seriously saying that the resultant linear acceleration of the Astronaut’s COM would be the same if you pushed his hip compared to pushing his head? To me it is clear from a look at Newton’s second law and intuitively from seeing how forces work in practice that you are mis-applying it in this case.

    Newton’s seconds law is mentioned here: http://en.wikipedia.org/wiki/Newton%27s_laws_of_motion#The_Three_Laws_Explained
    Note that it talks about a particle and linear acceleration. It does not encompass angular momentum created when a force is applied indirectly to an object’s COM when expressed simply as F=ma without incluing the inertia of the COM. I suspect you may not take my word for this so I would encourage you to read up on it and come to your own conclusion and sanity check your conclusion against readily observable phenomena or your experience of how things work in practice.

    You mentioned equation 1a. Briefly, if you want to apply second law mathematics to a running scenario, you need to take inertia of the COM into account as well as the applied forces to predict the subsequent complex acceleration of the object. You can only ignore rotational effects when the force is applied to the COM i.e. you can only use simple F=ma for a force applied directly on the COM. When the force is applied off centre, some of the force makes linear momentum and some makes angular momentum. Conservation principles clearly indicate that you cannot create more momentum on the object by pushing off centre compared to pushing on centre. Therefore the amount of linear acceleration created will clearly decrease the further away from the COM that the force is applied and the amount of angular acceleration will increase. The sum of the angular and linear momentum created will be proportional to the force applied, as per Newton’s seconds law. Or simply put, you are ignoring angular momentum when you apply Newton’s seconds law.

    Thanks for your offer to look at it from another angle, but I think using the Cavanagh and LaFortune force plate data will show very little fall as it is just constant pace running so the amount of horizontal acceleration created by the fall plus the further contribution from the correction of the fall, would be small in line with air resistance. Furthermore, we would need to agree on what angle the runner has at midstance to make a meaningful calculation, and that may just be a guess as the data does not contain angular measurement of COM to support.

  44. canute1 Says:

    Simbil, I am afraid we may have to agree to differ about the applicability of Newton’s second law. I believe common sense is only useful when guided by good intuition. Ultimately one has to do the experiment, though I think that mathematical application of Newton’s laws can be a useful guide to define the hypothesis to be tested.

    So I suggest that for the time being lets leave the discussion there. I suggest you look for evidence about what happens to the COM in late stance.
    I also think that it is constant pace running that matters most to a distance runner and I do not think we have any serious disagreement about accelerated running other than our difference about the role of linear acceleration. We both agree that the at foot fall the COM does not have to be far in front of the point of support and might even in some circumstances (eg strong head wind) actually be behind the point of support.

    I will do another blog posting on running mechanics in the fairly near future and would be delighted to receive your comments. However, I will probably devote my next posting to progress with my training plan and the issues of developing adequate leg muscle power and coordination.

  45. jonp Says:

    Canute,
    Really serious question. If you make your mind up on something, and then have evidence presented that it may not be correct, would you ever considering changing your mind? It seems to me that you are incredibly stubborn at acknowledging that you may not have been correct on something.

    I could point towards your discussions with simbil. But this time when you say:

    “think that his recommendation to keep the heel unweighted throughout foot strike also need comment. When the heel does not touch the ground at all during foot-strike, the shearing forces on the metatarsals and the tension on the Achilles are large. This presents little concern for a sprinter, but for a long distance runner it creates risk of either Achilles strain or metatarsal stress fracture.”

    I find it incredible that you have not listened to one word that anyone has discussed with you on this topic. Your ears are open but you are not listening (refuse to)! For the record I have run 2 and a half years without any injury or niggle, I never feel my heel bare weight. Why? Because I keep my ankle relaxed, I land under my body and keep a forward lean, that means that momentum will be taking bodyweight forward of the foot very quickly, unless I force the heel down (really bad). Why is it that you portray yourself as someone of science and yet you do not act in anyway like a scientist.

    I’m sorry if it doesn’t sound curtious, but it is in fact incredibly rude to not even acknowledge all those that have put effort in and give you real life experience of runners (of themselves and runners who they teach) who are not getting these problems running many miles (and please for god do not point me at the same 4 year old study) Instead you just repeat a mantra of the same things without any fair comment on the evidence against what you are saying.

    To repeat again: It is NOT about making sure the heel lands or does not land. it IS about keeping the ankle relaxed and landing under the body. You do NOT make sure the heel touches just in the same way that you do NOT make sure it stays off the ground. You just keep the ankle relaxed and let your muscles react to bodyweight the way they have evolved to.

    So please stop with all these mantras and start becoming someone who is looking for truth instead of trying to fit science to your on views no matter what it takes. That is not science, it is just continued self postulation.

    Angry from Manchester 🙂

  46. canute1 Says:

    Jon, I am willing to change an opinion when the evidence shows that I should. With regard to the question of the foot touching the ground, the recent discussion on the PoseTech site included a post for a Pose coach pointing out that the Pose Method of Running states that the heel might touch the ground, (in accord with my current opinion). With regard to the discussion with Simbil, quite simply, Simbil has presented no evidence apart from an appeal to common sense to justify his interpretation of Newton’s Second Law of Motion. The wikpedia site to which he refers does not support his interpretation. On the hand, even Fletcher, Dun and Romano agree with my interpretation (quite simply, equation 1a is the mathematical expression of what I am saying.

    Just as I have encouraged Simbil to look for evidence of what happens to the COM after the COM passes over the point of support, I would encourage you to do the same, as I think that is potentially key evidence regarding the proposal that a fall contributes to propulsion during running.

    Jeremy, no video yet, sorry

  47. jonp Says:

    Canute,
    It is interesting that you devote 2/3 of your response to me talking about your discussion with simbil, when my post was about your comment (yet again) on making sure that the foot bares weight. That speaks volumes about your own confidence on that.

    Nevertheless, my problem with the way you keep talking about landing is this; you maintain that the heel MUST bare weight. That is not the Pose position. The Pose Coach made it clear if MIGHT touch the ground. That is a world apart from you state which is MUST.

    Like I said above. The heel might bare weight on uneven ground or infact if the runner lands a little too much in front of their body. But if you land under your body 99% of the time your heel will never bare weight and it most definitely will not have the consequences you continue to spout. You talk with a commandment that if the heel does not touch then a distance runner will get injured – that is rubbish, and that is my problem with your comments.

    You are either not understanding what I am saying or are twisting the words to try and get approval that your opinion is correct.

    Can you understand the difference between MIGHT and MUST as I described above.

  48. Simon (simbil) Says:

    Canute,

    Looks like we have reached an impasse which is a shame. I enjoy reading your blog and discussing these issues with you as you generally show a high level of reason and logical thought. I’ve learnt a few things along the way in this latest discussion and have been happy to admit my occasional mistakes in order to continue a reasonable discussion.

    Perhaps you could answer one simple question so that I am sure I understand you completely on this point of your application of Newton’s second law:

    A 100m rod in deep space, mass 10kg, not under any acceleration.
    Scenario 1, 100N force applied perpendicularly to its COM for 1 second. Scenario 2, 100N force applied perpendicularly to one of its ends for 1 second.
    Is the resultant motion of the rod exactly the same in both cases?

    If you think the resultant motion would be the same, then there is indeed no point in trying to continue this discussion and we will have to agree to differ.
    If instead you agree that the 2 scenarios will produce different motion, maybe you will better understand what my comments about GRF and GT have been trying to get at.

  49. canute1 Says:

    Jon, I do not state that the heel must bear weight under all circumstances. However allowing the heel to bear some weight is likely to reduce strain on the Achilles and the shear stress on the metatarsals and I consider that is a sensible thing to do when running long distances (eg marathon). I acknowledge this issue remains controversial. You are no doubt aware of the discussion presented by Ross Tucker on Science of Sport http://www.sportsscientists.com/search?q=heel+striking. Perhaps the most important point he makes is that there is little convincing scientific evidence regarding the merits of heel striking (which is actually entails a more extreme form of weighting the heel than I recommend) and forefoot striking. He does nonetheless report the observation that 75% of the elite runners in the 2004 Sapporro International Half Marathon were heel strikers. It is simply not true to state that I ignore evidence.

  50. jonp Says:

    Canute,
    Of course I read that.

    I found it funny how he said it doesn’t matter which part of the foot you land on as long as you land under your body. Found it funny for two reasons:

    1) He spents half his blog banging on about lack of scientific evidence, then makes a STATEMENT that if it most important you land under the body without ANY scientific backing of that claim LOL makes him look a fool even if I actually agree with it!

    2) He completes misses the fact that if you land under your body you will not land on your heel – it’s impossible. So the the whole point of his blog is totally negated.

    Quality article – a laughed all night over that one.

  51. jonp Says:

    Is there any way to edit comments? I apologise for all the spelling and grammar mistakes in my previous comment.

  52. RICK Says:

    Canute, coach Al Lyman says to keep the heel unweighted, he does not say the heel can not touch down, I think what he is saying is to keep your weight over your fore to mid foot, which if you land close to your c o e is the natural place for your weight to be!
    I’ve run ball of the foot for 17 years without any tendon problems yet my brother has chronic tendon problems and he has always been a heel striker!

  53. RICK Says:

    OOOPS!! C.O.G not C.O.E, I’ve not landed at church for a long time :]

  54. jonp Says:

    Rick that is EXACTLY the point. You just need to land with your bodyweight over your ball of foot. Whatever happens after that should not be something you do consciously. In fact I believe Canute’s argument that the heel should touch down is even more injurious because it put a focus on trying to control your foot position on the ground (control is bad because it causes tension). Your point is exactly right, it’s about where your bodyweight is in relation to your foot. The focus is not really on the actually landing the foot in a set position at all. This is what is continually mentioned to Canute, but he never acknowledges it one bit after the discussions that have been had. That is why I got angry that he said the same thing he has been saying for a number of years and to me that is rude to the people who put the time in to clarify the point (Pose Method in this case). It is misinformation at best that is being presented.

  55. canute1 Says:

    Simbil,
    Thank you for specifying that particlar example of application of force of 100N for 1 sec either to the midpoint or the end of a 10Kg rod of length 100m in space.

    The resultant motion is not the same, because when the force is applied to the end of the rod, rotation occurs in addition to linear acceleration. Assuming Newton’s second law applies in both situations, the increased in linear momentum is the same, but the amount of work that must be done is greater when the force is applied to the end because the end moves further in this situation. Here are the calculations:

    In both cases the increase in linear momentum will be given by 100newton * 1 sec = 100 Kg.m/s (applying the formula for change in momentum based on Newtons’s second law, namely increase in momentum= force*time)

    When the force is applied to the midpoint, the distance that the midpoint moves during the 1 sec is given by s=0.5*a*t^2 = 0.5*(F/m)*t^2 = 0.5*(100/10)*1 = 5 m. Therefore the work done during the application of the force is 500 Kg.m^2/s^2.

    However when the force is applied to the end of the rod there will also be an increase in angular momentum because the end of the rod will move faster than the middle of the rod due to the inertia of the rod. When the force is applied for 1 sec at the end of the rod, the tangential acceleration relative to the axis of rotation (through the mid-point) is given by force*(distance from axis of rotation)/(moment of inertia).
    The moment of inertia for a long rod rotating around its midpoint is mass*length^2/12 (assuming cross sectional radius is negligible).
    Therefore, tangential acceleration is 100*50/(10*10000/12) =0.6 m/sec^2.

    Thus the tangential distance traveled by the end of the rod (relative to the COM) during 1 sec is 0.5*0.6*1= 0.3 m. The tangential path is almost exactly parallel to the direction of motion of the COM so the total distance that the end of the rod moves is almost exactly 5.3 m. If the distance through which the force is applied is 5.3 m. the work done during the application of the force to the end of the rod is 100*5.3 = 530 Kg.m^2/s^2.

    Thus, a greater amount of work is done when the force is applied to the end of the rod in order to provide the energy for the rotation. However the increase in linear velocity of the COM is identical in both situations.

    We are in complete agreement that the off-centre force will produce rotation. But these calculations are consistent with my previous statements that the increase in linear momentum is the same in both situations.

    I see the point of your statements about GRF and GT but as I have stated several times, I think you seriously under-estimate the linear acceleration.

  56. canute1 Says:

    Jon,
    You might have laughed at Ross Tucker’s article, but I hope you did not laugh at the evidence he presented from the Sapporro half marathon.
    Ross Tucker points out that there is in fact very little scientific evidence to provide a definitive answer to this debate. There is anecdotal evidence to support both sides of the argument. There are Pose runners who have suffered metatarsal fracture and there are heel strikers who have suffered Achilles tendonitis.
    Therefore I am not being disprespectful of you or anyone else in adopting my own opinion. In fact in my comment on Al Lyman’s recommnedations, I did not state that the heel must bear weight and I did not say Al Lyman was wrong. I merely pointed out that I believe the heel should touch the ground. My opinion is based on biomechanical principles, but I am quite happy to acknowledge that the issue of how much weight should be borne on the heel is quite controversial.

    The major issue that I was making in the PoseTech discussion is that the figures in Pose Method of Running are misleading. I believe that what Al Lyman, Rick, you, Cabletow and even the text of the Pose Method of Running state is in fact consistent with the assertion that keeping the heel quite high off the ground as shown in the figures in that book is not safe for a long distance runner.

  57. jonp Says:

    Canute, you are using assumption not evidence when talking about risks for long distance runners. Where are the examples of all the long distance runners that are currently breaking down because their heel didn’t happen to touch the ground (and do NOT confuse “heel didn’t touch” with “holding the heel up” ).

    Your quote:

    “I think that his recommendation to keep the heel unweighted throughout foot strike also need comment. When the heel does not touch the ground at all during foot-strike, the shearing forces on the metatarsals and the tension on the Achilles are large. This presents little concern for a sprinter, but for a long distance runner it creates risk of either Achilles strain or metatarsal stress fracture.”

    Like I say, the heel does not even need to touch the ground to run distances safely. That does NO mean you are holding the heel up consciously. I don’t think you are being clear to the reader here. But I will. If you foot lands very very close under your body (as in a good Pose trained runner) then the heel will not touch the ground and to force it to touch is injurous because you will stretch the achilles against the forward momentum of the body that is trying to pick the heel up.

    The issue is NOT about the heel touching it is about not consciously holding the foot/ankle rigidly – as I keep saying and you refuse to acknowledge and clearly never will because of the same inability that you have always had which is failure to change your point of view (because that would mean admitting you got something wrong in the first place)

    I have absolutely zero wear on the heel of my shoes – some of which are now 2 years old. I have never suffered one problem with achilles strain in all the time I have used Pose Method (and that includes the the first 6 months with less than adequate technique). I object to your insistence of risk of achilles damage or stress fracture if you don’t let the heel touch. I will repeat yet again, it is not an issue of the heel touching (or not) it is an issue of not holding tension in the ankle. I have also have seen first hand evidence of someone who took the instruction to let the heel touch literally and ended up straining the achilles because they were stretching it against momentum of the body trying to lift it off the ground.

  58. canute1 Says:

    Jon,
    I think that there is very little difference in practice between what Al Lyman, Rick, you, Cabletow and myself propose in regard to foot dynamics while on stance.
    We all believe that the heel should not be held high. I do state that the heel should touch the ground (as indeed did Cabletow when last spoke to him). I do not believe that it needs to bear much weight. In fact, to be as precise as possible, what I believe is that after initial contact under either the mid-foot or ball of the foot, the point of maximum weight bearing should move towards the heel so that the longitudinal arch takes up a portion of the load, during long distance running. As mentioned above, this is an area rich in anecdote but poor in good systematic evidence. I will be quite happy to adjust my opinion when good evidence becomes available.

    With regard to the question of landing with the point of support almost immediately under the COM, that is certainly the ideal when sprinting. However in order to land with the point of support almost immediately under the COM you necessarily have to spend only a short time on stance. This gets us back to the gravitational torque debate. This has led to an interesting debate about physics with Simbil, but I suggest we step back from the argument about physics and maths. If you recall the discussion of the videos at Loughborough, for most of us, including Pose coaches, the amount of time between footfall and the point of balance (the Pose) was not greatly different from the time between balance point and lift-off.
    In fact, my arguments about the effect of wind resistance, supported by the available force plate data for mid-foot runners, do indicate that the time between the point of balance and lift-off is a little longer, but nonetheless, the two periods are similar. If we spend a short time on stance, the vertical forces are necessarily large (e.g. if time on stance is one quarter of total gait time, average vertical GRF on stance is four times body weight and peak vertical GRF will be even greater, in order that average vertical GRF across the whole gait cycle matches body weight.)

    Thus, unless a runner has conditioned his/her leg muscle, bones and other connective tissues very well, landing with the point of support almost under the COM when running a marathon is risky. I think that failing to acknowledge this explicitly does increase the risks. One of the reasons I am starting my three year marathon preparation campaign with strengthening exercises is to deal with this. I also acknowledge that the Pose book contains many useful strengthening exercises. I simply wish that the book acknowledged these issues more clearly.

  59. Simon (simbil) Says:

    Hi Canute,

    Thanks for the response, I’m glad that the example has crystalised the issue.
    In a nutshell, I believe that Newton’s second law says that a net external force will create a net change in total momentum. The total momentum of the system being the sum of its linear and angular momentum.
    Your application of Newton’s second law is that a net external force will create a net change in linear momentum and an additional net change in angular momentum if applied off centre.

    I need to do some reading to see which approach is correct and will get back to you when I get to the bottom of it.

  60. jonp Says:

    Canute, I am not saying that the GRF is higher if you spend less time on the ground. What I am saying is that your foot and achilles attachment is perfectly capable of taking these forces (evolution made it so!). Problems only occur when you work against their natural function.

    I think this is the confusion. You are suggesting that a high GRF (say 3xBW) means that the heel should touch over long distance running so that it is not all absorbed through the achilles tendon. I am saying that the achilles tendon is very much capable of taking those forces if it is allowed to stretch elastically. The problem of the heel is simply that. If you hold the heel up with your calf you are not letting the achilles function properply (stretch) so it can get damaged. Conversely if you try and consciously put the heel down during stance you risk stretching it when it is trying to release, so again it can get damaged.

    The solution is to release tension in the ankle on landing so that the achilles can stretch and absorb as it is capable of, then DO NOT push off in second half of stance so that the tendon can release correctly.

    The issue is not about the amount of forces over a period of time, it is about correct application of the force. That is why it is quite okay to run long distance and never feel your heel touch; because you keep the ankle loose. Like I said before, the further in front of your body that the foot lands, the more chance that the heel will touch (and you shouldn’t try and prevent that). If we agree that you should land close under your body as possible then the natural consequence is that your heel will not touch.

    Your solution is to spread the force out through the skeletal system (heel touches). Pose solution is to let your body take care of it by keeping everything relaxed and not consciously do anything at landing.

  61. jonp Says:

    “I am not saying that the GRF is higher if you spend less time on the ground”

    Should have read:

    “I am not saying that the GRF ISN’T higher if you spend less time on the ground”

  62. canute1 Says:

    Simbil, I look forward to hearing from you after you have done some more reading. The crucial issue with regard to my argument is that linear momentum, angular momentum and energy must all be conserved. I do not believe that conservation of the total of linear and angular momentum is adequate to satisfy the requirements of Newtonian mechanics.

  63. canute1 Says:

    Jon, as I have remarked previously I do not think there is a large difference between your recommendation and what I recommend regarding foot dynamics. In particular, I do not advocate conscious placement of the heel on the ground, though I do recommend not consciously holding it off the ground. In general, I think the Pose emphasis on relaxation is highly desirable. In practice, what I advocate is mostly very similar to Pose and indeed my ideas were guided by Pose. My major differences with Dr Romanov are questions of the underlying theory. Maybe the theory does not matter very much, though the reason I continue to emphasize it is because I believe that in order to prepare oneself well for running safely, it is good to have an accurate understanding of the mechanics. However, when actually running, the mind should focus on few of the details.

  64. Simon (simbil) Says:

    Hi Canute,

    You are right about Newton’s second law and linear acceleration not being effected by the point of application of the force. Sorry for insisting otherwise, I should have looked into it as soon as the disagreement was clear. Humble pie duly consumed 🙂

    Looking back at the discussion we were having, that leaves a bit of a paradox with the empirical data where max horizontal GRF did not coincide with max horizontal acceleration. Will give that some thought.

    Regarding the hypothesis I put forward that angular momentum of the runner can be corrected by a rearward push in constant pace running, it is possible but seems like there would be more acceleration than necessary in that mechanism (as the linear momentum increase from the correction of angular momentum would be larger than I expected, due to my mis-application of Newton’s second law). So that hypothesis may fit heavily accelerated running better than constant pace running, at least until constant pace running requires significant constant acceleration (head wind, sprint).

    Another angle I need to consider is the idea that angular momentum from GT can be corrected instantaneously whilst still allowing linear momentum to develop from GT (so GT still doing useful work). This was mentioned by a chap on the Pose forums who seems to have a good grasp of mechanics so is worth following up.

  65. canute1 Says:

    Simbil,

    Thanks for your comment.

    As you remark, it does leave a paradox concerning the data presented in the figure 1 of the Fletcher, Dunn and Romanov paper on accelerated running. This figure appears to show that maximum horizontal GRF does not coincide with maximum horizontal acceleration of the COM. It is very hard to reconcile this with Newton’s second law. (Variation in air-resistance might account for small discrepancies). I have been thinking about this for some time and the only resolution I can offer is that figure 1 (and the main conclusion of the paper) is wrong. The material in figure 1 is not raw data. The graphs represent computed values and as far as I can see, the most likely explanation of the discrepancy is that some of these computed values are erroneous. I suspect that it is the computation of the horizontal acceleration of the COM that is wrong – possibly the software did not identify the true location of the COM. However I would be very pleased if you come up with an alternative explanation.

    I will also be interested to hear what you conclude regarding the possibility that linear momentum is generated as a result of angular momentum from GT being corrected instantaneously.

    My own opinion after examining Pose in some detail is that Pose theory does not provide a valid description of the mechanics of running, but nonetheless, it can foster a helpful perception that can result in a relaxed running style.

    In some circumstances, a perception that fosters a relaxed style is more valuable than correct understanding of the details of running mechanics, and for an amateur athlete, Pose is potentially a good style. Nonetheless, a few caveats are necessary.

    First, although Pose minimizes the risk of the injuries that arise from unnecessary muscle tension, it is not entirely free of risk.

    Secondly, for an athlete who wishes to reach world-champion level, it is probably better to be guided by a more realistic understanding of running mechanics.

    Thirdly, for an old-timer attempting to rebuild the muscle strength necessary to recover some of his former speed, it is almost certainly worthwhile to have a reasonably good understanding of the mechanics.

  66. jonp Says:

    Simbil, Canute.
    Do you have any studies showing the magnitude of hGRF, specifically does it vary with pace? If it does not vary very much then there is clearly a paradox at hand.

  67. Simon (simbil) Says:

    Jon,

    The only good force plate data I have is from a single study. I’ll see if I can find any other data – force plate data for an accelerating runner is what we really need and this would have been measured in the recent Pose study so hopefully that data will become available.

    Canute,

    It is possible that the study has computed the data incorrectly but I tend to think that would be the remaining conclusion once all others are exhausted.
    Logically, there seems to be only one other possibility which is that the hGRF experiences loss somehow. The loss could be from an external force (wind resistance is all there is and does not seem a likely candidate) and/or from the body loosing rigidity. If the torso looses rigid connection to the hip whilst the hGRF applies, then the system is acting as a deformable body rather than a rigid body. I remember that being a significant distinction for calculating the effects of a force but will need to read up on it to see if that could help explain this situation.

    As an old-timer who wants to run fast, I think you are right to build strength. In terms of running style, I think it boils down to simply using minimal necessary range of motion for your pace to decrease leverage and shear/twisting forces. But that’s a whole other topic conversation.

  68. Simon (simbil) Says:

    Jon,

    Over lunch, I looked for more data from force plates but could not find any. I will keep it in mind next time I am looking for information.

    Canute,

    Regarding horizontal GRF peaking after horizontal COM acceleration, I’ve been thinking more along the lines of a deforming object.
    I wonder if the effect we are seeing is down to the leg and lower part of the body being accelerated whilst mechanically partially disconnected from the rest of the runner due to joints allowing the movement to progress in the lower body rather than translating it to the upper body?
    In effect, the legs have to be accelerated from rest to a speed faster than the COM in order to overtake the body in time for landing. Dividing the horizontal GRF between the effect it has on the legs and the effect it has on the COM may explain the paradox.

  69. Jon Port Says:

    Simon,
    Thanks, reading the things that Dr Romanov is saying, I think it should be the case that hGRF should just be a reflection of bodyweight, thus it should not vary much between different paces. If you spot any that would be great. thanks.

  70. canute1 Says:

    Jon.
    I do not have force plate data during acceleration to different speeds. I am not aware of any reason to suspect a paradox in regard to the variation of the magnitude of hGRF. If we accept that gravity does no net work (which is required by the law if conservation of energy unless the COM ends at lower height) then the work of accelerating the runner must be done via hGRF. A runner who reaches a greater speed after given distance will have gained a greater amount of kinetic energy. Work is force*distance. If more work has been done within a given distance, force (hGRF) must have been greater. But maybe we should wait until we have data before speculating.

    Simbil,
    I have not lightly jumped to the conclusion that fig 1 in the F,D&R paper is likely to be wrong. Even since I first read the full document I have been trying to make sense of its internal inconsistencies. Figure 1 and equation 1a are mutually contradictory. Equation 1a is a statement of Newton’s second law (after ignoring air resistance). Figure 1 is not consistent with Newton’s second law. It is hard to see how both can provide a correct description of accelerating running. Furthermore, fig 1 is scarcely plausible even without applying any formal laws of physics. It shows the maximum horizontal acceleration of the COM occurring in the first half of the time on stance yet the maximum horizontal GRF is not until around 2/3 of the way through the stance period, while max GT is not until the end of stance. What force is applying the horizontal push?

    Simply treating legs separately from the body does not help. Consider a body that weighs 100 Kg and experiences a horizontal force of 50 newtons.
    If it behaves as a single rigid body, it accelerates at 0.5 m/s/s.
    If it consists of two detachable halves, and the force is applied to one half, this half, which weighs 50Kg, accelerates at 1.0 m/s/s. The other half will experience no horizontal acceleration.
    The COM of the composite (two part object) will be accelerated at an average rate of 0.5 m/s/s. So provided the COM is identified as the centre of mass of the composite object, it accelerates at the same rate as it would be a rigid body.

  71. Simon (simbil) Says:

    Hi Canute,

    Thanks for the reply – yes you are right of course about a composite model, the COM of the whole will still be affected by the acceleration of a part.

    As for the data itself, it is very mysterious and I will continue to think how it could be the case.
    I have a suspicion that there is another affect to consider that would only involve a vertical GRF but would give rise to horizontal COM acceleration; as the runner lands, the direction of velocity is forwards and downwards. Landing redirects the velocity to horizontal by midstance and upwards and forwards by terminal stance. This redirection could account for an apparent acceleration in the first part of stance. I think I am right in saying that momentum is conserved in an elastic collision, so if the momentum is forwards and downwards in flight, the ‘collision’ between the runner and the ground would conserve momentum and redirect it in a more forwards direction initially. However, the ‘collision’ continues on stance until the momentum is finally directed forwards and upwards, so I would expect this effect to produce apparent horizontal acceleration up to midstance and deceleration after midstance.

  72. Jon Port Says:

    Canute, thanks for the thoughts on hGRF. I think it is important that we find the data and not try and guess the data based on assumption alone. That takes us down a path of trying to fit things into our own model instead of trying to find the reality. I agree with simbil, just because we cannot understand an apparent paradox, does not mean that the presented facts must necessarily be wrong, but instead our understanding and the models that we create from our understanding might not be correct (or to summarise – lets not close doors but keep an open mind. If we close doors we don’t make any progress in finding the truth, which I hope is the intention of us all).

    I will look for some hGRF data. I am pretty (99%) sure that Dr Romanov has said in the past that hGRF magnitude hardly varies as pace changes i.e. it is representing bodyweight not a push activity.

    Here is another paradox (although I know it’s base in in perception). Why is it that the faster I run the lighter I feel on the ground. If I had to push-off harder I should “feel” more not less ground reaction? Another paradox 😉

  73. canute1 Says:

    Simbil,
    Newton’s second law states that the acceleration is in the direction of the applied force, so vertical GRF cannot produce horizontal acceleration.

    It is not correct to say that during an elastic impact, the down and forward motion prior to landing is converted to forward motion. It is more accurate to say that arresting the downward motion results in storage of elastic energy which can help drive the subsequent upward acceleration. The forward component of motion is largely preserved (consistent the law of conservation of momentum) unless some other horizontal force is applied. In many circumstances, such as when a fairly rigid leg strikes the ground obliquely, as happens in running (even in accelerated running) there is a backward directed horizontal braking force and some of the forward momentum is actually lost. Compensation for this loss can be provided by a backward push against the ground after the COM has passed over the point of support.

  74. canute1 Says:

    Jon
    We are in complete agreement about the need to examine evidence. However, it is also necessary to recognize that the amount of evidence supporting the accuracy of Newtonian mechanics for describing the motion of objects of human size moving at running speeds is so large that any credible account of running must be consistent with Newtonian mechanics. When there is a conflict, as in the F,M& R account of accelerated running, we must examine both the way Newton’s laws have been invoked and also the reported evidence.

    With regard to way Newton’s second law is evoked in equation 1a, I have pondered this for some time and apart from the omission of the small effect of air-resistance, I can see no fault in it (though there are peculiarities in the way equation 5 is derived by substitution of equations 3 and 4 into equation 2, but that is a different issue). It is therefore reasonable to question the reported evidence, especially as this evidence has been derived indirectly from observed data, without a detailed description of how this was done, and furthermore, has produced results which appear odd even without formal application of Newton’s laws. Nonetheless, I am still pondering the issue and also examining carefully the suggestions offered by Simbil.

    With regard to the apparent paradox of the perception of being lighter on your feet at higher speed, I do not think there is any paradox, if you are talking about running at steady speed. As speed increases time on stance decreases and the vertical GRF increases. However, data such as that from the Weyand study demonstrate that as speed increases from mid-range to higher speeds, the decrease in time on stance is proportionally larger than the increase in the size of the force. Thus the vertical impulse, which is the product of force *time actually decreases as speed increases. You probably perceive the impulse rather than the peak force, so it is not surprising you feel lighter on your feet.

  75. Simon (simbil) Says:

    Hi Canute,

    Yes, fair point, to redirect downwards and forwards momentum into more of a forwards direction will take a horizontal as well as vertical force.

    I’m at a bit of a loss to explain it at the moment.

  76. Simon (simbil) Says:

    Hi Canute,

    One other point that does spring to mind is the idea of a deformable object. If the hGRF applies against a spring like system, the hGRF will not immediately give rise to all of the acceleration – some of the acceleration will be delayed I think.

    For example, the difference between the same impulse applied to a steel ball and a football (assuming perfect elasticity) of the same mass. The steel ball will almost immediately move under the effect of a force whilst a football will first deform around the point of force application due to its softer nature. If the combination of football and impulse is perfectly elastic, it will still accelerate as much as the steel ball, but the acceleration will take longer to appear. So a snapshot of the GRF at the surface of each ball very soon after application of the force would show the same GRF but different horizontal COM acceleration compared to the steel ball. Another snapshot after the force (impulse) had finished would show that both balls are moving as predicted my F=ma.

    I’m not sure how that would relate to running, but thought it worth running past you first to see if you agree with the basic principle.

  77. canute1 Says:

    Simbil,
    I do not think that the physics of deformable objects will help resolve the dilemma. Although everyday experience suggests that the acceleration lags behind the force when the object deforms, I suspect that the perception arises because force simply rises slowly. If a push against a deformable object is compared with a push against a rigid object, in the case of the push against the deformable object, the force delivered is likely to rise more slowly because action and reaction must be equal and opposite, and the deformable object will not react as quickly. The more slowly rising force will last for longer to give the same final impulse.

    At any instant, I would predict acceleration of the COM will be equal to force at that instant divided by mass. The slower acceleration will last for longer and the final change in momentum will be the same if the impulse is the same.

    Everyday experience might suggest that some of the force is dissipated in deforming the object – that is true, but does not affect the transfer of momentum. As a result of the deformation the force will cover a greater distance so the energy delivered (force*distance) will be greater for a given impulse when the body suffers deformation.

    So I am inclined to think that Newton’s second law will still apply.

    You might like to imagine dropping a 10gm steel ball and a 20gm putty ball from a height of 1 metre onto a china plate. Maybe even do it with a cheap plate – experiments can be more fun than theorizing, though in this safety conscious age you should wear goggles. Because of elastic recoil, the change in momentum of the steel ball will be almost twice as great per gm, but because the steel ball has only half the weight, the transfer of momentum in each case will be almost exactly the same. Due to lack of deformation of the steel ball, the transfer of momentum will occur much more rapidly than with the putty ball, so the peak force will be much greater despite the same impulse. I predict that the plate will shatter under the impact of the steel ball, but will survive the bombardment by putty – so drop the putty ball first.

    With regard to the problem arising from the fact that F,D&R report that acceleration of the COM during accelerated running precedes the peak horizontal force, even if we accept that the acceleration might lag behind the time of onset of the force as a result of deformation, the problem remains because the predicted effect is opposite that reported by F,D&R.

  78. Simon (simbil) Says:

    Canute,

    Yes on reflection I agree – deformation just means that more work is done to apply the force. I find it hard to intuitively separate force and work.

    There seem to be only 2 possibilities; a runner does not obey Newton’s second law or that the study predicted the position of the COM incorrectly and shows invalid data. I might have chance to bring it up with Dr. Romanov next weekend to see if there is something else to consider.

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